jason bryan burt - virginia tech · 2020-01-17 · jason bryan burt dissertation submitted to the...
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A study of the crystal chemistry, electron density distributions, and hydrogen incorporation in the Al2SiO5 polymorphs
Jason Bryan Burt
Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree
of
Doctor of Philosophy in Geosciences
Committee Nancy L. Ross, Chair
Ross J. Angel G.V. Gibbs
Don Rimstidt Daniel Crawford
May 11, 2006 Blacksburg, Virginia
Keywords: Al2SiO5, high pressure, electron localization function (ELF), Polarized FTIR spectroscopy, and (3,-3) critical points
A study of the crystal chemistry, electron density distributions, and hydrogen incorporation in the Al2SiO5 polymorphs
Jason Burt
Advisor: Nancy L. Ross
Abstract The Al2SiO5 polymorphs have been examined to provide new insights into their chemical bonding, their crystal chemistry, their equations of state, and the incorporation of water in the form of hydroxyl in their structures. The Al2SiO5 polymorphs provide a unique structural assemblage for a crystal chemical examination due to the variation in Al coordination in the structures where Al is in 4-fold, 5-fold, and 6-fold in sillimanite, andalusite, and kyanite, respectively. Consequently, the Al2SiO5 polymorphs have been examined with a combination of experimental (high pressure X-ray diffraction and Polarized FTIR spectroscopy) and theoretical (VASP and Crystal 98) methods. An experimental high pressure X-ray diffraction study on andalusite and sillimanite has constrained their equation of state and the pressure derivatives of their bulk modulus with pressure. Additionally, the effect of pressure on the crystal structures has been examined, where the main structural response is compression of the AlO6 octahedra. Comparatively, compression of the AlO6 octahedra in andalusite is more anisotropic, while the major direction of axial compressibility in both structures is dependent on the orientation of the AlO6 octahedra. In order to better understand the crystal chemistry of the Al-O and Si-O bonds in the polymorphs, ELF isosurfaces were examined. ELF isosurfaces represent a graphical representation of the localized electron probability density. Six distinct types of ELF isosurfaces were observed in the Al2SiO5 polymorphs resulting from differences in the geometry, coordination, and coordinated cation atomic number surrounding the oxygens within the crystal structures. The ELF was also shown to be isostructurally related to electron density difference maps. In a combined experimental and theoretical investigation of the Al2SiO5 polymorphs, potential protonation sites within the crystal structures were determined at an atomic level with polarized FTIR spectroscopy and analysis of (3,-3) critical points of the negative Laplacian. The polarized FTIR spectra indicate the orientation of the OH dipole in the three polymorphs and the (3,-3) critical points indicate regions of locally concentrated electron density. Potential protonation sites were determined based on the value of the negative Laplacian, the underbonded nature of the oxygens, and the number of surrounding cations.
Acknowledgements
This dissertation is dedicated to my grandparents Mary Lou and Robert Seitz who have always been there for me and I hope will be around for many more years. This work is a culmination of twenty four years of education. It has been a long road, but it has been very full filling. I have been very fortunate to travel to many different places and experience different cultures and ideas. It has shaped who I am and who I hope to be. I would especially like to thank Nancy Ross, my advisor, who has helped me become a better scientist and helped support my research. If it wasn't for her I wouldn't have had the opportunity to travel to Australia to work with Mark Spackman or to California to work with George Rossman. Additionally, I would like to thank everyone in the department of Geosciences at Virginia Tech. I have had the opportunity to study under excellent people such as Jerry Gibbs, Ross Angel, Daniel Crawford, Don Rimdstidt, and Robert Tracy. I would also like to thank the graduate students at Virginia Tech. Through out the years I have met some extraordinary people who have become great friends and colleagues. I am especially in debt to Mariano Valezquez, Frank Evans, Robert Bodek Jr., Tracy Cail, Jennifer Stempien, Tristan Azbej, and Jamie Buscher. We have had some great and unforgettable times at Tech. I will always treasure their friendship. In addition to my grandparents, I would like to thank the rest of my family for always being there even when they didn't understand what I was doing. I would like to thank my mother, Susan Seitz. She has always supported and encouraged me and I wouldn't be where I am today without her. I would also like to thank my father, Greg Burt, and my step-mother, Suzie Burt, for their constant support throughout the years. I have come along way from my roots in Iowa, but I still cherish every opportunity to get back to the Midwest. I would like to acknowledge Andy Tice and Dawn Boldt. Though we have been separated by thousands of miles for the last 12 years we still remain great friends and will always be there for one another. Finally, as I near the end of one chapter of my life I look forward to the challenges to come. I am sincerely grateful to all the people that I have meet along the way and whom I will never forget.
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Table of Contents
Abstract.............................................................................................................................. ii Acknowledgements .......................................................................................................... iii Table of Contents ............................................................................................................. iv List of Tables .................................................................................................................... vi List of Figures.................................................................................................................. vii Chapter 1:Introduction .................................................................................................... 1
Crystal Structures and Crystal Chemistry of the Al2SiO5 polymorphs ........................... 3 Phase Equilibria Studies of the Al2SiO5 polymorphs...................................................... 7 Thermodynamic Properties of Al2SiO5 polymorphs ..................................................... 10 Water incorporation in the Al2SiO5 polymorphs .......................................................... 11 Objective of dissertation ............................................................................................... 12 References ..................................................................................................................... 13
Chapter 2: Equations of State and structure of andalusite to 9.8 GPa and sillimanite to 8.5 GPa ..................................................................................................... 21
Abstract ......................................................................................................................... 21 Introduction................................................................................................................... 22 Experimental Methods .................................................................................................. 26 Results and Discussion ................................................................................................. 36 References ..................................................................................................................... 45
Chapter 3: ELF isosurface maps for the Al2SiO5 polymorphs ................................... 48 Abstract ......................................................................................................................... 48 Introduction................................................................................................................... 49
Electron Localization Function (ELF) ...................................................................... 55 Methods and Calculations ............................................................................................ 57 Results ........................................................................................................................... 58
ELF isosurface maps for the Al2SiO5 polymorphs ................................................... 58 Comparison of ELF isosurfaces and electron density difference maps.................... 64
Conclusions................................................................................................................... 66 References ..................................................................................................................... 67
Chapter 4: Potential protonation sites in the Al2SiO5 polymorphs based on polarized FTIR spectroscopy and properties of the electron density distribution ... 70
Abstract ......................................................................................................................... 70 Introduction................................................................................................................... 71 Methods......................................................................................................................... 75
Polarized FTIR spectra ............................................................................................. 75 Critical point calculations ......................................................................................... 76
Results ........................................................................................................................... 77 Polarized FTIR spectra of andalusite ........................................................................ 77 (3,-3) Critical points displayed by a mapping of L(r) ............................................... 79
Andalusite ............................................................................................................. 79 Sillimanite ............................................................................................................. 82 Kyanite.................................................................................................................. 84
Discussion..................................................................................................................... 85
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References ..................................................................................................................... 96 Chapter 5: Conclusions ................................................................................................ 100 Appendix 1..................................................................................................................... 104 Appendix 2..................................................................................................................... 107
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List of Tables Table 1.1: Unit cell parameters, cation positions, and bond lengths for the Al2SiO5 polymorphs.............................................................................................................4 Table 1.2: Enthalpies and Entropies of the Al2SiO5 polymorphs................................11 Table 2.1: Isothermal bulk moduli, KTO, of andalusite and sillimanite......................25 Table 2.2: Unit cell parameters of sillimanite, space group Pbnm, from 1 bar to 8.543 GPa..............................................................................................................29 Table 2.3: Unit cell parameters of andalusite, space group Pnnm, from 1 bar to 9.828 GPa..............................................................................................................29 Table 2.4: Details of least-squares structure refinements for sillimanite at room pressure through 7.663 GPa................................................................................30 Table 2.5: Details of least-squares structure refinements for andalusite at room pressure through 9.828 GPa................................................................................31 Table 2.6: Positional and isotropic displacement parameters for sillimanite at 1 bar through 7.663 GPa...............................................................................................32 Table 2.7: Positional and isotropic displacement parameters for andalusite at 1 bar through 9.828 GPa...............................................................................................33 Table 2.8: Selected bond lengths (Å) and angles (°) for andalusite from 1 bar through 9.828 GPa...............................................................................................34 Table 2.9: Selected bond lengths (Å) and angles (°) for sillimanite from 1 bar through 7.663 GPa...............................................................................................35 Table 4.1: Composition of andalusite in wt % determined by electron microprobe analysis..................................................................................................................75 Table 4.2: Water concentrations determined by polarized IR....................................77 Table 4.3: Electron density properties for (3,-3) non-bonding critical points in the Al2SiO5 polymorphs.............................................................................................80 Table 4.4: The (3,-3) critical point Laplacian value vs. the distance the critical point is from the oxygen atom......................................................................................92
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List of Figures Figure 1.1: Al2SiO5 pressure and temperature diagram................................................2 Figure 1.2: View of the crystal structures down [001] for andalusite, sillimanite, and kyanite.....................................................................................................................5 Figure 2.1: Variation of the unit cell volume of andalusite between 1 bar and 9.8 GPa and for sillimanite between 1 bar and 8.6 GPa.........................................37 Figure 2.2: Variation of the normalized pressure, F, against the Eulerian strain, f, for andalusite and sillimanite.........................................................................38 Figure 2.3: Variations of axial lengths with pressure for andalusite and
sillimanite..............................................................................................................40 Figure 2.4: Variation of the normalized pressure, F, against the Eulerian strain, f, for the individual axes in andalusite and sillimanite.....................................41 Figure 2.5: The variation of octahedral Al1-O bond distances in sillimanite and
andalusite..............................................................................................................43 Figure 3.1: Differences between the ELF isosurfaces for the Al1-O6 and Al2-O6
octahedra in kyanite............................................................................................59 Figure 3.1: Differences between the ELF isosurfaces for the Al1-O6 and Al2-O6
octahedra in kyanite............................................................................................61 Figure 3.3: Distance oxygen is located above a plane defined by the surrounding two aluminum and one silicon cations verses the maximum lone pair ELF value in andalusite, sillimanite, and kyanite.....................................................63 Figure 3.4: Comparison of the ELF isosurfaces and static electron deformation densities................................................................................................................65 Figure 4.1: Polarized FTIR spectrum of andalusite with E parallel to the [100], [010], and [001].....................................................................................................78 Figure 4.2: The four types of coordinated oxygens in the Al2SiO5 polymorphs and their associated (3,-3) critical points...................................................................81 Figure 4.3: Projection of the (001) and (010) planes in andalusite, sillimanite, and kyanite with hydrogen atoms positioned along a vector 0.98 Å from the oxygen atoms through their corresponding (3,-3) critical points....................83 Figure 4.4: Polarized infrared spectrum of sillimanite with E parallel to [100], [010], and [001]...............................................................................................................86 Figure 4.5: Polarized FTIR spectrum of kyanite along the three orthogonal directions α, β, and γ............................................................................................87 Figure 4.6: A comparison of the three coordinated oxygen (3,-3) critical point L(r) values vs. the distance the oxygen atoms are from a plane defined by the three surrounding cations...................................................................................90 Figure 4.7: A comparison of the distance the (3,-3) critical points are located from the oxygens vs. the (3,-3) critical L(r) values for the oxygens coordinated to three cations kyanite, andalusite, and sillimanite.............................................93
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Chapter 1
Introduction
The Al2SiO5 polymorphs, kyanite, sillimanite, and andalusite, have been
extensively studied due to their abundance in metapelitic rocks and their use as
thermobarometers in metamorphic environments (e.g. Fyfe et al., 1958; Miyashiro, 1961;
Hietman, 1967; Carmichael, 1978; Kerrick, 1990, Hemmingway, 1991; and Olbricht et
al., 1994). Although there have been numerous phase equilibria studies of the Al2SiO5
polymorphs, there has been considerable debate over the past 50 years concerning the
location of the Al2SiO5 triple point. As stated by Holdaway (1971) and exemplified by
Figure 1.1:“The Al2SiO5 phase diagram is perhaps the most studied and least well defined
silicate phase diagram”. Experimental determination of the phase boundaries is difficult
because of the small free energy differences between the polymorphs, where the heat of
formation between the end members is not more than about 4190 J/mol (Holm and
Kleppa, 1966). It is not uncommon to find two or three of the polymorphs coexisting
metastably because of sluggish kinetics. The relative small difference in free energies
between the polymorphs is due to similarities in their crystal structures and chemical
bonding. Furthermore, the stabilities of the Al2SiO5 polymorphs are sensitive to
impurities, Al/Si order/disorder, defects, and surface area (e.g. fibrolite). In order to
understand the magnitude of these effects, it is necessary to have well-constrained
thermodynamic data, including the equations of state of the polymorphs, which allow one
to directly calculate the phase boundaries. In addition, water has been shown to be
incorporated into these nominally anhydrous minerals (Bell and Rossman, 1992).
Although the concentrations of hydrous components vary widely in structures (commonly
in the range of 10's to a few 100 ppm H2O by weight), such trace amounts of hydrous
species can have a disproportionately large effect on the physical, chemical, rheological,
electronic, and optical properties of the mineral. Kyanite, the high pressure polymorph,
has also been found in ultra-high pressure (UHP) eclogites (Dal Vesco, 1953; Lappin,
1960; Liati and Seidel, 1994; Brouwer and Engi, 2005) and has the greatest water content
of all three polymorphs (230 ppm wt % H20, Bell et al., 2004). Kyanite has therefore
been suggested as a potential candidate for water storage in Al-rich sediments that have
1
Figure 1.1: Al2SiO5 phase equilibrium modified from Zen’s (1969) summary. The numbers correspond to the equilibrium from the following studies: 1. Holdaway and Mukhodahyay (1993), 2. Pattison (1992), 3. Holdaway (1971), 4. Weill (1966), 5. Pugin and Khitarov (1968), 6. Holm and Kleppa (1966), 7. Althaus (1967), 8. Khitaroveet al. (1963), 9. Bell (1963), 10. Newton (1966a, b).
2
been subducted and subjected to high pressure and temperature (Schmidt et al., 1998). In
the sections below, I present a review of the crystal structures and crystal chemistry of the
Al2SiO5 polymorphs, their thermodynamic properties and factors such as impurities that
complicate prediction of their stabilities. Fundamental questions arise from these studies
that form the basis for this dissertation.
Crystal Structures and Crystal Chemistry of the Al2SiO5 polymorphs
The crystal structures of the Al2SiO5 polymorphs were first determined in the late
1920’s (Taylor, 1928, 1929; Naray-Szabo et al., 1929) and have subsequently been
refined and examined by neutron and X-ray diffraction studies (Burnham, 1963a, 1963b;
Burnham and Buerger, 1961; Finger and Prince, 1972; Winter and Ghose, 1979; Ralph et
al, 1984; Peterson and McMullan, 1986; Yang et al., 1997a, 1997b; Comodi et al., 1997;
Friedrich et al, 2004; and Burt et al., 2006). The crystal structures of the Al2SiO5
polymorphs are classified as nesosilicates because the SiO4 tetrahedra are “isolated” in
the structures and are connected by Al polyhedra in different coordination states. The
unit cell parameters, fractional coordinates, and bond distances are reviewed in Table 1.1.
Andalusite and sillimanite are both orthorhombic (space group Pnnm and Pbnm,
respectively) with infinite edge-sharing chains of aluminum octahedra that run parallel to
[001]. In andalusite, the chains of AlO6 octahedra are cross-linked by SiO4 tetrahedra
alternating with AlO5 polyhedra of aluminum in 5-fold coordination with oxygen (Fig.
1.2). There are four nonequivalent oxygen atoms in andalusite, all bonded to three
cations: O1 is bonded to two AlVI and one AlV, O2 is bonded to one SiIV and two AlVI,
O3 is bonded to one SiIV and two AlV, and O4 is bonded to one SiIV, one AlVI and one
AlV. In sillimanite, the chains of AlO6 octahedra are cross-linked by SiO4 tetrahedra
alternating with AlO4 tetrahedra (Fig. 1.2). There are four nonequivalent oxygen atoms
in sillimanite, three are bonded to three cations and one is bonded to two cations: O1 is
bonded to one SiIV and two Al1VI, O2 is bonded two AlVI and one AlIV, O3 is bonded to
one SiIV and one AlIV, and O4 is bonded to SiIV, AlVI and AlIV. The octahedrally
3
Table 1.1: Unit cell parameters, fractional coordinates, and selected bond lengths for the Al2SiO5 polymorphs
Minerals
abc αβγvolume (Å3)Cationsxyz
Bond Lengths (Å):
Avg
Poly. Vol.*
Q.E.**
Ang. Var.†
Anions O1 O2 O1 O2x 0.4233 0.4246 0.3605 0.3569y 0.3629 0.3629 0.4094 0.4341z 0.5000 0.0000 0.7500 0.2500
Minerals
abc αβγvolume (Å3)Cations Al3 Si2x 0.09980(5) 0.29102(5)y 0.38615(4) 0.33168(4)z 0.64043(6) 0.18937(5)
Bond Lengths (Å): (O2) 1.984(1) (O1) 1.640(1)(O3) 1.924(1) (O3) 1.629(1)(O5) 1.860(1) (O7) 1.624(1)(O6) 1.881(1) (O9) 1.646(1)(O6') 1.969(1)(O7) 1.885(1)
Avg 1.917 1.635
Poly. Vol.* 9.158(4) 2.236(1)Q.E.** 1.0178 1.0017Ang. Var.† 56.3 6.6Anions O1 O2 O3 O5 O6 O7 O8 O10x 0.1093 0.1229 0.2751 0.1084 0.1219 0.2823 0.2916 0.5015y 0.1469 0.6854 0.4544 0.1521 0.6306 0.4451 0.9468 0.2310z 0.1287 0.1811 0.9547 0.6667 0.6394 0.4287 0.4657 0.7560
1.912
9.122(4)1.01450.1
Andalusite1 Sillimanite2
(O10) 1.922(1)(O9) 1.929(1)(O6) 1.910(1)(O4) 1.890(1)(O3) 1.881(1)(O2) 1.937(1)
0.95040(6)0.69882(4)
909090
50.049(7)
Unit cell parameters7.4883(7)7.6808(7)5.7774(5)
0.9357
Unit cell parameters7.1200(4)7.8479(3)5.5738(3)89.974(3)
101.117(4)106.000(4)293.31(2)
Al4
1.015447.6
0.28350.9357
(09) 1.848(1)(O10) 1.850 (1)
1.902
8.983(4)
(O2) 1.873(1)(O6) 1.885(1)(O7) 1.972(1)(O8) 1.986(1)
0.29625(5)0.06488(4)0.70657(5)
Al10.32533(5)0.70412(4)0.45812(6)
Si1Al20.29740(5)
1.635
2.239(1)1.0011
4.2
(O4) 1.631(1)(O5) 1.642(1)(O8) 1.622(1)(O10) 1.645(1)
(O4x2) 1.645(2)
O4
0.11205(5)
41.9
0.91750(4)0.16469(6)
(O1) 1.816(1)(O1') 1.995(1)(O2) 1.846(1)(O4) 1.909(1)
Si.1533(1).3402(1)
0.75000
Al1
0.25.3449(1).1417(1)
Al2
0.51450.7500
(O1x2) 1.913(1)(O2x2) 1.868(1)(O4x2) 1.955(1) (O4x2) 1.796(2)
(O3) 1.711(3)(O2) 1.751(2) (O1) 1.641(2)
(O3) 1.574(3)
O30.47630.0015
O40.12520.2230
1.627
2.20291.00133.2327
1.763
2.7911.006120.2232
1.912
9.17491.010936.3647
0.2520(1).2460(1)
SiAl2.3705(1).1391(1)
0.5.2419(1)00
Al1
0.23050.13390.2394
(O1x2) 1.827(3)(O2x2) 1.891(3)(O4x2) 2.086(2)
(O1) 1.816 (4)(O3) 1.839(4)(O3) 1.899(4)
(O4x2) 1.814(3)
O30.10300.40030.0000
1 Andalusite data from Ralph et al. (1984); 2 Sillimanite data from Winter and Ghose (1979); 3 Kyanite data from Yang et al. (1997); *Polyhedral volume; **Quadratic Elongation; †Angle Variance
(O5) 1.934(1)(O8) 1.874(1)
1.896
8.917(4)1.0137
O90.50070.27520.2441
Kyanite3
18.02571.01149.5393
----
2.21091.004316.2307
O4
1.935 1.836
5.1527
1.631
(O1) 1.645(4)(O3) 1.618(4)
(O4x2) 1.630(2)
909090
342.45(6)
Unit cell parameters7.7980(7)
7.9031(10)5.5566(5)
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Figure 1.2: View of the crystal structures down [001] for (i) andalusite, (ii) sillimanite, and (iii) kyanite with the silicon atoms in blue, the aluminum atoms in green, and the oxygen atoms in red. Al1 is in 6-fold coordination in andalusite and sillimanite, while Al2 is in 5-fold coordination in andalusite and 4-fold coordination in sillimanite. All Al atoms are in 6-fold coordination in kyanite and all Si atoms are in 4-fold coordination in all three structures.
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coordinated Al are irregularly distorted with respect to ideal Oh symmetry in andalusite
and sillimanite with elongate Al-O4 bond distances. In sillimanite the tetrahedral Al and
Si polyhedra are also irregular with “abnormally short” Al-O3 and Si-O3 bond distances
(Burnham 1963a), while the Si tetrahedra in andalusite is not distorted with similar Si-O
bond distances. In contrast to andalusite and sillimanite, kyanite is triclinic and consists
of edge-sharing aluminum octahedral chains in a zig-zag pattern which are cross-linked
with alternating silicon tetrahedra and aluminum octahedra (Figure 1.2c). The four
distinct Al octahedra have different averaged Al-O bond distances. Al1 and Al2 define
the edge sharing octahedral chains and share five and four edges with neighboring
octahedra, respectively. The Al1 and Al2 chains are connected by the Al3 and Al4
octahedra, which also share five and four edges with neighboring octahedra, respectively.
Additionally, the Si tetrahedra also connect the Al1 and Al2 chains and have identical
average bond distances. There are ten crystallographically distinct oxygens in kyanite,
eight are bonded to three cations and two are bonded to four cations. All of the three
coordinated oxygens, O1, O3, O4, O5, O7, O8, O9, and O10, are bonded to one SiIV and
two AlVI, while the four coordinated oxygens, O2 and O6, are bonded to four AlVI. Due
to the arrangement of the oxygen atoms, the structure of kyanite can be described as
distorted cubic closest packed with the Al in the interstitial octahedral sites.
The crystal structures of the Al2SiO5 polymorphs as described above are very
similar, but also very different with respect to Al coordination. Aluminum is bonded to
oxygen in a variety of coordination environments (e.g. 4-fold, 5-fold, and 6-fold
coordination) in the three polymorphs, which is unique among mineral polymorphs.
Examination of their crystal chemistry, geometries, compressibility, bonding, and
structures is important for understanding their stability and why they are unique. The
similarity in the crystal structures is exemplified by the small free energy differences
between the polymorphs. The relative small difference in energies between the
polymorphs is related to their crystals structures and their stabilities can be examined in
terms of Pauling’s rules. Kyanite, the lowest energy phase at room pressure and
temperature (Berman and Brown, 1998; Hemingway et al., 1991; Holdaway and
Mukhopadhyay, 1993), satisfies Pauling’s second rule of local charge balance compared
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with sillimanite and andalusite where the sum of all the bonds to the ions do not always
equal the charge on the ion. However, kyanite has the largest number of shared
polyhedral edges which effectively destabilizes it according to Pauling’s third rule. On
the other hand, sillimanite is the least stable structure at room pressure and temperature
and has the lowest number of shared polyhedral edges, while andalusite’s number of
shared polyhedral edges is between kyanite and sillimanite as is its stability.
Additionally, Pauling’s first rule does not predict five fold coordination as seen in
andalusite. Clearly there are limitations in using Pauling’s rules which were developed in
1929 to gain insight into the stability and crystal chemistry of minerals such as
andalusite, kyanite and sillimanite. Gibbs et al. (1994; 1997; 1998; 1999; 2002; 2003;
2004; and 2005) have provided major advances in our understanding the crystal
chemistry and bonding in a number of silicates from electron density calculations.
Whereas many studies have focused on the nature of the Si-O bond, fewer studies have
examined the Al-O bond even though Al is the third most abundant element in the
Earth’s crust (Anderson, 1989). The Al2SiO5 polymorphs provide a model system in
which to apply electron density calculations to understand both the Al-O and Si-O
bonding in the structures which, in turn, can help explain the small differences in energy
and relative stabilities of the Al2SiO5 polymorphs.
Phase Equilibria Studies of the Al2SiO5 polymorphs
Due to the small energy differences between the structures of the Al2SiO5
polymorphs it is not surprising that experimental determinations of the phase boundaries
and the triple point has varied greatly (Figure 1.1). A comprehensive review of the
hydrothermal stability of the Al2SiO5 triple point was presented by Kerrick (1990) and
Zen (1969) where many of the previous equilibrium were discredited due to failure to
demonstrate equilibrium, incorrect calibration of pressure, imprecise temperature
controls, and improper starting materials (eg. fibrolite). Prior to 1990 the two most widely
used Al2SiO5 phase diagrams were from Richardson et al. (1969) and Holdaway (1971).
Newton (1987) concluded that there was no clear choice in determining which phase
diagram should be used. However, Kerrick (1990) argued against the use of
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Richardson’s (1969) phase diagram where they intensely ground their starting materials
because Newton (1969) demonstrated that extensive grinding of the starting material
seriously effects the experimental bracketing of the kyanite-sillimanite equilibrium. In
addition, Richardson’s (1969) sillimanite samples contained 30% by volume fibrolite.
Fibrolite has been arbitrarily defined (Kerrick and Speer, 1988) as fibrous
sillimanite crystals that are less than 10 µm. Fibrolite has been suggested to alter the P-T
stability field with reactions involving sillimanite due to possible Al/Si disorder,
dislocation densities, intergrowth materials, and grain boundary energies. Of the three
Al2SiO5 polymorphs, sillimanite is the only one with Al in tetrahedral sites and it has
been suggested that fibrolite has more Al/Si disorder than sillimanite (Chinner et al.,
1969; Holdaway, 1971; Greenwood, 1972) which may alter the P-T stability field.
Subsequent X-ray studies of fibrolite (Moore and Best, 1969; Cameron and Ashworth,
1979; Thomas, 1984; and Beger, 1979) indicate that the unit cell parameters are virtually
identical to sillimanite suggesting that there is no Al/Si disorder in fibrolite with respect
to sillimanite because increasing disorder causes increasing volume of the unit cell
(Berger, 1979). However, it was shown (Bish and Burnham, 1992) that fibrolite from
Brittany, France, has 18% Al/Si disorder, indicating that at least some fibrolite is
disordered which may be caused by the conditions of crystallization (Holdaway and
Mukhopadhyay, 1993). Dislocation densities calculations in fibrolite by Wenk (1983)
determined that fibrolite to contains 1x1010 /cm2 dislocation densities, but TEM analysis
of fibrolite from other localities (Doukhan et al., 1985; Kerrick, 1986) determined much
lower dislocation densities (1x108/cm2 and 5x108/cm2) which are related to the
dislocation densities in sillimanite and would not effect the stability (Kerrick, 1990).
Therefore Kerrick (1990) argued that dislocation densities are not an important factor in
examination of the stability relations of fibrolite and sillimanite. Kerrick (1990)
concluded that the only effect on the P-T stability field between fibrolite and sillimanite
is the result of differences in the grain boundary energy, though we now know that some
fibrolite may be disordered. Grain boundary energies were calculated by Holdaway
(1971) and determined that the relative surface energy difference between fibrolite and
sillimanite would shift the andalusite-sillimanite equilibrium boundary by 120 ≤ 25°C.
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These calculations are based on fibrolite samples with diameters of 0.3 µm and Kerrick
(1990) stated that only fibrolite crystals with diameters less that 0.5 µm would
appreciable effect the P-T equilibrium between phases. Thus, fibrolite in most instances
is exactly the same (crystal structure, stoichiometry, and abundance of lattice defects) as
sillimanite and will only effect equilibrium position of the P-T diagram if it is calculated
using small (less than 0.5 µm) or disordered samples.
Although not related to the crystal structure, phase equilibria calculated with
fibrolite samples may produce inaccurate boundaries due to intergrown materials
(Hodaway and Mukhopadhyay, 1993). Fibrolite commonly contains quartz and
corundum as intergrown minerals which may not be completely separated from the
samples using physical methods before the experiments. This may result in a
spontaneous reaction of quartz plus corundum forming an Al2SiO5 phase near an
equilibrium boundary. If there are seeds of two Al2SiO5 phases in the system then they
may both grow resulting in false stability measurements (Holdaway and Mukhopadhyay,
1993). Consequently, impurities (eg. intergrown materials) in fibrolite will result in
inaccurate P-T stability diagrams.
In an ideal world calculations of the stability between the different Al2SiO5 phases
would be conducted with stoichiometrically pure samples, but minor amounts of
transition elements (Ti, V, Cr, Mn, and Fe) can be incorporated into their structures
affecting their P-T stability. The effects of trace elements on the P-T diagram can be
examined by the studies on Fe3+ and Mn3+ incorporation in the Al2SiO5 polymorphs
(Grambling and Williams, 1985; Holdaway and Goodge, 1990; Holdaway and
Mukhopadhyay, 1993). Grambling and Williams (1985) calculated the effect of
partitioning of Fe3+ and Mn3+ into the polymorphs and the effect on the phase
relationship. Using the triple point defined by Holdaway (1971) to be stoichiometrically
pure, the triple point for the polymorphs containing small amounts (< 1 wt %) Fe3+ and
Mn3+ increases by 400 bars and 20°C. Thus, calculations of the equilibrium boundaries
between the phases must correct for impurities if phase equilibria or thermodynamic data
are used.
9
Thermodynamic Properties of Al2SiO5 polymorphs
So far the P-T stability of the Al2SiO5 polymorphs has been examined with
respect to phase equilibria studies, but calorimetric and equation of state data provide an
independent method for calculation of phase boundaries. The stability of the Al2SiO5
phases is determined with the Gibbs free energy equation (see chapter 2), while the
slopes of the equilibrium boundaries can be determined with the Clapeyron equation:
(dP/dT)equilibrium = ∆S/∆V (1.1)
Heat capacities and entropies of the Al2SiO5 polymorphs have been determined from
calorimetric studies by Todd (1950), Robie and Hemingway (1984), Salje (1986), and
Hemingway et al., (1991). Hemingway et al. (1991) determined the most accepted
thermodynamic values for the Al2SiO5 polymorphs, but they are based on
stoichiometrically pure phases. The impurities in the phases were examined by
Holdaway and Mukhopadhyay (1993) who refined the thermodynamic values to account
for elevated Fe2O3 in the samples. Calorimetric studies of the enthalpies, heat of
formation, of the Al2SiO5 polymorphs have been studied by Holm and Kleppa (1966),
Topor et al. (1989), Hemingway et al. (1991), and Berman and Brown (1985). In
addition to entropy and enthalpy, thermodynamic calculations of the phase boundaries for
the Al2SiO5 polymorphs require an understanding of the effect of pressure and
temperature on the volume of the unit cell. The thermal expansion, change in volume
with respect to temperature, was examined using X-ray diffraction on andalusite,
sillimanite, and kyanite by Winter and Ghose (1979), while the effects of pressure on the
volume of the unit cells have been examined in numerous theoretical and experimental
studies as summarized in Chapter 2. Holland and Powell (1998; updated 05/14/01) have
amassed a thermodynamic data base for most of the crustal minerals including the
Al2SiO5 polymorphs and determined the calculated triple point is similar to the
experiments of Holdaway (1971).
10
Ultimately, the phase relationships between the Al2SiO5 polymorphs are used to
constrain the pressure and temperature conditions of metamorphosed metapelitic rocks.
However, there is still controversy between the experimentally adopted triple point
(Holdaway, 1971) and the triple point determined from natural assemblages of low-P
metapellites (Pattison, 1992; Tinkham et al., 2001). The disagreement between the triple
point deduced from field relations and the experimentally determined triple point is
related to the equilibrium boundary between andalusite and sillimanite. The free energy
difference between sillimanite and andalusite is significantly smaller than between the
kyanite-andalusite or kyanite-sillimanite phases (Table 1.2) resulting in an ill-constrained
boundary between andalusite and sillimanite. Therefore, greater precision is required in
experimental data sets for constraining the equilibrium position of the andalusite-
sillimanite phases because of the subtle energetic effects between the two polymorphs.
Additionally, metal impurities and fibrolite have been considered to affect the phase
equilibrium, but the role of trace amounts of water in the polymorphs is still unknown.
Mineral S°298(J/mol K)1 S°298(J/mol K)2 S°298(J/mol K)3 ∆H°298(kJ/mol)1 ∆H°298(kJ/mol)2
Andalusite 91.39(14) 91.39(52) 91.60(52) -2589.9(30) -2589.66(300)
Sillimanite 95.87(54) 95.40(52) 95.08(52) -2586.1(30) -2586.37(300)
Kyanite 82.30(13) 82.80(50) 82.86(50) -2593.8(30) -2593.70(300)S1=Measurements for kyanite and andalusite from Hemingway (1984) and sillimanite from Hemingway et al., (1991). S2, H1 = Measurements from Hemingway et al., (1991). S3, H2 = Measurements from Holdaway and Mukhopadhyay (1993). Values from Hemingway (1984) and Hemingway et al., (1991) were adjusted to correct of impurities and to fit aluminum silicate reversals where necessary by Holdaway and Mukhopadhyay (1993).
Table 1.2: Enthalpy and Entropy of the Al2SiO5 polymorphs
Water incorporation in the Al2SiO5 polymorphs
Relatively small amounts of water may have a disproportionate effect on the
properties of minerals and the absolute concentration of water in nominally anhydrous
minerals can be examined with infrared spectroscopy (Bell and Rossman, 1992).
Previous infrared measurements of the Al2SiO5 polymorphs (Rossman and Smyth, 1990;
Beran, 1969, 1970, 1971; Beran et al., 1983, 1989, 1987; and Wilkins and Sabine, 1973)
have found that the concentration of OH in the structures ranged from 6200 ppm wt %
11
H2O to 90 ppm wt% H2O, though the higher values (6200 ppm wt % H2O) are not
realistic and not likely due to interstitial hydrogen. Numerous mechanisms have been
proposed for the incorporation of water within the Al2SiO5 polymorphs. Wilkins and
Sabine (1973) speculated that OH could be accommodated into the structures by 1)
substitution of SiO4 groups by (OH)4, 2) the H3O+ ion, 3) interstitial water, 4) OH ions
associated with dislocations, and 5) isolated “substitutional” OH ions. In addition, Beran
et al. (1983) and Hålenius (1979) proposed the removal and replacement of an Al cation
by the following mechanisms:
Al3+ + 3O2- 3(OH)- + Beran et al (1983)
Al3+ + O2- Fe2+ + OH- Halenius (1979)
Though potential mechanisms for the incorporation of hydroxyl groups in the Al2SiO5
polymorphs have been predicted, there have been no studies on the orientation of the
hydroxyl groups. There have also been no studies examining the polarized infrared
spectrum of andalusite, which can be used to determine the position and orientation of
OH in the structure. Furthermore, it has also been suggested that kyanite might transform
into the “Egg” phase, AlSiO3OH, in subduction environments (Schmidt et al., 1998).
Thus examination of water incorporation in the Al2SiO5 polymorphs will enhance our
understanding of the recycling of water between the mantle and the crust.
Objective of dissertation
It is clear from the studies outlined above that major questions still exist regarding
the Al2SiO5 polymorphs. In this dissertation, I present the results of three studies of the
Al2SiO5 polymorphs that provide new insights into the chemical bonding of the
polymorphs, their crystal chemistry, their equations of state, and the incorporation of
water in the form of hydroxyl in their structures. Chapter 2 presents results from a high-
pressure single crystal X-ray diffraction study of andalusite and sillimanite that provide
precise determinations of their equations of state as well as their structural response to
pressure. Chapter 3 examines electron localization function (ELF) isosurfaces of the
12
Al2SiO5 polymorphs, which is a graphical representation of bonded and nonbonded
regions of localized electron probability density. The ELF isosurfaces within the three
polymorphs are examined in relation to number of coordinated cations, geometry, and
variation in cation atomic number. Chapter 4 presents a methodology to determine the
location of hydrogen atoms in nominally anhydrous minerals such as the Al2SiO5
polymorphs based on a combination of experimental methods (single-crystal polarized
Fourier Transform Infrared Spectroscopy, FTIR) and theoretical calculations of the
Laplacian of electron density. The last chapter presents conclusions derived from these
studies.
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13
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14
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15
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16
Holm, J.L., and Kleppa, O.J., (1966) The Thermodynamic Properties of the Aluminum Silicates. American Mineralogist, 51, 1608-1622. Kerrick, D.M. (1986) Dislocation strain energy in the Al2SiO5 polymorphs. Physics and Chemistry of Minerals, 13, 221-226. Kerrick, D.M. (1990) The Al2SiO5 polymorphs. Mineralogical Society of America, America Reviews in Mineralogy, 22, 406 p. Kerrick, D.M. and Speer, J.A. (1988) The role of minor element solid solution of the andalusite-sillimanite equilibrium in metapelites and peraluminous granitoids. American Journal of Science, 288, 152-192. Khitarov, N.I., Pugin, V.A., Chzao-Bin, P., and Slutsky, A.B. (1963) Relations between andalusite, kyanite, and sillimanite at moderate temperatures and pressures: Geochemistry, 8, 235-244. Lappin, M.A. (1960): On the occurrence of kyanite in the eclogites of the Selje and Åheim districts, Nordfjord. Norsk geografisk tidsskrift, 40, 289-296. Liati, A. & Seidele, E. (1994): Sapphirine and högbomite in overprinted kyanite eclogites of central, N. Greece: first evidence of granulite-facies metamorphism. European Journal of Mineralogy, 6, 733-738. Liu, L-G. (1974) Disproportionation of kyanite to corundum plus stishovite at high pressure and temperature. Earth and Planetary Science Letters, 24, 224-228. Miyashiro, A. (1961) Evolution of metamorphic belts. Journal of Petrology, 2, 277-311. Moore, J.M. and Best, M.G. (1969) Sillimanite from two contact aureoles. American Mineralogist, 54, 975-979. Naray-Szabo, St., Taylor, W.H., and Jackson, W.W. (1929) The structure of kyanite. Zeitshcrift fur Kristallographie, 71, 117-130. Newton, R.C. (1966) Kyanite-andalusite equilibrium from 700°C to 800°C. Science, 153, 170-172. Newton, R.C. (1966b) Kyanite-sillimanite equilibrium at 750°C. Science, 151, 1222- 1225. Newton, R.C. (1969) Some high-pressure hydrothermal experiments on severely ground kyanite and sillimanite. American Journal of Science, 267, 278-284.
17
Newton, R.C. (1987) Thermodynamic analysis of phase equilibria in simple mineral systems. Chapter 1 in: Thermodynamic Modeling of Geological Materials: Minerals, Fluids, and Melts. I.S.E. Carmichael and H.P. Eugster, eds., Reviews in Mineralogy, 17, 1-33. Olbricht, W., Chatterjee, N.D., and Miller, K. (1994) Bayes estimation – anovel approach to derivation of internally consistent thermodynamic data for minerals, their uncertainties and correlations. 1. Theory. Physical Chemistry of Minerals, 21, 36- 49. Oganov, A.R., and Brodholdt, J.P. (2000) High-pressure phases in the Al2SiO5 system and the problem of aluminous phase in the Earth’s lower mantle: ab initio calculations. Physics and Chemistry of Minerals, 27, 430-439. Pauling, L. (1929) The principles determining the structure of complex ionic crystals. Journal of the American Chemical Society, 51, 1010–1026. Pattison, D.R.M. (1989) P-T conditions and the influence of graphite on politic phase relations in Ballachulish thermal aureole, Scotland. Journal of Petrology, 30, 1219-1244. Pattison, D.R.M. (1992) Stability of andalusite and sillimanite and the Al2SiO5 triple point: Constraints from Ballachulish aureole, Scottland. Journal of Geology, 100, 423-446. Peterson, R.C., and McMullan, R.K. (1986) Neutron diffraction studies of sillimanite. American Mineralogist, 71, 742-745. Pugin, V.A., and Khitarov, N.I. (1966) Sistema Al2O3-SiO2 v uloviyakh povyshennykh temperature i davleniy (The system Al2O3-SiO2 under high temperature and pressure). Geokhimiya 157-165 (English abstr. P. 165). Ralph, R. L., Finger, L.W., Hazen, R.M., Ghose, S. (1984) Compressibility and crystal structure of andalusite at high pressure. American Mineralogist, 69, 513-519. Richardson, S.W., Gilbert, M.C., and Bell, P.M. (1969) Experimental determination of kyanite-andalusite and andalusite-sillimanite equilibria: the aluminum silicate triple point. American Journal of Science, 267, 259-272. Robie, R. A., and Hemingway, B.S., (1984) Entropies of kyanite, andalusite, and sillimanite: additional constraints on the pressure and temperature of the Al2SiO5 triple point. American Mineralogist, 69, 298-306. Rossman, G.R. and Smith, J.R. (1990) Hydroxyl contents of accessory minerals in mantle eclogites and related rocks. American Mineralogist, 75, 775-780.
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Salje, E. (1986) Heat capacities and entropies of andalusite and sillimanite: The influence of fibrolitization on the phase diagram of the Al2SiO5 polymorphs. American Mineralogist, 71, 1366-1371. Schmidt, M.W., Poli, S., Comodi, P., and Zanazzi, P.F. (1997) High-pressure behavior of kyanite: decomposition of kyanite into stishovite and corundum. American Mineralogist, 82, 460-466. Schmidt, M.W., Finger, L.W., Angel, R.J., Dinnebier, R.E. (1998) Synthesis, crystal structure, and phase relations of AlSiO3OH, a high-pressure hydrous phase. American Mineralogist, 83, 881-888. Taylor, W.H. (1928) The structure of sillimanite and mullite. Zeitschrift für Kristallographie, 68, 503-521. Taylor, W.H. (1929) The crystal structure of andalusite Al2SiO5. Zeitschrift fur Kristallographie, 71, 205-218. Thomas, K.K. (1984) The origin of sillimanite is Essex, Connecticut. M.S. Thesis, Indiana University, 101p. Tinkham, D.K., Zuluaga, C.A., and Stowell, H.H. (2001) Metapelitic phase equilibria modeling in MnNCKFMASH: The effect of variable Al2O3 and MgO/(MgO + FeO) on mineral stability. Geological Materials Research, 3, 1-42. Todd, S.S. (1950) Heat capacities at low temperatures and entropies at 298.16K of andalusite kyanite, and sillimanite. Journal of the American Chemical Society, 72, 4742-4743. Topor, L., Klepa, O.J., Newton, R.C., and Kerrick, D.M. (1989) Molten salt calorimetry of Al2SiO5 polymorphs at 1000K. Eos, 70, 493. Vaughan, M. T., and Weidner, D.J. (1978) The relationship of elasticity and crystal structure in andalusite and sillimanite. Physics and Chemistry of Minerals, 3, 133-144. Weill, D.F. (1966) Stability relations in the Al2O3-SiO2 system calculated from solubilities in the Al2O3-SiO2-Na3AlF6 system. Geochimica Cosmochimica Acta, 30, 223-237. Wenk, H.R. (1983) Mullite-Sillimanite intergrowth from politic inclusions in Bergell tonalite. Neues Jahrbuch fur Mineralogie, 146, 1-14. Wilkins, R.W.T., and Sabine, W. (1973) Water content of some nominally anhydrous silicates. American Mineralogist, 58, 508-516.
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Winter, J.K., and Ghose, S. (1979) Thermal expansion and high-temperature crystal chemistry of the Al2SiO5 polymorphs. American Mineralogist, 64, 573-586. Yang, H., Hazen, R.M., Finger, L.W., Prewitt, C.T., and Downs, R.T. (1997a) Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure. Physics and Chemistry of Minerals, 25, 39-47. Yang, H., Downs, R.T., Finger, L.W., Hazen, R.M., and Prewitt, C.T. (1997b) Compressibility and crystal structure of kyanite, Al2SiO5, at high pressure. Physics and Chemistry of Minerals, 82, 467-474. Zen, E-an, (1961) The stability relations of the polymorphs of aluminum silicates: a survey and some comments. American Journal of Science, 267, 297-309.
20
Chapter 2
Equations of state and structures of andalusite to 9.8 GPa and sillimanite to 8.5 GPa
The results presented in this chapter have been published: Jason B. Burt, Nancy L. Ross, Ross J. Angel and Mario Koch, American Mineralogist (2006), 70, 319-326
Abstract
The equations of state and structures of andalusite and sillimanite have been
determined using high-pressure single-crystal X-ray diffraction. A third-order Birch-
Murnaghan equation of state fit to 14 P-V data points measured between 1 bar and 9.8
GPa for andalusite yields values of KT0= 144.2(7) GPa and K' =6.8(2). A similar analysis
for sillimanite involving a fit to 13 P-V data points between 1 bar and 8.5 GPa results in
KT0= 164(1) GPa and K'= 5.0(3). The axial compression of both structures is nonlinear
and highly anisotropic (~60%) with the c-axis being the least compressible axis in both
structures. The axial moduli determined with a parameterized form of the third-order
Birch-Murnaghan equation of state are: Ka0=163(1) GPa, Kb0=113.1(7) GPa, and
Kc0=297(1) GPa with K'a0=2.1(3), K'b0=5.08(19), and K'c0=11.1(4) for sillimanite, and
Ka0=99.6(7) GPa, Kb0=152.2(9) GPa, and Kc0=236(3) GPa with K'a0=5.83(19),
K'b0=7.6(3) , and K'c0=5.5(9) for andalusite. The major compression mechanism in both
structures involves shortening of bond lengths within the AlO6 octahedra with volume
reductions of 7.4% and 5.1% in sillimanite and andalusite, respectively, over the pressure
ranges studied. In andalusite there is also significant compression of the AlO5 polyhedra
and, to a lesser degree, the SiO4 tetrahedra that display reductions of 5.0% and 3.1% in
volume, respectively. In sillimanite there is no significant compression of either the AlO4
or SiO4 tetrahedra which behave as rigid, incompressible units.
21
Introduction
Accurate equation of state measurements for minerals such as the Al2SiO5
polymorphs are important because they provide vital input into thermodynamic databases
from which phase equilibria can be calculated. The stabilities of the Al2SiO5 polymorphs
are governed by the differences in the free energies of the polymorphs:
1
( , )P
o oT T TG H T S V P T d∆ = ∆ − ∆ + ∆∫ P (2.1)
where is the standard enthalpy of reaction and oH∆ oS∆ is the standard entropy of
reaction, which require requilibration with heat capacity data at non standard state
conditions. Accurate prediction of mineral equilibria therefore requires knowledge of the
heat capacity, thermal expansion and compressibility for the minerals involved. Because
of the fine balance between ∆H and –T∆S (Table 1.2), the term in Eqn.
(2.1) becomes an important factor for calculation of accurate phase equilibria. The
equation of state is determined by examining the change in a mineral’s volume with
increasing pressure:
0
( , )P
V P T dP∆∫
K0 = -V0 (∑P/∑V)P=0 (2.2)
where the subscript zero refers to room pressure values and V0 and K0 refer to the
material properties at P=0 at elevated temperature (standard state conditions). Up to
~1000 K P-V-T data sets can be considered linear with respect to temperature and the
variation of the bulk modulus with temperature can expressed as:
K0(T) = K0(T0) + (T-T0)(∑K/∑T)P (2.3)
22
where T0 is the reference temperature (room temperature). Typically the change in the
bulk modulus can be neglected due to the small change in the bulk modulus with
temperature (~.02GPa/K) for most minerals (Anderson, 1995).
Determination of the bulk modulus of mineral from a high pressure experiment is
calculated by fitting an equation of state (EoS) to the P-V data because there is no
thermodynamic basis for determining the exact EoS of a mineral. There are numerous
methods to model the equation of state, but for pressure conditions within terrestrial
planets the Birch-Murnaghan equation is normally adequate (Duffy and Wang, 1998).
The Birch–Murnaghan equation of state was developed (Birch, 1947) using a Taylor
series in finite strain, f, to expand the strain energy of a solid undergoing compression, F.
F = a0 + a1 f + a2 f 2 + a3 f 3 + a4 f 4 + …. (2.4)
The finite strain is based on Eulerian strain, fe = [(V0/V)2/3-1]/2, and the Birch-
Murnaghan equation expressed to the fourth order is equal to:
5/ 2 20 E E E 0 E
3 3 353 (1 2 ) 1 ( ' 4) '' ( ' 4)( ' 3)2 2 9
P K f f K f K K K K f⎛ ⎞⎛ ⎞= + + − + + − − +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
(2.5)
where ' ( / )K K P= ∂ ∂ and (Birch, 1947). 2'' ( / )K K P= ∂ ∂ 2
The order to which the Birch-Murnaghan equation of state is carried out to is best
visualized in a plot of the Eulerian strain, fe, versus “normalized stress”, Fe = P/3fe(1+2fe-
)5/2, because visualization of the precise EoS cannot be done due to the high precision in
current measurements of pressure and volume. If the fe-Fe plot is represented as a
horizontal line then the EoS state can be modeled as second order and K’ will be equal to
four, but if not then a third order Birch-Murnaghan equation of state is required with a
refineable K’ and an implied K’’ determined by Anderson (1995) equal to:
23
0
1" (3 ')(4 ')9
K K KK− ⎛= − − +⎜
⎝ ⎠35 ⎞
⎟ (2.6)
Measurements using the second order Birch-Murnaghan equation of state underestimate
the bulk modulus when K’ is greater than 4 and overestimate the bulk modulus when K’
is less then 4. Due to experimental improvements in constraining the pressure and
volume in a diamond anvil cell (DAC) we now know that many minerals have K’ not
equal to 4.
Ultimately, we are interested in extracting accurate equation of state
measurements for use in constructing mineral stability diagrams. The Birch-Murnaghan
equation of state is used to constrain KT0 and K’, but can only be used numerically to
determine . This integral is often evaluated algebraically with the
Murnaghan equation of state:
0
( , )P
V P T dP∆∫
'
0 1'
KoK VP
K V⎡ ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
(2.7)
where the bulk modulus is assumed to vary linearly with pressure (Murnaghan, 1937). At
high pressures the Murnaghan equation of state does not properly model the P-V data
resulting in inaccurate compressiblilities. However, at low pressures (below 3-4 GPa) the
Murnaghan equation of state can correctly model the P-V relationship for dP/dV
calculations. It should be noted that the KT and K’ parameters for each EoS model,
Birch-Murnaghan and Murnaghan, cannot be interchanged because the parameters define
the curvatures of the P-V parameters differently (Angel, 2001).
The equation of state of sillimanite was examined by Yang et al. (1997) using
single-crystal X-ray diffraction and by Friedrich et al. (2004) using synchrotron powder
24
Table 2.1 Isothermal Bulk moduli, KT0, of andalusite and sillimanite.
Method KT0 (GPa) K' Ref. Method KT0 (GPa) K' Ref.XRD (single crystal) 144.2(7) 6.8(2) [7] XRD (single crystal) 164(1) 5.0(3) [7]XRD (single crystal) 135(10) 4 [1] XRD (single crystal) 171(7) 4 [2]XRD (single crystal) 151(3) 4 [2] XRD (Powder) 176(11) 4 [6]Brillouin (Reuss) 158 [3] Brillouin (Reuss) 166.4 [3] Brillouin (Voigt) 165.9 [3] Brillouin (Voigt) 175.1 [3]Theoretical (DFT) 145.3 3.88 [4] Theoretical (DFT) 160.1 2.69 [4]Theoretical (DFT) 143.5 4 [4] Theoretical (DFT) 148 4 [4]Theoretical (DFT) 145 [5] Theoretical (DFT) 159 [5]Theoretical (THB) 191 [5] Theoretical (THB) 198 [5]
Andalusite Sillimanite
[1] Ralph et al. (1984); [2] Yang et al. (1997); [3] Vaughan and Weidner (1978); [4] Organov et al. (2001); [5] Winkler et al. (2001); [6] Friedrich et al. (2004); [7] this study.
X-ray diffraction (Table 2.1). These studies determined isothermal bulk moduli, KT0, of
171(7) GPa and 176(11) GPa, respectively, from P-V data collected to 5.29 GPa (Yang
et al. 1997) and 46 GPa (Friedrich et al. (2004). In both studies, the pressure derivative of
the bulk modulus, K', could not be constrained and was assumed to be equal to four.
Yang et al. (1997) also reanalyzed Ralph et al.’s (1984) earlier P-V data for andalusite
that was collected to 3.7 GPa and determined a KT0 = 151(3) GPa (also with K'
constrained to be 4), contrasting with the original determination of KT0=135(10) GPa. It
should be noted that the study by Ralph et al. (1984) was one of the first high-pressure
studies of a single crystal in a diamond anvil cell (DAC) using X-ray diffraction.
Vaughan and Weidner (Vaughan 1978) determined the adiabatic bulk modulus, KS, from
Brillouin spectroscopy measurements of andalusite and sillimanite to be 158 GPa and
166 GPa (Reuss bound values), respectively. Theoretical calculations of the bulk
modulus for andalusite and sillimanite have also been reported by Matsui (1996), Oganov
et al. (2001) and Winkler et al. (2001). Matsui (1996) reported a bulk modulus of 175
GPa for sillimanite and 104 GPa for andalusite based on a molecular dynamics
calculation. Oganov et al. (2001) calculated the bulk moduli of andalusite and sillimanite
to be 145.3 GPa and 160.1 GPa with K' values of 3.88 and 2.69, respectively, using the
VASP (Vienna Ab Initio Simulation Package) program, while Winkler et al. (2001)
calculated bulk moduli of andalusite and sillimanite to be 145 and 159 GPa, respectively,
25
using the CASTEP (CAmbridge Serial Total Energy Package) program. Calculations of
the equilibrium boundary between andalusite and sillimanite using the bulk moduli and
associated errors determined from previous experimental X-ray studies results in a range
~372 bars with temperature along the P-T path (see Appendix 1). Thus, for proper
experimental calculations of the P-T boundary for the Al2SiO5 polymorphs it is important
to constrain the bulk moduli and the errors involved in the calculations.
Even though these polymorphs have been extensively studied, it is clear from the
preceding discussion that there is a considerable spread in the values of KT0, especially
for andalusite. In addition, the previous X-ray diffraction experiments of both
polymorphs assumed K'=4. Recent improvements in determining both the volume and
pressure in single-crystal X-ray experiments allow more precise determinations of
equations of state (Angel 2001). Provided one has good quality single crystals, volumes
of single crystals loaded in diamond anvil cells (DACs) can be measured to better than 1
part in 10,000. Bulk moduli can be determined with esd’s of 1% or less and accurate
values of K' can also be determined (e.g. Angel 2001). We report here the equations of
state and high-pressure structural behavior of andalusite and sillimanite. The structural
studies provide information about the compressional mechanisms and their influence on
the equation of state. We address the questions of whether a second-order Birch-
Murnaghan equation of state is valid for andalusite and sillimanite, what structural
features control compression of the two structures, whether the compression mechanisms
are similar and how these affect the overall changes in the distortion of the structures. In
addition, this study extends the previous pressure ranges of high-pressure single-crystal
X-ray diffraction studies from 3.7 to 9.8 GPa for andalusite and 5.29 to 8.54 GPa for
sillimanite.
Experimental Methods
The sillimanite sample was kindly provided by Dr. Carl Francis, curator of the
Harvard mineral collection, and is from the Okkamitiya Sabaragamuiwa province of Sri
Lanka (sample #131013). The andalusite sample is from Minas Gerais, Brazil and was
26
obtained from a gem dealer in Idar Oberstein, Germany. An andalusite crystal measuring
272 x 112 x 56 µm and a sillimanite crystal measuring 130 x 112 x 30 µm were picked
based on their optical quality and X-ray diffraction peak profiles. Each crystal was loaded
in an ETH-type diamond anvil cell (Miletich et al. 2000) along with a quartz crystal and a
ruby chip for pressure calibration. Unit cell parameters were obtained from a Huber four
circle diffractometer using MoKα radiation (λ = 0.7107 Å) with a tube power of 50 kV
and 40 mA. The room pressure unit cell parameters were collected in the DAC without
fluid, while the high pressure data was collected using a 4:1 mixture of methanol:ethanol
as the pressure-transmitting medium. Tungsten was initially used as the gasket material
up to pressures of 6.5 GPa for andalusite and 6.3 GPa for sillimanite before deformation
of the gasket hindered further increases in pressure. The gaskets were replaced with
T301 steel and, in the case of andalusite, a gasket prepared with a 304 µm diameter hole
and thickness of 80 µm remained stable up to 9.8 GPa. The unit cell parameters (Tables
2.2 and 2.3) were calculated using a vector least squares fit of 22–35 reflections between
9± and 27± 2θ for andalusite and between 11± and 32± 2θ for sillimanite centered at 8
equivalent positions following the procedure of King and Finger (1979). The initial
unconstrained unit cell refinements did not deviate from orthorhombic symmetry for
either crystal throughout the pressure range studied. The volume of a quartz crystal
within the diamond anvil cell was used to determine the pressure from the third-order
Birch-Murnaghan equation of state of quartz: KT0=37.12(9) GPa and K0'=5.99(4) (Angel
1997). Equation of state parameters of andalusite and sillimanite were obtained by a
weighted-least-squares fit of the Birch-Murnaghan 3rd-order equation of state to the P-V
data using the program EosFit 5.2 (Angel 2001).
X-ray intensity data for andalusite were collected at 0.0001, 1.474(5), 2.512(6),
3.129(6), 3.932(7), 5.441(6), 7.565(8), and 9.828(9) GPa and at 0.0001, 1.548(5),
4.144(7), and 7.663(8) GPa for sillimanite using an Oxford Diffraction Xcalibur single
crystal X-ray diffractometer with monochromatized MoKα radiation (λ = 0.70923 Å),
tube power of 50kV and 40 mA, and a point detector. The data sets were collected using
the fixed Φ mode from 4° to 40° in θ for both samples with an omega scan of 0.05° per
second, scan width of 1.2° and a step number of 60 for andalusite and an omega scan of
27
0.02° per second, scan width of 1.2° and a step number of 60 for sillimanite. The peaks
were integrated using the program Win-IntegrStp v3.4 (Angel 2003) that performs a full
peak-profiling of the step-scan data based on the methods of Pavese and Artioli (1996).
Absorption corrections for the integrated intensities were made using ABSORB 6.0
(Angel 2004; Burnham 1966) that corrects for absorption by the crystal, components of
the DAC, and for gasket shadowing. Overall transmission through the DAC ranged from
and 0.16 to 0.37 for andalusite and 0.22 to 0.25 for sillimanite. Symmetrically-equivalent
reflections for both crystals were averaged in Laue group mmm and R(int) values are
given in Tables 2.4 and 2.5.
The crystal structure refinements were carried out with RFINE99, developed from
a previous version, RFINE4 (Finger 1974). Initial atomic coordinates for andalusite and
sillimanite were taken from Winter and Ghose (1979) and atomic scattering factors and
coefficients for dispersion correction from the International Tables for Crystallography
(Maslen et al. 1992; Creagh and McAuley 1992). Details of the refinements are given in
Tables 2.4 and 2.5, the refined atomic positions and displacement parameters are given in
Tables 2.6 and 2.7, and selected interatomic distances and angles for sillimanite and
andalusite are given in Tables 2.8 and 2.9, respectively.
28
Table 2.2. Unit cell parameters of sillimanite, space group Pbnm, from 1 bar to 8.543 GPa. The figures in parentheses represent 1 esd of last decimal place shown.
Pressure (GPa) a-axis (Å) b-axis (Å) c-axis (Å) Volume (Å3)
0.0001 7.48388(17) 7.6726(3) 5.76807(13) 331.208(18) 0.239(4) 7.48009(16) 7.6672(4) 5.76652(12) 330.71(2) 1.016(4) 7.46853(12) 7.6507(3) 5.76169(9) 329.220(14) 1.548(5) 7.46040(15) 7.6395(4) 5.75840(12) 328.190(19) 2.292(5) 7.44882(12) 7.6235(2) 5.75396(9) 326.745(13) 3.431(6) 7.43271(11) 7.6011(3) 5.7472(1) 324.694(13) 3.747(5) 7.42883(18) 7.5952(3) 5.74536(11) 324.150(17) 4.144(7) 7.42183(13) 7.5868(3) 5.74298(11) 323.375(16) 4.685(6) 7.41448(12) 7.5771(3) 5.74011(9) 322.479(13) 5.750(7) 7.39939(11) 7.5576(2) 5.73421(8) 320.667(11) 6.348(7) 7.39134(12) 7.5475(2) 5.73114(9) 319.717(13) 7.663(8) 7.3717(2) 7.5243(4) 5.72421(11) 317.503(19) 8.543(8) 7.36058(12) 7.5106(2) 5.72007(8) 316.221(12)
Table 2.3 Unit cell parameters of andalusite, space group Pnnm, from 1 bar to 9.828 GPa. The figures in parentheses represent 1 esd of last decimal place shown. Pressure (GPa) a-axis (Å) b-axis (Å) c-axis (Å) Volume (Å3) 0.0001 7.7930(3) 7.89734(17) 5.55583(14) 341.926(15) 0.605(4) 7.7780(4) 7.8868(2) 5.5513(2) 340.54(2) 1.474(5) 7.7568(3) 7.87268(18) 5.54488(15) 338.607(16) 2.265(5) 7.7381(3) 7.8602(2) 5.53919(18) 336.908(19) 2.512(6) 7.7320(3) 7.85659(16) 5.53642(16) 336.320(16) 3.129(6) 7.7186(4) 7.8467(2) 5.5329(2) 335.10(2) 3.932(7) 7.7014(3) 7.8354(2) 5.52629(17) 333.472(18) 4.586(7) 7.6877(3) 7.82600(17) 5.52187(15) 332.219(15) 5.051(7) 7.6783(4) 7.8197(2) 5.51841(18) 331.336(19) 5.441(6) 7.6704(3) 7.81452(18) 5.51589(16) 330.625(16) 6.516(8) 7.6494(5) 7.7997(3) 5.5085(2) 328.65(3) 7.565(8) 7.6313(3) 7.78625(19) 5.50175(14) 326.910(14)
8.465(8) 7.6145(4) 7.7753(2) 5.49544(18) 325.358(19) 9.828(9) 7.5922(8) 7.7600(5) 5.4872(4) 323.28(4)
29
Table 2.4 Details of least-squares structure refinements for sillimanite at room pressure through 7.663 GPa. Pressure (GPa): 0.0001 1.548(5) 4.144(7) 5.750(7) 7.663(8)ρcalc (g/cm3) 3.249 3.29 3.343 3.356 3.39
µ (mm-1) 1.123 1.137 1.155 1.159 1.171θ range for data collection 4° ~ 40° 4° ~ 40° 4° ~ 40° 4° ~ 40° 4° ~ 40°
Limiting Indices -13≤h≤13, -2≤k≤2, -10≤l≤10
-13≤h≤11, -2≤k≤3, -9≤l≤10
-11≤h≤12, -2≤k≤2, -9≤l≤10
-10≤h≤12, -2≤k≤2, -10≤l≤10
-13≤h≤10, -2≤k≤2, -9≤l≤9
No. refl. >2 I0/σ(I0) 837 845 764 776 696No. ind. Refl. (F>2σ(F)) 180 195 171 158 156Rint* 0.038(166) 0.041(180) .049(160) 0.041(140) 0.046(147)No. of paramters 22 22 22 22 22Gfit
† 1.17 1.32 1.11 1.23 1.23Extinction Factor (x10-4) 0.19(5) 0.29(5) 0.24(5) 0.36(6) 0.16(5)RW
‡§ 0.029(173) 0.038(188) 0.039(168) 0.040(150) 0.037(144)R║§ 0.026(173) 0.034(188) 0.035(168) 0.035(150) 0.033(144)*Internal residual on F (number of averaged reflections)†Gfit: estimated standard deviation of unit weight observation‡Rw=[Σw(|F0|-|Fc|)
2/Σ|F0|2]2
§Number of reflections used in refinement are in parentheses║R=Σ||F0|-|Fc||/Σ|F0|
30
Table 2.5 Details of least-squares structure refinements for andalusite at room pressure through 9.828 GPa. Pressure (GPa): 0.0001 1.474(5) 2.512(6) 3.129(6) 3.932(7) 5.441(6) 7.565(8) 9.828(9)ρcalc (g/cm3) 3.147 3.178 3.2 3.212 3.227 3.255 3.292 3.329µ (mm-1) 1.087 1.098 1.106 1.11 1.115 1.125 1.137 1.15θ range for data collection 4° ~ 40° 4° ~ 40° 4° ~ 40° 4° ~ 40° 4° ~ 40° 4° ~ 40° 4° ~ 40° 4° ~ 40°
Limiting Indices -5≤h≤6, -12≤k≤12, -9≤l≤9
-5≤h≤5, -12≤k≤12, -9≤l≤9
-5≤h≤6, -12≤k≤12, -9≤l≤9
-5≤h≤5, -12≤k≤13, -9≤l≤9
-5≤h≤6, -12≤k≤13, -9≤l≤9
-5≤h≤5, -12≤k≤12, -9≤l≤9
-9≤h≤9, -9≤k≤9, -9≤l≤9
-9≤h≤9, -9≤k≤9, -9≤l≤9
No. refl. >2 I0/σ(I0) 937 1020 967 1054 905 935 811 919No. ind. Refl. (F>2σ(F)) 282 300 305 322 270 297 285 270Rint
* 0.051(259) 0.042(269) 0.037(271) 0.037(280) 0.042(246) 0.043(271) 0.044(226) 0.063(252)No. of paramters 22 22 22 22 22 22 22 22Gfit
† 1.21 1.31 1.45 1.33 1.4 1.39 1.23 1.2
Extinction Factor (x10-4) 0.15(7) .22(5) .16 (5) .18(5) 0.36(6) .17(5) .16 (5) .09(6)RW
ठ0.043 (275) 0.039 (294) 0.041 (294) 0.037 (308) 0.045 (264) .043(286) 0.044 (272) 0.05 (250)
R║§ 0.032 (275) 0.031 (294) .0.34 (294) 0.030 (308) 0.038 (264) 0.036 (286) 0.039 (272) 0.043 (250)
║R=Σ||F0|-|Fc||/Σ|F0|
§Number of reflections used in refinement are in parentheses
*Internal residual on F (number of averaged reflections)
‡Rw=[Σw(|F0|-|Fc|)2/Σ|F0|
2]2
†Gfit: estimated standard deviation of unit weight observation
31
0.0001 1.548(5) 4.144(7) 5.750(7) 7.663(8)Al1 Biso 0.33(2) 0.40(3) 0.41(3) 0.28(4) 0.25(3)
x 0.14181(13) 0.14164(15) 0.1411(17) 0.14001(19) 0.1397(2)y 0.3451(5) 0.3439(7) 0.3410(7) 0.3378(8) 0.3389(7)
Biso 0.40(2) 0.49(3) 0.47(3) 0.31(4) 0.32(4)x 0.15318(12) 0.15356(14) 0.15455(16) 0.15466(17) 0.1550(2)y 0.3407(5) 0.3414(6) 0.3377(7) 0.3363(7) 0.3363(7)
Biso 0.39(2) 0.37(3) 0.44(3) 0.28(3) 0.25(4)x 0.3607(3) 0.3614(3) 0.3629(4) 0.3639(4) 0.3642(5)y 0.4075(12) 0.4054(15) 0.4080(15) 0.4142(18) 0.4117(16)
Biso 0.35(4) 0.41(5) 0.41(6) 0.41(7) 0.22(8)x 0.3572(3) 0.3562(4) 0.3556(4) 0.3545(4) 0.3550(5)y 0.4348(13) 0.4337(16) 0.4364(16) 0.4452(19) 0.4411(18)
Biso 0.42(4) 0.44(5) 0.48(6) 0.42(7) 0.55(9)x 0.4762(3) 0.4756(4) 0.4747(4) 0.4738(5) 0.4723(5)y 0.0022(12) 0.0040(15) 0.0051(15) 0.0047(16) 0.0033(2)
Biso 0.94(5) 0.94(7) 0.97(7) 0.85(8) 0.84(8)x 0.1258(2) 0.1261(3) 0.1267(3) 0.1275(3) 0.1285(3)y 0.2228(10) 0.2223(13) 0.2194(12) 0.2162(14) 0.2167(14)z 0.5151(2) 0.5148(3) 0.5154(3) 0.5154(4) 0.5148(6)
Biso 0.54(3) 0.61(4) 0.59(5) 0.47(5) 0.47(6)General fractional coordinates for the atoms: Al1 (0 0 0), Al2 (x y .25), Si (x y .75), O1 (x y .75), O2 (x y .25), O3 (x y .75), and O4 (x y z )
O2
O3
O4
Table 2.6: Positional and isotropic displacement parameters for sillimante at 1 bar through 7.663 GPa.
Al2
Si
O1
32
0.0001 1.474(5) 2.512(6) 3.129(6) 3.932(7) 5.441(6) 7.565(8) 9.828(9)z 0.2418(2) 0.24198(17) 0.2415(2) 0.24182(14) 0.2419(3) 0.2417(2) 0.2418(2) 0.2418(3)
Biso 0.44(3) 0.29(2) 0.31(2) 0.299(19) 0.31(3) 0.30(2) 0.30(3) 0.28(3)x 0.3703(4) 0.3704(2) 0.3700(4) 0.3699(2) 0.3702(6) 0.3695(4) 0.3694(2) 0.3693(3)y 0.13879(16) 0.13868(12) 0.13868(11) 0.13831(11) 0.13830(17) 0.13774(14) 0.1378(2) 0.1378(2)
Biso 0.41(3) 0.31(2) 0.31(2) 0.321(19) 0.31(3) 0.30(2) 0.36(3) 0.28(3)x 0.2465(4) 0.2464(2) 0.2466(3) 0.2466(2) 0.2472(5) 0.2475(3) 0.2471(2) 0.2479(2)y 0.25237(15) 0.25148(10) 0.25092(12) 0.25083(9) 0.25020(15) 0.24974(15) 0.2485(2) 0.24784(18)
Biso 0.40(2) 0.28(2) 0.301(19) 0.294(17) 0.28(2) 0.30(2) 0.37(3) 0.28(3)x 0.4224(7) 0.4217(6) 0.4208(8) 0.4203(5) 0.4215(10) 0.4203(8) 0.4194(5) 0.4187(6)y 0.3638(4) 0.3630(3) 0.3637(3) 0.3631(2) 0.3635(4) 0.3633(3) 0.3621(6) 0.3631(5)
Biso 0.43(5) 0.3159(4) 0.37(4) 0.33(3) 0.35(5) 0.3304(4) 0.39(5) 0.33(6)x 0.4254(7) 0.4257(6) 0.4270(8) 0.4272(5) 0.4259(11) 0.4287(8) 0.4290(5) 0.4309(6)y 0.3619(4) 0.3615(3) 0.3608(3) 0.3601(2) 0.3599(4) 0.3584(3) 0.3568(5) 0.3562(5)
Biso 0.42(5) 0.36(4) 0.34(5) 0.32(3) 0.38(6) 0.33(5) 0.37(6) 0.37(6)x 0.1017(7) 0.1018(6) 0.1044(9) 0.1020(5) 0.1045(12) 0.10377 0.1038(5) 0.1043(5)y 0.4012(3) 0.4004(3) 0.4001(3) 0.3998(3) 0.3996(4) 0.3999(3) 0.3990(5) 0.4003(5)
Biso 0.73(6) 0.70(4) 0.67(5) 0.71(4) 0.70(6) 0.75(5) 0.64(7) 0.77(7)x 0.2292(5) 0.2302(4) 0.2296(6) 0.2296(4) 0.2289(7) 0.2292(5) 0.2291(3) 0.2288(4)y 0.1341(2) 0.13261(12) 0.1320(2) 0.13146(17) 0.1315(3) 0.1303(2) 0.1290(3) 0.1285(4)z 0.2388(4) 0.2395(3) 0.2400(4) 0.2394(3) 0.2398(4) 0.2399(4) 0.2391(4) 0.2393)4)
Biso 0.52(4) 0.45(3) 0.47(3) 0.44(3) 0.40(4) 0.39(3) 0.37(4) 0.33(5)
O3
O4
General fractional coordinates for the atoms: Al1 (0 0 z ), Al2 (x y .5), Si (x y 0), O1 (x y .5), O2 (x y 0), O3 (x y 0), and O4 (x y z )
Table 2.7 Positional and isotropic displacement parameters for andalusite at 1 bar through 9.828 GPa.
Al2
Si
O1
O2
Al1
33
Table 2.8 Selected bond lengths (Å) and angles (°) for andalusite from 1 bar through 9.828 GPa.
