university of arizonazeitschrift fiir kristallographie, bd. 114, s.321-342 (1960)...

Zeitschrift fiir Kristallographie, Bd. 114, S. 321-342 (1960)

The crystal structure of meyerhofferite,

CaBaOa(OH)s .H20 *

By C. L. CHRIST and JOAN R. CLARK

U.S. Geological Survey, Washington, D.C.

With 2 figures

(Received April 14, 1960)

Auszug

Meyerhofferit, CaBaOa(OH).. H20 ist trikIin, in der Raumgruppe PI mit

a = 6,63, b = 8,35, c = 6,46 A (samtlich ::I:: 0,015 A), IX = 90046', f3 = 101 ° 59',y = 86°55' (samtlich::l:: 5'), Z = 2; Dichte: berechnet 2,125, gemessen 2,120.Die mit Hilfe der statistischenMethode von HAUPTMAN und KARLE aus 4193Inter-ferenzen berechneten Strukturfaktorvorzeichen lieJ3en die Aufstellung einerStruktur zu, deren Parameter anschlieJ3end durch mehrfache Elektronendichte-Projektionen und mittels der Methode der kIeinsten Quadrate verfeinert wurden.Fiir die endgiiltige Struktur ist der restliche Diskrepanzfaktor 0,14 aus 2678 In-terferenzen mit JFhk11 > O.

Meyerhofferit enthalt Polyionen [BaOa(OH)o] aus zwei B-O-Tetraedern undeinem B-O-Dreieck, die durch gemeinsame Sauerstoffionen ringformig ver-bunden sind. Die Polyion-InseIn sind miteinander durch Ca-O-Bindungen zuZickzackstreifen parallel [001] verkniipft. Diese Streifen wechseIn mit Wasser-molekiilen ab, mit denen sie iiber ein Netzwerk von Wasserstoffbindungenzusammenhangen. Die Struktur ist im Einklang mit der beobachteten Spaltbar-keit.

Abstract

Meyerhofferite, CaBaOa(OH).. H20, is triclinic PI, a = 6.63, b = 8.35,c = 6.46 A (all ::I:: 0.015 A), IX = 90046', f3 = 101059', y = 86055' (all ::I:: 05'),

Z = 2, density (g. cm-a): calc. 2.125, obs. 2.120. Signs for the observed reflec-tions, calculated by the statistical method of HAUPTMAN and KARLE, using4193 three-dimensional data, permitted the establishment of a trial structurewhich was refined by successive electron-density projections and least-squaresanalysis. For the final structure, the residual factor is 0.14 for 2678 terms with

IFhk11> O. Meyerhofferite contains the polyion [BaOa(OH).]-2 consisting of twoboron-oxygen tetrahedra and a boron-oxygen triangle linked at corners to form

* Studies of borate minerals (IX). Publication authorized by the Director,U.S. Geological Survey.

z. Kristallogr. Ed. 114, 5/6 21

322 C. L. CHRIST and JOAN R. CLARK

a ring. The insular polyions are linked together by calcium-oxygen bonds toform zigzag strings along [001]; the strings and the water molecule are in turnlinked by a network of hydrogen bonds. The structure is in good accord with theobserved cleavage.

Introduction

In the series 2CaO. 3B203 . xH20, meyerhofferite has x = 7;other known members of the series are colemanite, with x = 5; asynthetic compound, with x = 9; and inyoite, with x = 13. As partof a systematic investigation of the crystal structures of borateminerals, the crystal structure of each of the members of this series hasbeen determined. Colemanite was described by CHRIST, CLARK, andEVANS (1958), a preliminary note has appeared on meyerhofferite(CHRIST and CLARK, 1956), the synthetic compound was described byCLARKand CHRIST (1959), and inyoite was reported by CLARK (1959).The present paper presents the detailed results of the structureinvestigation of meyerhofferite; the phase determination which ledto the solution of the crystal structure is described in detail in anaccompanying paper (CLARK and CHRIST, 1960).

Experimental work

Crystal description, space group, and unit-cell dimensions

The crystals of meyerhofferite used in this study are synthetic andwere grown by W. T. SCHALLER, U.S. Geological Survey, on ulexitefragments placed in water and held at 70-80°C for approximately sixmonths (CHRIST, 1953). X-ray powder data and a description of themorphology, together with the cell constants originally obtained bySWITZER (PALACHE, 1938) are given by CHRIST (1953). Subsequently,x-ray precession patterns were taken with Zr-filtered Mo radiation on aquartz-calibrated precession camera. Film measurements were cor-rected for both horizontal and vertical film shrinkage to obtain thecrystallographic data given in CHRIST and CLARK (1956). These dataare repeated here in Table 1, together with the reciprocal cell elements,the projection elements, and the direct and reciprocal Cartesianmatrices.

Intensity measurements

For the intensity measurements multiple-film Weissenberg patternswere prepared using chiefly Zr-filtered Mo radiation; some small-anglereflections were obtained with Ni-filtered Cu radiation. For the Mo

Cartesian matrices* :

VI = 0.05214 v2 = 0.99855

6.485 0.435

6J62I

Direct matrix: 0 8.340 (in A)

- 1.377 - 0.112

0.1542 0 0.0329Reciprocal matrix: - 0.0080 0.1199 0.0004 (in A-I)

0 0 0.1548

Crystal structure of meyerhofferite, CaBaOa(OH)ij . H20 323

Table 1. Crystallographic data for meyerhofferite

Triclinic, space group PI - C} , Z = 2 [CaBaOa(OHh . H20]

Direct-cell elements:

a = 6.630 Ab = 8.352

C = 6.462(all ::!: 0.015 A)

cc = 90°46'{1 = 10P 59'y = 86°55'(all ::!: 05')

a:b:c = 0.794: 1 :0.774

(AMoK", = 0.7107 A; ACuK'" = 1.5418 A)

Volume = 349.5 Aa Density (g.cm-a), calc. 2.125, obs.[SCHALLER (1916) for the mineral]2.120

Reciprocal-cell elements:

a* = 0.1544 A-I

b* = 0.1199

c* = 0.1582

cx* = 89° 52'{1* = 78°02'y* = 92° 59'

po:qo:ro = 0.976:0.758: 1

Projection elements:

x' = 0.2124oy; = 0.0024

p; = 0.9977q~ = 0.7748

* Values calculated from direct- and reciprocal-cell elements using equationsgiven by EVANS (1948).

patterns three films interleaved with 0.0005 in. Ni foil were used foreach exposure. Patterns about [001] were taken for each level up tohk9, and the Okl, hOl and hll levels were also recorded. Exposuretimes were approximately 70 hours at 50 kV and 20 ma for each level,and, as necessary, short exposures of the order of 2-4 hours were also

21*


made in order to bring the stronger reflections into the range ofmeasurement. Intensities were estimated visually by comparison witha standard spot strip of intensities, prepared from the same meyer-hofferite crystal used for the other patterns. Controlled exposures onthe standard strip were made so that the intensity of the nth spot isgiven by In = Io(2t/2, where 10 corresponds to a barely perceptible

blackening of the film. In the reciprocal sphere of radius 8 = (sin ())J).

