peat units of three tetrahedra, they do not have thesame orientation in the two structures, and the largecations all lie in a sheet parallel to (101), but do nothave the same distribution in the sheet.

In order to determine whether these differenceswere real, Buerger and Prewitt (1961) collected three-dimensional x-ray intensities for wollastonite and re-fined the structure by least-squares. In addition, theyrefined pectolite using relatively crude intensity dataoriginally obtained by Buerger (1956). The final Rfactors for wollastonite and pectolite, respectively,were 8.9% and 17%. When the structures and x-raydata were interchanged, the wollastonite data couldnot be refined below 26% and the pectolite data notbelow 52%. Therefore, the structures as proposedmust be correct but different.

MINERALOGICAL SOCIETY OF AMERICA, SPECIAL PAPER 1, 1963

INTERNATIONALMINERALOGICALASSOCIATION,PAPERS, THIRD GENERAL MEETING

COMPARISON OF THE CRYSTAL STRUCTURES OF WOLLASTONITE AND PECTOLITE

C. T. PREWITT AND M. J. BUERGER

Cyrstallographic Laboratory, Massachusetts Institute of Technology, Cambridge, Mass.

ABSTRACT

Wollastonite, CaSi03, and pectolite, CaNaHSi30" have similar triclinic cells; because of this and their analogouschemical compositions they have long been regarded as belonging to the same mineral family. An examination of the re-sults of least-squares refinement reveals that although the structures contain similar metasilicate chains, they are not asclosely isotypic as had been supposed. The principal differences are in the location of the large cations between layers ofoxygen atoms parallel to (101) and in the relative orientations of the metasilicate chains.

The structures of both wollastonite and pectolite contain pseudomonoclinic subcells which are joined together on (100)to give an overall symmetry different from that of the subcell. The geometries of these subcells and the possibility of theirbeing joined in different ways are important in explaining the types of twinning which occur in wollastonite and pectolite.

INTRODUCTION

Pectolite and wollastonite belong to the same min-eral family and have distinct but related crystalstructures. Buerger and Prewitt (1961) have shownthat the crystal structures proposed by Buerger(1956) for pectolite and by Mamedov and Belov(1956) for wollastonite are correct. The presentpaper describes in detail the similarities and differ-ences between the two structures and attempts to ex-plain some of the puzzling features of these mineralswhich have been observed in the past.

CONFIRMATION OF THE STRUCTURES

Unit cell information for pectolite, wollastonite,and NaAs03 is given in Table 1. The similarity ofthe triclinic cells (space group pI) and the analogouschemical compositions indicate that these substancesmight have the same structure. A comparison of theresults given by Marnedov and Belov (1956) for wol-lastonite and Liebau (1956) for NaAs03 shows thatthese two structures are identical. If either of these iscompared to the pectolite structure given by Buerger(1956) certain discrepancies are noted. For example,while in both structures the silicate chains have re-

TABLE 1. UNIT CELLS OF WOLLASTONITE, NaAs03,

AND PECTOLITE

WollastoniteCa3Si30,

PectoliteCa,NaHSi30,

a 7.94 A 8.07 A 7.99 Ab 7.32 A 7.44 A 7.04Ac 7.70 A 7.32 A 7.02 Aa 90°02' 90° 90°31'(1 95°22' 91°30' 95°11'I' 103°26' 104° 102°28'

COMPARISON OF STRUCTURES

Figures 1 and 2 are projections along b of the wol-lastonite and pectolite structures, respectively. Co-ordinates for the figures in this paper were givenoriginally by Buerger and Prewitt (1961) and are re-produced in Table 2 with a few changes so that all co-ordinates refer to atoms in or near the same silicatechain. Unless otherwise noted, the origin for thefigures is that of the coordinates of Table 2.

Figures 1 and 2 reveal that the structures aretopologically different. For example, the bends be-tween the superposed Si1 and Si2 tetrahedra and theSi3 tetrahedron are reversed. The large cations, how-ever, occupy approximately the same positions in thetwo structures. One immediately wonders whetherthe misfit is merely a result of identical structuresbeing oriented in different ways. The authors spentsome time in considering this possibility and foundthat the structures can be oriented so that the silicate

293

294 C. T. PREWITT AND M. 1. BUERGER

o o

o

FIG. 1. Projection of the wollastonite structure along b.

o o

csraL 0;-

Lasinr

o

FIG. 2. Projection of the pectolite structure along b. Although the Si1 and Si, tetrahedra should not beexactly superimposed, they are presented this way to simplify the drawing.