0.0001 1.474(5) 2.512(6) 3.129(6) 3.932(7) 5.441(6) 7.565(8) 9.828(9)
Al1-O1 (x2) 1.824(3) 1.825(2) 1.819(3) 1.823(2) 1.816(4) 1.814(3) 1.817(3) 1.808(3)Al1-O2 (x2) 1.893(3) 1.889(2) 1.888(3) 1.8873(18) 1.888(4) 1.885(3) 1.885(3) 1.878(3)Al1-O4 (x2) 2.076(3) 2.069(3) 2.056(4) 2.050(3) 2.042(5) 2.031(4) 2.016(3) 2.003(3)AVG. 1.93 1.93 1.92 1.92 1.92 1.91 1.91 1.90Poly. Vol. 9.49(7) 9.44(6) 9.34(8) 9.34(5) 9.27(9) 9.20(7) 9.15(7) 9.00(7)
96.70(12) 96.56(9) 96.63(12) 96.45(9) 96.48(16) 96.44(13) 96.03(13) 96.27(15)177.97(17) 177.82(15) 177.4(2) 177.33(14) 177.9(3) 177.0(3) 176.82(16) 176.22(18)88.76(17) 89.10(13) 89.47(19) 89.45(12) 89.2(3) 89.60(18) 89.64(15) 89.52(16)90.57(16) 90.33(14) 90.19(19) 90.00(12) 90.2(3) 89.99(19) 89.74(15) 89.93(16)92.05(16) 91.89(14) 92.14(18) 92.31(12) 92.1(3) 92.69(18) 92.94(14) 93.36(16)88.64(17) 88.7(14) 88.22(18) 88.25(12) 88.4(3) 87.73(18) 87.70(14) 87.22(17)
QE* 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01AV† 18.36 17.43 18.11 17.34 17.13 17.83 16.20 18.15Al2-O1 1.822(3) 1.811(3) 1.811(3) 1.806(2) 1.808(4) 1.805(3) 1.788(5) 1.788(4)Al2-O3 1.889(3) 1.888(3) 1.885(3) 1.884(2) 1.880(4) 1.870(3) 1.870(4) 1.854(4)Al2-O3 1.831(6) 1.821(5) 1.837(7) 1.816(4) 1.83(1) 1.821(8) 1.812(4) 1.808(4)Al2-O4 (x2) 1.820(3) 1.808(2) 1.804(3) 1.804(2) 1.804(4) 1.795(3) 1.792(2) 1.786(3)AVG. 1.84 1.83 1.83 1.82 1.82 1.82 1.81 1.80Poly. Vol. 5.16(5) 5.08(4) 5.09(5) 5.04(3) 5.06(7) 5.00(6) 4.95(5) 4.90(5)
73.4(3) 73.7(2) 74.4(3) 73.92(19) 74.7(4) 74.4(3) 74.6(2) 74.4(2)160.5(4) 160.7(3) 161.5(4) 161.00(3) 161.4(6) 161.2(4) 161.40(18) 161.7(2)87.05(19) 87.03(17) 87.0(3) 87.05(15) 86.7(3) 86.8(3) 86.78(19) 87.3(2)105.7(2) 106.04(19) 105.9(3) 106.09(18) 105.7(3) 106.2(3) 106.44(16) 106.4(2)98.88(13) 99.08(11) 99.15(15) 99.11(10) 99.2(2) 99.27(15) 99.48(13) 99.49(13)
Si-O2 1.641(6) 1.639(4) 1.641(6) 1.636(4) 1.622(8) 1.629(6) 1.625(4) 1.625(5)Si-O3 1.629(5) 1.623(4) 1.607(6) 1.616(4) 1.606(8) 1.610(6) 1.603(4) 1.609(4)Si-O4 (x2) 1.628(2) 1.6292(17) 1.630(2) 1.6277(15) 1.625(2) 1.625(2) 1.617(3) 1.614(3)AVG. 1.63 1.63 1.63 1.63 1.62 1.62 1.62 1.62Poly. Vol. 2.22(3) 2.21(2) 2.20(3) 2.198(18) 2.17(3) 2.18(3) 2.15(2) 2.15(2)
102.0(2) 101.82(18) 101.4(3) 102.10(16) 101.2(4) 101.8(3) 101.8(2) 101.5(2)109.15(16) 109.17(12) 109.23(14) 108.94(11) 109.27(17) 108.98(16) 108.67(11) 109.0(2)110.88(18) 111.22(12) 111.28(19) 111.12(13) 111.0(2) 111.04(18 111.26(12) 111.19(14)
QE* 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00AV† 14.30 14.85 16.30 14.05 17.41 15.20 15.44 16.50
2.779(7) 2.772(7) 2.7687(15) 2.7671(11) 2.7635(17) 2.759(2) 2.7522(2) 2.745(2)O2-O2 2.471(7) 2.466(6) 2.461(7) 2.467(5) 2.474(10) 2.468(7) 2.479(8) 2.465(9)
2.468(7) 2.475(6) 2.468(8) 2.476(5) 2.458(10) 2.462(8) 2.474(8) 2.458(8)Al1'-Al1' 2.686(3) 2.8614(19) 2.862(2) 2.8569(16) 2.853(3) 2.850(3) 2.841(3) 2.834(3)
2.686(3) 2.6835(19) 2.674(2) 2.6760(16) 2.674(3) 2.666(3) 2.661(3) 2.653(3)4.153(7) 4.138(5) 4.112(8) 4.101(5) 4.084(9) 4.063(8) 4.033(5) 4.006(6)121.55(15) 121.78(11) 122.09(14) 121.92(9) 122.09(17) 122.09(14) 122.08(14) 122.20(16)111.74(18) 111.20(13) 111.2(2) 111.38(13) 111.6(2) 111.52(18) 111.49(13) 111.65(16)126.0(2) 126.14(16) 125.8(2) 125.78(25) 125.5(3) 125.5(2) 125.37(17) 125.1(2)
Al2-O3-Al2 106.6(3) 106.3(2) 105.6(3) 106.08(19) 105.3(4) 105.6(3) 105.4(2) 105.6(2)*Quadratic Elongation †Angle Variance
O4-Al1-O2
Bond or Angle
Pressure (GPa)
O1-Al1-O2O4-Al1-O1O4-Al1-O1O4-Al1-O2
O1-Al1-O2
O1-Al2-O4
O3-Al2-O3O3-Al2-O1O3-Al2-O1O4-Al2-O4
Al1-O4-Al2Al1-O4-SiAl2-O4-Si
O2-Si-O3O4-Si-O4O4-Si-O3
O1-O2
O1-O1
Al1-Al1O4-O4
34
0.0001 1.548(5) 4.144(7) 5.750(7) 7.663(8)1.916(3) 1.914(4) 1.893(5) 1.868(5) 1.867(5)1.863(3) 1.865(4) 1.855(4) 1.840(4) 1.838(4)1.954(7) 1.943(9) 1.914(9) 1.889(9) 1.887(9)
Avg. 1.91 1.91 1.89 1.87 1.86Poly. Vol 9.15(11) 9.11(14) 8.81(13) 8.46(14) 8.47(13)
99.85(19) 99.6(3) 100.4(3) 101.8(3) 101.4(2)O1-Al1-O2' 80.15(19) 80.4(3) 79.6(3) 78.2(3) 78.6(2)O1-Al1-O4 88.4(2) 88.0(3) 88.8(3) 90.3(4) 89.7(3)O1-Al1-O4' 91.6(2) 92.0(3) 91.2(3) 89.7(4) 90.2(3)O2-Al1-O4 90.4(3) 90.4(3) 91.3(4) 93.5(4) 92.8(4)O2-Al1-O4' 89.6(3) 89.6(3) 88.8(4) 86.5(4) 87.2(4)
QE* 1.01 1.01 1.01 1.02 1.02AV† 36.27 35.26 40.45 54.91 50.67
Al2-O2 1.753(5) 1.742(6) 1.749(6) 1.782(7) 1.764(7)Al2-O3 1.706(7) 1.698(8) 1.699(9) 1.712(9) 1.7114(11)
1.798(5) 1.789(6) 1.785(6) 1.781(8) 1.773(7)
Avg. 1.76 1.75 1.75 1.76 1.76Poly. Vol 2.79(5) 2.75(5) 2.75(6) 2.79(7) 2.75(7)
O2-Al2-O3 113.5(5) 113.6(5) 112.2(5) 108.9(5) 110.3(5)O2-Al2-O4 105.45(18) 105.3(2) 105.6(2) 106.3(2) 105.6(2)O3-Al2-O4 108.06(18) 107.9(2) 108.2(2) 108.8(3) 109.0(2)O4-Al2-O4' 116.5(5) 116.9(7) 117.3(6) 117.5(8) 117.2(7)QE 1.01 1.01 1.01 1.00 1.01AV† 20.46 22.30 20.49 17.04 18.67
Si-O1 1.635(4) 1.626(5) 1.636(5) 1.656(6) 1.643(6)Si-O3 1.572(8) 1.572(9) 1.590(10) 1.588(10) 1.569(12)
1.642(5) 1.645(7) 1.632(6) 1.635(7) 1.629(7)
Avg. 1.62 1.62 1.62 1.63 1.62Poly. Vol 2.19(4) 2.19(5) 2.19(5) 2.22(5) 2.18(6)
O1-Si-O3 109.8(5) 110.3(6) 108.0(6) 106.0(6) 106.6(5)O1-Si-O4 106.93(19) 106.6(3) 107.4(3) 108.2(3) 107.7(2)O3-Si-O4 110.9(2) 111.2(3) 111.3(3) 111.8(3) 111.8(4)O4-Si-O4' 111.2(5) 110.9(7) 111.3(7) 110.7(8) 111.2(7)QE 1.00 1.00 1.00 1.00 1.00AV† 4.05 5.02 4.09 5.65 5.72O1-O2 2.892(8) 2.888(9) 2.8800(11) 2.8775(16) 2.8665(15)O1-O2 2.433(8) 2.439(10) 2.400(10) 2.340(11) 2.347(10)Al1-Al1 2.884(0) 2.879(0) 2.871(0) 2.867(0) 2.857(0)O4-O4 3.907(15) 3.886(18) 3.828(17) 3.777(19) 3.775(18)Al1-O1-Si 129.26(9) 128.96(12) 128.93(11) 128.85(9) 128.77(10)Al1-O2-Al2 129.00(15) 129.46(11) 129.30(14) 128.6(2) 128.93(19)Al2-O3-Si 171.3(6) 171.0(5) 170.5(5) 170.8(6) 170.7(7)Al1-O4-Al2 116.7(3) 116.6(3) 116.1(3) 115.6(3) 115.7(3)Al1-O4-Si 125.3(3) 125.5(3) 125.4(3) 125.5(3) 125.1(3)Al2-O4-Si 114.1(6) 114.0(7) 114.4(6) 114.2(7) 114.3(7)O2-O1-O2 88.38(11) 88.50(12) 88.83(14) 89.11(18) 89.11(18)*Quadratic Elongation †Angle Variance
Si-O4 (x2)
Pressure (GPa)
Al1-O2 (x2)Al1-O4 (x2)
O1-Al1-O2
Al2-O4 (x2)
Al1-O1 (x2)
Bond or Angle
Table 2.9 Selected bond lengths (Å) and angles (°) for sillimanite at room pressure through 7.663 GPa.
35
Results and Discussion The variation of volume with pressure of sillimanite and andalusite is shown in
Figure 2.1. No phase transitions are observed in either polymorph over the pressure range
studied. A third-order Birch-Murnaghan equation of state fit to the P-V data yields values
of Vo=331.214(18) Å3, KT0=164(1) GPa, and K'=5.0(3) for sillimanite and Vo =
341.940(16) Å3, KT0=144.2(7) GPa, and K'=6.8(2) for andalusite. The equation of state
data is weighted based on uncertainties in pressure and volume using the effective
variance method (Orear, 1982). The largest difference between the observed and
calculated pressures is 0.043 GPa for sillimanite and 0.040 GPa for andalusite. The
weighted chi-squared values, Χw2=2.65 for sillimanite and Χw
2=1.58 for andalusite,
suggest that the errors in volume and/or pressure may have been underestimated in
sillimanite. The results from this study show that sillimanite is 12% less compressible
than andalusite. These Eos parameters are fortuitously close to those determined by
Oganov et al. (2001) and Winkler et al. (2001). Although the bulk moduli determined by
Oganov et al. (2001) are similar to those determined in this study the K' values are
significantly different. Vaughan and Weidner (1978) determined KS of andalusite and
sillimanite from Brillouin experiments and, while the KS of sillimanite is similar to KT
determined in this study, the KS of andalusite is ~10% higher. Previous high-pressure
single-crystal X-ray diffraction studies of andalusite and sillimanite determined higher KT
values as a result of K' being constrained to be equal to 4 (Yang et al. 1997).
The difference in K' can best be seen in a plot of normalized stress, Fe, against
Eulerian finite strain, fe (Fig. 2.2). The slope of a line fit to data in an F-f plot reflects the
value of K', while the intersection of the line with the normalized stress axis corresponds
to the bulk modulus at room temperature. It is clear from Figure 2.2 that andalusite has a
K' significantly greater than 4 and that sillimanite has a K' slightly greater than 4,
showing that a second-order Birch-Murnaghan equation of state is not an adequate
description of the P-V data. Indeed, a second-order Birch-Murnaghan equation of state
results in significantly worse fits: Χw2 doubles to 5.79 with a calculated KT0 of 167.7(5)
for sillimanite and Χw2 increases to 30.53 with a calculated KT0 of 154(1) for andalusite.
36
0.94
0.95
0.96
0.97
0.98
0.99
1.00
0.0 2.0 4.0 6.0 8.0 10.0Pressure (GPa)
V/V
o
Sillimanite
Andalusite
Figure 2.1: Variation of the unit cell volume ratio of andalusite (diamonds) between room pressure and 9.8 GPa and for sillimanite (squares) between room pressure and 8.6 GPa. The esd’s are smaller than the symbols shown and the lines are the EoS fit to the data.
37
140
145
150
155
160
0.000 0.005 0.010 0.015 0.020
Eulerian Strain f
Nor
mal
ized
Pre
ssur
e F
: GPa
(a)
150
155
160
165
170
175
180
0.000 0.004 0.008 0.012 0.016 0.020
Eulerian Strain f
Nor
mal
ized
Pre
ssur
e F
: GPa
(b)
Figure 2.2: Variation of the normalized pressure, F, against the Eulerian strain, f, for (a) andalusite and (b) sillimanite.
38
In addition, the largest difference between the observed and calculated pressures
increases to 0.05 GPa for sillimanite and 0.23 GPa for andalusite. The improvements in
the determination of KT0 and K' for andalusite and sillimanite are achieved by
improvements in peak-fitting algorithms and the use of quartz as an internal pressure
standard (e.g. Angel 2001). The use of quartz as an internal pressure standard improves
the precision of σp from 0.05 GPa to typically less than 0.01 GPa, which leads to a three-
fold reduction in the uncertainty of the bulk modulus. Further improvements to the
uncertainties are achieved by increasing the pressure range of the experiments while
maintaining the precision of the pressure.
The variation of the unit cell axes of sillimanite and andalusite with pressure also
display significant curvature (Fig. 2.3). We therefore determined the axial moduli using a
parameterized form of the third-order Birch-Murnaghan equation for volume using the
EosFit 5.2 program (Angel 2001) in which the individual axes are cubed. Results of this
analysis yield values of Ka0=163(1) GPa, Kb0=113.1(7) GPa, and Kc0=297(1) GPa with
K'a0=2.1(3), K'b0=5.1(2), and K'c0=11.1(4) for sillimanite and Ka0=99.6(7) GPa,
Kb0=152.2(9) GPa, and Kc0=236(3) GPa with K'a0=5.8(2), K'b0=7.6(3), and K'c0=5.5(9)
for andalusite. Thus the c-axis is the least compressible axis in both structures. The
compression of the two structures is anisotropic with a maximum anisotropy in
sillimanite of ~61% (c- to b-axis) and ~58% (c- to a-axis) in andalusite. There is a 31%
difference in compression between the a and b axes of sillimanite and a ~35% difference
in compression between the a and b axes of andalusite. The difference in K' of the axes is
shown in Figure 2.4, which represents the nonlinear nature of the axial compressibilities.
The K' of andalusite, 6.8(2), can be attributed to axial compressibilities that range from
K'c0 = 5.5 to K'b0 = 7.6(3). In contrast with andalusite, sillimanite shows a greater range
where the highest value is found along c, K'c0=11.1(4), and the smallest value is found
along a, K'a0=2.1(3). The latter is responsible for the lower K' of sillimanite compared
with andalusite. In addition, the axial compressibilities determined in this study indicate
that the compression anisotropy of sillimanite (βa:βb:βc = 1/Ka:1/Kb:1/Kc =
1.82:2.63:1.00) is slightly greater than that of andalusite (βa:βb:βc = 1/Ka:1/Kb:1/Kc
39
0.970
0.975
0.980
0.985
0.990
0.995
1.000
1.005
0.0 2.0 4.0 6.0 8.0 10.0Pressure (GPa)
d/do
c -axis
b -axis
a -axis
(a)
0.970
0.975
0.980
0.985
0.990
0.995
1.000
1.005
0.0 2.0 4.0 6.0 8.0 10.0Pressure (GPa)
d/do
c -axis
a -axis
b -axis
(b)
Figure 2.3: Variations in the ratios of the axial lengths with pressure for (a) andalusite and (b) sillimanite
40
100
120
140
160
100
120
140
160
180
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
240
260
280
300
320
340
Norm
aliz
ed P
ress
ure
F: G
Pa
Eulerian Strain f
Figure 2.4: Variation of the normalized pressure, F, against the Eulerian strain, f, for the individual axes in andalusite (white squares) and sillimanite (black squares).
41
2.37:1.55:1.00). The values for andalusite are in reasonable agreement with the linear
axial compressibilities determined by Ralph et al. (1984) (βa:βb:βc = 2.13:1.47:1.00).
Yang et al. (1997) reported values for sillimanite at room pressure (βa:βb:βc =
1.22:1.63:1.00) and noted that they changed significantly at 5.29 GPa (βa:βb:βc =
4.07:5.43:1.00) due to the nonlinear nature in the axial compressibilities. However,
linear compressibilities determined over the entire pressure range from Yang et al.’s
(1997) axial length vs. pressure data, βa:βb:βc = 1.93:2.62:1.00, are in good agreement
with this study.
The main compression mechanism within both structures is the reduction of bond
lengths within the polyhedra. In both andalusite and sillimanite, the [Al1O6] octahedron
is the most compressible unit in the structure as a result of the shortening of the Al-O4
bond, the longest bond in the octahedron. In andalusite, the Al1-O4 bond decreases from
2.076(3) Å to 2.003(3) Å (~3.5%) between 1 bar and 9.8 GPa while Al1-O2 decreases by
~0.8% and the Al1-O1, the shortest bond, decreases by ~0.9% (Table 2.8). Overall, the
volume of the octahedron decreases by ~5.1%. Within the [Al2O5] trigonal bipyramid,
all of the bond lengths decrease within the pressure range examined by ~1.9% except the
Al2-O3 bond in the (010) plane, which decreases by ~1.3% resulting in an overall
decrease in volume of ~5.0%. Within the SiO4 tetrahedra, all bonds decrease between 1
bar and 9.8 GPa by ~1.0% resulting in a decrease in the volume of ~3.2%. In the
[Al1O6] octahedron of sillimanite, all Al-O bonds decrease with increasing pressure. The
longest bond, Al1-OD, is the most compressible decreasing by ~3.4%, while the Al1-OA
bond decreases by ~2.6% and the Al1-OB bond decreases ~1.4% between 1 bar and 7.6
GPa. Overall, the volume of the octahedron decreases by ~7.4%. The [Al2O4] and [SiO4]
tetrahedra in sillimanite behave as rigid units and show no significant change throughout
the pressure range examined (Table 2.8). The incompressibility of the [Al2O4] and
[SiO4] tetrahedron is in contrast to Yang et al.’s (1997) study where they observed a
decrease in the volume of both tetrahedra. This apparent discrepancy is the consequence
of differences in the calculation of the estimated standard deviations of the polyhedral
volumes. We used estimated standard deviations from the bond lengths to recalculate the
42
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
0.0 2.0 4.0 6.0 8.0 10.0Pressure (GPa)
Al1
-O B
ond
Leng
ths (
Å)
(a)
Al-O4Al-O1Al-O2
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
0.0 2.0 4.0 6.0 8.0 10.0
Pressure (GPa)
Al1
-O B
ond
Leng
ths (
Å)
(b)Al-O4
Al-O1
Al-O2
Figure 2.5: The variation of octahedral Al1-O bond distances in (a) sillimanite and (b) andalusite.
43
maximum possible standard deviations in the polyhedral volumes.
The compression anisotropy of andalusite and sillimanite can, in large part, be
attributed to the compression of the Al-O bonds within the [Al1O6] octahedron. In both
structures, the [Al1O6] octahedron share edges and run parallel to the c-axis, which is the
least compressible axis in both structures. Orientation of the octahedra within the (001)
plane is shown in Figure 1.2 and determines which axial direction is the most
compressible. The most compressible axis corresponds to the direction of the most
compressible bond (Al1-O4) within the octahedra. The Al1-O4 bond is located ~30o
from the b-axis in sillimanite and ~30o from the a-axis in andalusite. The [AlO6]
octahedra in sillimanite rotate from 29.45(4)± to 30.66(6)± with respect to the b-axis,
while the rotation in andalusite changes from 30.33(4)± to 29.32(7)± with respect to the a-
axis. The role of the orientation of the [Al1O6] octahedra in determining the relative axial
compressibilities has been previously noted by Ralph et al. (1984), Vaughan and Weidner
(1978), and Yang et al. (1997).
The aluminum octahedra in andalusite and sillimanite are the most compressible
polyhedra in their structures, but the effect of pressure on the octahedra is different in
each, as seen in the decrease in the bond lengths and volumes of the octahedra. The only
major compression in the [Al1O6] octahedron of andalusite is along the Al-O4 bond,
while there is significant compression along all of the bonds within the [Al1O6]
octahedron of sillimanite (Fig. 2.5). Shortening of the O1-O2 distance perpendicular to
[100] in sillimanite results in the change of the O1-Al1-O2 angles and is reflected in a
change of the angle variance (Robinson 1971) from 36.27 to 50.67 between 1 bar and
7.66 GPa. Thus, due to a greater amount of axial shortening and bond bending the
overall compression of the aluminum octahedron in sillimanite, ~7.4%, is much greater
then that in andalusite, ~3.6%, between 1 bar and 7.6 GPa. The greater change in the
octahedral volume in sillimanite is also due to the compression of all Al-O bonds (Fig.
2.5a) compared with andalusite where there is compression only along the Al-O4 bond
(Fig. 2.5b). It is suggested that the incompressibility of the Al-O1 and Al-O2 bonds in
andalusite may be due to the compressibility of the [Al2O5] and [SiO4] polyhedra. This
44
is in contrast with sillimanite where all of the Al-O bonds in the octahedra are
compressible while the [Al2O4] and [SiO4] polyhedra are incompressible. Thus, there
seems to be a relationship between the compressibility or incompressibility of the
polyhedra surrounding the octahedra in andalusite and sillimanite and the compressibility
or incompressibility of the Al-O1 and Al-O2 bonds within the octahedra.
References
Anderson, O.L., (1995) Equations of state of solids for geophysics and ceramic science. Oxford University Press, Oxford, UK. Angel, R. J. (2001) Equations of state. In R.M. Hazen and R.T. Downs, Eds., High-
Temperature and High-Pressure Crystal Chemistry, 41, 35-60. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Washington, D.C.
Angel, R. J. (2003) Automated profile analysis for single-crystal diffraction data. Journal
of Applied Crystallography, 36, 295-300. Angel, R. J. (2004) Absorption corrections for diamond-anvil cells implemented in the
software package Absorb 6.0. Journal of Applied Crystallography, 37, 486-492. Angel, R. J., Allan, D.R., Miletich, R., and Finger, L.W. (1997) The use of quartz as an
internal pressure standard in high-pressure crystallography. Journal of Applied Crystallography, 30, 461-466.
Birch, F. (1947) Finite elastic strain of cubic crystals. Physical Reviews, 71, 809-824. Creagh, D.C. and McAuley, W.J. (1992) X-ray dispersion correction, In A.J.C. Wilson,
Ed., International tables for crystallography, vol C. Kluwer Academic Publishers, Dordrecht, 206-219.
Duffy, T.S., and Wang, Y. (1998) Pressure-Volume-Temperature Equation of State. In R.J. Hemley, Eds., Ultrahigh –Pressure Mineralogy: Physics and Chemistry of the Earth’s Interior, 37, 425–452, Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Washington, D.C. Finger, L. W., and Prince, E. (1974) A system of Fortran IV computer programs for
crystal structure computations. U.S. National Bureau of Standards Technical Note 854.
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Friedrich, A., Kunz, M., Winkler, B., and Le Bihan, T. (2004) High-pressure behavior of sillimanite and kyanite: compressibility, decomposition and indications of a new high-pressure phase. Zeitschrift fur Kristallographie, 219, 324-329.
Hazen, R. M., Downs, R.T., and Prewitt, C.T. (2000) Principles of comparative crystal
chemistry, high-temperature and high-pressure crystal chemistry. In R.M. Hazen and R.T. Downs, Eds., High-Temperature and High-Pressure Crystal Chemistry, 41, 1-30. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Washington, D.C.
Kerrick, D. M., (1990) Metamorphic reactions. In D. M. Kerrick, Ed., The Al2SiO5
polymorphs, 22, 223-253. Reviews in Mineralogy, The Mineralogical Society of America. Washington, D.C.
King, H. E., and Finger, L.W. (1979) Diffracted beam crystal centering and its
application to high-pressure crystallography. Journal of Applied Crystallography, 12, 374-378.
Maslen, E.N., Fox, A.G., and O'Keefe, M.A. (1992) X-ray scattering. In A.J.C. Wilson,
Ed., International tables for crystallography, vol C. Kluwer Academic Publishers, Dordrecht, 476-509.
Matsui, M. (1996) Molecular dynamics study of the structures and bulk moduli of
crystals in the system CaO-MgO-Al2O3-SiO2. Physics and Chemistry of Minerals, 23, 345-353.
Miletich R., Allan D.R, Kuhs WF (2000) High-pressure single crystal techniques. In R.
M. Hazen and R. T. Downs, Eds., 41, 445–519, Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Washington, D.C.
Murnaghan, F.D. (1937) Finite deformations of an elastic solid. American Journal of Mathmatics, 49, 235-260. Oganov, A. R., Price, D. G., and Brodholt, J. P. (2001) Theoretical investigation of
metastable Al2SiO5 polymorphs, Acta Crystallographica, A57, 548-557. Orear, J. (1982) Least-squares when both variables have uncertainties. American Journal
of Physics, 50, 912-916. Pavese, A. and Artioli, G., (1996) Profile-fitting treatment of single-crystal diffraction
data. Acta Crystallographica, A52, 890-897. Ralph, R. L., Finger, L.W., Hazen, R.M., Ghose, S. (1984) Compressibility and crystal
structure of andalusite at high pressure. American Mineralogist, 69, 513-519.
46
Robinson, K., Gibbs, G.V., and Ribbe, P.H., (1971) Quadratic elongation: A quantitative measure of distortion in coordination polyhedra. Science, 172, 567-570.
Vaughan, M. T., and Weidner, D.J. (1978) The relationship of elasticity and crystal
structure in andalusite and sillimanite. Physics and Chemistry of Minerals, 3, 133-144.
Winkler, B., Hytha, M., Warren, M.C., Milman, V., Gale, J.D., and Schreuer, J. (2001)
Calculation of the elastic constants of the Al2SiO5 polymorphs andalusite, sillimanite, and kyanite. Zeitschrift fur Kristallographie, 216, 67-70.
Winter, J. K., and Ghose, S. (1979) Thermal expansion and high-temperature crystal
chemistry of the Al2SiO5 polymorphs. American Mineralogist, 64, 573-586. Yang, H., Hazen, R.M., Finger, L.W., Prewitt, C.T., and Downs, R.T. (1997)
Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure. Physics and Chemistry of Minerals, 25, 39-47.
47
Chapter 3
ELF isosurface maps for the Al2SiO5 polymorphs
The results presented in this chapter have been published: Jason B. Burt, G.V. Gibbs
David F. Cox and Nancy L. Ross. Physics and Chemistry of Minerals, (2006), 33: 138-144
Abstract This study examines the ELF isosurfaces of the Al2SiO5 polymorphs kyanite, sillimanite,
and andalusite to see how differences in coordination and geometry of the cations and
anions affect the ELF isosurfaces. Examination of the ELF isosurfaces indicates that their
shapes are dependent on the coordination and geometry of the oxygen atoms and are not
sensitive to coordination of the surrounding cations. Thirteen of the eighteen
nonequivalent oxygen atoms in the Al2SiO5 polymorphs are bonded to two aluminum
atoms and one silicon atom (Al2-O-Si) and are associated with two different ELF
isosurface shapes. The shape of the ELF isosurface is dependent on the distance the
oxygen atom lies from a plane defined by the three surrounding cations: at a distance
greater than 0.2 Å the ELF can be defined as horseshoe shaped and at a distance less then
0.2 Å it can be described as concave hemispherical. This feature is also seen in the ELF
isosurfaces for the oxygens bonded to three aluminum atoms (Al3-O) where the
isosurfaces can be defined as trigonally toroidal and uniaxially trigonally toroidal. The
changes in the ELF isosurfaces for the three coordinated oxygens are also indicative of
changes in hybridization. The ELF isosurface for the two-fold coordinated oxygen (Al-
O-Si) has a large mushroom shaped isosurface along the Al-O bond and a concave
hemispherical isosurface along the Si-O. The four-fold coordinated oxygen (Al4-O)
contains two concave hemispherical isosurface along the shorter Al-O bonds and a
banana shaped isosurface which encompasses the longer Al-O bonds. In addition, this
study shows the isostructural homeomorphic relationship between the ELF isosurfaces
and electron density difference maps with respect to number and arrangement of
domains.
48
Introduction
It has only been in the last hundred years that scientists obtained a mathematical
understanding of atoms, molecules, and solids. Though the idea of the atom goes back to
the time of the ancient Greeks it wasn’t until the late nineteenth and early twentieth
century when scientists such as Thompson, Rutherford, Planck, Einstein, Bohr, de
Broglie, Heisenberg, Born, Dirac, and Schrödinger proved the existence and nature of
atoms (Gribbin, 1984). These pioneers developed what is known as quantum mechanics
which today allows us to use electron structure calculations to examine theoretically the
properties of minerals. The theoretical foundation behind quantum mechanics is given by
the time dependent Schrödinger equation:
( , ) ( , )H r t E r tΨ = Ψ (3.1)
This is an eigenvalue equation where H is the Hamiltonian differential operator, E is the
total energy of the system, and is the wavefunction. The wavefunction is a model for
the motion of all particles in the system and the square of the wavefunction is the
probability of finding the particles in some volume, dV, at some time (Hehre, 1986). The
Hamiltonian represents the sum of the potential and kinetic energy components of the
system and can be represented as:
Ψ
2
212 i
i i
H Vm
⎛ ⎞= − ∇ +⎜ ⎟⎝ ⎠
∑ (3.2)
where 2 2
22 2
2
2x y z∂ ∂ ∂
∇ = + +∂ ∂ ∂
(3.3)
The first term of the Hamiltonian represents the kinetic energy operator where h is
Planck’s constant and m is the mass of a particle. The second term is the potential energy
operator (V) and represents the Coulombic interaction between all particles in the system
(i.e. electrons and nuclei). Unfortunately, the exact solution for the energy of the system
from the Schrödinger equation is only obtainable for a limited number of problems (i.e. H
49
or He+). In order to determine the energy of systems with many electrons,
approximations must be used for the wavefunctions, the Hamiltonian, or both. According
to the variational principle the lower the energy the closer the approximated
wavefunction resembles the actual wavefunction and the calculated energy can never be
lower than the true energy as long as certain conditions are satisfied, such as the Pauli
exclusion principle (Tossell and Vaughan, 1992). In addition, the Born-Oppenheimer
approximation is often used to decouple the relative motions between the electrons and
the nuclei. The Born-Oppenheimer approximation is based on the mass and velocity
differences between the electrons and the nuclei. The nuclei can be thought to remain
stationary due to instantaneous changes in the positions of the electrons with respect to
changes in the position of the nuclei. Computational methods for determining solutions
to multiparticle systems can be divided into four classes: ab initio Hartree-Fock methods,
ab initio correlated methods, density functional methods, and semi-empirical methods
(Hehre, 1995).
In basic Hartree-Fock calculations the wavefunction is represented as a single
Slater determinant of the molecular orbitals to account for the asymmetry in the spin of
the electrons. The molecular orbitals are modeled as a linear combination of basis
functions which represent single electron orbitals and often correspond to the atomic
orbitals (Leach, 2001). The molecular orbitals are defined by:
1
N
i c iµ µµ
φ=
Ψ =∑ (3.4)
where icµ are the molecular orbital expansion coefficients and µφ are the basis functions.
The basis functions, single electron orbitals, are typically modeled with either Slater-type
atomic orbitals (STOs) or more commonly Gaussian-type atomic functions. In
accordance with the variational principle the molecular orbital expansion coefficients are
solved iteratively to obtain the lowest possible energy, which is known as self-consistent
field (SCF) theory. The molecular orbital expansion coefficients are determined based on
the modeling of the system. In closed shell systems the coefficients are determined from
50
the Roothaan-Hall equations and in open shell systems they can be described as either
spin-restricted Hartree-Fock (RHF) theory or spin-unrestricted Hartree-Fock (UHF)
theory (Hehre, 1986). A major drawback in basic Hartree-Fock calculations is in the
correlation of electronic motion. Hartree-Fock calculations tend to give higher energies
because the electrons are assumed to be moving in an average potential with the other
electrons and in actuality the electrons tend to avoid each other more than indicated in the
Hartree-Fock theory (Leach, 2001). In order to more accurately account for the electron-
electron interaction the configuration interaction (CI) and the many-body perturbation
theory models were devised. These techniques are referred to as correlated ab initio
methods, the second computational method class. In the CI method the electronic state is
described in relation to excited states to improve the electron-electron correlation. In the
many-body perturbation theory the energy of the system is corrected by treating the
electron correlation as a perturbation to the Hartree-Fock wave function. In a basic
retrospect, the standard ab initio Hartree-Fock calculations provide favorable equilibrium
geometries, but inadequate force constants and vibrational frequencies compared with the
correlated ab initio calculations (Cygan, 2001).
In contrast to Hartree-Fock calculations, density functional theory (DFT) is based
on the relationship between the energy of the system and the electron density distribution.
It was shown in a ground breaking paper by Hohenberg and Kohn (1964) that the ground
state energy of system can be calculated by a universal functional of the density,
[ ( )]F rρ , and the ground state of an interacting electron gas in an external potential v(r)
where [ ( )]F rρ is independent of v(r). The ground state energy of the system can be
defined as:
[ ( )] ( ) ( ) [ ( )]E r r r dr Fρ ν ρ ρ= + r∫ (3.5)
where [ ( )]F rρ is composed of the sum of the kinetic energy ( [ ]( )KEE rρ ), the electron-
electron Coulombic energy ( [ ]( )HE rρ ), and the exchange and correlation energy
functional ( [ ]( )xcE rρ ). Determination of the energy of an N-electron system was then
51
expanded by Kohn and Sham (1965) to include the electron-nuclear interactions and the
equation for the energy of a system with the expanded kinetic energy and electron-
electron Coulombic energy is:
21 2
1 21 1 2
1
( ) ( )1[ ( )] ( ) ( ) [ ( )]2 2
( )
N
i i XCi
MA
A A
r rE r r r dr dr dr Er r
Z r drr R
ρ ρρ ψ ψ
ρ
=
=
⎛ ⎞∇= − + +⎜ ⎟ −⎝ ⎠
−−
∑∫ ∫ ∫
∑∫
rρ (3.6)
where 2
1( ) ( )
N
ii
rρ ψ=
=∑ r (3.7)
The energy of a system is determined by the Kohn Sham scheme using a self-consistent
approach to derive a set of orbitals from an initial guess for the electron density. The
self-consistent approach uses an analogous Hartree-Fock-like equation for the Kohn-
Sham equations which is:
21 2
1 11 1 12
( ) ( ) ( ) ( )2
MA
xc i i iA A
Z r dr V r r rr r
ρ ψ εψ=
⎧ ⎫⎛ ⎞∇⎪ ⎪− − + + =⎨ ⎬⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭
∑ ∫ 1 (3.8)
where [ ( )][ ]( )
xcxc
E rV rr
δ ρδρ
⎛ ⎞= ⎜⎝ ⎠
⎟ (3.9)
xcV is the exchange-correlation potential and iε are the orbital energies. The Kohn-Sham
equations are iterated to improve the calculated value for the density which can then be
used to calculate the energy of the system (Leach, 2001). These theories in determining
the energy of a system based on the electron density resulted in the awarding of the Nobel
Prize in chemistry to Walter Kohn in 1998.
A key component in DFT calculations is that the ground state for a system is
exactly known if the exact exchange-correlation functionals are known. In other words,
the only approximations in the Kohn-Sham equations are for the exchange-correlation
functionals of the electron spin densities, which are not known. An important aspect of
52
DFT is that even simple approximations for the exchange-correlation functionals provide
good results (Leach, 2001). Two popular approximations for the exchange-correlation
funcitonals are the local density approximation (LDA) and the generalized gradient
approximation (GGA), though there are hybrid methods that use the ‘exact’ exchange
energy from the Slater determinant of the Kohn-Sham orbitals with the correlation
component from the local density approximation. The local density approximation
assumes that the exchange-correlation potential, [ ]xcV r , has the same value as the
exchange-correlation energy per electron as a function of density in a uniform electron
gas at a point r in the inhomogeneous electron distribution. In other words, the
exchange-correlation energy per electron as a function of density in a uniform electron
gas, which are known (Ceperley and Alder, 1980), produce functions for the exchange-
correlation functional that depend on the local constant (uniform) electron density at a
point in space. In the generalized gradient approximation (GGA), the exchange-
correlation functionals depend on the gradient of the local electron density at a point in
space in contrast to a uniform electron density employed in LDA calculations. The
choice of approximations is dependent on the system of interest. In molecular and
surface studies the GGA produces better energies, but for bulk materials (solids) either
GGA or LDA will produce favorable results (Cox, personal communication). In bulk
systems the GGA usually overestimates lattice parameters by 1% while the LDA usually
underestimates lattice parameters by 1-2%.
There are a number of strategies for solving the Kohn-Sham equations with regard
to the choice of basis sets used to for the Kohn-Sham orbitals. In particular two methods
will be considered because they are used in regard to this study, linear combination of
atomic orbitals (LCAO) and plane waves. In plane wave theory, the Kohn-Sham orbitals
are represented as a linear combination of plane waves which are related through vectors
in the reciprocal lattice. The equation for the wavefunctions of the orbitals is:
,( ) exp( ( ) )ki i k G
Gr a i k G rψ += + ⋅∑ (3.10)
53
where G represents the reciprocal lattice vectors and k is the wave vector. In plane wave
calculations only the valence electrons are considered and the core electrons are
considered to be incorporated into the nuclear core (Leach, 2001). This is justified
because the valence electrons are thought to be responsible for the chemical bonds and
the physical properties of the system whereas the core electrons are not affected by the
atomic environment. A major disadvantage using plane waves to represent the
wavefunctions for the valence electrons is that they show large oscillations near the
nuclei resulting in large kinetic energies which require many plane waves to properly
model the system. This problem is accounted for by using psuedopotentials to model the
wavefunctions near the nuclei with a potential function that has the same shape as the
wavefunction outside the core, but with fewer nodes. Essentially, the psuedopotentials
model the interaction of the valence electrons with nucleus and core electrons (Heine,
1970) while reducing the number of plane waves and the scale of the computational
problem (Leach, 2001). The second type of model for the Kohn-Sham orbitals is as a
linear combination of atomic orbitals, which was discussed above for the Hartree-Fock
theory and is modeled in the same fashion. The choice for the basis sets that represent
the Kohn-Sham orbitals is often dependent on the situation. The LCAO approach is
almost always used for molecular sytems, while either LCAO or plane waves are
commonly used for modeling solid state materials. Plane waves have an advantage in
modeling solid state materials (periodic systems) because they are represented as a
Fourier series.
The fourth and last type of computational method is the semi-empirical method.
This method uses empirically determined values in order to determine the solution to the
Schrodinger equation. This technique has the advantage of avoiding the computationally
expensive integration of electron interactions. Currently this technique is not used as
frequently as DFT and ab-initio calculations due to the success of current computational
capabilities, faster computers (Cygan, 2001).
Since the 1970’s molecular modeling has impacted the mineralogical and
geochemical community by providing information on the structure and formation of
54
minerals. Early studies using theoretical calculations in the geosciences examined
bonding (bond lengths and angles) with molecular clusters which could be used as
proxies for mineral systems (Gibbs et al., 1972, 1974; Louisnathan and Gibbs, 1972;
Tossell, 1975; and Tossell and Gibbs, 1978). Today, due to advance in computational
efficiency and improvements in computational theory, a greater understanding of crystal
structures is known from theoretic modeling, which can be used to determine the
properties of solid states (e.g. density of states, vibrational frequencies, electron densities,
equation of states, and chemical reactivities). In particular, quantum mechanical
calculations have been used to examine two properties of the Al2SiO5 polymorphs, the
electron localization function (ELF) and (3,-3) critical points of the negative Laplacian
(Chapter 4).
Electron Localization Function (ELF)
The ELF is a graphical representation of bonded and non bonded regions of
localized electron density for molecules and molecular systems. It was defined by Becke
and Edgecombe (1990) in relation to the probability of an electron seeing like spin states.
The electrons are highly localized where there is a low probability of seeing like spin
states and poorly localized where there is a high probability of seeing like spin states.
The ELF is defined by the equation:
2
,
1
( , , )1( , , )gas
ELFD x y z
D x y zσ
σ
=⎛ ⎞
+ ⎜ ⎟⎜ ⎟⎝ ⎠
(3.11)
where 2 25/3
,
( , , ) 1.3483 /( , , ) 8i
igas
D x y zD x y z
σσ σ σ
σσρ ψ ρ− ρ⎡ ⎤
= ∇ − ∇⎢ ⎥⎣ ⎦∑ (3.12)
The electron localization is accounted for by the leading term of a Taylor expansion of
the spherically averaged pair probability, Dσ, and is calibrated with respect to a uniform
electron gas with spin-density at the corresponding position, Dσ,gas. In an alternative
description of the ELF (Burdett and McCormick, 1998), the ELF is based on the nodal
55
properties of the occupied orbitals, rather than in terms of the pair probabilities. For the
majority of bonded systems of chemical interest, it has been demonstrated that the
dominant term in the ELF is ρ(r)s-5/3 Σi|∇ψ(r)i,s|2 (Burdett and McCormick, 1998), which
appears in the denominator of the ELF definition, where ρ(r)s = Σi|ψ(r)i,s|2
is the one-
electron orbital probability density and Σi|∇ψ(r)i,s|2 is the kinetic energy density at r. The
ELF values are thus dependent on determining the probability of finding a similar spin
state at r where i is defined to run over all one electron σ-spin states. Here the kinetic
energy density is related to the nodes of the orbital wavefunctions, since the kinetic
energy density of the electrons is related to the gradient or slope of the wavefunctions of
the orbitals (Burdett and McCormick, 1998). When there is a node in the wavefunction
there is a large gradient corresponding to a large kinetic energy which causes the
denominator in the ELF equation to be large resulting in a small ELF value, poorly
localized electrons. Alternatively, large ELF values occur when the gradient of the
wavefunction for the orbitals is small. The ELF was defined by Becke and Edgecombe
(1990) to be restricted to values between 0 and 1 where a value of 1 represents perfect
localization and a value of 0.5 represents a homogenous electron gas probability.
However, it should be noted that the ELF isosurface domains are not based on quantum
mechanical observables and are also unitless. The ELF isosurfaces were calculated with
density functional theory (DFT), which was examined in the previous section.
Initially, practical uses for the ELF included graphical representations of bonding
(Savin et al. 1991; Silvi and Savin, 1994), and it has been shown to correlate to the
Laplacian of the electron density distribution (Bader et al., 1996). In addition, the ELF
isosurfaces have been shown to be homeomorphically related to the electron density
distribution of minerals (Gibbs et al, 2005). In a study of the ELF isosurfaces of the
molecule H6Si2O7, Gibbs et al. (2003) showed that as the Si-O-Si angle decreases the
nucleophillic character of the oxygen increases making it more susceptible to
electrophillic attack. The non-bonded ELF isosurfaces can be thought of as regions of
lone pair electrons defined by the Lewis valence (1996) and the Gillespie-Nyholm
VSEPR (Gillespie, 1970) models and have been examined in a variety of molecular
situations (Chesnut, 2000) and for determining potential hydrogen protonation sites in
56
nominally anhydrous minerals (Gibbs et al, 2003, 2005). The ELF has also been shown
to be qualitatively comparable to other theoretical calculations (Savin et al, 1997) making
it a useful tool in understanding bonding and the geometric relationship between cation-
anion coordination in crystalline materials.
The ELF isosurface domains for the earth materials quartz, stishovite, periclase,
diopside, tremolite, talc, dickite, beryl, cordierite, wadeite, akermanite, low albite,
thortveitite, hurlbutite, and vanthoffite have been examined by Gibbs et al. (2005) to see
how the ELF domains change as a function of bridging vs. nonbridging oxygen and as the
electronegativty of M changes for a M-O-Si bond. This study examines the ELF
isosurfaces of the Al2SiO5 polymorphs kyanite, sillimanite, and andalusite to see how the
ELF isosurfaces change as a function of differing coordination state and geometry of the
cations and anions. The Al2SiO5 polymorphs are excellent candidates for this study due
the various aluminum coordination sites (4-fold, 5-fold, and 6-fold) and the 18
nonequivalent oxygens. The oxygens also occur in a variety of coordination
environments, two coordinated bond to aluminum and silicon (Al-O-Si), three and four
coordinated to aluminum (Al3-O and Al4-O), and three coordinated bond to two
aluminum and a silicon (Al2-O-Si), allowing us to examine how the coordination around
oxygen affects the ELF isosurfaces. In addition, the ELF isosurfaces will be compared
with electron density difference distribution maps to show their isostructural
homeomorphic relationship.
Methods and Calculations
The ELF was calculated using VASP (Vienna ab-initio Simulation package), the
periodic plane-wave density functional code of Kresse and Hafner (1993) and Kresse and
Furthmüller (1996). The structures were geometry optimized in VASP which employs
ultrasoft pseudopotentials (Vanderbilt, 1990) and the local density approximation (LDA)
to model the contribution of the exchange correlation to the total energy and the valence
electron density distribution. The kinetic energy cutoff for the runs was chosen to be of
sufficient magnitude to ensure convergence of the energy and the generation of a
minimum energy structure using a 3×3×3 Monkhorst-Pack (1976) k-point mesh. The
57
geometry optimization took place at a quasi-zero pressure minimum with constraints on
the observed space group for the atoms in the unit cell and run until the forces on each
atom were less than 0.01 eV/Å. The geometry optimized structures are in good
agreement with X-ray studies (Winter and Ghose, 1979) with bond lengths within ~1.5%.
The ELF isosurface maps were generated with a modified version of the three
dimensional visualization software of Terriberry et al. (2002), which now allows
visualization of two ELF isosurfaces. The two arbitrary ELF isosurfaces displayed on the
maps were chosen at values of 0.83 (gray isosurfaces) and 0.85 (pink isosurfaces)
because they represent a change from diffuse to localized ELF domains and because the
ELF isosurfaces are homeomorphically similar (topologically) to electron density
difference maps and the topology of the negative Laplacian of the electron density (L(r))
(Bader, 1996; Gibbs et al., 2005; Kirfel et al., 2005).
Results
ELF isosurface maps for the Al2SiO5 polymorphs
The shapes of the ELF isosurfaces in the Al2SiO5 polymorphs are dependent on
the geometry, number, and atomic number of the cations that surround the oxygens, but
not the coordination of the cations. This dependence can be seen in the Al-O6 octahedra
in kyanite (Fig. 3.1) where the bonding between Al1 and the O2 and O6 oxygens is
depicted by concave hemispherical isosurfaces along the bond vector, while the bonding
between the Al2 and the O2 and O6 oxygens is represented by the ends of a banana
shaped isosurface. The differences in the ELF isosurfaces surrounding the Al-O6
octahedra indicate that the ELF isosurfaces are determined by the surrounding oxygen
atoms rather than the coordination of the cation.
58
Figure 3.1: Differences between the ELF isosurfaces for the Al1-O6 and Al2-O6 octahedra in kyanite. Al1 contains concave hemispherical isosurfaces along the Al1-O2 and Al1-O6 bonds, while Al2 contains banana shaped isosurfaces along the Al2-O2 and Al2-O6 bonds. The gray isosurfaces represent ELF values of 0.83 whereas the pink represent values of 0.85.
59
There are six distinct types of ELF isosurfaces that surround the 18 nonequivalent
oxygens in the Al2SiO5 polymorphs (Fig. 3.2). These isosurfaces are similar to the ELF
isosurfaces seen in other silicate minerals (Gibbs et al., 2005), but are characterized by
changes in coordination and geometry. Of the four different types of oxygen
coordination, Al-O-Si, Al3-O, Al4-O, and Al2-O-Si, in the Al2SiO5 polymorphs the Al2-O-
Si is the most common occurring in 13 of the 18 oxygens. There are two distinct types of
ELF isosurfaces for the Al2-O-Si coordinated oxygens (Fig. 3.2i and 3.2ii). The ELF
isosurface between the silicon and oxygen is identical to ELF isosurfaces between silicon
and oxygen in other crustal minerals (Gibbs et al., 2005) and can be described to have a
concave hemispherical shape, which may be indicative of a more covalent bond. The
diffuse ELF isosurfaces that surround the oxygen aluminum interaction can be classified
to have either a concave hemispherical toroidal shape (Fig. 3.2i) or a horseshoe shape
(Fig. 3.2ii). Similar features are also seen in the ELF isosurfaces for the Al3-O
coordinated oxygens where the ELF isosurfaces can be defined as trigonally toroidal
(Fig. 3.2iii) and uniaxially trigonally toroidal (Fig. 3.2iv). The trigonally toroidal ELF
isosurface is localized on both sides of the oxygen atom, while the uniaxially trigonally
toroidal ELF isosurface is localized on one side of the oxygen atom. It is important to
point out the similarity in the isosurfaces for the oxygen with the trigonally toroidal shape
and those seen by Gibbs et al. (2005) for the oxygen surrounded by three silicon atoms.
The diffuse trigonally toroidal ELF isosurfaces for the Al3-O and the Si3-O are identical,
but the localized domains above and below the Al3-O oxygen atom do not become
isolated discrete domains at higher ELF values as is seen in the Si3-O ELF isosurfaces
indicating a dependence on the atomic number of the surrounding cations.
The difference in the ELF isosurfaces surrounding oxygens with similar bonded
cations is dependent on the distance the oxygen atom lies from a plane defined by the
three surrounding cations. At distances ≥0.2 Å the ELF isosurfaces adopt the horseshoe
and uniaxially trigonally toroidal shape, while the concave hemispherical toroidal and
trigonally toroidal shape is observed when the oxygen is less than 0.2Å from the plane
defined by the three surrounding cations. This indicates that the ELF isosurfaces are
dependent on the geometry of the surrounding cations and that the electrons become
60
Figure 3.2: ELF isosurfaces for the different types of coordinated oxygens in the Al2SiO5 polymorphs: (i and ii) Al2-O-Si, (iii and iv) Al3-O, (v) Al-O-Si, and (vi) Al4-O. The values for the ELF isosurfaces are given in Figure 3.1.
61
more localized, as seen in Figure 3.3, where greater ELF maximum values occur when
the oxygen is farther away from the plane defined by the surrounding cations. The 0.2 Å
threshold may be associated with a change in hybridization determined from changes of
the oxygen anions indicated by the differences in the ELF isosurfaces. Changes in
oxygen hybridization due to changes in geometry for three coordinated oxygens in
stishovite and the molecule H3O+ have been observed by Muscenti et al. (2005). They
observed that the relaxation of atoms on the (110) surface of stishovite occurs because of
electron-pair repulsion, and moves three coordinated oxygen atoms out of the plane
defined by the three surrounding silicon cations which are coplanar in the bulk material.
The effect of this relaxation on the ELF isosurface and charge density maps is to
eliminate the localization domain below the oxygen atom, leaving only the feature above
the oxygen atom. The changes in the isosurfaces are attributed to a change in the oxygen
atom hybridization from sp2 with a nonbonding lone pair (for the coplanar Si3-O
arrangement) to sp3 for the noncoplanar arrangement. This may explain the differences
in the ELF isosurfaces for the three coordinated oxygens in the Al2SiO5 polymorphs
where the uniaxially trigonally toroidal (Fig 3.2iv) and horseshoe shape (Fig. 3.2ii) have
ELF isosurfaces localized on one side of oxygen atom and are attributed to have an sp3
oxygen hybridization, while the concave hemispherical toroidal (Fig. 3.2i) and trigonally
toroidal (Fig. 3.2iii) ELF isosurfaces are localized on both sides of the oxygen
characteristic of an sp2 oxygen hybridization. Thus, differences in the ELF isosurfaces
around the 0.2 Å threshold are an indication of changes in hybridization of the oxygen
anions.
The other two types of coordinated oxygen ELF isosurfaces should be compared
with those seen by Gibbs et al. (2005) for the Si-O-Si bond. The ELF isosurface between
the O-Si atom for the Al-O-Si coordinated oxygen (Fig. 3.2v) is another relatively
localized concave hemispherical isosurface as seen between the other Si-O bonds, while
the ELF isosurface between the Al-O is more diffuse and can be described as mushroom
shaped. This could indicate that the Si-O bond is more covalent, while the Al-O bond is
more closed shell ionic. This is in contrast to the ELF isosurfaces for Si-O-Si
coordinated oxygen where similar concave hemispherical isosurfaces are located along
62
0.85
0.852
0.854
0.856
0.858
0.86
0.862
0.864
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Distance above cation defined plane
Max
ELF
val
ue
Figure 3.3: Distance oxygen is located above a plane defined by the surrounding two aluminum and one silicon cations verses the maximum lone pair ELF value in andalusite (pink boxes), sillimanite (orange triangles), and kyanite (blue diamonds).
63
the Si-O bonds, but a banana shaped isosurface is located perpendicular to the Si-O-Si
angle. However, the Si-O-Si isosurfaces are homeomorphic with the isosurfaces seen in
the Al4-O coordinated oxygens of kyanite (Fig. 3.2vi), which contain localized concave
hemispherical isosurfaces along the shorter Al-O bonds and a banana shaped ELF
isosurface perpendicular to the plane encompassing the two short Al-O bonds with the
ends of the banana shaped isosurface between the longer Al-O bonds. Unlike the banana
shaped isosurface on the Si-O-Si coordinated oxygen, which are irreducible, the banana
shaped isosurface on the Al4-O coordinated oxygen is reducible, splitting up into two
domains along the longer Al-O bonds. We see that within these two differing
coordinated oxygens that the electron probability density is dependent on the surrounding
cations and the bond lengths within their coordination spheres.
Comparison of ELF isosurfaces and electron density difference maps
A material’s ground state properties are uniquely defined by the electron density
distribution (Hohenberg and Kohn, 1964), which is used to calculate electron density
difference maps. A comparison between electron density difference maps for the
Al2SiO5 polymorphs, calculated by Dahoui et al. (2001) using experimental X-ray
diffraction data, and the ELF isosurfaces indicate a isostructural homeomorphic
relationship. The homeomorphic relationship is seen in the 2-dimensional ELF map
(values between 0 and 0.88) and the 2-dimensional electron density difference map for
the O-Al-O plane (Fig. 3.4). In addition to the 2-D ELF map, the ELF isosurfaces at
values of 0.85 and 0.83 are plotted to show the isosurfaces above the plane. The O-Al-O
plane for andalusite and sillimanite show the edge sharing aluminum octahedra which run
down the z-axis have ∆ρ maximum that are directed along the Al-O and Si-O bonds in
the electron density difference maps (Fig. 3.4i and 3.4ii). These maximum are
isostructurally similar to maxima seen in the dual ELF O-Al-O maps, but the ∆ρ
maximum are located closer to the oxygen atoms (~0.5 Å) than the ELF maximum (~0.7
Å). However, there are only two maximum domains located around the O2 oxygen of
sillimanite, while there are three ELF maximum domains. The O2 oxygen of sillimanite
is coordinated to three aluminum atoms in a roughly trigonally planar arrangement and it
64
Figure 3.4: Comparison of the ELF isosurfaces and static electron deformation densities taken from Dahoui et al., (2001) with positive (solid) and negative (dashed) contour intervals of ≤0.1e/Å3. The ELF maps contain 2-dimensional ELF values in the O-Al1-O plane from 0 to 0.88 and 3-dimensional ELF isosurfaces of 0.83 (white) and 0.85 (pink). The figure represents the ELF and electron density difference maps of the O-Al1-O planes in (i) andalusite, (ii) sillimanite, and (iii) kyanite.
65
is curious that there is no ∆ρ maximum along the shortest (1.75 Å) of the Al-O bonds
determined from experimental data because the geometry and arrangement of the cations
around the O2 suggests that there should be three maxima domains seen in the electron
density difference map. The lack of a third electron density domain could be due to the
difficulty in producing exact electron density difference maps from experimental data. In
addition to andalusite and sillimanite, the ELF isosurface maps and the electron density
difference maps for kyanite (Fig. 3.4iii) have similar shapes and maximum domain
locations. The ELF isosurfaces for the Al2SiO5 correspond to the experimental electron
density difference maps and while the 2-D electron density difference maps provide
information about the electron density within a plane, the ELF isosurface maps provide
information about electron probability density above and below the 2-dimensional plane.
This is especially evident in the ELF isosurface maps of sillimanite and andalusite (Fig.
3.4i and 3.4ii) where there are discrete lone pair features, which can be attributed to the
geometry of the cations surrounding the oxygens. Thus, ELF isosurface maps may be a
better tool for visualization of the location of bonded and lone pair electrons.
Conclusions
ELF isosurfaces depict the probability density for finding electrons around anions
within molecular and crystalline materials. The isosurfaces have been shown to be
dependent on the geometry and coordination of the surrounding cations and may be used
to understand bonding, hybridization, chemical reactivity, and potential hydrogen
incorporation within minerals by indicating regions of bonded and lone pair electrons. It
has been shown that small amounts of hydrogen are contained in the nominally
anhydrous Al2SiO5 polymorphs (Bell and Rossman, 1992) and examination of the ELF
isosurfaces may help pinpoint potential protonation sites, especially since there is an
indication for a change in hybridization when the oxygen atom is greater than 0.2 Å from
a plane defined by the three surrounding cations. In addition, the ELF isosurfaces are
shown to be isostructurally related to electron density difference maps with a similar
number and arrangement of the domains. Thus, the ELF is a promising tool for studying
and understanding the crystal chemistry of minerals.
66
References
Bader, R.F.W., Johnson, S., Tang, T.H., and Popelier, P.L.A. (1996) The Electron Pair. Journal of Physics and Chemistry, 100:15398-15415 Becke, A.D., Edgecombe, K.E. (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397-5403 Bell, DR, and Rossman, GR (1992) Water in Earth's Mantle: The Role of Nominally Anhydrous Minerals. Science 255:1391-1397. Burdett JK, McCormick TA, (1998) Electron localization in molecules and solids: The meaning of ELF. J Phys Chem A 102:6366-6372 Ceperley, D.M., and Alder, B.J. (1980) Ground state of the electron gas by a stochastic method. Physical Review Letters, 45, 566-569. Chesnut, D.B. (2000) An Electron Localization Function Study of the Lone Pair. J Phys Chem A, 104:11644-11650 Cygan, R.T. (2001) Molecular Modeling in Mineralogy and Geochemistr. In R.T Cygan and J.D. Kubicki, Eds., Molecular Modeling Theory: Applications in the Geosciences, 42, 1–35, Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Washington, D.C Dahaoui, S., Hansen, N.K., Protas, J., Krane, H.-G., Fischer, K., and Marnier, G. (1999) Electric properties of KTiOPO4 and NaTiOPO4 from temperature-dependent X- ray diffraction. J Appl Crystallogr 32:1-10 Gillespie RJ (1970) The valence-shell electron pair model of molecular geometry. J Chem Edu 47:18-23 Gibbs, G.V., Hamil, M.M., Bartell, L.S., and Hsiukang, Y. (1972) Correlations between Si-O bond length, Si-O-Si angle and bond overlap populations calculated using extended Hückel molecular orbital theory. American Mineralogist, 57, 1578- 1613. Gibbs, G.V., Louisnathan, S.J., Ribbe, P.H. and Phillips, M.W. (1974) Semiempirical molecular orbital calculations for the atoms of the tetrahedral framework in anorthite, low albite, maximum microcline and reednergnerite. In W. S. MacKenzie and J Zussman, Eds., The Feldspars, p. 49-67. Manchester University Press, Manchester. Gibbs, G.v., Cox, D.F., Boisen, M.B., Downs, R.T., and Ross, N.L. (2003) The electron localization function: a tool for locating favorable proton docking sites in the silica polymorphs. Phys Chem Minerals 30:305-316
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Gibbs GV, Cox DF, Ross NL, Crawford TD, Burt JB, Rosso KM (2005) A mapping of the electron localization function for earth materials. Phys Chem Minerals 32:208-221 Gribbin, J. (1984) In search of Schrödinger’s cat. 302p. Bantam Books, New York, NY. Hehre, W.J., Radom, L., Schleyer, P.V.R. (1986) Ab Initio Molecular Orbital Theory. 548p. John Wiley & Sons, New York, NY. Hehre, W.J. (1995) Practical solutions for Electronic Structure Calculations, Wavefunction. Irvine. Hohenberg P, Kohn W, (1964) Inhomogenous electron gas. Phys Rev B 136:864-871 Kirfel A, Lippmann T, Blaha P, Schwarz K, Cox DF, Rosso KM, Gibbs GV (2005) Electron density distribution and bond critical point properties for forsterite, Mg2SiO4, determined with high energy synchrotron radiation: A comparison of experimental and theoretical properties for earth materials. Phys Chem Miner 32:301-313 Kohn, W., and Sham, L.J. (1965) Self-Consistent Equations Exchange and Correlation Effects. Physical Review, 140, 1133-1138. Kresse, G., and Furthmuller, J. (1996) Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp Mater Sci 6:15-50 Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47:558-561 Leach, A.R., (2001) Molecular Modelling: Principles and applications. 2nd ed. 744p. Pearson Education Limited, England. Lewis GN (1966) Valence and the structure of atoms and molecules. Dover Press, New York Louisnathan, S.J., and Gibbs, G.V. (1972) Variation of Si-O distances in olivines, soda melilite and sodium metasilicate as predicted by semi-empirical molecular orbital calculations. American Mineralogist, 57, 1643-1663. Monkhorst HJ, Pack JD (1976) Special points for Brillouin zone integrations. Phys Rev B 3:5188-5192 Muscenti TM, Gibbs GV, Cox DF (2005) A simple chemical view of relaxations at stoichiometric (110) surfaces of rutile structure-type oxides: a first-principles study of stishovite, SiO2. Surf Sci 594:70-82
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Savin A, Becke AD, Flad J, Nesper R, Preuss H, von Scnering HG (1991) A new look at electron localization. Angew Chem Ind Ed Engl 30:409-412 Savin A, Nesper R, Wengert S, Fässler TF (1997) ELF: The electron localization function. Angew Chem Ind Ed Engl 36:1808-1832 Silvi, B., and Savin, A. (1994) Chemical bonds in minerals: topological analysis of the electron localization function. Min Mag 58A:842-843 Terriberry TB, Cox DF, Bowman DA (2002) A tool for the interactive 3D visualization of electronic structure in molecules and solids. Comput Chem 26:313-319 Tossell, J.A. (1975) The Electronic Structures of Silicon, Aluminum, and Magnesium in Tetrahedral Coordination with Oxygen from SCF-Xα MO Calculations. Journal of the American Chemical Society, 97, 4840-4844. Tossell, J.A., and Gibbs, G.V. (1978) The use of Molecuar-Orbital Calculations on Model Systems for the Prediction of Bridging-Bond-Angle Variations in Siloxanes, Silicates, Silicon Nitrides, and Silicon Sulfides. Acta Crystallographica Section A: Foundations of Crystallography, 34, 463-472. Tossell, J.A., and Vaughan, D.J. (1992) Theoretical Geochemistry: Applications of Quantum Mechanics in the Earth and Mineral Sciences. 514p. Oxford University Press, New York, NY. Vanderbilt D (1990) Soft self-consistent psuedopotentials in a generalized eigenvalue formalism. Phys Rev B 41:7892-7895 Winter, J.K., and Ghose, S. (1979) Thermal expansion and high-temperature crystal chemistry of the Al2SiO5 polymorphs. Amer Min 64:53-586.
69
Chapter 4
Potential protonation sites in the Al2SiO5 polymorphs based on polarized FTIR spectroscopy and properties of the electron density
distribution
The results presented in this chapter have been submitted to: Jason B. Burt, Nancy L. Ross, G.V. Gibbs, G.R. Rossman, and Kevin M. Rosso (2006) American Mineralogist.
Abstract Potential protonation sites for, kyanite, sillimanite, and andalusite, located in a
mapping of the (3,-3) critical points displayed by their L(r) = −∇2ρ(r) distributions, are
compared with polarized single-crystal FTIR spectra of kyanite and sillimanite
determined earlier and with andalusite measured in this study. For andalusite, seven
peaks were observed when the electric vector, E, is parallel to [001]: four intense ones at
3440 cm-1, 3460 cm-1, 3530 cm-1, and 3600 cm-1 and three weaker ones at 3480 cm-1,
3520 cm-1, and 3650 cm-1. Six peaks, three intense ones at 3440 cm-1, 3460 cm-1, and
3530 cm-1 and three weaker ones at 3480 cm-1, 3520 cm-1, and 3560 cm-1 when E
parallels [010]. No peaks were observed when E is parallel to [001]. The concentration of
water in andalusite varies between 110 and 168 ppm by weight % H2O. The polarized
spectra indicate that the OH vector is parallel to (001) of andalusite and sillimanite and
(11 1 ) of kyanite. Examination of the L(r) (3,-3) critical points in comparison with the
polarized FTIR indicates that H prefers to bond to the oxygen atoms O1 and O2 in
andalusite and O2 and O4 in sillimanite which also correspond to the underbonded
oxygen atoms and those with the largest L(r) maxima. In kyanite, comparison of the
FTIR spectrum and the critical points indicates that H will preferentially bond to the two
4-coordinated O2 and O6 atoms.
70
Introduction
It has been shown that trace amounts of water, present as structurally bound OH,
is often contained in many minerals normally considered to be anhydrous (Bell and
Rossman, 1992 and Rossman, 1996) with OH concentration varying widely, commonly
between 10 and a few 100 ppm H2O by weight. It is known that these trace amounts can
have a disproportionately large impact on the physical, chemical, rheological, electronic,
and optical properties of a mineral. As such, knowledge of where the H atoms are located
together with the amount of OH that is incorporated in a structure is essential for
improving our understanding the recycling of water between the Earth’s mantle and the
crust. Single crystal polarized infrared spectroscopy is currently the preferred
experimental method for studying and characterizing the properties of OH in nominally
anhydrous minerals given its sensitivity in determining the relative orientation of the OH
dipole vector and its capacity to determine quantitatively the concentration of OH. In
conjunction with IR techniques, analysis of the theoretical electron density distribution,
EDD, can be used to locate the lone pair and bond pair domains on the O atoms where
electrophilic H can attack and form an OH dipole.
As observed by Bader and MacDougall (1985), these domains can be found by
mapping the Laplacian, L(r) = −∇2ρ(r), of the EDD and determining the positions of the
(3,-3) critical points. It is well known that the EDD of a bonded system in a stationary
state adopts a configuration wherein the Hellmann-Feynman forces on all of the
constituent atoms must necessarily equal zero and the energy of the resulting
configuration is minimized (Bader, 1990). When these conditions prevail, the EDD
embodies the bulk of the secrets of the system, including its structure, its reactivity and
stability (Kraka and Cremer, 1992). As such, the distribution displays a unique
arrangement of highly localized domains of electron density connected by well defined
pathways of much less localized density. The formation of the domains is the response of
the distribution to the strong attractive forces exerted by the nuclei of the constituent
atoms. The highly localized domains of electron density are not only centered at or very
near the positions of the nuclei, but they also define the arrangement of the atoms and,
71
accordingly, the structure of the system. In contrast, the response of the EDD to the
attractive interactions between pairs of bonded atoms is very much weaker, resulting in
the formation of much lower lying pathways of localized density referred to as bond
paths along which there is a maximum density relative to any neighboring pathway
(Bader, 1990).
As is well known, a level line contour map constructed for a plane containing a
pair of bonded atoms not only displays high maxima at the positions of the atoms where
the electron density is highly localized but also displays a much lower lying ridge of
localized density that link the peaks together. Again, the peaks represent and define the
positions of the atoms and the low lying ridge represents the pathway of the bond path.
The value of the EDD along the ridge decays exponentially between the pair and adopts a
minimum value at a bond critical point, denoted as rc, where ∇ρ(rc) = 0 (Bader, 1990).
Accordingly, the EDD distribution of a system determines the positions of the atoms and
the structure of a material together with valuable information about its bonded
interactions. In contrast, however, it fails to display features that reflect the shell
structures of the atoms and the local maxima and minima in the valence shell that can be
ascribed to bonded and non-bonded concentrations of the EDD. Evidence for these
features is manifest in the properties of L(r). As observed by Bader (1990), L(r) is a
scalar field like the EDD that not only manifests the shell structure of the atoms as
concentric regions of locally concentrated and depleted spherical shells of electron
density, but it also manifests local maxima and minima in the valence shell region of an
atom where ρ(r) is locally concentrated and depleted, respectively. In general, at a given
point in EDD, L(r) provides a measure of the difference between the average value of ρ
on the surface of a sphere of radius dr centered at r and the value of ρ at r. When L(r) is
negative, ρ(r) is necessarily larger than it is on average in the immediate neighborhood of
r and when ρ(r) is smaller, the converse is true. In the case where L(r) is negative, ρ is
said to be locally concentrated at r and when L(r) is positive, ρ is said to be locally
depleted at r. The location of a local maximum in L(r) is determined by a point where
∇(∇2ρ) = 0. As L(r) is a maximum at r, its three curvatures, the eigenvalues of the
Hessian of ∇2ρ, λ1, λ2, and λ3, must necessarily be negative. Accordingly, the point is
72
referred to as a (3,-3) critical point. When L(r) is a minimum at r, the point is referred to
as a (3,+3) critical point. These critical points are denoted as non-bonding maxima and
minima, respectively.
In an important contribution to the study of chemical reactivity, the number and
the location of the (3,-3) and (3,+3) critical points for the L(r) distributions for a number
of molecules were found (Bader and MacDougall, 1985) to be in agreement in large part
with the number and location of the domains ascribed to the bonded and non-bonded
electron pairs embodied in Gillespie’s (1960) VSEPR model. Within this framework,
Bader and MacDougall (1985) formulated a theory of chemical activity based on the
numbers, the locations and the sizes of the bonded and non-bonded domains of locally
concentrated and locally depleted ρ in valence shell of the bonded atoms. Several
examples were considered in their study that show that domains of locally concentrated
and locally depleted ρ as determined by L(r) correlate with sites of potential electrophilic
and nucleophilic attack.
Recently, a connection was established between nucleophilic lone pair domains
revealed by (3,-3) critical point in L(r) and sites of potential H electrophilic attack at the
charge concentrations on the O atoms comprising earth materials (Gibbs et al., 2001). A
mapping of L(r) for quartz and coesite displayed (3,-3) maxima along the Si-O bond
vectors and on the reflex sides of the Si-O-Si angles. Maxima were also displayed along
the Si-O bond vectors of stishovite and directly above each O atom in the OSi3 plane
defined by three edge sharing SiO6 octahedra. Each maximum is a site of potential H
electrophilic attack. However, those ascribed to lone pair domains on the reflex sides of
the Si-O-Si angles associated with larger L(r) maxima were considered to be more
susceptible to H attack than bond pair domains along the Si-O bond vectors with smaller
maxima. More recently, a mapping of the (3,-3) critical points displayed for a variety of
nominally anhydrous earth materials (Gibbs et al., 2001, 2002; Ross et al., 2003) has
uncovered a number of potential positions for electrophilic proton attack. Indeed, the
combination of experimental polarized infrared spectroscopy together with a knowledge
of L(r) and its (3,-3) critical points has been shown to be a powerful strategy for
73
determining potential sites for protonation in Earth materials. For example, the polarized
infrared spectrum of stishovite has a large absorption bands when E of the IR radiation is
polarized perpendicular to [001], while there is virtually no absorption when it is parallel
to the [001] (Pawley et al., 1993), indicating that the OH dipole vector parallels (001).
These results are in agreement with a mapping of the electron localization function
(Gibbs et al., 2001) and L(r) (3,-3) critical points by Ross et al. (2003), where there are
two symmetrically equivalent maxima located on opposite sides of each O atom. The H
atom was located at a distance of 0.98Å along a vector radiating from the O atom through
the (3,-3) critical point which placed parallel to (001), consistent with the orientation of E
determined by the polarized infrared spectra. In addition, first principles calculations for
stishovite confirmed that the OH dipole vector is perpendicular to the OSi3 plane
paralleling (001) (Gibbs et al., 2004; Panero and Stixrude, 2004).
In this study, we employ this technique to study potential sites for protonation in
the Al2SiO5 polymorphs, kyanite, sillimanite, and andalusite. The differences in the
orientation of the polyhedra and the variation in the coordination numbers of the Al
containing coordination polyhedra (e.g. 4 and 6 in sillimanite, and 4 and 5 in andalusite
and 6 in kyanite) make them an excellent model system for contrasting and correlating
these features with the polarized infrared spectra and the locations of the (3,-3) critical
points provided by a mapping of L(r). In addition, it has been suggested that kyanite may
play a role in subducting water into the mantle, especially if it transforms to AlSiO3OH
during subduction (Schmidt et al., 1998). Previous IR measurements for the Al2SiO5
polymorphs (Rossman and Smyth, 1990; Beran, 1969, 1970, 1971; Beran et al., 1983,
1989, 1987; and Wilkins and Sabine, 1973) show that OH is present in the polymorphs.
Further, recent FTIR measurements along three mutually orthogonal axes have
determined a maximum, in the samples studied, of 230 ppm H2O by wt. in kyanite (Bell
et al. 2004) and 200 ppm H2O by wt. in sillimanite (Beran et al., 1989). Determining the
total amount of H2O with IR requires measurement along three orthogonal axes
(Libowitzky and Rossman, 1996). Such studies have provided the basis for the current
study of the polarized FTIR spectra for single crystals of andalusite in which a connection
is made between the (3,-3) critical point properties and the polarized infrared spectra for
74
all three polymorphs, the potential sites for H are deduced and the orientations of the OH
dipole vectors are determined. The non-bonding maxima, (3,-3) critical points, are
referenced with respect to their magnitude for a greater conceptual understanding because
larger negative Laplacian values represent larger regions of localized electron density.
Methods
Polarized FTIR spectra
Three andalusite samples were measured using polarized FTIR spectroscopy with
E set parallel in succession along three zones ([100], [010] and [001]). Sample 129784
was obtained from the Harvard mineral collection and kindly donated by Dr. Carl Francis
comes from Embitipitiyain in the Sabaragamaura Provience of Sri Lanka. Samples
GRR278 and LOG are from unknown locations in Brazil and were provided by George
Rossman and Hunt Country Jewelers, Hillsboro Virginia, respectively. Sample
compositions (Table 4.1) were analyzed on a Cameca SX50 Electron Microprobe at the
Department of Geosciences, Virginia Tech. Operating conditions included an
accelerating potential of 15 kV and a beam current of 20 nA. Standards include natural
and synthetic silicates and oxides, and on-line data reduction of raw data was done using
a PAP (ZAF-type) matrix-correction program. All samples were oriented using a using an
Oxford Diffraction Xcalibur single-crystal X-ray diffractometer with monochromatized
Table 4.1: Composition of andalusite in wt % determined by electron microprobe analysisSample SiO2 TiO2 Al2O3 Cr2O3 MgO MnO FeO Total
129784 36.616 0.055 62.947 0.035 0.054 0 0.253 99.96
GRR278 37.175 0.029 62.47 0.037 0.035 0 0.189 99.935
LOG 36.316 0.021 62.77 0.027 0.031 0 0.273 99.438
MoKα radiation (λ = 0.70923 Å) and a CCD detector. For each sample, three slabs were
ground down to ~1 mm corresponding to [100], [010] and [001] oriented perpendicular to
one of the slabs, similar to the sample procedure described by Jacobsen et al. (2005). The
75
IR spectra for each sample was collected at Caltech with a Nicolet Magna 860
spectrometer fitted with a CaF2 beam splitter, tungsten-halogen source, MCT-A detector,
a LiIO3 polarizer, and a spectrometer resolution of 2 cm-1. E was oriented parallel to
each of the zones using transmitted light microscopy and positioned in an optically pure
and inclusion free region of the crystals.
The baseline and total integrated absorbance were determined with the Omnic
E.S.P. 5.2 software of the FTIR spectrometer. Background corrections are a potential
source of imprecision in IR analysis and though a background correction was applied, the
high quality of the crystals resulted in a minimal background correction. The total
integrated absorbance for each sample was measured between 3700 and 3200 cm-1
corresponding to the absorption peaks and normalized for a 1 cm thick crystal.
Critical point calculations
The theoretical EDD for the Al2SiO5 polymorphs, andalusite, sillimanite, and
kyanite, were generated with the Crystal98 software (Dovesi et al, 1996, Pisani 1996,
Saunders et al. 1998, Pisani et al. 2000) and the (3,-3) critical point properties for the L(r)
distributions were mapped using Crystal98 wavefunctions in the program TOPOND
(Gatti 1997). The Crystal98 program employs density functional theory (DFT) using the
Kohn-Sham (Kohn and Sham 1965) strategy. We chose to use the local density
approximation (LDA) (Vosko et al. 1980) to compute the wave functions and the static
EDD, as this approach has performed well in our past research (e.g., Gibbs et al., 2001).
The wavefunctions were computed using a linear combination of atomic orbitals (LCAO)
and periodic boundary conditions necessary for modeling crystalline materials.
Molecular orbital calculations typically use Gaussian basis functions, which tend to
include diffuse functions that in the Crystal code result in an over-estimate of the orbital
overlap and numerical instability in crystalline materials. We therefore employed basis
functions specifically designed for Crystal98. The basis functions used, which provide
good results are a 65-111G basis set optimized for Si4+ (Darco et al. 1993), a 8-411G
basis set optimized for O2- (McCarthy and Harrison 1994), and a 85-11G basis set
76
optimized for Al3+ (Catti et al. 1994). The unit cell, space group types, and nonequivalent
atomic positions used in the calculations for the three Al2SiO5 polymorphs were
determined by Winter and Ghose (1979).
Results
Polarized FTIR spectra of andalusite
The polarized infrared spectra of andalusite is given in Figure 4.1. Seven
anisotropic peaks are observed when the E is oriented parallel to [100], four strong peaks
at 3440 cm-1, 3460 cm-1, 3530 cm-1, and 3600 cm-1 and three weak peaks at 3480 cm-1,
3520 cm-1, and 3650 cm-1. Six peaks are observed when E parallel with [010], three
strong at 3440 cm-1, 3460 cm-1, and 3530 cm-1 and three weak peaks at 3480 cm-1, 3520
cm-1, and 3560 cm-1. However, no peaks were observed when E was set parallel to [001].
In the absence of an andalusite-specific calibration, the total concentration of
water in andalusite was determined from the calibration of the IR spectrum for kyanite
(Bell et al., 2004) and is related to the “total” integrated absorbance (Abstot) of the IR
peaks by the following equation (modified due to the density difference between kyanite
and andalusite):
H2O (in ppm by weight) = 0.128 (≤0.002) × Integrated-Abstot (4.1)
where 2 2
tot 1 1 2 2 3 31 1
Abs 1 Abs d + 1/t Abs d + 1/t Absv v v
v v
t ν ν=2
1v∫ ∫ ∫ (4.2)
and the region of integration is between 3700 to 3300 cm-1, t1, t2, and t3 are the
thicknesses of the slices along the three orthogonal directions, and Abs1, Abs2, and Abs3
are the integrated absorbance in the three directions. The concentration of water in the
three samples of andalusite (Table 4.2) varies between 110 and 168 ppm H2O by weight.
77
Figure 4.1: Polarized FTIR spectra of andalusite with E parallel to the (a) [100], (b) [010], and (c) [001].