= 0.9 A-I there are 4342 independent reflections; 2678 of these hadobservable intensities, 1515 had intensities below the threshold ofobservation and were assigned the value zero, and 149 reflections, allwith 8 > 0.8 A-I, were not recorded and were omitted from thecompilation of data.

The equi-inclination Weissenberg instrument used for this studycovered a 2000 traverse at one setting, so that two settings wererequired for each upper level in order to record the entire 3600 range.Weissenberg-instrument geometry for upper-level films is such thatdistortion occurs in the recording of reflections, some being contractedand some, extended. Systematic differences in intensity readings aretherefore inevitable. In order to eliminate the systematic errors,comparison was made of different readings for the same reflectionwhich had registered on a given level with each type of distortion.The comparison was carried out for as many reflections as possible oneach level, and an average linear scale factor relating readings forcontracted and extended reflections was found. This scale factor wasthen multiplied into readings for the extended reflections in order toplace all readings on approximately the same scale.

The estimated intensities were corrected for Lorentz and po-larization factors to obtain the F~k/S. For this correction the 1JLpfactor was calculated for each reciprocal lattice point, as a function ofits cylindrical coordinates, by punched-card methods. Small andnearly equant crystals, about 0.2 mm on edge, were used to mini-mize absorption effects, but no absorption corrections were made.The F~k/S from various films were all put on the same relative scaleby the use of appropriate film factors. Through the use of the triple-film technique, together with short and long exposures, a rangeof intensities from 1 to 8000 and of F~kl from 1 to about 800 wasobtained*.

* The ranges of 1 to 10,000 and 1 to 3,000 referred to as ranges of Fik! inprevious publications by the authors on colemanite, inyoite and CaB303(OH).. 2H20 are actually ranges of intensities.

Crystal structure of meyerhofferite, CaBaOa(OH)s . H20 325

Other considerations

In preparation for application of the Hauptman-Karle phase-determination procedures to the meyerhofferite data, a K(s) curve(KARLE and HAUPTMAN, 1953) was prepared for meyerhofferite(CLARKand CHRIST, 1960). Initially the factor [K(O)]'/' was used toplace the data on an approximate absolute scale. At all later stages ofthe study, observed and calculated structure factors were related byuse of the scaling constant k, where kE/Fol = EIFel-

Refinement of the projection data was carried out with an averageisotropic temperature factor, determined by the method of WILSON(1942). Maxima on the electron-density projections were located by themethod of BOOTH (1948). Refinement of the three-dimensional datawas carried out using one-fifth of the 2678 data that have /Fol > 0,selected by arranging the terms in order of increasing s and takingevery fifth one. This portion of the data was given eleven cycles ofleast-squares refinement on a Burroughs 205 digital computer with aprogram developed by D. E. ApPLEMAN and E. MONASTERSKI, U.S.Geological Survey. Non-diagonal terms were neglected in the solutionof the normal equations, except for those terms involving both thetemperature and scale factors. Atomic scattering curves were used asfollows: for boron, the BO curve of IBERS (1957), for all oxygen atoms,the 00 curve of BERGHUIS et al. (1955), and for calcium, a curve con-structed by plotting the BERGHUIS et al. values for CaD for (sin ())/J..;:::: 0.3 A-I and smoothing in to t = 18 at (sin ())/J.. = o.

Determination and refinement of the structure

The structural problem consists in determining the coordinates forone calcium, three boron, and nine oxygen atoms (including OH-and H20) in the positions 2(i) of space group PI (Internat. Tables,1952). Direct determination of the signs of 2303 ofthe 2678 terms with

lFol > 0 was made with Hauptman-Karle statistical procedures(CLARK and CHRIST, 1960). The projection data with known signs

(FhkO' FhOl' Fokl) were then used to calculate the three electron-density projections, each taken on a plane normal to a principal crys-tallographic axis. One of these, (!y(x, z), was shown in the preliminarynote (Fig.1, CHRIST and CLARK, 1956). The three maps consideredtogether with a ball model were readily interpreted, and from positionsof peak maxima, atomic coordinates were assigned to all thirteen atomsin the asymmetric unit (Table 2, column 1). From structure factorsbased on these coordinates signs were obtained for over 90% of the


Table 2. Atomic positional parameters and temperature coefficients for meyerhofferite

AtomI

Parameter 2 Stage of refinement 1

(1) (2)I

(3) (4)

Ca x 0.014 0.010 0.010 0.010Y 0.377 0.377 0.377 0.377z 0.243 0.243 0.244 0.244B 0.75

01 x 0.410 0.407 0.406 0.406Y 0.732 0.734 0.733 0.732z 0.313 0.327 0.331 0.331B 0.99

02(OH) x 0.419 0.422 0.423 0.423Y 0.890 0.889 0.887 0.888z 0.660 0.651 0.643 0.643B 1.36

03 x 0.118 0.115 0.116 0.116Y 0.782 0.776 0.776 0.776z 0.500 0.502 0.495 0.493B 1.09

04(OH) x 0.340 0.339 0.336 0.335Y 0.461 0.461 0.461 0.461z 0.206 0.211 0.203 0.201B 1.15

Os x 0.058 0.058 0.062 0.063Y 0.644 0.642 0.650 0.652z 0.148 0.145 0.150 0.151B 0.70

Oe(OH) x 0.173 0.165 0.167 0.167Y 0.370 0.374 0.378 0.378z 0.615 0.615 0.617 0.617B 1.02

07(H2O) x 0.157 0.132 0.148 0.151Y 0.108 0.104 0.109 0.109z 0.202 0.211 0.216 0.217B 1.55

Os(OH) x 0.146 0.145 0.151 0.151Y 0.117 0.126 0.123 0.123z 0.792 0.797 0.800 0.800B 1.19