COMPARISON OF WOLLASTONITE AND PECTOLITE 295

TABLE 2. ATOM COORDINATES FOR WOLLASTONITE

AND PECTOLITE-

Wollastonite PectoliteAtom ----------

x y z Atom x y z--- ---------- --- -------

Cal .1985 .4228 .7608 Cal .857 .596 .146Ca, .2027 .9293 .7640 Ca, .843 .074 .139cs, .5034 .7505 .5280 Na .552 .265 .344Sil .1852 .3870 .2687 Sil .221 .402 .337Si, .1849 .9545 .2692 Si, .210 .954 .344Si, .3970 .7235 .0560 Si3 .451 .735 .14801 .5709 .7686 .1981 01 .652 .788 .1250, .4008 .7259 -. 1698 O2 .322 .702- .05703 .3037 .4635 .4641 03 .185 .496 .5380, .3017 .9374 .4655 0, .171 .839 .54105 - .0154 .3746 .2657 05 .070 .393 .17106 - .0175 .8681 .2647 06 .053 .896 .17907 .2732 .5118 .0919 07 .396 .533 .27508 .2713 .8717 .0940 08 .402 .906 .2750, .2188 .1784 .2228 0, .260 .182 .381

chains are nearly superposed. This is accomplishedby interchanging the a and c axes and shifting theorigin of one of the structures. Figure 3 shows projec-tions along b of wollastonite and pectolite in whichthe silicate chains are oriented to correspond with oneanother. The y coordinates of the atoms in the re-spective chains are about as close to each other asare the x and z coordinates. The locations of thelarge cations, however, are not similar. In fact, thelarge cations occupy completely different intersticesbetween oxygens when the structures are oriented in

----asinr

C sina

\

PECTOLITE

this way. The structures must then be different eventhough the packing of oxygens is roughly similar.The authors originally thought that this kind of com-parison might be more useful than the conventionalone, but further investigation as reported belowshowed that the conventional orientations should beretained.

PSEUDOMONOCLINIC SYMMETRY

A number of investigators have commented on theunusual features which are observed in x-ray diffrac-tion photographs of wollastonite and pectolite .Among these features are a mirror symmetry be-tween relative even-numbered reciprocal latticelevels normal to b", and the presence of a substructurealong b with a period of b/2 as indicated by the aver-age spot intensity in even-numbered reciprocal-lattice levels normal to b* being greater than in theodd-numbered levels. Ito (1950) discussed these ef-fects and proposed that triclinic wollastonite could beconstructed by starting with a hypothetical mono-clinic cell and shifting successive cells along (100)in increments of ± lb. To this pseudomonoclinic cellhe attributed a symmetry of P2/m or P21/m. Figures4 and 5 show that both wollastonite and pectolite canindeed be so regarded, and that the space group ofthis unit, which is infinite in the band c directionsand one unit cell thick along a, is P2t/m. Liebau(1956) also noticed that NaAs03 can be so regarded.

This shift between successive pseudo monoclinicunits not only determines the triclinic symmetry in

o

asinr

\

WOLLASTONITE

FIG.3. Projections of the pectolite and wollastonite structures along b. The origin and orientation of wollastonite has been changed fromthat of Fig. 1 so that the silicate chains in wollastonite have the same orientation as in pectolite.

296 C. T. PREWITT AJ.VD M. J. BUERGER

FIG. 4. Projection of the wollastonite structure along c. The mirror planes and screw axes are elements of the pseudomonoclinic unit.

pectolite and wollastonite, but also is the key to twin-ning in these minerals and probably will be found tobe significant in other triclinic metasilicates as well.The results of the different shifts which can be madeare discussed in another section of this paper.