78
Table 4.2: water concentrations determined by polarized IRSample number 129874 GRR274 LOG
IR integ/cm (α + β + γ) 1141.2 866.6 751.6
H2O (ppm by weight) 167.76 127.39 110.48
(3,-3) Critical points displayed by a mapping of L(r)
Andalusite
Andalusite is orthorhombic with Pnnm space group type. It consists of chains
edge-sharing AlO6 that run parallel to [001], that are cross-linked by SiO4 tetrahedra
alternating in succession with AlO5 coordination polyhedra. There are four nonequivalent
O atoms in the structure, O1, O2, O3, and O4. Each is coordinated by three M atoms
(M=Al,Si) with O1 coordinated to three Al atoms (Fig. 4.2a) and O2, O3, and O4
coordinated by two Al and one Si atom (Fig. 4.2b). O1 and O2 each display two (3,-3)
critical points denoted O1cp1, O1cp2, O2cp3, and O2cp4, located 0.358 Å, 0.356 Å, 0.353 Å,
and 0.359 Å, respectively, from the O atoms with O1 0.2 Å and O2 0.36 Å from a plane
defined by and containing the three surrounding M cations. O1cp2 is further from the
plane defined by the three coordinating M atoms than O1cp1 and has a larger L(r) value
with larger curvatures λ1, λ2, and λ3 (Table 4.3). This trend is also displayed by the
critical points O2cp3 and O2cp4. O3 has three (3,-3) critical points, where two are
equivalent, O3cp5 and O3cp6, each at a distance of 0.357 Å from O3 and the third , O3cp7,
is located along the Si-O bond vector at a distance of 0.368 Å. The O3cp7 represents a
critical point between two atoms, as outlined by Bader (1984), and is not considered to be
a potential site for H protonation. O3 is located in a plane defined by the three
coordinating M atoms with the two critical points, O3cp5 and O3cp6, on either side of the
O having equivalent L(r) and λ1, λ2, and λ3, values due to the symmetry of the sites. The
fourth nonequivalent oxygen, O4, has two critical points, O4cp8 and O4cp9, at distances of
0.354 Å and 0.356 Å from the O atom, respectively. O4 is displaced 0.09Å off the plane
defined by the three coordinating M-cations. The end result is that the critical point that is
79
Table 4.3: Electron density properties for (3,-3) non-bonding critical points in the Al2SiO5 polymorphs(3,-3) ρ(r) R Laplacian lambda1 lambda2 lambda 3Critical Point e/Å3 Å e/Å5 e/Å5 e/Å5 e/Å5
O1cp1 5.693 0.3552 8.809E+01 -8.647E+03 -1.425E+02 -8.253E+01 0.3850 0.3698 0.7500O1cp2 5.565 0.3575 8.246E+01 -8.287E+03 -1.163E+02 -5.485E+01 0.3500 0.4548 0.7500O2Cp3 5.554 0.3569 8.203E+01 -8.276E+03 -8.299E+01 -7.900E+01 0.3396 0.4774 0.2500O2cp4 5.574 0.3564 8.289E+01 -8.334E+03 -8.563E+03 -8.338E+01 0.3767 0.3919 0.2500O3cp5 5.534 0.3573 8.033E+01 -8.232E+03 -1.168E+02 -5.113E+00 0.4451 0.0367 0.7500O4cp6 5.756 0.3543 9.111E+01 -8.811E+03 -1.594E+02 -1.025E+02 0.1663 0.2004 -0.4901O4cp7 5.610 0.3564 8.465E+01 -8.401E+03 -1.297E+02 -7.459E+01 0.0784 0.2309 -0.4895
O1cp1 5.474 0.3584 7.862E+01 -8.020E+03 -6.675E+01 -6.542E+01 0.4636 0.3411 0.5000O1cp2 5.637 0.356 8.527E+01 -8.503E+03 -9.219E+01 -8.263E+01 0.3807 0.3791 0.5000O2cp3 5.799 0.3533 9.272E+01 -8.943E+03 -1.679E+02 -9.287E+01 0.4600 0.3350 0.0000O2cp4 5.479 0.3587 7.879E+01 -8.029E+03 -1.016E+02 -4.347E+01 0.3981 0.4000 0.0000O3cp5 5.570 0.357 8.180E+01 -8.262E+03 -1.010E+02 -3.569E+01 0.0968 0.4084 0.0626O3cp6 5.570 0.357 8.180E+01 -8.262E+03 -1.010E+02 -3.569E+01 0.0968 0.4084 -0.0626O3cp7 5.200 0.3686 6.727E+01 -6.429E+03 -8.015E+01 -2.125E+01 0.1363 0.3672 0.0000O4cp8 5.726 0.3557 9.012E+01 -8.761E+03 -1.584E+02 -9.733E+01 0.2472 0.0948 0.2187O4cp9 5.634 0.3557 8.598E+01 -8.506E+03 -1.351E+02 -8.282E+01 0.2072 0.1634 0.2750
O1cp1 5.759 0.3535 9.070E+01 -8.825E+03 -1.735E+02 -7.056E+01 0.0765 0.1511 0.1670O1cp2 5.510 0.3585 7.971E+01 -8.114E+03 -1.147E+02 -3.557E+01 0.1320 0.1364 0.0806O2cp3 5.370 0.3626 7.546E+01 -7.471E+03 -9.682E+01 -4.336E+01 0.1620 -0.3089 0.2353O2cp4 5.652 0.3537 8.571E+01 -8.543E+03 -7.647E+01 -6.220E+01 0.0920 -0.3531 0.1457O2cp5 5.363 0.3641 7.521E+01 -7.419E+03 -9.827E+01 -4.451E+01 0.1254 -0.2677 0.1793O3cp6 5.741 0.3515 9.016E+01 -8.787E+03 -1.608E+02 -8.233E+01 0.3195 0.4588 -0.0664O3cp7 5.553 0.3601 8.181E+01 -8.234E+03 -1.182E+02 -5.272E+01 0.2260 0.4559 -0.0396O4cp8 5.752 0.3506 9.052E+01 -8.812E+03 -1.650E+02 -8.161E+01 0.3287 -0.0465 -0.0229O4cp9 5.549 0.3609 8.151E+01 -8.218E+03 -1.192E+02 -4.917E+01 0.2341 -0.0902 -0.0936O5cp10 5.523 0.3585 8.040E+01 -8.146E+03 -1.159E+02 -4.267E+01 0.1275 0.1757 -0.2747O5cp11 5.757 0.3534 9.072E+01 -8.829E+03 -1.682E+02 -7.786E+01 0.0805 0.1335 -0.3914O6cp12 5.587 0.3557 8.279E+01 -8.383E+03 -5.284E+01 -4.887E+01 0.0939 -0.3457 -0.3348O6cp13 5.350 0.3639 7.471E+01 -7.439E+03 -8.634E+01 -4.336E+01 0.1602 -0.3562 -0.3972O6cp14 5.357 0.3611 7.501E+01 -7.446E+03 -8.781E+01 -4.025E+01 0.1158 -0.4166 -0.3604O7cp15 5.753 0.3533 9.086E+01 -8.833E+03 -1.608E+02 -9.028E+01 0.3259 0.4446 0.4711O7cp16 5.557 0.3581 8.219E+01 -8.253E+03 -1.211E+02 -5.610E+01 0.2369 0.4547 0.4007O8cp17 5.757 0.3529 9.086E+01 -8.842E+03 -1.578E+02 -8.993E+01 0.3369 -0.0326 0.4475O8cp18 5.549 0.3586 8.174E+01 -8.224E+03 -1.171E+02 -5.330E+01 0.2450 -0.0847 0.4690O9cp19 5.561 0.3554 8.218E+01 -8.250E+03 -1.255E+02 -5.328E+01 -0.4698 0.3202 0.2506O9cp20 5.748 0.3563 9.052E+01 -8.804E+03 -1.647E+02 -8.601E+01 0.4826 0.2281 0.2352O10cp21 5.763 0.3555 9.114E+01 -8.841E+03 -1.662E+02 -8.896E+01 0.4825 0.2684 -0.2445O10cp22 5.549 0.3556 8.163E+01 -8.211E+03 -1.224E+02 -5.086E+01 -0.4679 0.2016 -0.2377
Sillimanite
Andalusite
Kyanite
x y z
80
Figure 4.2: The four types of coordinated oxygens (red) in the Al2SiO5 polymorphs and their associated (3,-3) critical points (yellow). (a) Oxygen coordinated to three Al atoms (maroon) as in andalusite and sillimanite. (b) Oxygen coordinated to two Al atoms and one Si atom (blue) as in andalusite, sillimanite and kyanite. (c) Oxygen coordinated to an Al and a Si atom as in sillimanite. (d) Oxygen coordinated to four Al atoms as in kyanite.
81
located farthest from the cation plane, O4cp8, has larger L(r) and curvature values. Thus,
there are eight critical points on the four nonequivalent O atoms that are potential
hydrogen protonation sites.
Based on the (3,-3) critical points, potential OH dipole orientations within
andalusite can be examined by placing a hydrogen 0.98 Å along a vector through the
(3,-3) critical point originating from an oxygen (Fig. 4.3a and 4.3b). Hydrogen locations
if bound to O1 or O2 and associated with the (3,-3) critical points would be located
within the (001) plane. Hydrogen atoms associated with O1cp1 and O1cp2 would be
oriented along the zones [210] and [210] in the (001) plane, while the H atoms associated
with O2cp3 would be orientated along the [ 6 50] and [ 6 50] zones and those associated
with O2cp4 would be orientated along the [230] and [230] zones. Hydrogen positioned
along a vector through the (3,-3) critical points around O3 would be located nearly within
the (010) plane and directed along [119], [119], [117], and [11 7 ]. Unlike potential H
positions near the O1, O2, and O3 atoms, H positioned near O4 are not located within or
close to a plane which is perpendicular with one of orthonormal unit cell axis. Due to the
symmetry of the crystal there are eight approximate zones that are associated with the
O4cp8, [121], [1 2 1], [121], [1 2 1], [ 2 53], [253], [253], and [ 2 5 3], and O4cp9, [ 4 56],
[ 4 56], [45 6 ], [45 6 ], [6 7 8], [ 6 78 ], [ 6 7 8 ], and [678], critical points.
Sillimanite
Sillimanite is orthorhombic in the Pbmn space group type and its crystal structure
is similar to andalusite with edge-sharing octahedra (AlO6) that run parallel with [001],
cross-linked by alternating AlO4 and SiO4 tetrahedra. As in andalusite, there are four
nonequivalent oxygens, O1, O2, O3, and O4, but their cation coordination is variable
with O1 and O4 coordinated to two Al atoms and one Si (Fig. 4.2b), O2 is coordinated to
three Al atoms (Fig. 4.2a), and O3 is coordinated to an Al and a Si atom (Fig. 4.2c).
Thus, there are seven nonequivalent (3,-3) critical point localities in sillimanite (Fig. 4.2).
82
Figure 4.3: Projection of the (001) and (010) planes in (a) andalusite, (b) sillimanite, and (c) kyanite with hydrogen atoms (yellow) positioned along a vector 0.98 Å from the oxygen atoms through their corresponding (3,-3) critical points.
83
The O1 atom is 0.18 Å above a plane defined by the three surrounding cations with two
critical points, O1cp1 and O1cp2, at distances of 0.355 Å and 0.358 Å from the O atom,
respectively. The O1cp1 has larger L(r) and curvature, λ1, λ2, and λ3, values than O1cp2
and is farther from the plane defined by the three surrounding M cations. The O2 atom is
nearly positioned in a plane defined by the three surrounding M cations (0.02 Å) and its
two (3,-3) critical points, O2cp3 and O2cp4, have nearly identical L(r) and curvature, λ1,λ2,
and λ3, values. O2cp3 and O2cp4 are located at distances of 0.357 Å and 0.356 Å,
respectively, from the O. O3 has one (3,-3) critical point, which is at the reflex side of
the bent Al-O-Si angle (Fig. 4.2c). Similar to O1, O4 is 0.2 Å outside of the plane
defined by the three surrounding cations and has two critical points, O4cp6 and O4cp7, at
distances of 0.354 Å and 0.356 Å, respectively, from the O atom. As seen in O1, the (3,-
3) critical point (O4cp6) which is farthest from the plane defined by the three surrounding
cations has larger L(r) and curvature, λ1,λ2, and λ3, values.
Modeling of potential hydrogen locations based on (3,-3) critical points indicates
that H incorporated into the sillimanite structure is located within the (001) plane (Fig.
4.3c and 4.3d). The OH dipoles and their orientation in the (001) plane are: O1cp1;
[ 2 30] and [230], O1cp2; [140] and [140], O2cp3 and O2cp4; [120] and [120], O3cp5;
[110] and [110], O4cp6; [ 2 10] and [210], and O4cp7; [510] and [510].
Kyanite
Unlike andalusite and sillimanite, kyanite is triclinic belonging to the P1 space
group consisting of edge-sharing AlO6 octahedra in a zigzag pattern which are cross
linked with SiO4 tetrahedra and AlO6 octahedra. There are 10 nonequivalent oxygens in
kyanite with two different types of coordination. Two of the oxygens (O2 and O6) are
coordinated to four Al atoms (Fig. 4.2d), while the other eight (O1, O3, O4, O5, O7, O8,
O9, O10) are coordinated to two Al and one Si atoms (Fig. 4.2b). There are 22 distinct
(3,-3) critical points at distances from the O of ~0.35 Å (table 4.4). The two O atoms in
four-coordination with Al are associated with three (3,-3) critical points, but only one on
84
each O is thought to be a potential site for protonation (O2cp4 and O6cp12) as seen below.
The other two (O2cp3, O2cp5, O6cp13, and O6cp 14) are located along the shorter Al-O bonds
comparable to the O3cp7 critical point in andalusite and are not thought to be potential
protonation sites. The eight other nonequivalent oxygens coordinated to two Al atoms
and a Si have two (3,-3) critical points, which may be potential protonation sites. The
eight oxygens are > 0.2 Å from the plane defined by the surrounding cations and may be
associated with sp3 hybridization (Burt et al., 2006). Of the two (3,-3) critical points on
each three coordinated O, the critical point that is farthest from the plane defined by three
surrounding M cations has the largest Laplacian, L(r), and curvature, λ1, λ2, and λ3,
values.
As in andalusite and sillimanite, orientation of potential OH dipoles (Fig. 4.3e and
4.3f) may be examined by placing a H 0.98 Å along a vector from an O through the (3,-3)
critical point. There are 18 directions for the OH dipole orientation in kyanite which are
associated with the 10 distinct oxygens (O1: [101] and [31 5]; O2: [677]; O3: [91 4 ] and
[8 01]; O4: [313] and [956]; O5: [113] and [326]; O6: [111]; O7: [101] and [513]; O8:
[ 7 33] and [320]; O9: [461] and [251]; and O10: [120] and [7 7 1]). Although potential
OH dipole orientations occur in numerous directions in kyanite, there are four (3,-3)
critical points (O2cp4, O3cp7, O4cp9, and O6cp12) where the OH dipole associated with the
critical points would be located within the ( )11 1 plane which is important when
examining the polarized infrared spectra of kyanite.
Discussion
Polarized infrared spectroscopy has been used to determine potential sites where
H is located in the Al2SiO5 polymorphs. Examination of the polarized infrared spectra of
andalusite (Fig. 4.1) indicates that the OH is located within the (001) plane. This is also
observed in the polarized infrared spectra of sillimanite measured by Beran et al. (1989)
and shown in Figure 4.4 where there are distinct peaks when E is parallel to [100] and
[010] but no distinguishable peaks are observed when E is parallel to [001]. Examination
85
Sillimanite- Reinbolt Hills
0
0.1
0.2
0.3
0.4
0.5
300031003200330034003500360037003800
wavenumber (cm-1)
Abs
orba
nce
E || a
E || b
E || c
Figure 4.4: Polarized infrared spectrum of sillimanite with E parallel to [100], [010], and [001]. This figure was taken and modified from Beran et al. (1989).
86
Figure 4.5: Polarized FTIR spectrum of kyanite along the three orthogonal directions α, β, and γ. This figure is taken from Bell et al. (2004).
87
of the polarized infrared spectra of kyanite is more complicated because kyanite is
triclinic. For kyanite, Bell et al. (2004) collected polarized spectra along three orthogonal
directions (Fig. 4.5) and indicate that the location of the OH dipole is in the (11 1 ) plane.
Thus, hydrogen is located in the (001) planes of andalusite and sillimanite and within the
(11 1 ) plane of kyanite determined from the polarized infrared spectra.
The (3,-3) critical points indicate regions of localized electron density around
oxygen atoms and can therefore be used to identify potential sites for protonation that can
be compared with the polarized FTIR spectra. In sillimanite, H positioned along a vector
from an O through its critical point at distances of 0.98 Å would be located within the
(001) plane (Figure 4.3c and 4.3d) which is consistent with results from the polarized
infrared spectra. The disadvantage of all potential H being located in the (001) plane as
predicted by the location of the (3,-3) critical points is that no distinct O atoms within the
sillimanite crystal structure can defined as a preferential protonation sites. However,
andalusite and kyanite have OH dipoles defined by the (3,-3) critical points in multiple
orientations in the crystal structures and comparison with the polarized infrared spectrum
can determine distinct oxygens which will be preferential hydrogen protonation sites. In
andalusite, the spectra indicate that H is located in the (001) plane. O1 and O2 are the
only O atoms where hydrogen could correlate with the (3,-3) critical points and be
located in the (001) plane. In kyanite there are four O atoms and four (3,-3) critical
points that correspond to H in the ( )11 1 plane, O2cp4, O3cp7, O4cp9, and O6cp12. Thus, if
H is associated with the (3,-3) critical points then it will only be bonded to O2, O3, O4, or
O6 in kyanite. The potential protonation sites in the Al2SiO5 polymorphs are obtained
from examination of the (3,-3) critical points in correlation with the results from the
polarized FTIR spectra.
Although we have used (3,-3) critical points in conjunction with the results from
the polarized FTIR spectra of the Al2SiO5 polymorphs to determine potential protonation
sites within their structures, we still do not know why these O atoms appear to be
preferred over the others. The question arises whether we can examine the (3,-3) critical
88
point properties of any mineral and determine potential protonation sites or whether
factors such as bond valence, coordination number, and geometry outweigh quantitative
evaluation of the critical point values as outlined Bader and MacDougall (1984). This
question can be examined with the Al2SiO5 polymorphs because of the variation in
geometry and coordination in conjunction with the variety of bonded cations. In
determining where a proton would likely bond in a structure we might assume that there
may be higher probability at a critical point with a larger L(r) value, e.g. greater local
concentration of electron density. It is seen that the (3,-3) critical point values are
affected by the arrangement of the cations surrounding the three-coordinated oxygens and
as indicated previously, the critical points that are farthest from the surrounding cation
planes have larger L(r) values. If a three-coordinated O were to be protonated, we would
assume due to electrostatic repulsions that the proton would bond near the critical point
that is farthest from the surrounding cations, corresponding to the larger L(r) values as
shown by Bader and MacDougall (1985). Comparison of the L(r) values at the (3,-3)
critical points and the distance the oxygens are from the plane defined by the three
surrounding cations (Fig. 4.6) suggest that the L(r) values for the critical points that are
farthest from the cation plane increase with increasing oxygen distance while the L(r) of
the critical points that are closest to the cation plane decrease with increasing oxygen
distance. It is also important to note that this trend is dependent on the atomic number of
the surrounding cations. In the Al2SiO5 polymorphs there are two types of three
coordinated O atoms, those coordinated to three Al atoms and those coordinated to two
Al atoms and one Si. An O coordinated to three Al atoms has lower L(r) values at
comparable O distances compared to one which is coordinated to a Si and two Al atoms,
suggesting the L(r) values are related to the surrounding cations. The trends for the
increase and decrease in the L(r) values with increasing O distance indicate a correlation
even though there is apparent scatter in the data (Fig. 4.6). However, there could be more
than one trend for a given (3,-3) critical point and cation configuration (e.g. Al2-O-Si
orAl3-O). O3 in andalusite is contained in the plane defined by the three surrounding
cations and does not correspond to any of the trends for the other O that are surrounded
by two Al atoms and a Si (Fig. 4.6). This may be due to a change in hybridization of the
O as it increases its distance from the cation plane. It has previously been suggested that
89
76.0
78.0
80.0
82.0
84.0
86.0
88.0
90.0
92.0
94.0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Distance oxygen is above cation defined plane
L(r
)
Figure 4.6: A comparison of the three coordinated oxygen (3,-3) critical point L(r) values vs. the distance the oxygen atoms are from a plane defined by the three surrounding cations. The lines represent the trend for increasing L(r) values for the critical point that is farthest from the cations and decreasing L(r) values for the critical point that is closest to the cations with increasing oxygen distance. The graph displays oxygen distance vs. L(r) values for the oxygen atoms that are coordinated to two aluminum atoms and one silicon atom in sillimanite (diamond), andalusite (squares), and kyanite (triangles) and the oxygen atoms that are coordinated to three aluminum atoms in andalusite (asterisk) and sillimanite (crosses).
90
there is a change in hybridization from sp2 to sp3 when an O atom surrounded by two Al
and one Si is greater then 0.2 Å (Burt et al., 2006) which may affect the susceptibility for
oxygen protonation. Thus, the geometry of the surrounding cations, hybridization, and
surrounding cation atomic numbers may affect the values of L(r) at the critical points
around the oxygens. In addition to changes in the L(r) values with variation in the
distance the oxygen is from the surrounding cation plane, there are trends displayed by
the Al2SiO5 polymorphs in relation to the critical point - oxygen distance for the three
coordinated oxygens and their L(r) values (Table 4.4). Examination of the distance the
critical points are from the three coordinated oxygen atoms in relation to the L(r) values
are dependent on the polymorph and indicate that the critical points that are closer to the
oxygens have smaller L(r) values then those that are farther from the oxygen atoms in
andalusite and sillimanite (Fig. 4.7, line a), while there are two vertical lines that are
indicative of the relationship between the critical point oxygen distance and the L(r)
values that dependent on how far the critical point is from the cation defined plane in
kyanite (Fig. 4.7, line b and c). In other words, the (3,-3) critical points in kyanite have
similar L(r) values with varying critical point - oxygen distances for the critical points
that are closest to the cation plane (Fig. 4.7, line b) and farthest from the cation plane
(Fig. 4.7, line c) while the L(r) values increase with decreasing distance to the oxygen in
andalusite and sillimanite. The different trends within the Al2SiO5 polymorphs between
the critical point – oxygen distance and the L(r) values is not as yet understood, but may
be due to the relatively small range the oxygens are from the plane defined by the three
surrounding cations compared to the larger ranges in sillimanite and andalusite. In order
to fully understand this, a greater data set is required with a greater variety in oxygen –
critical point distances and oxygen – surrounding cation plane distances. The relative
trends in the critical point examination indicate that as the three-coordinated oxygen gets
farther from a plane defined by the three surrounding cations then the L(r) of the critical
point that is farthest from the plane should increase while the critical point oxygen
distance should decrease. Although the oxygens with large L(r) are indicative of being
potential protonation sites, there are other factors which may also influence protonation.
The polarized infrared spectra of andalusite indicate that hydrogen is located parallel to
the (001) plane corresponding to critical points on O1 and O2 where those oxygens are
91
critical point L (r) c.p.-oxygen distance (Å)
O1cp1 88.090 0.355O1cp2 82.460 0.358O2cp3 82.030 0.357O2cp4 82.890 0.356O4cp6 91.110 0.354O4cp7 84.650 0.356
O1cp1 78.620 0.358O1cp2 85.270 0.356O2cp3 92.720 0.353O2cp4 78.790 0.359O3cp5 81.800 0.357O3cp6 81.800 0.357O4cp8 90.120 0.355O4cp9 85.980 0.356
O1cp1 90.700 0.354O1cp2 79.710 0.359O3cp6 90.160 0.352O3cp7 81.810 0.360O4cp8 90.520 0.351O4cp9 81.510 0.361O5cp10 80.400 0.359O5cp11 90.720 0.353O7cp15 90.860 0.353O7cp16 82.190 0.358O8cp17 90.860 0.353O8cp18 81.740 0.359O9cp19 82.180 0.355O9cp20 90.520 0.356O10cp21 91.140 0.356O10cp22 81.630 0.356
sillimanite
andalusite
kyanite
Table 4.4: The critical point Laplacian value vs. the distance the critical point is from the oxygen atom
92
0.35
0.352
0.354
0.356
0.358
0.36
0.362
75.0 77.0 79.0 81.0 83.0 85.0 87.0 89.0 91.0 93.0 95.0
L(r)
C.P
. - O
xyge
n D
ista
nce Line c
Line b
Line a
Figure 4.7: A comparison of the distance the (3,-3) critical points are located from the oxygens vs. the (3,-3) critical L(r) values for the oxygens coordinated to three cations kyanite (triangles), andalusite (squares), and sillimanite (diamonds). The lines represent trends in L(r) values vs. critical point oxygen distance for andalusite and sillimanite (line a) and kyanite (line b and line c).
93
coordinated to three cations. O1 is coordinated to three Al atoms, while O2 is
coordinated to two Al atoms and a Si. If a proton would dock to any oxygen in
andalusite, then it would most likely dock to the oxygen that has the highest L(r) values
(Bader and MacDougall, 1985), O1, which also has the shortest critical point – oxygen
distance of any oxygen in andalusite. Though this oxygen correlates with the polarized
FTIR and critical point analysis the O2 does as well. O2 does not have the largest L(r)
value, but it is underbonded with a bond valence of 1.88 (Brown and Altermatt, 1985).
Thus the two oxygen atoms which correlate with the FTIR and location of the (3,-3)
critical points are the underbonded oxygen and the oxygen with the largest L(r) value,
namely O1 and O2. Thus, the underbonded nature of O2 might affect potential
protonation negating relative values of L(r). Unlike andalusite all oxygen atoms in
sillimanite are potential protonation sites according to the polarized FTIR and location of
the critical points, but we may hypothesize that the two most likely protonated oxygens in
sillimanite are O4 and O2 because O4 has the largest L(r) value and O2 is underbonded
(Brown and Altermatt, 1985) with a bond valence of 1.87. We have thus assumed that
we can predict the location of proton in andalusite and sillimanite based on the value of
L(r) and the underbonded nature of an oxygen atom. Can we apply this procedure to
kyanite?
As in andalusite and sillimanite, potential protonation sites in kyanite can be
predicted based on the location of the (3,-3) critical points in relation to the polarized
FTIR spectrum. The FTIR analysis indicates that hydrogen is located parallel to the
(11 1 ) plane and in conjunction with the examination of the (3,-3) critical points indicate
that the potential protonation sites in kyanite are O2cp4, O3cp7, O4cp9, and O6cp12. Unlike
andalusite and sillimanite, there are no underbonded oxygen atoms in kyanite and all
three-coordinated oxygens are bound to two AlO6 and one SiO4 coordinated polyhedra.
The two potential protonation sites, O3cp7 and O4cp, corresponding to three-coordinated
oxygens are the critical points around the oxygens that are closest to the plane defined by
the three surrounding cations. Consideration of electrostatic interactions in comparison
to (3,-3) critical points that are farther away from the surrounding cation plane suggest
that these oxygen atoms seem unlikely to be protonated, especially when compared to
94
other critical points on other oxygen displaying larger L(r) values and less electrostatic
interference. According to the Bader-MacDougall model (1985) potential protonation
sites on the three-coordinated oxygen in kyanite would be located farther away from the
cation plane and have larger L(r) values. The remaining two potential protonation sites,
O2cp4 and O6cp12, are coordinated to four octahedrally-coordinated Al atoms. These
critical points are located equidistant from the longer Al-O bonds and are more likely
sites for protonation than the three coordinated oxygen due to the lack of electrostatic
interference. Structurally kyanite is known to have dislocations and a common
dislocation occurs in the (100) plane along [001] where there are no Si-O bonds which
are broken (Grobety and Veblen, 1995). The orientation of the OH dipole, if bound to
O2 and O6 through the O2cp4 and O6cp12 critical points, would be located in the
dislocation plane. Thus, dislocations in kyanite might be responsible for the protonation
at these sites or hydrogen incorporation may result in dislocations along this plane.
In the discussion above, we have not considered charge balance which is required
for the incorporation of a proton into the Al2SiO5 structures. This study has concentrated
on examination of the polarized FTIR spectra in relation to the (3,-3) critical point
properties. There would have to be defect in the structure such as a site vacancy or an Al,
Mg, or other +2 cation substitution for a proton to be incorporated into these structures to
account for the charge imbalance. This study suggests that potential protonation sites in
mineral structures may be predicted from (3,-3) critical points in conjunction with
polarized FTIR spectra without modeling defects though Si substitution may be necessary
for hydrogen incorporation in the Al2SiO5 polymorphs.
In determining potential protonation sites in a mineral’s crystal structure it is
important to examine the coordination of potential protonated oxygens, L(r) values, and
whether any of the oxygens are underbonded. The OH dipole is located parallel to the
(001) plane of andalusite and sillimanite as seen in the polarized FTIR spectrum and in
comparison with the (3,-3) critical points it is suggested that hydrogen will be located
near the O1 and O2 oxygens in andalusite and near the O2 and O4 oxygens in sillimanite.
This corresponds to the underbonded oxygen and the oxygen with the largest L(r) value,
95
where each oxygen is coordinated to three cations. The oxygens that have the largest
L(r) values also have the highest electron localization function (ELF) values (Burt et. al.,
2006) and may correspond to an alternative method for determining potential protonation
sites. As in andalusite and sillimanite, the polarized FTIR spectrum of kyanite is
anisotropic indicating that the OH dipole is located parallel to the ( )11 1 plane. Though
there are numerous three coordinated oxygens, hydrogen is most likely coordinated to the
four coordinated oxygens as indicated above from examination of the (3,-3) critical
points. It is thus necessary to examine a mineral’s crystal structure and oxygen
coordination when determining potential protonation sites. It is our hope that future
experiments on a variety of minerals will provide a basis for determining hydrogen
protonation sites from critical point information through examination of crystal
structures, geometry, coordination, and L(r) magnitude.
References Bader, R.F.W. (1990) Atoms in Molecules. 438 p. Oxford University Press, Oxford, U.K. Bader, R.F.W., MacDougall, P.J., and Lau, C.D.H. (1984) Bonded and Non-bonded Charge Concentrations and Their Relation to Molecular Geometry and Reactivity. J. Am. Chem. Soc., 106, 1594-1605. Bader, R.F.W.a and Macdougall., P.J. (1985) Toward a Theory of Chemical Reactivity Based on the Charge Density. J. Am. Chem. Soc., 107, 6788-6795. Bell, D.R., and Rossman, G.R. (1992) Water in Earth's Mantle: The Role of Nominally Anhydrous Minerals. Science, 255, 1391-1397. Bell, D.R., Rossman, G.R., Makdener, J. Endisch, D., and Rauch, F. (2004) Hydroxide in kyanite: A quantitative determination of the absolute amount and calibration of the IR spectrum. American Mineralogist, 89, 998-1003. Beran, A. (1970) Ultrarotspektroskopischer Nachweis von OH-Gruppen in den Mineralen der "Al2SiO5" - Mokifikationen. Österr Akad Wiss, Math-Naturw Kl, Anzeiger, 184-185. Beran, A.. (1971) Messung des Ultrarot-Pleochroismus nom Mineralen. Der Pleochroismus der OH-Strckfrequenz in Disthen. Tschermaks Min Petr Mitt, 16, 129-135.
96
Beran, A., and Gotzinger, M. A. (1987) the Quantitative IR Spectroscopic Determination of Structural OH Groups in Kyanites. Mineralogy and Petrology, 36(41-49). Beran, A., and Zeman, J. (1969) Messung des Ultrarot-Pleochroismus von Mineralen VIII. Der Pleochroismus der OH-Streckfrequenz in Andalusit. Tschermaks Miner. u. Petrogr. Mitt., 13, 285-292. Beran, A., Hafner, St., and Zemann, J. (1983) Untersuchungen über den Einbau von Hydroxilgruppen im Edelstein-Sillimanit. Neues Jahrbuch für Mineralogie Monatshefte, 219-226. Beran, A., Rossman, G. R., and Grew, E. S. (1989) The hydrous component of Sillimanite. American Mineralogist, 74, 812-817. Brown, I.D., and Altermatt, D.,B. (1985) Bond-valence parameters obtained from a systematic analysis of the Inorganic Crystal Structure Database. Acta Crystallographica, Section B: Structural Science, 41(4), 244-247. Burt, J.B., Gibbs, G.V., Cox, D.F., and Ross, N.L., (2006) ELF isosurface maps for the Al2SiO5 polymorphs. Phys. Chem. of Minerals, 33, 138-144. Catti, M., Valerio, G., Dovesi, R., Causa, M. (1994) Quantum-mechanical calculation of the solid-state equilibrium MgO+alpha-Al2O3-reversible-arrow-MgAl2O4 (spinel) versus pressure. Physical Review, B49(20), 14179-14187. Darco, P., Sandrone, G., Dovesi, R., Orlando, R., Saunders, V.R. (1993) A Quantum Mechanical Study of the Perovskite Structure Type of MgSiO3. Physics and Chemistry of Minerals, 20, 407-414. Dovesi, R., Saunders, V.R., Roetti, C., Causa, M., Harrison, N.N., Orlando, R., and Apra, E. (1996) CRYSTAL95 User's Manual. 170 p, Torino, Italy. Gatti, C. (1997) TOPOND96 User's Manual. 15 p, Milano, Italy. Gibbs, G.V., Boisen, M.B., Beverley, L.L., and Rosso, K.M. (2001) A computational quantum chemical study of the bonded interactions in Earth materials and structurally and chemically related molecules. In R.T. Cygan and J.D. Kubicki, Ed. Molecular Modeling Theory: Applications in the Geosciences, 42, p. 345-376. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Washington, D.C. Gibbs, G.V., Cox, D.F., Crawford, T.D., Boisen, M.B., Jr., and Lim, M. (2002) A mapping of the electron localization function for the silica polymorphs: evidence for domains of electron pairs and sites of potential electrophilic attack. Physics and Chemistry of Minerals, 29(5), 307-318.
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Gibbs, G.V., Cox, D.F., and Ross, N.L. (2004) A modeling of the structure and favorable H-docking sties and defects for the high-pressure silica polymorph stishovite. Phys. Chem. Minerals, 31, 232-239 Gillespie, R.J. (1991) The VSEPR model of molecular geometry. 248 p. Allyn and Bacon, Boston, MA. Grobety, B.H.a.V., D. (1995) HRTEM-study of stacking faults and polytypism in kyanite. European Journal of Mineralogy, 7, 807-818. Jacobsen, S.D., Demouchy, S., Frost, D.J., Ballaran, T.,B., and Kung, J. (2005) A systematic study of OH in hydrous wadsleyite from polarized FTIR spectroscopy and single-crystal X-ray diffraction: Oxygen sites for hydrogen storage in Earth's interior. American Mineralogist, 90, 61-70. Lewis, G.N. (1916) The atom and the molecule. Journal of the American Chemical Society, 38, 762-785. Lewis, G.N. (1966) Valence and the structure of atoms and molecules. Dover Press, New York, New York. Libowitzky, E., and Rossman, G. R. (1997) An IR absorption calibration for water in minerals. American Mineralogist, 82, 1111-1115. MacDougall, P.J. (1989) The Laplacian of the electron charge distribution. Ph.D. Thesis, p. 128. McMaster University. McCarthy, M.I.a.H., N.M. (1994) Ab initio determination of the bulk properties of MgO. Phiscal Review, B49, 8574-8582. Panero, W.R., and Stixrude, L.P. (2004) Hydrogen incorporation in stishovite at high pressure and symmetric hydrogen bonding in δ-AlOH. Earth and Planetary Science Letters, 221, 421-431. Pawley, A.R., McMillan, P.F., and Holloway, J.R. (1993) Hydrogen in Stishovite, with Implications for Mantle Water Content. Science, 261, 1024-1026. Pisani, C. (1996) Quantum Mechanical Ab Initio Calculation of the Properties of Crystalline Materals. 328 p. Springer-Verlag. Pisani, C., Dovesi, R., Roetti, C., Causa, M., Orlando, R., Casassa, S., and Saunders, V.R.,. (2000) CRYSTAL and EMBED, two computational tools for the ab initio study of electronic properties of crystals. International Journal of Quantum Chemistry, 77, 1032-1048.
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Ross, N.L., Gibbs, G.V., and Rosso, K.M. (2003) Potential docking sites and positions of hydrogen in high-pressure silicates. American Mineralogist, 88, 1452-1459. Rossman, G.R. (1996) Studies of OH in nominally anhydrous minerals. Physics and Chemistry of Minerals, 23, 299-304. Rossman, G.R. and Smith, J.R. (1990) Hydroxyl contents of accessory minerals in mantle eclogites and related rocks. American Mineralogist, 75, 775-780. Wilkins, R.W.T., and Sabine, W. (1973) Water content of some nominally anhydrous silicates. American Mineralogist, 58, 508-516.
99
Chapter 5
Conclusions
Experimental and theoretical studies on the Al2SiO5 polymorphs have been
conducted in order to gain better understand their crystal chemistry, equation of state,
chemical bonding, and incorporation of trace elements such as hydrogen in their
structures. This powerful combination of experimental and theoretical methods provides
a methodology that may be applied to understanding the structure-property relations of
other mineral systems.
High-pressure single-crystal X-ray diffraction studies of andalusite and sillimanite
have resolved discrepancies about the bulk moduli, the pressure derivatives of their bulk
moduli with pressure, and the effect of pressure on their crystal structures. The bulk
moduli are 144.2(7) GPa and 164(1) GPa with K’ values of 6.8(2) and 5.0(3) for
andalusite and sillimanite, respectively. The esd’s of the bulk moduli measured in this
study are a factor of seven lower than previously published values. In addition, this study
has shown that K’ is not equal to 4 as commonly assumed for many crustal minerals and
therefore the equation of state of andalusite and sillimanite must be represented with a
third-order Birch-Murnaghan equation of state. A similar study is needed for kyanite, but
unfortunately it is very difficult to find high-quality single crystals required for a study
such as this.
In andalusite and sillimanite, the main structural response to pressure is
compression of the AlO6 octahedra. However, in andalusite, the more compressible
phase, compression of the AlO6 octahedra is more anisotropic. Moreover, there is
significant compression of the AlO5 polyhedra in the structure of andalusite whereas
there is no significant change in the volume of the AlO4 tetrahedra of sillimanite with
pressure. The SiO4 tetrahedra in andalusite and sillimanite do not show any significant
compression with pressure and can be considered as rigid units in the structures. It is
therefore the relative compression of the individual Al-O bonds that controls the axial
100
compression of both structures which is highly nonlinear and highly anisotropic, with the
c-axis being the least compressible axis in both structures. This study illustrates how an
understanding of the structure and bonding at the atomic scale can be related to
macroscopic thermodynamic properties such as the bulk modulus.
In order to understand more fully the character of the Al-O and Si-O bonding in
the Al2SiO5 polymorphs, ELF isosurfaces were constructed which provide graphical
representations of spatial localization of the probability electron density distribution for
the bonded and nonbonded regions in the crystal structures. This is the first study that
focuses on the role of aluminum in structures containing a variety of coordination
environments, including AlO4, AlO5 and AlO6. It is also one of the first studies that
investigate the role of anions and their coordination environment in the structure. The
Al2SiO5 polymorphs have a wide variety of oxygen sites, ranging from 2-, 3- and 4-
coordinated sites. There are six distinct ELF isosurfaces surrounding the oxygen anions
in the Al2SiO5 polymorphs and there shapes are dependent on the geometry of the
surrounding cations, their coordination number, and the atomic number of the
surrounding cations. This is explicitly seen in the 3-coordinated oxygens where the
maximum ELF value increases with increasing distance of the oxygen from a plane
defined by the three surrounding cations. Furthermore, there is a change in the ELF
isosurfaces when the oxygens are greater than 0.2Å from the cation defined plane. The
change is shape of the ELF isosurfaces has been attributed to a change in hybridization of
the oxygen atoms, sp2 to sp3. The shapes of the ELF isosurfaces have also been used
qualitatively to examine the nature of the bonds within the structures where the Al-O
bond has greater ionic character due to the diffuse ELF isosurface then the Si-O bond,
more covalent, as seen in the 2-coordinated oxygen, Al-O-Si, in sillimanite. In addition,
the ELF isosurfaces have been shown to be isostructurally homeomorphic to electron
density difference maps of the Al2SiO5 polymorphs, suggesting the ELF isosurface maps
may provide a useful tool for visualization of electron density in crystal structures.
The objective of third part of the project was to understand, at the atomic level,
the interaction of protons in the Al2SiO5 polymorphs and to identify potential sites for
101
protonation in their structures. This study combined experimental and theoretical
techniques that fully complement one another. Polarized FTIR spectroscopy in
combination with calculations of the (3,-3) critical points of the negative Laplacian were
used to determine the location and orientation of potential protonation sites. Polarized
FTIR spectroscopy indicates that the OH dipole is located in the (001) planes of
andalusite and sillimanite and within the (111) plane of kyanite. The (3,-3) critical points
were used to determine which oxygens are most likely to be protonated. The (3,-3)
critical points reveal regions of locally concentrated electron density and examination of
the critical points associated with the 3-coordinated oxygens reveal that the Laplacian
values increase with increasing distance of the oxygen from a plane defined by the
surrounding cations. This situation is fortuitously similar to the ELF study and shows a
correlation between the ELF and the electron density. Potential protonation sites are
expected to occur at critical points with high Laplacian values. In andalusite and
sillimanite we see that, if hydrogen were to form hydroxyl groups with the oxygens
corresponding to the largest Laplacian values, then those hydroxyls would be oriented
within (001) corresponding well with results from the polarized FTIR study.
Additionally, we see that O-H bonds corresponding to the polarized FTIR can also be
located at the underbonded oxygens. This indicates that potential protonation sites in
andalusite and sillimanite correspond with the largest Laplacian values and the
underbonded oxygens. In kyanite, potential protonation sites corresponding with the
polarized FTIR are located on the 4-coordinated oxygen atoms in contrast to the 3-
coordinated oxygens in andalusite and sillimanite. Thus, hydrogen positions in the
Al2SiO5 polymorphs are dependent on the value of the Laplacian, the underbonded nature
of the oxygens, and the geometry of the coordinated oxygens.
In conclusion, the Al2SiO5 polymorphs have been examined at the atomic scale
with both experimental and theoretical methods in order to better understand how
bonding changes with structure, how bonding controls their compression, and how
potential sites for electrophilic attack by protons can be identified through studies of the
electron density. The equation of state data presented in this dissertation will provide
important input into thermodynamic databases that are not only used to calculate the
102
triple point of the Al2SiO5 polymorphs, but are also be used to calculate the phase
equilibria of other mineral reactions involving andalusite and sillimanite. The ELF has
shown how the probability electron density distribution is dependent of the environment
of the oxygen anions and that it can be used as a proxy for electron density. The ELF
isosurfaces may be used in the future to examine favorable sites for electrophilic attack in
minerals based on the shape and geometry of the oxygens and their surrounding cations.
A systematic investigation of the ELF isosurfaces in a variety of mineral structures will
also form the basis for new insights that will advance our understanding of crystal
chemistry. Finally, potential protonation sites in the Al2SiO5 polymorphs were examined
by evaluating the critical point properties of the electron density leading to a spatial
mapping of sites of potential electrophilic distribution in the structures that were
compared with polarized FTIR spectra. This methodology can be used to determine the
protonation sites in other nominally anhydrous minerals and may therefore be used in the
future to understand the role of water in deep mantle minerals where any water, if
present, is most likely incorporated in the form of hydroxyl in phases such as