Ou(OH) x 0.329 0.334 0.330 0.330Y 0.672 0.673 0.668 0.668z 0.955 0.955 0.956 0.957B 1.08

Crystal structure of meyerhofferite, CaBaOa(OH)5 . H2O 327

Table 2 (continued)

Atom parameter2!Stage of refinement 1

(1) (2)I

(3) (4)

Bl x 0.312 0.318 0.322 0.321

Y 0.798 0.792 0.798 0.798z 0.489 0.497 0.487 0.485B 0.86

B2 x 0.308 0.308 0.290 0.285

Y 0.642 0.642 0.634 0.634z 0.183 0.183 0.173 0.167B 0.74

B3 x 0.050 0.030 0.034 0.037

Y 0.233 0.278 0.269 0.267z 0.710 0.683 0.695 0.698B 0.78

Residual, RhkO 0.19 0.18hOl 0.19 0.16Okl 0.21 0.16hkl 0.1473 0.1454

Scale factor, khkO 2.5 2.5hOl 2.4 2.4Okl 2.6 2.7hkl 2.93 2.734

Average isot~opic B

hkO 0.66 0.66hOl 1.00 1.00Okl 0.94 0.94hkl 0.873

1 Stages of refinement: (1) from peak positions on electron-density projec-tions calculated with signs determined by Hauptman-Karle procedures;(2) from peak positions of second set of electron-density projections; (3) at end

of 5 cycles of least-squares refinement for one-fifth of three-dimensional data,average isotropic B; (4) final parameters at end of 11 cycles of least-squaresrefinement for one-fifth of three-dimensional data, individual isotropic B's.

2 x, y, z in cycles; B in A2; standard errors in B: EOa = 0.03, EO = 0.17

BE = 0.17 A~.3 For 535 terms with IF hkZI > O.4 For 2678 terms with IFhkZI > O.

328 C. L. CHRISTand JOAN R. CLARK

Table3. Oomparison of observed and calculated structure factors for hkl data of meverlwUerite. CalculatedFhldare based ou the atomic parameters of Table 2. column 4

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59

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Crystal structure of meyerhofferite, CaBsOs(OH)5 H20

P.

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,

"12

6,

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,

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>0

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J

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=16-"_12

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,

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->7-.)

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7,

-57-76

H'-'J>9

=I~>9

-326

35-:

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"_b,

o-, ,.,J)

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oo

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5

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b,

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Table 3 (cordinued)

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),

=Z-7-,=16-"_12

4125

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-),i;9

->0-H4116>0:761J,.o-.

-J-,5_6

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:76,,;.9-,

=~

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76

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31'.0>}12

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n

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n>02565

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9,76

11,

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=16}E876,,J,o-.

-J-,,_6: ~-,J7 ,

6(),,o-,

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J

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"-5,,-9,-,,,-J7

5

= ~-,-J5,

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J

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n75

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=~-,

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":761J,

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329

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J_6o

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->0

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,,6

n

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"-25

9,_6>0

= ~

"",


Table3 (continued)

"1'.1

,1'.1

,1'.1

"1'.1

"1'.1

"1',1

2-1) J , 288 10 n .'" ~I7 ."

"o ~2 J9 J7

()'5 6 .7

.".6 -9 -, u u . J . , .6 .5,

n' . 289 - . 10 ., -5, , . : ~,

"_6 7 ,

:, ., ., . 7 ,

."u 9 , ., .5 5 _7

"n 0 -53

":16

u

"

., 5 6 7."

"

., -, -." "

.,: .n u , .. , .. .9 -1

., -10 J6 .u -,'9

"J 0 5 -10

,."

. 3." ~: -"

,

." ", , ,

"10 -u -, -,

"0 u 7 6

.5 . . -10 J 5" 3: . '" -0 -," "

10 -I~" "

0 ., , ,: -3 -,

-110 9

-. u , 7 . 7 5 5 .7 . .,u u ., 0 _u

"7 .. .. ." "

7 -u I.u U

=~-; .. .U ~;

, .0 .,"

. ," ", ., . .,

-~~ 1 9 ,-"

.5 . 1 .,0 , . -5 7 5 ,5 .. -5 . _u ." u . J. . ." "

.6 5 5 -. .. 7 ; , 5 -" _1 , , u ,-. .7 .u

"-5

".6 5 . ::~

, .7 I:l " "

-. , -, . . -5 5 . , 00 I-l~ . ': 10 . 5 : ~"

0" "

0'"

, 7 0." "

,5

"u .5 -,

''9 "

OJ .. 9 -, ->7"

.,." u 5 - 6 -9 -OJ U -, .,

"5 ,

-, , 7,7 , , .5

-"6 6 -3

-:u u 9 .5 , ,

-. 10"

. 7 . -u .. . .. 10 -OJ"

. , . I-9

-">7 0 ." U ." -, .5 , 9 -, -5 , ,

.", . . . -OJ . _6 -. . . , .6 ., I

-u , ., .3-"

.7 .7 7 , .7" "

_12 -, -, . , .

", -. . , 7 6

" ".. -, ..OJ . ..

"n , , ., ., 5 :1~ '9 -9 .00

", OJ5 . .5 .,

" -"9 ." . . 3 ." 5

", ."0 -. u . 7 ." . , J7 J6 .u .,

u .""

.. 10 , , 7 , , .J6 10 0108 .0

"7 n , 9 .7 7 , ., ,

" ": .

9 .5"

-7 , n"

: 3 0 .>7

". ,. . , , u .. 7 .10 9 . , . . ." "

7 ." "7 U ,

"5 . 6 7 , , .. -,

" "6 ,

6 .U 9 : -" n , 5 , ,"

., _u" 1

, I,'7 n

" ",

.",6 . .u .,

"., .00 I. ., 3 7 .10 U , .. 0 -. ., ., 5 15

"5 -" n ," "

,: ~. -, , -, -" "

, .6 ,," "

5" "

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, ., ,,:1!

, . -26"

0 J7

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0 U , .10 ., . . .u"

., -7 :16 -"n -, .,

". ." "

,-" "

.,.1

, .5 .."