It is interesting to note how closely the refinedatom coordinates conform to the monoclinic sym-metry. The coordinates were refined in the spacegroup pI so that all atoms were in the general posi-tion with no restrictions on x, y or z. Table 3 gives thewollastonite and pectolite coordinates transformedto the pseudomonoclinic cell using the cell trans-formation'

Pseudomonoclinic

[1 -i 01Triclinic [0 1 0

001

and adding 0.125 to the transformed y coordinates.For the atoms Ca3, Si3, 01, O2 and 09 in wollasto-

nite, which would be on the mirror plane in P21/m,the y coordinates should be .250 or .750. The verysmall deviations of about .001 (or .007 A) are withinthe expected accuracy of the measurements. Theother atoms which are related by the mirror planesalso show little deviation from the positions theywould occupy if the monoclinic symmetry held. Ifthe space group P21/m is assumed, then the following

1 This transformation is not exact when there is a departure ofa (triclinic) from 900

; a in wollastonite is nearly 900 and departsfrom 900 by only 31' in pectolite.

paired atoms are equivalent and occupy the generalposition:

05,06 07,080,,0,

Ca3, Si3, 01, O2 and 09 are each in the special posi-tions m.

Although the atoms in pectolite have the samepseudoequipoint distributions as do those in wol-lastonite, the refined coordinates for the pectoliteatoms do not conform as closely to the monoclinicsymmetry. For example, the y coordinate of 09 is .242as compared with .250 if 09 were on the mirror plane.This is a deviation of about 0.06 A. A detailed refine-ment of pectolite now being carried out in this labo-ratory has shown that these deviations in the pecto-lite coordinates are real.

The pseudosymmetry gives rise to the strong sub-structure along b, since all the atoms except 07 and08 in both wollastonite and pectolite and Na in pecto-lite have x and z coordinates similar to another atomof the same type located tb away. It is interestingthat Ca3 and its inversion equivalent in wollastonitehave similar x and z coordinates and are approxi-mately th apart, while Na and its inversion equiv-alent in pectolite do not have similar x and z co-ordinates even though they are separated by th. Thisis one of the major differences between these minerals.

The similarities and differences between wollstoniteand pectolite brought out in this section seem to bemore useful in describing the structures than dothose in the last section where a special orientation ofone of the structures was used to show how~the sili-

COMPARISON OF WOLLASTONITE AND PECTOLITE 297

\

DISTRIBUTIONOF Ca ANDNa

The main difference in the wollastonite and pecto-lite structures is in the way the large cations are dis-tributed in the sheet parallel to (101). Figures 6 and7 show parts of the wollastonite and pectolite struc-tures projected onto (101) of the pseudomonocliniccell. Only the silicate chains on the upper side of (101)are shown.

The Ca in wollastonite are arranged in a nearlyplanar hexagonal pattern which is separated intobands 3 Ca columns wide running in the b directionand parallel to the silicate chains. The Na and Ca inpectolite are also arranged in a hexagonal patternwith bands consisting of 2 Ca columns bounded oneither side by a half-filled Na column. Because eachof these bands is translated by tb with respect toneighboring bands, every other Na in a particularNa column is missing. This is necessary becauseotherwise the Na-Na distances between neighboringNa columns would be much too small.

FIG. 5. Projection of pectolite along c corresponding to that of wollastonite of Fig. 4. Note that the orien-tations of the silicate chains are different in the two structures.

cate chains could be superposed. Because of this, theauthors feel that the conventional orientation shouldbe retained and that while the other aspect is interest-ing, it will not be useful except, for example, in aclassification of metasilicates based on oxygen pack-mg.

TABLE 3. ATOM COORDINATES OF WOLLASTONITE AND

PECTOLITE REFERRED TO A PSEUDO MONOCLINIC

CELL P2I/m (ORIGIN AT I)

Pseudo- Wollastonite Pectolite

equipointAtom x )' z Atom x y a

~-------- ---- __ --- _-- ---------4f 2Cal .1985 .4982 .7608 2eal .857 .507 .146

2e., .2027 .0038 .7440 2e., .843 -.002 .139

2e 2ea, .5034 .7496 .5280 2Na .552 .252 .344

4f 2Sil .1852 .4657 .2687 2Si, .221 .472 .3372Si, .1849 .0333 .2692 2Si, .210 1. 026 .344