(Mg,Fe)SiO3 perovskite, stishovite and post-stishovite phases, and magnesiowustite,
(Mg,Fe)O. This methodology may also be applied to mineral reactions that occur at the
Earth’s surface as it can not only identify potential sites for electrophilic attack, but it can
also identify potential sites for nucleophilic attack. We anticipate that this coupling of
knowledge of the electron density distribution of earth-forming materials with
experimental measurements will significantly advance the fields of mineralogy, petrology
and geochemistry.
103
Appendix 1
The variation in bulk moduli reported in the literature for andalusite and sillimanite can be correlated to a range for the phase boundary between the two polymorphs by: At phase boundary (values from Table 1):
1
0 (P
o oT T TG H T S V P T∆ = = ∆ − ∆ + ∆∫ , )dP
mol
mol
at 298.15 K: ( 2589660 2586370) 3290 /
(91.60 95.08) 3.48 /
oT
oT
H j
S j
∆ = − + = −
∆ = − = −
298.15( 3.48) 3290 2252.44 /o oT TT S H j mol∆ −∆ = − + =
From the Murnaghan equation of state:
(1 1/ '),
1
'( , ) 1 1' 1
KPT T o
T
K V PKV P T dpK K
−⎡ ⎤⎛ ⎞⎢ ⎥∆ = +⎜ ⎟−
−⎢ ⎥⎝ ⎠⎣ ⎦
∫
Andalusite: Upper Limit: KTO=125GPa K’=4 VT,O=51.34cm3/mol
33/ 4
,1
(125 )(51.34 / ) 4(1 ) 14 1 125
P
T PGPa cm mol PV dp
GPa⎡ ⎤= + −⎢ ⎥− ⎣ ⎦∫
3 342139.17 (1 ) 2139.17125
cm P cmGPa GPamol GPa mol
= + −
1Pa= 1J/m3 3 9
31 10 12139.17 ( )( ) 21391701 100
cm Pa m JGPamol GPa cm mol
×=
42139170 (1 ) 2139170125
J Pmol GPa mol
= + −J
Lower Limit: KTO=154 GPa K’=4 VT,O=51.34 cm3/mol
33/ 4
,1
(154 )(51.34 / ) 4(1 ) 14 1 154
P
T PGPa cm mol PV dp
GPa⎡ ⎤= + −⎢ ⎥− ⎣ ⎦∫
3 342635.45 (1 ) 2635.45154
cm P cmGPa GPamol GPa mol
= + −
1Pa= 1J/m3 3 9
31 10 12635.45 ( )( ) 2635453.331 100
cm Pa m JGPamol GPa cm mol
×=
42635453.33 (1 ) 2635453.33154
J Pmol GPa mol
= + −J
104
Sillimanite:
Upper Limit: KTO=164 K’=4 VT,O=49.88cm3/mol
33/ 4
,1
(164 )(49.88 / ) 4(1 ) 14 1 164
P
T PGPa cm mol PV dp
GPa⎡ ⎤= + −⎢ ⎥− ⎣ ⎦∫
3 342726.77 (1 ) 2726.77164
cm P cmGPa GPamol GPa mol
= + −
1Pa= 1J/m3 3 9
31 10 12726.77 ( )( ) 27267701 100
cm Pa m JGPamol GPa cm mol
×=
42726770 (1 ) 2726770164
J P Jmol GPa mol
= + −
Lower Limit: KTO=187 GPa K’=4 VT,O=49.88cm3/mol
33/ 4
,1
(187 )(49.88 / ) 4(1 ) 14 1 187
P
T PGPa cm mol PV dp
GPa⎡ ⎤= + −⎢ ⎥− ⎣ ⎦∫
3 343109.18 (1 ) 3109.18
187cm P cmGPa GPamol GPa mol
= + −
1Pa= 1J/m3 3 9
31 10 13109.18 ( )( ) 3109186.671 100
cm Pa m JGPamol GPa cm mol
×=
43109186.67 (1 ) 3109186.67187
J Pmol GPa mol
= + −J
Determination of the pressure for the phase boundary at 298 K for the upper and lower bulk moduli limits.
1
( , )P
o oT TT S H V P T dP∆ −∆ = ∆∫
Lower Limit:
, ,1 1 1
( , )and sill
and sill
P PP
T P T PV P T dP V dp V dp∆ = −∫ ∫ ∫
42252.44 / (2635453.33 (1 ) 2635453.33 )154
4(3109186.67 (1 ) 3109186.67 )187
J P Jj molmol GPa molJ P J
mol GPa mol
= + −
+ −
−
P = 1.59994 GPa
(pressure calculated with an excel spreadsheet)
105
Upper Limit:
, ,1 1 1
( , )and sill
and sill
P PP
T P T PV P T dP V dp V dp∆ = −∫ ∫ ∫
42252.44 / (2139166.66 (1 ) 2139166.66 )125
4(2726773.33 (1 ) 2726773.33 )164
J Pj molmol GPa mol
J Pmol GPa mol
= + −
+ −
J
J
r
P = 1.637136 GPa
(pressure calculated with an excel spreadsheet)
Range in pressure between upper and lower phase boundary at 298 K:
1.637136 1.5994 0.0372 372low highP P GPa GPa GPa ba− = − = =
In the pressure and temperature range examined above neither andalusite nor sillimanite is stable, but this exercise can still examine the range in the phase boundary for any pressure and temperature with variations in bulk moduli. These calculations were determined at room temperature because for calculations at higher temperature the thermal expansion coefficient and the heat capacity data will be required in the calculations.
106
107
Appendix 2 Structure factor's after corrected for absorption and hkl values for the X-ray diffraction study of andalusite and sillimanite. Sillimanite P = 0.0001 GPa
h k l FO esd. h k l FO esd. -13 0 1 1.8642 0.088 0 0 -4 29.7530 0.302 -13 0 -1 1.6414 0.103 0 0 -2 14.4047 0.108 -12 -1 0 2.5768 0.102 0 0 2 14.3096 0.104 -12 -1 -2 2.3679 0.077 0 0 4 31.4800 0.311 -12 0 4 0.8062 0.189 0 0 6 6.8531 0.11 -12 1 2 2.4005 0.089 0 0 8 14.1901 0.182 -12 1 0 2.8937 0.101 0 2 -4 1.9635 0.035 -11 1 -1 0.9391 0.132 0 2 3 1.4652 0.056 -11 1 0 2.5397 0.066 0 2 4 2.2909 0.057 -11 1 1 1.0796 0.137 0 2 6 1.9689 0.052 -11 1 2 2.0707 0.122 1 2 8 6.0036 0.175 -11 1 4 2.1455 0.077 1 2 7 0.6970 0.15 -11 0 5 0.6186 0.212 1 2 6 9.5816 0.113 -11 -1 -4 2.0950 0.073 1 2 5 1.8975 0.045 -11 -1 -2 2.2924 0.067 1 2 4 11.0115 0.115 -11 -1 -1 1.1443 0.097 1 2 -4 11.2899 0.128 -11 -1 0 2.4875 0.084 1 2 -5 1.7530 0.057 -11 -1 2 2.2430 0.071 1 1 -8 1.7315 0.072 -10 -2 -2 1.8374 0.064 1 1 -6 7.7189 0.106 -10 -2 0 4.2279 0.14 1 1 -5 1.0653 0.07 -10 -1 4 1.5972 0.094 1 1 -4 3.0818 0.088 -10 -1 2 2.2366 0.07 1 1 -3 3.1854 0.21 -10 -1 0 2.3236 0.056 1 1 -2 13.7120 0.107 -10 -1 -2 2.4096 0.057 1 1 2 13.8867 0.1 -10 -1 -6 1.8454 0.086 1 1 3 3.5553 0.269 -10 0 -6 7.9384 0.167 1 1 4 3.3243 0.086 -10 0 -4 4.7173 0.126 1 1 6 7.7625 0.109 -10 0 -2 10.6987 0.18 1 1 8 1.5783 0.079 -10 0 0 5.1737 0.136 1 1 9 1.1670 0.114 -10 0 2 10.9179 0.143 1 1 10 2.9500 0.068 -10 0 4 4.6015 0.143 1 0 9 1.6656 0.083 -10 0 6 7.2387 0.158 1 0 5 2.1845 0.052 -10 1 2 2.4509 0.065 1 0 1 2.5043 0.046 -10 1 0 2.2284 0.083 1 0 -1 2.5946 0.053 -10 1 -4 1.8417 0.076 1 0 -3 1.8551 0.098 -10 2 2 1.9396 0.073 1 0 -5 2.2682 0.046 -9 2 4 6.5939 0.14 1 0 -9 1.6125 0.086 -9 2 2 8.5400 0.135 1 -1 -10 3.3662 0.097 -9 2 1 0.8701 0.114 1 -1 -8 1.7270 0.085
108
-9 2 0 7.5792 0.136 1 -1 -7 1.2037 0.09 -9 1 -4 4.3599 0.144 1 -1 -6 7.7739 0.106 -9 1 -2 2.5844 0.074 1 -1 -5 1.1764 0.059 -9 1 -1 1.9411 0.06 1 -1 -4 3.3267 0.119 -9 1 0 5.1853 0.124 1 -1 -3 3.7676 0.171 -9 1 1 1.7678 0.09 1 -1 -2 13.8502 0.119 -9 1 2 2.4916 0.051 1 -1 2 12.6221 0.112 -9 1 3 2.4329 0.055 1 -1 3 2.8446 0.176 -9 1 4 4.0508 0.141 1 -1 4 3.0434 0.112 -9 1 6 1.7086 0.091 1 -1 5 1.0097 0.061 -9 0 5 0.9404 0.123 1 -1 6 7.3858 0.153 -9 -1 -7 1.9363 0.094 1 -1 7 1.1857 0.093 -9 -1 -6 1.3965 0.137 1 -2 5 1.6562 0.049 -9 -1 -4 3.9778 0.139 1 -2 4 9.2882 0.091 -9 -1 -3 2.1747 0.064 1 -2 -4 11.4225 0.12 -9 -1 -2 2.5175 0.082 1 -2 -5 1.8804 0.053 -9 -1 -1 1.9066 0.055 1 -2 -6 9.6908 0.118 -9 -1 0 5.1602 0.132 1 -2 -8 5.8054 0.14 -9 -1 1 1.9757 0.054 2 -2 -8 4.6028 0.172 -9 -1 2 2.5587 0.077 2 -2 -6 2.3214 0.048 -9 -1 3 2.1697 0.071 2 -2 -4 8.8904 0.1 -9 -1 4 4.0813 0.152 2 -2 -2 2.7998 0.083 -9 -1 5 1.0644 0.11 2 -2 4 6.9718 0.109 -9 -2 2 7.8095 0.136 2 -1 8 4.7842 0.18 -9 -2 1 0.4880 0.166 2 -1 6 2.5403 0.054 -9 -2 0 7.3513 0.115 2 -1 4 11.1480 0.163 -9 -2 -2 8.2228 0.132 2 -1 2 1.0903 0.03 -9 -2 -3 1.4216 0.075 2 -1 1 1.6170 0.031 -9 -2 -4 6.0117 0.159 2 -1 0 18.3424 0.198 -8 -2 -4 1.4751 0.067 2 -1 -1 1.6671 0.037 -8 -2 0 1.7681 0.06 2 -1 -2 1.1334 0.031 -8 -2 1 1.6711 0.054 2 -1 -3 1.3974 0.047 -8 -1 6 3.0069 0.055 2 -1 -4 12.2073 0.134 -8 -1 4 4.3058 0.167 2 -1 -6 2.8826 0.06 -8 -1 2 4.9610 0.136 2 -1 -8 5.6507 0.144 -8 -1 1 2.4331 0.044 2 -1 -10 1.1920 0.155 -8 -1 0 5.5609 0.11 2 0 -8 1.5901 0.079 -8 -1 -1 2.7242 0.07 2 0 -6 6.3574 0.11 -8 -1 -2 4.8253 0.124 2 0 -4 3.8984 0.112 -8 -1 -3 2.0689 0.06 2 0 -2 9.9030 0.092 -8 -1 -4 4.1657 0.141 2 0 0 6.8642 0.063 -8 -1 -6 3.1041 0.126 2 0 2 9.3010 0.086 -8 -1 -7 1.2846 0.111 2 0 4 3.8229 0.098 -8 -1 -8 2.0049 0.084 2 0 6 6.3147 0.105 -8 0 -4 10.7464 0.142 2 1 8 5.6931 0.163 -8 0 0 13.7912 0.172 2 1 6 2.8320 0.069 -8 0 2 0.8819 0.101 2 1 4 12.2083 0.117 -8 0 4 11.0644 0.115 2 1 3 1.2838 0.034 -8 1 6 3.4087 0.123 2 1 2 1.1722 0.029 -8 1 4 4.5202 0.163 2 1 1 1.6601 0.038 -8 1 3 2.2516 0.053 2 1 0 19.0457 0.219
109
-8 1 2 5.1284 0.114 2 1 -1 1.5453 0.058 -8 1 1 2.2742 0.047 2 1 -2 1.0468 0.044 -8 1 0 5.2410 0.119 2 1 -3 1.4609 0.032 -8 1 -1 2.3464 0.068 2 1 -4 12.1367 0.132 -8 1 -2 4.9723 0.133 2 1 -6 2.7895 0.07 -8 1 -3 2.2135 0.057 2 1 -8 5.6998 0.141 -8 1 -4 4.5366 0.119 2 2 -4 8.9516 0.105 -8 1 -5 1.8834 0.067 2 2 2 2.6425 0.067 -8 1 -6 3.5646 0.122 2 2 3 0.9947 0.043 -8 2 -2 0.5125 0.166 2 2 4 8.8070 0.103 -8 2 -1 1.4808 0.066 2 2 6 2.3577 0.052 -8 2 0 1.7504 0.057 2 2 7 0.7378 0.135 -8 2 1 1.7489 0.056 2 2 8 4.7009 0.132 -8 2 4 1.5957 0.095 3 2 8 2.5355 0.073 -7 2 4 1.9345 0.074 3 2 7 1.5007 0.078 -7 2 1 0.8491 0.087 3 2 6 4.4194 0.133 -7 2 0 2.2555 0.071 3 2 4 4.4159 0.104 -7 1 -6 4.6738 0.145 3 2 3 2.2082 0.06 -7 1 -4 2.0292 0.062 3 2 2 8.5131 0.095 -7 1 -2 7.8223 0.105 3 2 -3 2.2562 0.049 -7 1 0 2.6113 0.059 3 2 -4 4.2691 0.098 -7 1 2 7.8812 0.138 3 1 -8 3.0817 0.1 -7 1 4 2.1228 0.053 3 1 -6 3.2695 0.09 -7 1 6 5.0790 0.151 3 1 -5 1.8615 0.056 -7 1 7 1.1844 0.109 3 1 -4 5.3243 0.091 -7 0 7 2.6335 0.075 3 1 -2 8.4459 0.153 -7 0 5 1.8846 0.076 3 1 -1 1.0697 0.036 -7 0 3 3.8670 0.15 3 1 0 2.5059 0.068 -7 0 1 3.3681 0.117 3 1 2 8.4423 0.131 -7 0 -1 3.7767 0.106 3 1 4 5.0292 0.097 -7 0 -3 3.7494 0.11 3 1 5 1.8277 0.059 -7 0 -5 1.8536 0.096 3 1 6 3.0649 0.079 -7 0 -7 2.7083 0.072 3 1 7 0.7645 0.13 -7 -1 -8 1.3221 0.103 3 1 8 2.8384 0.085 -7 -1 -6 4.7631 0.142 3 1 9 1.6907 0.1 -7 -1 -4 1.9676 0.055 3 0 9 1.1963 0.133 -7 -1 -2 7.4537 0.1 3 0 5 1.0958 0.076 -7 -1 0 2.8006 0.086 3 0 1 1.4353 0.036 -7 -1 2 7.7371 0.122 3 0 -1 1.4699 0.031 -7 -1 4 1.9789 0.058 3 0 -3 1.0148 0.048 -7 -1 6 4.3315 0.144 3 0 -5 2.3616 0.08 -7 -2 4 1.7529 0.058 3 0 -9 0.9026 0.149 -7 -2 0 2.2454 0.069 3 -1 -10 1.7915 0.093 -7 -2 -4 1.9492 0.053 3 -1 -8 2.9743 0.09 -6 -2 -6 3.5619 0.089 3 -1 -7 0.9168 0.11 -6 -2 -5 1.3259 0.068 3 -1 -6 3.0914 0.108 -6 -2 -4 3.4084 0.107 3 -1 -5 1.6920 0.055 -6 -2 -3 1.6986 0.047 3 -1 -4 5.2187 0.107 -6 -2 -2 5.5919 0.098 3 -1 -3 0.6526 0.069 -6 -2 -1 1.8025 0.04 3 -1 -2 8.4623 0.12 -6 -2 0 4.7761 0.092 3 -1 0 2.7195 0.073
110
-6 -2 1 1.6882 0.043 3 -1 1 0.9578 0.033 -6 -2 2 5.3868 0.095 3 -1 2 8.2199 0.143 -6 -2 3 1.3673 0.061 3 -1 5 1.6285 0.068 -6 -2 4 3.3441 0.09 3 -1 8 2.4966 0.058 -6 -1 6 0.4295 0.215 3 -2 3 1.9388 0.036 -6 -1 5 1.7108 0.068 3 -2 -2 8.8718 0.086 -6 -1 4 6.6038 0.11 3 -2 -3 2.2689 0.042 -6 -1 3 2.0332 0.046 3 -2 -4 4.7578 0.123 -6 -1 1 2.5995 0.063 3 -2 -6 4.5327 0.133 H K L Intensity Esd H K L Intensity Esd -6 -1 0 9.1533 0.11 3 -2 -7 1.4767 0.091 -6 -1 -1 2.7177 0.07 3 -2 -8 2.6090 0.062 -6 -1 -3 1.8005 0.085 4 -2 -8 5.7168 0.153 -6 -1 -4 6.1424 0.117 4 -2 -6 3.9901 0.134 -6 -1 -5 1.6716 0.062 4 -2 -4 11.6628 0.142 -6 -1 -8 3.2264 0.098 4 -2 -2 8.3302 0.106 -6 0 -6 3.9521 0.13 4 -2 0 15.4998 0.172 -6 0 -4 13.4404 0.164 4 -2 1 0.3806 0.104 -6 0 -2 6.4828 0.111 4 -2 2 7.1850 0.104 -6 0 0 17.7927 0.185 4 -2 4 9.5720 0.109 -6 0 2 6.6346 0.109 4 -1 4 3.9230 0.097 -6 0 4 14.4682 0.156 4 -1 2 4.3854 0.077 -6 0 6 4.0518 0.12 4 -1 1 1.7919 0.099 -6 0 8 7.1048 0.153 4 -1 0 4.9051 0.174 -6 1 9 0.8115 0.202 4 -1 -1 2.0183 0.08 -6 1 8 3.2615 0.115 4 -1 -2 4.7851 0.089 -6 1 7 0.9762 0.12 4 -1 -4 3.8748 0.108 -6 1 5 1.9171 0.058 4 -1 -6 3.0752 0.086 -6 1 4 6.5760 0.105 4 -1 -8 2.1571 0.091 -6 1 3 2.0458 0.049 4 0 -8 5.1841 0.176 -6 1 1 2.7956 0.095 4 0 -6 9.7283 0.119 -6 1 0 8.9855 0.082 4 0 -4 10.2013 0.123 -6 1 -1 2.6297 0.073 4 0 -2 14.8771 0.156 -6 1 -3 1.9671 0.083 4 0 0 16.5863 0.2 -6 1 -4 6.4944 0.109 4 0 2 14.0646 0.14 -6 1 -5 1.8660 0.058 4 0 4 9.5367 0.121 -6 2 -4 3.3426 0.13 4 0 6 8.9066 0.163 -6 2 -3 1.6925 0.057 4 0 8 4.7422 0.14 -6 2 -2 5.6090 0.097 4 1 8 2.1189 0.07 -6 2 0 4.8053 0.108 4 1 6 3.0370 0.083 -6 2 1 1.5669 0.055 4 1 4 3.8505 0.116 -6 2 2 5.6382 0.097 4 1 2 4.6832 0.075 -6 2 4 3.5436 0.137 4 1 0 4.7463 0.176 -6 2 6 3.3693 0.112 4 1 -1 2.3213 0.167 -5 2 6 9.5456 0.14 4 1 -2 4.6073 0.083 -5 2 5 2.8407 0.077 4 1 -4 4.2224 0.097 -5 2 4 11.1063 0.128 4 1 -6 3.0778 0.1 -5 2 3 1.5435 0.049 4 2 -4 11.6916 0.109 -5 2 2 15.0764 0.152 4 2 -2 8.3559 0.112 -5 2 1 3.2811 0.109 4 2 0 17.2253 0.206 -5 2 0 13.9547 0.154 4 2 2 8.0882 0.1
111
-5 2 -1 3.2779 0.113 4 2 4 11.1827 0.144 -5 2 -2 15.2944 0.153 4 2 6 3.8921 0.131 -5 2 -3 1.5506 0.048 4 2 8 5.8792 0.178 -5 2 -4 10.4385 0.109 5 2 8 6.1072 0.169 -5 1 -4 2.5266 0.08 5 2 6 9.2779 0.128 -5 1 -3 2.7486 0.154 5 2 4 10.3820 0.133 -5 1 -2 7.5785 0.101 5 2 2 14.8662 0.172 -5 1 -1 1.7750 0.039 5 2 1 3.3872 0.112 -5 1 0 2.7951 0.089 5 2 0 14.2676 0.171 -5 1 1 1.8427 0.046 5 2 -1 3.4496 0.09 -5 1 2 7.8668 0.092 5 2 -2 15.5354 0.177 -5 1 3 2.6466 0.073 5 2 -3 1.7071 0.072 -5 1 4 2.8734 0.077 5 2 -4 11.0456 0.119 -5 1 6 4.6249 0.129 5 2 -5 2.7757 0.106 -5 1 7 2.2869 0.072 5 1 -7 2.1368 0.063 -5 0 7 1.3760 0.088 5 1 -6 4.5596 0.128 -5 0 3 2.1151 0.086 5 1 -4 3.0066 0.117 -5 0 -1 0.9610 0.062 5 1 -3 2.6832 0.076 -5 -1 -7 1.9889 0.068 5 1 -2 7.9513 0.099 -5 -1 -6 4.4722 0.127 5 1 -1 1.7756 0.04 -5 -1 -4 2.8692 0.079 5 1 0 3.0293 0.09 -5 -1 -3 2.5794 0.072 5 1 1 1.6427 0.039 -5 -1 -2 7.6240 0.091 5 1 2 7.7465 0.111 -5 -1 -1 1.7581 0.038 5 1 3 2.6228 0.057 -5 -1 0 2.7585 0.067 5 1 4 2.7651 0.075 -5 -1 1 1.6949 0.039 5 1 5 0.6716 0.123 -5 -1 2 8.0432 0.11 5 1 6 4.3289 0.129 -5 -1 3 2.6625 0.075 5 1 7 1.9818 0.068 -5 -1 4 2.7371 0.045 5 0 3 1.7420 0.068 -5 -1 6 4.3725 0.156 5 0 1 0.9731 0.05 -5 -1 7 2.0353 0.072 5 0 -1 1.0376 0.048 -5 -2 5 2.6233 0.094 5 0 -3 2.0189 0.073 -5 -2 4 9.9399 0.123 5 0 -5 0.5165 0.149 -5 -2 2 14.9863 0.171 5 0 -7 1.1691 0.11 -5 -2 1 3.3732 0.096 5 -1 -8 0.9357 0.172 -5 -2 0 14.1086 0.149 5 -1 -7 1.9802 0.068 -5 -2 -1 3.3531 0.099 5 -1 -6 4.8675 0.132 -5 -2 -2 15.1686 0.168 5 -1 -4 2.7845 0.067 -5 -2 -3 1.6393 0.043 5 -1 -3 2.8069 0.073 -5 -2 -4 10.5906 0.133 5 -1 -2 7.7511 0.102 -5 -2 -5 2.8283 0.06 5 -1 -1 1.7323 0.044 -5 -2 -6 9.4868 0.125 5 -1 0 2.7218 0.068 -5 -2 -7 0.6919 0.162 5 -1 1 1.7534 0.037 -5 -2 -8 5.9104 0.167 5 -1 2 7.3625 0.112 -4 -2 -8 5.2589 0.169 5 -1 3 2.4603 0.117 -4 -2 -6 3.8820 0.124 5 -1 4 2.4723 0.077 -4 -2 -4 11.8856 0.134 5 -1 6 4.1558 0.118 -4 -2 -2 8.0887 0.082 5 -2 4 8.6765 0.129 -4 -2 0 16.6414 0.176 5 -2 2 13.0043 0.165 -4 -2 2 7.7128 0.1 5 -2 1 2.8926 0.094 -4 -2 4 10.6143 0.119 5 -2 0 13.3584 0.161
112
-4 -1 6 3.0952 0.091 5 -2 -1 3.8750 0.108 -4 -1 4 4.1849 0.112 5 -2 -2 15.4154 0.183 -4 -1 2 4.7639 0.079 5 -2 -3 1.7222 0.045 -4 -1 0 5.5469 0.149 5 -2 -4 10.7866 0.139 -4 -1 -2 4.5702 0.094 5 -2 -5 2.7999 0.073 -4 -1 -4 4.2513 0.096 5 -2 -6 9.7824 0.128 -4 -1 -6 3.1817 0.089 6 -2 -7 0.6387 0.193 -4 -1 -8 2.2162 0.109 6 -2 -6 3.9257 0.101 -4 0 -8 5.6254 0.144 6 -2 -4 3.7206 0.101 -4 0 -6 9.6681 0.152 6 -2 -2 5.6351 0.11 -4 0 -4 10.1849 0.103 6 -2 -1 1.4655 0.051 -4 0 -2 14.1475 0.137 6 -2 0 4.5715 0.105 -4 0 0 16.5003 0.18 6 -2 2 5.0122 0.121 -4 0 2 14.5288 0.132 6 -2 4 2.8866 0.075 -4 0 4 10.0852 0.102 6 -1 5 1.8450 0.065 -4 0 6 9.9892 0.111 6 -1 4 6.1114 0.121 -4 0 8 4.7392 0.153 6 -1 3 1.7487 0.055 -4 1 9 0.8413 0.156 6 -1 1 2.7064 0.065 -4 1 8 2.1539 0.09 6 -1 0 8.7698 0.122 -4 1 6 3.0844 0.069 6 -1 -1 2.7191 0.078 -4 1 4 4.2697 0.097 6 -1 -3 2.1873 0.068 -4 1 2 4.7061 0.076 6 -1 -4 6.6114 0.127 -4 1 1 2.1080 0.143 6 -1 -5 1.8903 0.058 -4 1 0 5.1055 0.132 6 -1 -8 3.5771 0.118 -4 1 -2 4.6787 0.075 6 0 -8 8.3564 0.153 -4 1 -3 0.6083 0.083 6 0 -6 4.4247 0.135 -4 1 -4 4.2031 0.097 6 0 -4 14.3615 0.163 -4 1 -6 3.1607 0.091 6 0 -2 6.6043 0.103 -4 2 -4 11.2643 0.119 6 0 0 18.0442 0.206 -4 2 -3 0.4763 0.12 6 0 2 6.3807 0.11 -4 2 -2 8.4444 0.102 6 0 4 13.3374 0.179 -4 2 0 17.1831 0.177 6 0 6 3.8330 0.098 -4 2 2 8.4401 0.088 6 1 8 3.0422 0.063 -4 2 4 11.8909 0.12 6 1 5 1.7566 0.058 -4 2 6 4.0013 0.089 6 1 4 6.1105 0.123 -4 2 8 5.6348 0.203 6 1 3 1.9488 0.051 -3 2 8 2.2832 0.084 6 1 1 2.6242 0.074 -3 2 7 1.6323 0.081 6 1 0 9.0216 0.125 -3 2 6 4.6044 0.135 6 1 -1 2.6394 0.076 -3 2 4 4.1574 0.161 6 1 -3 2.0953 0.043 -3 2 3 2.4019 0.056 6 1 -4 6.7329 0.145 -3 2 2 8.9767 0.098 6 1 -5 1.9031 0.058 -3 2 -4 4.1753 0.102 6 2 -4 3.6930 0.113 -3 1 -8 3.0795 0.077 6 2 -3 1.5918 0.05 -3 1 -6 2.8075 0.131 6 2 -2 5.5693 0.115 -3 1 -5 1.9326 0.078 6 2 -1 1.5662 0.052 -3 1 -3 0.8944 0.055 6 2 0 4.5872 0.114 -3 1 -2 8.1753 0.14 6 2 2 5.4286 0.098 -3 1 0 2.5486 0.065 6 2 3 1.6135 0.057 -3 1 1 1.0736 0.033 6 2 4 3.6108 0.103 -3 1 2 8.3852 0.119 6 2 7 1.2521 0.093
113
-3 1 3 0.8910 0.061 7 2 7 1.0416 0.115 -3 1 4 5.3139 0.094 7 2 4 1.8877 0.055 -3 1 5 1.7018 0.056 7 2 0 2.2009 0.094 -3 1 6 3.1457 0.09 7 2 -4 1.8898 0.076 -3 1 8 2.8399 0.108 7 1 -6 4.9151 0.151 -3 1 10 1.4614 0.111 7 1 -2 7.5311 0.12 -3 0 9 1.3888 0.104 7 1 0 2.4709 0.112 -3 0 7 0.8119 0.191 7 1 2 7.5027 0.119 -3 0 5 1.2579 0.082 7 1 4 1.8516 0.075 -3 0 1 1.5201 0.027 7 1 6 4.3340 0.149 -3 0 -1 1.5175 0.032 7 1 8 1.4469 0.098 -3 0 -5 1.0019 0.092 7 0 7 2.6803 0.085 -3 -1 -10 2.1678 0.108 7 0 3 3.7414 0.128 -3 -1 -8 3.0403 0.096 7 0 1 3.4010 0.087 -3 -1 -6 3.1881 0.089 7 0 -1 3.6551 0.125 -3 -1 -5 1.9111 0.08 7 0 -3 3.8119 0.108 -3 -1 -4 5.3661 0.12 7 0 -5 1.9026 0.067 -3 -1 -3 0.7295 0.062 7 0 -7 2.9975 0.088 -3 -1 -2 8.1425 0.091 7 -1 -6 5.0747 0.145 -3 -1 -1 1.0821 0.033 7 -1 -4 2.1948 0.055 -3 -1 0 2.3660 0.069 7 -1 -2 7.4718 0.101 -3 -1 1 1.0431 0.03 7 -1 0 2.6948 0.06 -3 -1 2 8.3603 0.16 7 -1 2 7.5597 0.111 -3 -1 3 0.7623 0.054 7 -1 4 1.9097 0.056 -3 -1 4 5.0185 0.098 7 -1 6 4.0826 0.118 -3 -1 5 1.8616 0.058 7 -2 0 2.1379 0.047 -3 -1 6 3.1574 0.09 7 -2 -4 1.8290 0.066 -3 -1 8 2.6739 0.067 8 -2 -4 1.4405 0.081 -3 -2 4 3.7908 0.096 8 -2 -3 0.8743 0.116 -3 -2 3 2.1023 0.055 8 -2 0 1.6728 0.067 -3 -2 -1 1.1294 0.038 8 -1 6 2.7739 0.061 -3 -2 -2 8.7732 0.106 8 -1 4 4.1407 0.134 -3 -2 -3 2.3000 0.037 8 -1 3 1.9450 0.058 -3 -2 -4 4.0561 0.117 8 -1 2 4.8066 0.129 -3 -2 -6 4.5775 0.139 8 -1 1 2.3346 0.083 -3 -2 -7 1.5120 0.08 8 -1 0 5.4692 0.113 -3 -2 -8 2.3976 0.064 8 -1 -1 2.2268 0.051 -2 -2 -8 4.4326 0.149 8 -1 -2 4.9153 0.131 -2 -2 -6 2.3460 0.058 8 -1 -3 2.0285 0.058 -2 -2 -4 8.7851 0.113 8 -1 -4 4.2919 0.172 -2 -2 -2 2.7817 0.067 8 -1 -5 1.8484 0.071 -2 -2 4 7.6900 0.095 8 -1 -6 3.4150 0.069 -2 -1 8 4.6006 0.159 8 -1 -7 1.4762 0.102 -2 -1 6 2.6408 0.074 8 0 -4 11.0113 0.127 -2 -1 4 12.1049 0.121 8 0 0 13.7661 0.159 -2 -1 3 1.4554 0.036 8 0 4 10.3143 0.152 -2 -1 2 1.2307 0.027 8 1 6 3.0089 0.098 -2 -1 1 1.6574 0.085 8 1 5 1.5983 0.078 -2 -1 0 19.1732 0.185 8 1 4 4.5279 0.15 -2 -1 -1 1.5619 0.05 8 1 3 2.1881 0.064 -2 -1 -2 1.2675 0.037 8 1 2 5.1038 0.115
114
-2 -1 -3 1.3662 0.041 8 1 1 2.2166 0.062 -2 -1 -4 12.0989 0.124 8 1 0 5.3391 0.109 -2 -1 -6 2.8330 0.109 8 1 -1 2.2110 0.077 -2 -1 -8 5.7508 0.141 8 1 -2 4.8932 0.118 -2 0 -8 1.4188 0.097 8 1 -3 2.0730 0.054 -2 0 -6 6.5873 0.136 8 1 -4 4.6207 0.13 -2 0 -4 4.0605 0.098 8 1 -6 3.3068 0.087 -2 0 -2 9.9240 0.081 8 2 -3 0.9320 0.108 -2 0 0 6.9149 0.087 8 2 -1 1.5074 0.063 -2 0 2 9.8870 0.083 8 2 1 1.7432 0.053 -2 0 4 3.8098 0.102 8 2 4 1.5162 0.076 -2 0 6 6.4973 0.104 8 2 5 1.4521 0.085 -2 0 8 1.6248 0.078 9 2 4 6.0119 0.163 -2 1 8 5.8046 0.161 9 2 3 1.3512 0.081 -2 1 6 2.6767 0.068 9 2 2 8.2860 0.131 -2 1 4 12.0209 0.113 9 2 0 7.3199 0.127 -2 1 3 1.5281 0.034 9 2 -1 0.9499 0.097 -2 1 2 1.1788 0.03 9 2 -2 8.4016 0.149 -2 1 1 1.6503 0.068 9 1 -5 1.0703 0.123 -2 1 0 19.2494 0.19 9 1 -4 4.3889 0.149 -2 1 -1 1.6670 0.031 9 1 -3 2.3575 0.058 -2 1 -2 1.2102 0.033 9 1 -2 2.5329 0.109 -2 1 -3 1.4423 0.039 9 1 -1 1.9215 0.068 -2 1 -4 12.0861 0.138 9 1 0 4.9967 0.145 -2 1 -6 2.9146 0.066 9 1 1 2.0039 0.058 -2 1 -8 5.5554 0.187 9 1 2 2.5297 0.072 -2 2 -4 8.9857 0.105 9 1 3 2.3173 0.057 -2 2 2 2.8298 0.07 9 1 4 4.2075 0.143 -2 2 4 8.9491 0.111 9 0 5 0.7529 0.181 -2 2 6 2.2939 0.049 9 -1 -7 2.0039 0.091 -2 2 8 4.3467 0.171 9 -1 -6 1.7644 0.088 -1 2 8 6.1107 0.185 9 -1 -4 4.0950 0.131 -1 2 6 9.7823 0.13 9 -1 -3 2.3437 0.059 -1 2 5 1.8579 0.047 9 -1 -2 2.3709 0.08 -1 2 4 11.4850 0.112 9 -1 -1 1.9769 0.064 -1 2 -4 11.3486 0.101 9 -1 0 4.7660 0.144 -1 2 -5 1.8544 0.042 9 -1 1 1.7912 0.072 -1 1 -8 1.7598 0.069 9 -1 2 2.4111 0.053 -1 1 -6 7.6463 0.103 9 -1 3 2.1125 0.071 -1 1 -5 1.0792 0.062 9 -1 4 3.4803 0.098 -1 1 -4 3.1278 0.082 9 -2 0 6.9413 0.133 -1 1 -3 2.1716 0.101 9 -2 -2 7.8429 0.133 -1 1 -2 14.0523 0.116 9 -2 -4 5.9447 0.15 -1 1 2 13.7063 0.115 10 -1 4 1.5717 0.086 -1 1 3 3.4673 0.246 10 -1 2 0.0870 0.067 -1 1 4 3.1082 0.093 10 -1 0 1.9765 0.067 -1 1 5 1.1765 0.065 10 -1 -2 2.3933 0.074 -1 1 6 7.5660 0.114 10 -1 -6 1.7860 0.091 -1 1 7 1.2833 0.09 10 0 -6 8.0643 0.225 -1 1 8 1.5945 0.078 10 0 -4 4.6204 0.149 -1 1 10 2.8533 0.092 10 0 -2 10.9487 0.133
115
-1 0 7 0.6426 0.149 10 0 0 4.6080 0.143 -1 0 5 2.2055 0.048 10 0 2 10.0935 0.162 -1 0 1 2.6504 0.044 10 0 4 3.9043 0.159 -1 0 -1 2.6427 0.04 10 0 6 6.8908 0.161 -1 0 -5 2.2127 0.048 10 1 6 1.7182 0.089 -1 0 -7 0.7460 0.121 10 1 4 1.4620 0.098 -1 0 -9 1.6600 0.088 10 1 2 1.9479 0.07 -1 -1 -10 3.5056 0.101 10 1 0 2.5725 0.116 -1 -1 -6 7.4535 0.122 10 1 -2 2.2647 0.072 -1 -1 -4 3.4056 0.078 10 1 -4 1.8541 0.086 -1 -1 -3 4.0982 0.192 10 2 0 4.4190 0.146 -1 -1 -2 13.9544 0.118 10 2 2 2.0139 0.064 -1 -1 2 13.5235 0.121 11 1 -3 0.6918 0.238 -1 -1 4 3.1203 0.095 11 1 -2 2.2505 0.084 -1 -1 5 1.1112 0.056 11 1 0 2.6045 0.059 -1 -1 6 7.4222 0.123 11 1 2 2.2429 0.073 -1 -1 7 1.0863 0.086 11 1 4 1.8751 0.083 -1 -2 5 1.5793 0.044 11 0 1 0.5646 0.201 -1 -2 4 9.3272 0.111 11 -1 -2 2.1350 0.071 -1 -2 -4 11.3820 0.123 11 -1 0 2.3533 0.072 -1 -2 -5 1.9285 0.045 11 -1 1 1.1392 0.111 -1 -2 -6 9.8665 0.127 11 -1 2 2.0086 0.078 -1 -2 -8 5.5156 0.181 12 -1 0 2.4880 0.071 0 -2 -6 1.9080 0.055 12 -1 -2 2.1783 0.082 0 -2 -4 2.0092 0.049 12 1 2 2.3307 0.071 0 -2 -3 1.6751 0.037 12 1 0 2.6135 0.129 0 -2 4 1.7083 0.042 13 0 1 1.8569 0.087 0 0 -8 15.4171 0.231 13 0 -1 1.8767 0.091 0 0 -6 7.3419 0.1
P = 1.548(5) GPa
h k l FO Esd h k l FO Esd -13 -1 -1 0.9996 0.129 0 0 6 7.0526 0.137 -12 -1 4 1.9600 0.083 0 0 8 15.0410 0.173 -12 -1 2 2.0712 0.082 0 0 10 3.7078 0.119 -12 -1 0 2.4401 0.072 0 2 -8 0.7888 0.118 -11 -1 -4 1.7443 0.074 0 2 -6 2.0426 0.049 -11 -1 -3 1.3326 0.104 0 2 -4 2.0611 0.041 -11 -1 -2 1.8773 0.071 0 2 -3 1.5767 0.067 -11 -1 0 2.2853 0.068 0 2 4 1.5302 0.078 -11 -1 3 1.4366 0.09 0 2 6 1.7676 0.078 -11 -1 4 1.8148 0.092 1 2 6 9.4954 0.119 -11 -2 3 1.9637 0.068 1 2 5 1.7678 0.055 -11 -2 2 2.7635 0.088 1 2 4 10.8770 0.123 -11 -2 -1 1.6085 0.071 1 2 -3 0.6271 0.048 -11 -2 -2 2.8913 0.069 1 2 -4 11.0437 0.118 -10 -2 -2 1.7544 0.074 1 2 -5 1.8651 0.045 -10 -2 0 3.6310 0.145 1 2 -6 9.6482 0.13 -10 -2 2 1.7416 0.062 1 2 -8 5.8470 0.135 -10 -2 4 3.0790 0.081 1 1 -7 1.4567 0.068
116
-10 -1 6 1.5414 0.1 1 1 -6 7.5556 0.111 -10 -1 4 1.8038 0.068 1 1 -4 3.2486 0.084 -10 -1 2 2.2077 0.075 1 1 -3 2.4341 0.13 -10 -1 1 0.7834 0.12 1 1 -2 13.5069 0.121 -10 -1 0 1.9466 0.063 1 1 2 13.4802 0.152 -10 -1 -2 2.1735 0.064 1 1 3 3.7595 0.151 -10 -1 -4 1.5005 0.081 1 1 4 3.1840 0.097 -10 0 -6 6.1564 0.166 1 1 6 6.6819 0.121 -10 0 -4 4.1604 0.15 1 1 8 1.8152 0.065 -10 0 -2 9.8594 0.134 1 0 9 1.9218 0.073 -10 0 0 4.9341 0.134 1 0 5 2.1178 0.075 -10 0 2 9.8769 0.154 1 0 -1 2.5866 0.044 -10 1 2 2.4763 0.058 1 0 -3 1.6449 0.071 -10 1 0 1.9583 0.077 1 0 -5 2.2039 0.079 -9 1 -5 0.7202 0.145 1 -1 -6 7.1023 0.126 -9 1 -4 3.8523 0.154 1 -1 -4 3.0614 0.095 -9 1 -3 2.1837 0.071 1 -1 -2 13.1668 0.109 -9 1 -2 2.4482 0.067 1 -1 3 2.3512 0.188 -9 1 0 5.0076 0.138 1 -1 4 3.1810 0.098 -9 1 1 1.9951 0.053 1 -1 6 7.2424 0.123 -9 1 2 2.4816 0.082 1 -1 8 1.6481 0.065 -9 1 3 2.4763 0.087 1 -2 8 5.0132 0.186 -9 1 4 4.2715 0.14 1 -2 6 9.5307 0.106 -9 -1 -6 1.3997 0.088 1 -2 5 1.7547 0.041 -9 -1 -4 3.6376 0.133 1 -2 4 10.9922 0.1 -9 -1 -3 2.3078 0.101 1 -2 -4 10.1227 0.115 -9 -1 -2 2.2194 0.064 1 -2 -5 1.5889 0.054 -9 -1 -1 1.9610 0.062 1 -2 -6 8.4808 0.122 -9 -1 0 4.8776 0.136 2 -2 -6 2.0468 0.046 -9 -1 1 1.9887 0.054 2 -2 -5 0.9998 0.071 -9 -1 2 2.3308 0.057 2 -2 -4 8.3868 0.111 -9 -1 3 2.4531 0.053 2 -2 5 1.0526 0.065 -9 -1 4 3.7632 0.163 2 -2 6 2.1971 0.058 -9 -1 5 1.0125 0.107 2 -2 7 0.7293 0.108 -9 -1 7 1.9732 0.086 2 -1 8 5.8081 0.141 -9 -2 4 5.4690 0.143 2 -1 6 2.4524 0.07 -9 -2 2 7.4424 0.127 2 -1 4 11.7125 0.138 -9 -2 0 6.2734 0.117 2 -1 2 1.1192 0.027 -9 -2 -2 6.6513 0.146 2 -1 1 1.6955 0.046 -9 -2 -4 4.5745 0.139 2 -1 0 17.2341 0.183 -8 -2 -5 1.2247 0.086 2 -1 -1 1.5890 0.052 -8 -2 -1 1.3927 0.054 2 -1 -2 1.1256 0.042 -8 -2 1 1.3970 0.055 2 -1 -3 1.5039 0.038 -8 -2 4 1.2779 0.073 2 -1 -4 11.9849 0.131 -8 -1 8 2.3143 0.078 2 -1 -6 2.6944 0.084 -8 -1 6 3.0042 0.112 2 -1 -7 0.9144 0.091 -8 -1 5 1.8227 0.08 2 -1 -8 4.8659 0.176 -8 -1 4 4.4182 0.128 2 0 -8 1.6285 0.081 -8 -1 3 2.1616 0.056 2 0 -6 6.3341 0.111 -8 -1 2 4.2523 0.159 2 0 -4 3.6315 0.085 -8 -1 0 4.8976 0.126 2 0 -2 9.7172 0.093
117
-8 -1 -1 2.2679 0.1 2 0 0 6.7554 0.071 -8 -1 -2 4.4684 0.111 2 0 2 9.4667 0.085 -8 -1 -3 1.9185 0.049 2 0 4 3.5645 0.084 -8 -1 -4 3.9094 0.136 2 0 6 6.3686 0.112 -8 -1 -5 1.6229 0.063 2 0 8 1.6888 0.069 -8 -1 -6 2.5446 0.077 2 0 10 2.9124 0.08 -8 0 -4 9.9847 0.162 2 1 8 5.8035 0.138 -8 0 -2 0.9266 0.08 2 1 6 2.5998 0.093 -8 0 0 13.0948 0.155 2 1 4 11.4520 0.141 -8 0 4 10.6751 0.121 2 1 3 1.4070 0.031 -8 1 5 2.0627 0.063 2 1 2 1.1755 0.034 -8 1 4 4.2704 0.144 2 1 1 1.6675 0.05 -8 1 3 2.3751 0.073 2 1 0 18.6755 0.216 -8 1 2 4.8249 0.136 2 1 -1 1.7480 0.055 -8 1 1 2.2831 0.139 2 1 -2 1.1675 0.029 -8 1 0 5.5955 0.107 2 1 -3 1.4528 0.034 -8 1 -1 2.4860 0.05 2 1 -4 11.9172 0.134 -8 1 -2 4.5785 0.114 2 1 -5 1.0388 0.056 -8 1 -4 3.9819 0.142 2 1 -6 2.6694 0.089 -7 2 1 0.5979 0.106 2 1 -8 5.5554 0.139 -7 2 0 2.2923 0.077 2 2 -8 4.2500 0.157 -7 2 -4 1.8000 0.079 2 2 -6 2.1343 0.045 -7 1 -6 4.4917 0.208 2 2 -4 8.9273 0.114 -7 1 -4 2.1060 0.047 2 2 -3 0.9913 0.044 -7 1 -2 7.5083 0.113 2 2 -2 2.6737 0.075 -7 1 -1 0.8877 0.089 2 2 3 1.0716 0.036 -7 1 1 0.8207 0.078 2 2 4 8.6561 0.125 -7 1 2 7.4740 0.112 2 2 5 0.8056 0.092 -7 1 4 2.3764 0.051 2 2 6 2.1702 0.046 -7 1 6 5.0195 0.142 2 2 7 0.6597 0.129 -7 0 7 3.0074 0.109 3 2 7 1.4900 0.088 -7 0 5 2.0158 0.059 3 2 6 4.4118 0.117 -7 0 3 3.5880 0.117 3 2 4 3.8927 0.104 -7 0 1 3.5757 0.106 3 2 3 2.2897 0.073 -7 0 -1 3.4559 0.117 3 2 2 8.3645 0.106 -7 0 -3 3.5446 0.17 3 2 1 1.2472 0.068 -7 0 -5 1.7260 0.065 3 2 0 5.9655 0.089 -7 0 -7 2.6657 0.065 3 2 -1 1.2475 0.047 -7 -1 -6 3.8434 0.164 3 2 -2 8.6750 0.094 -7 -1 -4 1.8035 0.054 3 2 -3 2.2501 0.057 -7 -1 -3 0.7802 0.08 3 2 -4 3.9991 0.097 -7 -1 -2 6.9376 0.123 3 2 -6 4.5959 0.117 -7 -1 0 2.6875 0.085 3 2 -7 1.5238 0.064 -7 -1 2 7.1007 0.097 3 2 -8 2.2698 0.073 -7 -1 4 2.0864 0.047 3 1 -9 1.5865 0.082 -7 -1 5 0.9494 0.087 3 1 -6 3.2795 0.119 -7 -1 6 4.3162 0.142 3 1 -5 1.9275 0.054 -7 -1 8 0.9275 0.22 3 1 -4 5.3113 0.087 -7 -2 4 1.7120 0.063 3 1 -2 7.9889 0.166 -7 -2 0 1.9924 0.08 3 1 -1 1.0424 0.034 -7 -2 -1 0.4398 0.118 3 1 0 2.4002 0.068
118
-7 -3 2 3.9259 0.123 3 1 1 1.0777 0.028 -6 -2 -6 2.7290 0.09 3 1 2 8.1598 0.143 -6 -2 -5 0.9954 0.075 3 1 4 4.6921 0.093 -6 -2 -4 2.8618 0.079 3 1 5 1.8348 0.047 -6 -2 -2 4.8572 0.106 3 1 6 2.9394 0.098 -6 -2 -1 1.6202 0.044 3 1 8 3.0600 0.075 -6 -2 0 3.8909 0.127 3 0 9 0.9201 0.137 -6 -2 1 1.7088 0.045 3 0 3 0.8277 0.048 -6 -2 2 5.1987 0.102 3 0 1 1.4957 0.039 -6 -2 3 1.4404 0.05 3 0 -1 1.5032 0.029 -6 -2 4 3.1013 0.127 3 0 -3 0.9368 0.044 -6 -2 5 1.2585 0.063 3 0 -7 0.9665 0.094 -6 -2 6 3.2233 0.097 3 0 -9 1.2985 0.096 -6 -1 9 1.1478 0.12 3 -1 -8 2.4635 0.1 -6 -1 8 3.2066 0.091 3 -1 -6 2.9809 0.083 -6 -1 5 1.8982 0.058 3 -1 -4 4.9047 0.103 -6 -1 4 6.0538 0.112 3 -1 -2 8.2780 0.14 -6 -1 3 1.7747 0.096 3 -1 -1 1.0539 0.032 -6 -1 1 2.5796 0.071 3 -1 0 2.5589 0.07 -6 -1 0 8.6186 0.106 3 -1 1 1.0499 0.032 -6 -1 -1 2.5307 0.107 3 -1 2 7.2569 0.12 -6 -1 -3 1.8491 0.048 3 -1 4 4.9126 0.107 -6 -1 -4 5.9074 0.119 3 -1 6 3.1491 0.104 -6 -1 -5 1.6591 0.053 3 -1 8 2.8342 0.121 -6 -1 -8 2.4368 0.081 3 -1 9 1.8001 0.082 -6 0 -8 5.8821 0.155 3 -2 7 1.6589 0.067 -6 0 -6 3.5222 0.118 3 -2 4 4.3374 0.092 -6 0 -4 13.2197 0.145 3 -2 3 2.2297 0.056 -6 0 -2 5.9233 0.09 3 -2 -3 2.0655 0.057 -6 0 0 17.5352 0.191 3 -2 -4 4.1721 0.116 -6 0 2 6.0010 0.102 4 -2 -4 10.9549 0.134 -6 0 4 13.8465 0.181 4 -2 2 7.6371 0.101 -6 0 6 4.1233 0.121 4 -2 4 11.0998 0.15 -6 0 8 7.3499 0.164 4 -1 8 2.2781 0.062 -6 1 5 1.8600 0.054 4 -1 4 4.0295 0.115 -6 1 4 6.5211 0.118 4 -1 2 4.6357 0.09 -6 1 3 2.0038 0.042 4 -1 0 5.5168 0.152 -6 1 1 2.7712 0.085 4 -1 -1 1.3524 0.103 -6 1 0 8.6318 0.096 4 -1 -2 4.6735 0.077 -6 1 -1 2.7527 0.076 4 -1 -4 3.8744 0.113 -6 1 -3 1.9688 0.047 4 -1 -6 3.0671 0.078 -6 1 -4 6.1966 0.108 4 -1 -8 2.0733 0.065 -6 1 -5 1.7668 0.055 4 0 -8 5.0126 0.148 -6 1 -8 2.8138 0.09 4 0 -6 9.4917 0.122 -6 2 -5 1.3673 0.066 4 0 -4 9.9216 0.127 -6 2 -4 3.3997 0.062 4 0 -2 14.2498 0.156 -6 2 -3 1.5226 0.049 4 0 0 16.2540 0.193 -6 2 -2 5.3701 0.133 4 0 2 14.0071 0.145 -6 2 0 4.5476 0.101 4 0 4 9.6541 0.126 -6 2 1 1.7870 0.052 4 0 6 9.5187 0.131 -6 2 2 5.7185 0.105 4 0 8 5.2097 0.147
119
-6 2 3 1.5711 0.096 4 1 8 2.4015 0.073 -5 2 4 11.0787 0.143 4 1 6 3.1021 0.083 -5 2 3 1.7564 0.045 4 1 4 4.0601 0.104 -5 2 2 15.8985 0.189 4 1 2 4.3695 0.075 -5 2 1 3.5644 0.109 4 1 0 5.2129 0.103 -5 2 0 14.6486 0.163 4 1 -2 4.6667 0.079 -5 2 -1 3.2753 0.113 4 1 -3 0.6790 0.074 -5 2 -2 15.0732 0.17 4 1 -4 4.1465 0.093 -5 2 -3 1.6031 0.063 4 1 -6 3.0800 0.084 -5 2 -4 10.4413 0.124 4 1 -8 2.3260 0.072 -5 2 -5 2.6816 0.074 4 2 -8 6.0551 0.171 -5 2 -6 8.5284 0.168 4 2 -6 3.8448 0.144 -5 1 -6 4.0763 0.133 4 2 -4 11.5011 0.145 -5 1 -4 2.7494 0.08 4 2 -2 7.8898 0.095 -5 1 -3 2.7290 0.112 4 2 0 16.2981 0.2 -5 1 -2 7.3892 0.087 4 2 2 7.7824 0.121 -5 1 -1 1.9922 0.042 4 2 4 10.8898 0.156 -5 1 0 2.5251 0.072 4 2 6 3.9481 0.124 -5 1 1 1.9494 0.053 5 2 6 9.1105 0.171 -5 1 2 7.6832 0.104 5 2 5 2.7225 0.064 -5 1 3 2.7293 0.083 5 2 4 10.0993 0.162 -5 1 4 2.7297 0.084 5 2 3 1.7150 0.041 -5 1 5 0.7790 0.091 5 2 2 14.8213 0.189 -5 1 6 4.4887 0.187 5 2 1 3.1866 0.11 -5 1 7 2.3798 0.059 5 2 0 13.9006 0.158 -5 0 3 1.9274 0.072 5 2 -1 3.4045 0.101 -5 0 1 0.9346 0.058 5 2 -2 14.7076 0.175 -5 0 -1 1.1417 0.037 5 2 -3 1.5102 0.042 -5 0 -3 1.7703 0.048 5 2 -4 10.8425 0.138 -5 -1 -8 1.1399 0.15 5 2 -5 2.9147 0.105 -5 -1 -7 1.8787 0.06 5 2 -6 9.5819 0.134 -5 -1 -6 3.8661 0.131 5 1 -7 2.1886 0.057 -5 -1 -5 0.8378 0.081 5 1 -6 4.2622 0.139 -5 -1 -4 2.6142 0.053 5 1 -4 2.8174 0.088 -5 -1 -3 2.5532 0.093 5 1 -3 2.7626 0.082 -5 -1 -2 7.2283 0.096 5 1 -2 7.7573 0.093 -5 -1 -1 1.8725 0.066 5 1 -1 1.8290 0.091 -5 -1 0 2.5460 0.074 5 1 0 2.6657 0.073 -5 -1 1 1.8733 0.052 5 1 1 1.8438 0.051 -5 -1 2 7.7366 0.124 5 1 2 7.4838 0.108 -5 -1 3 2.8436 0.085 5 1 3 2.6529 0.072 -5 -1 4 2.7406 0.076 5 1 4 2.6210 0.101 -5 -1 6 4.2995 0.132 5 1 7 2.1394 0.072 -5 -1 8 1.3712 0.099 5 1 8 1.1882 0.103 -5 -2 6 8.8580 0.125 5 0 7 0.8054 0.135 -5 -2 5 2.6727 0.066 5 0 3 1.7225 0.048 -5 -2 4 10.2194 0.124 5 0 1 1.1150 0.045 -5 -2 3 1.5570 0.053 5 0 -1 1.1025 0.04 -5 -2 2 14.0534 0.176 5 0 -3 1.8945 0.087 -5 -2 1 3.0529 0.102 5 -1 -7 2.0326 0.062 -5 -2 0 12.5836 0.162 5 -1 -6 4.2417 0.13
120
-5 -2 -1 2.9030 0.088 5 -1 -4 2.6374 0.066 -5 -2 -2 13.1024 0.159 5 -1 -3 2.8137 0.065 -5 -2 -4 9.0364 0.118 5 -1 -2 7.4834 0.09 -5 -2 -5 2.1449 0.071 5 -1 -1 1.9605 0.064 -5 -2 -6 7.5917 0.136 5 -1 0 2.7343 0.078 -4 -2 -6 3.3731 0.066 5 -1 1 1.7982 0.037 -4 -2 -4 9.5182 0.125 5 -1 2 7.6051 0.103 -4 -2 -2 6.8170 0.093 5 -1 3 2.8365 0.111 -4 -2 0 14.7059 0.172 5 -1 4 2.7320 0.062 -4 -2 2 7.3675 0.105 5 -1 6 4.0567 0.13 -4 -2 4 11.1277 0.127 5 -1 7 1.9894 0.072 -4 -2 6 3.6434 0.109 5 -2 6 8.7573 0.175 -4 -2 8 5.1352 0.184 5 -2 5 2.6020 0.058 -4 -1 8 2.2880 0.067 5 -2 4 10.1334 0.155 -4 -1 6 3.0460 0.109 5 -2 3 1.5928 0.042 -4 -1 4 4.1530 0.092 5 -2 2 14.4568 0.145 -4 -1 2 4.7127 0.076 5 -2 1 3.1556 0.091 -4 -1 0 5.0261 0.076 5 -2 0 13.3561 0.154 -4 -1 -1 1.3107 0.075 5 -2 -1 3.0489 0.094 -4 -1 -2 4.2902 0.089 5 -2 -2 13.9881 0.175 -4 -1 -4 3.9308 0.11 5 -2 -3 1.5524 0.044 -4 -1 -6 2.9053 0.112 5 -2 -4 9.7591 0.13 -4 -1 -8 1.8424 0.075 6 -2 -2 5.3030 0.12 -4 0 -8 4.8574 0.146 6 -2 0 4.3797 0.113 -4 0 -6 9.3510 0.136 6 -2 1 1.2276 0.115 -4 0 -4 9.5954 0.107 6 -2 2 5.4125 0.095 -4 0 -2 13.6809 0.14 6 -2 3 1.6300 0.049 -4 0 0 16.0706 0.148 6 -2 4 3.0006 0.086 -4 0 2 14.2517 0.148 6 -1 8 3.2568 0.068 -4 0 4 9.6908 0.122 6 -1 4 6.2789 0.103 -4 0 6 9.7466 0.136 6 -1 3 1.9532 0.051 -4 0 8 5.4117 0.148 6 -1 1 2.4302 0.071 -4 1 8 2.4413 0.061 6 -1 0 8.6719 0.113 -4 1 6 3.0403 0.088 6 -1 -1 2.6777 0.095 -4 1 4 4.2822 0.093 6 -1 -3 2.2173 0.072 -4 1 2 4.5892 0.08 6 -1 -4 5.5729 0.112 -4 1 0 4.8470 0.152 6 0 -8 7.2555 0.171 -4 1 -2 4.5126 0.081 6 0 -6 3.7892 0.126 -4 1 -4 4.0104 0.098 6 0 -4 13.8982 0.159 -4 1 -7 0.6740 0.124 6 0 -2 6.2768 0.099 -4 1 -8 2.2160 0.083 6 0 0 17.6952 0.219 -4 2 -7 0.7235 0.115 6 0 2 5.9919 0.113 -4 2 -4 9.8745 0.114 6 0 4 13.5501 0.197 -4 2 -2 8.2446 0.09 6 0 6 3.5473 0.195 -4 2 4 11.9007 0.15 6 0 8 7.2561 0.151 -3 2 6 4.3206 0.141 6 1 8 2.9963 0.147 -3 2 4 4.2331 0.115 6 1 5 1.8507 0.065 -3 2 3 2.2258 0.048 6 1 4 6.0786 0.117 -3 2 -3 2.2116 0.069 6 1 3 1.9919 0.066 -3 2 -6 4.2498 0.118 6 1 1 2.6634 0.085 -3 2 -7 1.5111 0.063 6 1 0 8.7041 0.113
121
-3 1 -9 1.6763 0.096 6 1 -1 2.8791 0.113 -3 1 -8 2.9187 0.065 6 1 -3 1.9422 0.052 -3 1 -6 2.9530 0.101 6 1 -4 6.3859 0.133 -3 1 -3 0.7753 0.048 6 1 -5 1.8149 0.074 -3 1 -2 8.1236 0.183 6 1 -8 3.3887 0.12 -3 1 -1 1.0714 0.028 6 1 -9 0.8559 0.166 -3 1 0 2.4418 0.072 6 2 -6 3.5527 0.132 -3 1 1 1.1037 0.03 6 2 -4 3.5012 0.123 -3 1 2 8.1958 0.17 6 2 -3 1.5711 0.06 -3 1 3 0.6417 0.058 6 2 -2 5.8348 0.121 -3 1 4 5.2225 0.085 6 2 -1 1.7881 0.047 -3 1 5 2.0002 0.063 6 2 0 4.3985 0.095 -3 1 6 3.0058 0.087 6 2 1 1.7767 0.067 -3 1 7 0.6921 0.125 6 2 2 5.6215 0.111 -3 1 8 3.1290 0.1 6 2 3 1.4074 0.06 -3 0 9 1.0726 0.122 6 2 4 3.3879 0.142 -3 0 1 1.4633 0.035 6 2 6 3.4203 0.104 -3 0 -1 1.4936 0.031 7 3 -2 4.6074 0.187 -3 0 -5 1.2466 0.061 7 2 6 0.7647 0.128 -3 0 -7 0.9979 0.095 7 2 0 2.2675 0.062 -3 -1 -8 2.6097 0.068 7 2 -4 1.8821 0.058 -3 -1 -6 2.8874 0.095 7 1 -8 1.2564 0.129 -3 -1 -5 1.6903 0.05 7 1 -6 4.3131 0.185 -3 -1 -4 4.9591 0.113 7 1 -4 2.0918 0.076 -3 -1 -2 7.6826 0.099 7 1 -3 0.8850 0.083 -3 -1 -1 1.0295 0.031 7 1 -2 7.4784 0.117 -3 -1 0 2.3435 0.061 7 1 0 2.8784 0.102 -3 -1 1 1.0669 0.027 7 1 2 7.6005 0.096 -3 -1 2 8.2893 0.13 7 1 4 2.0911 0.064 -3 -1 3 0.6050 0.058 7 1 6 4.5940 0.159 -3 -1 4 4.7418 0.097 7 0 7 2.7651 0.083 -3 -1 5 1.8809 0.046 7 0 3 3.4547 0.101 -3 -1 6 3.1173 0.095 7 0 1 3.4623 0.092 -3 -1 8 3.1281 0.101 7 0 -1 3.3249 0.112 -3 -2 8 2.1550 0.06 7 0 -3 3.9893 0.116 -3 -2 7 1.5861 0.061 7 0 -5 1.8376 0.071 -3 -2 6 4.1237 0.133 7 0 -7 2.7860 0.065 -3 -2 4 4.2059 0.09 7 -1 -6 4.5520 0.155 -3 -2 3 2.1922 0.059 7 -1 -4 1.9195 0.067 -3 -2 2 7.5647 0.084 7 -1 -2 7.5845 0.118 -3 -2 0 5.0624 0.079 7 -1 0 2.5945 0.072 -3 -2 -1 1.0540 0.041 7 -1 2 7.6606 0.109 -3 -2 -2 7.1373 0.085 7 -1 4 2.1362 0.05 -3 -2 -3 1.9464 0.047 7 -1 6 4.3867 0.158 -3 -2 -4 4.0830 0.124 7 -2 4 1.6407 0.066 -3 -2 -6 4.0332 0.12 7 -2 0 2.1627 0.044 -3 -2 -7 1.3269 0.087 8 -1 6 3.0377 0.102 -2 -2 -6 1.8107 0.071 8 -1 4 4.3388 0.13 -2 -2 -4 7.6250 0.098 8 -1 3 2.1837 0.051 -2 -2 -3 0.8882 0.045 8 -1 2 4.5717 0.129 -2 -2 2 2.4454 0.087 8 -1 1 2.3635 0.044
122
-2 -2 3 1.0097 0.036 8 -1 0 5.6990 0.133 -2 -2 4 8.6608 0.097 8 -1 -1 2.5273 0.061 -2 -2 5 0.9872 0.089 8 -1 -2 4.7883 0.13 -2 -2 6 2.3371 0.077 8 -1 -3 2.2421 0.067 -2 -2 8 4.1015 0.117 8 -1 -4 4.2868 0.104 -2 -1 8 5.5506 0.157 8 0 -4 10.6614 0.149 -2 -1 6 2.8299 0.113 8 0 0 13.1417 0.166 -2 -1 4 11.9303 0.123 8 0 4 10.4529 0.138 -2 -1 3 1.3519 0.032 8 0 8 6.1668 0.183 -2 -1 2 1.0737 0.027 8 1 7 1.5900 0.091 -2 -1 1 1.7292 0.052 8 1 6 2.9409 0.151 -2 -1 0 17.4393 0.185 8 1 5 1.5594 0.068 -2 -1 -1 1.6638 0.032 8 1 4 4.3120 0.155 -2 -1 -2 1.3243 0.041 8 1 3 2.3374 0.071 -2 -1 -3 1.3710 0.031 8 1 2 4.9264 0.119 -2 -1 -4 11.4306 0.123 8 1 1 2.5336 0.065 -2 -1 -7 0.8604 0.098 8 1 0 5.3633 0.115 -2 -1 -8 4.7426 0.143 8 1 -1 2.4179 0.045 -2 0 -10 2.4840 0.073 8 1 -2 4.6312 0.139 -2 0 -6 6.0201 0.116 8 1 -3 2.2194 0.051 -2 0 -4 3.7211 0.09 8 1 -4 4.5524 0.115 -2 0 -2 9.2877 0.08 8 1 -5 1.8259 0.062 -2 0 0 6.8888 0.07 8 1 -6 3.1404 0.104 -2 0 2 9.5999 0.081 8 1 -7 1.5435 0.085 -2 0 4 3.7167 0.098 8 1 -8 2.3787 0.076 -2 0 6 6.2132 0.11 8 2 -5 1.2997 0.084 -2 0 8 1.4618 0.079 8 2 -4 1.3711 0.071 -2 1 8 5.4812 0.141 8 2 -3 1.0899 0.084 -2 1 6 2.5752 0.074 8 2 -1 1.5740 0.052 -2 1 4 11.7701 0.128 8 2 0 1.4666 0.063 -2 1 3 1.3811 0.038 8 2 1 1.5947 0.052 -2 1 2 1.3431 0.028 8 2 5 1.5129 0.076 -2 1 1 1.7195 0.046 9 2 4 5.7937 0.163 -2 1 0 19.2469 0.183 9 2 2 8.0310 0.133 -2 1 -1 1.7608 0.058 9 2 0 7.2807 0.116 -2 1 -2 1.1034 0.033 9 2 -1 0.8461 0.094 -2 1 -4 12.0073 0.142 9 2 -2 8.4443 0.149 -2 1 -6 2.6530 0.058 9 2 -3 1.3348 0.076 -2 1 -8 5.2483 0.145 9 2 -4 6.0991 0.136 -2 2 -6 2.1014 0.065 9 1 -7 1.9027 0.079 -2 2 -4 8.9510 0.117 9 1 -4 4.0429 0.153 -2 2 4 9.1139 0.114 9 1 -3 2.4273 0.079 -2 2 6 2.2977 0.051 9 1 -2 2.5177 0.047 -1 2 6 9.7837 0.144 9 1 -1 2.1419 0.063 -1 2 5 1.8535 0.05 9 1 0 4.9784 0.139 -1 2 4 11.2945 0.115 9 1 1 2.0353 0.055 -1 2 -3 0.6339 0.05 9 1 2 2.3155 0.082 -1 2 -4 11.0098 0.135 9 1 3 2.3747 0.097 -1 2 -5 1.9815 0.048 9 1 4 4.2555 0.139 -1 2 -6 9.5077 0.116 9 1 6 1.8300 0.082 -1 2 -8 5.3600 0.159 9 -1 -4 3.9022 0.143
123
-1 1 -8 1.5838 0.069 9 -1 -3 2.4941 0.056 -1 1 -6 7.3573 0.153 9 -1 -2 2.4236 0.055 -1 1 -4 3.0838 0.085 9 -1 0 5.2004 0.129 -1 1 -2 14.3403 0.127 9 -1 1 1.9725 0.061 -1 1 2 13.6263 0.118 9 -1 2 2.3851 0.058 -1 1 3 2.7106 0.15 9 -1 3 2.3964 0.078 -1 1 4 3.0412 0.11 9 -1 4 4.2740 0.134 -1 1 5 0.8674 0.063 10 -1 2 2.1338 0.073 -1 1 6 7.5251 0.102 10 -1 0 2.1344 0.062 -1 1 8 1.5604 0.077 10 -1 -2 2.3471 0.079 -1 0 9 2.0462 0.066 10 0 -4 4.2600 0.15 -1 0 5 2.1838 0.047 10 0 -2 10.5909 0.127 -1 0 1 2.5632 0.047 10 0 0 5.3857 0.142 -1 0 -5 2.1719 0.056 10 0 2 10.5771 0.142 -1 0 -9 1.4742 0.087 10 0 4 4.4443 0.132 -1 -1 -9 0.7677 0.159 10 0 6 7.2806 0.157 -1 -1 -8 1.1704 0.111 10 1 4 1.7787 0.074 -1 -1 -6 6.8473 0.162 10 1 2 2.2904 0.058 -1 -1 -4 2.9521 0.079 10 1 0 2.0032 0.063 -1 -1 -3 2.2915 0.139 10 1 -2 2.2778 0.06 -1 -1 -2 13.9618 0.126 10 1 -4 1.7447 0.076 -1 -1 2 13.6482 0.092 10 1 -6 1.8572 0.079 -1 -1 3 2.5180 0.111 10 2 -4 3.1447 0.109 -1 -1 4 2.9387 0.088 10 2 -3 0.6010 0.163 -1 -1 5 1.0440 0.057 10 2 -2 1.7602 0.07 -1 -1 6 7.4915 0.099 10 2 0 4.4294 0.126 -1 -2 8 5.5508 0.137 10 2 2 1.8468 0.064 -1 -2 6 9.0575 0.117 11 2 2 3.5072 0.09 -1 -2 5 1.7687 0.039 11 2 1 1.9798 0.071 -1 -2 4 11.0229 0.1 11 2 0 3.3964 0.118 -1 -2 3 0.4922 0.056 11 2 -1 2.0314 0.089 -1 -2 -3 0.5823 0.059 11 2 -2 3.4569 0.085 -1 -2 -4 9.8122 0.121 11 2 -3 2.2715 0.066 -1 -2 -5 1.5881 0.045 11 1 -3 1.4173 0.087 -1 -2 -6 8.3285 0.108 11 1 -1 1.1064 0.098 -1 -2 -7 0.7647 0.109 11 1 0 2.4628 0.073 0 -2 -6 1.8905 0.048 11 1 1 1.3665 0.081 0 -2 -4 1.7540 0.068 11 1 2 2.1069 0.069 0 -2 3 1.4170 0.037 11 0 -1 0.6706 0.151 0 -2 4 1.9202 0.051 11 0 -3 0.8235 0.144 0 -2 6 2.0789 0.047 12 0 0 0.4425 0.255 0 -2 7 0.9654 0.109 12 1 2 2.2166 0.071 0 0 -10 3.2797 0.082 12 1 0 2.9008 0.084 0 0 -8 14.1360 0.195 12 1 -2 2.4021 0.073 0 0 -6 6.8307 0.14 12 1 -4 2.3177 0.079 0 0 -4 29.1122 0.318 13 1 -2 2.1539 0.086 0 0 -2 13.9107 0.116 13 1 -1 1.0946 0.123 0 0 2 14.0397 0.102 13 1 1 0.9130 0.138 0 0 4 29.1651 0.287
124
P = 4.144(7) GPa
h k l FO Esd h k l FO Esd -12 -1 -2 0.8877 0.098 0 0 10 2.2818 0.066 -11 1 -2 1.3219 0.071 0 2 -7 0.8260 0.063 -11 1 1 0.7401 0.105 0 2 -6 1.3014 0.044 -11 -1 -2 0.9312 0.077 0 2 -4 0.9584 0.035 -11 -1 0 1.3726 0.059 0 2 -3 0.9184 0.043 -11 -1 3 1.0209 0.092 0 2 3 0.8570 0.045 -11 -1 4 0.8174 0.095 0 2 6 1.3774 0.047 -10 -2 0 2.5166 0.073 0 2 7 0.8617 0.072 -10 -1 4 0.8084 0.083 1 2 6 5.6994 0.111 -10 -1 2 1.4754 0.055 1 2 5 1.1721 0.04 -10 -1 0 0.9674 0.093 1 2 4 6.4775 0.092 -10 -1 -2 1.3325 0.057 1 2 3 0.3578 0.05 -10 0 -4 2.3006 0.091 1 2 -4 6.7005 0.102 -10 0 -2 5.4007 0.163 1 2 -5 1.2143 0.037 -10 0 0 2.7776 0.127 1 2 -6 5.4836 0.124 -10 0 2 6.1309 0.129 1 2 -8 3.1757 0.12 -10 0 4 2.5809 0.083 1 1 -6 4.3180 0.107 -10 0 6 4.0779 0.165 1 1 -5 0.6655 0.05 -10 1 2 1.4594 0.058 1 1 -4 2.0182 0.073 -10 1 0 1.1878 0.06 1 1 -3 1.2495 0.047 -10 1 -2 1.4525 0.056 1 1 -2 8.1447 0.094 -9 1 -4 2.3323 0.113 1 1 2 8.2155 0.092 -9 1 -3 1.6235 0.061 1 1 3 1.5990 0.086 -9 1 -2 1.3493 0.052 1 1 4 1.9865 0.063 -9 1 -1 1.4161 0.049 1 1 6 4.3977 0.102 -9 1 0 3.0907 0.119 1 0 5 1.4817 0.033 -9 1 1 1.4134 0.057 1 0 1 1.5722 0.043 -9 1 2 1.2610 0.056 1 0 -1 1.5806 0.042 -9 1 3 1.4970 0.053 1 0 -5 1.4082 0.04 -9 1 4 2.6436 0.101 1 0 -9 0.8805 0.11 -9 -1 -6 0.8403 0.099 1 -1 -8 0.7295 0.09 -9 -1 -4 2.3220 0.065 1 -1 -7 0.6111 0.106 -9 -1 -3 1.3283 0.058 1 -1 -6 4.3713 0.107 -9 -1 -2 1.3075 0.05 1 -1 -5 0.5761 0.06 -9 -1 -1 1.2327 0.05 1 -1 -4 1.9058 0.061 -9 -1 0 3.0180 0.084 1 -1 -3 1.6233 0.165 -9 -1 1 1.3142 0.056 1 -1 -2 7.9619 0.098 -9 -1 4 2.4331 0.093 1 -1 1 4.1338 0.138 -9 -2 4 2.8836 0.155 1 -1 3 1.7157 0.1 -9 -2 2 4.1340 0.139 1 -1 4 1.8238 0.086 -9 -2 0 3.4339 0.126 1 -1 6 4.2873 0.1 -9 -2 -2 3.9994 0.148 1 -2 6 5.5304 0.136 -9 -2 -3 0.9374 0.062 1 -2 5 1.0209 0.042 -9 -2 -4 2.7121 0.082 1 -2 4 6.2851 0.098 -8 -2 -5 0.6840 0.092 1 -2 -4 5.9138 0.115 -8 -1 7 0.8225 0.094 1 -2 -6 4.9451 0.116 -8 -1 6 1.5422 0.066 2 -2 -6 1.2264 0.047 -8 -1 5 1.0545 0.065 2 -2 -4 4.9809 0.113
125
-8 -1 4 2.4917 0.115 2 -2 -3 0.6399 0.045 -8 -1 3 1.2757 0.048 2 -2 3 0.6216 0.045 -8 -1 2 2.5134 0.084 2 -2 5 0.6584 0.059 -8 -1 1 1.3897 0.047 2 -2 6 1.4064 0.047 -8 -1 0 2.9522 0.132 2 -1 8 3.1794 0.15 -8 -1 -1 1.5013 0.06 2 -1 2 0.6802 0.028 -8 -1 -2 2.5688 0.102 2 -1 1 1.0900 0.025 -8 -1 -3 1.1712 0.056 2 -1 0 11.1242 0.125 -8 -1 -4 2.3479 0.084 2 -1 -1 1.0228 0.051 -8 -1 -5 0.9938 0.064 2 -1 -2 0.7304 0.027 -8 -1 -6 1.4548 0.064 2 -1 -3 0.8601 0.042 -8 0 -8 3.3815 0.126 2 -1 -4 7.0690 0.112 -8 0 -4 5.9503 0.116 2 -1 -7 0.4492 0.115 -8 0 0 7.7262 0.128 2 -1 -8 3.2169 0.103 -8 0 4 6.2103 0.138 2 0 -6 3.8103 0.103 -8 1 6 1.9579 0.068 2 0 -4 2.2769 0.077 -8 1 4 2.6414 0.097 2 0 -2 5.7572 0.082 -8 1 2 2.7927 0.084 2 0 0 4.0131 0.057 -8 1 1 1.5571 0.041 2 0 2 5.5419 0.073 -8 1 0 3.3213 0.109 2 0 4 2.2940 0.077 -8 1 -1 1.5481 0.044 2 0 6 3.6410 0.112 -8 1 -2 2.6659 0.147 2 0 8 0.9322 0.075 -8 1 -3 1.3072 0.064 2 0 10 1.7481 0.067 -8 1 -4 2.7578 0.091 2 1 6 1.6162 0.04 -8 1 -5 1.0521 0.065 2 1 5 0.3230 0.096 -8 1 -6 1.7252 0.104 2 1 4 7.0029 0.114 -8 2 -2 0.5201 0.102 2 1 3 0.8668 0.033 -8 2 0 0.9283 0.058 2 1 2 0.6387 0.029 -7 2 0 1.2712 0.048 2 1 1 1.0933 0.031 -7 2 -2 0.5119 0.08 2 1 0 11.3355 0.134 -7 1 -6 2.8165 0.06 2 1 -1 1.0615 0.035 -7 1 -4 1.3879 0.046 2 1 -2 0.7160 0.026 -7 1 -3 0.5043 0.088 2 1 -3 0.9476 0.028 -7 1 -2 4.2473 0.1 2 1 -4 7.0660 0.095 -7 1 0 1.7464 0.035 2 1 -6 1.5192 0.045 -7 1 2 4.5659 0.108 2 1 -8 3.0976 0.131 -7 1 3 0.6411 0.075 2 1 -9 0.5419 0.121 -7 1 4 1.1426 0.053 2 2 -8 2.8233 0.083 -7 1 6 2.8189 0.078 2 2 -6 1.4493 0.043 -7 0 7 1.7736 0.078 2 2 -4 5.3628 0.11 -7 0 3 2.4437 0.08 2 2 -2 1.5604 0.045 -7 0 1 2.2763 0.06 2 2 4 5.0641 0.119 -7 0 -1 2.3059 0.082 2 2 6 1.4026 0.042 -7 0 -3 2.1725 0.088 3 2 7 0.8803 0.105 -7 0 -7 1.6100 0.06 3 2 6 2.8759 0.115 -7 -1 -6 2.2942 0.075 3 2 4 2.4226 0.079 -7 -1 -4 1.2559 0.047 3 2 3 1.5271 0.043 -7 -1 -2 4.1070 0.11 3 2 2 5.0954 0.103 -7 -1 0 1.7525 0.048 3 2 1 0.8846 0.029 -7 -1 1 0.9308 0.048 3 2 -1 0.9794 0.027 -7 -1 2 3.9110 0.149 3 2 -2 5.3725 0.088
126