U -, , ,., .. . . -, , ,5 U -, , .u .10 , .5 .. J., , , 0" "

.. .n" : ~.. -" . , ., .15 ..-, .. . . _u

"-5 7 . -, .n , .,

".,-, -00 9 ., , 7 -, -'7

"1610 . ." :1~ -, '5.6

" "

.,

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, 5 ., 0"

, .7 -1~ I.7 .16 u -. ." "

. . n 9 . _1~ n . .. 10-. ., 6 .," "

- 9 . ,"

.7 -9 ., 10-9 9 6 .6

." 16 .10 , , 0"

, .00 , ,-"

.. : ~-;~"

.u . . 0"

-. 09 9 .7 .-u .

" ." . 6 0 -. : -, , .,."

., .9 ,5 , .n : .." " "

7

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10, ,,6 . .00 -, .n, . , . . 7 .""

, .7 .

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7"

9 . . . _u u 0 .,; -7 7

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, 0" "

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, ,"

9 ., .. .. ., .,, -; 9 u-~~

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-, .. . -, .000 ., 9 ., ,

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. -, _6 ., .... 9"

7" "

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.16"

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. ," " "

n" : ~: ~.. 6., 9 ; -" "

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50"

n 6 .00-, -, ,

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, . -n .; ,.":16

, .," "

-. .5 , . .50" ."

, ,: ~-, 00

"., . , 5

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, . ,." .5 -7 . ." .. 5 , ,53

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, .J6 J6"

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.n .." ." 9 : ." . ., .6

9 ,: ~7 .". . n -0 7 , .. 00. .0 . , u ..

" _1~ 7 7 7 6 -, ..7 .6 7 ., 0

"-.

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9 , , . ." "() ~11 ...

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",

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, ., . 5 .7 : 0

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0 , 5 n - . 5 0 . ,5 -. '9 "., ... . ." '; "

u u , . , 6 ; ." "-,

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," " " "

-, _:Z u ., ..: ~-" " "

5 0 . 7 . . -u"

.."

., ,-0 ,

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". -50

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:16"

u"

n u:16 -5

, .. ., -6 , .,." " -" 9 :

., ,.; 5 ."

J6 : ~, .6

" ".u . ,

.1~,

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."., 7 ,,

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" ":16

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9 -, 0."

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, 6 0 ,,' : u". , 6 -. -, 7 ."

_u-"

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,-u U

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." ", .3

."24 , u 7 . . _12 -. 7 9 , , 66 71

_J~, -, .,

" "-, , .n , . . ., ,

"-7 -OJ n : " " ." 9 7 . 0 >7 ..

0 -, 5 -7 6 -15 ., 6 7 -. ., .5 5 , 7 -. 0"

, ; -" -50". ; 5 ., -, , ,

"-, 5

" = ~"9

"

, ., , 5 _20

" " "

, -00"

..- . -" "

-00 -, , , u -15" =L

.5." "i -"

.00 5

" ".1

9 . _6"

2J-; , _12 U

-" : "0 5 , .7 .00 :-,

-" .: -n -, ."

-50"

,

" "_B ,

-5,

-", 0 5 ,

-"u -9 6 7

-0 ."

; . - . -, , , . ; .B 9 ." .>7 .;"

7 -" U ,"

-u"

Crystal structure of meyerhofferite, CaBaOa(OH). H2O 331

Table 3 (continued)

"1'.1

,1'.1

"1'.1 F, 1'.1 F 1'.1

"1'.1

1121 -, T:. 5 .~ :!"61 -,."

~~5 2"PI n , "J11% ,-.j _6 6 -n 27 26 ,

-~_12 -n n

-" " "n n -12

" -" "-n 9

"-" -J _HI

"-29 )0 -, , , . -: n

-" -,

iu 2 -, -7 6" "

-, _6 , , , Jg 5 ,"

," "

. -. -, , , -. :~" . , ,

-'9 20 -."

, - , ,"H

-" "n 9 -. 26

"- 7 - . -

}-

,

"7

'"-7

, . -. -, -" "-, ,

-, 7 : :~:

"n , -23

" -j

" "-, . -, -.-. 20

"-, _2%

" -" -n 31%1 -. 7 -, ,7

-:-j -

,-"

15 _n . n , . -, ,

. : ~-n 15 _6" "

_12 ."

. 1 n"1 -, ,

" "-7 -)0 '7 -n

,

"- . -. ,

" "-, -" " - ,

l~, ,,' n ..

" -; ~-" ,:~-31

"_6 n

'"-,

"n _6 9

"-n .6 ,-"

_12 9'"

, . . -n". -,j -,

-"n _n

" "9 , 7

-" ",

- ~,. -n 15 :,6"

9-" -;

, -, 7 . -, ,- . ,

-.,j

":z 7 :~~

"7

"~~,

" " -, _1~

"-, 31"

-n" "

.-"

, , ,: ~,

: ~-, _12 n -., _n ,1 -12 n , -, , ,

_1~"

-1) -6 !!"1Io2, n

"

, 30"

-, -7 7-, , T"7

., ; -", . -J<

"_. n

"-. _6 , n 9"

S , , ,"

J< :: ~-, 7-7 -, ,

"-. " -7 . n ,

- .-" "

,.. -" ", .

"- . ,

-" "-, -5J

"-, ,

-, , 6 , 9 . - . 2}

" : ~" ~~-" -1-," . 7 -s,

-" '9 -2 -"., -15

-"-H 7 6 n 7

")0 -, , -s -" " -" -,

-",

1 -1 6 ,-,

"n - .

" "-n .

-'j -, 1 -" "-,

-" n : ~-, , ., ~~6 ,-"

, ; . n 20 - . 7 7 ; - .Ta J

"n

-", ; n

" : ~, .1 -, 7

",

~~_6, . , 6 _32" -" -" -17

" : -,

-. , . , . -. , :t~ H n-"

, 7 -.n , 7 - .-"

n ,-'9 ~Z -. -" - , 7 ,

"_n

"7 6 -.

"-n -, -n - . . -2: -, , -J ,

62}

" -" '"_H 7 ,

-,

-n"

-. . -J -n"

-n -")1%2 - .

, _t~"7 -, . -, , . -,

"'9

, n 7 -. n -h" ~.16

" "- . -n n -, - .

"_n

" "h h

"1 -"9 -7

, -, -. : n"

H -h ., .:~~ 15

" "-

, -0 - 7-"

15 -,

", ,

"~, ,:l~ -, -, -. 7 -, ,

: 17"

- ." "-)0

"-. -,

". 15 15 -H .; -

,." ".

" " -",

-" - . , , 7 7 : ~-, ,, -5J

"_12 ,

-". ,

-, .