2c 2Si, .3970 .7492 .0560 2Si, .451 .747 .148

2e 20, .5709 .7509 .1981 201 .652 .750 .125

2e 20, .4008 .7507 -.1698 20, .322 .746 -.057

4f 20, .3037 .5126 .4641 20, .185 .575 .53820. . 3017 .4870 .4655 20 • .171 .921 .541

41 20, .0039 .5035 .2657 20, .070 .500 .17520, - 0044 .9975 .2647 206 .053 1.008 .179

4f 207 .2732 .5685 .0919 207 .396 .559 .27520, .2713 .9287 .0940 20, [.402 .930 .275

2, 20, .2188 .2487 .2228 20, .260 .242 .381

INTERATOMICDISTANCES AND INTERBOND ANGLES

Interatomic distances and angles given in Table 4were calculated for wollastonite and pectolite using acomputer program written by Busing and Levy(1959). The Si-O distances in both wollastonite andpectolite show a considerable variation, the lengthsapparently being determined by the coordinations ofthe oxygens. Table 5 gives the coordination and dis-

298 C. T. PREWITT AND M. J. BUERGER

FIG. 6. Structure of wollastonite projected onto (101) of four adjacent pseudo monoclinic cells. Only the silicate chains on the near side of(101) are shown. The axial directions are for the pseudomonoclinic cell.

tances of cations around the oxygens. It can be seenthat, for 01 through 06 in wollastonite, the Si-O dis-tances are longer when an oxygen is coordinated by3 Ca than when coordinated by 2 Ca. The situationis different for 07 through 09 because these oxygensare coordinated by 2 Si as well as Ca, showing thatPauling's electrostatic valence rule does not hold.The Si-O distances here are larger than in either ofthe examples above. The coordination of oxygens inwollastonite can thus be divided into three classes:

It is felt that an analysis of the pectolite inter-atomic distances before a detailed refinement is com-pleted would be premature, particularly since therange in Si-O distances is so great, varying from 1.58A for Si2-09 to 1.75 A for Si2-Os. This may be a realvariation, however, since Morimoto et al. (1960) re-ported a range of 1.58-1. 74 A for Si-O in clinoensta-tite.

Cal and Ca2 in wollastonite are octahedrally co-ordinated by six oxygen atoms at average distances of2.383A for Cal and 2.388A for Ca2. Ca3 is surroundedby six oxygen atoms at an average distance of 2.390Aand by an additional oxygen (09) at 2.642A. The

1. Oxygen (01, O2, 03, 0,) coordinated by 1 Si and 3 Ca;2. Oxygen (05, 06) coordinated by 1 Si and 2 Ca;3. Oxygen (07, 08, 0,) coordinated by 2 Si and 1 Ca.

FIG. 7. Structure of pectolite projected onto (101) of the four adjacent pseudomonoclinic cells. Only the silicate chains on the nearside of (101) are shown. The most likely location for the hydrogen bond is indicated by the line between the labeled 03 and04•

COMPARISON OF WOLLASTONITE AND PECTOLITE 299

TABLE4. INTERATOMICDISTANCESANDINTERBONDANGLESIN WOLLASTONITEANDPECTOLITE

Interatomic Distances

Atoms Wollastonite Pectolite-------- ---------- ---------

Sil 03 1.618 A 1.63 A05 1. 572 1.5907 1.65, 1.600, 1.647 1.67o., 1.62, 1.62

Si, 0, 1.61, 1.6306 1.581 1.6108 1.650 1.750, 1.637 1.58o., 1.621 1.64

Si3 01 1.59, 1.59O2 1.59, 1.6807 1.66. 1.6808 1.67, 1.63o.. 1.63, 1.65

Cal 01 2.548 2.33O2 2.437 2.3103 2.32, 2.3505 2.302 2.3505' 2.4406 2.272 2.3407 2.4lzo., 2.38, 2.35

Ca, 01 2.501 2.3002 2.421 2.250, 2.316 2.3205 2.368 2.5106 2.316 2.3506' - 2.4508 2.406

o.. 2.388 2.36

Ca, 01 2.43,O2 2.349

03 2.429

0/ 2.335

0, 2.44,0/ 2.34,0, 2.642o., 2.390 (excluding

Ca3-0,)