-7 -1 4 1.1338 0.057 3 2 -3 1.3217 0.079 -7 -1 6 2.5957 0.105 3 2 -4 2.5689 0.115 -7 -2 4 0.9289 0.056 3 2 -6 2.6540 0.115 -7 -2 0 1.0691 0.043 3 1 -8 1.6555 0.054 -7 -2 -3 0.6178 0.064 3 1 -6 1.8099 0.068 -7 -2 -4 0.9426 0.055 3 1 -5 1.0974 0.048 -6 -2 -6 1.6862 0.05 3 1 -4 3.0345 0.092 -6 -2 -5 0.5010 0.095 3 1 -3 0.3771 0.059 -6 -2 -3 0.8179 0.05 3 1 -2 4.6868 0.132 -6 -2 -2 2.8815 0.094 3 1 0 1.6185 0.046 -6 -2 -1 0.9160 0.047 3 1 1 0.8198 0.024 -6 -2 0 2.1053 0.083 3 1 2 4.9143 0.098 -6 -2 1 0.9491 0.044 3 1 3 0.3429 0.063 -6 -2 2 2.9512 0.113 3 1 4 2.8821 0.086 -6 -2 4 1.6856 0.043 3 1 5 1.1762 0.044 -6 -2 5 0.7236 0.069 3 1 6 1.8249 0.042 -6 -1 8 1.6708 0.077 3 0 5 0.7465 0.061 -6 -1 5 1.1554 0.05 3 0 3 0.6021 0.04 -6 -1 4 3.5835 0.104 3 0 1 0.9305 0.03 -6 -1 3 1.1898 0.058 3 0 -1 0.9478 0.025 -6 -1 1 1.7668 0.067 3 0 -5 0.9299 0.052 -6 -1 0 5.1843 0.098 3 0 -9 0.5585 0.134 -6 -1 -1 1.7293 0.045 3 -1 -8 1.6983 0.06 -6 -1 -3 1.2453 0.039 3 -1 -6 1.7521 0.069 -6 -1 -4 3.4277 0.127 3 -1 -4 3.0167 0.111 -6 -1 -5 1.1225 0.051 3 -1 -2 4.9200 0.101 -6 -1 -6 0.5522 0.106 3 -1 -1 0.7532 0.027 -6 -1 -8 1.3888 0.067 3 -1 0 1.5591 0.052 -6 0 -8 3.2097 0.122 3 -1 2 4.6039 0.117 -6 0 -4 8.0046 0.122 3 -1 3 0.4626 0.051 -6 0 -2 3.3711 0.09 3 -1 4 2.9379 0.086 -6 0 0 10.4502 0.132 3 -1 7 0.4880 0.12 -6 0 2 3.5799 0.088 3 -1 8 1.6870 0.055 -6 0 4 6.7042 0.131 3 -1 9 0.9652 0.085 -6 0 6 2.3718 0.075 3 -2 7 0.9838 0.066 -6 0 8 4.5564 0.149 3 -2 4 2.4993 0.104 -6 1 3 1.3405 0.051 3 -2 3 1.5604 0.039 -6 1 1 1.7742 0.078 3 -2 2 4.9840 0.078 -6 1 0 5.2280 0.084 3 -2 -3 1.3956 0.042 -6 1 -1 1.8471 0.051 3 -2 -4 2.2460 0.079 -6 1 -3 1.4370 0.038 3 -2 -6 2.2858 0.094 -6 1 -4 3.7026 0.105 4 -2 -6 2.2230 0.071 -6 1 -5 1.2650 0.055 4 -2 -4 6.5383 0.137 -6 1 -8 1.4848 0.065 4 -2 -2 4.6477 0.084 -6 2 -5 0.8647 0.065 4 -2 2 4.4636 0.102 -6 2 -4 1.9449 0.066 4 -2 4 6.8486 0.108 -6 2 -2 2.8748 0.118 4 -2 6 2.3788 0.048 -6 2 -1 0.9807 0.044 4 -1 8 1.4948 0.069 -6 2 0 2.5235 0.08 4 -1 6 1.8431 0.043 -6 2 1 0.7633 0.061 4 -1 4 2.7187 0.112 -6 2 2 3.4026 0.108 4 -1 2 2.6938 0.093
127
-6 2 4 1.8296 0.065 4 -1 0 3.2419 0.101 -5 2 5 1.6902 0.053 4 -1 -2 2.7467 0.083 -5 2 4 6.3727 0.129 4 -1 -4 2.4160 0.096 -5 2 3 0.9702 0.043 4 -1 -6 1.8608 0.049 -5 2 2 9.0789 0.116 4 0 -8 3.0034 0.122 -5 2 1 2.0491 0.063 4 0 -6 5.3129 0.144 -5 2 0 8.2529 0.106 4 0 -4 6.0022 0.089 -5 2 -1 2.0115 0.061 4 0 -2 8.5014 0.123 -5 2 -2 9.1542 0.127 4 0 0 9.6914 0.151 -5 2 -3 0.9547 0.045 4 0 2 8.5540 0.095 -5 2 -4 6.0828 0.117 4 0 4 5.7355 0.096 -5 2 -5 1.5903 0.044 4 0 6 5.6329 0.131 -5 2 -6 5.2920 0.118 4 0 8 3.0859 0.127 -5 1 -7 1.0027 0.067 4 1 8 1.4214 0.092 -5 1 -6 2.5400 0.104 4 1 6 1.8324 0.05 -5 1 -4 1.6988 0.046 4 1 2 2.5381 0.075 -5 1 -3 1.7913 0.074 4 1 0 3.2960 0.089 -5 1 -2 4.7436 0.08 4 1 -2 2.6116 0.074 -5 1 -1 1.3647 0.038 4 1 -4 2.3852 0.096 -5 1 0 1.6192 0.036 4 1 -6 1.8305 0.055 -5 1 1 1.3962 0.043 4 1 -8 1.5170 0.057 -5 1 2 4.5763 0.103 4 2 -4 6.8177 0.132 -5 1 3 1.8322 0.056 4 2 -2 4.7036 0.076 -5 1 4 1.6442 0.052 4 2 0 9.8449 0.151 -5 1 6 2.5257 0.113 4 2 2 4.3939 0.085 -5 1 7 1.3107 0.06 4 2 4 6.9939 0.105 -5 0 3 1.1249 0.038 4 2 6 2.2650 0.074 -5 0 1 0.7781 0.036 5 2 6 5.3228 0.152 -5 0 -3 1.5065 0.04 5 2 5 1.7518 0.045 -5 -1 -8 0.5108 0.121 5 2 4 6.3323 0.123 -5 -1 -6 2.1506 0.09 5 2 3 1.0865 0.041 -5 -1 -4 1.5443 0.067 5 2 2 8.9775 0.128 -5 -1 -3 1.7536 0.043 5 2 1 2.0584 0.062 -5 -1 -2 4.3725 0.079 5 2 0 8.2817 0.12 -5 -1 -1 1.3143 0.06 5 2 -1 2.2020 0.088 -5 -1 0 1.4771 0.055 5 2 -2 8.8679 0.124 -5 -1 1 1.3275 0.048 5 2 -3 1.0045 0.04 -5 -1 2 4.4907 0.08 5 2 -4 6.5770 0.11 -5 -1 3 1.7681 0.046 5 2 -5 1.7179 0.04 -5 -1 4 1.5429 0.045 5 2 -6 5.7053 0.117 -5 -1 7 1.5108 0.068 5 1 -6 2.6733 0.082 -5 -2 6 5.1258 0.125 5 1 -4 1.6579 0.044 -5 -2 5 1.5972 0.066 5 1 -3 1.9487 0.049 -5 -2 4 5.9446 0.104 5 1 -2 4.6352 0.105 -5 -2 3 0.9679 0.051 5 1 -1 1.3670 0.047 -5 -2 2 8.0804 0.111 5 1 0 1.5488 0.041 -5 -2 1 1.9648 0.06 5 1 1 1.3687 0.028 -5 -2 0 7.2832 0.113 5 1 2 4.6271 0.085 -5 -2 -1 1.7199 0.063 5 1 3 1.7164 0.069 -5 -2 -2 7.7621 0.116 5 1 4 1.4455 0.037 -5 -2 -4 4.9013 0.104 5 1 6 2.4023 0.106
128
-5 -2 -5 1.4569 0.046 5 1 7 1.3998 0.058 -5 -2 -6 4.3474 0.123 5 1 8 0.5543 0.125 -4 -2 -6 1.8429 0.059 5 0 -1 0.7332 0.043 -4 -2 -4 5.9154 0.096 5 0 -3 1.0653 0.061 -4 -2 -2 3.8921 0.086 5 0 -5 0.3880 0.106 -4 -2 0 9.0898 0.098 5 0 -7 0.7102 0.103 -4 -2 2 4.4506 0.079 5 -1 -7 1.3160 0.06 -4 -2 4 6.6692 0.113 5 -1 -6 2.7237 0.103 -4 -2 6 2.1697 0.052 5 -1 -4 1.6468 0.048 -4 -1 8 1.3732 0.062 5 -1 -3 1.7231 0.054 -4 -1 6 1.7622 0.076 5 -1 -2 4.3075 0.091 -4 -1 4 2.5684 0.078 5 -1 -1 1.2790 0.056 -4 -1 2 2.7148 0.074 5 -1 0 1.6205 0.045 -4 -1 0 3.2507 0.099 5 -1 1 1.3883 0.034 -4 -1 -1 0.8125 0.031 5 -1 2 4.4733 0.083 -4 -1 -2 2.6338 0.082 5 -1 3 1.7468 0.057 -4 -1 -4 2.4259 0.088 5 -1 4 1.5538 0.07 -4 -1 -6 1.5601 0.055 5 -1 7 1.3733 0.057 -4 0 -8 2.6153 0.102 5 -2 6 5.6187 0.117 -4 0 -6 5.3993 0.138 5 -2 5 1.6832 0.05 -4 0 -4 5.8552 0.11 5 -2 4 6.1053 0.144 -4 0 -2 8.7243 0.1 5 -2 3 0.9103 0.044 -4 0 0 10.0312 0.122 5 -2 2 8.8356 0.129 -4 0 2 8.7750 0.102 5 -2 1 1.9102 0.087 -4 0 4 5.7535 0.108 5 -2 0 8.0184 0.114 -4 0 6 5.6755 0.126 5 -2 -1 2.0664 0.067 -4 0 8 3.3295 0.107 5 -2 -2 8.8519 0.112 -4 1 7 0.5237 0.106 5 -2 -3 0.9484 0.048 -4 1 4 2.5519 0.096 5 -2 -4 6.1656 0.097 -4 1 2 2.4954 0.084 5 -2 -5 1.5545 0.048 -4 1 1 0.8974 0.035 6 -2 -4 1.6094 0.06 -4 1 0 3.3228 0.081 6 -2 -2 3.1325 0.103 -4 1 -1 1.2134 0.09 6 -2 -1 1.0638 0.064 -4 1 -2 2.6421 0.089 6 -2 0 2.2963 0.064 -4 1 -4 2.6309 0.099 6 -2 1 0.8583 0.061 -4 2 -4 6.9770 0.115 6 -2 2 3.1150 0.106 -4 2 -2 4.5587 0.078 6 -2 3 0.7774 0.071 -4 2 2 4.6637 0.079 6 -1 8 1.7775 0.062 -4 2 4 6.6929 0.102 6 -1 6 0.6594 0.091 -4 2 5 0.4059 0.101 6 -1 5 1.2285 0.054 -4 2 6 2.4018 0.092 6 -1 4 3.8658 0.103 -3 2 6 2.7542 0.055 6 -1 3 1.2621 0.046 -3 2 4 2.5822 0.079 6 -1 1 1.7669 0.051 -3 2 3 1.5806 0.044 6 -1 0 5.2334 0.097 -3 2 -2 5.0589 0.083 6 -1 -1 1.6817 0.048 -3 2 -3 1.4616 0.038 6 -1 -3 1.2867 0.044 -3 2 -6 2.6718 0.103 6 -1 -4 3.8224 0.103 -3 2 -7 1.0518 0.056 6 -1 -5 1.1481 0.053 -3 1 -8 1.5412 0.055 6 0 -8 4.2987 0.146 -3 1 -6 1.7973 0.078 6 0 -6 2.1302 0.111 -3 1 -4 2.9254 0.087 6 0 -4 8.3354 0.127
129
-3 1 -2 5.0462 0.092 6 0 -2 3.3510 0.09 -3 1 -1 0.7381 0.027 6 0 0 10.7374 0.127 -3 1 0 1.4582 0.049 6 0 2 3.4040 0.091 -3 1 2 5.2870 0.138 6 0 4 8.2968 0.121 -3 1 3 0.4621 0.051 6 0 6 2.2599 0.085 -3 1 4 3.0600 0.086 6 0 8 4.5272 0.153 -3 1 5 1.0969 0.044 6 1 8 1.8030 0.085 -3 1 6 1.9930 0.063 6 1 5 1.2161 0.049 -3 1 8 1.8596 0.058 6 1 4 3.6194 0.105 -3 0 9 0.6954 0.11 6 1 1 1.7353 0.057 -3 0 3 0.5338 0.055 6 1 0 5.0272 0.096 -3 0 1 0.9320 0.024 6 1 -1 1.7807 0.083 -3 0 -1 0.8777 0.025 6 1 -3 1.3059 0.047 -3 -1 -8 1.5378 0.056 6 1 -4 3.9010 0.108 -3 -1 -6 1.8116 0.055 6 1 -6 0.6302 0.084 -3 -1 -5 1.0581 0.047 6 1 -8 1.9278 0.128 -3 -1 -4 2.8747 0.095 6 2 -6 2.2729 0.074 -3 -1 -2 4.7786 0.097 6 2 -5 0.8754 0.063 -3 -1 -1 0.7246 0.026 6 2 -4 1.8094 0.063 -3 -1 0 1.4699 0.064 6 2 -2 3.0259 0.094 -3 -1 2 4.9747 0.106 6 2 -1 1.0464 0.046 -3 -1 3 0.3949 0.057 6 2 0 2.3689 0.07 -3 -1 4 3.0964 0.089 6 2 1 0.9246 0.046 -3 -1 5 1.1417 0.057 6 2 2 3.2026 0.095 -3 -1 6 1.9554 0.064 6 2 4 1.8691 0.067 -3 -1 7 0.4851 0.103 6 2 6 1.9697 0.072 -3 -1 8 1.8271 0.057 7 2 4 1.1151 0.052 -3 -2 7 0.9060 0.065 7 2 0 1.2898 0.045 -3 -2 6 2.6074 0.086 7 1 -6 2.6667 0.092 -3 -2 4 2.4215 0.071 7 1 -4 1.3416 0.049 -3 -2 3 1.4441 0.03 7 1 -3 0.4709 0.1 -3 -2 2 4.7407 0.076 7 1 -2 4.4541 0.107 -3 -2 1 0.8726 0.027 7 1 0 1.9946 0.085 -3 -2 -1 0.7740 0.04 7 1 2 4.0524 0.106 -3 -2 -2 4.1733 0.091 7 1 6 2.6650 0.154 -3 -2 -3 1.3381 0.029 7 0 7 1.7576 0.07 -3 -2 -4 2.2764 0.06 7 0 5 1.1350 0.067 -3 -2 -6 2.3021 0.049 7 0 3 2.3068 0.097 -2 -2 -6 1.2387 0.046 7 0 1 2.1808 0.075 -2 -2 -5 1.0997 0.049 7 0 -1 2.1483 0.086 -2 -2 -4 4.4483 0.084 7 0 -5 1.2053 0.055 -2 -2 2 1.5045 0.06 7 -1 -6 2.5434 0.099 -2 -2 4 5.0284 0.091 7 -1 -5 0.5408 0.105 -2 -2 8 1.7772 0.195 7 -1 -2 4.3627 0.106 -2 -1 8 3.3381 0.141 7 -1 0 1.8219 0.076 -2 -1 6 1.6805 0.042 7 -1 4 1.4106 0.046 -2 -1 4 7.1562 0.095 7 -1 5 0.3179 0.184 -2 -1 3 0.9168 0.029 7 -1 6 2.7849 0.096 -2 -1 2 0.6418 0.039 7 -2 4 0.9895 0.059 -2 -1 1 1.0207 0.035 7 -2 0 1.2261 0.044 -2 -1 0 10.4705 0.135 8 -2 2 0.5026 0.092
130
-2 -1 -1 0.9715 0.032 8 -2 3 0.8200 0.071 -2 -1 -2 0.7125 0.026 8 -1 6 1.7821 0.055 -2 -1 -3 0.9076 0.03 8 -1 5 0.9457 0.092 -2 -1 -4 6.7942 0.096 8 -1 4 2.7443 0.103 -2 -1 -6 1.4511 0.043 8 -1 3 1.4367 0.048 -2 -1 -8 2.7330 0.085 8 -1 2 2.4395 0.135 -2 0 -10 1.4607 0.073 8 -1 1 1.4095 0.079 -2 0 -6 3.6715 0.103 8 -1 0 3.0975 0.111 -2 0 -4 2.2413 0.075 8 -1 -1 1.4529 0.047 -2 0 -2 5.5802 0.064 8 -1 -2 2.8286 0.082 -2 0 0 4.0374 0.068 8 -1 -3 1.2873 0.056 -2 0 2 5.8078 0.065 8 -1 -4 2.6949 0.091 -2 0 4 2.1856 0.069 8 0 -4 5.7255 0.149 -2 0 6 3.5337 0.119 8 0 -2 0.4687 0.131 -2 0 8 0.7497 0.091 8 0 0 7.9429 0.139 -2 1 8 3.2578 0.119 8 0 4 6.1423 0.116 -2 1 4 7.0546 0.111 8 0 8 3.5888 0.125 -2 1 3 1.0002 0.03 8 1 6 1.7783 0.066 -2 1 2 0.6161 0.036 8 1 5 0.9343 0.071 -2 1 1 1.0534 0.037 8 1 4 2.7956 0.081 -2 1 0 11.3301 0.149 8 1 3 1.3509 0.051 -2 1 -1 1.0645 0.019 8 1 2 2.8951 0.114 -2 1 -2 0.7096 0.027 8 1 1 1.4720 0.047 -2 1 -4 7.0359 0.096 8 1 0 3.4611 0.107 -2 1 -6 1.4907 0.039 8 1 -1 1.4397 0.041 -2 1 -8 3.0234 0.12 8 1 -2 2.9386 0.113 -2 2 -6 1.2994 0.044 8 1 -4 2.7699 0.093 -2 2 -4 5.2074 0.087 8 1 -6 1.6318 0.096 -2 2 3 0.6192 0.044 8 1 -7 0.4897 0.198 -2 2 4 5.3080 0.113 8 2 -4 0.8446 0.074 -1 2 6 5.7442 0.104 8 2 -1 0.9978 0.053 -1 2 5 1.0587 0.046 8 2 1 1.0969 0.051 -1 2 4 6.5076 0.11 8 2 2 0.6209 0.075 -1 2 -4 6.5879 0.098 8 2 5 0.5039 0.142 -1 2 -5 1.4991 0.066 9 2 3 0.8987 0.075 -1 2 -6 5.6747 0.103 9 2 2 4.7844 0.133 -1 1 -8 0.8924 0.079 9 2 0 3.6453 0.14 -1 1 -7 0.7682 0.065 9 2 -2 4.7983 0.128 -1 1 -6 4.3966 0.11 9 2 -4 3.0634 0.195 -1 1 -4 1.8420 0.072 9 1 -4 2.3999 0.122 -1 1 -3 1.2768 0.059 9 1 -3 1.6492 0.049 -1 1 -2 7.3357 0.083 9 1 -2 1.4072 0.086 -1 1 -1 3.5860 0.122 9 1 -1 1.3939 0.056 -1 1 2 8.1782 0.068 9 1 0 3.1571 0.12 -1 1 3 1.7491 0.101 9 1 2 1.5003 0.049 -1 1 4 2.0987 0.069 9 1 3 1.4919 0.056 -1 1 6 4.3829 0.1 9 1 4 2.5530 0.103 -1 1 8 1.0198 0.069 9 1 6 0.7651 0.101 -1 0 9 0.9006 0.112 9 -1 -4 2.5138 0.109 -1 0 5 1.4505 0.05 9 -1 -3 1.5430 0.077 -1 0 1 1.6461 0.04 9 -1 -2 1.3757 0.053
131
-1 0 -1 1.5591 0.045 9 -1 -1 1.3570 0.05 -1 0 -3 0.5200 0.042 9 -1 0 3.0600 0.133 -1 0 -5 1.2897 0.044 9 -1 1 1.3007 0.055 -1 -1 -7 0.7186 0.072 9 -1 2 1.3836 0.057 -1 -1 -6 4.0444 0.103 9 -1 3 1.5052 0.055 -1 -1 -5 0.5563 0.063 9 -1 4 2.6758 0.075 -1 -1 -4 1.7612 0.084 9 -1 5 0.6132 0.117 -1 -1 -3 2.0871 0.102 10 -1 4 0.8206 0.089 -1 -1 -2 7.9135 0.094 10 -1 2 1.3574 0.064 -1 -1 2 8.1399 0.086 10 -1 0 1.3290 0.058 -1 -1 3 1.1913 0.057 10 -1 -2 1.4780 0.057 -1 -1 4 1.9658 0.052 10 0 -6 4.2151 0.168 -1 -1 6 3.6758 0.113 10 0 -4 2.6810 0.107 -1 -2 8 3.4550 0.112 10 0 -2 6.3733 0.132 -1 -2 6 5.4578 0.134 10 0 0 3.0894 0.13 -1 -2 5 1.0467 0.041 10 0 2 6.1032 0.127 -1 -2 4 6.5524 0.097 10 0 4 2.6652 0.088 -1 -2 -4 5.7982 0.089 10 0 6 4.0120 0.169 -1 -2 -6 4.7701 0.112 10 1 2 0.7844 0.111 0 -2 -6 1.1305 0.054 10 1 0 1.2754 0.056 0 -2 3 1.0674 0.063 10 1 -2 1.4419 0.059 0 -2 4 0.8338 0.038 10 1 -4 0.8726 0.082 0 -2 6 1.2562 0.056 10 1 -6 0.9506 0.092 0 -2 7 0.6487 0.082 10 2 -3 0.4676 0.129 0 0 -10 1.8479 0.07 10 2 -2 1.2002 0.069 0 0 -8 8.4761 0.152 10 2 0 2.5350 0.118 0 0 -6 4.0720 0.134 11 1 0 1.4502 0.062 0 0 -4 17.1092 0.205 11 -1 0 1.1870 0.069 0 0 -2 8.2593 0.106 11 -1 2 1.0027 0.108 0 0 2 8.4492 0.084 12 1 0 1.6175 0.066 0 0 4 17.5290 0.184 12 1 -2 1.3827 0.069 0 0 6 3.7969 0.114 0 0 8 8.8879 0.132
P = 5.750(7) GPa
h k l FO Esd h k l FO Esd -12 1 0 1.6060 0.06 1 2 4 5.3429 0.083 -11 -1 -3 1.1715 0.066 1 2 -3 0.3321 0.05 -11 -1 0 1.3760 0.049 1 2 -4 5.3731 0.11 -11 -1 1 0.7897 0.075 1 2 -5 0.8342 0.044 -10 -1 2 1.1591 0.05 1 2 -6 4.4543 0.137 -10 -1 -2 1.2500 0.045 1 2 -7 0.4601 0.089 -10 -1 -4 0.7949 0.072 1 1 -6 3.3975 0.12 -10 0 -6 3.8144 0.122 1 1 -4 1.5953 0.036 -10 0 -2 5.2045 0.172 1 1 -2 6.9047 0.078 -10 0 0 2.5878 0.122 1 1 2 6.7150 0.112 -10 0 2 4.0379 0.162 1 1 3 2.0020 0.153 -10 0 4 2.2482 0.101 1 1 4 1.6775 0.062 -10 0 6 3.7293 0.107 1 1 5 0.4688 0.06 -10 1 4 0.6079 0.12 1 1 6 3.1470 0.105
132
-10 1 -4 0.6331 0.11 1 0 5 1.1865 0.042 -10 2 0 2.3128 0.084 1 0 1 1.3614 0.059 -9 2 2 4.0048 0.134 1 0 -1 1.4145 0.039 -9 2 0 3.4981 0.128 1 0 -5 1.1288 0.037 -9 1 -4 2.1111 0.057 1 -1 -9 0.5789 0.103 -9 1 1 1.3784 0.058 1 -1 -6 3.6339 0.119 -9 1 2 1.1579 0.064 1 -1 -4 1.4148 0.068 -9 1 3 1.3478 0.049 1 -1 -2 6.5934 0.082 -9 1 4 2.1263 0.091 1 -1 3 2.5281 0.112 -9 0 -5 0.8150 0.117 1 -1 4 1.5815 0.055 -9 -1 -4 2.2478 0.07 1 -1 6 3.8482 0.124 -9 -1 -3 1.4015 0.051 1 -1 7 0.7855 0.058 -9 -1 0 2.8900 0.084 1 -1 8 1.0243 0.058 -9 -1 1 1.2419 0.048 1 -1 9 0.3756 0.164 -9 -1 2 1.2372 0.04 1 -2 6 4.5329 0.126 -9 -1 3 1.4898 0.039 1 -2 4 5.2597 0.091 -9 -1 4 2.2437 0.046 1 -2 3 0.1963 0.079 -9 -1 6 0.5044 0.166 1 -2 -4 5.3678 0.11 -9 -2 2 3.8308 0.146 1 -2 -6 4.8176 0.126 -9 -2 0 3.7218 0.103 2 -2 -4 4.5733 0.095 -9 -2 -2 3.8164 0.164 2 -2 3 0.6372 0.031 -8 -1 6 1.5591 0.061 2 -2 6 1.0916 0.04 -8 -1 4 2.2643 0.075 2 -1 8 2.9956 0.094 -8 -1 2 2.2118 0.08 2 -1 6 1.3719 0.036 -8 -1 1 1.4624 0.066 2 -1 3 0.7872 0.027 -8 -1 0 2.8840 0.092 2 -1 2 0.6778 0.033 -8 -1 -1 1.4998 0.039 2 -1 1 0.8715 0.035 -8 -1 -2 2.4894 0.065 2 -1 0 9.1076 0.125 -8 -1 -3 1.3008 0.037 2 -1 -1 0.9488 0.018 -8 -1 -4 2.4595 0.077 2 -1 -3 0.7579 0.025 -8 -1 -5 1.0053 0.057 2 -1 -4 5.7516 0.102 -8 -1 -6 1.7046 0.049 2 -1 -6 1.4242 0.037 -8 0 -8 3.2415 0.098 2 -1 -8 3.2386 0.097 -8 0 -4 5.3749 0.142 2 0 -10 1.6872 0.065 -8 0 0 6.6193 0.129 2 0 -6 3.1545 0.096 -8 0 4 5.1605 0.123 2 0 -4 1.9074 0.064 -8 0 8 3.5823 0.111 2 0 -2 4.7043 0.075 -8 1 5 1.2902 0.063 2 0 0 3.3248 0.053 -8 1 4 2.4674 0.101 2 0 2 4.5231 0.069 -8 1 2 2.3761 0.066 2 0 4 1.8102 0.047 -8 1 1 1.3604 0.037 2 0 6 2.9980 0.122 -8 1 0 2.8279 0.111 2 0 8 0.5467 0.121 -8 1 -1 1.4085 0.041 2 1 8 2.7998 0.083 -8 1 -2 2.3623 0.074 2 1 4 5.5345 0.142 -8 1 -6 1.6831 0.045 2 1 3 0.6076 0.041 -8 2 -3 0.6481 0.068 2 1 2 0.5400 0.025 -7 2 5 0.5139 0.095 2 1 1 0.9249 0.025 -7 2 0 0.9769 0.048 2 1 0 9.3990 0.134 -7 1 -6 2.4134 0.099 2 1 -1 0.8900 0.023 -7 1 -2 3.6896 0.109 2 1 -3 0.7277 0.028 -7 1 0 1.6001 0.042 2 1 -4 6.0503 0.115
133
-7 1 2 3.5374 0.13 2 1 -6 1.4804 0.046 -7 1 3 0.5084 0.071 2 1 -8 3.0264 0.077 -7 1 6 2.4145 0.047 2 2 -7 0.7900 0.066 -7 0 7 1.5404 0.056 2 2 -4 4.5486 0.103 -7 0 3 2.0474 0.071 2 2 4 4.4097 0.122 -7 0 1 1.9616 0.055 2 2 5 0.4464 0.084 -7 0 -1 2.1032 0.07 3 2 6 2.3405 0.054 -7 0 -3 2.0356 0.06 3 2 4 2.1848 0.071 -7 0 -5 1.1084 0.05 3 2 3 1.3497 0.029 -7 0 -7 1.6230 0.071 3 2 2 4.4723 0.074 -7 -1 -6 2.2844 0.059 3 2 -2 4.4873 0.093 -7 -1 -2 3.6530 0.126 3 2 -3 1.3810 0.046 -7 -1 0 1.6683 0.062 3 2 -4 2.2544 0.07 -7 -1 2 3.4019 0.128 3 2 -6 2.2227 0.084 -7 -1 4 1.1448 0.055 3 1 -9 0.9060 0.07 -7 -1 6 2.3188 0.053 3 1 -7 0.4682 0.094 -7 -2 4 0.9044 0.047 3 1 -6 1.6397 0.037 -7 -2 0 1.1402 0.04 3 1 -4 2.4599 0.082 -7 -2 -4 0.9865 0.049 3 1 -2 3.8813 0.106 -6 -2 -4 1.5002 0.05 3 1 -1 0.6682 0.025 -6 -2 -2 3.1035 0.096 3 1 0 1.3062 0.033 -6 -2 -1 0.8393 0.037 3 1 1 0.6835 0.024 -6 -2 0 1.9633 0.051 3 1 2 3.8902 0.097 -6 -2 2 3.0606 0.089 3 1 4 2.6291 0.072 -6 -2 4 1.5324 0.041 3 1 6 1.4859 0.038 -6 -2 5 0.7390 0.061 3 0 1 0.8010 0.018 -6 -2 6 2.0547 0.051 3 0 -1 0.7768 0.023 -6 -1 8 1.7454 0.053 3 0 -5 0.6542 0.057 -6 -1 4 2.9381 0.092 3 -1 -8 1.4438 0.062 -6 -1 3 1.1308 0.036 3 -1 -6 1.6398 0.04 -6 -1 1 1.6028 0.054 3 -1 -5 0.9481 0.048 -6 -1 0 4.2829 0.104 3 -1 -4 2.5258 0.088 -6 -1 -1 1.5838 0.055 3 -1 -2 4.3234 0.129 -6 -1 -3 1.1467 0.048 3 -1 -1 0.6032 0.03 -6 -1 -5 1.0583 0.061 3 -1 0 1.2736 0.022 -6 0 -8 4.1873 0.159 3 -1 1 0.7219 0.02 -6 0 -6 1.7690 0.047 3 -1 2 4.4330 0.111 -6 0 -4 6.7461 0.135 3 -1 4 2.4715 0.096 -6 0 -2 2.6793 0.128 3 -1 6 1.4972 0.051 -6 0 0 8.8014 0.168 3 -1 8 1.3718 0.078 -6 0 2 2.8562 0.098 3 -1 9 1.0769 0.061 -6 0 4 6.9562 0.168 3 -2 4 2.0917 0.056 -6 0 6 1.9834 0.061 3 -2 3 1.2544 0.051 -6 0 8 3.9117 0.128 3 -2 2 4.3620 0.087 -6 1 8 1.8115 0.049 3 -2 -2 4.1861 0.087 -6 1 4 3.0736 0.152 3 -2 -3 1.2957 0.034 -6 1 3 1.2022 0.035 3 -2 -4 2.0377 0.081 -6 1 0 4.1213 0.127 3 -2 -5 0.4009 0.082 -6 1 -1 1.5550 0.037 3 -2 -7 0.8840 0.064 -6 1 -3 1.1659 0.038 4 -2 -6 1.9562 0.067 -6 1 -4 3.2072 0.087 4 -2 -4 5.9166 0.121
134
-6 1 -8 1.6698 0.058 4 -2 -2 3.8825 0.096 -6 2 -6 1.8717 0.044 4 -2 0 8.6822 0.12 -6 2 -4 1.4499 0.062 4 -2 2 4.0765 0.079 -6 2 -2 2.9180 0.102 4 -2 4 6.0619 0.127 -6 2 0 2.0420 0.055 4 -2 6 1.8414 0.071 -6 2 1 0.6671 0.058 4 -1 8 1.2386 0.064 -6 2 2 2.9850 0.115 4 -1 6 1.4811 0.047 -6 2 4 1.5964 0.077 4 -1 4 2.4195 0.053 -5 2 6 4.7545 0.145 4 -1 2 2.2487 0.057 -5 2 5 1.4150 0.048 4 -1 0 2.8424 0.087 -5 2 4 5.2656 0.125 4 -1 -2 2.1815 0.059 -5 2 2 7.6825 0.13 4 -1 -4 2.3298 0.059 -5 2 1 1.8616 0.051 4 -1 -6 1.5939 0.037 -5 2 0 6.5215 0.126 4 -1 -8 1.0663 0.06 -5 2 -1 1.6366 0.071 4 0 -8 2.8931 0.117 -5 2 -2 7.6304 0.13 4 0 -6 4.8836 0.13 -5 2 -4 5.1577 0.126 4 0 -4 4.8258 0.125 -5 2 -6 4.4873 0.134 4 0 -2 7.3925 0.106 -5 1 -7 1.1493 0.091 4 0 0 7.9805 0.11 -5 1 -6 2.1869 0.109 4 0 2 7.1950 0.098 -5 1 -5 0.6137 0.066 4 0 4 4.8204 0.132 -5 1 -4 1.3778 0.101 4 0 6 4.7690 0.129 -5 1 -3 1.5689 0.08 4 0 8 2.6787 0.077 -5 1 -2 3.7653 0.105 4 1 6 1.5663 0.032 -5 1 -1 1.2512 0.031 4 1 4 2.1795 0.085 -5 1 0 1.2557 0.047 4 1 2 2.2356 0.065 -5 1 2 3.9643 0.106 4 1 1 0.7518 0.055 -5 1 3 1.7133 0.035 4 1 0 2.6016 0.067 -5 1 4 1.2630 0.058 4 1 -2 2.3283 0.066 -5 1 7 1.4180 0.053 4 1 -4 2.1326 0.081 -5 1 8 0.5077 0.139 4 1 -6 1.6015 0.032 -5 0 3 1.0917 0.046 4 1 -8 1.1943 0.062 -5 -1 -4 1.4156 0.034 4 2 -6 1.9170 0.058 -5 -1 -3 1.6248 0.032 4 2 -4 5.7816 0.156 -5 -1 -2 3.6343 0.127 4 2 -2 3.9254 0.103 -5 -1 -1 1.2045 0.028 4 2 0 8.4946 0.149 -5 -1 0 1.3661 0.056 4 2 2 3.9150 0.091 -5 -1 1 1.2039 0.034 4 2 4 5.7074 0.134 -5 -1 2 3.8097 0.104 4 2 6 2.0208 0.063 -5 -1 3 1.5989 0.053 5 2 6 4.4924 0.165 -5 -1 4 1.2974 0.048 5 2 5 1.6223 0.063 -5 -1 6 2.3667 0.078 5 2 4 5.4465 0.119 -5 -1 7 1.1300 0.049 5 2 2 6.9584 0.136 -5 -1 8 0.8371 0.07 5 2 1 1.7487 0.044 -5 -2 6 4.6323 0.148 5 2 0 6.8739 0.116 -5 -2 4 5.3661 0.124 5 2 -1 1.6932 0.049 -5 -2 3 0.8435 0.041 5 2 -2 7.2570 0.14 -5 -2 2 7.5445 0.124 5 2 -4 5.3717 0.119 -5 -2 1 1.8504 0.046 5 2 -5 1.3768 0.056 -5 -2 0 6.7785 0.113 5 1 -7 1.1700 0.055 -5 -2 -1 1.7470 0.043 5 1 -6 2.4223 0.08
135
-5 -2 -2 7.4064 0.132 5 1 -4 1.2828 0.034 -5 -2 -4 4.9629 0.155 5 1 -3 1.6448 0.04 -5 -2 -5 1.3475 0.066 5 1 -2 3.8504 0.108 -5 -2 -6 4.8509 0.157 5 1 -1 1.2574 0.033 -4 -2 -6 2.0194 0.051 5 1 0 1.3124 0.026 -4 -2 -4 5.7810 0.125 5 1 1 1.2958 0.024 -4 -2 -2 3.8382 0.103 5 1 2 3.8833 0.083 -4 -2 0 8.5804 0.145 5 1 3 1.6283 0.04 -4 -2 2 3.8794 0.09 5 1 4 1.3288 0.045 -4 -2 3 0.2760 0.08 5 1 6 2.4069 0.065 -4 -2 4 5.8702 0.153 5 1 7 1.1670 0.049 -4 -1 8 1.2368 0.078 5 0 7 0.6856 0.074 -4 -1 7 0.6467 0.074 5 0 3 1.1503 0.044 -4 -1 6 1.5723 0.036 5 0 -3 1.1714 0.047 -4 -1 4 2.3047 0.08 5 -1 -6 2.3474 0.062 -4 -1 2 2.0952 0.077 5 -1 -4 1.3713 0.042 -4 -1 0 2.8540 0.097 5 -1 -3 1.6901 0.038 -4 -1 -2 2.4086 0.069 5 -1 -2 3.9217 0.094 -4 -1 -4 2.3674 0.084 5 -1 -1 1.2433 0.032 -4 -1 -6 1.4676 0.047 5 -1 0 1.3206 0.023 -4 0 -8 2.7920 0.059 5 -1 1 1.2166 0.023 -4 0 -6 5.0127 0.116 5 -1 2 3.6944 0.117 -4 0 -4 4.9359 0.111 5 -1 3 1.6371 0.056 -4 0 -2 7.2246 0.101 5 -1 6 2.3508 0.098 -4 0 0 8.3511 0.128 5 -1 7 1.2859 0.046 -4 0 2 7.2675 0.102 5 -2 6 4.7872 0.139 -4 0 4 4.8579 0.117 5 -2 5 1.5512 0.037 -4 0 6 4.8614 0.125 5 -2 4 5.0071 0.138 -4 0 8 2.6572 0.077 5 -2 3 0.8820 0.039 -4 1 6 1.5516 0.039 5 -2 2 7.5022 0.107 -4 1 5 0.3894 0.093 5 -2 1 1.7604 0.051 -4 1 4 2.1867 0.076 5 -2 0 6.8968 0.12 -4 1 2 2.3542 0.07 5 -2 -1 1.6591 0.059 -4 1 0 3.0726 0.172 5 -2 -2 7.5429 0.122 -4 1 -1 1.0065 0.068 5 -2 -3 1.0288 0.064 -4 1 -2 2.3018 0.068 5 -2 -4 5.2083 0.123 -4 1 -4 2.2268 0.075 5 -2 -6 4.6944 0.146 -4 1 -8 1.2293 0.051 6 -2 -4 1.5095 0.036 -4 2 -4 6.0774 0.123 6 -2 -3 0.9600 0.047 -4 2 -2 3.9049 0.093 6 -2 -2 2.9685 0.114 -4 2 0 8.4934 0.129 6 -2 0 2.0295 0.059 -4 2 2 3.7505 0.122 6 -2 2 2.8524 0.113 -4 2 4 5.6571 0.117 6 -2 4 1.6688 0.054 -4 2 6 1.7485 0.086 6 -2 6 2.1066 0.07 -3 2 6 2.3018 0.075 6 -1 7 0.4629 0.117 -3 2 4 2.2313 0.094 6 -1 5 1.0130 0.051 -3 2 3 1.3652 0.027 6 -1 4 3.4234 0.108 -3 2 2 4.4670 0.105 6 -1 3 1.2174 0.032 -3 2 -2 4.4248 0.076 6 -1 1 1.6555 0.053 -3 2 -3 1.4351 0.047 6 -1 0 3.7071 0.113 -3 1 -9 0.7997 0.086 6 -1 -1 1.5978 0.074
136
-3 1 -6 1.6216 0.038 6 -1 -3 1.2597 0.036 -3 1 -4 2.6190 0.095 6 -1 -4 3.0487 0.119 -3 1 -2 4.1747 0.095 6 -1 -8 1.6197 0.071 -3 1 0 1.2954 0.024 6 0 -8 4.1578 0.159 -3 1 1 0.6223 0.031 6 0 -6 1.8236 0.054 -3 1 2 4.1129 0.153 6 0 -4 5.5291 0.122 -3 1 4 2.4713 0.066 6 0 -2 2.7445 0.093 -3 1 5 0.9971 0.041 6 0 0 8.8262 0.161 -3 1 6 1.6479 0.052 6 0 2 2.9424 0.096 -3 1 8 1.4138 0.047 6 0 4 6.7198 0.146 -3 0 7 0.5484 0.083 6 0 6 1.8477 0.064 -3 0 1 0.7488 0.023 6 0 8 3.7093 0.19 -3 0 -1 0.7833 0.019 6 1 5 1.0380 0.047 -3 0 -3 0.4679 0.06 6 1 4 3.3172 0.123 -3 0 -7 0.5937 0.077 6 1 3 1.2595 0.041 -3 -1 -8 1.5106 0.048 6 1 1 1.5889 0.042 -3 -1 -6 1.6734 0.053 6 1 0 4.4413 0.095 -3 -1 -5 0.9907 0.046 6 1 -1 1.6773 0.039 -3 -1 -4 2.7391 0.083 6 1 -4 3.1573 0.104 -3 -1 -2 4.3113 0.109 6 1 -7 0.8150 0.092 -3 -1 -1 0.6615 0.021 6 1 -8 1.6253 0.051 -3 -1 0 1.2638 0.036 6 2 -5 0.7168 0.066 -3 -1 1 0.6347 0.024 6 2 -4 1.4924 0.038 -3 -1 2 4.2814 0.097 6 2 -3 0.7708 0.045 -3 -1 4 2.6562 0.083 6 2 -2 2.5449 0.115 -3 -1 5 1.1041 0.035 6 2 0 2.1333 0.063 -3 -1 8 1.5557 0.05 6 2 2 2.8833 0.101 -3 -2 7 0.9603 0.049 7 2 0 1.0460 0.041 -3 -2 6 2.4384 0.059 7 1 -6 2.2400 0.101 -3 -2 5 0.5568 0.064 7 1 -5 0.6787 0.065 -3 -2 4 2.0396 0.062 7 1 -2 3.4527 0.115 -3 -2 3 1.2345 0.037 7 1 0 1.4819 0.036 -3 -2 2 4.3490 0.112 7 1 2 3.5811 0.098 -3 -2 -2 4.4629 0.077 7 1 6 2.4782 0.073 -3 -2 -3 1.2886 0.041 7 0 7 1.5305 0.046 -3 -2 -4 1.8917 0.07 7 0 5 1.0699 0.047 -3 -2 -6 2.3631 0.066 7 0 3 2.1060 0.067 -2 -2 -6 1.1584 0.056 7 0 1 2.0119 0.04 -2 -2 -5 0.7242 0.067 7 0 -1 1.8784 0.054 -2 -2 -4 4.3976 0.111 7 0 -3 1.9655 0.065 -2 -2 -3 0.6210 0.033 7 0 -5 1.2157 0.042 -2 -2 4 4.4819 0.106 7 0 -7 1.6048 0.045 -2 -2 5 0.8284 0.061 7 -1 -6 2.3895 0.053 -2 -2 6 1.1725 0.041 7 -1 -2 3.6661 0.119 -2 -1 8 2.9299 0.088 7 -1 0 1.4700 0.036 -2 -1 6 1.3600 0.035 7 -1 1 0.4857 0.067 -2 -1 4 5.8209 0.131 7 -1 2 3.4156 0.12 -2 -1 3 0.7772 0.024 7 -1 4 1.1671 0.042 -2 -1 2 0.5903 0.023 7 -1 6 2.3059 0.074 -2 -1 1 0.8974 0.033 7 -2 2 0.5431 0.067 -2 -1 0 9.3818 0.158 7 -2 -3 0.4178 0.088
137
-2 -1 -1 0.8900 0.024 8 -2 -1 0.7983 0.075 -2 -1 -4 5.9910 0.119 8 -2 2 0.4341 0.091 -2 -1 -6 1.2665 0.047 8 -1 7 1.0169 0.066 -2 -1 -8 3.1267 0.123 8 -1 6 1.6229 0.046 -2 0 -10 1.5614 0.071 8 -1 4 2.3543 0.04 -2 0 -6 3.1009 0.086 8 -1 2 2.3651 0.083 -2 0 -4 1.8231 0.043 8 -1 1 1.3878 0.042 -2 0 -2 4.6003 0.087 8 -1 0 3.0278 0.115 -2 0 0 3.3967 0.083 8 -1 -1 1.4194 0.051 -2 0 2 4.6303 0.075 8 -1 -4 2.3659 0.045 -2 0 4 1.8086 0.073 8 -1 -6 1.5787 0.044 -2 0 6 3.0874 0.13 8 0 -8 3.1524 0.12 -2 1 8 2.9728 0.096 8 0 -4 5.3388 0.146 -2 1 4 5.9991 0.123 8 0 -2 0.7174 0.059 -2 1 3 0.7669 0.027 8 0 0 6.5010 0.121 -2 1 1 0.9399 0.02 8 0 2 0.6989 0.056 -2 1 0 9.4111 0.123 8 0 4 5.3402 0.133 -2 1 -4 6.0785 0.138 8 0 8 3.1815 0.131 -2 1 -6 1.4997 0.036 8 1 4 2.3353 0.056 -2 1 -8 2.8849 0.123 8 1 2 2.4645 0.078 -2 2 -4 4.5395 0.104 8 1 1 1.3447 0.059 -2 2 4 4.6097 0.115 8 1 0 2.7992 0.106 -1 2 6 4.4378 0.162 8 1 -1 1.3926 0.046 -1 2 5 0.8837 0.041 8 1 -2 2.4282 0.068 -1 2 4 5.4417 0.1 8 1 -4 2.2678 0.054 -1 2 -4 5.4994 0.118 8 1 -5 1.0894 0.059 -1 2 -6 4.6428 0.149 8 1 -6 1.6257 0.045 -1 1 -7 0.7660 0.055 8 2 -3 0.5323 0.076 -1 1 -6 3.6735 0.107 8 2 -2 0.7037 0.071 -1 1 -4 1.6697 0.051 8 2 2 0.5712 0.07 -1 1 -3 1.6376 0.105 8 2 3 0.5753 0.072 -1 1 -2 6.9873 0.101 9 2 2 3.8080 0.133 -1 1 2 6.6814 0.078 9 2 0 3.4897 0.125 -1 1 4 1.6255 0.077 9 2 -1 0.4198 0.119 -1 1 6 3.4420 0.119 9 2 -2 3.9910 0.153 -1 0 9 0.6971 0.113 9 1 -5 0.9262 0.076 -1 0 5 1.1718 0.03 9 1 -4 2.2372 0.09 -1 0 1 1.4251 0.046 9 1 -3 1.4624 0.049 -1 0 -1 1.3328 0.043 9 1 -1 1.2068 0.04 -1 0 -3 1.0383 0.076 9 1 0 2.8148 0.09 -1 0 -5 1.2060 0.034 9 1 2 1.1868 0.046 -1 -1 -6 3.7119 0.152 9 1 4 2.0931 0.085 -1 -1 -4 1.8079 0.065 9 -1 -4 2.1440 0.098 -1 -1 -2 7.0228 0.111 9 -1 -3 1.4937 0.045 -1 -1 2 6.7546 0.087 9 -1 -2 1.1074 0.046 -1 -1 3 1.7501 0.093 9 -1 0 2.5511 0.083 -1 -1 4 1.5828 0.062 9 -1 2 1.1202 0.053 -1 -1 6 3.7205 0.116 9 -1 3 1.4275 0.049 -1 -1 7 0.6146 0.076 9 -1 4 2.2575 0.041 -1 -2 6 4.2736 0.116 9 -1 5 0.9287 0.062 -1 -2 5 0.6248 0.052 9 -2 2 4.1067 0.154
138
-1 -2 4 5.3507 0.094 9 -2 0 3.4027 0.112 -1 -2 -3 0.3452 0.052 9 -2 -1 0.4123 0.123 -1 -2 -4 5.2715 0.113 9 -2 -2 3.6932 0.177 -1 -2 -6 4.4781 0.164 10 -2 0 2.3088 0.111 0 -2 -6 1.1713 0.042 10 -1 4 0.9450 0.072 0 -2 3 0.9704 0.034 10 -1 -1 0.3086 0.183 0 -2 6 1.2805 0.044 10 -1 -4 0.7541 0.106 0 0 -10 2.2035 0.097 10 0 -6 3.8549 0.127 0 0 -8 7.0801 0.174 10 0 -4 2.3537 0.057 0 0 -6 3.4147 0.123 10 0 -2 5.2879 0.134 0 0 -4 14.2831 0.218 10 0 0 2.6379 0.089 0 0 -2 6.8981 0.107 10 0 2 4.9503 0.148 0 0 2 6.9384 0.098 10 0 4 2.3699 0.047 0 0 4 14.4575 0.186 10 0 6 3.4129 0.192 0 0 6 3.6893 0.11 10 1 2 1.1491 0.05 0 0 8 7.2033 0.188 10 1 -5 0.4995 0.125 0 0 10 1.7473 0.085 11 1 2 0.9898 0.07 0 2 6 1.2102 0.072 11 -1 0 1.2558 0.053 0 2 7 0.5232 0.086 11 -1 2 0.9509 0.124 1 2 6 4.5517 0.126
P = 7.663(8) GPa
h k l FO Esd h k l FO Esd -13 0 -1 1.9017 0.108 1 2 -6 7.1697 0.114 -12 1 0 2.0442 0.097 1 2 -8 4.0931 0.133 -11 1 -1 1.0453 0.153 1 1 -8 1.2743 0.114 -11 1 0 1.5273 0.115 1 1 -6 5.4426 0.143 -11 -1 -2 0.9894 0.17 1 1 -4 2.5305 0.08 -10 -1 -2 1.8649 0.087 1 1 -2 9.8073 0.1 -10 0 -6 5.3856 0.2 1 1 2 10.1220 0.1 -10 0 -4 3.5255 0.081 1 1 4 2.4045 0.053 -10 0 -2 7.7391 0.136 1 1 6 5.2352 0.133 -10 0 0 3.7506 0.139 1 1 8 1.3064 0.112 -10 0 2 7.4446 0.138 1 0 5 1.7949 0.05 -10 0 4 2.8875 0.111 1 0 1 2.1922 0.045 -10 0 6 4.4110 0.225 1 0 -1 2.0660 0.05 -10 1 4 1.0232 0.153 1 0 -3 2.7333 0.087 -10 1 2 1.4820 0.106 1 0 -5 1.6331 0.058 -10 1 0 1.2726 0.121 1 -1 -6 5.5605 0.127 -10 1 -2 1.4784 0.127 1 -1 -4 2.7056 0.094 -10 2 0 3.3972 0.078 1 -1 -2 9.8887 0.098 -9 2 2 5.2472 0.153 1 -1 2 9.7872 0.108 -9 2 0 4.4470 0.121 1 -1 3 2.4939 0.175 -9 2 -2 5.6781 0.146 1 -1 4 2.5492 0.05 -9 2 -4 4.1148 0.112 1 -1 6 5.4710 0.143 -9 1 -6 0.8507 0.198 1 -2 8 4.2955 0.113 -9 1 -4 3.2926 0.078 1 -2 6 6.9304 0.146 -9 1 -1 2.0595 0.078 1 -2 4 7.9054 0.091 -9 1 0 3.8011 0.113 1 -2 -4 7.9059 0.12 -9 1 3 2.3435 0.067 1 -2 -5 1.4016 0.077
139
-9 1 4 3.0293 0.071 1 -2 -6 6.7616 0.116 -9 -1 -4 3.3681 0.091 2 -2 -4 6.6734 0.12 -9 -1 -3 2.1773 0.084 2 -2 -3 0.8317 0.067 -9 -1 -1 1.9129 0.081 2 -2 2 2.1662 0.047 -9 -1 0 3.9794 0.096 2 -2 3 0.7439 0.081 -9 -1 1 2.1581 0.093 2 -2 4 6.5752 0.101 -9 -1 2 1.6134 0.084 2 -2 6 1.8155 0.063 -9 -1 3 2.1469 0.073 2 -2 8 3.3247 0.103 -9 -1 4 3.1791 0.067 2 -1 8 4.3121 0.115 -9 -2 2 5.2941 0.163 2 -1 6 2.1427 0.058 -9 -2 0 4.8891 0.141 2 -1 4 8.7719 0.115 -8 -2 -1 1.3040 0.097 2 -1 2 0.7734 0.048 -8 -1 6 2.1986 0.08 2 -1 1 1.3596 0.036 -8 -1 4 3.6135 0.107 2 -1 0 13.8168 0.159 -8 -1 2 3.3774 0.139 2 -1 -4 8.6960 0.125 -8 -1 1 2.0149 0.064 2 0 -6 4.0471 0.111 -8 -1 0 3.9761 0.159 2 0 -4 2.8490 0.079 -8 -1 -1 2.1498 0.061 2 0 -2 6.5715 0.065 -8 -1 -2 3.3612 0.088 2 0 0 4.9359 0.068 -8 -1 -3 1.7859 0.074 2 0 2 6.8781 0.068 -8 -1 -4 3.8191 0.094 2 0 4 2.6397 0.08 -8 -1 -5 1.0743 0.143 2 0 6 4.3801 0.143 -8 -1 -6 2.3883 0.091 2 1 6 2.0136 0.058 -8 0 -4 7.8864 0.146 2 1 4 8.7794 0.104 -8 0 4 7.3078 0.141 2 1 3 1.1800 0.044 -8 1 6 2.0857 0.09 2 1 1 1.3550 0.042 -8 1 4 2.9609 0.096 2 1 0 13.7897 0.164 -8 1 2 3.2566 0.079 2 1 -1 1.3744 0.029 -8 1 1 2.0566 0.07 2 1 -2 0.7490 0.055 -8 1 0 4.1624 0.133 2 1 -3 0.9639 0.072 -8 1 -1 2.0345 0.065 2 1 -4 8.5953 0.12 -8 1 -2 3.2506 0.118 2 1 -6 2.1487 0.075 -8 1 -4 3.4236 0.073 2 1 -8 4.5379 0.117 -8 2 3 0.8328 0.135 2 2 -8 3.2684 0.079 -7 2 -4 1.2735 0.095 2 2 -4 6.4561 0.115 -7 1 -6 3.1394 0.124 2 2 -3 0.9127 0.07 -7 1 -5 0.7547 0.177 2 2 4 6.4840 0.119 -7 1 -4 1.8640 0.069 2 2 6 1.6101 0.083 -7 1 -3 0.7407 0.137 3 2 6 3.1678 0.085 -7 1 -2 5.5254 0.139 3 2 4 2.7040 0.069 -7 1 0 2.0013 0.086 3 2 3 1.8923 0.046 -7 1 2 4.8491 0.171 3 2 -2 6.2816 0.106 -7 1 6 3.2312 0.09 3 2 -3 1.9986 0.046 -7 0 7 2.0844 0.099 3 2 -4 2.9501 0.08 -7 0 5 1.5090 0.09 3 2 -6 3.2249 0.083 -7 0 3 3.1512 0.067 3 2 -7 1.2805 0.132 -7 0 1 2.8303 0.085 3 1 -8 2.4165 0.084 -7 0 -1 3.2156 0.089 3 1 -6 2.3303 0.082 -7 0 -3 3.2221 0.083 3 1 -5 1.8996 0.087 -7 0 -5 1.7436 0.082 3 1 -4 3.7204 0.078 -7 0 -7 2.1688 0.101 3 1 -2 5.6776 0.133
140
-7 -1 -6 3.4150 0.101 3 1 0 1.8729 0.042 -7 -1 -4 1.8553 0.071 3 1 1 1.0227 0.04 -7 -1 -3 0.6749 0.191 3 1 2 6.4449 0.161 -7 -1 -2 5.3216 0.143 3 1 4 3.9502 0.105 -7 -1 0 2.3244 0.052 3 1 5 1.2233 0.09 -7 -1 2 5.4946 0.127 3 1 6 2.3352 0.055 -7 -1 6 3.4843 0.076 3 1 8 2.1760 0.089 -7 -2 4 1.1674 0.107 3 0 1 1.1364 0.036 -6 -2 -4 1.9948 0.074 3 0 -1 1.2222 0.034 -6 -2 -2 4.1968 0.117 3 0 -5 1.1216 0.086 -6 -2 0 2.7315 0.066 3 -1 -8 2.1165 0.095 -6 -2 1 1.4328 0.092 3 -1 -6 2.3117 0.067 -6 -2 2 4.5371 0.153 3 -1 -5 1.4106 0.071 -6 -2 6 2.8255 0.079 3 -1 -4 3.4999 0.136 -6 -1 8 2.3767 0.084 3 -1 -2 5.3981 0.189 -6 -1 5 1.7449 0.074 3 -1 -1 1.0844 0.037 -6 -1 4 4.4799 0.121 3 -1 0 1.8394 0.074 -6 -1 1 2.1437 0.107 3 -1 1 1.0759 0.045 -6 -1 0 6.2056 0.107 3 -1 2 5.9038 0.096 -6 -1 -1 2.9048 0.085 3 -1 3 0.5781 0.097 -6 -1 -4 4.6408 0.121 3 -1 4 3.9285 0.12 -6 0 -8 6.2243 0.168 3 -1 5 1.4314 0.069 -6 0 -6 2.3440 0.08 3 -1 6 2.4388 0.061 -6 0 -4 9.9314 0.167 3 -1 7 0.6270 0.206 -6 0 -2 3.9663 0.09 3 -1 8 2.4005 0.085 -6 0 0 12.8878 0.146 3 -2 8 1.8242 0.092 -6 0 2 3.9173 0.108 3 -2 6 3.2078 0.096 -6 0 4 9.4285 0.126 3 -2 4 3.1234 0.128 -6 0 6 2.5214 0.063 3 -2 3 2.0081 0.041 -6 0 8 6.1290 0.167 3 -2 2 6.2826 0.08 -6 1 5 1.7220 0.075 3 -2 -2 6.3643 0.083 -6 1 4 4.3581 0.128 3 -2 -3 1.9774 0.042 -6 1 1 2.1931 0.065 3 -2 -4 3.2037 0.099 -6 1 0 6.5588 0.103 3 -2 -6 3.5006 0.098 -6 1 -1 2.2471 0.062 4 -2 -6 2.7717 0.061 -6 1 -3 1.8469 0.076 4 -2 -5 0.5873 0.188 -6 1 -4 4.5272 0.125 4 -2 -4 8.6376 0.131 -6 1 -8 2.6466 0.086 4 -2 0 12.5841 0.152 -6 2 -6 2.7388 0.064 4 -2 2 5.6827 0.109 -6 2 -4 1.8738 0.068 4 -2 4 8.4187 0.101 -6 2 -2 4.1930 0.108 4 -2 6 2.6129 0.058 -6 2 0 2.9051 0.057 4 -1 6 2.0610 0.08 -6 2 2 4.1010 0.109 4 -1 5 0.8766 0.131 -6 2 3 1.0370 0.093 4 -1 4 3.2136 0.072 -5 2 5 2.0489 0.083 4 -1 2 3.1889 0.088 -5 2 4 7.4628 0.136 4 -1 1 0.9081 0.076 -5 2 2 11.0258 0.136 4 -1 0 4.1801 0.099 -5 2 1 2.6518 0.062 4 -1 -4 3.0928 0.117 -5 2 0 9.0516 0.099 4 -1 -6 2.0781 0.078 -5 2 -1 2.6831 0.054 4 -1 -8 1.6727 0.128 -5 2 -2 11.0410 0.142 4 0 -8 3.9697 0.12
141
-5 2 -3 1.3406 0.066 4 0 -6 7.2659 0.131 -5 2 -4 7.6736 0.125 4 0 -4 6.9069 0.118 -5 2 -6 6.8109 0.164 4 0 -2 9.9065 0.11 -5 1 -7 1.5814 0.12 4 0 0 11.3457 0.144 -5 1 -6 3.4831 0.111 4 0 2 10.6713 0.13 -5 1 -5 0.9847 0.109 4 0 4 7.1870 0.11 -5 1 -4 2.2478 0.054 4 0 6 7.2082 0.138 -5 1 -3 2.6496 0.043 4 0 8 3.7406 0.124 -5 1 -2 5.6272 0.098 4 1 8 1.9303 0.109 -5 1 -1 2.0086 0.039 4 1 6 2.2509 0.06 -5 1 0 2.0209 0.05 4 1 4 3.2021 0.087 -5 1 1 1.9203 0.051 4 1 3 0.4118 0.148 -5 1 2 5.7254 0.099 4 1 2 3.2755 0.088 -5 1 6 3.4659 0.102 4 1 1 1.4074 0.065 -5 1 7 1.8917 0.082 4 1 0 4.0714 0.236 -5 0 3 1.5237 0.071 4 1 -2 3.1603 0.085 -5 0 -1 0.7915 0.083 4 1 -4 3.2181 0.086 -5 0 -7 1.1923 0.126 4 1 -6 2.2669 0.07 -5 -1 -7 1.4285 0.151 4 1 -8 1.8758 0.103 -5 -1 -6 3.3871 0.082 4 2 -6 2.7442 0.075 -5 -1 -3 2.7627 0.087 4 2 -4 8.4702 0.127 -5 -1 -2 5.5333 0.118 4 2 -2 5.5257 0.099 -5 -1 -1 2.0320 0.049 4 2 0 12.7744 0.13 -5 -1 0 2.0314 0.041 4 2 2 5.7169 0.086 -5 -1 1 2.0500 0.037 4 2 4 8.6320 0.13 -5 -1 2 5.7897 0.104 5 2 5 2.2712 0.069 -5 -1 3 2.3653 0.084 5 2 4 8.0245 0.146 -5 -1 4 1.7657 0.057 5 2 2 11.3971 0.154 -5 -1 6 3.4188 0.072 5 2 1 2.6340 0.039 -5 -2 6 6.9583 0.136 5 2 0 10.1530 0.129 -5 -2 4 7.3971 0.122 5 2 -1 2.4919 0.072 -5 -2 2 11.1010 0.15 5 2 -2 10.8610 0.122 -5 -2 1 2.7189 0.068 5 2 -3 1.2693 0.065 -5 -2 0 9.9004 0.114 5 2 -4 7.3858 0.149 -5 -2 -1 2.5506 0.058 5 2 -6 6.4902 0.16 -5 -2 -2 11.3007 0.139 5 1 -7 1.8806 0.079 -5 -2 -4 7.5856 0.148 5 1 -6 3.2287 0.084 -4 -2 -4 8.7372 0.125 5 1 -4 1.7975 0.064 -4 -2 -2 5.6225 0.087 5 1 -3 2.7558 0.075 -4 -2 0 12.7021 0.156 5 1 -2 5.6637 0.111 -4 -2 2 5.7376 0.09 5 1 -1 1.8893 0.046 -4 -2 4 8.5532 0.14 5 1 0 2.0206 0.058 -4 -2 6 2.7666 0.082 5 1 1 1.9628 0.052 -4 -1 8 1.8569 0.111 5 1 2 5.7151 0.1 -4 -1 6 2.5795 0.097 5 1 3 2.4241 0.048 -4 -1 4 3.4762 0.112 5 1 4 2.0189 0.079 -4 -1 2 3.1831 0.09 5 1 6 3.0877 0.082 -4 -1 0 3.8386 0.17 5 0 9 1.1152 0.156 -4 -1 -2 3.2414 0.083 5 0 3 1.7815 0.118 -4 -1 -4 3.3800 0.104 5 0 -7 1.1683 0.134 -4 -1 -6 2.3416 0.07 5 0 -9 1.0355 0.176
142
-4 -1 -8 2.2305 0.09 5 -1 -6 3.1384 0.079 -4 0 -8 3.7307 0.1 5 -1 -4 1.6767 0.065 -4 0 -6 7.1082 0.175 5 -1 -3 2.4116 0.064 -4 0 -4 7.0810 0.14 5 -1 -2 5.5050 0.095 -4 0 -2 10.7699 0.128 5 -1 -1 2.2211 0.067 -4 0 0 11.6619 0.359 5 -1 0 1.8571 0.048 -4 0 2 10.4593 0.128 5 -1 1 2.0185 0.037 -4 0 4 7.2649 0.111 5 -1 2 5.6529 0.107 -4 0 6 7.2917 0.13 5 -1 3 2.6406 0.062 -4 0 8 4.0526 0.1 5 -1 4 2.1871 0.078 -4 1 4 3.2987 0.076 5 -1 5 0.8119 0.133 -4 1 2 3.3255 0.102 5 -1 6 3.2925 0.055 -4 1 0 4.3343 0.173 5 -1 7 1.9641 0.088 -4 1 -2 3.2754 0.094 5 -2 6 6.9759 0.137 -4 1 -4 3.2743 0.074 5 -2 5 2.3107 0.053 -4 1 -6 2.2714 0.064 5 -2 4 7.2331 0.12 -4 2 -6 2.8946 0.069 5 -2 2 10.5798 0.126 -4 2 -4 8.8255 0.127 5 -2 1 2.5154 0.068 -4 2 -2 5.4252 0.096 5 -2 0 9.6804 0.135 -4 2 0 12.2606 0.152 5 -2 -1 2.5068 0.078 -4 2 2 5.3826 0.106 5 -2 -2 11.0067 0.152 -4 2 4 8.5107 0.127 5 -2 -3 1.3873 0.071 -4 2 6 2.4347 0.071 5 -2 -4 7.4225 0.109 -3 2 6 3.3813 0.055 6 -2 -2 4.2045 0.11 -3 2 4 2.7879 0.105 6 -2 -1 0.9460 0.103 -3 2 3 1.9196 0.056 6 -2 0 2.8496 0.058 -3 2 -2 6.2195 0.086 6 -2 1 1.5197 0.078 -3 2 -3 1.9949 0.048 6 -2 2 4.0041 0.126 -3 2 -4 2.9994 0.089 6 -2 3 1.1884 0.078 -3 2 -6 3.3004 0.101 6 -2 6 2.6626 0.061 -3 2 -7 1.5805 0.09 6 -1 8 2.1894 0.114 -3 2 -8 1.6295 0.137 6 -1 4 4.3449 0.145 -3 1 -6 2.3785 0.066 6 -1 3 1.6499 0.08 -3 1 -5 1.5890 0.065 6 -1 1 2.4394 0.042 -3 1 -4 3.8973 0.11 6 -1 0 6.0036 0.115 -3 1 -3 0.4961 0.111 6 -1 -1 2.3825 0.075 -3 1 -2 5.9897 0.096 6 -1 -5 1.2126 0.197 -3 1 -1 0.9061 0.046 6 0 -8 5.5124 0.157 -3 1 0 1.8799 0.047 6 0 -6 2.3208 0.074 -3 1 1 0.9514 0.046 6 0 -4 9.7376 0.157 -3 1 4 3.7156 0.113 6 0 -2 3.8928 0.09 -3 1 5 1.1904 0.08 6 0 0 12.5246 0.142 -3 1 6 2.1648 0.071 6 0 2 3.8783 0.091 -3 1 8 1.8707 0.098 6 0 4 10.1145 0.138 -3 0 5 0.7417 0.122 6 0 6 2.3510 0.075 -3 0 1 1.1931 0.042 6 0 8 5.6445 0.194 -3 0 -1 1.2763 0.035 6 1 5 1.6452 0.088 -3 0 -5 1.0409 0.101 6 1 4 4.5331 0.125 -3 -1 -8 2.3252 0.079 6 1 1 2.4473 0.055 -3 -1 -6 2.4258 0.072 6 1 0 5.8664 0.09 -3 -1 -5 1.7637 0.078 6 1 -1 2.5336 0.063
143
-3 -1 -4 3.7804 0.103 6 1 -4 4.7159 0.126 -3 -1 -2 5.5856 0.217 6 1 -5 1.7969 0.07 -3 -1 0 1.8896 0.048 6 1 -8 2.3385 0.083 -3 -1 1 1.0953 0.065 6 2 -6 2.6236 0.062 -3 -1 2 6.2978 0.149 6 2 -4 2.0025 0.073 -3 -1 4 3.7367 0.099 6 2 -2 3.7840 0.129 -3 -1 5 1.8150 0.076 6 2 -1 1.3660 0.083 -3 -1 6 2.3701 0.055 6 2 0 2.4952 0.093 -3 -1 8 2.1238 0.081 6 2 2 3.9462 0.127 -3 -2 7 1.2669 0.107 6 2 4 2.1263 0.062 -3 -2 6 3.2476 0.101 7 2 0 1.5074 0.088 -3 -2 4 2.8502 0.074 7 2 -1 1.3743 0.077 -3 -2 3 2.0000 0.043 7 2 -4 1.1977 0.094 -3 -2 2 6.3236 0.079 7 1 -6 3.3533 0.073 -3 -2 -3 1.9355 0.05 7 1 -2 4.7187 0.122 -3 -2 -4 3.5478 0.094 7 1 0 2.3276 0.05 -3 -2 -6 3.2068 0.12 7 1 2 5.4234 0.138 -2 -2 -4 6.5660 0.118 7 1 4 2.0307 0.077 -2 -2 4 6.4836 0.109 7 1 6 3.4491 0.077 -2 -2 6 1.8086 0.061 7 0 5 1.7953 0.079 -2 -2 8 3.4263 0.066 7 0 3 3.0928 0.068 -2 -1 8 3.7416 0.136 7 0 1 2.8094 0.069 -2 -1 6 2.0334 0.058 7 0 -1 3.0610 0.065 -2 -1 4 8.5429 0.117 7 0 -5 1.4698 0.096 -2 -1 3 1.1158 0.044 7 0 -7 2.1062 0.109 -2 -1 1 1.3599 0.027 7 -1 -6 3.5338 0.095 -2 -1 0 13.9729 0.151 7 -1 -2 5.1638 0.141 -2 -1 -1 1.3720 0.028 7 -1 0 2.1054 0.054 -2 -1 -2 0.8776 0.054 7 -1 1 0.6924 0.125 -2 -1 -3 1.1416 0.048 7 -1 2 5.2409 0.135 -2 -1 -4 8.9737 0.114 7 -1 4 1.7857 0.071 -2 -1 -6 2.2233 0.064 7 -1 6 3.4807 0.115 -2 -1 -8 33.6375 3.423 7 -1 8 1.0926 0.173 -2 0 -4 2.7461 0.068 8 -2 3 0.7613 0.157 -2 0 -2 6.8262 0.086 8 -2 5 1.1004 0.14 -2 0 0 4.8622 0.061 8 -1 6 1.8345 0.09 -2 0 2 7.0567 0.082 8 -1 5 1.6106 0.105 -2 0 4 2.5407 0.071 8 -1 4 3.4080 0.081 -2 1 6 2.0532 0.059 8 -1 3 1.8316 0.071 -2 1 4 8.7001 0.125 8 -1 2 3.1440 0.081 -2 1 3 1.1844 0.066 8 -1 1 2.0516 0.065 -2 1 1 1.3244 0.031 8 -1 0 4.4116 0.135 -2 1 0 13.7486 0.153 8 -1 -2 3.3580 0.068 -2 1 -1 1.4002 0.039 8 -1 -3 1.8949 0.078 -2 1 -3 1.2685 0.05 8 -1 -5 1.4178 0.138 -2 1 -4 8.5876 0.12 8 0 -4 7.7778 0.149 -2 1 -6 2.1081 0.079 8 0 0 9.6345 0.201 -2 1 -8 3.7943 0.155 8 0 4 7.8011 0.146 -2 2 -8 3.3078 0.084 8 1 6 2.2454 0.091 -2 2 -4 5.9751 0.116 8 1 5 1.5155 0.099 -2 2 -2 2.1865 0.046 8 1 4 3.3342 0.06
144
-2 2 3 0.8002 0.082 8 1 3 1.7765 0.09 -2 2 4 6.6127 0.089 8 1 2 3.2548 0.074 -1 2 6 6.9388 0.123 8 1 1 1.8577 0.079 -1 2 5 1.1923 0.076 8 1 0 4.2969 0.146 -1 2 4 7.9561 0.129 8 1 -2 3.3251 0.097 -1 2 -4 7.3466 0.135 8 1 -4 3.2320 0.075 -1 2 -6 7.0970 0.133 8 2 -2 0.5278 0.24 -1 2 -8 4.2849 0.099 8 2 -1 1.5084 0.08 -1 1 -6 5.2238 0.138 9 2 1 0.6348 0.197 -1 1 -4 2.8998 0.082 9 2 0 5.0358 0.137 -1 1 -2 9.7465 0.12 9 2 -2 6.1025 0.141 -1 1 2 9.9483 0.103 9 1 -4 3.4355 0.084 -1 1 3 3.0294 0.24 9 1 -3 1.9944 0.097 -1 1 4 2.1101 0.07 9 1 -2 1.4959 0.099 -1 1 6 5.3580 0.144 9 1 0 4.1032 0.123 -1 0 1 2.0155 0.056 9 1 1 1.8576 0.09 -1 0 -1 2.0105 0.054 9 1 2 1.4937 0.098 -1 0 -3 1.8999 0.086 9 1 3 2.3248 0.069 -1 0 -5 1.7438 0.059 9 1 4 3.4138 0.082 -1 -1 -6 5.6085 0.134 9 1 5 1.0491 0.193 -1 -1 -4 2.4962 0.09 9 -1 -4 3.1414 0.093 -1 -1 -2 9.6018 0.112 9 -1 -3 2.3367 0.067 -1 -1 2 9.6809 0.101 9 -1 -2 1.5960 0.082 -1 -1 3 1.7524 0.116 9 -1 0 3.8559 0.137 -1 -1 4 2.6471 0.056 9 -1 3 2.1586 0.086 -1 -1 6 5.1164 0.118 9 -1 4 3.6620 0.092 -1 -1 7 0.9475 0.123 9 -2 4 3.6668 0.155 -1 -2 8 4.2606 0.122 9 -2 3 1.3886 0.099 -1 -2 6 6.4304 0.126 9 -2 2 5.9168 0.132 -1 -2 5 1.4906 0.065 9 -2 0 4.8381 0.135 -1 -2 4 7.9093 0.111 9 -2 -2 5.7682 0.145 -1 -2 -4 8.0311 0.113 10 -2 0 3.2996 0.134 -1 -2 -5 1.3330 0.07 10 -1 -2 1.7789 0.091 -1 -2 -6 7.1990 0.137 10 0 -6 5.1459 0.275 0 -2 -6 1.8230 0.069 10 0 -4 3.3325 0.071 0 -2 -4 1.4273 0.092 10 0 -2 6.8297 0.164 0 -2 3 1.2109 0.046 10 0 0 4.1323 0.117 0 -2 6 2.0856 0.06 10 0 2 7.1631 0.144 0 0 -8 10.9936 0.163 10 0 4 3.4073 0.1 0 0 -6 5.0776 0.143 10 0 6 5.3938 0.131 0 0 -4 20.4307 0.227 10 1 0 1.1973 0.117 0 0 -2 10.2218 0.116 11 1 -2 1.8247 0.096 0 0 2 9.8331 0.098 11 1 -1 1.0862 0.153 0 0 4 21.4291 0.236 11 1 0 1.9519 0.096 0 0 6 5.2237 0.116 11 1 1 1.3679 0.127 0 0 8 10.8448 0.174 11 1 2 1.2836 0.13 1 2 6 6.8167 0.138 11 -1 -2 1.6837 0.098 1 2 5 1.2962 0.073 11 -1 -1 0.8664 0.184 1 2 4 8.1831 0.111 11 -1 2 1.6145 0.101 1 2 -4 7.8296 0.124 11 -1 4 1.7239 0.106 12 -1 0 2.3921 0.079
145
Andalusite P = 0.0001 GPa
h k l FO Esd h k l FO Esd -6 -9 0 3.3773 0.14 1 -1 -5 3.4508 0.098 -6 -9 -1 0.8709 0.164 1 -1 -4 3.9003 0.088 -5 -9 -3 3.8429 0.153 1 -1 -3 2.7166 0.088 -5 -9 -2 1.7412 0.108 1 -1 -2 7.1625 0.093 -5 -9 -1 4.5309 0.139 1 -1 2 6.8381 0.16 -5 -9 0 2.9242 0.116 1 -1 3 2.6719 0.082 -5 -9 1 4.7247 0.139 1 -1 4 3.4571 0.087 -5 -9 2 1.7657 0.087 1 -1 5 3.1625 0.112 -5 -9 3 3.6785 0.13 1 -1 6 3.7101 0.114 -5 -8 4 0.7631 0.168 1 0 7 1.2769 0.094 -5 -8 2 2.7973 0.063 1 0 5 4.9757 0.109 -5 -8 -1 0.7829 0.15 1 0 3 4.7964 0.097 -5 -8 -2 2.4423 0.084 1 0 1 8.6955 0.151 -5 -7 -4 2.8354 0.103 1 0 -1 9.0428 0.187 -5 -7 -3 2.9711 0.125 1 0 -3 5.1861 0.106 -5 -7 -2 4.1109 0.143 1 0 -5 5.1011 0.095 -5 -7 -1 3.4464 0.166 1 0 -7 1.3022 0.114 -5 -7 0 3.8919 0.117 1 1 -7 1.2574 0.092 -5 -7 1 3.7602 0.115 1 1 -6 4.0304 0.112 -5 -7 2 4.2941 0.124 1 1 -5 3.2744 0.104 -5 -7 3 2.9805 0.151 1 1 -4 3.9520 0.111 -5 -7 4 3.1128 0.104 1 1 -3 2.7119 0.077 -5 -6 4 1.4251 0.091 1 1 -2 7.4169 0.102 -5 -6 3 1.1159 0.096 1 1 -1 5.5267 0.112 -5 -6 2 4.8418 0.111 1 1 0 7.1457 0.092 -5 -6 0 1.7353 0.067 1 1 1 5.3553 0.09 -5 -6 -2 4.8318 0.14 1 1 2 6.7374 0.141 -5 -6 -3 0.9344 0.114 1 1 3 2.3942 0.078 -5 -6 -4 1.2501 0.087 1 1 4 3.4967 0.1 -5 -5 -2 3.6920 0.12 1 1 5 3.0949 0.1 -4 -3 -3 3.4171 0.096 1 1 6 3.5427 0.129 -4 -3 -4 0.9748 0.076 1 1 7 0.8071 0.135 -4 -3 -5 2.4732 0.066 1 2 6 1.6580 0.07 -4 -4 -6 4.9951 0.157 1 2 4 3.5067 0.087 -4 -4 -4 8.9955 0.126 1 2 3 0.7907 0.059 -4 -4 -2 8.9178 0.132 1 2 2 7.4421 0.138 -4 -4 0 11.8379 0.158 1 2 1 0.5700 0.036 -4 -4 2 9.3048 0.108 1 2 0 6.2953 0.081 -4 -4 4 9.2857 0.121 1 2 -1 0.5973 0.043 -4 -5 5 1.4735 0.107 1 2 -2 8.1662 0.118 -4 -5 4 2.3089 0.109 1 2 -4 3.7244 0.133 -4 -5 3 2.7368 0.09 1 2 -6 1.9011 0.063 -4 -5 1 3.0199 0.094 1 3 -7 3.6741 0.144 -4 -5 0 3.6386 0.092 1 3 -6 2.3214 0.091 -4 -5 -1 2.6458 0.105 1 3 -5 4.1391 0.103
146
-4 -5 -3 2.8463 0.098 1 3 -4 4.0544 0.125 -4 -5 -4 2.3788 0.064 1 3 -3 6.2301 0.095 -4 -5 -5 1.4864 0.098 1 3 -2 5.4041 0.077 -4 -6 -6 5.3678 0.171 1 3 -1 5.8292 0.114 -4 -6 -2 8.9821 0.145 1 3 0 3.7298 0.056 -4 -6 2 9.2992 0.108 1 3 1 5.6233 0.079 -4 -6 6 5.4108 0.146 1 3 2 4.9610 0.077 -4 -7 5 3.0073 0.094 1 3 3 5.4057 0.104 -4 -7 3 2.0840 0.073 1 3 4 3.5650 0.092 -4 -7 1 3.5556 0.121 1 3 5 3.8010 0.137 -4 -7 -1 3.3555 0.108 1 3 6 2.1933 0.082 -4 -7 -3 2.0193 0.07 1 3 7 3.4540 0.113 -4 -7 -5 2.7854 0.159 1 4 7 2.2525 0.076 -4 -8 -4 3.7451 0.14 1 4 5 2.1179 0.075 -4 -8 -2 4.0092 0.129 1 4 4 1.3052 0.062 -4 -8 0 4.5804 0.115 1 4 3 4.2388 0.085 -4 -8 2 4.3829 0.12 1 4 1 4.9430 0.149 -4 -8 4 3.6909 0.154 1 4 0 2.7813 0.069 -4 -9 1 0.8752 0.13 1 4 -1 5.0714 0.09 -4 -9 0 3.3142 0.098 1 4 -3 4.7976 0.116 -4 -9 -2 1.2650 0.104 1 4 -4 1.5219 0.058 -4 -10 -2 2.4097 0.11 1 4 -5 2.1950 0.056 -4 -10 -1 0.8246 0.138 1 4 -7 2.5966 0.08 -4 -10 2 2.4657 0.078 1 5 -7 4.7110 0.142 -3 -10 2 1.4137 0.108 1 5 -6 1.7681 0.08 -3 -10 1 1.5103 0.089 1 5 -5 4.9085 0.134 -3 -10 0 1.1432 0.122 1 5 -4 4.4166 0.112 -3 -10 -1 1.3131 0.102 1 5 -3 7.8979 0.126 -3 -10 -2 0.9158 0.174 1 5 -2 3.0481 0.087 -3 -9 -4 2.3708 0.079 1 5 -1 8.0118 0.111 -3 -9 -3 4.5522 0.144 1 5 0 5.6604 0.074 -3 -9 -2 1.9540 0.083 1 5 1 7.6307 0.097 -3 -9 -1 5.4772 0.136 1 5 2 2.8836 0.094 -3 -9 0 2.5494 0.131 1 5 3 7.2792 0.11 -3 -9 1 5.6667 0.141 1 5 4 4.0485 0.133 -3 -9 2 2.1995 0.068 1 5 5 4.3249 0.124 -3 -9 3 4.3971 0.134 1 5 6 1.6082 0.08 -3 -9 4 2.1380 0.079 1 5 7 4.1824 0.148 -3 -8 3 2.3051 0.072 1 6 5 0.9994 0.108 -3 -8 1 2.0130 0.063 1 6 4 3.0575 0.1 -3 -8 -1 2.0785 0.059 1 6 2 2.2238 0.089 -3 -8 -3 2.2436 0.079 1 6 0 4.0440 0.1 -3 -8 -5 1.1334 0.117 1 6 -2 2.2500 0.061 -3 -7 -5 2.6090 0.078 1 6 -6 1.0074 0.116 -3 -7 -4 3.8453 0.164 1 7 -5 3.5571 0.153 -3 -7 -3 2.4453 0.093 1 7 -4 3.5363 0.106 -3 -7 -1 2.7385 0.127 1 7 -3 3.6526 0.116 -3 -7 0 5.3034 0.1 1 7 -2 3.2608 0.109 -3 -7 1 3.1680 0.134 1 7 -1 4.5067 0.097 -3 -7 3 2.5339 0.092 1 7 0 4.5575 0.111 -3 -7 4 4.1364 0.123 1 7 1 4.4894 0.098
147
-3 -7 5 2.5461 0.07 1 7 2 3.2291 0.11 -3 -6 4 3.5244 0.118 1 7 3 3.0813 0.126 -3 -6 1 0.6822 0.099 1 7 4 3.4336 0.124 -3 -6 0 4.8225 0.101 1 7 5 3.1797 0.126 -3 -6 -3 1.3418 0.079 1 8 0 2.9161 0.094 -3 -6 -4 3.1871 0.12 1 8 -1 2.2911 0.069 -3 -5 -6 3.3733 0.151 1 8 -2 1.0500 0.087 -3 -5 -4 2.2824 0.063 1 8 -3 1.5748 0.089 -3 -5 -3 2.2883 0.06 1 8 -4 2.5334 0.073 -3 -5 -2 6.4084 0.114 2 10 -1 1.6183 0.085 -3 -5 -1 1.8100 0.065 2 10 0 5.5860 0.161 -3 -5 0 2.9790 0.089 2 9 4 3.2989 0.111 -3 -5 1 1.7488 0.069 2 9 2 5.0004 0.157 -3 -5 2 6.6192 0.086 2 9 0 4.6145 0.13 -3 -5 3 2.1910 0.08 2 9 -2 5.5023 0.172 -3 -5 5 0.8895 0.109 2 9 -4 3.6799 0.17 -3 -5 6 3.3975 0.183 2 8 -5 2.3605 0.083 -3 -4 6 0.9880 0.116 2 8 -4 1.2842 0.089 -3 -4 3 2.2714 0.064 2 8 -3 2.8468 0.087 -3 -4 2 2.0282 0.07 2 8 -2 3.3072 0.124 -3 -4 1 4.1190 0.083 2 8 -1 3.1811 0.115 -3 -4 -1 3.8773 0.086 2 8 0 1.4308 0.068 -3 -4 -2 2.0569 0.059 2 8 1 3.1914 0.117 -3 -4 -3 2.2095 0.046 2 8 2 3.2352 0.105 -3 -4 -5 3.2902 0.124 2 8 3 2.5585 0.071 -3 -3 -7 2.8519 0.136 2 8 4 0.7271 0.159 -3 -3 -6 5.0242 0.121 2 8 5 2.2241 0.084 -3 -3 -4 1.5637 0.06 2 6 -6 1.2822 0.107 -3 -3 -3 5.1813 0.098 2 6 -5 2.0338 0.073 -3 -3 -2 9.6365 0.124 2 6 -4 6.1902 0.115 -3 -3 -1 5.6790 0.104 2 6 -3 2.2415 0.052 -3 -3 0 2.5912 0.084 2 6 -2 1.7085 0.054 -3 -3 1 5.9920 0.079 2 6 -1 2.5449 0.061 -3 -3 2 9.9593 0.115 2 6 0 7.7181 0.111 -3 -3 3 5.1949 0.104 2 6 1 2.5669 0.087 -3 -3 4 1.5982 0.059 2 6 2 1.6403 0.055 -3 -3 5 2.9791 0.119 2 6 3 2.1059 0.059 -3 -3 6 5.0758 0.149 2 6 4 5.7939 0.131 -3 -3 7 2.7686 0.078 2 6 5 1.8210 0.078 -3 -2 6 1.0248 0.107 2 6 6 1.2432 0.106 -3 -2 5 1.3713 0.082 2 5 6 4.1153 0.133 -3 -2 4 4.6373 0.111 2 5 4 4.9017 0.101 -3 -2 -4 4.5422 0.124 2 5 2 7.4054 0.122 -3 -2 -5 1.2416 0.132 2 5 1 1.1719 0.052 -3 -2 -6 0.7925 0.11 2 5 0 6.8714 0.09 -3 -1 -5 5.1208 0.128 2 5 -1 1.2234 0.053 -3 -1 -4 5.6075 0.114 2 5 -2 8.1619 0.111 -3 -1 -3 4.9628 0.084 2 5 -4 5.3525 0.109 -3 -1 4 5.5708 0.1 2 5 -6 4.7553 0.145 -3 -1 5 5.2782 0.144 2 4 -6 8.9793 0.131 -2 2 -5 2.3383 0.082 2 4 -5 1.8481 0.066