"n

" "-. -2}"

T'"

-, _12" "

, , , -)0': - , - ,

"-," " : - ,

:~~., . ,

-20"

,-,

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20" "

, . _1 , ,-" " : ~,-,

".. 7 -n 9 ,,, , , , ,

- 7 ,-" "-,

" ". , 7 n - . - . - 7 7 .

" " - 9"

,-. -" "

, , ,"

_,-,

"., ,

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-," -,

-7 .,"

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-, , , -.

" " -",

-, -, , ~n '" ." '"-, , , -,

" " -" 7:I~ -" "

-n" : "

15 -, -, . -

, -J8 2}-n - 7

"9 . - 5 . -, -. -: 7 -

, "_16

")117 .

.1-H -;, , , , 7 -7 -, -J8

" " -"-"-,

-"H .

"n -

, -, - . , , , ,-" -: ..

",

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", ,

"..

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-" ~J7 _n

"i"" -. -, -.,"

~_12"

_n - , - , 22 ."

,'J 6 .,

"15

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" -"7 i 1 -, ,

"-; _. -. 7 .

" "!!"108 -. . _n - , -.H -7 -s 7 , 15

" : -. -" 7, ~, ,

", -, . , -. -30

", -15 :1~

"-..

j), _>u ,

:16 -9"

-," ~Z 7 - . 7

-". 20 .,,

'9"

, :;, _:10 ." "

.,H,J . . ,7 c, 6 -n 6 . .

1 -. n -,

- . -, ,. 22 199 -, -, - . ,

-" " ", -, , .

: , ,-7 -. -20

"; _1~ n

"-,

: ~-, ,

7 ,: ~15

",

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.;, .

J'"

. -J , .-" "

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,-

,.:, ,

1,

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, - , , - . -". 6 . -,-"

7 -. -" ", , ,

- , J8 J8." "

J -; _n , -, . , . ., n -, -,

-."

n-"

. -, .1

.., J8 :1~ -,-,-"

n . . -n -, -, _s -, , n ..

:;, -., n , _0

-"_6

-, , ~, . _n

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- .-i

!!"nlo"

- . . -3S" -"

,-, n

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:~ -7 . .,"

jl08 -,_6 -," : ~-; "

, . ,-

,:

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, ,;" - . - 9 - . - .

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, ,- .-, -n .. _6 5

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1 5 6 7 . - .-" " ~.1 5

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, . -.I g5 ,1 -"

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H -, , -, ."

10 6 -.. _w-,

",

'".6

"-. -. -29

". _10 , -10 U -, -. ,

9 -, 9 . ,

" ",

"n -n . -

,-n ... , , , -, : ~10

" - . .,-" - . -, , 5

7 , ,- . , -32 ;~ -, -n '1310

, .. .6 -20 20 -, -, -

," : ~" "

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1 ~I"

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-, .

-'9 21 - " - ~-7 - 9 -, -,"

-, 6 -, -5J -:n ~~-

,-

, 9 -. ,: - 7 6 _10 _1,

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".. -.., 7 7 -7

,: -, , , :1~

"3:9 -,0 ,

T' .. 6 -.. , -, ; . . -.-. 10 , , -. _12 -15"

T710 ," "

,-;

,-, -n .. -, -n 12

"6 . , -15 ~l 6 7

-j , 7 . .. n-"

. 5. - 5 ,"

, 10"-, -. 1~ 0 -7 ~~~5

-~, 6 -. , -, ,

-, -., -. - 5 ,-

, . -.,"

, ,_6 .. , u -, , , , 20"

, u ,: ~-7 : ~_6 .. .. 15 . -; . . -J<

".

-" ". ,: -, , 0 -

, -, 0 ,:,Z

, !!IIo. -7 -, 6 -, , -, _l~ , -. -.-, n 7 7 -, 6 ., -, u-"-.. ,

", 6 - ~9 :? -, ~~'; -J 7

-12 -, ..-"

n"

; _6 -, ,

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f 126,

: : ~:,

.:_6 , 6 . _6 ... -,

" : ~J -, -" "-, -..

'". 7 6 -, . _6

-", , - ,

"


Table 3 (continued)

'. 1'.1 '. 1'.1 '. 1'.1,

I'.!,

1'.1,

1',1

"} '99 -, ;;3' " "

~1, -. 5 58", .,, , ->9

"0" -;

3"7 10 5 ,->0 >0 -, -0 7 7 -H

"0

" ",

6 -, , _0- 3 , , 6

" "-, 0 . 0

", -) 0 ->0 H -. 6 5 -, -, -, 6 -,

-"."

-, -5 6 -, , 7 . -. 6 -)"

H -, 73 -7 -, )1

"_6 3 . 3 7

"-. -. , -) ,

,I -) -7 -"

H ,-H

"-, ) -. -:,

- .-" >9 -, 7 ,

:, _6 , -50 -7 -5

">9 :.9 -, 0 : ~_H _6 -,

-, . _6 _,6

"4710

"-

, -19"

,- 7 -7-, -. : ~, 6 -, -, )0

"-, _0 -. _1~-) _ 6 7 7

I -. -3"

>7 !6 to , -,-. . -, -pO"

>0 -. _,6

" I_0 ->0 7

-, _7-"

H H ~_6 -5 ,6"

7 _H )

-6, -H . 6 , -6 -" "

)->0 -"

_6-7 7

-" -) , )

7 : Z 0, )

'H, -.-. _6. _-0 , 0 _,6

", 5 , _i >0 0 ,

3' H ,"

~~5 - 3 -, 7 -,-"

H 0 , -7~-7

_6 , -, ,-"

6 -, , , H"-, >0 H 7 -

) 0 -H . -, -i 7 , ,, . H , ->7"

-. .-" -7 -

) 6 -7,

0 -i . . -, If -5 -. _-13 >0 -. . , , ,-, 7

"_6 .

'"5 -

)-

, -. . -, ,-, . 6 ->7

":.7 _0 H ->1 >0 _6 . ) _6 ,, -5 : " ".. H -; >0

" "-7 , , 7 ,

-. ~H , )i - 7 6 "5"~11

) ,-:~

"--,)

-" "

, _6 _0 _7 0". gl 7 , 6 , , , 7 , , 7 -, 6 7

- :,

-" "0 -, 6 - 7 0 -5 -, ,

H 0 _H H -, -, ,i -, . -)

" ""

, -, H"

-, . . -, . -. -" ", -7 -,

-" " -) -, , -. 7 -) _H -5 -. ., 5 -) H >1 -. i

, 6 . -. _0 _6 , .7 -, - . pO

"_-5 ,

-" "6121 -, - 7

-" "6 -7 6 -, , 5g , _i 0)

5 H -, -. 6 ,, )0"

_6 6 6 -," "

>0 6 -, -,,-" " : Z ->7 >7 H ->0 -, -.