Na O2 2.3203 2.460, 2.5407 2.5007' 2.9708 2.5708' 2.970, 2.32o., 2.45 (excluding

Na-O,',Na-08')

Interatomic Distances

Atoms

3.11

Wollastonite Pectolite

Si2

Si3

3.165

3.1163.103.04

Si2 Si3 3.125

Interbond Angles

Sil-O,-Si,Si2-08-Si,Si,-07-Sil

PectoliteWollastonite

Ca-O sheet is similar to a brucite sheet separated intoslabs running along b and distorted by the presenceof 09•

The coordination of Cal and Ca2 in pectolite issimilar to that of Cal and Ca2 in wollastonite with anaverage Cal-O distance of 2.35 A and an average Ca2-o distance of 2.36 A. Na is surrounded by 6 oxygenatoms at an average distance of 2.45 A and twofurther oxygen atoms, both at 2.97 A.

The most probable location for the hydrogen bondin pectolite is between 03 and 04• These atoms areseparated by 2.44 A which is short even for a hydro-gen bond. This is represented by a line betweenthe labelled 03 and 04 in Fig. 7. This separation ismuch less than that between similar atoms in the wol-lastonite chain as seen in Fig. 6. Buerger (1956)attributed the presence of a shorter b axis in pectolitethan in wollastonite to the hydrogen bond.

In both structures, the silicon-oxygen-silicon angleshave the same distribution, with Sil-09-Si2 beinglarger than Si2-Os-Si3 and Si3-07-Si1, which are ap-proximately equal. This difference results from thesomewhat abnormal location of 09 in the oxygensheet.

TWINNING

One of the most interesting aspects of the pectoliteand wollastonite structures is the way in whichtwinning can occur. Mention has already been madeof the way in which pseudo monoclinic sub cells arefitted together to give a triclinic structure. This isshown schematically in Fig. Sb. It is also possible toreverse the shift between successive pseudo mono-clinic sub cells to give the sequence shown in Fig. Sa,which corresponds to a twinned structure. If, how-ever, the shift is reversed in each successive cell, theeffect is as shown in Fig. Sc. This latter sequence was

300 C. T. PREWITT AND M. J. BUERGER

TABLE 5. COORDINATION OF OXYGENS IN WOLLASTONITEAND PECTOLITE

Wollastonite Pectolite

AtomsInteratomicDistances

O2 Si3

CalCa,cs,

03 SilCa,Ca,Ca,'

InteratomicDistances

1.59, A2.5482.316

2.43,

1.5992.437

2.36,2.34,

1.6182.32,2.4292.335

1.61,2.4212.44,

Caa' I 2.34,

1.5812.2722.501

1.65,1.665

2.4b

1.650

1.673

2.406

1.647

1.6372.64,

Atoms

05 SilCalCal'Ca2

07 Silsr,NaNa'

08 Si2Si3

NaNa'

Ca/ 2.45

1.59 A2.332.30

1.682.312.252.32

1.632.352.46

1.632.322.54

1.592.352.442.51

1.612.342.35

1.601.682.50

1.751.632.57

1.671.582.39

suggested by Ito (1950) for parawollastonite' whichwas originally distinguished from wollastonite byPeacock (1935a).

1The Commission on Mineral Data recommended at the meet-ing of the International Mineralogical Association in Washington,D. C., April 17-20, 1962, that wollastonite and parawollasto-nite be redesignated wollastonite-1T and wollastonite-2M, re-spectively.

1 !l[tCj]l! 1

TWINNED

TRICLINIC

I ! ! ! MONOCLINIC

FIG. 8a (top), b (middle) and c (bottom). Three ways in whichthe pseudomonoclinic unit can be stacked on (100) to producedifferent overall diffraction effects.