148
-2 1 4 3.6174 0.096 2 4 -3 2.7328 0.109 -2 1 -4 3.5025 0.089 2 4 -2 16.3524 0.205 -2 1 -6 3.4782 0.122 2 4 -1 3.2216 0.098 -2 0 -6 2.6332 0.096 2 4 0 1.4417 0.05 -2 0 -4 1.3383 0.061 2 4 1 3.3018 0.074 -2 0 4 1.3648 0.057 2 4 2 15.7510 0.227 -2 0 6 2.5223 0.087 2 4 3 2.2387 0.089 -2 -1 4 3.6548 0.093 2 4 5 1.6446 0.064 -2 -1 2 7.5899 0.094 2 4 6 8.2880 0.152 -2 -1 -1 0.6828 0.037 2 3 7 1.6981 0.082 -2 -1 -2 7.3797 0.102 2 3 6 1.8655 0.07 -2 -1 -4 3.5283 0.107 2 3 5 1.2067 0.087 -2 -1 -6 3.4233 0.126 2 3 4 1.7451 0.059 -2 -2 -7 1.6168 0.081 2 3 3 1.5534 0.048 -2 -2 -4 8.8049 0.112 2 3 2 3.1652 0.079 -2 -2 -3 2.5222 0.08 2 3 0 1.9433 0.074 -2 -2 -1 2.4325 0.067 2 3 -1 0.9394 0.054 -2 -2 0 12.6898 0.15 2 3 -2 3.5942 0.073 -2 -2 1 2.4229 0.061 2 3 -3 1.7005 0.052 -2 -2 3 2.3596 0.073 2 3 -4 1.7689 0.053 -2 -2 4 8.5805 0.124 2 3 -5 1.3909 0.096 -2 -2 5 2.4606 0.067 2 3 -6 2.0878 0.067 -2 -2 7 1.3821 0.098 2 3 -7 1.7170 0.085 -2 -3 7 1.5496 0.098 2 2 -5 2.7633 0.062 -2 -3 4 1.5961 0.057 2 2 -4 9.1582 0.117 -2 -3 3 1.5457 0.053 2 2 -3 2.3492 0.103 -2 -3 2 3.5767 0.074 2 2 -1 2.4287 0.077 -2 -3 0 1.8568 0.071 2 2 0 12.1325 0.127 -2 -3 -2 3.4407 0.072 2 2 1 2.2773 0.06 -2 -3 -3 1.6912 0.052 2 2 2 0.7049 0.054 -2 -3 -4 1.6934 0.054 2 2 3 2.2632 0.063 -2 -3 -5 0.9613 0.123 2 2 4 8.3699 0.156 -2 -3 -6 1.9052 0.09 2 2 5 2.4926 0.067 -2 -3 -7 1.6754 0.085 2 2 7 1.6007 0.08 -2 -4 -7 1.2649 0.105 2 1 4 3.5514 0.099 -2 -4 -6 8.6634 0.141 2 1 2 7.2543 0.149 -2 -4 -5 1.8891 0.059 2 1 1 0.7357 0.033 -2 -4 -3 2.5035 0.084 2 1 -2 7.6964 0.121 -2 -4 -2 15.7822 0.219 2 1 -4 3.8271 0.088 -2 -4 -1 3.1329 0.081 2 1 -6 3.6985 0.121 -2 -4 0 2.0202 0.062 2 0 -6 2.6897 0.136 -2 -4 1 3.2438 0.074 2 0 -4 1.6079 0.049 -2 -4 2 15.7370 0.176 2 0 4 1.4382 0.052 -2 -4 3 2.3939 0.088 2 -1 6 3.6212 0.12 -2 -4 5 1.7757 0.07 2 -1 4 3.6883 0.1 -2 -4 6 8.3462 0.157 2 -1 -4 3.9656 0.096 -2 -5 4 5.1611 0.107 2 -2 5 2.3166 0.118 -2 -5 2 7.8975 0.081 3 1 -5 5.6704 0.116 -2 -5 1 1.2396 0.051 3 1 -4 6.3093 0.09 -2 -5 0 7.0799 0.108 3 1 3 5.4621 0.113 -2 -5 -1 1.1939 0.051 3 1 4 5.6269 0.119
149
-2 -5 -2 7.8404 0.117 3 1 5 5.5353 0.116 -2 -5 -4 5.1265 0.116 3 2 5 1.3277 0.082 -2 -5 -5 1.7639 0.066 3 2 4 4.6589 0.115 -2 -5 -6 4.3126 0.167 3 2 -4 5.2025 0.092 -2 -6 -6 1.2325 0.113 3 2 -5 1.4711 0.074 -2 -6 -5 1.8906 0.072 3 2 -6 0.6511 0.171 -2 -6 -4 6.2001 0.127 3 3 -7 3.3151 0.081 -2 -6 -3 2.1674 0.08 3 3 -6 5.7084 0.122 -2 -6 -2 1.6943 0.052 3 3 -5 3.0418 0.101 -2 -6 -1 2.7450 0.087 3 3 -4 1.6406 0.055 -2 -6 0 7.6194 0.114 3 3 -3 5.4731 0.105 -2 -6 1 2.5676 0.072 3 3 -2 10.2637 0.154 -2 -6 2 1.6951 0.055 3 3 -1 6.3637 0.099 -2 -6 3 2.1640 0.07 3 3 0 2.6176 0.076 -2 -6 4 6.1395 0.112 3 3 1 5.7736 0.099 -2 -6 5 1.9985 0.088 3 3 2 9.6078 0.125 -2 -6 6 1.1153 0.116 3 3 3 5.0658 0.098 -2 -8 -5 2.3317 0.078 3 3 4 1.5749 0.055 -2 -8 -4 1.1606 0.101 3 3 5 3.1031 0.117 -2 -8 -3 2.7221 0.129 3 3 6 5.1251 0.125 -2 -8 -2 3.3588 0.116 3 3 7 2.9525 0.092 -2 -8 -1 3.3216 0.101 3 4 7 0.8154 0.165 -2 -8 0 1.5355 0.065 3 4 3 2.0958 0.081 -2 -8 1 3.1556 0.145 3 4 2 1.9861 0.058 -2 -8 2 3.4960 0.118 3 4 1 3.9049 0.076 -2 -8 4 0.9320 0.138 3 4 -1 4.1611 0.078 -2 -8 5 2.3094 0.106 3 4 -2 2.2036 0.058 -2 -9 4 3.3129 0.166 3 4 -3 2.3390 0.076 -2 -9 2 5.3685 0.122 3 4 -5 3.4556 0.106 -2 -9 0 4.6501 0.119 3 5 -6 3.8307 0.137 -2 -9 -2 5.2081 0.165 3 5 -4 2.3256 0.087 -2 -9 -4 3.6111 0.169 3 5 -3 2.5659 0.068 -2 -10 0 5.8518 0.142 3 5 -2 6.5667 0.128 -2 -10 1 1.5728 0.082 3 5 -1 1.7647 0.051 -1 -8 4 2.4301 0.081 3 5 0 2.8626 0.088 -1 -8 3 1.4687 0.09 3 5 1 1.7101 0.049 -1 -8 2 1.0666 0.09 3 5 2 6.6241 0.104 -1 -8 1 2.3001 0.082 3 5 3 2.1100 0.051 -1 -8 0 3.2582 0.121 3 5 5 0.8816 0.111 -1 -8 -1 2.3876 0.065 3 5 6 3.5402 0.097 -1 -8 -2 0.8516 0.138 3 6 2 0.9097 0.081 -1 -7 -5 3.5380 0.138 3 6 0 4.7005 0.098 -1 -7 -3 3.7312 0.117 3 6 -2 0.9966 0.078 -1 -7 -2 3.4359 0.145 3 6 -4 3.3618 0.118 -1 -7 -1 4.2751 0.099 3 7 -5 2.7603 0.096 -1 -7 0 4.3624 0.105 3 7 -4 4.2327 0.137 -1 -7 1 4.4687 0.098 3 7 -3 2.3261 0.1 -1 -7 2 3.5796 0.117 3 7 -1 3.4281 0.124 -1 -7 4 3.2818 0.11 3 7 0 4.9892 0.113 -1 -7 5 3.3303 0.149 3 7 1 3.0397 0.084 -1 -7 6 1.8295 0.096 3 7 3 2.3354 0.075
150
-1 -6 5 1.0885 0.094 3 7 4 4.2610 0.127 -1 -6 4 2.8878 0.116 3 7 5 2.2735 0.076 -1 -6 2 2.1905 0.089 3 8 3 2.0993 0.087 -1 -6 0 4.3156 0.085 3 8 2 1.2655 0.093 -1 -6 -2 2.4226 0.066 3 8 1 2.0214 0.064 -1 -6 -4 3.2919 0.115 3 8 -1 2.0740 0.06 -1 -6 -6 1.0883 0.121 3 8 -2 1.5323 0.071 -1 -5 -7 4.7057 0.154 3 8 -3 2.5044 0.066 -1 -5 -6 1.8027 0.082 3 9 -4 2.2189 0.082 -1 -5 -5 4.7959 0.112 3 9 -3 4.8009 0.133 -1 -5 -4 4.1810 0.103 3 9 -2 2.1154 0.08 -1 -5 -3 7.5969 0.089 3 9 -1 5.3966 0.125 -1 -5 -2 3.0439 0.094 3 9 0 2.7868 0.069 -1 -5 -1 7.8243 0.116 3 9 1 5.5036 0.119 -1 -5 0 5.9595 0.088 3 9 2 1.9044 0.073 -1 -5 1 7.8129 0.116 3 9 3 4.3450 0.147 -1 -5 2 2.9898 0.106 3 9 4 2.1711 0.079 -1 -5 3 7.8151 0.09 3 10 2 1.0199 0.155 -1 -5 4 4.4368 0.099 3 10 0 1.5149 0.086 -1 -5 5 4.9014 0.13 4 10 2 2.2433 0.11 -1 -5 6 1.7159 0.089 4 9 2 1.3136 0.095 -1 -5 7 4.1295 0.172 4 9 0 2.8469 0.094 -1 -4 7 2.5182 0.093 4 8 -4 3.6573 0.147 -1 -4 5 2.0132 0.066 4 8 -2 4.1530 0.122 -1 -4 4 1.4003 0.059 4 8 0 4.5239 0.148 -1 -4 3 4.6993 0.083 4 8 2 4.3312 0.128 -1 -4 1 5.0285 0.071 4 8 4 3.5435 0.128 -1 -4 0 2.7248 0.071 4 7 5 3.0740 0.137 -1 -4 -1 4.9476 0.118 4 7 3 2.0675 0.067 -1 -4 -3 4.5302 0.083 4 7 -1 3.3998 0.146 -1 -4 -4 1.3318 0.063 4 7 -3 2.1160 0.072 -1 -4 -5 2.0829 0.058 4 7 -5 3.2153 0.158 -1 -4 -7 2.7935 0.1 4 6 -6 5.6698 0.156 -1 -3 -7 3.7411 0.119 4 6 -3 0.5545 0.156 -1 -3 -6 2.6242 0.065 4 6 -2 9.4499 0.157 -1 -3 -5 3.8126 0.125 4 6 2 9.3819 0.126 -1 -3 -4 4.0630 0.106 4 6 4 0.7564 0.121 -1 -3 -3 6.0802 0.103 4 6 6 5.3256 0.138 -1 -3 -2 5.3747 0.082 4 5 5 1.4969 0.079 -1 -3 -1 5.5690 0.108 4 5 4 2.5119 0.078 -1 -3 0 3.7213 0.062 4 5 3 2.5342 0.119 -1 -3 1 5.7848 0.083 4 5 1 2.8768 0.097 -1 -3 2 5.2993 0.073 4 5 0 3.4483 0.092 -1 -3 3 5.8570 0.11 4 5 -1 2.7782 0.101 -1 -3 4 3.8852 0.09 4 5 -3 2.8343 0.089 -1 -3 5 3.6791 0.116 4 5 -4 2.7573 0.096 -1 -3 6 2.2133 0.064 4 5 -5 1.8453 0.078 -1 -3 7 3.1667 0.141 4 4 -4 10.0214 0.141 -1 -2 7 0.8258 0.14 4 4 -2 9.6443 0.152 -1 -2 4 3.6214 0.119 4 4 0 11.7887 0.163 -1 -2 3 0.9059 0.053 4 4 2 9.2450 0.107
151
-1 -2 2 7.8370 0.122 4 4 4 9.1552 0.142 -1 -2 1 0.5681 0.039 4 4 6 5.2842 0.129 -1 -2 0 6.7248 0.091 4 3 5 2.4557 0.066 -1 -2 -1 0.6077 0.035 4 3 3 3.6734 0.096 -1 -2 -2 7.9273 0.095 5 5 2 3.8524 0.104 -1 -2 -3 0.8382 0.06 5 5 3 1.3774 0.073 -1 -2 -4 3.9681 0.092 5 6 3 0.5832 0.185 -1 -2 -6 1.9727 0.063 5 6 2 5.0415 0.122 -1 -2 -7 1.1432 0.105 5 6 0 1.7027 0.062 -1 -1 -6 3.8479 0.154 5 6 -4 1.5035 0.084 -1 -1 -5 3.2845 0.101 5 7 -4 3.0878 0.121 -1 -1 -4 4.0274 0.105 5 7 -3 3.2110 0.122 -1 -1 -3 2.8670 0.085 5 7 -2 4.4058 0.124 -1 -1 -2 7.0047 0.114 5 7 -1 3.9393 0.143 -1 -1 -1 5.4871 0.092 5 7 0 3.9262 0.115 -1 -1 0 7.4317 0.102 5 7 1 3.6508 0.117 -1 -1 1 5.7014 0.066 5 7 2 4.1304 0.131 -1 -1 2 6.9802 0.139 5 7 3 3.0291 0.104 -1 -1 3 2.6929 0.103 5 7 4 2.7420 0.094 -1 -1 4 3.8025 0.095 5 7 5 2.5333 0.133 -1 -1 5 3.1313 0.109 5 8 4 0.9063 0.131 -1 -1 6 3.4670 0.123 5 8 3 1.4571 0.089 -1 0 7 1.1816 0.114 5 8 2 2.8055 0.073 -1 0 5 4.6593 0.109 5 8 0 1.2935 0.083 -1 0 3 5.0326 0.175 5 8 -1 1.2015 0.086 -1 0 1 8.8989 0.093 5 8 -2 2.5745 0.116 -1 0 -1 8.7270 0.143 5 8 -4 0.9857 0.148 -1 0 -3 5.3274 0.098 5 9 -3 4.2500 0.147 -1 0 -5 4.6822 0.105 5 9 -2 1.9065 0.094 -1 1 -7 1.0180 0.107 5 9 -1 4.3188 0.149 -1 1 -6 3.7602 0.116 5 9 0 3.2564 0.115 -1 1 -5 3.3582 0.096 5 9 1 4.6856 0.135 -1 1 -4 3.7528 0.085 5 9 2 1.9242 0.078 -1 1 -3 2.7962 0.068 5 9 3 3.3125 0.192 -1 1 -2 6.8549 0.108 5 10 0 0.9540 0.128 -1 1 2 6.9081 0.136 6 9 0 3.7717 0.146 -1 1 3 2.4346 0.085 6 9 -1 0.7792 0.156 -1 1 4 3.7252 0.102 -6 -10 -1 1.1894 0.113 -1 1 5 3.0278 0.107 -6 -10 0 4.6506 0.16 -1 1 6 3.8050 0.111 -5 -9 -5 3.3849 0.141 -1 2 6 1.6179 0.081 -5 -9 -4 2.2202 0.082 -1 2 5 0.8836 0.099 -5 -9 4 2.3916 0.082 -1 2 4 3.4075 0.105 -5 -9 5 3.5539 0.163 -1 2 3 0.8368 0.058 -5 -10 2 3.3438 0.141 -1 2 2 7.6912 0.123 -5 -11 -4 1.3138 0.14 -1 2 -2 7.9895 0.101 -5 -11 -3 2.4139 0.085 -1 2 -3 0.9370 0.05 -5 -11 -1 2.4343 0.102 -1 2 -4 3.7219 0.087 -5 -11 0 1.5672 0.105 -1 2 -6 1.7802 0.075 -5 -11 1 2.2299 0.099 -1 3 -7 3.8103 0.105 -5 -11 3 1.9791 0.103 -1 3 -6 2.3824 0.084 -5 -12 2 2.6584 0.095
152
-1 3 -5 3.6928 0.112 -5 -12 0 1.7935 0.101 -1 3 -4 3.8403 0.1 -5 -12 -2 2.7715 0.098 -1 3 -3 5.8381 0.096 -5 -12 -3 0.8498 0.182 -1 3 3 5.6184 0.101 -4 -10 6 1.3796 0.157 -1 3 4 3.7136 0.11 -4 -9 4 2.4335 0.109 -1 3 5 3.6405 0.113 -4 -9 -4 2.6765 0.071 -1 3 6 2.2295 0.087 -4 -9 -6 1.2474 0.131 -1 4 -3 4.4198 0.095 -4 -8 -6 2.5548 0.108 -1 4 -4 1.4099 0.064 -4 -8 6 2.5061 0.091 -1 4 -5 2.0987 0.066 -4 -5 -7 1.2777 0.123 0 6 -2 7.3064 0.105 -3 -5 -7 1.8286 0.086 0 6 0 3.3564 0.112 -3 -5 7 1.7450 0.093 0 6 2 7.0297 0.143 -3 -5 8 1.1667 0.149 0 6 4 2.0953 0.065 -3 -6 8 2.0520 0.1 0 5 5 2.0845 0.068 -3 -6 -8 2.2016 0.093 0 5 3 2.3571 0.058 -3 -7 -8 2.0901 0.107 0 5 1 3.3722 0.095 -3 -7 8 2.1299 0.109 0 5 -1 3.9631 0.081 -3 -8 7 1.4408 0.124 0 5 -3 2.5709 0.096 -3 -9 -6 1.0933 0.146 0 5 -5 2.2566 0.068 -3 -9 -5 4.4109 0.153 0 4 -6 2.7946 0.134 -3 -9 5 4.0130 0.17 0 4 -4 2.9764 0.118 -3 -9 6 0.8182 0.217 0 4 -2 6.5677 0.09 -3 -10 5 1.4381 0.114 0 4 0 8.5211 0.095 -3 -10 4 1.2813 0.121 0 4 2 5.9319 0.098 -3 -10 -4 1.1756 0.138 0 4 4 2.6012 0.092 -3 -11 -1 3.1080 0.095 0 4 6 2.6628 0.098 -3 -11 0 1.0487 0.149 0 3 7 2.1286 0.091 -3 -11 1 3.0135 0.1 0 3 5 3.3786 0.11 -3 -11 2 3.9196 0.142 0 3 3 4.8761 0.098 -2 -8 -6 1.9227 0.096 0 3 1 6.0494 0.079 -2 -8 6 1.9985 0.086 0 3 -1 6.4777 0.094 -2 -6 -8 2.9279 0.151 0 3 -3 5.1630 0.11 -2 -6 -7 0.7163 0.239 0 3 -5 4.0084 0.131 -2 -6 8 2.9660 0.107 0 3 -7 2.1704 0.077 -2 -5 9 1.4971 0.129 0 2 -6 6.6972 0.124 -2 -5 8 2.3464 0.098 0 2 -4 1.6385 0.047 -2 -5 -8 2.5283 0.119 0 2 -2 11.8297 0.162 -2 -3 8 0.8551 0.165 0 2 0 2.5820 0.053 -2 -3 -8 1.2036 0.116 0 2 2 11.0849 0.209 -2 -2 -9 1.2573 0.129 0 2 4 1.4708 0.069 -2 -2 -8 4.0460 0.122 0 2 6 6.2076 0.116 -2 -2 8 3.8326 0.181 0 1 5 1.8712 0.056 -2 -1 8 2.1365 0.111 0 1 3 6.6242 0.15 -2 -1 -8 1.7265 0.089 0 1 1 7.3748 0.13 -1 0 -9 2.3014 0.091 0 1 -1 7.5786 0.152 -1 -1 -9 1.9912 0.095 0 1 -3 7.3188 0.096 -1 -1 -8 1.9025 0.092 0 1 -5 1.9837 0.064 -1 -1 8 1.4298 0.145 0 1 -7 3.8181 0.14 -1 -2 8 1.4070 0.116 0 0 -6 5.0053 0.108 -1 -3 -8 1.4931 0.118 0 0 -4 20.8373 0.272 -1 -5 8 1.8358 0.099
153
0 0 -2 10.0605 0.134 0 -4 8 1.3812 0.119 0 0 2 9.4807 0.255 0 -2 -8 1.0660 0.154 0 0 4 19.2945 0.501 0 -2 8 1.1598 0.118 0 0 6 4.6537 0.108 0 0 -8 10.1469 0.155 0 -1 7 3.5831 0.156 0 0 8 9.6085 0.193 0 -1 5 1.8786 0.058 0 4 -8 1.2450 0.117 0 -1 3 7.0618 0.151 1 5 -8 1.8233 0.101 0 -1 1 7.4751 0.118 1 3 8 1.3646 0.124 0 -1 -1 7.8543 0.131 1 3 9 1.5305 0.119 0 -1 -3 7.6088 0.093 1 2 -8 1.5592 0.112 0 -1 -5 1.9538 0.08 1 1 -9 1.9063 0.105 0 -1 -7 4.0564 0.132 1 1 9 1.3255 0.135 0 -2 -6 6.8745 0.117 1 0 9 2.2171 0.101 0 -2 -4 1.4882 0.061 1 -1 -8 1.9403 0.096 0 -2 -2 11.7475 0.154 2 1 8 1.7655 0.114 0 -2 0 2.6472 0.061 2 1 -8 1.9480 0.094 0 -2 2 11.4208 0.19 2 2 -8 4.6494 0.149 0 -2 4 1.5971 0.048 2 2 8 3.7920 0.174 0 -2 6 6.5014 0.135 2 3 9 1.1232 0.15 0 -3 5 3.6016 0.132 2 5 8 2.2930 0.094 0 -3 3 5.2231 0.086 2 5 -8 2.6788 0.099 0 -3 1 6.5180 0.078 2 5 -9 1.2835 0.147 0 -3 -1 6.4100 0.086 2 6 -8 2.9609 0.131 0 -3 -3 5.1624 0.094 2 6 7 1.0421 0.14 0 -3 -5 3.9412 0.129 2 6 8 3.2269 0.126 0 -3 -7 2.0901 0.124 2 8 -6 2.0861 0.088 0 -4 -6 3.1279 0.131 2 8 6 1.6156 0.118 0 -4 -4 2.8699 0.104 3 11 -2 3.9516 0.199 0 -4 -2 6.3738 0.116 3 11 -1 2.8665 0.13 0 -4 0 8.6387 0.112 3 10 -4 0.9929 0.146 0 -4 2 6.3743 0.079 3 10 -5 1.3781 0.13 0 -4 4 2.9858 0.106 3 9 -6 1.3855 0.133 0 -4 6 3.1093 0.108 3 9 5 4.1581 0.152 0 -5 5 2.3183 0.082 3 8 -7 1.4329 0.118 0 -5 3 2.1351 0.109 3 7 -7 1.6827 0.123 0 -5 1 3.6512 0.081 3 7 8 2.0114 0.11 0 -5 -1 3.6628 0.101 3 6 8 1.9355 0.108 0 -5 -3 2.3586 0.084 3 6 -8 2.1171 0.1 0 -6 -4 2.2329 0.061 3 5 -7 1.6787 0.108 0 -6 -2 7.4544 0.106 3 5 7 1.5719 0.106 0 -6 0 3.2927 0.096 3 5 8 1.1840 0.135 0 -6 2 7.4766 0.103 4 5 7 1.4012 0.118 0 -6 4 2.3407 0.075 4 8 -6 3.0813 0.076 1 -4 4 1.3971 0.07 4 8 6 2.7135 0.082 1 -4 3 4.6480 0.11 4 9 4 2.5324 0.097 1 -3 -6 2.5807 0.09 4 9 -4 2.4822 0.122 1 -3 -5 3.6118 0.125 4 9 -6 1.3065 0.137 1 -3 -4 4.3093 0.103 4 10 -6 1.7905 0.113 1 -3 -3 6.4493 0.097 4 11 2 0.8458 0.161 1 -3 3 6.0524 0.119 4 12 0 3.5089 0.193 1 -3 4 3.8923 0.108 5 12 2 2.9083 0.084
154
1 -3 5 3.8122 0.112 5 12 0 1.4530 0.124 1 -3 7 3.9326 0.148 5 12 -2 2.6683 0.152 1 -2 7 1.1479 0.107 5 11 -4 1.4449 0.131 1 -2 6 1.7529 0.074 5 11 -3 2.4405 0.088 1 -2 4 3.6244 0.088 5 11 -1 2.4045 0.088 1 -2 3 0.6287 0.077 5 11 1 2.4311 0.084 1 -2 2 7.9745 0.139 5 11 3 2.4243 0.085 1 -2 -2 8.1523 0.109 5 11 4 1.2450 0.141 1 -2 -3 0.9720 0.052 5 11 5 1.3841 0.15 1 -2 -4 3.7466 0.105 5 10 -2 3.9626 0.133 1 -2 -5 0.8126 0.103 5 9 -5 4.1408 0.14 1 -2 -6 2.1054 0.068 5 9 -4 2.5693 0.084 1 -2 -7 0.9520 0.14 5 9 4 2.4816 0.081 1 -1 -7 0.8138 0.174 5 9 5 3.6714 0.119 1 -1 -6 3.9092 0.138 6 10 -1 1.2029 0.113 6 10 0 4.7133 0.153
P = 1.474(5) GPa
h k l FO Esd h k l FO Esd -5 -6 2 7.9686 0.116 0 0 -4 29.4867 0.408 -5 -6 0 2.5617 0.072 0 0 -2 14.4516 0.234 -5 -6 -2 7.0954 0.17 0 0 2 14.0769 0.343 -5 -6 -3 1.2395 0.09 0 0 4 28.2881 0.624 -5 -6 -4 2.0639 0.069 0 0 6 6.9348 0.147 -5 -7 -5 3.5771 0.162 0 0 8 15.0935 0.272 -5 -7 -4 4.4490 0.147 0 1 7 5.5427 0.133 -5 -7 -3 4.3411 0.132 0 1 5 2.7241 0.082 -5 -7 -2 6.0354 0.117 0 1 3 10.0088 0.195 -5 -7 -1 5.2507 0.145 0 1 1 11.0244 0.176 -5 -7 0 5.9827 0.123 0 1 -1 10.4358 0.269 -5 -7 1 5.5512 0.118 0 1 -3 10.7517 0.155 -5 -7 2 6.3179 0.137 0 1 -5 2.9782 0.083 -5 -7 3 4.4797 0.152 0 1 -7 5.4872 0.178 -5 -7 4 4.6936 0.151 0 2 -8 1.3563 0.095 -5 -8 4 1.9043 0.081 0 2 -6 9.8365 0.132 -5 -8 3 2.7095 0.071 0 2 -4 2.2923 0.078 -5 -8 2 4.2656 0.139 0 2 -2 16.8242 0.286 -5 -8 1 1.6794 0.062 0 2 0 3.6750 0.065 -5 -8 0 2.2164 0.069 0 2 2 16.3934 0.28 -5 -8 -1 1.6096 0.076 0 2 4 2.1515 0.052 -5 -8 -2 3.7509 0.139 0 2 6 9.9667 0.176 -5 -8 -3 2.4535 0.068 0 2 8 1.2137 0.151 -5 -8 -4 1.8163 0.071 0 3 7 3.2963 0.105 -5 -8 -5 0.5994 0.182 0 3 5 5.6776 0.136 -5 -9 -5 5.4881 0.188 0 3 3 7.2043 0.131 -5 -9 -4 3.8415 0.162 0 3 1 8.7237 0.079 -5 -9 -3 5.8387 0.201 0 3 -1 8.7796 0.178 -5 -9 -2 2.7348 0.081 0 3 -3 7.5376 0.119 -5 -9 -1 6.8678 0.134 0 3 -5 5.5777 0.105
155
-5 -9 0 4.7212 0.16 0 3 -7 3.1743 0.112 -5 -9 1 7.1083 0.15 0 4 -8 1.7739 0.105 -5 -9 2 2.5558 0.069 0 4 -6 4.0852 0.141 -5 -9 3 6.1072 0.165 0 4 -4 4.1812 0.107 -5 -9 4 4.0298 0.118 0 4 -2 8.9550 0.154 -5 -10 4 0.9513 0.143 0 4 0 12.3232 0.129 -5 -10 2 5.0690 0.166 0 4 2 9.0673 0.1 -5 -10 0 1.1858 0.097 0 4 4 4.1951 0.104 -5 -10 -2 4.9573 0.146 0 4 6 4.3727 0.142 -5 -10 -4 0.9890 0.126 0 5 3 3.6271 0.101 -5 -11 -3 3.5077 0.116 0 5 1 5.4495 0.085 -5 -11 -1 3.3793 0.121 0 5 -1 5.3064 0.101 -5 -11 0 2.7828 0.096 0 5 -3 3.3239 0.131 -5 -11 1 3.5840 0.111 0 5 -5 3.1945 0.125 -5 -11 2 0.6699 0.203 0 5 -7 1.9059 0.071 -5 -11 3 3.8931 0.12 0 6 -4 3.0129 0.101 -5 -12 2 4.2693 0.156 0 6 -2 9.6279 0.139 -5 -12 0 2.7457 0.075 0 6 0 4.5407 0.125 -5 -12 -2 3.8260 0.151 0 6 2 9.8673 0.1 -4 -12 0 5.5219 0.172 0 6 4 3.1530 0.074 -4 -12 2 3.4385 0.115 1 8 4 3.0244 0.139 -4 -11 1 1.3783 0.095 1 8 3 1.9805 0.057 -4 -11 0 0.9979 0.111 1 8 2 1.1805 0.073 -4 -11 -2 0.8768 0.139 1 8 1 3.7500 0.103 -4 -11 -3 1.3099 0.104 1 8 0 3.8826 0.154 -4 -10 -6 2.4732 0.091 1 8 -1 3.4871 0.143 -4 -10 -2 3.7239 0.15 1 8 -2 1.0428 0.072 -4 -10 2 4.0686 0.15 1 8 -3 2.1579 0.052 -4 -10 6 2.6230 0.097 1 8 -4 3.0053 0.101 -4 -9 6 1.5186 0.102 1 7 -6 2.5465 0.11 -4 -9 4 4.2183 0.134 1 7 -5 4.7333 0.147 -4 -9 2 2.0636 0.073 1 7 -4 4.8571 0.142 -4 -9 1 0.9438 0.116 1 7 -3 5.1100 0.136 -4 -9 0 4.5677 0.134 1 7 -2 4.2016 0.107 -4 -9 -1 0.9361 0.097 1 7 -1 6.3775 0.112 -4 -9 -2 2.0890 0.063 1 7 0 6.4391 0.114 -4 -9 -4 3.8111 0.149 1 7 1 6.2509 0.097 -4 -9 -6 1.1305 0.152 1 7 2 5.0911 0.109 -4 -8 -6 3.6081 0.138 1 7 3 5.4367 0.113 -4 -8 -2 6.3080 0.144 1 7 4 5.4982 0.12 -4 -8 0 7.1155 0.111 1 7 5 4.8935 0.142 -4 -8 2 6.5719 0.119 1 7 6 2.8288 0.076 -4 -8 4 5.1135 0.141 1 6 6 1.5984 0.095 -4 -8 6 4.4450 0.131 1 6 4 4.3279 0.12 -4 -7 5 4.6549 0.191 1 6 2 3.2714 0.086 -4 -7 3 3.0702 0.063 1 6 0 6.1987 0.106 -4 -7 1 5.1155 0.107 1 6 -2 3.0782 0.093 -4 -7 0 1.2578 0.069 1 6 -4 4.4631 0.127 -4 -7 -1 4.6082 0.116 1 6 -5 1.5481 0.061 -4 -7 -3 2.7960 0.068 1 6 -6 1.6040 0.087 -4 -7 -5 4.1993 0.263 1 5 -8 2.8517 0.142
156
-4 -6 -6 7.8003 0.201 1 5 -7 6.5636 0.196 -4 -6 -5 1.3347 0.071 1 5 -6 2.2924 0.082 -4 -6 -2 12.9136 0.197 1 5 -5 6.4964 0.158 -4 -6 -1 1.0607 0.065 1 5 -4 6.2445 0.13 -4 -6 0 1.2175 0.068 1 5 -3 11.1697 0.165 -4 -6 2 13.6753 0.123 1 5 -2 4.0716 0.087 -4 -6 3 0.6741 0.126 1 5 -1 10.9345 0.156 -4 -6 5 1.3946 0.095 1 5 0 8.4958 0.108 -4 -6 6 8.0695 0.17 1 5 1 11.3869 0.102 -4 -5 5 2.3067 0.062 1 5 2 4.1242 0.092 -4 -5 4 3.9386 0.115 1 5 3 9.8990 0.155 -4 -5 3 4.1592 0.109 1 5 4 6.2702 0.119 -4 -5 1 4.0486 0.108 1 5 5 7.2136 0.119 -4 -5 0 5.2725 0.095 1 5 6 2.4144 0.064 -4 -5 -1 4.0497 0.103 1 5 7 6.1075 0.168 -4 -5 -2 0.8196 0.067 1 5 8 2.9035 0.086 -4 -5 -3 3.5684 0.141 1 4 7 4.2219 0.162 -4 -5 -5 2.2709 0.06 1 4 5 3.1219 0.091 -4 -5 -6 0.6062 0.146 1 4 4 1.9817 0.045 -4 -4 -6 7.4176 0.179 1 4 3 6.4268 0.089 -4 -4 -4 13.6015 0.194 1 4 1 7.3422 0.129 -4 -4 -3 0.5640 0.101 1 4 0 3.7772 0.097 -4 -4 -2 13.1078 0.216 1 4 -1 7.0834 0.114 -4 -4 0 17.4847 0.169 1 4 -3 7.0793 0.133 -4 -4 2 13.7834 0.12 1 4 -4 2.0291 0.04 -4 -4 4 14.4142 0.162 1 4 -5 3.0139 0.105 -4 -3 -3 5.3006 0.1 1 4 -7 3.4892 0.102 -4 -3 -4 1.1237 0.071 1 3 -9 2.3349 0.079 -4 -3 -5 3.3773 0.14 1 3 -8 2.6849 0.103 -3 -1 -5 7.7539 0.176 1 3 -7 5.6163 0.165 -3 -1 -4 8.3710 0.134 1 3 -6 3.6715 0.123 -3 -1 -3 7.6065 0.138 1 3 -5 5.6760 0.132 -3 -1 4 8.7768 0.109 1 3 -4 5.7441 0.1 -3 -1 5 8.0459 0.114 1 3 -3 8.8915 0.13 -3 -2 5 2.2652 0.083 1 3 -2 8.0106 0.136 -3 -2 4 6.9976 0.101 1 3 -1 8.4113 0.136 -3 -2 -2 0.9604 0.043 1 3 0 5.5181 0.074 -3 -2 -4 6.6072 0.151 1 3 1 8.3452 0.073 -3 -2 -5 1.9031 0.071 1 3 2 7.4544 0.106 -3 -3 -7 4.2343 0.145 1 3 3 8.4612 0.133 -3 -3 -6 7.4761 0.132 1 3 4 5.5879 0.094 -3 -3 -5 4.5581 0.124 1 3 5 5.5397 0.108 -3 -3 -4 2.3076 0.055 1 3 6 3.4057 0.093 -3 -3 -3 7.6065 0.115 1 3 8 2.4480 0.099 -3 -3 -2 13.8630 0.208 1 3 9 2.5176 0.085 -3 -3 -1 8.5850 0.118 1 2 8 2.6547 0.077 -3 -3 0 3.7992 0.118 1 2 6 2.6708 0.061 -3 -3 1 8.7328 0.09 1 2 4 5.6264 0.109 -3 -3 2 14.8082 0.118 1 2 3 1.1018 0.046 -3 -3 3 7.4501 0.09 1 2 2 11.6319 0.161 -3 -3 4 2.3715 0.08 1 2 1 0.9003 0.031
157
-3 -3 5 4.7174 0.138 1 2 0 9.3293 0.077 -3 -3 6 8.2103 0.15 1 2 -1 0.9915 0.024 -3 -3 7 4.4849 0.206 1 2 -2 11.4446 0.181 -3 -4 6 1.5214 0.085 1 2 -3 1.2125 0.039 -3 -4 3 3.3060 0.104 1 2 -4 5.5803 0.104 -3 -4 2 2.7611 0.083 1 2 -6 2.5953 0.085 -3 -4 1 6.0374 0.077 1 2 -8 2.2224 0.112 -3 -4 -1 5.8612 0.102 1 1 -9 2.7550 0.079 -3 -4 -2 2.5143 0.104 1 1 -8 2.4431 0.089 -3 -4 -3 3.5043 0.097 1 1 -6 5.6175 0.129 -3 -4 -5 4.6251 0.154 1 1 -5 4.9010 0.098 -3 -4 -7 0.8915 0.116 1 1 -4 5.7584 0.086 -3 -5 -8 1.3685 0.127 1 1 -3 3.9844 0.117 -3 -5 -7 2.3973 0.099 1 1 -2 10.4366 0.192 -3 -5 -6 5.0646 0.139 1 1 -1 7.9311 0.188 -3 -5 -5 1.3383 0.072 1 1 0 10.4024 0.138 -3 -5 -4 3.2107 0.1 1 1 1 7.8045 0.111 -3 -5 -3 3.2677 0.105 1 1 2 10.2008 0.196 -3 -5 -2 9.4591 0.159 1 1 3 3.7677 0.096 -3 -5 -1 2.6359 0.086 1 1 4 5.3485 0.109 -3 -5 0 4.3080 0.123 1 1 5 4.4706 0.105 -3 -5 1 2.6299 0.092 1 1 6 5.7111 0.145 -3 -5 2 8.9408 0.102 1 1 8 2.7679 0.102 -3 -5 3 3.4561 0.097 1 1 9 2.9699 0.079 -3 -5 4 3.2442 0.126 1 0 9 3.7473 0.179 -3 -5 5 1.2780 0.085 1 0 5 6.9570 0.144 -3 -5 6 5.5180 0.155 1 0 3 7.1257 0.128 -3 -5 7 2.6301 0.065 1 0 1 13.2578 0.204 -3 -6 8 3.3890 0.096 1 0 -1 13.1529 0.311 -3 -6 7 1.0403 0.164 1 0 -3 7.3045 0.169 -3 -6 4 4.6799 0.12 1 0 -5 7.2911 0.121 -3 -6 3 1.7555 0.071 1 0 -7 2.0824 0.07 -3 -6 2 1.6782 0.048 1 -1 -8 2.8116 0.088 -3 -6 0 7.2997 0.116 1 -1 -6 5.9314 0.134 -3 -6 -2 1.7070 0.044 1 -1 -5 4.7141 0.141 -3 -6 -3 1.6966 0.055 1 -1 -4 5.5711 0.108 -3 -6 -4 4.2127 0.152 1 -1 -3 4.1652 0.079 -3 -6 -7 1.2269 0.098 1 -1 2 10.2641 0.197 -3 -6 -8 3.2643 0.074 1 -1 3 3.9417 0.131 -3 -7 -8 3.2641 0.081 1 -1 4 5.5475 0.132 -3 -7 -5 4.0827 0.118 1 -1 5 4.9999 0.117 -3 -7 -4 5.7946 0.133 1 -1 6 5.7861 0.12 -3 -7 -3 3.8000 0.137 1 -1 7 1.6367 0.069 -3 -7 -1 4.8401 0.11 1 -1 8 2.7857 0.101 -3 -7 0 8.0215 0.099 1 -2 8 2.5987 0.075 -3 -7 1 4.7049 0.105 1 -2 6 2.6820 0.068 -3 -7 3 3.7911 0.125 1 -2 5 1.0979 0.093 -3 -7 4 6.3320 0.12 1 -2 4 5.5367 0.12 -3 -7 5 4.0744 0.135 1 -2 3 1.0281 0.049 -3 -7 7 2.2196 0.074 1 -2 2 12.0646 0.174 -3 -7 8 3.2530 0.071 1 -2 -2 11.7391 0.162
158
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159
-2 -8 6 2.9762 0.104 2 3 7 2.2097 0.09 -2 -7 -3 0.3438 0.228 2 3 5 2.0712 0.065 -2 -6 -8 4.8669 0.168 2 3 4 2.1514 0.066 -2 -6 -7 1.9229 0.088 2 3 3 2.1414 0.06 -2 -6 -6 1.9104 0.075 2 3 2 5.0936 0.076 -2 -6 -4 9.2061 0.164 2 3 0 2.7891 0.078 -2 -6 -3 3.2510 0.117 2 3 -1 1.6980 0.101 -2 -6 -2 2.3242 0.083 2 3 -2 4.9246 0.094 -2 -6 -1 3.6397 0.111 2 3 -3 2.2601 0.067 -2 -6 0 11.8487 0.146 2 3 -4 2.2730 0.084 -2 -6 1 3.8029 0.095 2 3 -5 2.0572 0.055 -2 -6 2 2.3970 0.058 2 3 -6 2.8693 0.11 -2 -6 3 3.3173 0.087 2 3 -7 2.5161 0.067 -2 -6 4 9.2107 0.143 2 4 -7 1.8583 0.067 -2 -6 5 2.9393 0.094 2 4 -6 12.8255 0.21 -2 -6 6 1.8003 0.077 2 4 -5 2.6922 0.073 -2 -6 7 1.6065 0.091 2 4 -4 1.0408 0.071 -2 -6 8 4.9049 0.202 2 4 -3 3.7229 0.105 -2 -5 8 3.9047 0.147 2 4 -2 22.2652 0.338 -2 -5 6 6.1533 0.161 2 4 -1 4.7838 0.097 -2 -5 5 2.3754 0.062 2 4 0 2.4096 0.06 -2 -5 4 7.4245 0.119 2 4 1 4.5860 0.072 -2 -5 2 11.7007 0.088 2 4 2 23.5607 0.243 -2 -5 1 1.6081 0.037 2 4 3 3.6619 0.091 -2 -5 0 10.3778 0.118 2 4 5 2.6116 0.073 -2 -5 -1 1.6008 0.039 2 4 6 12.5897 0.194 -2 -5 -2 11.3757 0.18 2 4 9 0.9147 0.166 -2 -5 -4 7.3119 0.126 2 5 9 1.6851 0.118 -2 -5 -5 2.3866 0.051 2 5 8 3.3819 0.119 -2 -5 -6 6.7075 0.133 2 5 6 6.3344 0.145 -2 -5 -8 3.9839 0.095 2 5 5 2.2803 0.06 -2 -4 -9 0.8377 0.187 2 5 4 7.3317 0.123 -2 -4 -7 1.8922 0.062 2 5 2 10.9993 0.115 -2 -4 -6 12.5046 0.204 2 5 1 1.5727 0.037 -2 -4 -5 2.4481 0.074 2 5 0 9.9114 0.115 -2 -4 -3 3.7015 0.101 2 5 -1 1.5910 0.037 -2 -4 -2 22.5138 0.325 2 5 -2 11.1745 0.184 -2 -4 -1 4.7619 0.08 2 5 -4 7.4908 0.129 -2 -4 0 2.7909 0.109 2 5 -5 2.2811 0.055 -2 -4 1 4.2211 0.073 2 5 -6 6.6556 0.127 -2 -4 2 23.1758 0.218 2 5 -8 3.7452 0.145 -2 -4 3 3.4543 0.099 2 5 -9 1.5841 0.133 -2 -4 5 2.6448 0.048 2 6 -8 5.0217 0.131 -2 -4 6 12.6295 0.178 2 6 -7 1.7675 0.072 -2 -4 9 1.1701 0.14 2 6 -6 1.9497 0.066 -2 -3 8 1.8064 0.086 2 6 -5 2.7468 0.072 -2 -3 7 2.2570 0.131 2 6 -4 9.0605 0.138 -2 -3 6 2.6645 0.105 2 6 -3 3.2643 0.088 -2 -3 5 2.0978 0.061 2 6 -2 2.3343 0.06 -2 -3 4 2.6530 0.076 2 6 -1 3.8358 0.105 -2 -3 3 2.0549 0.081 2 6 0 11.5143 0.133
160
-2 -3 2 5.0975 0.095 2 6 1 3.7107 0.096 -2 -3 0 2.8152 0.074 2 6 2 2.4599 0.076 -2 -3 -1 0.9829 0.065 2 6 3 3.0070 0.076 -2 -3 -2 5.0273 0.088 2 6 4 9.0599 0.116 -2 -3 -3 2.1371 0.078 2 6 5 2.7691 0.113 -2 -3 -4 2.4602 0.061 2 8 -6 2.6233 0.118 -2 -3 -5 1.8841 0.072 2 8 -5 3.2145 0.137 -2 -3 -6 2.7626 0.076 2 8 -4 1.7281 0.075 -2 -3 -7 2.2938 0.057 2 8 -3 3.9042 0.167 -2 -3 -8 1.6780 0.075 2 8 -2 4.6443 0.135 -2 -3 -9 1.7254 0.104 2 8 -1 4.6409 0.127 -2 -2 -8 5.7286 0.151 2 8 0 2.2247 0.068 -2 -2 -7 2.0356 0.067 2 8 1 4.4011 0.115 -2 -2 -6 0.7177 0.11 2 8 3 4.0995 0.118 -2 -2 -5 3.6556 0.111 2 8 4 1.7670 0.074 -2 -2 -4 12.6403 0.176 2 8 5 3.0142 0.116 -2 -2 -3 3.4527 0.08 2 8 6 2.7512 0.077 -2 -2 -2 1.0191 0.037 2 9 4 5.5553 0.158 -2 -2 -1 3.5309 0.076 2 9 2 8.0666 0.122 -2 -2 0 17.8452 0.201 2 9 -2 7.6268 0.124 -2 -2 1 3.5285 0.063 2 9 -4 4.6327 0.162 -2 -2 3 3.5019 0.096 2 10 0 8.1980 0.126 -2 -2 4 12.9762 0.177 2 10 1 2.1067 0.075 -2 -2 5 3.6294 0.16 3 11 -2 5.1267 0.177 -2 -2 7 2.1051 0.073 3 11 1 4.0742 0.158 -2 -1 6 5.3383 0.148 3 11 2 5.6224 0.156 -2 -1 4 5.4805 0.091 3 10 2 1.9689 0.07 -2 -1 2 11.3345 0.148 3 10 0 2.3457 0.067 -2 -1 -1 1.0954 0.032 3 10 -1 2.3780 0.069 -2 -1 -2 10.7812 0.159 3 10 -2 1.7249 0.068 -2 -1 -4 5.5022 0.118 3 10 -4 2.2883 0.062 -2 -1 -6 5.2164 0.158 3 10 -5 2.1135 0.071 -2 -1 -8 2.8365 0.074 3 9 -6 1.7995 0.087 -2 0 -8 1.2360 0.096 3 9 -5 6.0129 0.177 -2 0 -6 3.9948 0.156 3 9 -4 3.0476 0.125 -2 0 -4 1.9985 0.049 3 9 -3 6.6292 0.172 -2 0 4 2.1046 0.064 3 9 -2 2.9047 0.088 -2 0 6 4.4232 0.152 3 9 -1 8.0366 0.121 -2 1 6 4.9957 0.129 3 9 0 4.0265 0.183 -2 1 4 5.4953 0.096 3 9 1 7.7172 0.159 -2 1 -3 0.6200 0.059 3 9 2 2.9430 0.087 -2 1 -4 5.1456 0.112 3 9 3 6.4679 0.171 -2 1 -5 0.5075 0.13 3 9 4 3.2562 0.089 -2 1 -6 5.1376 0.119 3 9 5 6.4993 0.165 -2 2 -5 3.6222 0.118 3 9 6 1.9407 0.085 -1 4 -3 6.3544 0.113 3 8 7 1.8884 0.086 -1 4 -4 1.8716 0.04 3 8 6 0.9571 0.13 -1 4 -5 2.5640 0.121 3 8 5 1.6966 0.074 -1 3 -7 4.9383 0.234 3 8 3 2.7352 0.141 -1 3 -6 3.4312 0.073 3 8 2 1.9615 0.052 -1 3 -5 4.6933 0.115 3 8 1 3.1658 0.058
161
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162
-1 -1 8 2.6888 0.073 3 4 -5 4.9455 0.128 -1 -1 9 2.5149 0.09 3 3 -7 4.7718 0.145 -1 -2 8 2.7961 0.073 3 3 -6 8.2885 0.158 -1 -2 6 2.5155 0.07 3 3 -5 4.6312 0.123 -1 -2 4 5.6403 0.094 3 3 -3 7.7926 0.119 -1 -2 3 1.1942 0.048 3 3 -2 14.3555 0.22 -1 -2 2 11.6398 0.156 3 3 -1 8.6683 0.149 -1 -2 1 0.8255 0.027 3 3 0 3.6610 0.101 -1 -2 0 9.6575 0.124 3 3 1 8.6331 0.088 -1 -2 -1 0.9123 0.025 3 3 2 14.4599 0.168 -1 -2 -2 11.2285 0.148 3 3 3 7.8586 0.122 -1 -2 -3 1.1588 0.046 3 3 4 2.3281 0.08 -1 -2 -4 5.5544 0.123 3 3 5 4.3747 0.114 -1 -2 -6 2.5140 0.085 3 3 6 7.7034 0.127 -1 -2 -7 1.5309 0.077 3 3 7 4.4702 0.141 -1 -2 -8 2.6343 0.093 3 2 6 1.0726 0.081 -1 -3 -9 2.4949 0.082 3 2 5 1.8970 0.116 -1 -3 -8 2.6742 0.064 3 2 4 7.1470 0.14 -1 -3 -7 5.4121 0.158 3 2 2 0.8612 0.073 -1 -3 -6 3.5968 0.119 3 2 -2 0.9635 0.06 -1 -3 -5 5.7464 0.11 3 2 -4 7.2570 0.172 -1 -3 -4 5.7749 0.123 3 2 -5 2.6123 0.072 -1 -3 -3 8.6401 0.127 3 1 -5 8.2687 0.157 -1 -3 -2 7.1858 0.115 3 1 -4 9.2732 0.143 -1 -3 -1 8.2479 0.136 3 1 3 6.9815 0.128 -1 -3 0 5.6554 0.073 3 1 4 8.8715 0.136 -1 -3 1 8.7313 0.08 3 1 5 8.2408 0.117 -1 -3 2 7.6616 0.094 4 3 5 3.7392 0.109 -1 -3 3 8.9850 0.123 4 3 3 5.6218 0.094 -1 -3 4 5.9189 0.095 4 4 -4 14.4565 0.208 -1 -3 5 5.6385 0.11 4 4 -2 13.3699 0.193 -1 -3 7 5.3283 0.154 4 4 0 17.7421 0.195 -1 -3 8 2.5946 0.074 4 4 2 13.8476 0.133 -1 -3 9 2.4149 0.113 4 4 4 14.2022 0.19 -1 -4 7 3.7013 0.134 4 4 6 8.0600 0.143 -1 -4 5 2.9321 0.095 4 5 5 2.2956 0.055 -1 -4 4 1.9518 0.057 4 5 3 3.8465 0.118 -1 -4 3 6.7128 0.1 4 5 2 0.8956 0.068 -1 -4 1 7.2157 0.105 4 5 1 3.9838 0.104 -1 -4 -1 7.3401 0.222 4 5 0 5.3367 0.089 -1 -4 -3 6.4167 0.098 4 5 -1 4.1126 0.094 -1 -4 -4 2.0065 0.046 4 5 -2 1.0390 0.064 -1 -4 -5 3.0266 0.111 4 5 -3 3.8998 0.129 -1 -4 -7 3.9449 0.155 4 5 -4 3.9320 0.111 -1 -5 -8 2.7411 0.092 4 5 -5 2.4484 0.053 -1 -5 -7 7.0469 0.136 4 6 -6 8.9199 0.179 -1 -5 -6 2.5892 0.065 4 6 -5 1.4138 0.078 -1 -5 -5 7.0718 0.17 4 6 -4 1.4944 0.066 -1 -5 -4 6.3725 0.119 4 6 -2 13.4633 0.187 -1 -5 -3 10.9541 0.156 4 6 -1 1.3600 0.051 -1 -5 -2 4.1390 0.088 4 6 1 1.1032 0.068
163
-1 -5 -1 11.2408 0.159 4 6 2 13.3494 0.127 -1 -5 1 10.9017 0.102 4 6 4 1.2825 0.078 -1 -5 2 4.3093 0.087 4 6 6 8.3688 0.188 -1 -5 3 11.1126 0.122 4 7 5 4.2267 0.14 -1 -5 4 6.5103 0.126 4 7 2 0.3932 0.177 -1 -5 5 7.5355 0.134 4 7 1 4.6911 0.121 -1 -5 6 2.6178 0.065 4 7 -1 4.7758 0.109 -1 -5 7 6.7198 0.183 4 7 -3 2.6953 0.08 -1 -5 8 2.7439 0.076 4 7 -5 4.3914 0.23 -1 -6 4 4.6509 0.113 4 8 -6 4.1577 0.191 -1 -6 3 0.5866 0.138 4 8 -4 5.6525 0.159 -1 -6 2 3.3737 0.104 4 8 -2 6.1359 0.142 -1 -6 -2 3.5698 0.106 4 8 0 7.0557 0.112 -1 -6 -4 4.6558 0.112 4 8 2 6.0259 0.128 -1 -6 -5 1.5812 0.065 4 8 3 0.9552 0.092 -1 -6 -6 1.6768 0.09 4 8 4 5.6425 0.158 -1 -7 -6 3.0675 0.095 4 9 2 2.0348 0.062 -1 -7 -5 5.1042 0.132 4 9 0 4.3884 0.139 -1 -7 -4 5.3095 0.126 4 9 -4 3.4370 0.094 -1 -7 -3 5.0811 0.119 4 9 -5 1.4476 0.107 -1 -7 -2 4.6238 0.117 4 9 -6 1.6385 0.087 -1 -7 -1 6.8304 0.14 4 10 -6 2.3784 0.077 -1 -7 1 6.6007 0.116 4 10 -2 3.2332 0.105 -1 -7 2 5.1532 0.103 4 10 2 4.0774 0.126 -1 -7 3 5.1320 0.11 4 10 6 2.3731 0.086 -1 -7 4 4.9931 0.12 4 11 4 0.3954 0.414 -1 -7 5 5.0727 0.135 4 11 2 1.1209 0.108 -1 -7 6 3.0226 0.097 4 11 1 1.4494 0.082 -1 -8 4 3.4137 0.091 4 11 0 1.1069 0.107 -1 -8 3 2.2624 0.09 4 11 -1 1.4532 0.085 -1 -8 2 1.4209 0.059 4 11 -2 1.2517 0.105 -1 -8 1 3.4249 0.149 4 12 -2 3.2186 0.124 -1 -8 -1 3.4821 0.111 5 12 2 4.1233 0.129 -1 -8 -3 2.2548 0.059 5 12 0 2.1948 0.073 -1 -8 -4 3.3167 0.101 5 12 -2 3.9758 0.153 0 -6 -4 3.3908 0.087 5 11 -4 2.1593 0.1 0 -6 -2 10.3088 0.171 5 11 -1 3.6531 0.103 0 -6 2 10.9594 0.115 5 11 1 3.5470 0.087 0 -6 4 3.4253 0.127 5 11 3 3.4933 0.091 0 -5 5 3.4496 0.082 5 11 4 2.0744 0.088 0 -5 3 3.3009 0.1 5 10 -2 4.8153 0.151 0 -5 1 5.8718 0.083 5 10 -4 1.0602 0.124 0 -5 -1 5.4594 0.122 5 9 -4 4.0060 0.166 0 -5 -3 3.7149 0.11 5 9 -3 5.8073 0.21 0 -5 -5 3.3844 0.113 5 9 -2 2.8631 0.081 0 -4 -6 4.4922 0.134 5 9 -1 6.9566 0.145 0 -4 -4 4.3031 0.1 5 9 0 5.0201 0.183 0 -4 -2 9.0752 0.134 5 9 1 7.0396 0.171 0 -4 2 8.7728 0.082 5 9 2 2.8111 0.113 0 -4 4 4.2005 0.116 5 9 3 5.5696 0.144 0 -4 6 4.3656 0.147 5 9 4 4.1270 0.129
164
0 -4 8 1.9178 0.073 5 9 5 5.6316 0.188 0 -3 7 3.5104 0.12 5 8 4 1.8547 0.066 0 -3 5 5.4453 0.109 5 8 3 2.4780 0.067 0 -3 3 6.9371 0.127 5 8 2 3.9609 0.112 0 -3 1 9.5555 0.078 5 8 1 1.5146 0.062 0 -3 -1 9.2251 0.143 5 8 0 2.1459 0.082 0 -3 -3 7.5442 0.105 5 8 -1 1.6762 0.058 0 -3 -5 5.5891 0.131 5 8 -2 4.1165 0.137 0 -3 -7 3.2110 0.078 5 8 -3 2.6082 0.089 0 -2 -6 10.1301 0.157 5 8 -4 1.8485 0.093 0 -2 -4 2.3097 0.058 5 7 -4 4.2814 0.145 0 -2 -2 16.8997 0.247 5 7 -3 4.8967 0.133 0 -2 2 17.0759 0.26 5 7 -2 6.9454 0.127 0 -2 4 2.2796 0.067 5 7 -1 5.2087 0.156 0 -2 6 9.8738 0.178 5 7 0 5.5462 0.112 0 -1 7 5.6353 0.134 5 7 2 6.1589 0.129 0 -1 5 2.8430 0.082 5 7 3 4.3342 0.174 0 -1 3 10.4570 0.204 5 7 4 4.5087 0.148 0 -1 1 10.9419 0.168 5 7 5 4.3677 0.171 0 -1 -1 10.7112 0.237 5 6 4 2.1937 0.059 0 -1 -3 10.6539 0.187 5 6 3 1.2056 0.073 0 -1 -5 3.0416 0.089 5 6 2 7.7341 0.115 0 -1 -7 5.3063 0.131 5 6 0 2.6608 0.098 0 0 -8 14.6329 0.241 5 6 -2 8.0532 0.139 0 0 -6 7.2189 0.146
P = 2.512(6) GPa
h k l FO Esd h k l FO Esd -5 -6 2 6.7381 0.12 0 0 8 11.4069 0.215 -5 -7 -1 4.8620 0.12 0 1 7 4.3233 0.145 -5 -7 0 4.5486 0.164 0 1 5 2.4297 0.075 -5 -7 1 4.4592 0.14 0 1 3 9.3134 0.169 -5 -7 2 5.3737 0.137 0 1 1 8.9098 0.182 -5 -7 3 3.7973 0.119 0 1 -1 9.0092 0.187 -5 -7 4 3.6532 0.12 0 1 -3 8.9161 0.114 -5 -8 3 2.1093 0.075 0 1 -5 2.2516 0.079 -5 -8 2 3.2975 0.108 0 1 -7 4.8730 0.131 -5 -8 1 1.4083 0.082 0 2 -6 8.0068 0.125 -5 -8 0 2.2200 0.058 0 2 -4 1.8176 0.077 -5 -8 -2 3.6004 0.097 0 2 -2 13.8251 0.211 -5 -9 -2 2.3536 0.061 0 2 0 3.1175 0.068 -5 -9 -1 6.2045 0.144 0 2 2 14.0971 0.192 -5 -9 0 4.2980 0.124 0 2 4 1.8096 0.046 -5 -9 1 5.9912 0.138 0 2 6 7.8395 0.118 -5 -9 2 2.2348 0.062 0 3 9 2.0706 0.087 -5 -9 3 5.0196 0.154 0 3 7 2.3942 0.066 -5 -9 4 3.6507 0.101 0 3 5 4.4400 0.106 -5 -10 4 0.6058 0.209 0 3 3 6.1037 0.103 -5 -10 3 0.8388 0.156 0 3 1 7.5984 0.107
165
-5 -10 2 3.8356 0.162 0 3 -1 7.8043 0.145 -5 -10 -1 83.7955 0.766 0 3 -3 6.1716 0.094 -5 -10 -2 3.6411 0.168 0 3 -5 4.3640 0.115 -5 -11 -1 3.1955 0.072 0 3 -7 2.7653 0.063 -5 -11 0 2.1942 0.08 0 4 -6 3.2477 0.121 -5 -11 1 2.8413 0.117 0 4 -4 2.5696 0.113 -5 -11 3 3.1799 0.062 0 4 -2 7.6859 0.129 -5 -12 2 3.4087 0.116 0 4 0 10.2686 0.148 -5 -12 0 2.2130 0.077 0 4 2 7.7900 0.112 -4 -12 -4 3.8356 0.145 0 4 4 3.7881 0.099 -4 -12 -2 2.9057 0.094 0 4 6 3.5269 0.119 -4 -12 0 4.2968 0.183 0 5 5 2.8450 0.085 -4 -12 2 2.9150 0.089 0 5 3 2.9032 0.148 -4 -11 1 1.0631 0.115 0 5 1 4.4767 0.091 -4 -10 -5 0.7687 0.172 0 5 -1 4.6628 0.095 -4 -10 -2 3.3983 0.107 0 5 -3 3.1902 0.12 -4 -10 2 3.3408 0.14 0 5 -5 3.0260 0.078 -4 -10 6 2.5604 0.078 0 6 -4 2.5936 0.085 -4 -9 4 2.7098 0.157 0 6 -2 8.6427 0.128 -4 -9 2 1.6643 0.08 0 6 0 3.7970 0.092 -4 -9 0 3.8257 0.139 0 6 2 8.5108 0.135 -4 -9 -4 3.3808 0.096 0 6 4 2.7290 0.053 -4 -8 -4 4.7568 0.128 0 6 6 4.9331 0.136 -4 -8 -2 5.6311 0.145 0 7 3 4.3382 0.115 -4 -8 0 6.2634 0.117 0 7 1 3.6740 0.103 -4 -8 2 5.5432 0.144 0 7 -1 3.3133 0.109 -4 -8 4 4.7861 0.142 0 8 2 3.6440 0.131 -4 -8 5 0.4073 0.266 1 9 -2 4.2398 0.187 -4 -8 6 3.4238 0.113 1 9 -1 1.2283 0.072 -4 -7 5 3.5915 0.106 1 9 0 2.4845 0.068 -4 -7 3 2.1692 0.061 1 9 2 4.1954 0.168 -4 -7 2 0.5397 0.153 1 9 4 2.2172 0.061 -4 -7 1 3.7924 0.097 1 9 5 1.2164 0.116 -4 -7 0 1.4080 0.095 1 8 5 2.7374 0.053 -4 -7 -1 3.7167 0.113 1 8 4 2.4857 0.09 -4 -7 -3 2.3038 0.05 1 8 3 2.0146 0.054 -4 -7 -5 3.6931 0.111 1 8 1 3.1098 0.08 -4 -6 -5 1.2182 0.091 1 8 0 3.5271 0.115 -4 -6 -4 1.1540 0.082 1 8 -1 3.1292 0.086 -4 -6 -2 11.1558 0.106 1 8 -2 1.2425 0.072 -4 -6 2 10.8570 0.107 1 8 -3 1.8500 0.06 -4 -6 5 0.7390 0.137 1 8 -4 2.5160 0.071 -4 -6 6 6.9853 0.143 1 7 -5 4.1159 0.15 -4 -5 3 3.0204 0.109 1 7 -4 4.4087 0.136 -4 -5 2 0.5543 0.11 1 7 -3 4.8093 0.143 -4 -5 1 3.5963 0.112 1 7 -2 4.1933 0.123 -4 -5 0 4.5804 0.095 1 7 -1 5.1856 0.136 -4 -5 -1 3.5498 0.104 1 7 0 5.3476 0.131 -4 -5 -3 3.2559 0.104 1 7 1 5.5577 0.116 -4 -5 -4 3.3117 0.062 1 7 2 4.1947 0.149 -4 -4 2 11.7319 0.128 1 7 3 4.2903 0.124
166
-4 -4 3 0.7254 0.091 1 7 4 4.1408 0.128 -4 -4 4 11.9763 0.128 1 7 5 4.1299 0.14 -4 -4 6 6.8776 0.135 1 7 6 2.3665 0.083 -4 -3 5 3.1691 0.107 1 6 8 1.7603 0.113 -4 -3 3 4.7392 0.104 1 6 7 0.9312 0.136 -3 0 5 3.6072 0.128 1 6 6 1.2004 0.095 -3 -1 3 6.5895 0.102 1 6 4 3.3744 0.141 -3 -1 4 7.2813 0.141 1 6 2 3.0822 0.117 -3 -1 5 6.1649 0.112 1 6 0 5.0569 0.096 -3 -1 7 3.4321 0.143 1 6 -2 3.1379 0.093 -3 -2 8 2.7862 0.064 1 6 -4 3.6106 0.108 -3 -2 7 0.7828 0.133 1 6 -6 1.6520 0.068 -3 -2 6 0.8814 0.102 1 5 -7 5.7570 0.162 -3 -2 5 2.2301 0.073 1 5 -6 2.1877 0.054 -3 -2 4 5.7879 0.137 1 5 -5 6.1753 0.112 -3 -2 -4 5.7732 0.113 1 5 -4 5.3454 0.103 -3 -3 -5 3.7634 0.123 1 5 -3 9.3423 0.131 -3 -3 -4 1.9591 0.044 1 5 -2 3.5322 0.098 -3 -3 -3 6.2407 0.111 1 5 -1 9.7010 0.174 -3 -3 -2 13.0005 0.132 1 5 0 7.2224 0.117 -3 -3 -1 7.5920 0.195 1 5 1 9.1322 0.135 -3 -3 0 3.4855 0.187 1 5 2 3.9237 0.098 -3 -3 1 7.2738 0.171 1 5 3 9.0573 0.127 -3 -3 2 12.4425 0.126 1 5 4 5.2387 0.103 -3 -3 3 5.9826 0.092 1 5 5 5.9507 0.158 -3 -3 4 1.8657 0.077 1 5 6 2.0750 0.076 -3 -3 5 3.9054 0.121 1 5 7 5.5411 0.147 -3 -3 6 6.3756 0.151 1 5 8 2.2069 0.102 -3 -3 7 3.6713 0.093 1 5 9 2.7054 0.07 -3 -4 7 1.0786 0.111 1 4 7 3.0238 0.103 -3 -4 6 0.7069 0.137 1 4 5 2.6744 0.074 -3 -4 3 2.8349 0.078 1 4 3 5.4067 0.095 -3 -4 2 1.9660 0.039 1 4 1 6.4243 0.194 -3 -4 1 4.7327 0.1 1 4 0 3.1561 0.078 -3 -4 -1 5.3700 0.084 1 4 -1 6.4942 0.124 -3 -4 -2 1.9280 0.051 1 4 -3 5.7991 0.122 -3 -4 -3 3.1427 0.113 1 4 -5 2.4838 0.065 -3 -4 -5 3.8744 0.151 1 4 -7 3.3928 0.118 -3 -5 -6 4.4377 0.167 1 4 -8 0.8275 0.172 -3 -5 -5 1.3873 0.069 1 3 -8 1.9826 0.07 -3 -5 -4 2.9160 0.066 1 3 -7 4.6837 0.141 -3 -5 -3 2.9044 0.056 1 3 -6 2.9078 0.09 -3 -5 -2 8.0164 0.089 1 3 -5 4.9950 0.113 -3 -5 -1 1.9843 0.077 1 3 -4 4.6456 0.107 -3 -5 0 3.7066 0.11 1 3 -3 7.7473 0.116 -3 -5 1 2.3287 0.075 1 3 -2 6.6292 0.165 -3 -5 2 8.0011 0.087 1 3 -1 7.3528 0.096 -3 -5 3 2.5902 0.089 1 3 0 4.4170 0.076 -3 -5 4 3.0279 0.118 1 3 1 7.6353 0.124 -3 -5 6 4.4962 0.15 1 3 2 6.8900 0.18 -3 -5 7 2.1492 0.067 1 3 3 7.5484 0.096
167
-3 -6 8 2.1166 0.085 1 3 4 4.7899 0.113 -3 -6 7 1.5481 0.097 1 3 5 4.7273 0.109 -3 -6 4 3.7289 0.116 1 3 6 3.1685 0.089 -3 -6 3 1.8581 0.077 1 3 7 4.2620 0.183 -3 -6 2 1.3566 0.062 1 3 8 1.9716 0.106 -3 -6 0 5.9064 0.098 1 3 9 1.9015 0.079 -3 -6 -2 1.4156 0.062 1 2 8 2.1135 0.068 -3 -6 -3 1.7348 0.063 1 2 6 1.8904 0.056 -3 -6 -4 3.8165 0.108 1 2 5 0.7839 0.098 -3 -6 -6 1.0994 0.106 1 2 4 4.9046 0.088 -3 -6 -7 1.2254 0.103 1 2 2 9.5322 0.149 -3 -7 -7 1.1520 0.156 1 2 1 0.8069 0.026 -3 -7 -5 3.3832 0.08 1 2 0 7.4305 0.145 -3 -7 -4 4.6710 0.145 1 2 -1 0.8263 0.027 -3 -7 -3 3.2946 0.085 1 2 -2 9.6427 0.138 -3 -7 -1 3.9576 0.109 1 2 -3 0.9764 0.044 -3 -7 0 6.6815 0.115 1 2 -4 4.4771 0.101 -3 -7 1 3.9039 0.111 1 2 -5 1.3572 0.077 -3 -7 3 3.1848 0.09 1 2 -6 2.1704 0.053 -3 -7 4 5.1744 0.124 1 2 -7 1.1299 0.092 -3 -7 5 3.4105 0.076 1 2 -8 2.1023 0.074 -3 -7 8 2.8637 0.068 1 1 -9 2.2782 0.085 -3 -8 7 1.7346 0.087 1 1 -8 2.2191 0.07 -3 -8 3 3.0167 0.066 1 1 -6 4.7303 0.115 -3 -8 2 1.6312 0.059 1 1 -5 3.6919 0.123 -3 -8 1 2.7714 0.069 1 1 -4 4.7957 0.103 -3 -8 -1 2.7891 0.08 1 1 -3 3.5314 0.148 -3 -8 -2 1.6550 0.058 1 1 -2 8.7555 0.117 -3 -8 -3 2.7325 0.097 1 1 -1 6.7973 0.141 -3 -8 -5 1.6971 0.082 1 1 0 8.4686 0.231 -3 -9 -5 4.8170 0.194 1 1 1 6.4586 0.125 -3 -9 -4 2.7772 0.075 1 1 2 8.7456 0.114 -3 -9 -3 5.4921 0.159 1 1 3 3.4198 0.17 -3 -9 -2 2.3974 0.056 1 1 4 4.6281 0.089 -3 -9 -1 6.3768 0.123 1 1 5 4.0375 0.118 -3 -9 0 2.9280 0.111 1 1 6 4.2555 0.123 -3 -9 1 6.4949 0.145 1 1 8 2.1132 0.076 -3 -9 2 2.4132 0.077 1 0 7 1.3988 0.071 -3 -9 3 5.4961 0.138 1 0 5 5.9133 0.109 -3 -9 4 2.6723 0.069 1 0 3 6.2133 0.14 -3 -9 5 5.3229 0.155 1 0 -1 11.0015 0.203 -3 -9 6 1.7123 0.091 1 0 -3 6.5399 0.147 -3 -10 2 1.4867 0.078 1 0 -5 5.7135 0.119 -3 -10 0 2.1498 0.071 1 0 -7 1.5913 0.067 -3 -10 -1 1.7950 0.067 1 0 -9 2.8089 0.088 -3 -10 -2 1.3970 0.088 1 -1 -9 1.7432 0.084 -3 -10 -3 1.0123 0.109 1 -1 -8 2.1692 0.074 -3 -10 -4 1.8165 0.076 1 -1 -2 8.7802 0.111 -3 -10 -5 1.6079 0.089 1 -1 2 8.6906 0.118 -3 -11 -5 2.6584 0.07 1 -1 3 3.5124 0.177 -3 -11 -4 0.9785 0.143 1 -1 4 4.2270 0.088
168
-3 -11 -3 3.3961 0.162 1 -1 5 3.7977 0.104 -3 -11 -2 4.5038 0.217 1 -1 6 4.9988 0.114 -3 -11 -1 3.5932 0.158 1 -1 7 1.3863 0.084 -3 -11 0 1.5891 0.077 1 -2 6 2.2410 0.047 -3 -11 1 3.5929 0.132 1 -2 5 1.3029 0.071 -3 -11 2 5.0180 0.167 1 -2 4 4.6249 0.113 -3 -11 3 3.8180 0.114 1 -2 3 0.9562 0.042 -2 -11 0 1.1636 0.114 1 -2 2 9.6729 0.1 -2 -10 -4 5.4273 0.152 1 -2 -2 9.5448 0.094 -2 -10 -3 1.4161 0.084 1 -2 -4 4.7983 0.103 -2 -10 -2 0.8495 0.126 1 -2 -5 1.4577 0.06 -2 -10 -1 1.9036 0.061 1 -2 -6 2.1233 0.061 -2 -10 0 6.7572 0.13 1 -3 -8 2.1411 0.067 -2 -10 1 1.9155 0.062 1 -3 -7 4.4409 0.133 -2 -9 4 4.4694 0.149 1 -3 -6 2.8399 0.082 -2 -9 2 6.7745 0.125 1 -3 -5 4.4750 0.109 -2 -9 0 5.8534 0.131 1 -3 -4 4.8506 0.091 -2 -9 -2 6.6054 0.123 1 -3 -3 7.3614 0.085 -2 -9 -4 4.6930 0.161 1 -3 -2 6.5148 0.153 -2 -9 -6 4.3641 0.222 1 -3 3 7.4452 0.092 -2 -8 -6 2.3490 0.1 1 -3 4 4.6700 0.107 -2 -8 -5 2.7142 0.073 1 -3 5 4.6630 0.109 -2 -8 -3 3.4391 0.139 1 -4 -3 5.2042 0.092 -2 -8 -1 3.9740 0.15 1 -4 -4 1.7139 0.042 -2 -8 0 1.8751 0.049 1 -4 -5 2.6014 0.081 -2 -8 1 3.6021 0.131 1 -4 -7 3.2443 0.096 -2 -8 2 3.8967 0.131 1 -5 -6 2.2354 0.054 -2 -8 3 3.5111 0.09 1 -5 -5 5.9921 0.147 -2 -8 5 3.0607 0.097 1 -5 -4 5.2787 0.104 -2 -8 6 2.5230 0.062 1 -5 -3 9.3128 0.103 -2 -7 1 0.6515 0.128 2 -3 -5 1.9639 0.046 -2 -6 -8 3.4251 0.126 2 -2 -5 3.1022 0.084 -2 -6 -7 1.3346 0.096 2 -2 -4 10.3677 0.127 -2 -6 -4 7.7289 0.133 2 -1 -8 2.1379 0.068 -2 -6 -3 2.5388 0.077 2 0 -8 1.1570 0.096 -2 -6 -2 1.8027 0.062 2 0 -6 3.2311 0.098 -2 -6 -1 3.1698 0.083 2 0 -4 1.8501 0.037 -2 -6 0 9.8784 0.107 2 0 4 1.8490 0.045 -2 -6 1 3.0808 0.118 2 0 6 3.1732 0.102 -2 -6 2 1.9987 0.055 2 1 4 4.6602 0.112 -2 -6 3 2.6601 0.054 2 1 2 9.3623 0.125 -2 -6 4 7.8396 0.105 2 1 -2 9.1675 0.127 -2 -6 5 2.3737 0.081 2 1 -4 4.5783 0.103 -2 -6 7 1.4808 0.086 2 1 -6 4.2471 0.16 -2 -6 8 4.0871 0.122 2 1 -8 2.5343 0.063 -2 -5 8 3.3278 0.099 2 2 -8 4.9416 0.184 -2 -5 6 5.2512 0.145 2 2 -7 1.8857 0.065 -2 -5 5 1.8719 0.055 2 2 -5 2.8598 0.092 -2 -5 4 5.8994 0.111 2 2 -4 10.6391 0.146 -2 -5 2 9.5652 0.098 2 2 -3 2.9512 0.086 -2 -5 1 1.0866 0.049 2 2 -1 2.8641 0.063
169
-2 -5 0 8.5376 0.096 2 2 0 14.9947 0.273 -2 -5 -2 9.3767 0.09 2 2 1 2.8037 0.093 -2 -5 -4 5.9588 0.103 2 2 3 2.8038 0.068 -2 -5 -6 5.1140 0.132 2 2 4 10.5072 0.135 -2 -5 -8 3.1414 0.127 2 2 5 2.8855 0.077 -2 -4 -6 10.5501 0.131 2 2 7 1.6827 0.064 -2 -4 -4 0.7211 0.096 2 3 7 2.0181 0.065 -2 -4 -3 2.9522 0.102 2 3 6 2.2811 0.068 -2 -4 -2 19.1659 0.177 2 3 5 2.2235 0.085 -2 -4 -1 3.8217 0.108 2 3 4 2.0571 0.136 -2 -4 1 4.0946 0.08 2 3 3 1.6245 0.064 -2 -4 2 19.3966 0.187 2 3 2 4.3069 0.118 -2 -4 3 3.1532 0.082 2 3 0 2.6119 0.203 -2 -4 6 10.3646 0.17 2 3 -1 1.6550 0.104 -2 -4 8 0.7530 0.152 2 3 -2 4.1143 0.106 -2 -3 9 1.4828 0.096 2 3 -3 1.5979 0.061 -2 -3 8 1.1851 0.113 2 3 -4 1.9862 0.055 -2 -3 7 1.8672 0.072 2 3 -5 1.9366 0.066 -2 -3 6 2.0993 0.057 2 3 -6 2.4620 0.051 -2 -3 5 1.9028 0.069 2 3 -7 1.8772 0.08 -2 -3 4 2.1285 0.076 2 4 -9 1.0861 0.135 -2 -3 3 1.7770 0.068 2 4 -6 10.5139 0.179 -2 -3 2 4.4045 0.134 2 4 -5 2.2248 0.063 -2 -3 -1 1.3660 0.088 2 4 -3 3.1686 0.081 -2 -3 -2 4.3030 0.124 2 4 -2 18.6923 0.274 -2 -3 -3 1.7202 0.041 2 4 -1 3.9777 0.075 -2 -3 -4 2.3777 0.085 2 4 0 2.7757 0.216 -2 -3 -5 1.9333 0.079 2 4 1 3.9755 0.099 -2 -3 -6 2.4360 0.065 2 4 2 18.9962 0.258 -2 -3 -7 1.8790 0.067 2 4 3 2.9178 0.078 -2 -2 -7 1.5953 0.081 2 4 5 2.2704 0.053 -2 -2 -5 2.9471 0.09 2 4 6 10.5124 0.144 -2 -2 -4 10.6627 0.138 2 5 8 3.3702 0.087 -2 -2 -3 2.7576 0.059 2 5 6 5.5812 0.136 -2 -2 -1 2.8007 0.063 2 5 5 1.9313 0.057 -2 -2 0 15.3035 0.171 2 5 4 5.9755 0.131 -2 -2 1 2.8849 0.063 2 5 2 9.5361 0.145 -2 -2 3 2.9029 0.083 2 5 0 8.6122 0.14 -2 -2 4 10.6062 0.139 2 5 -1 1.2368 0.071 -2 -2 5 2.8571 0.109 2 5 -2 9.5352 0.126 -2 -2 6 0.7147 0.118 2 5 -4 5.8387 0.102 -2 -2 8 4.8589 0.185 2 5 -5 1.7697 0.085 -2 -1 8 2.2733 0.064 2 5 -6 5.6829 0.13 -2 -1 6 4.0606 0.132 2 5 -8 3.3318 0.12 -2 -1 4 4.4624 0.102 2 6 -8 3.4226 0.142 -2 -1 2 9.5086 0.137 2 6 -7 1.5444 0.087 -2 -1 -2 9.3589 0.101 2 6 -5 2.2633 0.131 -2 -1 -3 0.5646 0.087 2 6 -4 7.7702 0.161 -2 -1 -4 4.6174 0.124 2 6 -3 2.5085 0.076 -2 -1 -6 4.2939 0.144 2 6 -2 1.8634 0.046 -2 0 -6 3.1069 0.089 2 6 -1 2.8724 0.093
170
-2 0 -4 1.7237 0.041 2 6 0 9.7066 0.168 -2 0 4 1.7181 0.041 2 6 1 2.8742 0.093 -2 0 6 3.3464 0.095 2 6 2 1.8632 0.065 -2 1 8 2.1641 0.074 2 6 3 2.5085 0.076 -2 1 7 0.6609 0.149 2 6 4 7.8770 0.13 -2 1 4 4.4884 0.1 2 6 5 2.4384 0.06 -2 1 3 0.6460 0.072 2 6 8 4.2735 0.126 -2 3 6 2.5430 0.066 2 7 4 0.5636 0.147 -1 5 3 9.4561 0.11 2 7 -5 0.7586 0.12 -1 5 4 5.4812 0.118 2 8 -6 2.4936 0.067 -1 5 5 6.3731 0.14 2 8 -5 2.3758 0.131 -1 5 6 2.1827 0.055 2 8 -4 1.5688 0.068 -1 4 7 3.2988 0.091 2 8 -3 3.3916 0.067 -1 4 5 2.7844 0.058 2 8 -2 3.4026 0.103 -1 4 4 1.6635 0.043 2 8 -1 3.7468 0.167 -1 4 3 5.4520 0.12 2 8 0 1.9372 0.068 -1 3 -5 4.5630 0.126 2 8 1 4.2068 0.121 -1 3 -4 4.6734 0.094 2 8 2 3.9257 0.126 -1 3 -3 7.6000 0.093 2 8 3 3.4018 0.086 -1 3 2 6.5860 0.132 2 8 6 2.5744 0.071 -1 3 3 7.3742 0.105 2 8 7 1.9884 0.078 -1 3 4 4.6928 0.1 2 9 6 4.7144 0.191 -1 3 5 5.0212 0.124 2 9 4 4.3608 0.137 -1 3 6 2.6370 0.11 2 9 2 6.2517 0.132 -1 3 7 4.2128 0.147 2 9 -2 6.9556 0.128 -1 3 8 2.0477 0.069 2 9 -4 4.4802 0.148 -1 2 6 2.1172 0.053 2 10 -3 1.6424 0.075 -1 2 5 1.5236 0.075 2 10 -1 1.9347 0.063 -1 2 4 4.6665 0.088 2 10 0 6.7309 0.167 -1 2 3 1.2246 0.039 2 10 1 1.8622 0.063 -1 2 2 9.5577 0.126 2 10 3 1.5751 0.08 -1 2 -2 9.6542 0.117 2 10 4 5.6009 0.184 -1 2 -4 4.4489 0.147 2 11 0 0.9930 0.143 -1 2 -5 1.3517 0.057 3 11 -3 3.5627 0.142 -1 2 -6 2.0517 0.052 3 11 -2 4.6792 0.171 -1 1 -6 4.4466 0.132 3 11 -1 3.6542 0.121 -1 1 -5 3.7240 0.125 3 11 0 1.0001 0.125 -1 1 -4 4.2278 0.119 3 11 1 3.3174 0.164 -1 1 -3 3.8162 0.142 3 11 3 3.2838 0.136 -1 1 -2 8.7514 0.113 3 11 4 1.3464 0.097 -1 1 5 3.8666 0.117 3 11 5 2.7228 0.084 -1 1 6 4.6483 0.136 3 10 6 0.9321 0.145 -1 1 7 1.2553 0.097 3 10 5 1.9197 0.087 -1 1 8 2.3011 0.065 3 10 4 1.9465 0.076 -1 1 9 2.0206 0.101 3 10 2 1.5647 0.082 -1 0 9 3.1266 0.124 3 10 1 1.5668 0.083 -1 0 7 1.3519 0.076 3 10 0 2.0721 0.064 -1 0 5 5.7865 0.095 3 10 -3 0.5929 0.221 -1 0 3 6.5503 0.25 3 10 -4 1.9608 0.069 -1 0 1 10.9114 0.197 3 9 -5 5.2814 0.178 -1 0 -3 5.8325 0.123 3 9 -4 2.6499 0.071