" i -; ->0 -,3 -, ,i

, >0 6 : ~6 7 -H"

,"

- , _0i -. -" >1 7 , __12

:!, -,."

->0 _7 , -, 7 7 6: ~6116

0~~" -H 6 7 -, _6 6 7 , >0 ,

-," -" -, 6

-"H -7 ->7

'I. -. i .-, -pO

" -", ,

" "-. )

~-, -,: l H H ii126

, . -, . -, , 6 ,6 15 7)

-) . H -, J -:

, ->0 -, , ,-" g 6 0

-, -, ,i"

) ,-H 7 6 0 H , -)-, >0 i -) , _" -"

-) -," "

." "-7 _,6

"-. , 0 _0 -1) -, -, -'7

"~-15

"-,"

H 7" "

-, , , 5 ~~6 -: -) 6 5 : ":1~ " "6

-" 15 -, -15 ~~-. :z 6 , ,-7 ,

I, -) >9 , -, -, . 0 -" "-H , 7

"-. _H , , _7 _6 H

"-, , ,

-" -, )-"

n -, . . 7"

-, -, -, :-"

, ,"

16 _6

">7 6 -, -, -, . -) -,

-". , ,

-7 -" ", -5 6 -, H H -. 15

",

1)' -i 0 -1) 1) -. 3 . . 7 ,; ->0 -9,

- 5 -, ,

"-, H 9 -, , . 3 _H _H , _6 0

H -, -, -pO -. . , -,-"

0 -7">0 _6 5 -J -, ,

-H, , 7 ,: _-IJ -, -,

-"9 , , -. , 6 _12- :l, _H 6122

,"

-, ,, -, , -, ->9"

-1) -,"

1) H _7 ,->0 -)

7 1)

"-6

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>0 6 7 _-11 -,6 0 : Z 7

,5132 -5 : l

, 5 , , 6"7 -., -;~ "-)

"7 ,6 15 . _w

i i."

:1~, H -5 -'7 >7 7 _1~_H

"-1

", _6 -, 6 6 7 -,,

"-H : . : ~6 7

I. 5 6 0, . ,

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", _w

"0 -15 ~~,H 7, 7 '5 ~~:I~ 5 5 J

-"16 . 7 W

-," "

_7 7 6 -5 -, . , , H) , ,

-, ) . i H H I -",6 -H -) 6 , 0 ,

"-) -pO

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-"1) , , .-.

" ~Z7 _6 , J , 5107 -7

, -," " " -" "-, -IE 6 H

",

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" "-, -" ;6 -, , ,_6 ,i 5 _H H , ,6 ,6 ,

: ~6 -)"

-,-7

". , 0 _20

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"-3 -" "-, -, , ) -, 7 -, , , 6 -) . -, -16 16 -. >0

"-, 6 7 , _H H _,6

", -. . _6

"H -5 -J

->0 -, , ,"

>7 -) -,) 1) . ,"

-7, _6

-5-H)

5 0 5 5 - . 6 , ) . , -. -~~ 15 -7 16

-"Dot ~"Lc. 7 -, -, -, _,6 >7 , _6 7 -, }'2 -, _w

-1) ->0"

-,"

H _6 pO

",

"1)

->0 _H H -,"-"

,-3

-" "-7

_0 0 _6 7 -H -, ->0 6 .,~~J -, -. . . -. . -, -, 5

-" " "_H

-'" ", -, ) ,

:16 " "-

, 0 -1) -9,

", -.H J _ 6 -1)

"-19 19 -)

-" "612) 9 H . 6

>0 -J : ~7, _H -

, 6 -. 6 . H 5 i-1), 1) 1) -. -" >0

"-, -5 5 >0 -1) H ,~, _0

:1~ 7 7:~~

_H"

_6 , ,; i . 6 I "7-" "

7 , 6 : Z "-) 6 ->0 ,

6 , 5 -H -. H 5 g) _6

-1~"

7 -1)"

J , ,I ->7 ~~4"108

,:1~ 6 _i

, , -.'" i -, H 7 7 6 ,

5 5,

-J3 -7 6 ,

"_H H .:11

-"1) . J , 0 5

"-, , 7 -7 i '" "5E8 -,

~" "-, -:

,," "

6-I

0 .-'J

1) -,0 ) , 7 -, , 7 ->0 H , 6 . -) .-, -," . -

, , 6 . , 6 , 9 0 _H

"-. -,-, ; J 1)

"5 -,"

"5 , -,

-" "-5 7

-3 =2~, -, . 1)

'", -pP

"-, 7 , _6 -)-. , -. , ~17 15 )

" '"-) -, , -7 -,

-5" "

0 7 6 -JJ ;~,

7

'" -. , -, ,_6-" "

,-12 H ,

", -7 7 -, . -, -.'7 "

6"

0" "

0"

H _6 ,'7

, J-, ,=l 7 6 -, _21 -,

-"15 -7 . : 6 -7 .-, -,

-" "15

"-, 3 -, -7 : 7 i-," , -5 H

'"_J -17 >7 -) 5 6 -, -5 6 -,

-H -, _6 -; -, -, -. -1)"

->0 6 6 ~, .-"

_6 -7,

- ')1)

"-5 6 6 _H _H

'"9

'"-1) , -, . -6 ->0

'"-6

,-"

6 ,-," 'J,-" "

-, -9 -7 -7 -7 -1) , 0 5 ,1)' . ->0 -, -. J -, ,

b 12 ~_6-

, 5 .