Peacock (1935b) found that the twin law in pecto-lite is such that b is the twin axis with (100) as thecomposition plane. This is eonsistent with Fig. Sasince a rotation of lS0° around b of one of thepseudomonoclinic units would be approximatelyequivalent to translating it by tb along a neighboringcell. This is not exactly true unless the cell is actuallymonoclinic, thus making a (triclinic) equal to 90°.The authors have taken x-ray photographs of severaltwinned pectolite crystals from various localities andhave found that the diffraction effects substantiatethe above ideas. Fig. 9a represents part of the com-posite reciprocal lattice of twinned pectolite. Whenthe members of the twin are present in equal amount,oscillating-crystal photographs around b, as well asc-axis precession photographs, show an apparentmirror plane normal to b. Close examination of thefilms reveals, however, that the registry of super-posed spots is not perfect and that the registry isslightly different in different specimens.

If the pseudo monoclinic cells are joined as in Fig.Sc, the para.wollastonite structure is formed havingan overall monoclinic symmetry with a doubling ofthe cell along a. The symmetry of this monocliniccell should be P2t/ a with extra centers of symmetry,not required by the space group," being present. In anattempt to refine the structure of para wollastonite,

'Tolliday (1958) gives the systematic absences in the para-wollastonite diffraction pattern as: for hkl, 2h+k=4n+2, and forOkO as k=2n+1.

COMPARISON OF WOLLASTONITE AND PECTOLITE 301

b'

•TWINNED TRICLINIC MONOCLINIC

FIG. 9a (left), 9b (middle) and 9c (right). Reciprocal lattices cor-responding to the geometries shown in Figs. 8a, 8b and 8c.

however, Tolliday (195S) found that the structurecould not be refined using the centrosymmetric spacegroup P2t! a and that when the non-centrosymmetricspace group P2l was assumed, the refinement pro-ceeded satisfactorily. Since no coordinates, structurefactors or R factors were published, the validity ofthis assumption cannot be evaluated. This is an ex-tremely important point in the crystal chemistry ofCa Sif), and one which should be resolved.

One of the interesting features of Figs. 9a, 9b and9c is that the reciprocal-lattice levels with k even areidentical (when a = 90°) and that the differences be-tween triclinic, monoclinic and twinned compositereciprocal lattices occur in only the odd levels. It issimpler for wollastonite than for pectolite to alternateto form the para wollastonite type because a in wol-lastonite is 90° (within experimental error) and be-cause the symmetry of the repeating unit in wollasto-nite is nearly monoclinic, i.e., the Si, and Si2 tetra-hedra, as well as Cal and Ca2, are symmetrically equiv-alent. The authors examined several wollastonitespecimens from the Monte Somma, Italy, Csiklova,Romania, and Crestmore, California, localities be-fore finding one which gave a para wollastonite dif-fraction pattern." Continuous radiation streaks alongreciprocal lattice rows parallel to a* were observed inthe b-axis Weissenberg photographs with k odd forthe monoclinic as well as several triclinic specimens.This effect was interpreted by Jeffrey (1953) as atype of disorder due to the presence of regions of wol-lastonite and para wollastonite, but it could also bethought of as an irregular sequence of pseudornono-clinic subcells.

Peacock (1935a) was unable to find any twinnedtriclinic wollastonite in the material available tohim. Spencer (1903), however, reported a twinnedwollastonite crystal from Chiapas, Mexico, which

3 The parawollastonite crystal (locality: Crestmore, California)was supplied by Professor A. Pabst from a specimen, 138-80, inthe University of California collection.

Q'

would presumably give a diffraction pattern similarto our twinned pectolite. It is possible that some ofthe material reported in the literature as orderedparawollastonite is actually twinned wollastonite.One could be misled by diffraction photographs if themembers of the twin were present in equal amounts.

One point which should be brought out here is thatthe way in which these pseudomonoclinic units fittogether results in what Ito (1950) called "space-group twinning" and "structure twinning." The"space-group twinning" is seen in the joining ofpseudo monoclinic cells to give an overall triclinic or adifferent monoclinic symmetry, while "structuretwinning" corresponds to our twinned pectolite.Dornberger-Schiff (1956) has developed a generalclassification of order-disorder structures which in-cludes the "space-group twinning" concept.