171
-1 0 -5 5.6805 0.113 3 9 -3 5.5113 0.137 -1 0 -7 1.4434 0.084 3 9 -2 2.5899 0.052 -1 -1 -8 2.4349 0.063 3 9 -1 6.9365 0.149 -1 -1 -6 4.6692 0.115 3 9 0 3.3294 0.135 -1 -1 -5 3.7635 0.114 3 9 1 6.5345 0.138 -1 -1 -4 4.7309 0.086 3 9 2 2.3983 0.103 -1 -1 -3 3.5599 0.186 3 9 3 5.5669 0.144 -1 -1 -2 8.5621 0.099 3 9 5 5.3099 0.167 -1 -1 -1 6.5329 0.067 3 9 6 1.5226 0.098 -1 -1 0 8.8106 0.118 3 8 7 2.1445 0.074 -1 -1 1 6.8562 0.049 3 8 5 1.6786 0.077 -1 -1 2 7.9105 0.129 3 8 3 2.8513 0.076 -1 -1 3 3.7981 0.274 3 8 2 1.6829 0.058 -1 -1 4 4.6342 0.103 3 8 1 2.4386 0.085 -1 -1 5 3.8016 0.102 3 8 -1 2.8898 0.085 -1 -1 6 3.8015 0.137 3 8 -2 1.6333 0.077 -1 -2 8 1.9993 0.094 3 8 -3 2.7308 0.06 -1 -2 7 1.1937 0.101 3 8 -7 1.8549 0.106 -1 -2 5 1.3168 0.075 3 7 -8 2.9351 0.069 -1 -2 4 4.5638 0.088 3 7 -7 1.9700 0.082 -1 -2 3 0.9281 0.045 3 7 -5 3.3624 0.13 -1 -2 2 9.7363 0.094 3 7 -4 5.2161 0.169 -1 -2 1 0.7701 0.029 3 7 -3 3.2081 0.08 -1 -2 0 8.1934 0.114 3 7 -1 3.8784 0.112 -1 -2 -1 0.8814 0.028 3 7 0 6.7365 0.128 -1 -2 -2 9.0903 0.096 3 7 1 3.7022 0.12 -1 -2 -4 4.5713 0.087 3 7 3 3.3343 0.103 -1 -2 -6 1.8626 0.06 3 7 4 5.2754 0.128 -1 -2 -8 2.0340 0.069 3 7 5 2.9450 0.099 -1 -3 -9 1.9396 0.079 3 7 7 1.9885 0.076 -1 -3 -7 4.4167 0.173 3 6 7 1.2827 0.111 -1 -3 -6 2.9554 0.075 3 6 4 3.7464 0.139 -1 -3 -5 4.7590 0.121 3 6 3 1.7970 0.066 -1 -3 -4 4.7065 0.095 3 6 2 1.5939 0.053 -1 -3 -3 7.4631 0.086 3 6 1 0.9424 0.079 -1 -3 -2 6.4620 0.118 3 6 0 5.8922 0.123 -1 -3 -1 7.1566 0.068 3 6 -2 1.4659 0.053 -1 -3 0 4.5473 0.083 3 6 -3 1.8583 0.085 -1 -3 1 7.3997 0.079 3 6 -4 3.7364 0.125 -1 -3 2 6.6149 0.213 3 6 -8 2.2815 0.089 -1 -3 3 7.8213 0.094 3 5 -8 1.3409 0.108 -1 -3 4 4.5369 0.091 3 5 -7 2.0990 0.071 -1 -3 5 4.4119 0.135 3 5 -6 4.1822 0.168 -1 -3 6 2.7912 0.087 3 5 -4 2.6851 0.099 -1 -3 8 2.0172 0.068 3 5 -3 2.9029 0.08 -1 -4 7 2.9935 0.104 3 5 -2 7.8165 0.119 -1 -4 5 2.7157 0.089 3 5 -1 2.2359 0.053 -1 -4 4 1.5690 0.053 3 5 0 3.5768 0.103 -1 -4 3 5.7300 0.084 3 5 1 2.3519 0.046 -1 -4 1 6.6955 0.149 3 5 2 8.0329 0.121 -1 -4 0 2.9393 0.089 3 5 3 2.7343 0.074
172
-1 -4 -1 6.4296 0.102 3 5 4 3.1159 0.114 -1 -4 -3 5.4746 0.084 3 5 5 1.0801 0.102 -1 -4 -4 1.5905 0.046 3 5 6 4.2953 0.178 -1 -4 -5 2.6092 0.084 3 4 5 4.6756 0.119 -1 -4 -7 2.7437 0.142 3 4 3 3.1930 0.107 -1 -5 -9 2.6142 0.07 3 4 2 1.9086 0.083 -1 -5 -8 2.3022 0.078 3 4 1 5.3053 0.108 -1 -5 -7 5.8238 0.152 3 4 -1 5.1388 0.091 -1 -5 -6 2.0800 0.055 3 4 -2 1.9777 0.039 -1 -5 -5 6.0022 0.125 3 4 -3 2.9699 0.12 -1 -5 -4 5.1936 0.103 3 4 -5 4.3387 0.118 -1 -5 -3 9.3277 0.105 3 3 -7 3.6688 0.105 -1 -5 -2 3.6446 0.091 3 3 -6 6.6581 0.144 -1 -5 -1 9.7539 0.091 3 3 -5 3.9446 0.123 -1 -5 0 7.2141 0.098 3 3 -4 2.0757 0.041 -1 -5 1 9.7316 0.11 3 3 -3 6.2421 0.105 -1 -5 2 3.6526 0.107 3 3 -2 12.3467 0.162 -1 -5 3 9.4127 0.104 3 3 -1 7.3909 0.188 -1 -5 4 5.2341 0.104 3 3 0 3.7740 0.185 -1 -5 5 5.9698 0.113 3 3 1 7.1694 0.181 -1 -5 6 2.1590 0.068 3 3 2 12.6389 0.16 -1 -5 7 5.3185 0.175 3 3 3 6.4934 0.12 -1 -6 4 3.6662 0.133 3 3 4 2.1315 0.041 -1 -6 2 3.1267 0.105 3 3 5 4.0589 0.142 -1 -6 0 5.2028 0.106 3 2 4 6.0453 0.112 -1 -6 -2 3.0021 0.104 3 2 -4 6.0311 0.101 -1 -6 -4 3.4186 0.115 3 2 -8 2.9908 0.059 -1 -6 -5 1.2547 0.087 3 1 -7 3.6185 0.11 -1 -7 -7 2.2825 0.066 3 1 -5 6.7363 0.14 -1 -7 -5 4.0077 0.137 3 1 -4 7.2273 0.129 -1 -7 -4 4.3653 0.129 3 1 -3 6.8795 0.114 -1 -7 -3 4.4371 0.113 3 0 -5 3.7274 0.122 -1 -7 -2 4.2043 0.126 4 3 -3 4.9600 0.113 -1 -7 -1 5.4547 0.118 4 3 -5 2.9098 0.13 -1 -7 0 5.7675 0.122 4 4 -6 6.7961 0.17 -1 -7 1 5.6163 0.105 4 4 -4 11.9121 0.174 -1 -7 2 4.1646 0.108 4 4 -2 11.6973 0.191 -1 -7 3 4.4668 0.143 4 5 4 3.0658 0.116 -1 -7 4 4.1682 0.125 4 5 3 3.4090 0.113 -1 -7 5 4.0808 0.155 4 5 2 0.7659 0.08 -1 -8 4 2.3888 0.071 4 5 1 3.3743 0.123 -1 -8 3 1.8747 0.055 4 5 0 4.3401 0.114 -1 -8 1 3.0046 0.075 4 5 -1 3.5179 0.101 -1 -8 0 3.2385 0.096 4 5 -3 3.1922 0.106 -1 -8 -1 3.0020 0.1 4 5 -4 3.1575 0.124 -1 -8 -3 1.7388 0.062 4 5 -5 1.7905 0.064 -1 -8 -4 2.1512 0.091 4 5 -7 2.0231 0.07 -1 -8 -5 3.1460 0.1 4 6 -6 7.1117 0.145 -1 -9 -5 1.3639 0.089 4 6 -5 1.2299 0.082 -1 -9 -4 2.1108 0.073 4 6 -2 10.9725 0.149 -1 -9 -2 4.0284 0.141 4 6 2 10.9944 0.161
173
-1 -9 -1 0.7546 0.121 4 6 4 1.2655 0.076 -1 -9 0 2.9318 0.094 4 7 5 3.4287 0.145 -1 -9 2 4.4504 0.159 4 7 3 1.9971 0.058 0 -8 -2 3.8359 0.131 4 7 1 4.0846 0.155 0 -7 1 3.5811 0.139 4 7 -1 3.9665 0.139 0 -7 -1 3.3607 0.109 4 7 -3 2.2361 0.056 0 -7 -3 4.0370 0.138 4 7 -5 3.5857 0.108 0 -6 -6 5.0036 0.144 4 8 -6 3.4941 0.149 0 -6 -4 2.7343 0.087 4 8 -4 4.3395 0.223 0 -6 -2 8.7558 0.112 4 8 -2 4.8484 0.128 0 -6 0 3.7858 0.122 4 8 0 5.9648 0.147 0 -6 2 8.2959 0.096 4 8 2 4.8523 0.151 0 -6 4 2.6893 0.062 4 8 4 4.9910 0.137 0 -5 5 2.9302 0.092 4 9 4 3.2446 0.169 0 -5 3 3.0759 0.087 4 9 0 3.8943 0.107 0 -5 1 4.7764 0.124 4 9 -2 1.7064 0.067 0 -5 -1 4.4986 0.08 4 9 -4 3.4415 0.094 0 -5 -3 2.9306 0.107 4 9 -5 1.4110 0.093 0 -5 -5 2.9101 0.074 4 10 -6 2.1208 0.08 0 -4 -6 3.5114 0.11 4 10 -2 3.3695 0.104 0 -4 -4 3.3512 0.125 4 10 2 3.3537 0.105 0 -4 -2 7.2962 0.078 4 11 3 1.7006 0.09 0 -4 0 10.1978 0.107 4 11 1 1.5374 0.081 0 -4 2 7.6517 0.086 4 11 -1 1.5529 0.084 0 -4 4 3.1567 0.085 4 11 -2 0.9924 0.123 0 -4 6 3.5551 0.114 4 11 -3 1.2260 0.11 0 -3 7 2.6334 0.075 4 11 -5 1.0231 0.134 0 -3 5 4.2843 0.12 4 12 -2 2.7589 0.086 0 -3 3 5.8189 0.084 4 12 0 4.4354 0.19 0 -3 1 7.9209 0.081 4 12 4 3.5541 0.107 0 -3 -1 7.5494 0.06 5 12 -2 3.2267 0.146 0 -3 -3 5.9321 0.089 5 11 -3 3.1991 0.079 0 -3 -5 3.9735 0.13 5 11 -1 3.1745 0.09 0 -3 -7 2.6146 0.089 5 11 0 2.1748 0.075 0 -3 -9 1.7564 0.083 5 11 1 3.1439 0.097 0 -2 -6 8.4489 0.184 5 10 2 4.1105 0.138 0 -2 -4 1.7528 0.046 5 10 -2 4.1039 0.098 0 -2 -2 14.1533 0.155 5 9 -4 3.3758 0.15 0 -2 0 3.0844 0.046 5 9 -3 5.5777 0.143 0 -2 2 13.9597 0.147 5 9 -2 2.1655 0.071 0 -2 4 1.8498 0.039 5 9 0 4.0952 0.157 0 -2 6 6.9233 0.162 5 9 1 5.8225 0.163 0 -1 7 4.3706 0.14 5 9 2 2.6457 0.071 0 -1 5 2.3491 0.045 5 8 2 3.4842 0.11 0 -1 3 8.5078 0.158 5 8 1 1.3266 0.088 0 -1 1 8.8966 0.092 5 8 0 2.1243 0.057 0 -1 -1 8.8132 0.101 5 8 -1 1.5200 0.072 0 -1 -3 8.7890 0.182 5 8 -2 3.6646 0.107 0 -1 -5 2.3687 0.042 5 8 -3 2.1695 0.067 0 -1 -7 4.6080 0.135 5 8 -4 1.8834 0.07 0 0 -8 12.0448 0.199 5 7 -4 3.7794 0.142
174
0 0 -6 5.5038 0.128 5 7 -3 3.6802 0.133 0 0 -4 24.9686 0.408 5 7 -2 5.3537 0.125 0 0 -2 11.8347 0.208 5 7 -1 4.8251 0.125 0 0 2 12.4211 0.199 5 7 0 4.9810 0.149 0 0 4 25.7037 0.435 5 7 1 4.6395 0.13 0 0 6 5.5827 0.117 5 6 -2 7.0055 0.128
P = 3.129(6) GPa
h k l FO Esd h k l FO Esd -5 -6 2 8.2311 0.112 0 1 -5 2.9303 0.054 -5 -6 0 3.1151 0.08 0 1 -7 5.4547 0.144 -5 -6 -2 8.1509 0.134 0 2 -8 1.2908 0.107 -5 -6 -4 2.1424 0.082 0 2 -6 10.1081 0.151 -5 -7 -5 4.0146 0.14 0 2 -4 2.3376 0.047 -5 -7 -4 4.3647 0.142 0 2 -2 17.0517 0.26 -5 -7 -3 4.2968 0.152 0 2 0 3.6895 0.061 -5 -7 -2 6.3564 0.136 0 2 2 17.1012 0.279 -5 -7 -1 5.9135 0.138 0 2 4 2.2306 0.065 -5 -7 0 5.9668 0.133 0 2 6 10.1712 0.189 -5 -7 1 5.6788 0.118 0 2 8 1.5398 0.089 -5 -7 2 6.7204 0.129 0 3 7 3.2493 0.067 -5 -7 3 4.9042 0.151 0 3 5 5.5871 0.122 -5 -8 4 2.3120 0.062 0 3 3 7.2486 0.127 -5 -8 3 2.6602 0.067 0 3 1 9.2107 0.091 -5 -8 2 4.2987 0.151 0 3 -1 9.5696 0.158 -5 -8 -1 1.8100 0.056 0 3 -3 7.5007 0.119 -5 -8 -2 3.9720 0.138 0 3 -5 5.7755 0.124 -5 -8 -3 2.5466 0.063 0 3 -7 3.2373 0.084 -5 -8 -4 2.0861 0.098 0 3 -9 2.5894 0.101 -5 -9 -5 5.4996 0.174 0 4 -8 2.0270 0.077 -5 -9 -4 3.2418 0.11 0 4 -6 4.2600 0.149 -5 -9 -3 5.6747 0.189 0 4 -4 4.2597 0.107 -5 -9 -2 2.8044 0.09 0 4 -2 9.2033 0.127 -5 -9 -1 7.3037 0.153 0 4 0 12.5086 0.126 -5 -9 0 4.7106 0.168 0 4 2 9.3263 0.121 -5 -9 1 6.9461 0.151 0 4 4 4.1149 0.102 -5 -9 2 2.9801 0.088 0 4 6 4.3789 0.15 -5 -9 3 5.9938 0.159 0 5 5 3.2027 0.107 -5 -9 4 4.1895 0.184 0 5 3 3.7691 0.118 -5 -10 2 4.9358 0.163 0 5 1 5.7421 0.079 -5 -10 -2 4.4737 0.19 0 5 -1 5.7897 0.109 -5 -11 -4 2.1521 0.088 0 5 -3 3.7472 0.114 -5 -11 -3 3.6524 0.129 0 5 -5 3.2212 0.109 -5 -11 0 2.8698 0.068 0 5 -7 1.3431 0.119 -5 -11 1 4.1093 0.109 0 6 -6 5.8149 0.133 -5 -11 3 3.5760 0.12 0 6 -4 3.1121 0.069 -5 -12 2 3.8668 0.142 0 6 -2 9.3643 0.145 -5 -12 0 2.6897 0.084 0 6 0 4.4509 0.109 -5 -12 -2 3.7857 0.097 0 6 2 10.5088 0.102
175
-4 -12 -2 3.7698 0.113 0 6 4 3.1127 0.083 -4 -12 0 5.3313 0.176 0 7 -3 5.2583 0.129 -4 -12 2 3.5794 0.162 1 9 -2 5.5157 0.147 -4 -11 5 1.2256 0.122 1 9 -1 1.2262 0.085 -4 -11 3 1.5557 0.09 1 8 4 2.7507 0.109 -4 -11 1 1.5218 0.092 1 8 3 2.1687 0.057 -4 -10 -6 2.6245 0.104 1 8 1 3.7249 0.115 -4 -10 -2 3.7672 0.129 1 8 0 3.6920 0.1 -4 -10 -1 0.7989 0.118 1 8 -1 3.7767 0.113 -4 -10 1 0.7822 0.135 1 8 -3 2.1799 0.048 -4 -10 2 4.3664 0.158 1 8 -4 2.8313 0.11 -4 -10 6 2.7067 0.077 1 8 -5 2.9759 0.089 -4 -9 5 2.1543 0.085 1 7 -7 2.6326 0.085 -4 -9 4 3.8824 0.151 1 7 -6 3.0658 0.08 -4 -9 2 1.9988 0.062 1 7 -5 4.8450 0.176 -4 -9 1 1.3716 0.072 1 7 -4 4.5333 0.127 -4 -9 0 4.6343 0.155 1 7 -3 5.3635 0.117 -4 -9 -2 2.1289 0.055 1 7 -2 4.7788 0.105 -4 -9 -4 4.1558 0.097 1 7 -1 6.7221 0.112 -4 -9 -5 1.8039 0.073 1 7 0 6.7868 0.101 -4 -9 -6 1.5729 0.088 1 7 1 6.3223 0.155 -4 -9 -7 1.1253 0.118 1 7 2 5.0299 0.104 -4 -8 -6 4.5321 0.153 1 7 3 5.4048 0.127 -4 -8 -4 5.4389 0.152 1 7 4 5.4378 0.121 -4 -8 -2 6.4032 0.134 1 7 5 4.7585 0.15 -4 -8 -1 0.4871 0.185 1 6 4 4.2829 0.12 -4 -8 0 7.0485 0.115 1 6 2 3.4236 0.093 -4 -8 2 6.3189 0.146 1 6 0 6.0222 0.091 -4 -8 4 5.7683 0.185 1 6 -2 3.4310 0.102 -4 -8 6 4.1401 0.216 1 6 -4 4.4558 0.14 -4 -7 5 4.4140 0.152 1 6 -5 1.4019 0.072 -4 -7 3 2.5852 0.047 1 6 -6 2.0039 0.058 -4 -7 1 4.6058 0.14 1 6 -7 1.0437 0.105 -4 -7 0 1.0206 0.108 1 5 -8 2.9384 0.069 -4 -7 -1 4.1765 0.141 1 5 -7 6.4563 0.158 -4 -7 -3 2.6445 0.076 1 5 -6 2.3897 0.079 -4 -7 -4 1.2507 0.112 1 5 -5 7.2272 0.148 -4 -7 -5 4.5495 0.142 1 5 -4 6.1951 0.169 -4 -6 -6 7.7795 0.172 1 5 -3 11.4311 0.158 -4 -6 -4 1.4187 0.063 1 5 -2 4.2032 0.116 -4 -6 -2 12.4913 0.252 1 5 -1 11.4410 0.169 -4 -6 -1 1.6665 0.051 1 5 0 8.8953 0.105 -4 -6 0 1.4548 0.054 1 5 1 11.7498 0.102 -4 -6 2 13.1921 0.127 1 5 2 4.0829 0.087 -4 -6 5 1.2701 0.084 1 5 3 10.6887 0.128 -4 -6 6 8.4681 0.178 1 5 4 6.7866 0.125 -4 -5 5 2.1280 0.057 1 5 5 7.1254 0.114 -4 -5 4 3.7475 0.124 1 5 6 2.4023 0.076 -4 -5 3 3.7645 0.117 1 5 7 6.5935 0.195 -4 -5 1 3.8716 0.107 1 4 7 3.5454 0.126 -4 -5 0 5.3528 0.095 1 4 5 2.9601 0.091
176
-4 -5 -1 4.1356 0.13 1 4 4 1.9135 0.068 -4 -5 -2 1.0849 0.059 1 4 3 6.6774 0.091 -4 -5 -3 3.9411 0.105 1 4 1 7.5367 0.084 -4 -5 -4 3.5428 0.147 1 4 0 3.7179 0.1 -4 -5 -5 2.1064 0.056 1 4 -1 7.5544 0.116 -4 -5 -7 2.1052 0.081 1 4 -2 0.5871 0.067 -4 -4 -6 7.8528 0.158 1 4 -3 6.8964 0.111 -4 -4 -4 13.4567 0.191 1 4 -4 1.8856 0.061 -4 -4 -2 13.6223 0.194 1 4 -5 2.8433 0.114 -4 -4 -1 0.7273 0.067 1 4 -7 4.1769 0.147 -4 -4 0 17.9492 0.198 1 4 -8 0.7451 0.206 -4 -4 2 13.9862 0.132 1 3 -8 2.6100 0.078 -4 -4 4 13.9739 0.158 1 3 -7 5.6557 0.135 -4 -3 -3 5.7542 0.1 1 3 -6 2.7899 0.132 -4 -3 -5 3.4237 0.109 1 3 -5 5.9869 0.118 -3 0 -5 4.1370 0.114 1 3 -4 5.9684 0.089 -3 -1 -7 4.4055 0.142 1 3 -3 8.7682 0.133 -3 -1 -5 7.3847 0.14 1 3 -2 8.1899 0.161 -3 -1 -4 8.7316 0.141 1 3 -1 8.7338 0.15 -3 -1 -3 8.0022 0.13 1 3 0 5.9514 0.069 -3 -2 6 1.2817 0.08 1 3 1 8.6948 0.065 -3 -2 5 2.3277 0.089 1 3 2 7.7048 0.15 -3 -2 4 7.4365 0.11 1 3 3 9.0830 0.134 -3 -2 -4 7.1005 0.113 1 3 4 5.7840 0.108 -3 -2 -5 2.3898 0.068 1 3 5 5.6123 0.125 -3 -2 -6 1.0164 0.08 1 3 6 3.6043 0.125 -3 -3 -7 4.2906 0.136 1 3 7 5.5997 0.181 -3 -3 -6 7.8148 0.132 1 3 8 2.1015 0.083 -3 -3 -5 4.2457 0.136 1 2 8 2.5397 0.079 -3 -3 -4 2.3917 0.07 1 2 6 2.5287 0.076 -3 -3 -3 7.5353 0.106 1 2 5 1.4135 0.07 -3 -3 -2 14.0587 0.184 1 2 4 5.6714 0.126 -3 -3 -1 8.4728 0.159 1 2 3 1.1745 0.04 -3 -3 0 4.3393 0.234 1 2 2 11.4371 0.158 -3 -3 1 9.3249 0.16 1 2 1 1.1214 0.026 -3 -3 2 14.9557 0.113 1 2 0 10.2118 0.109 -3 -3 3 7.9054 0.099 1 2 -1 1.0585 0.032 -3 -3 4 2.4194 0.084 1 2 -2 11.2433 0.175 -3 -3 5 4.2492 0.137 1 2 -4 6.0477 0.09 -3 -3 6 8.2123 0.158 1 2 -5 1.4803 0.061 -3 -4 6 0.8336 0.128 1 2 -6 2.8525 0.087 -3 -4 5 5.1938 0.138 1 2 -8 2.7098 0.13 -3 -4 3 3.8209 0.103 1 1 -8 2.7342 0.084 -3 -4 2 2.0823 0.066 1 1 -7 1.4737 0.08 -3 -4 1 6.2971 0.077 1 1 -6 5.6009 0.143 -3 -4 0 1.1958 0.045 1 1 -5 4.8857 0.108 -3 -4 -1 6.2788 0.123 1 1 -4 5.6974 0.11 -3 -4 -2 2.2464 0.069 1 1 -3 4.4071 0.206 -3 -4 -3 3.6624 0.096 1 1 -2 10.6114 0.178 -3 -4 -5 5.0509 0.113 1 1 -1 7.5651 0.188 -3 -5 -7 2.6590 0.089 1 1 0 10.6581 0.15
177
-3 -5 -6 5.5397 0.195 1 1 1 7.9815 0.104 -3 -5 -5 1.4770 0.069 1 1 2 10.0523 0.2 -3 -5 -4 3.6281 0.115 1 1 3 4.2739 0.167 -3 -5 -3 3.3065 0.104 1 1 4 5.6538 0.122 -3 -5 -2 10.0659 0.152 1 1 5 4.6646 0.131 -3 -5 -1 2.9508 0.077 1 1 6 5.9521 0.113 -3 -5 0 4.5742 0.084 1 1 7 1.5110 0.087 -3 -5 1 2.7660 0.092 1 1 8 2.7203 0.113 -3 -5 2 9.9525 0.104 1 1 9 2.7074 0.07 -3 -5 3 3.6788 0.107 1 0 9 3.3944 0.129 -3 -5 4 3.3590 0.133 1 0 5 6.7721 0.14 -3 -5 5 1.4694 0.068 1 0 3 7.2862 0.179 -3 -5 6 4.5801 0.169 1 0 1 13.4110 0.219 -3 -5 7 2.5976 0.09 1 0 -1 12.7145 0.605 -3 -6 4 4.7425 0.118 1 0 -3 7.7290 0.182 -3 -6 3 1.8100 0.059 1 0 -5 6.9640 0.126 -3 -6 2 1.7236 0.054 1 0 -7 2.1439 0.073 -3 -6 0 6.9687 0.089 1 -1 -8 2.8405 0.116 -3 -6 -2 1.7568 0.06 1 -1 -7 1.8061 0.078 -3 -6 -3 2.1673 0.068 1 -1 -6 5.8904 0.139 -3 -6 -4 4.4394 0.145 1 -1 -5 4.8189 0.111 -3 -6 -7 1.4946 0.081 1 -1 -4 5.6012 0.129 -3 -6 -8 2.9834 0.075 1 -1 -3 4.7115 0.193 -3 -7 -8 3.3751 0.091 1 -1 -2 10.7704 0.151 -3 -7 -7 1.9936 0.087 1 -1 2 10.6471 0.208 -3 -7 -5 4.0456 0.155 1 -1 3 3.8139 0.106 -3 -7 -4 6.0870 0.138 1 -1 4 4.8461 0.104 -3 -7 -3 3.8859 0.134 1 -1 5 4.5991 0.099 -3 -7 -1 3.8853 0.147 1 -1 6 5.8356 0.116 -3 -7 0 8.2462 0.122 1 -1 7 1.4206 0.096 -3 -7 1 4.8731 0.107 1 -1 8 2.7915 0.083 -3 -7 3 4.1618 0.105 1 -1 9 2.8565 0.074 -3 -7 4 6.2236 0.139 1 -2 8 2.5341 0.072 -3 -7 5 3.8278 0.116 1 -2 7 1.3352 0.075 -3 -7 7 1.8614 0.08 1 -2 5 1.3276 0.056 -3 -8 7 2.1948 0.076 1 -2 4 5.7873 0.125 -3 -8 5 1.9654 0.073 1 -2 2 11.6877 0.169 -3 -8 3 3.0478 0.135 1 -2 -2 11.8663 0.167 -3 -8 2 1.9711 0.067 1 -2 -3 1.2504 0.042 -3 -8 1 3.3258 0.097 1 -2 -4 5.7699 0.14 -3 -8 -1 3.1178 0.101 1 -2 -5 1.5709 0.066 -3 -8 -2 1.8081 0.063 1 -2 -6 2.7926 0.065 -3 -8 -3 3.0598 0.092 1 -2 -7 1.2551 0.089 -3 -8 -5 2.0371 0.068 1 -3 -6 3.5556 0.108 -3 -9 -5 6.7148 0.147 1 -3 -5 5.7720 0.156 -3 -9 -4 3.2825 0.096 1 -3 -4 5.7692 0.134 -3 -9 -3 6.4654 0.148 1 -3 -3 9.3844 0.141 -3 -9 -2 2.8334 0.097 1 -3 2 8.3410 0.187 -3 -9 -1 8.0479 0.169 1 -3 3 8.6663 0.134 -3 -9 0 4.2833 0.148 1 -3 4 5.6566 0.106 -3 -9 1 8.6785 0.116 1 -3 5 5.8234 0.122
178
-3 -9 2 2.6286 0.078 1 -3 6 3.5455 0.119 -3 -9 3 6.8193 0.133 1 -3 7 5.7389 0.143 -3 -9 4 3.3660 0.103 1 -4 5 3.2217 0.092 -3 -9 5 6.2736 0.154 1 -4 4 1.8651 0.046 -3 -9 6 1.9257 0.081 1 -4 3 7.0338 0.091 -3 -9 7 3.8943 0.173 2 -2 4 13.1736 0.215 -3 -10 5 2.1631 0.072 2 -2 5 3.6919 0.115 -3 -10 4 2.3358 0.064 2 -1 6 5.1438 0.151 -3 -10 3 1.2446 0.09 2 -1 4 5.5284 0.102 -3 -10 2 1.7792 0.074 2 -1 3 0.7928 0.05 -3 -10 1 2.1198 0.083 2 -1 -4 5.6513 0.123 -3 -10 0 2.8252 0.125 2 -1 -5 1.1908 0.09 -3 -10 -2 1.8749 0.081 2 0 -6 3.5498 0.127 -3 -10 -4 2.0987 0.076 2 0 -4 2.1386 0.072 -3 -11 -2 6.0699 0.192 2 0 2 0.3978 0.065 -3 -11 -1 4.5817 0.125 2 0 4 2.0858 0.059 -3 -11 1 4.1244 0.207 2 0 8 1.1456 0.12 -3 -11 3 4.2458 0.153 2 1 6 5.0974 0.14 -2 -10 -1 2.6078 0.088 2 1 5 1.0240 0.077 -2 -10 1 2.3349 0.055 2 1 4 5.0054 0.095 -2 -9 4 5.5021 0.151 2 1 2 11.3316 0.185 -2 -9 2 8.1303 0.118 2 1 1 1.2501 0.032 -2 -9 -2 7.7929 0.164 2 1 -2 11.4098 0.16 -2 -9 -4 5.7197 0.205 2 1 -3 0.7214 0.061 -2 -8 -6 3.0326 0.08 2 1 -4 5.5590 0.105 -2 -8 -5 3.6092 0.088 2 1 -6 5.4540 0.122 -2 -8 -4 2.1923 0.055 2 2 -8 6.2220 0.158 -2 -8 -3 3.8141 0.122 2 2 -7 2.1655 0.074 -2 -8 -2 4.5446 0.148 2 2 -5 3.6685 0.113 -2 -8 -1 4.9588 0.112 2 2 -4 13.0479 0.209 -2 -8 1 4.7287 0.123 2 2 -3 3.5048 0.086 -2 -8 2 4.9162 0.121 2 2 -1 3.3376 0.076 -2 -8 3 3.4701 0.12 2 2 0 18.1543 0.169 -2 -8 4 1.9635 0.057 2 2 1 3.4832 0.06 -2 -8 5 3.3113 0.084 2 2 3 3.3666 0.085 -2 -8 6 2.6293 0.126 2 2 4 12.4587 0.196 -2 -8 7 2.4047 0.088 2 2 5 3.7963 0.118 -2 -6 -8 5.4307 0.155 2 2 7 2.0981 0.066 -2 -6 -7 1.7325 0.074 2 2 8 6.1802 0.206 -2 -6 -6 1.8439 0.068 2 2 9 1.9049 0.082 -2 -6 -5 2.8933 0.085 2 3 9 1.8657 0.093 -2 -6 -4 9.6184 0.169 2 3 8 1.4571 0.088 -2 -6 -3 3.1021 0.097 2 3 7 2.2221 0.069 -2 -6 -2 2.2549 0.046 2 3 6 2.9654 0.095 -2 -6 -1 3.7090 0.097 2 3 5 2.4159 0.08 -2 -6 0 11.8978 0.139 2 3 4 2.4403 0.048 -2 -6 1 3.4472 0.105 2 3 3 2.0535 0.069 -2 -6 2 2.3080 0.065 2 3 2 5.3752 0.135 -2 -6 3 3.2323 0.128 2 3 0 2.6936 0.052 -2 -6 4 9.6628 0.107 2 3 -1 1.9163 0.1 -2 -6 5 2.8110 0.081 2 3 -2 5.2363 0.143
179
-2 -6 6 1.8552 0.072 2 3 -3 2.1094 0.055 -2 -6 7 1.6709 0.079 2 3 -4 2.2577 0.055 -2 -6 8 4.8838 0.155 2 3 -5 2.2659 0.05 -2 -5 8 3.9299 0.117 2 3 -6 2.8724 0.108 -2 -5 6 6.3065 0.187 2 3 -7 2.3298 0.08 -2 -5 5 2.2310 0.051 2 3 -8 1.4536 0.088 -2 -5 4 7.1952 0.129 2 4 -7 1.7738 0.074 -2 -5 2 11.6415 0.101 2 4 -6 13.1704 0.167 -2 -5 1 1.4258 0.064 2 4 -5 2.5874 0.054 -2 -5 0 10.2614 0.118 2 4 -4 1.0936 0.064 -2 -5 -2 11.5697 0.163 2 4 -3 3.5327 0.094 -2 -5 -4 7.3054 0.132 2 4 -2 22.8344 0.347 -2 -5 -5 2.1697 0.053 2 4 -1 4.7559 0.089 -2 -5 -6 6.5076 0.15 2 4 0 2.9028 0.189 -2 -5 -8 4.2014 0.192 2 4 1 4.7646 0.083 -2 -4 -9 1.3657 0.113 2 4 2 24.0669 0.269 -2 -4 -6 12.2747 0.189 2 4 3 3.5438 0.106 -2 -4 -5 2.6485 0.092 2 4 6 12.7864 0.203 -2 -4 -3 3.6922 0.096 2 4 7 1.8095 0.075 -2 -4 -2 22.6779 0.328 2 5 6 6.2850 0.138 -2 -4 -1 4.6463 0.091 2 5 5 2.1612 0.066 -2 -4 0 3.3836 0.153 2 5 4 7.3472 0.124 -2 -4 1 4.7186 0.08 2 5 2 11.3328 0.105 -2 -4 2 23.1681 0.233 2 5 1 1.3377 0.053 -2 -4 3 3.8274 0.098 2 5 0 10.0728 0.094 -2 -4 5 2.4651 0.088 2 5 -1 1.4449 0.058 -2 -4 6 12.5648 0.213 2 5 -2 11.5220 0.159 -2 -3 7 2.3328 0.065 2 5 -4 7.4076 0.147 -2 -3 6 2.8037 0.054 2 5 -5 2.1225 0.077 -2 -3 5 2.6174 0.083 2 5 -6 6.6491 0.13 -2 -3 4 2.6135 0.107 2 5 -7 1.3829 0.095 -2 -3 3 1.9756 0.068 2 5 -8 3.8857 0.166 -2 -3 2 5.2741 0.112 2 6 -8 4.7965 0.181 -2 -3 1 1.3687 0.102 2 6 -6 1.2282 0.135 -2 -3 0 2.6591 0.068 2 6 -5 2.9926 0.064 -2 -3 -2 5.2492 0.118 2 6 -4 9.7295 0.151 -2 -3 -3 1.9896 0.062 2 6 -3 3.1096 0.112 -2 -3 -4 2.5567 0.081 2 6 -2 2.2190 0.079 -2 -3 -5 2.4433 0.068 2 6 -1 3.5446 0.108 -2 -3 -6 2.8810 0.086 2 6 0 11.9989 0.115 -2 -3 -7 2.1406 0.084 2 6 1 3.6073 0.097 -2 -3 -8 1.0943 0.111 2 6 2 2.2681 0.073 -2 -3 -9 2.1583 0.075 2 6 3 3.0060 0.071 -2 -2 -9 1.9428 0.081 2 6 4 9.6901 0.13 -2 -2 -8 5.6576 0.217 2 6 5 2.8511 0.075 -2 -2 -7 2.2669 0.079 2 6 7 1.5780 0.087 -2 -2 -5 3.6053 0.123 2 6 8 5.0511 0.181 -2 -2 -4 12.6746 0.189 2 7 0 0.9705 0.073 -2 -2 -3 3.5922 0.09 2 7 -1 1.2141 0.08 -2 -2 -1 3.4474 0.082 2 8 -7 2.4446 0.07 -2 -2 0 17.9493 0.19 2 8 -6 2.9544 0.136
180
-2 -2 1 3.4907 0.061 2 8 -5 3.3625 0.098 -2 -2 3 3.3259 0.093 2 8 -4 1.9403 0.06 -2 -2 4 12.5551 0.189 2 8 -3 4.2249 0.148 -2 -2 5 3.6310 0.108 2 8 -2 4.7426 0.124 -2 -2 6 0.7531 0.111 2 8 -1 4.2413 0.156 -2 -2 8 5.7348 0.202 2 8 0 2.4800 0.093 -2 -1 6 5.1935 0.123 2 8 1 4.6816 0.113 -2 -1 4 5.5692 0.098 2 8 2 4.7332 0.134 -2 -1 2 11.5560 0.13 2 8 3 3.9360 0.142 -2 -1 -1 1.2403 0.038 2 8 4 1.9919 0.067 -2 -1 -2 11.0709 0.188 2 8 5 3.3225 0.112 -2 -1 -4 5.5340 0.104 2 8 6 2.8992 0.071 -2 -1 -6 5.1855 0.117 2 9 4 5.5041 0.152 -2 -1 -8 2.8820 0.083 2 9 2 7.9446 0.126 -2 0 -8 1.2735 0.089 2 9 0 6.9321 0.12 -2 0 -6 4.1099 0.12 2 9 -2 7.8217 0.163 -2 0 -4 2.2965 0.033 2 9 -4 5.2415 0.148 -2 0 -2 0.5250 0.058 2 10 -3 1.6110 0.091 -2 0 4 2.1597 0.05 2 10 -1 2.1885 0.066 -2 0 6 4.1588 0.128 2 10 0 8.2239 0.141 -2 1 4 5.6066 0.097 2 10 1 2.1712 0.06 -2 1 -4 5.5736 0.097 3 11 -3 4.2170 0.144 -2 1 -5 1.0523 0.07 3 11 -2 7.9137 0.341 -2 1 -6 4.9883 0.142 3 11 -1 4.2921 0.128 -2 2 -5 3.6940 0.11 3 11 1 4.3161 0.126 -2 2 -4 12.5957 0.158 3 11 2 5.6718 0.19 -1 4 -3 6.4298 0.135 3 10 4 2.3151 0.066 -1 4 -4 1.8575 0.055 3 10 2 1.7971 0.072 -1 4 -5 3.0193 0.113 3 10 1 2.1207 0.066 -1 3 -7 5.6862 0.163 3 10 0 2.7100 0.062 -1 3 -6 3.7582 0.107 3 10 -1 2.3655 0.059 -1 3 -5 5.6169 0.104 3 10 -2 1.9638 0.066 -1 3 -4 5.1384 0.141 3 10 -5 2.2955 0.069 -1 3 -3 8.8574 0.15 3 9 -7 3.6893 0.132 -1 3 -2 7.4734 0.17 3 9 -6 1.8087 0.094 -1 3 3 8.6949 0.137 3 9 -5 5.8716 0.2 -1 3 4 5.1356 0.107 3 9 -4 3.4168 0.12 -1 3 5 5.8621 0.12 3 9 -3 6.8003 0.16 -1 3 6 3.5042 0.115 3 9 -2 3.2357 0.07 -1 2 7 1.6867 0.079 3 9 -1 8.3264 0.132 -1 2 6 2.6594 0.063 3 9 0 4.1935 0.131 -1 2 5 1.1942 0.062 3 9 1 7.8079 0.126 -1 2 4 5.5904 0.107 3 9 2 2.7135 0.077 -1 2 3 1.2723 0.04 3 9 3 6.4395 0.151 -1 2 2 11.2834 0.156 3 9 4 3.2554 0.102 -1 2 -2 10.7367 0.167 3 9 5 6.2794 0.15 -1 2 -3 1.1392 0.044 3 9 6 1.8229 0.083 -1 2 -4 5.8586 0.094 3 8 5 1.7816 0.089 -1 2 -5 1.4081 0.053 3 8 3 3.3261 0.138 -1 2 -6 2.5395 0.131 3 8 1 3.3766 0.104 -1 2 -8 2.5471 0.077 3 8 -1 3.1606 0.131
181
-1 1 -9 2.6351 0.077 3 8 -2 2.0490 0.058 -1 1 -8 2.7959 0.055 3 8 -3 3.0983 0.156 -1 1 -6 5.7763 0.132 3 8 -5 1.8034 0.077 -1 1 -5 4.5337 0.133 3 8 -7 2.4582 0.071 -1 1 -4 5.7104 0.103 3 7 -7 1.7459 0.091 -1 1 -3 4.1864 0.148 3 7 -5 4.1481 0.118 -1 1 -2 10.3149 0.18 3 7 -4 6.1510 0.165 -1 1 2 10.4095 0.19 3 7 -3 3.8229 0.136 -1 1 3 3.9556 0.187 3 7 -1 4.6921 0.117 -1 1 4 5.6521 0.117 3 7 0 8.0587 0.125 -1 1 5 4.4585 0.104 3 7 1 4.7225 0.111 -1 1 6 5.8231 0.136 3 7 3 3.8474 0.14 -1 1 7 1.6627 0.069 3 7 4 6.0221 0.148 -1 0 5 7.0353 0.135 3 7 7 2.0770 0.076 -1 0 3 7.5850 0.234 3 7 8 3.1169 0.165 -1 0 1 13.7054 0.354 3 6 8 2.8443 0.143 -1 0 -1 12.4625 0.313 3 6 7 1.5552 0.087 -1 0 -3 7.8061 0.116 3 6 4 4.6387 0.134 -1 0 -5 7.1092 0.132 3 6 3 2.1684 0.084 -1 0 -7 2.2458 0.07 3 6 2 1.8286 0.051 -1 0 -9 3.6811 0.114 3 6 0 7.1153 0.106 -1 -1 -9 2.6431 0.104 3 6 -1 0.8669 0.075 -1 -1 -8 2.8382 0.073 3 6 -2 1.8160 0.053 -1 -1 -7 1.6137 0.065 3 6 -3 1.8734 0.09 -1 -1 -6 5.5655 0.17 3 6 -4 4.8193 0.124 -1 -1 -5 4.4689 0.178 3 5 -7 2.4602 0.089 -1 -1 -4 5.7497 0.108 3 5 -6 5.6110 0.176 -1 -1 -3 4.5871 0.157 3 5 -4 3.5244 0.096 -1 -1 -2 10.4357 0.176 3 5 -3 3.4649 0.118 -1 -1 -1 7.9464 0.174 3 5 -2 9.6801 0.17 -1 -1 0 10.6281 0.164 3 5 -1 2.8728 0.093 -1 -1 1 8.1823 0.082 3 5 0 4.4203 0.088 -1 -1 2 10.3868 0.182 3 5 1 2.6532 0.095 -1 -1 3 3.7781 0.178 3 5 2 9.8088 0.112 -1 -1 4 5.5897 0.114 3 5 3 3.6157 0.104 -1 -1 5 4.5466 0.122 3 5 4 3.4732 0.098 -1 -1 6 5.5618 0.122 3 5 5 1.5213 0.064 -1 -1 7 1.8146 0.065 3 5 6 5.2262 0.153 -1 -2 8 2.6483 0.064 3 5 7 2.5505 0.074 -1 -2 6 2.3017 0.051 3 4 7 0.5439 0.215 -1 -2 5 1.2961 0.065 3 4 5 5.2450 0.128 -1 -2 4 5.5699 0.135 3 4 3 3.5851 0.098 -1 -2 3 0.9476 0.05 3 4 2 2.0775 0.056 -1 -2 2 11.5643 0.161 3 4 1 6.2516 0.098 -1 -2 1 1.0145 0.031 3 4 -1 6.4131 0.104 -1 -2 0 10.0117 0.107 3 4 -2 2.2483 0.068 -1 -2 -1 1.0564 0.024 3 4 -3 3.6574 0.103 -1 -2 -2 11.4431 0.194 3 4 -5 5.2523 0.129 -1 -2 -3 1.2307 0.038 3 4 -6 1.0602 0.105 -1 -2 -4 5.5894 0.114 3 4 -7 0.8755 0.141 -1 -2 -5 1.5213 0.07 3 3 -6 8.3305 0.156
182
-1 -2 -6 2.6412 0.07 3 3 -5 4.4058 0.158 -1 -2 -7 1.5902 0.074 3 3 -4 2.4558 0.079 -1 -2 -8 2.7760 0.088 3 3 -3 7.9968 0.115 -1 -2 -9 1.1188 0.122 3 3 -2 14.8390 0.216 -1 -3 -9 2.6191 0.067 3 3 -1 9.0107 0.173 -1 -3 -8 2.1814 0.071 3 3 0 4.2653 0.18 -1 -3 -7 5.6623 0.149 3 3 1 8.6110 0.134 -1 -3 -6 3.4767 0.107 3 3 2 14.8127 0.154 -1 -3 -5 5.7231 0.12 3 3 3 7.6063 0.118 -1 -3 -4 5.8404 0.115 3 3 4 2.4344 0.084 -1 -3 -3 8.8681 0.122 3 3 5 4.3629 0.114 -1 -3 -2 8.1710 0.221 3 3 6 7.1495 0.172 -1 -3 -1 8.4974 0.129 3 3 7 4.1877 0.205 -1 -3 0 5.7007 0.072 3 2 6 0.9675 0.086 -1 -3 1 8.7595 0.068 3 2 5 2.1451 0.061 -1 -3 2 7.9903 0.123 3 2 4 7.1342 0.107 -1 -3 3 8.9824 0.124 3 2 -4 7.6174 0.113 -1 -3 4 5.6787 0.089 3 2 -5 2.5806 0.105 -1 -3 5 5.7408 0.102 3 1 3 8.3257 0.129 -1 -3 6 3.6400 0.094 3 1 4 8.8997 0.129 -1 -3 7 5.5748 0.142 3 1 5 8.1538 0.153 -1 -3 8 2.3756 0.074 3 1 7 3.9912 0.16 -1 -3 9 2.5062 0.088 3 0 5 4.3670 0.117 -1 -4 8 0.8020 0.149 4 3 4 1.3416 0.054 -1 -4 7 3.8616 0.12 4 3 3 5.4775 0.103 -1 -4 5 3.1789 0.07 4 4 -4 13.2602 0.195 -1 -4 4 1.8681 0.042 4 4 -2 14.3772 0.23 -1 -4 3 6.8181 0.087 4 4 -1 0.8616 0.102 -1 -4 1 7.8785 0.111 4 4 0 18.3164 0.189 -1 -4 -1 7.2860 0.118 4 4 2 14.3609 0.125 -1 -4 -3 6.4356 0.119 4 4 4 13.2800 0.195 -1 -4 -4 1.9642 0.04 4 4 6 8.4271 0.177 -1 -4 -5 3.0720 0.094 4 5 7 2.1447 0.071 -1 -4 -7 4.0018 0.11 4 5 5 2.2130 0.059 -1 -4 -8 1.2464 0.096 4 5 4 3.7550 0.12 -1 -5 -7 6.9964 0.191 4 5 3 3.6770 0.111 -1 -5 -6 2.6049 0.076 4 5 2 0.8909 0.069 -1 -5 -5 7.2417 0.12 4 5 1 4.1402 0.117 -1 -5 -4 6.3187 0.1 4 5 0 5.2802 0.116 -1 -5 -3 10.8798 0.135 4 5 -1 4.1562 0.107 -1 -5 -2 4.3117 0.086 4 5 -2 0.7951 0.079 -1 -5 -1 11.6680 0.166 4 5 -3 3.7121 0.116 -1 -5 1 11.4218 0.102 4 5 -4 3.8438 0.136 -1 -5 2 4.1740 0.086 4 5 -5 2.4001 0.052 -1 -5 3 11.5820 0.179 4 6 -6 8.5939 0.17 -1 -5 4 6.4781 0.099 4 6 -5 1.4109 0.075 -1 -5 5 6.4526 0.129 4 6 -4 1.5914 0.063 -1 -5 6 2.5759 0.07 4 6 -2 13.3807 0.179 -1 -5 7 6.8112 0.174 4 6 -1 1.3176 0.061 -1 -5 8 2.7245 0.13 4 6 0 1.2353 0.054 -1 -6 8 2.2969 0.07 4 6 1 1.4527 0.052
183
-1 -6 6 1.8179 0.063 4 6 2 13.4551 0.108 -1 -6 5 1.2168 0.074 4 6 6 8.2398 0.147 -1 -6 4 4.5228 0.128 4 7 5 4.5671 0.144 -1 -6 2 3.4776 0.101 4 7 3 2.6388 0.065 -1 -6 -2 3.9150 0.115 4 7 1 4.2660 0.112 -1 -6 -4 4.4201 0.115 4 7 -1 4.4308 0.131 -1 -6 -5 1.2270 0.077 4 7 -2 0.7833 0.101 -1 -6 -6 1.9685 0.064 4 7 -3 2.2721 0.079 -1 -7 -5 4.8134 0.151 4 7 -5 4.5236 0.125 -1 -7 -4 5.1884 0.118 4 8 -6 4.1396 0.146 -1 -7 -3 5.0173 0.116 4 8 -4 5.8784 0.172 -1 -7 -2 5.0585 0.13 4 8 -2 6.5813 0.119 -1 -7 -1 6.4574 0.153 4 8 0 7.2301 0.119 -1 -7 1 6.3976 0.102 4 8 2 6.4223 0.119 -1 -7 3 5.2143 0.112 4 8 4 5.4975 0.167 -1 -7 4 5.1628 0.118 4 8 6 4.3096 0.151 -1 -7 5 5.1526 0.131 4 9 5 1.8741 0.088 -1 -7 6 2.8281 0.096 4 9 4 3.1964 0.095 -1 -7 7 2.8648 0.095 4 9 2 1.9518 0.066 -1 -8 5 3.3550 0.13 4 9 0 4.4222 0.146 -1 -8 4 2.7869 0.085 4 9 -2 1.9679 0.081 -1 -8 3 2.4683 0.061 4 9 -4 3.4502 0.12 -1 -8 1 3.9431 0.114 4 9 -5 1.7780 0.091 -1 -8 -1 3.5294 0.165 4 10 -6 2.7137 0.07 -1 -8 -3 2.2984 0.057 4 10 -2 4.2142 0.158 -1 -8 -4 3.0445 0.076 4 10 -1 0.8719 0.108 -1 -9 2 5.3328 0.125 4 10 2 4.2298 0.154 0 -7 3 5.2979 0.123 4 10 6 2.6493 0.075 0 -6 -4 3.1915 0.1 4 11 3 1.3377 0.151 0 -6 -2 10.2214 0.186 4 11 2 1.1623 0.106 0 -6 2 10.6845 0.128 4 11 -1 1.5247 0.088 0 -6 4 3.1443 0.094 4 11 -2 1.3094 0.093 0 -6 6 6.0695 0.167 4 12 -2 4.0859 0.095 0 -5 5 3.3783 0.099 4 12 -1 0.9782 0.127 0 -5 3 3.8034 0.114 4 12 0 5.4067 0.209 0 -5 1 6.0435 0.09 4 12 2 3.7581 0.163 0 -5 -1 5.6440 0.095 5 13 0 1.4032 0.111 0 -5 -3 3.6732 0.134 5 12 3 0.8047 0.165 0 -5 -5 3.7125 0.106 5 12 2 3.7575 0.125 0 -4 -6 5.5637 0.15 5 12 0 2.6163 0.069 0 -4 -4 4.3216 0.106 5 12 -2 3.9715 0.127 0 -4 -2 9.4875 0.131 5 11 -1 3.6877 0.112 0 -4 2 9.3720 0.087 5 11 0 2.4248 0.062 0 -4 4 4.1516 0.109 5 11 1 3.7329 0.132 0 -4 6 4.4704 0.128 5 11 3 3.5925 0.154 0 -3 9 2.4954 0.081 5 11 4 2.0964 0.077 0 -3 7 3.2205 0.083 5 10 2 5.0334 0.166 0 -3 5 5.4301 0.123 5 10 -2 4.9127 0.169 0 -3 3 7.4317 0.096 5 10 -4 0.8416 0.144 0 -3 1 9.0430 0.063 5 9 -4 4.3968 0.14 0 -3 -1 9.1528 0.141 5 9 -3 5.2783 0.192
184
0 -3 -3 7.4495 0.125 5 9 -2 2.9607 0.077 0 -3 -5 5.5076 0.12 5 9 -1 7.4584 0.141 0 -3 -7 3.2556 0.102 5 9 0 5.0596 0.14 0 -2 -6 10.5324 0.168 5 9 1 7.2085 0.13 0 -2 -4 2.2371 0.047 5 9 2 2.8458 0.073 0 -2 -2 17.4422 0.267 5 9 3 6.2515 0.14 0 -2 2 17.2933 0.26 5 9 4 4.0600 0.142 0 -2 4 2.1877 0.071 5 9 5 5.7928 0.172 0 -2 6 10.1831 0.185 5 8 4 1.8070 0.078 0 -1 7 5.6655 0.136 5 8 3 2.6855 0.087 0 -1 5 2.8648 0.081 5 8 2 4.2862 0.163 0 -1 3 10.3776 0.206 5 8 0 2.6410 0.108 0 -1 1 10.9250 0.159 5 8 -1 1.6938 0.084 0 -1 -1 10.7409 0.234 5 8 -2 3.9859 0.132 0 -1 -3 10.6462 0.152 5 8 -4 2.3139 0.061 0 -1 -5 2.9440 0.091 5 7 -2 6.2455 0.126 0 -1 -7 5.6004 0.176 5 7 -1 5.7507 0.13 0 0 -8 15.2094 0.213 5 7 0 5.9805 0.113 0 0 -6 7.1651 0.191 5 7 1 5.8105 0.113 0 0 -4 29.0740 0.364 5 7 2 6.6722 0.116 0 0 -2 14.1252 0.243 5 7 4 4.3460 0.151 0 0 2 13.5797 0.329 5 7 5 4.5090 0.15 0 0 4 28.9974 0.697 5 6 4 2.2034 0.058 0 0 6 6.8037 0.139 5 6 3 1.1555 0.078 0 0 8 14.7049 0.296 5 6 2 8.1673 0.111 0 1 7 5.3866 0.131 5 6 1 0.8621 0.1 0 1 5 2.6971 0.085 5 6 0 2.7562 0.081 0 1 3 10.4170 0.265 5 6 -2 7.7956 0.12 0 1 1 10.8338 0.182 0 1 -1 10.1510 0.248 0 1 -3 10.7184 0.168
P = 3.932(7) GPa
h k l FO Esd h k l FO Esd -5 -8 2 3.0230 0.071 0 1 5 2.0146 0.046 -5 -8 0 2.1749 0.068 0 1 3 7.4440 0.134 -5 -9 -1 4.8961 0.162 0 1 1 7.4151 0.156 -5 -9 0 3.4092 0.16 0 1 -1 6.9888 0.187 -5 -9 1 5.2360 0.144 0 1 -3 7.8322 0.156 -5 -9 3 4.0450 0.171 0 1 -7 3.7152 0.152 -5 -10 2 3.2833 0.088 0 2 -6 7.1882 0.142 -5 -10 0 1.0457 0.121 0 2 -4 1.5421 0.056 -5 -11 1 2.3784 0.091 0 2 -2 11.9419 0.197 -4 -13 0 2.1496 0.115 0 2 0 2.4453 0.084 -4 -12 -2 2.6957 0.082 0 2 2 12.0915 0.2 -4 -12 0 3.6265 0.203 0 2 4 1.7581 0.058 -4 -12 2 2.6906 0.084 0 2 6 6.6288 0.123 -4 -12 4 3.3319 0.085 0 3 7 2.4659 0.064 -4 -11 3 1.1876 0.128 0 3 5 3.8970 0.132
185
-4 -11 1 1.0181 0.145 0 3 3 5.1591 0.096 -4 -11 -1 0.8843 0.167 0 3 1 6.1808 0.123 -4 -10 -2 3.1951 0.104 0 3 -1 6.1799 0.133 -4 -10 2 3.1666 0.073 0 3 -3 5.0794 0.092 -4 -9 4 2.6727 0.094 0 3 -5 3.5280 0.169 -4 -9 0 3.1454 0.089 0 3 -7 2.3333 0.12 -4 -9 -4 2.6549 0.101 0 4 -6 2.9846 0.122 -4 -8 -4 3.9638 0.132 0 4 -4 3.0750 0.086 -4 -8 -2 4.4295 0.134 0 4 -2 6.4333 0.119 -4 -8 0 5.0444 0.187 0 4 0 8.6975 0.15 -4 -8 2 4.6039 0.145 0 4 2 6.4281 0.113 -4 -8 4 4.2345 0.126 0 4 4 3.0655 0.081 -4 -8 5 0.3443 0.371 0 4 6 3.2239 0.097 -4 -8 6 2.9543 0.075 0 4 8 1.3374 0.117 -4 -7 5 2.9232 0.094 0 5 7 1.0641 0.111 -4 -7 3 1.6473 0.07 0 5 5 2.4450 0.08 -4 -7 1 3.3832 0.135 0 5 3 2.6647 0.086 -4 -7 -1 3.2980 0.066 0 5 1 3.9742 0.098 -4 -7 -3 1.8425 0.065 0 5 -1 3.7574 0.107 -4 -7 -5 2.7312 0.095 0 5 -3 2.8784 0.072 -4 -6 -2 9.1855 0.159 0 5 -5 2.6170 0.068 -4 -6 -1 1.5271 0.089 0 6 -4 2.2497 0.058 -4 -6 1 2.4288 0.129 0 6 -2 7.1151 0.139 -4 -6 2 9.5113 0.131 0 6 0 3.1327 0.096 -4 -6 4 1.3312 0.079 0 6 2 7.0933 0.12 -4 -6 6 5.8850 0.2 0 6 4 2.5194 0.07 -4 -5 4 2.7696 0.072 0 6 6 4.2915 0.157 -4 -5 3 2.5573 0.071 0 7 3 3.9416 0.117 -4 -5 1 2.8598 0.12 0 7 1 3.1430 0.113 -4 -5 0 4.0294 0.133 0 7 -1 3.0727 0.097 -4 -5 -1 3.0324 0.111 0 7 -3 3.7269 0.13 -4 -5 -3 2.6016 0.062 0 8 0 14.9820 0.287 -4 -5 -4 2.5461 0.086 0 8 2 3.2362 0.137 -4 -4 2 10.2221 0.121 1 10 0 2.6446 0.083 -4 -4 4 10.3195 0.156 1 9 -2 3.6069 0.139 -3 -1 4 6.0265 0.117 1 9 -1 1.1520 0.076 -3 -1 5 5.6475 0.116 1 9 0 2.4794 0.062 -3 -2 5 2.0858 0.093 1 9 2 3.6872 0.118 -3 -2 4 5.2792 0.123 1 8 5 2.3421 0.101 -3 -2 -4 5.1660 0.1 1 8 4 1.8539 0.069 -3 -2 -5 1.4853 0.084 1 8 3 1.5882 0.062 -3 -3 -6 5.8249 0.127 1 8 1 3.0781 0.097 -3 -3 -5 3.1451 0.1 1 8 0 2.9243 0.131 -3 -3 -4 1.6649 0.055 1 8 -1 2.9739 0.106 -3 -3 -3 4.8459 0.133 1 8 -5 2.3364 0.085 -3 -3 -2 11.3437 0.09 1 7 -6 1.9156 0.107 -3 -3 -1 6.4938 0.18 1 7 -5 3.6232 0.099 -3 -3 0 3.2670 0.224 1 7 -4 3.6418 0.111 -3 -3 1 6.5598 0.162 1 7 -3 3.5427 0.129 -3 -3 2 10.6463 0.093 1 7 -2 3.7391 0.122 -3 -3 3 5.1360 0.088 1 7 -1 4.4759 0.14
186
-3 -3 4 1.7366 0.056 1 7 0 4.6736 0.13 -3 -3 5 3.2484 0.131 1 7 1 4.8071 0.109 -3 -3 6 5.6852 0.126 1 7 2 3.5672 0.119 -3 -3 7 3.1243 0.111 1 7 3 3.6428 0.136 -3 -4 5 3.5880 0.105 1 7 4 3.4774 0.132 -3 -4 3 2.7771 0.089 1 7 5 3.3218 0.116 -3 -4 2 1.5163 0.086 1 7 6 2.0829 0.065 -3 -4 1 4.4755 0.096 1 7 7 2.1702 0.072 -3 -4 -1 4.1773 0.104 1 6 8 1.7150 0.104 -3 -4 -2 1.7483 0.072 1 6 6 1.4466 0.098 -3 -4 -3 2.6422 0.085 1 6 4 3.1342 0.105 -3 -4 -5 3.7700 0.111 1 6 2 2.7243 0.101 -3 -5 -6 3.8374 0.106 1 6 0 4.1473 0.098 -3 -5 -4 2.4922 0.078 1 6 -2 2.4294 0.072 -3 -5 -3 2.4272 0.065 1 6 -4 3.0062 0.097 -3 -5 -2 6.8004 0.103 1 6 -6 1.4268 0.078 -3 -5 -1 2.0972 0.044 1 5 -8 2.2115 0.08 -3 -5 0 3.2996 0.11 1 5 -7 4.6982 0.217 -3 -5 1 2.0504 0.056 1 5 -6 1.9820 0.074 -3 -5 2 6.7811 0.135 1 5 -5 4.8262 0.129 -3 -5 3 2.6139 0.071 1 5 -4 4.2410 0.14 -3 -5 4 2.7879 0.105 1 5 -3 7.9250 0.161 -3 -5 5 1.0121 0.119 1 5 -2 2.7028 0.089 -3 -5 6 3.6878 0.09 1 5 -1 7.8025 0.146 -3 -6 8 2.3839 0.077 1 5 0 6.2170 0.126 -3 -6 4 3.0369 0.12 1 5 1 8.0927 0.146 -3 -6 3 1.7565 0.078 1 5 2 3.3168 0.09 -3 -6 0 4.8698 0.122 1 5 3 8.0087 0.129 -3 -6 -2 1.4359 0.071 1 5 4 4.6281 0.124 -3 -6 -3 1.6851 0.061 1 5 5 5.0903 0.126 -3 -6 -4 3.1561 0.112 1 5 6 1.8636 0.064 -3 -6 -6 1.1137 0.105 1 5 7 4.9762 0.16 -3 -7 -7 1.6382 0.123 1 5 8 1.8605 0.097 -3 -7 -5 3.0678 0.082 1 5 9 2.1280 0.103 -3 -7 -4 4.3003 0.138 1 4 7 2.8546 0.073 -3 -7 -3 2.3566 0.091 1 4 6 0.5690 0.201 -3 -7 -1 2.8079 0.082 1 4 5 2.3285 0.084 -3 -7 0 5.7923 0.104 1 4 4 1.2832 0.065 -3 -7 1 3.4318 0.12 1 4 3 4.6205 0.112 -3 -7 3 2.7379 0.075 1 4 2 0.4689 0.092 -3 -7 4 4.5407 0.172 1 4 1 5.4548 0.108 -3 -7 5 2.8471 0.065 1 4 0 2.5877 0.07 -3 -7 8 2.4579 0.078 1 4 -1 5.5343 0.151 -3 -8 7 1.4446 0.122 1 4 -3 4.7603 0.092 -3 -8 3 2.3053 0.088 1 4 -5 2.0894 0.097 -3 -8 2 1.1849 0.093 1 4 -7 2.9967 0.082 -3 -8 1 2.3273 0.108 1 3 -9 1.9730 0.097 -3 -8 -1 2.2782 0.06 1 3 -7 3.9783 0.175 -3 -8 -2 1.2458 0.09 1 3 -6 2.7389 0.077 -3 -8 -3 2.3027 0.061 1 3 -5 4.0177 0.111 -3 -8 -6 0.8752 0.148 1 3 -4 3.8931 0.098
187
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188
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189
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190
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191
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192
-1 -7 -3 3.6984 0.107 3 5 2 6.8650 0.136 -1 -7 -2 3.6895 0.119 3 5 3 2.3558 0.06 -1 -7 -1 4.5362 0.122 3 5 4 2.9221 0.086 -1 -7 0 4.8783 0.117 3 5 6 3.6402 0.145 -1 -7 1 4.0775 0.135 3 5 7 2.0122 0.075 -1 -7 2 3.7563 0.114 3 4 5 3.6593 0.156 -1 -7 3 3.9589 0.096 3 4 3 2.8638 0.12 -1 -7 4 3.5561 0.096 3 4 2 1.4789 0.05 -1 -7 5 3.5653 0.097 3 4 1 4.4236 0.095 -1 -8 5 2.4319 0.058 3 4 -1 4.4831 0.114 -1 -8 4 2.0718 0.09 3 4 -2 1.5157 0.089 -1 -8 3 1.6593 0.061 3 4 -3 2.4760 0.107 -1 -8 1 2.8141 0.112 3 4 -5 3.5820 0.124 -1 -8 0 2.8595 0.081 3 3 -7 3.1753 0.062 -1 -8 -1 2.9564 0.073 3 3 -6 5.5851 0.162 -1 -8 -2 0.8392 0.095 3 3 -5 3.1531 0.106 -1 -8 -3 1.6025 0.061 3 3 -3 5.1337 0.112 -1 -8 -4 1.7206 0.087 3 3 -2 10.3023 0.184 -1 -8 -5 2.3048 0.062 3 3 -1 6.4580 0.171 -1 -9 -4 1.6758 0.088 3 3 0 3.5371 0.222 -1 -9 -3 0.6533 0.161 3 3 1 6.4562 0.155 -1 -9 -2 3.7671 0.095 3 3 2 10.1729 0.167 -1 -9 0 2.1975 0.072 3 3 3 5.1215 0.108 -1 -9 2 3.9500 0.099 3 3 4 1.7299 0.055 -1 -10 0 2.6527 0.066 3 3 5 3.1944 0.105 -1 -10 -2 1.5956 0.072 3 3 6 5.6938 0.147 0 -8 -2 3.1494 0.099 3 2 5 1.6514 0.09 0 -8 0 14.5940 0.25 3 2 4 5.1641 0.128 0 -7 3 3.4559 0.125 3 2 -4 4.9664 0.146 0 -7 1 3.2727 0.093 3 2 -5 2.0745 0.105 0 -7 -1 3.2678 0.107 3 1 -5 5.4271 0.177 0 -7 -3 3.8130 0.107 3 1 -4 5.8754 0.164 0 -6 -6 4.1978 0.19 4 4 -4 9.7845 0.189 0 -6 -4 2.0792 0.061 4 4 -2 9.8301 0.22 0 -6 -2 7.2782 0.099 4 5 4 2.4817 0.066 0 -6 0 3.1227 0.125 4 5 3 2.7268 0.065 0 -6 2 7.4580 0.105 4 5 1 2.9583 0.145 0 -6 4 2.2317 0.047 4 5 0 3.5568 0.123 0 -5 5 2.5769 0.093 4 5 -1 2.8103 0.113 0 -5 3 2.8010 0.083 4 5 -3 2.5425 0.094 0 -5 1 4.0111 0.081 4 5 -4 2.2099 0.055 0 -5 -1 4.0889 0.081 4 6 -6 5.9006 0.162 0 -5 -3 2.7506 0.07 4 6 -5 0.7436 0.17 0 -5 -5 2.5057 0.054 4 6 -4 1.0533 0.102 0 -5 -7 1.1116 0.112 4 6 -3 0.5489 0.143 0 -4 -6 3.2163 0.081 4 6 -2 8.9527 0.164 0 -4 -4 2.5979 0.067 4 6 -1 3.9708 0.17 0 -4 -2 6.3223 0.075 4 6 2 9.2337 0.17 0 -4 0 8.7978 0.113 4 7 5 2.9993 0.111 0 -4 2 6.3306 0.074 4 7 3 1.7978 0.065 0 -4 4 2.8833 0.09 4 7 1 3.5365 0.1
193
0 -4 6 3.0651 0.099 4 7 -1 3.2520 0.111 0 -3 7 2.2712 0.065 4 7 -3 1.7251 0.061 0 -3 5 4.0467 0.12 4 7 -5 2.8841 0.16 0 -3 3 5.4063 0.08 4 8 -6 2.8662 0.091 0 -3 1 6.3393 0.058 4 8 -4 3.7843 0.256 0 -3 -1 6.3546 0.069 4 8 -2 4.4698 0.159 0 -3 -3 5.1954 0.079 4 8 0 4.7477 0.158 0 -3 -5 3.7163 0.128 4 8 2 4.4236 0.149 0 -3 -7 2.2031 0.07 4 8 4 4.0656 0.157 0 -2 -6 6.9880 0.135 4 9 5 1.3104 0.115 0 -2 -4 1.3996 0.056 4 9 4 2.8527 0.071 0 -2 -2 12.0453 0.105 4 9 2 1.3482 0.096 0 -2 0 2.5593 0.065 4 9 0 3.1804 0.102 0 -2 2 11.8559 0.12 4 9 -4 2.7512 0.084 0 -2 6 7.1111 0.11 4 10 -2 2.9263 0.139 0 -1 7 3.9118 0.172 4 10 2 3.1066 0.075 0 -1 5 2.0496 0.066 4 11 3 1.3784 0.117 0 -1 3 7.5108 0.162 4 12 -4 3.4404 0.124 0 -1 1 7.3753 0.075 4 12 -2 2.7615 0.093 0 -1 -1 7.5158 0.083 4 12 0 3.8839 0.131 0 -1 -3 7.2200 0.102 4 12 2 1.8903 0.161 0 -1 -5 2.0092 0.067 4 13 0 2.1061 0.099 0 -1 -7 3.8443 0.129 5 11 -1 2.7321 0.099 0 -1 -9 0.7778 0.171 5 11 0 1.8312 0.084 0 0 -8 10.7634 0.178 5 10 -2 3.5892 0.116 0 0 -6 4.7319 0.116 5 9 -3 4.5168 0.174 0 0 -4 20.7862 0.314 5 9 -2 1.8535 0.093 0 0 -2 10.1509 0.172 5 9 -1 4.9290 0.166 0 0 2 10.6242 0.155 5 9 0 3.5242 0.185 0 0 4 21.2639 0.324 5 9 1 4.9466 0.147 0 0 6 4.7322 0.117 5 8 0 2.1908 0.06 0 0 8 10.3563 0.154 5 8 -2 3.0515 0.084 0 1 7 3.9673 0.105
P = 3.932(7) GPa
h k l FO Esd h k l FO Esd -5 -7 0 4.7973 0.124 0 0 4 24.7943 0.45 -5 -7 1 4.4026 0.126 0 0 6 5.3144 0.141 -5 -7 2 5.2643 0.151 0 0 8 9.6883 0.238 -5 -7 3 3.6894 0.137 0 1 7 4.2600 0.146 -5 -8 4 2.2505 0.068 0 1 5 1.9708 0.085 -5 -8 3 2.2712 0.089 0 1 3 8.8452 0.145 -5 -8 2 3.2945 0.08 0 1 1 8.7580 0.15 -5 -8 1 1.7244 0.068 0 1 -1 8.3867 0.159 -5 -8 0 2.6164 0.051 0 1 -3 8.5348 0.13 -5 -9 -1 6.2943 0.152 0 1 -5 2.1583 0.051 -5 -9 0 4.3479 0.174 0 1 -7 4.2194 0.169 -5 -9 1 6.0193 0.138 0 2 -6 7.6883 0.145 -5 -9 2 2.2055 0.082 0 2 -4 1.8485 0.037 -5 -9 3 4.9331 0.187 0 2 -2 13.3869 0.151
194
-5 -9 4 3.8782 0.081 0 2 0 2.8675 0.081 -5 -10 2 3.8296 0.136 0 2 2 14.0060 0.185 -5 -11 -1 3.1500 0.112 0 2 4 1.6381 0.054 -5 -11 0 2.1169 0.078 0 2 6 8.0662 0.123 -5 -11 1 3.2915 0.07 0 3 9 2.0941 0.078 -5 -11 3 3.0522 0.066 0 3 7 2.1372 0.074 -4 -12 -2 3.1565 0.075 0 3 5 4.4588 0.11 -4 -12 0 3.9997 0.197 0 3 3 6.0467 0.09 -4 -12 2 3.2007 0.076 0 3 1 7.2794 0.127 -4 -11 5 1.2607 0.121 0 3 -1 7.1642 0.109 -4 -11 4 0.6271 0.211 0 3 -3 5.4893 0.099 -4 -11 1 1.5103 0.094 0 3 -5 4.5981 0.107 -4 -11 -1 1.5057 0.107 0 3 -7 2.5494 0.09 -4 -11 -2 1.3616 0.096 0 4 -6 3.9188 0.13 -4 -10 -4 0.8473 0.167 0 4 -4 2.7924 0.13 -4 -10 -2 3.4944 0.151 0 4 -2 7.4587 0.123 -4 -10 2 3.8608 0.176 0 4 0 10.0286 0.145 -4 -10 6 2.3719 0.101 0 4 2 7.4924 0.121 -4 -9 4 3.2314 0.09 0 4 4 3.5956 0.105 -4 -9 2 1.6017 0.072 0 4 6 3.7893 0.068 -4 -9 0 3.5668 0.112 0 4 8 1.6514 0.083 -4 -9 -1 1.3441 0.081 0 5 7 1.4933 0.088 -4 -9 -2 1.5545 0.075 0 5 3 3.2565 0.117 -4 -9 -4 3.0581 0.081 0 5 1 4.7334 0.088 -4 -8 -4 4.5989 0.193 0 5 -1 4.5221 0.08 -4 -8 -2 5.4003 0.15 0 5 -3 3.1468 0.13 -4 -8 0 5.9693 0.128 0 5 -5 3.0722 0.074 -4 -8 2 4.9909 0.128 0 6 -4 2.5936 0.057 -4 -8 4 4.7010 0.13 0 6 -2 7.9368 0.141 -4 -8 6 3.3574 0.126 0 6 0 3.4738 0.107 -4 -7 5 3.3437 0.082 0 6 2 8.0477 0.125 -4 -7 4 0.5728 0.178 0 6 4 2.4990 0.067 -4 -7 1 3.5045 0.107 0 6 6 4.2661 0.142 -4 -7 -1 3.4135 0.108 0 7 5 1.3456 0.087 -4 -7 -3 1.8864 0.059 0 7 3 4.4475 0.115 -4 -7 -5 2.7922 0.146 0 7 1 3.5177 0.116 -4 -6 -4 1.4547 0.069 0 7 -1 3.7184 0.094 -4 -6 -2 9.8756 0.108 0 8 2 3.4122 0.116 -4 -6 1 1.7410 0.055 0 8 4 13.6076 0.186 -4 -6 2 10.0617 0.132 1 9 -2 4.2866 0.151 -4 -6 5 1.1224 0.105 1 9 0 2.4009 0.056 -4 -6 6 6.2072 0.147 1 9 1 1.2809 0.071 -4 -5 4 3.2248 0.071 1 9 2 4.0009 0.132 -4 -5 3 2.8717 0.067 1 9 3 0.5131 0.184 -4 -5 1 3.1193 0.106 1 9 4 1.9042 0.071 -4 -5 0 4.6121 0.095 1 8 5 2.7647 0.093 -4 -5 -1 3.1351 0.11 1 8 4 2.0199 0.065 -4 -5 -3 2.9868 0.084 1 8 3 1.9327 0.059 -4 -4 2 11.5298 0.103 1 8 1 3.1811 0.077 -4 -4 4 10.9562 0.141 1 8 0 2.6933 0.071 -4 -4 6 6.2603 0.155 1 8 -1 3.1948 0.121
195
-4 -3 5 2.7791 0.085 1 8 -3 1.9702 0.059 -4 -3 4 1.5415 0.062 1 8 -4 2.0461 0.056 -3 0 5 3.5332 0.113 1 7 -6 2.3543 0.06 -3 -1 3 6.6989 0.11 1 7 -5 4.1154 0.144 -3 -1 4 7.2585 0.172 1 7 -4 3.9511 0.17 -3 -1 5 6.2914 0.147 1 7 -3 4.0836 0.119 -3 -1 7 3.3005 0.122 1 7 -2 4.3280 0.131 -3 -2 6 0.9273 0.114 1 7 -1 4.8867 0.108 -3 -2 4 5.5934 0.106 1 7 0 5.4234 0.106 -3 -3 -5 3.6862 0.125 1 7 1 5.6285 0.103 -3 -3 -4 1.8533 0.058 1 7 2 3.9457 0.164 -3 -3 -3 6.1221 0.088 1 7 3 3.8375 0.119 -3 -3 -2 13.1492 0.099 1 7 4 4.0321 0.138 -3 -3 -1 7.4419 0.197 1 7 5 4.0096 0.149 -3 -3 0 3.6568 0.24 1 7 6 2.2814 0.074 -3 -3 1 7.3343 0.176 1 7 7 1.9194 0.092 -3 -3 2 12.3523 0.109 1 6 8 1.9342 0.083 -3 -3 3 5.9790 0.094 1 6 6 1.6610 0.071 -3 -3 4 1.9154 0.057 1 6 3 0.7742 0.09 -3 -3 5 3.5249 0.086 1 6 2 3.5002 0.084 -3 -3 6 6.3281 0.135 1 6 0 4.8095 0.109 -3 -3 7 3.2247 0.152 1 6 -2 3.1606 0.09 -3 -4 5 4.0364 0.13 1 6 -4 3.6349 0.123 -3 -4 3 3.4209 0.111 1 5 -7 5.4036 0.159 -3 -4 2 1.4645 0.098 1 5 -6 1.9099 0.074 -3 -4 1 5.3910 0.097 1 5 -5 5.8305 0.164 -3 -4 -1 4.6307 0.091 1 5 -4 5.1383 0.104 -3 -4 -3 3.4315 0.114 1 5 -3 9.9033 0.147 -3 -4 -5 4.1173 0.167 1 5 -2 3.2992 0.092 -3 -5 -6 4.3811 0.147 1 5 -1 9.2033 0.157 -3 -5 -5 1.1718 0.08 1 5 0 7.1208 0.13 -3 -5 -4 2.9215 0.059 1 5 1 9.3341 0.126 -3 -5 -3 2.5311 0.067 1 5 2 3.5828 0.091 -3 -5 -2 7.9362 0.113 1 5 3 9.0737 0.136 -3 -5 -1 2.4229 0.044 1 5 4 5.4091 0.112 -3 -5 0 3.6241 0.131 1 5 5 6.0623 0.125 -3 -5 1 2.3889 0.066 1 5 6 2.0746 0.07 -3 -5 2 7.7016 0.106 1 5 7 5.1816 0.192 -3 -5 3 2.8665 0.085 1 5 8 2.4796 0.08 -3 -5 4 3.1160 0.106 1 5 9 2.7204 0.131 -3 -5 5 0.9374 0.107 1 4 8 0.7476 0.182 -3 -5 6 4.3426 0.135 1 4 7 3.1211 0.093 -3 -5 7 2.0504 0.071 1 4 5 2.7541 0.07 -3 -6 7 0.9554 0.161 1 4 3 5.3711 0.099 -3 -6 6 1.1589 0.098 1 4 1 6.3433 0.123 -3 -6 4 3.6110 0.109 1 4 0 2.8308 0.083 -3 -6 3 1.9526 0.08 1 4 -1 6.3074 0.114 -3 -6 2 1.8162 0.069 1 4 -3 5.7636 0.09 -3 -6 0 5.4045 0.103 1 4 -4 1.4531 0.054 -3 -6 -2 1.7226 0.05 1 4 -5 2.5727 0.059 -3 -6 -3 1.8280 0.053 1 4 -7 3.0081 0.072
196
-3 -6 -4 3.4420 0.102 1 4 -8 0.8948 0.138 -3 -6 -6 1.1232 0.105 1 3 -8 2.1215 0.072 -3 -7 -5 3.5803 0.117 1 3 -7 4.4243 0.164 -3 -7 -4 5.1146 0.127 1 3 -6 3.0017 0.057 -3 -7 -1 4.0997 0.135 1 3 -5 4.7440 0.11 -3 -7 0 6.5752 0.123 1 3 -4 4.6339 0.119 -3 -7 1 4.0280 0.171 1 3 -3 7.5556 0.12 -3 -7 3 3.1234 0.102 1 3 -2 6.7951 0.153 -3 -7 4 4.9055 0.133 1 3 -1 7.6059 0.121 -3 -7 5 3.4609 0.089 1 3 0 4.3631 0.079 -3 -7 7 1.5643 0.106 1 3 1 7.4325 0.101 -3 -7 8 2.8119 0.071 1 3 2 6.6842 0.193 -3 -8 7 1.8644 0.09 1 3 3 7.7665 0.117 -3 -8 3 2.7970 0.086 1 3 4 4.5408 0.11 -3 -8 2 1.3626 0.084 1 3 5 4.6089 0.108 -3 -8 1 2.7325 0.068 1 3 6 3.0371 0.063 -3 -8 -3 2.6133 0.055 1 3 7 4.4059 0.16 -3 -8 -5 1.6530 0.086 1 3 8 1.8797 0.075 -3 -8 -6 0.6586 0.179 1 2 6 1.9523 0.061 -3 -9 -5 4.9252 0.164 1 2 5 1.1748 0.06 -3 -9 -4 2.7562 0.064 1 2 4 4.9447 0.109 -3 -9 -3 4.9496 0.155 1 2 2 9.1926 0.112 -3 -9 -2 2.2941 0.075 1 2 1 0.9226 0.028 -3 -9 -1 5.4582 0.138 1 2 0 7.8211 0.14 -3 -9 0 3.5218 0.114 1 2 -1 0.9200 0.024 -3 -9 1 6.8166 0.146 1 2 -2 8.7912 0.106 -3 -9 2 2.2423 0.057 1 2 -3 0.8208 0.056 -3 -9 3 5.4487 0.138 1 2 -4 4.7312 0.118 -3 -9 5 5.1373 0.158 1 2 -5 1.2431 0.08 -3 -10 5 1.7859 0.085 1 2 -6 2.0603 0.05 -3 -10 2 1.4726 0.081 1 2 -8 2.1869 0.075 -3 -10 0 2.3308 0.06 1 1 -9 2.1686 0.077 -3 -10 -2 1.2255 0.098 1 1 -8 2.1694 0.065 -3 -10 -4 2.0609 0.071 1 1 -6 4.6435 0.118 -3 -10 -5 1.7475 0.098 1 1 -5 3.9297 0.103 -3 -11 -5 2.4070 0.098 1 1 -4 4.5193 0.09 -3 -11 -4 1.2251 0.127 1 1 -3 3.6120 0.159 -3 -11 -3 3.2768 0.109 1 1 -2 8.3020 0.116 -3 -11 -2 4.6478 0.164 1 1 -1 6.7194 0.118 -3 -11 -1 3.6599 0.081 1 1 0 8.3963 0.207 -3 -11 1 3.4884 0.086 1 1 1 6.2625 0.093 -3 -11 2 4.7255 0.163 1 1 2 8.4079 0.14 -3 -11 3 3.4001 0.123 1 1 3 3.4300 0.147 -2 -10 -5 1.5363 0.09 1 1 4 3.9324 0.101 -2 -10 -4 5.3764 0.165 1 1 5 3.9625 0.12 -2 -10 -3 1.2733 0.098 1 1 6 4.4148 0.136 -2 -10 -1 1.7469 0.067 1 1 8 2.2414 0.065 -2 -10 0 6.0354 0.135 1 0 5 5.5435 0.101 -2 -10 1 1.7135 0.077 1 0 3 6.0539 0.172 -2 -10 3 1.5212 0.086 1 0 -1 10.5588 0.168 -2 -9 4 3.8982 0.143 1 0 -3 5.8023 0.129