"-7 1;89 ,

:Jg -7 :t~ -. H 7 -, -5 7H

; 7 -, ; -,'" : ~6 6

>0, 6 -, _H 589 6

: J -. ,, _0 7-"

-, 7 , ,-5 -5 i, H _-13 -, 6 ,

7 -, _6 77 -, , 5 ". -, I J 6 ,-7 -, 76 6 , H _1

_0I . -. 1 55 -,

'"; 6

-" "b510,

-",6 , _0 -. ) ,

". )

Crystal structure of meyerhofferite, CaB303(OH)s H2O 333

Table 3 (continued),

1'.1,

1'.1,

1'.1,

I'.],

1'.1,

I'.:0310 -22 'i

, , -, '8102 , 857 -, '9 ~5 -, 101 , -,,-;

,'"

9 . _6 -. J , , -,~. - , , , -, -, , , , ,- J. , -9 , ,

-, _ , , -9 22 -, -9 ,i., _r -J -. , -9 -J . , -, _'J-. -, -," 9 , J ~" 9 -, -,

'"-,., J -, , 6 , ,

1 -:-, -, 7 : ~,., , ., , , J -," - J , , .-, -, -, -22 9 , -, ; , . , .. 1065 -,., , .,

'7 n . , _6 -, . 1,

till ,:tE -, . - ~, .J .,

. ~-,. .7 -, -, , 7 , -, ; ,-, ., .H , -, , . , .: , ., , ,-. .1 7106 J .J 5

, -,'"

., -, . .,1111 : , -, , , . J . "976 J ,

-;"

, . . ., .H 22 -. - , , . , ..: -, , 22 H ., . .5 , 5 . ., .,, , -n n

=Z. , ., _, , H ~~-J

,7 , ,

1 -, -, : ~.; ; -" -. . ;6 ., ,"

25 :,6 9 , , .,,"

H ; .'7 '7 -J 859 J . J . , J. .n 22 . .H , . .5 , , ., ., .H; -, ,6 , , H 810) _H 25 ; , , .. .: '"

-,'""

, -, , 9 , , ,'"

-, H TO ~6 -,,." '7 . , , , , -, , . .n

"-, . ,

.:. .,-

, . J . , , ,'" '"

.,. : J., 22

".J .J , ,

" ". . ., . , , -,-, ., .,

" ", .,"

'"., . ,

"., , . :~-J ~.5 ..,

",

", ., .i H : ~. ,., ., , ; , ___10 , . , ..

-~-, -, , -, , .27"

., , 967 , -,-, 'J ". , .J . , ., ,

1 . , ., . .:z ." " :16

, , -, 8~ 10, . . , J.,

- . -. ., , ; . , ., . .., , .H , . ,"

., : ~J ., -, J-"

., "7 ~7,

: ~." H :1~ . , ,- , -J_n , . , , ,

'9i 1 ,." 22 10107 ,

." -, 7 -, -, , , . . , , ; -,

7112- .. , , -, . , , , - , 22 ,- J

", 5 . , ., , , ., -J ., , , 27

": .. , ,"

., : ~, , . , , , , ., ,-,

"J .J , -, , -, .5 .J . , -, ,

7 , , .,-"

, ; ., .,." . ,

" ", . ~, 5 , -H .,

" "- , ,

- J .H"

, , -25 25 BIO' -, . ."" '"

. -, 5 ,

. 25"

-, _, ,: . , , ,

- J ., -,

; -, ,-,

"25 5 .. , , J 5 TO2 8 . ,

"H .J -

, , ,-"

, ., _, , ,- 5 , . ., -22

"., , , , 5 , ., H , , . , , .. ., , .j , , , -, ,

-, .,

", ,

- . ,.,"

, . , .J , . -1~, .5 ., , .. , - , ,.,

-" " - , , 5 ; 22 ., , ,-

, .J -J_,

.J .. 5 ., -H"

., ,: Z ., ,

- J -, IT 5 . ,..

" "-, ., . , , -, J ,

:~-, -5 -", , 27

"., , .5 5 ;-, J 788 . ..

-" " ." : ~., ., -,-7 J 7 ., -, , 992 9~9

"., , . ,.. ., , ,

- J , , . . .,"

, ,., _1~ 1 .J .,." 27 , , , , , ., ,

-"., H - 5 22

'i, . ; - . -J , ., .,

-n . ; 22 , _6 ., 5 -, . , , .J J

-",

: ~., , , ,.1

..;J'"

16 -, .,

'i :~3

, . -, 22

"J -

, 1071 . .,.1

-"27 , , ., - . , ., , ., .,

: 5 - . ., , -," -. ,: ~, 22

'i IT" .,,-, , , -H .. , , ., , ,

7 -t~ : l -, , '895 .; - ." "

J - J , ; .,, 22 -5, , .,

." ". H 22 ,, .22 H .,

-~~ ", . . J J . _, , . ,, 22

"-, H , ., - .

"., , , , -,, -2 :z J 1

., - 5 .H ,-

, -5 . . ,, .'5"

,- . -, . - . .J . , .,

."

27 -, -, ; . : i -, .J , .J ... ., , 769 ., 5 -, 22 .. , . , ,., .5.1 5 . . .J -, H

" - 5 .. - 5 .,""

., 22 ,- . , , .," -: ., , _, , ,

: ~., : ; . , -. . '9: J :z_, IT 5 J - ., ,

-, ., . , , , J

-5, . - . ,

: ~5 .1, . J I1\"72 , , ; . ,-, -" "

, , ,."

, , , . ,'"

..-, 27"

- . , , - , , . ,- 5 ,

- 5 . H"

-, .22" - , ., , _, , , , ., ,

_1~ 22 , -J., ., .J'"

.: -, -5 , J . J

"- . ., ,

." H -, .,-

, . , -, ,_i H .,

_1~,_n

-, -, .-, ,

:16 . , .'"

. -J 22."

, .6 , , .. , -5 ,-2g

,- . 17' :~

It -, ., _, . 8:6 - . .. , -.

".,

. 71010 ,-"

, -, 6 .,- 5 .. - ,, .. J - . , H

"- J . -J .22 g IT It 10 - ., . , , . -

, , ., -. ., , J ,7 -, , , J 5 - . .5

-" "-

, -22 22 , . ,, 5 , ,- . , H

"., J _ , J . -J, , , .. , ; .,

'"., ,

-, . , ,, .," H ., .J ,

-, .,

-, .,

'" -, .,, J : ~J , J -

, , -, H"

., ,, .J .. , _H H-"

,I1\"" . -J .., , _-5 ., : ~'" "

9810 5 . , ., .., , 8101" " ." "

, -22 22 1., .5 ,., -5 ,

: -22"

-J J ," '"

. -, . ,.,:

, , -. " "5 , ; .,

"IT 1r.5 -,., 5 , ,

- 5 .,'"

, -25"

. , ; ...,-:~ 25 ,

-27 25 -, 5 , J '7 25 , ,"

..., H , ., H ., -. , -,'"

, ., . -,"., -, . : ~., -. , -, ,- , _1 , ,

:z .. , ; -, , 9 -g., -. .,, ,

" "-," -, -,

" ::l - . -, -,:tE -

, , , .1 , 887 -, ., , , , , .,

".'"