CONCLUSIONS

It has been established that wollastonite and pecto-lite have many structural similarities but yet mustbe classified as having different structures. Whetherthe pseudo monoclinic unit found in both wollastoniteand peetolite will be of significance in an overallclassification of the triclinie metasilicates will dependon the results of structural investigation of such min-erals as bustamite, rhodonite and pyroxmangite.This pseudo monoclinic unit at present appears to beimportant in determining the relations betweendifferent modifications of a particular mineral in thewollastonite series. Its departure from actual mono-clinic symmetry may also be a controlling factor indetermining what forms of a particular triclinicmetasilicate can occur. Certainly, any study of thestability relations of wollastonite and parawollasto-nite would have to be concerned with the details ofthe structures to a greater extent than is usual in suchinvestigations, because the difference in energy be-tween the two structures must be quite small.

ACKNOWLEDGMENTS

The authors wish to express thanks to ProfessorClifford Frondel and Dr. Alden Carpenter of HarvardUniversity, Professor Adolf Pabst of the Universityof California, and Dr. George Switzer of the U. S.National Museum for supplying much of the materialused in this investigation, and to Donald R. Peacorfor many helpful discussions. This work was sup-ported by the National Science Foundation. Thecomputations were carried out at the M.I.T. Com-putation Center.

302 C. T. PREWITT AND M. J. BUERGER

BUERGER,M. J. (1956) The determination of the crystal structureof pectolite, Ca,NaHSi,09. Zeit. Krist. 108, 248-261.

--- AND C. T. PREWITT (1961) The crystal structures ofwollastonite and pectolite. Proc. Nat. Acad. Sci. 47, 1884-1888.

BUSING,WILLIAMR. ANDHENRI A. LEVY (1959) A crystallo-graphic function and error program for the IBM 704. Oak RidgeNatl. Lab. Central Files No. 59-12-3. Oak Ridge, Tenn. 1-95.

COLLINS,H. F. (1903) Notes on the wollastonite rock-mass andit associated minerals, of the Santa Fe Mine, State of Chiapas,Mexico. Mineral. Mag. 13,356-362.

DORNBERGER-SCHIFF,K. (1956) On order-disorder structures(OD-structures). Acta Cryst. 9, 593-601.

ITo, T. (1950) X-ray Studies on Polymorphism. Maruzen, Tokyo,93-110.

JEFFERY,J. W. (1953) Unusual diffraction effects from a crystal

REFERENCES

of wollastonite, Acta Cryst. 6, 821-825.LIEBAU,FRIEDRICH(1956) Uber die Kristallstruktur des Natrium-

polyarsenats, (NaAs03)x. Acta Cryst. 9, 811-817.MAMEDOV,K. S. ANDN. V. BELOV(1956) Crystal structure of

wollastonite. Dokl. Akad. Nauk. SSSR, 107,463-466.MORIMOTO,N., D. E. ApPLEMANANDH. T. EVANS(1960) The

crystal structures of clinoenstatite and pigeonite. Zeit. Krist.114, 120-147.

PEACOCK,M. A. (1935a) On wollastonite and parawollastonite.Am. Jour. Sci. 30,495-529.

-- (1935b) On pectolite. Zeit. Krist. 90, 97-111.SPENCER,L. J. (1903) see paper by Collins, H. F.TOLLIDAY,JOAN (1958) Crystal structure of (1-wollastonite.

Nature, 182, 1012-1013.

DISCUSSION

HANSADLER(Washington, D. C.): Why do you think the hydro-gen bonding occurs within the chains rather than between thechains in pectolite?

AUTHORS'REPLY:The unusually short oxygen-oxygen distance of2.44 A is taken as evidence of the location of hydrogen between03 and 0,. In recent work with new data, we found an anomalyin three-dimensional difference maps which would correspond tothis hydrogen location.

J. D. H. DONNAY:(Baltimore, Md.): Does the wollastonite struc-

ture satisfactorily account for the cleavages parallel to the b axis?The cleavages were redetermined by Peacock.

AUTHORS'REPLY:Certainly the nature of the silicate chains doesaccount for the fact that the good cleavages are parallel to the baxis in both wollastonite and pectolite. Peacock lists five cleav-ages for wollastonite, (100), (102), (001), (101), and (101), withthe first three being perfect cleavages. While these can be qualita-tively justified in an examination of the structure, no work hasbeen done with regard to proving that these are the most likelycleavages.