197
-2 -9 3 0.8107 0.116 1 0 -5 5.7365 0.11 -2 -9 2 5.8292 0.183 1 0 -9 2.7478 0.104 -2 -9 0 5.5065 0.138 1 -1 -9 2.2137 0.073 -2 -9 -2 6.4856 0.138 1 -1 -8 2.1164 0.07 -2 -9 -4 4.3684 0.153 1 -1 -7 1.4057 0.072 -2 -9 -6 4.4872 0.127 1 -1 -6 4.6295 0.125 -2 -8 -7 1.7680 0.088 1 -1 -2 8.5781 0.142 -2 -8 -6 2.4285 0.078 1 -1 2 8.4300 0.118 -2 -8 -5 2.7193 0.056 1 -1 3 3.2864 0.154 -2 -8 -4 1.6936 0.074 1 -1 4 4.4579 0.098 -2 -8 -3 3.2187 0.103 1 -1 5 3.6697 0.114 -2 -8 -2 3.6973 0.117 1 -1 6 4.6490 0.164 -2 -8 -1 3.9824 0.103 1 -1 7 1.4301 0.071 -2 -8 0 2.0699 0.049 1 -2 6 1.8769 0.054 -2 -8 1 3.9325 0.119 1 -2 5 1.7428 0.068 -2 -8 2 4.0199 0.096 1 -2 4 4.6507 0.097 -2 -8 3 3.4224 0.076 1 -2 3 0.8426 0.048 -2 -8 6 2.4757 0.065 1 -2 2 9.2581 0.149 -2 -7 -1 0.8869 0.095 1 -2 -2 9.1424 0.094 -2 -6 -8 3.9403 0.123 1 -2 -4 4.6953 0.096 -2 -6 -7 1.1573 0.158 1 -3 -8 2.1342 0.067 -2 -6 -5 2.2684 0.06 1 -3 -7 4.5057 0.188 -2 -6 -4 7.7636 0.127 1 -3 -6 3.0444 0.112 -2 -6 -3 2.4766 0.067 1 -3 -5 4.6191 0.115 -2 -6 -2 1.6993 0.053 1 -3 -4 4.6309 0.101 -2 -6 -1 2.7866 0.1 1 -3 -3 7.1746 0.092 -2 -6 0 9.7104 0.106 1 -3 -2 6.7776 0.183 -2 -6 1 2.9311 0.082 1 -3 3 7.4707 0.115 -2 -6 2 1.6968 0.045 1 -3 4 4.6657 0.097 -2 -6 3 2.3585 0.08 1 -3 5 4.5989 0.11 -2 -6 4 7.9418 0.129 1 -4 -2 0.7362 0.061 -2 -6 5 1.7916 0.063 1 -4 -3 5.3942 0.101 -2 -6 6 1.5872 0.073 1 -4 -4 1.4377 0.049 -2 -6 8 3.9033 0.164 1 -4 -5 2.4393 0.073 -2 -5 8 2.8272 0.145 1 -4 -7 3.0795 0.09 -2 -5 6 4.8464 0.184 1 -5 -5 6.0415 0.114 -2 -5 5 1.6505 0.065 1 -5 -4 5.2446 0.106 -2 -5 4 5.7862 0.129 1 -5 -3 8.7864 0.117 -2 -5 2 9.3230 0.084 1 -5 -2 3.3849 0.101 -2 -5 0 8.4358 0.094 2 -3 -5 1.7933 0.055 -2 -5 -1 0.9394 0.08 2 -3 -6 2.5186 0.089 -2 -5 -2 9.4334 0.1 2 -2 -5 2.7940 0.099 -2 -5 -3 1.0601 0.067 2 -2 -4 9.9140 0.106 -2 -5 -4 5.7524 0.105 2 -1 -6 4.3193 0.126 -2 -5 -6 5.4388 0.142 2 0 -6 3.1900 0.132 -2 -5 -8 2.9551 0.112 2 0 -4 1.7607 0.053 -2 -4 -7 1.4077 0.085 2 0 4 1.6449 0.038 -2 -4 -6 10.3016 0.164 2 1 6 4.3987 0.128 -2 -4 -5 2.1287 0.07 2 1 5 1.2355 0.059 -2 -4 -3 2.9936 0.083 2 1 4 3.5071 0.098 -2 -4 -2 18.8186 0.173 2 1 2 9.3910 0.138
198
-2 -4 -1 3.9295 0.08 2 1 -2 9.0415 0.151 -2 -4 0 3.0518 0.178 2 1 -3 0.5403 0.073 -2 -4 1 3.7724 0.089 2 1 -4 4.2418 0.106 -2 -4 2 17.9765 0.168 2 1 -5 1.0929 0.083 -2 -4 3 2.6600 0.086 2 1 -8 2.3415 0.066 -2 -4 5 2.0048 0.053 2 2 -9 1.3956 0.126 -2 -4 6 10.2611 0.127 2 2 -8 5.2359 0.156 -2 -4 7 1.4955 0.088 2 2 -7 1.7032 0.069 -2 -3 6 2.5119 0.053 2 2 -5 3.0911 0.097 -2 -3 5 1.8683 0.057 2 2 -4 10.1960 0.152 -2 -3 4 2.1028 0.081 2 2 -3 2.7262 0.088 -2 -3 3 1.4614 0.077 2 2 -1 2.6793 0.075 -2 -3 2 4.0717 0.172 2 2 0 14.4674 0.238 -2 -3 1 1.5904 0.145 2 2 1 2.6823 0.072 -2 -3 0 2.1208 0.059 2 2 3 2.7273 0.078 -2 -3 -2 4.1015 0.103 2 2 4 10.1322 0.146 -2 -3 -4 2.0981 0.08 2 2 5 2.8198 0.047 -2 -3 -5 2.1573 0.064 2 2 7 1.8313 0.071 -2 -3 -6 2.3876 0.071 2 3 6 2.4770 0.086 -2 -2 -5 2.9312 0.073 2 3 5 2.1929 0.057 -2 -2 -4 10.1717 0.121 2 3 4 1.9664 0.078 -2 -2 -3 2.7795 0.063 2 3 2 4.2319 0.118 -2 -2 -1 2.5201 0.076 2 3 1 1.3708 0.077 -2 -2 0 14.5884 0.165 2 3 0 2.0669 0.091 -2 -2 1 2.7699 0.063 2 3 -2 4.0184 0.115 -2 -2 3 2.6373 0.058 2 3 -3 1.5242 0.066 -2 -2 4 9.5728 0.119 2 3 -4 2.0466 0.059 -2 -2 5 2.8100 0.092 2 3 -5 2.1595 0.054 -2 -2 7 1.5964 0.075 2 3 -6 2.5605 0.05 -2 -2 8 4.8606 0.173 2 3 -8 0.8385 0.145 -2 -2 9 1.1804 0.131 2 3 -9 1.7967 0.087 -2 -1 8 2.1949 0.071 2 4 -9 1.0488 0.145 -2 -1 6 4.0053 0.125 2 4 -6 10.2314 0.169 -2 -1 4 4.4558 0.088 2 4 -5 2.0384 0.06 -2 -1 2 9.1026 0.154 2 4 -3 2.7474 0.108 -2 -1 -2 8.3649 0.114 2 4 -2 18.3273 0.269 -2 -1 -4 4.1431 0.115 2 4 -1 3.9396 0.104 -2 -1 -5 1.4074 0.085 2 4 0 3.5066 0.213 -2 -1 -6 4.3025 0.126 2 4 1 3.6951 0.077 -2 0 -6 3.3736 0.092 2 4 2 18.5633 0.255 -2 0 -4 1.8202 0.061 2 4 3 2.8877 0.089 -2 0 4 1.5595 0.043 2 4 5 2.1167 0.067 -2 0 6 3.2277 0.078 2 4 6 9.5219 0.132 -2 1 8 2.2873 0.07 2 5 8 3.0200 0.095 -2 1 5 1.4002 0.095 2 5 7 1.3005 0.116 -2 1 4 4.2983 0.105 2 5 6 4.8086 0.147 -2 1 3 0.6813 0.059 2 5 5 1.5213 0.064 -2 3 6 2.5159 0.05 2 5 4 5.7453 0.159 -2 3 5 1.9805 0.062 2 5 2 9.6215 0.145 -1 5 2 2.9836 0.121 2 5 0 8.5746 0.118 -1 5 3 9.2059 0.121 2 5 -2 8.9328 0.143
199
-1 5 4 5.1954 0.14 2 5 -4 5.6454 0.135 -1 5 5 6.1958 0.116 2 5 -5 1.7481 0.055 -1 5 6 1.8430 0.062 2 5 -6 5.4758 0.13 -1 4 7 2.8814 0.113 2 5 -7 1.6190 0.078 -1 4 6 0.6723 0.128 2 5 -8 3.3358 0.105 -1 4 5 2.7337 0.076 2 6 -8 4.1249 0.158 -1 4 4 1.5580 0.052 2 6 -6 1.4610 0.091 -1 4 3 5.4890 0.11 2 6 -5 2.3989 0.096 -1 3 -5 4.6243 0.127 2 6 -4 7.9557 0.132 -1 3 -4 5.0354 0.135 2 6 -3 2.5877 0.073 -1 3 -3 7.6240 0.103 2 6 -2 1.6641 0.046 -1 3 2 6.6646 0.17 2 6 -1 2.9696 0.074 -1 3 3 7.0467 0.092 2 6 0 9.8518 0.152 -1 3 4 4.7123 0.107 2 6 1 2.7369 0.11 -1 3 5 4.7299 0.14 2 6 2 1.7899 0.048 -1 3 7 4.2124 0.169 2 6 3 2.6051 0.063 -1 3 8 1.9463 0.073 2 6 4 7.9146 0.144 -1 2 4 4.6588 0.094 2 6 5 2.0619 0.076 -1 2 2 9.2505 0.103 2 6 6 1.4464 0.086 -1 2 -2 9.2403 0.123 2 6 8 4.3007 0.124 -1 2 -4 4.5890 0.164 2 7 5 0.6404 0.162 -1 2 -5 1.3486 0.063 2 7 1 1.0667 0.083 -1 2 -6 2.1909 0.049 2 7 -4 0.5803 0.207 -1 1 -6 4.9724 0.125 2 7 -5 0.8658 0.129 -1 1 -5 3.7168 0.105 2 8 -6 2.4441 0.088 -1 1 -4 3.9400 0.108 2 8 -5 2.2137 0.067 -1 1 -3 3.3290 0.125 2 8 -4 1.7935 0.064 -1 1 -2 8.3147 0.097 2 8 -3 3.2027 0.091 -1 1 5 3.5468 0.108 2 8 -2 3.9143 0.125 -1 1 6 4.6086 0.143 2 8 -1 3.8290 0.136 -1 1 7 1.2925 0.087 2 8 0 2.1479 0.056 -1 1 8 2.3871 0.088 2 8 1 3.6257 0.109 -1 1 9 2.2073 0.113 2 8 2 3.8191 0.149 -1 0 9 2.4355 0.117 2 8 3 3.1306 0.118 -1 0 7 1.6807 0.073 2 8 4 1.7800 0.067 -1 0 5 5.4709 0.108 2 8 5 2.5018 0.119 -1 0 3 5.9289 0.144 2 8 7 1.9248 0.092 -1 0 1 10.4866 0.161 2 9 6 4.4434 0.181 -1 0 -3 5.8767 0.222 2 9 4 4.3088 0.15 -1 0 -5 5.5740 0.116 2 9 2 6.1877 0.159 -1 0 -7 1.5196 0.074 2 9 0 5.1379 0.144 -1 -1 -8 2.3783 0.063 2 9 -2 6.1035 0.201 -1 -1 -7 1.1155 0.102 2 9 -4 4.3536 0.141 -1 -1 -6 4.4364 0.135 2 10 -1 1.7603 0.069 -1 -1 -5 3.6448 0.107 2 10 0 6.1283 0.136 -1 -1 -4 4.4939 0.093 2 10 1 1.7114 0.076 -1 -1 -3 3.6771 0.223 2 10 3 1.4019 0.094 -1 -1 -2 8.5754 0.128 2 10 4 5.0031 0.197 -1 -1 -1 6.4119 0.071 2 10 5 1.2965 0.114 -1 -1 0 8.7465 0.137 3 11 -3 3.3639 0.101 -1 -1 1 6.7077 0.074 3 11 -2 4.5505 0.191
200
-1 -1 2 8.4295 0.123 3 11 -1 3.2763 0.08 -1 -1 3 3.3348 0.197 3 11 0 1.3515 0.095 -1 -1 4 4.4345 0.125 3 11 1 3.2817 0.099 -1 -1 5 3.3431 0.108 3 11 2 4.9242 0.155 -1 -1 7 0.9289 0.117 3 11 3 3.1199 0.12 -1 -1 8 1.8880 0.087 3 11 5 2.2303 0.085 -1 -1 9 2.1102 0.075 3 10 4 2.0887 0.074 -1 -2 6 1.9444 0.055 3 10 2 1.4872 0.083 -1 -2 5 1.0952 0.078 3 10 1 1.6193 0.091 -1 -2 4 4.7527 0.097 3 10 0 2.2661 0.071 -1 -2 2 8.9893 0.097 3 10 -3 1.0870 0.125 -1 -2 1 0.9077 0.025 3 10 -4 2.2116 0.069 -1 -2 0 8.1573 0.091 3 10 -5 1.7294 0.085 -1 -2 -1 0.9296 0.026 3 9 -5 4.6526 0.258 -1 -2 -2 9.1472 0.108 3 9 -4 2.5286 0.061 -1 -2 -4 4.7647 0.104 3 9 -3 5.5800 0.155 -1 -2 -5 1.2337 0.062 3 9 -2 2.1964 0.058 -1 -2 -6 2.1092 0.061 3 9 -1 6.4257 0.165 -1 -2 -8 2.2475 0.069 3 9 1 6.3397 0.161 -1 -3 -9 1.7133 0.091 3 9 2 2.4571 0.066 -1 -3 -8 1.6367 0.086 3 9 3 5.5136 0.15 -1 -3 -7 4.3366 0.142 3 9 4 2.7147 0.076 -1 -3 -6 2.9242 0.08 3 9 5 5.3216 0.175 -1 -3 -5 4.5799 0.144 3 8 3 2.7681 0.069 -1 -3 -4 4.5033 0.114 3 8 2 1.5023 0.068 -1 -3 -3 6.6887 0.084 3 8 1 2.5720 0.055 -1 -3 -2 6.5817 0.204 3 8 -1 2.8619 0.077 -1 -3 -1 7.1688 0.082 3 8 -3 2.8528 0.078 -1 -3 0 4.3979 0.067 3 8 -5 1.7036 0.08 -1 -3 1 7.1127 0.067 3 8 -7 1.9031 0.098 -1 -3 2 6.4846 0.235 3 7 -8 2.7648 0.072 -1 -3 3 7.5487 0.088 3 7 -7 1.8363 0.094 -1 -3 4 4.6327 0.092 3 7 -5 3.3748 0.125 -1 -3 5 4.4378 0.115 3 7 -4 4.8489 0.151 -1 -3 7 4.5177 0.159 3 7 -3 3.1880 0.09 -1 -4 7 3.0933 0.078 3 7 -1 3.8445 0.13 -1 -4 5 2.0136 0.084 3 7 0 6.5638 0.131 -1 -4 4 1.4637 0.055 3 7 1 4.4577 0.124 -1 -4 3 5.6299 0.104 3 7 3 3.2766 0.089 -1 -4 1 6.0459 0.097 3 7 4 4.9146 0.13 -1 -4 0 2.7511 0.119 3 7 5 3.4647 0.098 -1 -4 -1 6.0032 0.106 3 6 4 3.6852 0.146 -1 -4 -2 0.6936 0.06 3 6 3 1.9536 0.071 -1 -4 -3 5.3916 0.085 3 6 2 1.8536 0.071 -1 -4 -4 1.5393 0.058 3 6 0 5.4933 0.096 -1 -4 -5 2.5632 0.062 3 6 -2 1.6548 0.077 -1 -4 -7 3.0367 0.077 3 6 -3 1.8277 0.075 -1 -5 -9 2.5619 0.074 3 6 -4 3.6549 0.111 -1 -5 -8 2.4645 0.079 3 6 -7 1.4020 0.092 -1 -5 -7 5.3946 0.149 3 6 -8 2.3465 0.077 -1 -5 -6 1.9375 0.061 3 5 -6 4.5340 0.141
201
-1 -5 -4 5.4822 0.101 3 5 -5 1.1456 0.086 -1 -5 -3 8.9147 0.113 3 5 -4 2.7974 0.089 -1 -5 -2 3.3295 0.112 3 5 -3 2.7856 0.091 -1 -5 -1 9.4101 0.089 3 5 -2 7.6918 0.156 -1 -5 0 7.4418 0.105 3 5 -1 2.1348 0.057 -1 -5 1 9.5255 0.108 3 5 0 3.5207 0.13 -1 -5 2 2.9591 0.091 3 5 1 2.4226 0.068 -1 -5 3 9.2288 0.095 3 5 2 8.0928 0.14 -1 -5 4 5.2876 0.124 3 5 3 2.8483 0.09 -1 -5 5 5.7757 0.118 3 5 4 3.3999 0.093 -1 -5 6 1.8375 0.08 3 5 5 1.3761 0.076 -1 -5 7 4.9520 0.151 3 5 6 4.4431 0.151 -1 -6 6 1.5548 0.085 3 4 5 4.4825 0.129 -1 -6 5 1.1859 0.086 3 4 3 3.3316 0.1 -1 -6 4 3.2281 0.112 3 4 2 1.6266 0.054 -1 -6 2 3.0165 0.081 3 4 1 5.2074 0.102 -1 -6 0 5.1486 0.087 3 4 -1 5.3599 0.102 -1 -6 -1 0.8836 0.108 3 4 -2 1.4814 0.071 -1 -6 -2 3.1809 0.122 3 4 -3 3.2604 0.108 -1 -6 -4 3.6638 0.119 3 4 -5 4.2834 0.12 -1 -6 -8 1.8303 0.088 3 3 -7 3.6587 0.096 -1 -7 -7 2.0394 0.088 3 3 -6 6.3945 0.149 -1 -7 -6 2.3525 0.068 3 3 -5 3.3259 0.086 -1 -7 -5 4.0098 0.156 3 3 -4 1.9545 0.066 -1 -7 -4 3.7571 0.13 3 3 -3 5.7766 0.114 -1 -7 -3 4.1525 0.113 3 3 -2 12.1576 0.174 -1 -7 -2 4.3721 0.14 3 3 -1 7.0605 0.185 -1 -7 -1 5.1369 0.108 3 3 0 3.9818 0.22 -1 -7 0 5.5198 0.116 3 3 1 7.2271 0.192 -1 -7 1 5.0335 0.1 3 3 2 12.2148 0.172 -1 -7 2 4.2723 0.126 3 3 3 6.1286 0.118 -1 -7 3 4.2591 0.115 3 3 4 1.7035 0.096 -1 -7 4 3.8565 0.134 3 3 5 3.4173 0.104 -1 -7 5 4.0047 0.142 3 2 -4 5.9954 0.101 -1 -7 6 2.4936 0.058 3 2 -5 1.7714 0.074 -1 -8 4 1.8811 0.06 3 1 -7 3.5220 0.1 -1 -8 3 1.8308 0.059 3 1 -5 6.6803 0.135 -1 -8 1 3.2206 0.087 3 1 -4 7.1200 0.138 -1 -8 0 2.6065 0.129 3 1 -3 6.8664 0.097 -1 -8 -1 2.8277 0.101 3 0 -5 3.9506 0.114 -1 -8 -3 2.0078 0.073 4 3 -5 3.0448 0.103 -1 -8 -5 2.9191 0.082 4 4 -6 6.3927 0.191 -1 -9 -5 1.3839 0.09 4 4 -4 11.2917 0.184 -1 -9 -4 1.9663 0.076 4 4 -2 11.3267 0.194 -1 -9 -3 0.6152 0.161 4 5 3 3.1710 0.079 -1 -9 -2 4.3127 0.142 4 5 1 3.5669 0.116 -1 -9 0 2.6635 0.063 4 5 0 4.4768 0.096 -1 -9 1 0.8176 0.102 4 5 -1 3.1563 0.1 -1 -9 2 4.6617 0.13 4 5 -3 2.9034 0.063 0 -8 -4 13.6141 0.126 4 5 -4 3.3691 0.1 0 -8 -2 3.5910 0.088 4 6 -6 6.4886 0.246
202
0 -7 1 3.8579 0.09 4 6 -2 10.2801 0.159 0 -7 -1 3.6488 0.108 4 6 2 10.4710 0.145 0 -7 -3 4.3141 0.139 4 7 5 3.5518 0.102 0 -6 -6 5.0257 0.136 4 7 3 1.9541 0.056 0 -6 -4 2.6521 0.083 4 7 1 3.5021 0.14 0 -6 -2 7.9856 0.1 4 7 -1 3.8976 0.118 0 -6 0 3.4557 0.095 4 7 -3 1.8359 0.073 0 -6 2 8.2768 0.119 4 7 -5 3.1869 0.117 0 -6 4 2.4091 0.043 4 7 -6 0.4046 0.285 0 -5 5 2.9444 0.068 4 8 -6 3.4210 0.092 0 -5 3 3.3333 0.101 4 8 -4 4.5146 0.174 0 -5 1 4.2222 0.091 4 8 0 5.8177 0.132 0 -5 -1 4.6219 0.082 4 8 2 5.4027 0.136 0 -5 -3 3.1884 0.085 4 8 4 4.5761 0.14 0 -5 -5 2.7445 0.064 4 9 5 1.5965 0.097 0 -5 -7 1.3400 0.089 4 9 4 3.1374 0.093 0 -4 -8 1.7246 0.085 4 9 2 1.4899 0.077 0 -4 -6 3.4307 0.103 4 9 1 1.3919 0.08 0 -4 -4 3.1769 0.093 4 9 0 3.7575 0.13 0 -4 -2 7.4075 0.072 4 9 -1 0.9749 0.133 0 -4 0 9.7703 0.09 4 9 -4 3.2616 0.088 0 -4 2 7.4263 0.089 4 9 -6 0.9181 0.152 0 -4 4 2.9992 0.133 4 10 -6 2.5689 0.073 0 -3 5 4.4516 0.136 4 10 -4 0.3703 0.371 0 -3 3 5.8073 0.091 4 10 -2 3.5107 0.131 0 -3 1 7.6829 0.072 4 10 2 3.4319 0.154 0 -3 -1 7.3505 0.079 4 11 1 1.4289 0.097 0 -3 -3 5.7319 0.092 4 12 0 4.2825 0.146 0 -3 -5 3.7675 0.098 4 12 2 3.4263 0.091 0 -3 -7 2.3000 0.057 5 11 -3 2.8940 0.099 0 -2 -6 8.4275 0.146 5 11 -1 3.4020 0.093 0 -2 -4 1.6284 0.047 5 11 0 1.9726 0.079 0 -2 -2 14.0264 0.145 5 11 1 2.9361 0.114 0 -2 0 2.7976 0.067 5 10 -2 3.8911 0.131 0 -2 2 14.1573 0.171 5 9 -4 3.5150 0.115 0 -2 4 1.5743 0.067 5 9 -3 5.0403 0.193 0 -2 6 6.9919 0.13 5 9 -2 2.3118 0.067 0 -1 7 4.6902 0.133 5 9 -1 5.5213 0.175 0 -1 5 2.2041 0.076 5 9 0 4.3055 0.156 0 -1 3 8.1294 0.159 5 9 1 5.8232 0.16 0 -1 1 8.4703 0.101 5 8 1 1.7079 0.074 0 -1 -1 8.5565 0.109 5 8 0 2.7661 0.067 0 -1 -3 8.4399 0.13 5 8 -1 1.3898 0.082 0 -1 -5 2.2298 0.045 5 8 -2 3.4872 0.113 0 -1 -7 4.1500 0.138 5 8 -3 2.4164 0.07 0 0 -8 11.9386 0.203 5 8 -4 1.9245 0.088 0 0 -6 5.5184 0.119 5 7 -3 3.6718 0.125 0 0 -4 22.8281 0.489 5 7 -2 5.3507 0.135 0 0 -2 11.6913 0.213 5 7 -1 4.6373 0.132 0 0 2 11.9024 0.195 5 7 0 4.6757 0.121
203
P = 7.565(8) GPa
h k l FO Esd h k l FO Esd -9 -7 -2 3.5182 0.121 0 -2 2 9.4954 0.113 -9 -7 0 1.4458 0.087 0 -2 -2 9.9836 0.116 -9 -7 3 1.1753 0.104 0 -2 -6 5.2705 0.152 -9 -8 1 1.1746 0.107 0 -3 -3 4.0476 0.116 -9 -8 -1 1.5276 0.08 0 -3 3 4.0370 0.081 -9 -9 -2 2.2896 0.069 0 -3 5 2.8601 0.091 -9 -9 2 2.1057 0.084 1 -2 -5 0.5667 0.131 -8 -9 2 1.4352 0.084 1 -2 -4 3.3953 0.094 -8 -9 -2 1.4061 0.088 1 -2 -3 0.5854 0.053 -8 -8 -4 3.5417 0.207 1 -2 4 3.3334 0.093 -8 -8 0 4.4133 0.186 1 -2 5 0.6858 0.085 -8 -8 4 3.6525 0.145 1 -1 7 0.9035 0.103 -8 -7 5 0.9037 0.149 1 -1 6 3.0353 0.097 -8 -7 3 1.5497 0.079 1 -1 5 2.5059 0.054 -8 -7 1 1.5176 0.069 1 -1 4 2.7708 0.062 -8 -7 0 1.8387 0.072 1 -1 3 2.0577 0.05 -8 -7 -1 1.3932 0.081 1 -1 2 5.7337 0.081 -8 -6 -3 1.3697 0.085 1 -1 -2 5.6800 0.105 -8 -6 -2 4.0851 0.142 1 -1 -3 2.2944 0.086 -8 -6 -1 1.1181 0.091 1 -1 -4 2.8674 0.104 -8 -6 1 0.9204 0.105 1 -1 -5 2.4050 0.055 -8 -6 2 4.1934 0.133 1 -1 -6 3.2289 0.096 -8 -5 3 1.0298 0.097 1 -1 -8 1.5811 0.073 -8 -5 2 1.8536 0.069 1 0 -9 1.7054 0.098 -8 -5 0 0.8838 0.097 1 0 -7 0.9941 0.106 -8 -5 -2 1.9675 0.057 1 0 -5 3.6642 0.115 -7 -4 3 2.8297 0.068 1 0 -3 3.5757 0.093 -7 -4 2 1.0252 0.077 1 0 -1 7.1346 0.113 -7 -4 1 2.2091 0.064 1 0 1 6.9848 0.111 -7 -4 0 1.0789 0.066 1 0 3 3.6579 0.079 -7 -4 -1 2.2042 0.053 1 0 5 3.9610 0.12 -7 -4 -2 0.9618 0.08 1 1 9 1.0601 0.115 -7 -4 -3 3.0655 0.099 1 1 6 3.0498 0.113 -7 -5 -5 3.0572 0.092 1 1 5 2.6909 0.157 -7 -5 -4 3.6453 0.117 1 1 4 3.2435 0.119 -7 -5 -3 3.7299 0.114 1 1 3 2.2401 0.051 -7 -5 -2 1.9247 0.057 1 1 2 6.0723 0.091 -7 -5 -1 4.2714 0.119 1 1 1 3.9799 0.069 -7 -5 0 4.2937 0.12 1 1 0 5.7383 0.088 -7 -5 2 1.9241 0.052 1 1 -1 4.3264 0.058 -7 -5 3 3.7510 0.179 1 1 -2 5.8285 0.074 -7 -5 4 3.3051 0.202 1 1 -3 2.0310 0.051 -7 -5 5 2.7045 0.073 1 1 -4 2.9575 0.123 -7 -5 6 1.6632 0.074 1 1 -5 2.4318 0.069 -7 -6 2 0.8361 0.107 1 1 -6 3.0537 0.087 -7 -6 0 0.9661 0.084 1 2 -8 1.4894 0.077 -7 -6 -1 1.7056 0.055 1 2 -4 3.0244 0.134
204
-7 -6 -4 0.9248 0.1 1 2 -2 5.9078 0.079 -7 -7 -6 2.8991 0.069 1 2 -1 0.6807 0.033 -7 -7 -4 1.8959 0.09 1 2 0 5.4939 0.081 -7 -7 -3 2.1876 0.107 1 2 2 5.9028 0.102 -7 -7 -2 3.8761 0.138 1 2 4 3.3804 0.108 -7 -7 -1 2.8591 0.093 1 3 4 3.0504 0.094 -7 -7 0 2.5831 0.069 1 3 3 4.7638 0.09 -7 -7 1 2.9235 0.086 1 3 2 4.1352 0.082 -7 -7 2 3.4343 0.16 1 3 1 4.9914 0.077 -7 -7 3 2.4703 0.065 1 3 0 2.9382 0.068 -7 -7 4 1.8852 0.089 1 3 -1 4.7440 0.064 -7 -7 5 2.1386 0.066 1 3 -2 4.7519 0.117 -7 -7 6 2.8798 0.071 1 3 -3 4.9094 0.086 -7 -8 4 1.1518 0.092 1 3 -4 3.2597 0.107 -7 -8 1 1.0731 0.085 1 3 -5 2.9266 0.096 -7 -8 0 0.9395 0.117 1 3 -6 2.0231 0.061 -7 -8 -1 0.7290 0.142 1 4 -5 1.6482 0.048 -7 -8 -2 0.9536 0.12 1 4 -3 3.4614 0.091 -7 -8 -5 0.8566 0.13 1 4 2 0.6481 0.051 -6 -8 -4 2.1160 0.069 1 4 3 3.6164 0.09 -6 -8 -3 1.3264 0.075 1 4 4 0.9348 0.058 -6 -8 -2 3.9124 0.171 2 5 -4 3.8088 0.129 -6 -8 -1 1.4652 0.081 2 5 -3 0.7398 0.071 -6 -8 0 2.3648 0.115 2 5 -2 6.2269 0.102 -6 -8 1 1.6376 0.061 2 5 0 6.0670 0.102 -6 -8 2 3.7769 0.135 2 5 2 6.1751 0.085 -6 -6 -4 2.9266 0.15 2 5 3 0.7684 0.068 -6 -6 -3 1.6974 0.054 2 5 4 3.7167 0.112 -6 -6 -1 1.4490 0.058 2 5 5 0.9074 0.079 -6 -6 0 4.8253 0.124 2 5 6 2.8761 0.146 -6 -6 3 1.4090 0.084 2 4 6 6.9838 0.159 -6 -6 4 3.7886 0.15 2 4 5 1.4385 0.053 -6 -6 7 1.2925 0.096 2 4 3 1.8230 0.07 -6 -5 4 2.1059 0.058 2 4 2 12.3742 0.133 -6 -5 0 2.6721 0.057 2 4 1 2.2998 0.067 -6 -5 -4 1.9222 0.063 2 4 0 1.6370 0.039 -6 -5 -7 1.0749 0.107 2 4 -1 2.5835 0.108 -6 -4 -6 3.2589 0.123 2 4 -2 12.8099 0.101 -6 -4 -4 2.5019 0.091 2 4 -3 1.9256 0.073 -6 -4 -3 1.0569 0.071 2 4 -5 1.3884 0.051 -6 -4 -2 5.1745 0.147 2 4 -6 7.0443 0.129 -6 -4 -1 1.1322 0.06 2 3 -7 1.1082 0.085 -6 -4 0 3.7354 0.127 2 3 -5 1.3333 0.061 -6 -4 1 1.4279 0.068 2 3 -4 1.2310 0.059 -6 -4 2 5.6959 0.12 2 3 -3 1.0401 0.054 -6 -4 4 2.2089 0.06 2 3 -2 2.7379 0.087 -6 -4 6 3.0802 0.112 2 3 0 1.1807 0.04 -6 -3 5 1.3180 0.071 2 3 1 0.8101 0.059 -6 -3 4 0.9578 0.081 2 3 2 2.5562 0.08 -6 -3 -2 0.7755 0.109 2 3 3 0.9514 0.047 -6 -3 -3 0.9888 0.086 2 3 4 1.2153 0.053
205
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208
-3 -3 5 2.3283 0.047 4 1 -4 2.3541 0.045 -3 -3 6 4.2535 0.135 4 1 -3 1.9333 0.042 -3 -3 7 2.2290 0.073 4 1 -2 0.7521 0.055 -3 -4 5 2.9712 0.088 4 1 -1 4.2761 0.097 -3 -4 3 2.3704 0.062 4 1 3 2.1641 0.052 -3 -4 1 3.8366 0.086 4 1 4 1.9570 0.044 -3 -4 -1 3.5468 0.089 4 1 5 3.2148 0.091 -3 -4 -3 2.4252 0.065 5 2 -6 3.8644 0.13 -3 -4 -5 2.8831 0.066 5 2 -4 1.8584 0.057 -3 -5 -6 2.9888 0.079 5 2 -2 6.9835 0.112 -3 -5 -4 1.6861 0.094 5 2 0 2.2984 0.072 -3 -5 -3 1.8425 0.057 5 2 1 0.7506 0.088 -3 -5 -2 5.0819 0.121 5 2 2 6.9250 0.098 -3 -5 -1 1.6370 0.054 5 2 3 0.8032 0.092 -3 -5 0 2.3233 0.111 5 2 4 1.6159 0.082 -3 -5 1 1.6715 0.041 5 3 4 1.3835 0.055 -3 -5 2 5.5694 0.104 5 3 3 2.3256 0.059 -3 -5 3 1.8965 0.071 5 3 2 2.5145 0.087 -3 -5 4 2.0934 0.054 5 3 1 2.1698 0.074 -3 -5 6 3.2167 0.108 5 3 0 1.8148 0.034 -3 -6 4 2.4650 0.077 5 3 -1 2.3154 0.041 -3 -6 3 1.0286 0.067 5 3 -2 2.1976 0.085 -3 -6 2 1.3322 0.053 5 3 -3 2.5090 0.053 -3 -6 0 3.1169 0.101 5 3 -4 1.2268 0.06 -3 -6 -2 1.3531 0.054 5 3 -5 1.2806 0.063 -3 -6 -3 1.2077 0.067 5 3 -7 1.4984 0.08 -3 -6 -4 2.4033 0.048 5 4 -7 1.5459 0.09 -2 -5 4 3.7867 0.143 5 4 -5 2.4216 0.057 -2 -5 3 0.7021 0.077 5 4 -3 2.4101 0.131 -2 -5 2 6.0209 0.125 5 4 -2 1.5841 0.043 -2 -5 0 5.9376 0.122 5 4 -1 3.3982 0.102 -2 -5 -2 6.0843 0.1 5 4 0 1.2893 0.073 -2 -5 -4 3.9593 0.127 5 4 1 3.6850 0.092 -2 -5 -5 1.1180 0.073 5 4 2 1.6732 0.042 -2 -4 -6 6.7533 0.145 5 4 3 2.6884 0.078 -2 -4 -5 1.2744 0.073 5 4 4 1.0008 0.073 -2 -4 -3 1.9388 0.068 5 4 5 2.5812 0.077 -2 -4 -2 12.3357 0.19 5 4 6 0.8748 0.112 -2 -4 -1 2.6863 0.077 5 5 3 0.9159 0.071 -2 -4 1 2.7288 0.082 5 5 2 3.3022 0.089 -2 -4 2 12.4211 0.162 5 5 1 0.6787 0.102 -2 -4 3 2.0174 0.066 5 5 -2 3.1539 0.101 -2 -4 5 1.6674 0.078 5 5 -4 1.0110 0.074 -2 -4 6 6.9613 0.12 5 5 -5 0.7579 0.149 -2 -3 6 1.5781 0.062 5 5 -6 1.8324 0.083 -2 -3 4 1.4156 0.055 5 6 -6 2.8478 0.123 -2 -3 2 2.5543 0.081 5 6 -4 1.4414 0.065 -2 -3 0 1.2839 0.027 5 6 -3 0.3409 0.209 -2 -3 -2 2.8137 0.078 5 6 -2 4.6259 0.126 -2 -3 -4 1.1603 0.058 5 6 0 1.8990 0.052 -2 -3 -6 1.7159 0.053 5 6 2 4.5227 0.118
209
-2 -3 -7 0.9847 0.09 5 6 3 0.7059 0.096 -2 -2 -8 2.9934 0.107 5 6 4 1.2856 0.068 -2 -2 -7 0.8541 0.126 5 6 6 2.9888 0.085 -2 -2 -5 2.0578 0.047 5 7 6 2.3644 0.072 -2 -2 -4 6.5598 0.126 5 7 5 2.4454 0.056 -2 -2 -3 1.9132 0.067 5 7 4 2.4458 0.066 -2 -2 -2 0.4495 0.105 5 7 3 2.3677 0.065 -2 -2 -1 1.6014 0.063 5 7 2 3.4349 0.15 -2 -2 0 9.6310 0.153 5 7 1 2.7567 0.094 -2 -2 1 1.9383 0.057 5 7 0 3.4507 0.121 -2 -2 3 1.8898 0.034 5 7 -1 2.9912 0.167 -2 -2 4 6.6644 0.127 5 7 -2 3.3993 0.109 -2 -2 5 2.0079 0.055 5 7 -3 2.3246 0.054 -2 -2 7 1.0677 0.097 5 7 -4 2.3466 0.085 -2 -2 8 3.5125 0.122 5 7 -5 2.2932 0.062 -2 -1 4 3.1479 0.121 5 8 0 1.8549 0.065 -2 -1 3 0.4382 0.07 5 8 1 1.0439 0.078 -2 -1 2 6.1276 0.095 5 8 2 2.4145 0.07 -2 -1 1 0.7829 0.024 5 8 3 1.8185 0.059 -2 -1 0 4.6614 0.104 6 8 4 2.0266 0.071 -2 -1 -1 0.7619 0.027 6 8 3 1.4526 0.069 -2 -1 -2 6.0097 0.094 6 8 2 3.6214 0.162 -2 -1 -3 0.5317 0.06 6 8 1 1.6692 0.061 -2 -1 -4 2.9003 0.115 6 8 0 2.6437 0.056 -2 -1 -6 2.9140 0.087 6 8 -1 1.5280 0.064 -2 0 -6 2.4170 0.054 6 8 -2 4.1584 0.141 -2 0 4 1.1980 0.046 6 7 0 0.7305 0.101 -2 0 6 2.1430 0.047 6 7 3 0.8772 0.1 -2 1 6 2.9704 0.094 6 6 6 0.4809 0.244 -2 1 4 3.0001 0.1 6 6 4 3.3142 0.147 -2 1 -4 3.0212 0.077 6 6 3 1.5499 0.063 -1 2 6 1.5026 0.074 6 6 1 1.4243 0.072 -1 2 4 3.0306 0.078 6 6 0 4.5606 0.135 -1 2 -4 3.0269 0.104 6 6 -3 1.6793 0.066 -1 1 -6 3.1239 0.078 6 6 -4 3.0359 0.164 -1 1 -5 2.3327 0.09 6 5 -4 1.9743 0.063 -1 1 -4 2.9864 0.082 6 5 -3 1.2167 0.066 -1 1 -3 1.9476 0.066 6 5 0 2.7657 0.049 -1 1 -2 5.6786 0.098 6 5 4 2.1146 0.055 -1 1 2 5.7267 0.086 6 4 6 3.2338 0.08 -1 1 4 3.0069 0.084 6 4 4 2.4598 0.071 -1 1 5 2.7278 0.127 6 4 2 5.3182 0.112 -1 1 6 3.2380 0.08 6 4 1 1.2424 0.064 -1 1 8 1.5345 0.097 6 4 0 3.6803 0.097 -1 0 7 1.0159 0.111 6 4 -1 1.2892 0.055 -1 0 5 3.8195 0.116 6 4 -2 4.9900 0.132 -1 0 3 4.0277 0.141 6 4 -4 2.5400 0.072 -1 0 1 6.8173 0.108 6 4 -6 3.2739 0.084 -1 0 -1 7.0000 0.14 6 3 -6 0.6518 0.145 -1 0 -3 3.7539 0.086 6 3 2 1.2639 0.061 -1 0 -5 3.5607 0.108 7 4 -3 2.8876 0.076
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-1 0 -5 3.6213 0.112 7 4 -1 2.3632 0.084 -1 0 -3 3.9330 0.093 7 4 1 2.0176 0.046 -1 0 -1 7.0767 0.123 7 4 3 2.8415 0.129 -1 0 1 6.7362 0.103 7 5 5 2.8097 0.109 -1 0 3 3.8577 0.101 7 5 4 3.4601 0.117 -1 0 5 3.5741 0.147 7 5 3 3.9683 0.146 -1 1 8 1.7823 0.068 7 5 2 1.8733 0.054 -1 1 6 3.2921 0.09 7 5 1 4.0558 0.136 -1 1 5 2.5278 0.124 7 5 -1 4.1032 0.122 -1 1 4 2.9449 0.083 7 5 -2 1.8661 0.104 -1 1 3 2.1185 0.1 7 5 -3 3.9213 0.118 -1 1 2 5.7617 0.076 7 5 -4 3.7324 0.093 -1 1 -2 5.7664 0.092 7 5 -5 2.6836 0.163 -1 1 -3 2.1116 0.046 7 6 -5 1.3648 0.084 -1 1 -4 2.8793 0.097 7 6 -3 1.1507 0.097 -1 1 -5 2.5078 0.073 7 6 1 1.4280 0.068 -1 1 -6 3.1611 0.079 7 6 3 1.1107 0.086 -1 1 -7 0.8157 0.098 7 7 6 2.8969 0.148 -1 2 -5 0.8021 0.075 7 7 5 2.1538 0.069 -1 2 -4 3.0231 0.136 7 7 3 2.4594 0.054 -1 2 4 2.8426 0.117 7 7 2 3.8093 0.133 -1 2 6 1.4776 0.061 7 7 1 3.0183 0.105 0 3 -5 2.7797 0.069 7 7 0 2.2318 0.055 0 3 -3 3.7846 0.088 7 7 -1 2.9804 0.087 0 3 3 3.7773 0.091 7 7 -2 3.6924 0.123 0 3 7 1.7319 0.066 7 7 -3 2.3888 0.065 0 2 8 0.7295 0.144 7 7 -5 2.4044 0.061 0 2 6 5.5851 0.126 7 7 -6 2.5814 0.073 0 2 4 1.1898 0.043 7 8 -4 0.8006 0.13 0 2 2 9.5910 0.123 7 8 -3 0.8583 0.118 0 2 -2 9.7864 0.131 7 8 -2 0.8719 0.113 0 2 -4 0.9729 0.046 7 8 0 1.1029 0.085 0 1 -7 3.0133 0.137 7 9 0 1.0602 0.112 0 1 -5 1.4160 0.056 8 9 2 1.4476 0.094 0 1 -3 5.5169 0.08 8 8 4 3.9026 0.129 0 1 -1 5.8086 0.085 8 8 0 4.7825 0.149 0 1 1 5.8343 0.101 8 8 -4 3.9762 0.146 0 1 3 5.6058 0.089 8 7 -3 1.7202 0.073 0 1 5 1.4803 0.047 8 7 -1 1.0973 0.108 0 1 7 2.9372 0.072 8 6 2 4.0052 0.157 0 0 8 8.3100 0.142 8 6 1 1.0151 0.106 0 0 6 3.7175 0.116 8 6 -1 0.8215 0.129 0 0 4 16.7111 0.191 8 6 -2 4.0577 0.119 0 0 2 8.8236 0.115 8 6 -3 1.4229 0.075 0 0 -2 7.6400 0.14 8 5 -2 2.0379 0.056 0 0 -4 16.5990 0.256 8 5 1 1.4548 0.067 0 0 -6 3.6037 0.128 8 5 2 1.8501 0.059 0 0 -8 8.2309 0.149 9 7 2 3.6582 0.113 0 -1 -7 3.0703 0.071 9 7 1 1.2552 0.097 0 -1 -5 1.4419 0.05 9 7 -1 1.4626 0.081 0 -1 -3 5.4315 0.108 9 7 -2 3.4074 0.141
211
0 -1 -1 5.7610 0.097 9 8 -1 1.5402 0.082 0 -1 1 5.8775 0.084 9 8 0 1.2422 0.093 0 -1 3 5.2096 0.097 9 8 1 1.5173 0.09 0 -1 5 1.6435 0.052 9 9 2 2.0732 0.081 0 -1 7 2.7622 0.117 9 9 -3 0.4407 0.279 0 -2 6 5.2207 0.158
P = 9.828(9) GPa
h k l FO Esd h k l FO Esd -9 -7 -1 1.4712 0.086 -1 -2 4 2.9637 0.102 -9 -7 1 1.3828 0.101 -1 -2 5 0.5253 0.127 -9 -7 2 3.4946 0.128 -1 -2 6 1.2274 0.065 -9 -8 3 0.3970 0.36 -1 -2 8 1.6082 0.077 -9 -8 2 1.0955 0.123 -1 -3 7 2.9304 0.118 -9 -8 1 1.2204 0.107 -1 -3 6 1.9602 0.05 -9 -8 0 1.0318 0.127 -1 -3 5 2.9894 0.097 -9 -8 -2 1.3497 0.105 -1 -3 4 3.0339 0.093 -9 -8 -3 0.8340 0.161 -1 -3 3 4.6097 0.099 -9 -9 -1 1.5655 0.289 -1 -3 2 4.2633 0.092 -9 -9 0 1.8282 0.08 -1 -3 1 4.7634 0.08 -9 -9 2 2.1348 0.124 -1 -3 0 2.6506 0.063 -8 -9 2 1.3655 0.096 -1 -3 -1 4.4898 0.076 -8 -9 -2 1.2099 0.131 -1 -3 -2 3.7075 0.091 -8 -8 -5 0.9705 0.151 -1 -3 -3 4.8086 0.083 -8 -8 -4 3.7163 0.221 -1 -3 -4 2.7221 0.102 -8 -8 0 4.6740 0.167 -1 -3 -5 3.1488 0.115 -8 -8 4 3.7898 0.159 -1 -3 -6 1.8309 0.072 -8 -7 0 1.1993 0.105 -1 -4 -7 1.9484 0.075 -8 -7 -1 1.3753 0.081 -1 -4 -5 1.8061 0.047 -8 -6 -3 1.2948 0.116 -1 -4 -3 3.3947 0.091 -8 -6 -2 4.0994 0.125 -1 -4 -2 0.6557 0.184 -8 -6 -1 1.2464 0.083 -1 -4 2 0.8387 0.049 -8 -6 1 1.0755 0.105 -1 -4 3 3.3903 0.098 -8 -6 2 4.1995 0.158 -1 -4 5 1.5577 0.065 -8 -5 2 1.9224 0.07 -1 -4 6 0.7728 0.33 -8 -5 1 1.5550 0.075 0 -3 -4 0.5178 0.088 -8 -5 -1 1.5568 0.066 0 -3 -3 3.5926 0.091 -8 -5 -2 1.9007 0.063 0 -3 3 3.6340 0.098 -7 -4 3 2.8835 0.091 0 -3 4 0.8469 0.178 -7 -4 2 1.1891 0.082 0 -3 5 2.4912 0.098 -7 -4 1 2.2200 0.048 0 -2 6 5.2213 0.139 -7 -4 0 1.2858 0.059 0 -2 4 1.1595 0.052 -7 -4 -1 2.3321 0.091 0 -2 2 9.5339 0.207 -7 -4 -2 1.0212 0.082 0 -2 -2 9.6463 0.14 -7 -4 -3 2.7303 0.095 0 -2 -6 5.5572 0.115 -7 -5 -5 2.5570 0.174 0 -1 -5 1.1800 0.059 -7 -5 -4 3.2057 0.142 0 -1 -3 5.5534 0.125 -7 -5 -3 3.9145 0.136 0 -1 -1 5.6237 0.091 -7 -5 -2 2.0560 0.085 0 -1 1 5.3387 0.138
212
-7 -5 0 4.4098 0.163 0 -1 3 4.7395 0.097 -7 -5 1 3.9752 0.154 0 -1 5 1.2379 0.052 -7 -5 2 2.1458 0.052 0 -1 7 2.6834 0.078 -7 -5 3 3.7006 0.135 0 0 9 0.6279 0.622 -7 -5 4 3.3843 0.146 0 0 8 6.8673 0.182 -7 -5 5 2.9617 0.099 0 0 7 0.6343 0.129 -7 -5 6 1.1240 0.126 0 0 6 3.6483 0.095 -7 -6 1 1.4149 0.07 0 0 4 17.0188 0.234 -7 -6 0 0.9315 0.09 0 0 3 1.2401 0.079 -7 -6 -1 1.5629 0.066 0 0 2 7.8902 0.15 -7 -6 -3 0.7915 0.124 0 0 -1 0.2001 0.029 -7 -7 -6 2.8668 0.1 0 0 -2 7.1292 0.284 -7 -7 -5 2.3166 0.08 0 0 -4 15.7608 0.461 -7 -7 -4 1.7645 0.099 0 0 -6 3.2510 0.126 -7 -7 -3 2.5968 0.08 0 0 -8 7.3807 0.183 -7 -7 -2 3.7797 0.142 0 1 -7 2.4415 0.097 -7 -7 -1 2.6212 0.094 0 1 -5 1.1377 0.063 -7 -7 0 2.1842 0.064 0 1 -3 4.8709 0.154 -7 -7 1 2.9446 0.093 0 1 -2 0.3124 0.172 -7 -7 2 3.9430 0.163 0 1 -1 4.8601 0.196 -7 -7 3 2.3678 0.058 0 1 1 5.5023 0.095 -7 -7 4 2.0240 0.067 0 1 2 0.4280 0.129 -7 -7 5 1.9415 0.114 0 1 3 5.1131 0.111 -7 -7 6 2.7923 0.132 0 1 5 1.2970 0.085 -7 -8 4 0.5366 0.213 0 1 7 2.8844 0.08 -7 -8 -2 1.0311 0.098 0 2 6 5.3407 0.134 -7 -8 -5 0.7485 0.55 0 2 4 1.0419 0.047 -7 -9 -2 1.1067 0.336 0 2 2 9.4986 0.148 -6 -8 -4 2.0311 0.084 0 2 -2 8.6171 0.284 -6 -8 -3 1.0834 0.11 0 2 -4 1.0156 0.158 -6 -8 -2 3.8446 0.14 0 2 -6 4.1622 0.174 -6 -8 -1 1.5912 0.065 0 3 -5 1.9501 0.066 -6 -8 0 2.3515 0.063 0 3 -3 3.4094 0.118 -6 -8 2 4.0475 0.133 0 3 3 3.5257 0.092 -6 -8 4 1.9424 0.149 0 3 7 1.6143 0.081 -6 -7 0 0.9298 0.096 1 4 -5 1.6007 0.065 -6 -7 -1 0.6076 0.141 1 4 -3 3.2357 0.099 -6 -7 -2 0.9389 0.283 1 4 -2 0.6463 0.051 -6 -7 -4 0.8670 0.373 1 4 2 0.6658 0.052 -6 -6 -7 0.9611 0.142 1 4 3 3.3193 0.092 -6 -6 -4 3.0523 0.122 1 4 4 0.9526 0.055 -6 -6 -3 1.4979 0.064 1 4 5 1.7688 0.056 -6 -6 -1 1.5715 0.055 1 3 8 1.1008 0.116 -6 -6 0 5.0897 0.116 1 3 5 3.1361 0.117 -6 -6 1 1.4495 0.069 1 3 4 3.0396 0.072 -6 -6 4 3.7141 0.183 1 3 3 4.5332 0.104 -6 -6 7 1.3403 0.35 1 3 2 4.0144 0.083 -6 -5 7 0.9461 0.136 1 3 1 4.6849 0.064 -6 -5 4 2.1046 0.089 1 3 0 2.9408 0.062 -6 -5 3 0.7074 0.108 1 3 -1 4.6873 0.081 -6 -5 2 0.6470 0.128 1 3 -2 3.9119 0.132
213
-6 -5 0 2.7951 0.064 1 3 -3 4.4966 0.128 -6 -5 -4 2.2033 0.093 1 3 -4 2.7553 0.107 -6 -5 -7 0.6288 0.673 1 3 -5 2.2583 0.08 -6 -4 -6 3.2305 0.088 1 3 -6 2.0362 0.05 -6 -4 -5 1.0447 0.093 1 3 -7 2.3256 0.127 -6 -4 -4 2.4693 0.051 1 2 -4 2.6631 0.13 -6 -4 -3 0.9941 0.076 1 2 -2 5.3294 0.16 -6 -4 -2 5.2678 0.141 1 2 -1 0.6682 0.03 -6 -4 -1 1.4034 0.063 1 2 0 5.5383 0.077 -6 -4 0 3.7143 0.107 1 2 1 0.6845 0.027 -6 -4 1 1.1545 0.208 1 2 2 5.5079 0.127 -6 -4 2 5.6150 0.106 1 2 4 3.0399 0.093 -6 -4 3 0.8631 0.09 1 2 6 0.5740 0.415 -6 -4 4 2.4018 0.113 1 2 7 0.8446 0.11 -6 -4 6 3.1942 0.151 1 1 8 1.1742 0.109 -6 -3 5 1.0833 0.088 1 1 6 2.7383 0.124 -6 -3 2 1.2526 0.074 1 1 5 2.3285 0.068 -6 -3 0 1.3722 0.05 1 1 4 2.7834 0.101 -5 -2 6 3.7301 0.141 1 1 3 2.0142 0.049 -5 -2 4 2.0843 0.071 1 1 2 5.6544 0.145 -5 -2 3 1.0901 0.187 1 1 1 4.0749 0.083 -5 -2 2 6.6959 0.108 1 1 0 5.4706 0.071 -5 -2 0 2.1947 0.06 1 1 -1 3.7048 0.125 -5 -2 -1 0.4922 0.109 1 1 -2 5.1352 0.186 -5 -2 -2 6.5032 0.104 1 1 -3 1.9156 0.082 -5 -2 -4 1.8146 0.058 1 1 -4 2.6311 0.121 -5 -3 -6 1.2353 0.101 1 1 -5 2.1948 0.075 -5 -3 -4 1.4502 0.053 1 1 -6 3.2879 0.155 -5 -3 -3 2.2655 0.058 1 0 -7 0.9724 0.091 -5 -3 -2 2.4073 0.057 1 0 -5 3.2001 0.105 -5 -3 -1 2.1769 0.081 1 0 -3 3.2912 0.191 -5 -3 0 1.7686 0.039 1 0 -1 5.9545 0.246 -5 -3 1 2.3294 0.05 1 0 1 6.3729 0.186 -5 -3 2 2.3197 0.056 1 0 3 3.7464 0.079 -5 -3 3 2.2966 0.053 1 0 5 3.4877 0.104 -5 -3 4 1.2073 0.074 1 -1 8 1.5226 0.078 -5 -3 5 1.3396 0.065 1 -1 6 3.0230 0.123 -5 -4 7 1.5289 0.082 1 -1 5 2.2784 0.065 -5 -4 6 1.0807 0.095 1 -1 4 3.0863 0.114 -5 -4 5 2.1159 0.08 1 -1 3 1.9277 0.077 -5 -4 4 0.9675 0.271 1 -1 2 5.4023 0.12 -5 -4 3 2.6841 0.09 1 -1 -2 4.8523 0.168 -5 -4 2 1.5539 0.044 1 -1 -3 2.0747 0.078 -5 -4 1 3.8958 0.1 1 -1 -4 2.5394 0.116 -5 -4 0 1.2917 0.051 1 -1 -5 2.2991 0.084 -5 -4 -1 3.5852 0.102 1 -1 -6 2.5598 0.113 -5 -4 -2 1.4366 0.05 1 -1 -8 1.6215 0.076 -5 -4 -3 2.8239 0.093 1 -2 -6 1.2498 0.071 -5 -4 -5 2.4620 0.09 1 -2 -5 0.6574 0.109 -5 -4 -7 1.4974 0.095 1 -2 -4 3.1485 0.093 -5 -5 -6 1.8371 0.067 1 -2 4 3.2743 0.103
214
-5 -5 -3 1.0278 0.067 1 -2 6 1.0925 0.093 -5 -5 -2 3.0404 0.097 2 -1 -6 2.7850 0.104 -5 -5 0 0.9260 0.068 2 -1 -4 2.7860 0.078 -5 -5 2 3.2862 0.131 2 -1 4 2.8109 0.133 -5 -5 6 1.6798 0.073 2 -1 6 2.8021 0.089 -5 -5 7 0.5089 0.26 2 0 6 2.1625 0.07 -5 -6 7 1.0631 0.119 2 0 4 1.0152 0.052 -5 -6 6 2.6521 0.075 2 0 2 0.5390 0.045 -5 -6 4 1.3481 0.071 2 0 -4 0.9736 0.049 -5 -6 2 4.6602 0.122 2 0 -6 1.8833 0.051 -5 -6 0 1.9472 0.057 2 1 -6 2.4562 0.109 -5 -6 -2 4.4658 0.122 2 1 -4 2.9276 0.098 -5 -6 -6 3.1539 0.083 2 1 -2 5.1123 0.185 -5 -7 -6 2.3826 0.075 2 1 -1 0.8147 0.025 -5 -7 -5 2.4214 0.107 2 1 0 4.6285 0.081 -5 -7 -4 2.5715 0.083 2 1 1 0.7570 0.027 -5 -7 -3 2.2594 0.119 2 1 2 5.7589 0.13 -5 -7 -2 3.4357 0.122 2 1 4 2.6928 0.095 -5 -7 -1 3.1449 0.11 2 1 6 2.7788 0.068 -5 -7 0 3.4165 0.12 2 1 8 1.7715 0.069 -5 -7 1 2.7789 0.123 2 2 8 3.1796 0.134 -5 -7 2 3.4334 0.102 2 2 7 1.2785 0.077 -5 -7 3 2.3791 0.077 2 2 5 1.9468 0.059 -5 -7 4 2.4264 0.066 2 2 4 6.0975 0.14 -5 -7 5 2.3166 0.086 2 2 3 1.6706 0.051 -5 -8 2 2.3165 0.141 2 2 1 1.7868 0.054 -5 -8 0 2.2016 0.081 2 2 0 8.9887 0.109 -5 -8 -1 1.2480 0.073 2 2 -1 1.5791 0.05 -5 -8 -2 2.4523 0.061 2 2 -2 0.3690 0.101 -5 -8 -3 1.7119 0.065 2 2 -3 1.6067 0.057 -4 -7 1 1.9209 0.054 2 2 -4 5.9869 0.162 -4 -7 0 0.9776 0.217 2 2 -5 1.8280 0.058 -4 -7 -1 1.9980 0.058 2 2 -7 0.7691 0.145 -4 -7 -2 0.8000 0.09 2 2 -8 2.9632 0.097 -4 -6 -6 4.2214 0.176 2 3 -6 1.5120 0.066 -4 -6 -5 0.7920 0.112 2 3 -5 1.0905 0.072 -4 -6 -4 1.1425 0.074 2 3 -4 1.0971 0.058 -4 -6 -3 1.0040 0.082 2 3 -2 2.4135 0.083 -4 -6 -2 7.2941 0.143 2 3 0 1.0490 0.114 -4 -6 1 0.5684 0.383 2 3 2 2.5236 0.09 -4 -6 2 6.7036 0.127 2 3 3 0.7944 0.061 -4 -6 6 4.4855 0.149 2 3 4 1.1280 0.059 -4 -5 5 0.5397 0.154 2 3 5 1.2116 0.065 -4 -5 4 2.1034 0.054 2 3 6 1.6556 0.059 -4 -5 3 1.7323 0.046 2 4 6 6.5815 0.169 -4 -5 1 2.0710 0.041 2 4 5 1.3515 0.055 -4 -5 0 2.9969 0.106 2 4 4 0.8000 0.264 -4 -5 -1 1.8370 0.044 2 4 3 1.8132 0.04 -4 -5 -3 1.7769 0.048 2 4 2 12.2738 0.132 -4 -5 -4 2.1194 0.048 2 4 1 2.4766 0.089 -4 -5 -7 0.9555 0.147 2 4 0 1.5540 0.04
215
-4 -5 -8 1.4554 0.118 2 4 -1 1.7494 0.08 -4 -4 -8 3.6403 0.166 2 4 -2 12.1946 0.19 -4 -4 -6 3.9535 0.158 2 4 -3 1.7230 0.049 -4 -4 -5 0.4974 0.498 2 4 -5 0.3813 0.554 -4 -4 -4 7.7295 0.125 2 4 -6 6.3272 0.138 -4 -4 -2 7.4808 0.13 2 4 -7 0.8738 0.108 -4 -4 0 10.0544 0.117 2 5 -5 0.6308 0.107 -4 -4 1 0.4972 0.269 2 5 -4 3.6170 0.129 -4 -4 2 7.5618 0.094 2 5 -2 5.7011 0.094 -4 -4 4 7.5379 0.102 2 5 0 4.9930 0.119 -4 -4 6 3.9125 0.162 2 5 2 5.6466 0.113 -4 -4 8 3.8655 0.157 2 5 3 0.7071 0.235 -4 -3 5 1.6878 0.086 2 5 4 3.4254 0.132 -4 -3 3 3.1128 0.113 2 5 6 3.2723 0.139 -4 -3 2 0.7520 0.205 3 6 -4 2.1467 0.069 -4 -3 1 3.2709 0.086 3 6 -2 1.5644 0.047 -4 -3 0 1.5077 0.034 3 6 0 3.2364 0.106 -4 -3 -1 3.5904 0.104 3 6 1 0.6405 0.082 -4 -3 -2 0.7317 0.065 3 6 2 1.4799 0.055 -4 -3 -3 2.9484 0.076 3 6 3 1.0286 0.068 -4 -3 -5 2.1438 0.059 3 6 4 2.3027 0.052 -4 -3 -7 1.6313 0.079 3 5 7 1.1135 0.113 -4 -2 -6 3.9087 0.106 3 5 6 2.8385 0.163 -4 -2 -5 0.8141 0.095 3 5 5 0.6582 0.127 -4 -2 -2 6.9659 0.099 3 5 4 1.3518 0.246 -4 -2 -1 1.5053 0.041 3 5 3 1.9723 0.07 -4 -2 1 1.6278 0.037 3 5 2 4.9264 0.114 -4 -2 2 7.1228 0.093 3 5 1 1.5830 0.044 -4 -2 3 0.8020 0.063 3 5 0 2.3658 0.081 -4 -2 6 4.1551 0.113 3 5 -1 1.6408 0.051 -4 -2 8 1.2532 0.334 3 5 -2 5.2753 0.102 -4 -1 5 2.9858 0.115 3 5 -3 1.7254 0.054 -4 -1 4 2.2238 0.069 3 5 -4 1.8354 0.046 -4 -1 3 2.1098 0.057 3 5 -5 0.9076 0.099 -4 -1 2 0.5770 0.081 3 5 -6 2.8087 0.098 -4 -1 -3 2.1074 0.052 3 5 -7 1.1218 0.102 -4 -1 -4 2.1487 0.063 3 4 -5 2.7354 0.084 -4 -1 -5 3.8750 0.201 3 4 -3 2.1514 0.073 -3 0 7 2.4421 0.057 3 4 -2 0.7816 0.056 -3 0 5 2.4947 0.053 3 4 -1 3.5859 0.08 -3 0 3 4.3989 0.095 3 4 1 3.4153 0.082 -3 0 -3 4.1305 0.095 3 4 3 2.0755 0.038 -3 0 -5 2.4152 0.07 3 4 5 2.5964 0.104 -3 -1 -7 2.4223 0.091 3 3 7 2.1143 0.074 -3 -1 -5 4.1300 0.132 3 3 6 4.0662 0.13 -3 -1 -4 4.5739 0.118 3 3 5 2.1308 0.043 -3 -1 -3 4.1455 0.089 3 3 4 0.7131 0.294 -3 -1 -1 5.5195 0.079 3 3 3 3.7280 0.096 -3 -1 0 6.0208 0.073 3 3 2 7.7892 0.106 -3 -1 1 5.4783 0.087 3 3 1 4.1790 0.1 -3 -1 3 4.1109 0.092 3 3 0 2.1694 0.089
216
-3 -1 4 4.3341 0.096 3 3 -1 4.2950 0.072 -3 -1 5 4.5375 0.107 3 3 -2 7.8054 0.149 -3 -1 7 2.1979 0.06 3 3 -3 3.6907 0.099 -3 -1 8 2.0614 0.09 3 3 -4 1.0979 0.057 -3 -2 8 1.8520 0.073 3 3 -5 1.9714 0.057 -3 -2 5 1.2623 0.078 3 3 -6 3.9315 0.16 -3 -2 4 3.3519 0.107 3 3 -7 2.2606 0.062 -3 -2 1 0.2852 0.589 3 2 -8 1.4827 0.347 -3 -2 0 9.6163 0.1 3 2 -6 0.7910 0.329 -3 -2 -1 0.6362 0.212 3 2 -4 3.6003 0.122 -3 -2 -4 3.6542 0.102 3 2 -1 0.6915 0.187 -3 -2 -5 1.2552 0.066 3 2 0 9.3041 0.128 -3 -2 -8 1.7614 0.075 3 2 1 0.6348 0.233 -3 -3 -7 2.2591 0.062 3 2 2 0.4495 0.271 -3 -3 -6 4.0482 0.161 3 2 4 3.5332 0.106 -3 -3 -5 2.2205 0.06 3 2 5 0.8019 0.099 -3 -3 -4 1.2178 0.058 3 2 8 1.7719 0.084 -3 -3 -3 3.9322 0.094 3 1 7 2.2224 0.111 -3 -3 -2 8.3305 0.105 3 1 5 4.4128 0.106 -3 -3 -1 4.3022 0.086 3 1 4 4.2096 0.096 -3 -3 0 2.0946 0.044 3 1 3 4.0648 0.085 -3 -3 1 4.6500 0.077 3 1 1 5.0297 0.068 -3 -3 2 8.1262 0.105 3 1 0 6.6015 0.098 -3 -3 3 3.7896 0.089 3 1 -1 5.4275 0.1 -3 -3 4 0.5885 0.31 3 1 -3 3.7248 0.134 -3 -3 5 2.2364 0.061 3 1 -4 4.3710 0.136 -3 -3 6 4.2034 0.144 3 1 -5 4.0895 0.133 -3 -3 7 2.4058 0.065 3 1 -7 2.1264 0.067 -3 -4 5 3.0378 0.11 3 0 -7 2.2465 0.077 -3 -4 3 2.2245 0.071 3 0 -5 2.4014 0.082 -3 -4 1 3.7078 0.08 3 0 -4 1.0433 0.157 -3 -4 -1 3.7792 0.11 3 0 -3 3.8178 0.147 -3 -4 -3 2.4609 0.058 3 0 3 4.2572 0.102 -3 -4 -5 2.8697 0.099 3 0 5 2.5061 0.06 -3 -5 -7 1.3127 0.087 4 1 -5 3.0371 0.109 -3 -5 -6 3.0203 0.1 4 1 -4 2.0617 0.061 -3 -5 -5 0.6795 0.109 4 1 -3 2.0069 0.096 -3 -5 -4 1.9803 0.046 4 1 3 2.1588 0.057 -3 -5 -3 1.6971 0.049 4 1 4 2.0931 0.061 -3 -5 -2 5.2741 0.113 4 1 5 3.0095 0.164 -3 -5 -1 1.6683 0.042 4 2 6 3.9895 0.123 -3 -5 0 2.6082 0.07 4 2 5 0.7541 0.102 -3 -5 1 1.6386 0.04 4 2 2 6.8219 0.101 -3 -5 2 5.4557 0.09 4 2 1 1.4845 0.039 -3 -5 3 1.7034 0.049 4 2 -1 1.4499 0.037 -3 -5 4 1.8192 0.053 4 2 -2 6.2398 0.105 -3 -5 5 1.1419 0.076 4 2 -3 0.6495 0.074 -3 -5 6 2.9375 0.068 4 2 -5 0.9612 0.073 -3 -6 4 1.8536 0.114 4 2 -6 3.8956 0.128 -3 -6 3 1.0127 0.079 4 3 -7 1.7330 0.075 -3 -6 2 1.3355 0.178 4 3 -5 1.7688 0.052
217
-3 -6 1 0.4784 0.123 4 3 -4 0.8459 0.073 -3 -6 0 3.2316 0.1 4 3 -3 2.8422 0.079 -3 -6 -1 0.7831 0.251 4 3 -2 0.8915 0.052 -3 -6 -2 1.6384 0.045 4 3 -1 3.1842 0.086 -3 -6 -4 2.3604 0.064 4 3 0 1.3755 0.044 -2 -5 5 0.8632 0.083 4 3 1 3.5068 0.08 -2 -5 4 3.7167 0.127 4 3 2 0.8671 0.058 -2 -5 3 0.9266 0.066 4 3 3 2.8089 0.065 -2 -5 2 6.3623 0.087 4 3 5 1.8797 0.063 -2 -5 0 5.5404 0.104 4 4 7 1.2713 0.277 -2 -5 -1 0.6092 0.28 4 4 6 4.1235 0.138 -2 -5 -2 6.1517 0.114 4 4 4 7.1118 0.118 -2 -5 -3 0.9249 0.061 4 4 2 7.2884 0.112 -2 -5 -4 3.6921 0.114 4 4 1 0.7366 0.066 -2 -5 -5 0.5259 0.14 4 4 0 9.5770 0.133 -2 -5 -6 3.3362 0.12 4 4 -1 0.5123 0.081 -2 -4 -7 0.8204 0.368 4 4 -2 7.3157 0.095 -2 -4 -6 6.9834 0.12 4 4 -4 7.2693 0.143 -2 -4 -4 0.5279 0.109 4 4 -5 0.5323 0.446 -2 -4 -3 1.8986 0.049 4 4 -6 3.7826 0.169 -2 -4 -2 12.5721 0.154 4 5 -4 1.9319 0.075 -2 -4 -1 2.4810 0.083 4 5 -3 1.7336 0.05 -2 -4 0 1.5763 0.033 4 5 -1 1.8744 0.046 -2 -4 1 2.5852 0.082 4 5 0 2.8494 0.092 -2 -4 2 12.8270 0.147 4 5 1 1.8154 0.041 -2 -4 3 1.8965 0.062 4 5 3 1.7123 0.05 -2 -4 6 6.5893 0.151 4 5 4 2.0593 0.054 -2 -4 7 0.9185 0.11 4 5 5 0.9913 0.083 -2 -3 6 0.8471 0.339 4 5 8 1.1471 0.12 -2 -3 5 1.0956 0.095 4 6 6 3.6329 0.213 -2 -3 4 1.0564 0.061 4 6 2 6.5647 0.143 -2 -3 3 0.8076 0.057 4 6 1 0.8171 0.083 -2 -3 2 2.6238 0.09 4 6 0 0.8059 0.091 -2 -3 0 1.1626 0.036 4 6 -1 1.1899 0.083 -2 -3 -1 0.9814 0.049 4 6 -2 6.8480 0.102 -2 -3 -2 2.4462 0.077 4 6 -6 3.9800 0.171 -2 -3 -4 1.1553 0.057 4 7 -1 1.8870 0.05 -2 -3 -5 1.3632 0.063 4 7 1 1.8568 0.053 -2 -3 -6 1.6017 0.056 4 7 3 0.9173 0.089 -2 -2 -8 2.7989 0.19 5 8 -2 2.4261 0.061 -2 -2 -7 0.9321 0.103 5 8 0 2.1591 0.062 -2 -2 -6 0.8836 0.258 5 8 2 2.6420 0.075 -2 -2 -5 1.9561 0.075 5 8 3 1.6128 0.065 -2 -2 -4 6.4818 0.106 5 7 6 2.2957 0.084 -2 -2 -3 1.6529 0.046 5 7 5 2.3376 0.076 -2 -2 -1 1.6118 0.046 5 7 4 2.2590 0.089 -2 -2 0 9.3747 0.099 5 7 3 2.4356 0.09 -2 -2 1 1.7785 0.044 5 7 2 3.2246 0.164 -2 -2 3 1.6853 0.047 5 7 1 2.8778 0.094 -2 -2 4 6.5649 0.115 5 7 0 3.2251 0.092 -2 -2 5 2.0094 0.046 5 7 -1 2.8464 0.099
218
-2 -2 8 3.2287 0.089 5 7 -2 3.1902 0.124 -2 -2 9 1.2079 0.145 5 7 -3 2.3154 0.069 -2 -1 8 1.2895 0.324 5 7 -4 1.9937 0.125 -2 -1 6 2.9128 0.106 5 7 -5 2.4282 0.07 -2 -1 4 3.2473 0.092 5 6 -4 1.3745 0.068 -2 -1 2 5.9030 0.119 5 6 -2 4.5889 0.11 -2 -1 1 0.7573 0.03 5 6 2 4.5677 0.132 -2 -1 0 4.7776 0.061 5 6 4 1.2696 0.074 -2 -1 -1 0.9100 0.023 5 6 6 2.8829 0.096 -2 -1 -2 6.1208 0.074 5 5 6 1.7956 0.083 -2 -1 -3 0.5378 0.061 5 5 2 3.0174 0.11 -2 -1 -4 3.1048 0.087 5 5 0 1.0053 0.057 -2 -1 -6 2.8746 0.096 5 5 -2 2.7452 0.077 -2 -1 -8 1.4913 0.091 5 5 -6 1.4889 0.088 -2 0 -6 1.9313 0.053 5 4 -8 0.4166 0.292 -2 0 -4 1.0482 0.056 5 4 -5 2.2514 0.056 -2 0 4 1.1171 0.047 5 4 -3 2.5548 0.094 -2 0 6 2.2758 0.046 5 4 -2 1.0526 0.193 -2 1 6 2.9714 0.101 5 4 -1 3.4694 0.13 -2 1 4 2.9246 0.099 5 4 0 1.3413 0.048 -2 1 3 0.7393 0.156 5 4 1 3.6253 0.115 -2 1 -4 0.7533 0.044 5 4 2 1.4583 0.049 -1 2 4 0.7547 0.04 5 4 3 2.5911 0.08 -1 2 -4 0.6476 0.057 5 4 5 2.2404 0.051 -1 1 -7 0.2836 0.158 5 4 7 0.7796 0.151 -1 1 -4 0.7109 0.044 5 3 6 1.0671 0.095 -1 1 -3 0.5207 0.046 5 3 5 1.2502 0.078 -1 1 -2 1.3617 0.067 5 3 4 1.3204 0.057 -1 1 2 1.4458 0.052 5 3 3 2.3195 0.06 -2 0 4 1.1235 0.051 5 3 2 2.5149 0.056 -2 0 6 2.2002 0.054 5 3 1 2.0408 0.059 -2 1 6 2.8707 0.085 5 3 0 1.6629 0.035 -2 1 4 2.8516 0.109 5 3 -1 2.1859 0.046 -2 1 -4 0.4485 0.211 5 3 -2 2.2608 0.046 -1 2 4 0.7441 0.041 5 3 -3 2.1127 0.058 -1 2 -4 0.8193 0.039 5 3 -4 1.1618 0.071 -1 1 -4 0.6760 0.041 5 3 -5 1.0834 0.098 -1 1 -2 1.3189 0.068 5 3 -6 0.4735 0.22 -1 1 2 1.4974 0.061 5 2 -6 3.4505 0.089 -1 1 4 0.7472 0.037 5 2 -4 1.9038 0.062 -1 1 5 0.5536 0.067 5 2 -2 6.4428 0.108 -1 0 5 0.9896 0.041 5 2 -1 0.4711 0.455 -1 0 3 0.8879 0.035 5 2 0 2.2713 0.064 -1 0 1 1.6884 0.052 5 2 2 6.4820 0.101 -1 0 -1 1.8086 0.044 5 2 4 1.6697 0.06 -1 0 -3 0.9480 0.038 6 3 -5 1.0419 0.291 -1 0 -5 0.7291 0.053 6 3 -2 1.1602 0.063 -1 -1 -7 0.5439 0.31 6 3 -1 0.8180 0.072 -1 -1 -6 0.5987 0.087 6 3 0 1.2251 0.053 -1 -1 -4 0.8095 0.035 6 3 2 0.7435 0.306 -1 -1 -2 1.5249 0.047 6 3 3 0.6930 0.332
219
-1 -1 -1 1.0670 0.042 6 4 6 3.3038 0.099 -1 -1 0 1.4619 0.037 6 4 4 2.3695 0.074 -1 -1 1 1.0342 0.044 6 4 2 5.1458 0.144 -1 -1 2 1.3202 0.06 6 4 1 0.6247 0.356 -1 -1 3 0.5735 0.034 6 4 0 3.4619 0.133 -1 -1 4 0.7331 0.037 6 4 -1 1.1515 0.072 -1 -1 5 0.3623 0.307 6 4 -2 5.2979 0.107 -1 -1 6 0.6606 0.083 6 4 -4 2.1386 0.077 -1 -2 7 0.3907 0.45 6 4 -6 3.3430 0.096 -1 -2 6 0.5839 0.231 6 5 -7 1.0075 0.13 -1 -2 4 0.7943 0.042 6 5 -4 1.6475 0.06 -1 -2 2 1.5187 0.065 6 5 -3 0.7557 0.115 -1 -2 1 0.3005 0.029 6 5 0 2.9429 0.081 -1 -2 0 1.5153 0.05 6 5 1 0.3934 0.171 -1 -2 -1 0.2823 0.03 6 5 2 0.3655 0.171 -1 -2 -2 1.5437 0.066 6 5 4 2.0066 0.055 -1 -2 -4 0.9118 0.033 6 6 4 3.1055 0.138 -1 -3 -5 0.7995 0.051 6 6 3 1.3574 0.079 -1 -3 -4 0.7875 0.038 6 6 0 4.6372 0.14 -1 -3 -3 1.2090 0.059 6 6 -3 1.4857 0.07 -1 -3 -2 1.0580 0.034 6 6 -4 3.9307 0.15 -1 -3 0 0.7226 0.027 6 7 0 0.9209 0.092 -1 -3 1 1.3039 0.043 6 8 4 2.0463 0.09 -1 -3 2 1.2090 0.038 6 8 3 1.2595 0.081 -1 -3 3 1.2758 0.034 6 8 2 3.5766 0.18 -1 -3 4 0.7830 0.04 6 8 1 1.3968 0.084 -1 -3 6 0.4735 0.093 6 8 0 2.4324 0.069 -1 -4 6 0.7796 0.219 6 8 -1 1.0194 0.109 -1 -4 3 0.9221 0.034 6 8 -2 3.9173 0.196 0 -3 5 0.8268 0.049 6 8 -3 1.2826 0.263 0 -3 3 1.0269 0.031 7 9 0 0.5983 0.583 0 -3 -3 0.9643 0.03 7 8 0 0.5044 0.176 0 -2 -6 1.4161 0.052 7 8 1 0.9068 0.123 0 -2 -2 2.5644 0.062 7 8 2 0.5252 0.212 0 -2 2 2.5398 0.063 7 7 6 2.6534 0.082 0 -2 6 1.3090 0.096 7 7 5 2.0780 0.077 0 -1 3 1.2585 0.049 7 7 4 1.8430 0.083 -2 0 4 1.1309 0.046 7 7 3 1.9003 0.068 -2 0 6 2.0769 0.076 7 7 2 3.6194 0.213 -2 1 6 2.9368 0.097 7 7 1 2.5806 0.118 -2 1 4 2.8768 0.078 7 7 0 2.3420 0.08 -2 1 -6 0.7235 0.062 7 7 -1 2.8499 0.069 -2 0 4 1.2386 0.064 7 7 -2 3.7717 0.134 -2 0 6 2.1468 0.05 7 7 -3 2.2744 0.074 -2 1 6 2.9240 0.068 7 6 -5 1.2984 0.132 -2 1 -4 2.7387 0.084 7 6 -3 1.0600 0.092 -2 1 4 2.9419 0.085 7 6 -2 1.0428 0.084 -2 1 6 2.9532 0.105 7 6 -1 1.4945 0.061 -1 2 -6 1.0966 0.07 7 6 1 1.3708 0.07 -1 2 -4 3.1059 0.123 7 6 2 0.9254 0.103 -1 2 4 2.8869 0.086 7 6 3 0.9439 0.11
220
-1 1 7 0.9491 0.1 7 6 4 0.9938 0.1 -1 1 6 2.7810 0.067 7 6 5 1.3257 0.089 -1 1 5 2.3693 0.084 7 5 5 2.7447 0.085 -1 1 4 2.9531 0.118 7 5 4 3.3798 0.114 -1 1 3 1.8188 0.07 7 5 3 3.9512 0.128 -1 1 2 5.4284 0.115 7 5 2 2.1698 0.07 -1 1 -2 5.1460 0.177 7 5 1 3.7787 0.179 -1 1 -3 1.9165 0.074 7 5 0 4.4058 0.131 -1 1 -4 2.7889 0.112 7 5 -1 4.1053 0.122 -1 1 -5 2.2187 0.066 7 5 -2 2.0029 0.058 -1 1 -6 2.6099 0.113 7 5 -3 3.9038 0.139 -1 0 -7 0.8133 0.11 7 5 -4 3.3703 0.097 -1 0 -5 3.3302 0.116 7 5 -5 2.7713 0.085 -1 0 -3 3.5233 0.093 7 5 -6 1.0171 0.121 -1 0 -1 6.8917 0.111 7 4 -3 2.4458 0.085 -1 0 1 6.5437 0.165 7 4 -2 1.0619 0.076 -1 0 3 3.5360 0.103 7 4 -1 2.0789 0.08 -1 0 5 3.4410 0.119 7 4 1 2.2095 0.068 -1 0 9 1.4125 0.342 7 4 2 0.9826 0.078 -1 -1 9 1.4147 0.123 7 4 3 2.7736 0.08 -1 -1 8 1.4783 0.085 8 5 -2 1.6266 0.081 -1 -1 6 2.8427 0.081 8 5 0 0.7690 0.368 -1 -1 5 2.4879 0.058 8 5 2 1.5876 0.076 -1 -1 4 2.6541 0.154 8 6 4 0.9819 0.112 -1 -1 3 1.9972 0.051 8 6 2 3.4552 0.149 -1 -1 2 5.3338 0.109 8 6 -2 3.8042 0.167 -1 -1 1 3.9609 0.082 8 6 -3 1.2323 0.098 -1 -1 0 5.7951 0.057 8 7 -3 1.2011 0.098 -1 -1 -1 4.1401 0.057 8 7 -1 1.3075 0.083 -1 -1 -2 5.6695 0.081 8 7 0 1.3799 0.081 -1 -1 -3 2.1355 0.049 8 7 1 1.4069 0.086 -1 -1 -4 3.0423 0.102 8 7 3 1.5351 0.08 -1 -1 -5 2.3448 0.096 8 8 4 3.4658 0.161 -1 -1 -6 3.0269 0.063 8 8 3 0.8548 0.129 -1 -1 -8 1.3849 0.101 8 8 0 4.6041 0.196 -1 -1 -9 1.1434 0.121 8 9 -2 1.1457 0.128 -1 -2 -6 1.1464 0.067 8 9 2 1.4321 0.088 -1 -2 -4 2.9950 0.101 9 9 2 2.0058 0.152 -1 -2 -3 0.5486 0.217 9 9 -2 1.9301 0.107 -1 -2 -2 5.7424 0.08 9 8 -2 1.2176 0.1 -1 -2 -1 0.7199 0.028 9 8 -1 1.1752 0.109 -1 -2 0 5.6073 0.053 9 7 1 1.8934 0.077 -1 -2 2 5.7200 0.11 9 7 0 1.4127 0.087 -1 -2 3 0.5485 0.184 9 7 -2 3.6338 0.141