, , ,: ~-5 ., ,

- . -._n , -. , , 6 J .,'"

., ., 22 ., .." -t~ .. -:~ 27 5 - J -,

" "., , , IT. , ;7105

'". ,

'", ; ., ., ., ., .: _H , -, -, H J -, .,

"Iii?" -22

", .,. , -, .. , - , -, , , , . -. ,7 , , .,

".; . 5 ., -, 1 . .J, -22 22 -7 .: ,

: ~.," -1 .5 -, ,:

, -, ., "985 J"

-. -.-22 H ., -, . , , , , ,:~, , , .," -, :: ~-

, , . , ,"

, _H 9 J , -, , ,

334 C. L. CHRIST and J DAN R. CLARK

projection terms with lFol > O. Using these terms a second set ofelectron-density projections was prepared. Coordinates (Table 2,column 2) found from the peak maxima of this second set of mapswere taken as the beginning ones for digital-computer least-squaresrefinement.

As stated above, in order to facilitate refinement only one-fifth ofthe 2678 data with lFol > 0 were used. Five cycles of refinement witha general isotropic temperature factor were completed and the reosuIting coordinates and factors are given in Table 2, column 3, togetherwith the residual (0.147) for the 536 hkl terms used. Finally six cyclesof least-squares refinement (536 terms) using an individual isotropiotemperature factor for each atom were completed; this refinementwas stopped when the shifts indicated in coordinates became less thanthe calculated errors. The final set of coordinates, the individualtemperature factors, the scale factor and residual (0.145) for all2678 hkl terms with lFol > 0 are given in Table 2, column 4. Calculatedstructure factors based on these parameters are compared with theobserved structure factors in Table 3.

The standard errors associated with the atomic parameterscalculated from the least-squares analysis were obtained by the sameprocedure as that outlined in Table 3 of our paper on the structure ofCaB303(OH)s . 2H20 (CLARK and CHRIST, 1959). Because of the use ofthree-dimensional data in the present case the errors are smaller thanthose found for CaB303(OH)5 . 2H20. Taking into account the un.certainty in the values of the cell dimensions, we assign the followingstandard errors for the interatomic distances in meyerhofferite:

Ca-O ::J:0.02 A, O-O::J: 0.025 A, B-O::J: 0.03 A, B-B::J: 0.03 AtCa-Ca ::J:0.01 A.

Description and discussion of the structureThe principal structural features of meyerhofferite are illustrated

in Figs. 1 and 2. The crystal contains insular polyion rings of com.position [B303(OH)5]-2 consisting of two boron-oxygen tetrahedra anda boron-oxygen triangle linked at corners. This is the same polyionfound in the synthetic compound CaB303(OHh . 2H20 (CLARK andCHRIST, 1959), and in inyoite CaB303(OH)5 . 4H20 (CLARK, 1959); theinfinite chains found in colemanite, CaB304(OH)3' H20 (CHRIST,CLARK, and EVANS, 1958), consist of the polymerization product ofthese insular polyions described by the schematic reaction:

n[B303(OH)5]-2 = [B304(OH)3]~2n+ nH20.

Crystal structure of meyerhofferite, CaB303(OH)s . H20 335

As in the three previous studies mentioned above, assignment ofthe hydrogen atoms was carried out by assuming that those oxygensnot shared between two borons in the polyion represent hydroxylgroups, and that the single unattached oxygen represents a watermolecule. Thus the formula 2 CaO . 3 B20a . 7 H20 representing the

Fig. 1. Projection of the structure of meyerhofferite, CaB303(OH)s . H20, on aplane normal to [010]. The small black circles represent boron atoms, the smallopen circles oxygen atoms, the double circles water molecules, and the largerstippled circles calcium atoms. The number designations of the atoms correspond

to those given in Tables 4, 6, and 8. The dashed lines represent hydrogen bonds.Those dashed lines ending in an arrowhead indicate that the bond is associated

with the atom translated one unIt in the b direction.

chemical analysis becomes CaBaOa(OH)s . H20. The arrangement ofoxygens bonded to two borons, and hydroxyls bound to one boron(together with the single water molecule) accounts satisfactorily forthe hydrogen content of the crystal. In fact, this way of inferring thepositions of the hydrogen atoms is of general validity in hydratedborates and constitutes one of four rules that govern the structure and


composition of the polyions (or their polymerization products) oc-curring in these compounds*.

In meyerhofferite, successive polyions are linked through calcium-oxygen bonds to form endless zigzag strings along [001]; these stringsare viewed along [001] in Fig.2. Each calcium is surrounded by anirregular octahedron of four hydroxyls, one oxygen, and one watermolecule as nearest neighbors, with an additional oxygen and hydroxyl

Origin

a sin f3

+

Fig. 2. Projection of the structure of meyerhofferite, CaB303(OHh . H20, on aplane normal to [001]. The dashed lines show the coordination of the calcium.The Ca-O~ and Ca-O~ bonds (and their centrosymmetric equivalents) shownare between the calcium and the oxygens in the adjoining cell below the planeof the drawing, so that endless zigzag strings are formed along [001]. The number

designations of the atoms correspond to those given in Table 7.

* It has been shown elsewhere (CHRIST, 1959) that four rules seeminglygovern the nature of the polyions occurring in hydrated borates: (1) boron wiII linkeither three oxygens to form a triangle, or four oxygens to form a tetrahedron;(2) polynuclear anions are formed by corner sharing only of boron-oxygen

triangles or tetrahedra in such a manner that a compact group of low to mediumnegative charge results; (3) in the polyions of hydrated borates, those oxygensnot shared by two borons always attach a proton and exist as hydroxyl groups;(4) the insular groups may polymerize in various ways by splitting out water.

With these four rules it has been found possible to correlate the hydratedborates of known crystal structures and to postulate the structural formulas fora number of hydrated borates whose crystal structures have not yet beenworked out (CHRIST, 1960).

Triangle around Bl

B1-01 1.34A 01-B1-02* 124.0°B1-02 * 1.35 01-B1-Oa 121.3

B1-Oa 1.39 Oa-Bl-02* 114.7-

Average 1.36 A 1: = 360.0°

Tetrahedron around B2

B2-01 1.46 A 01-B2-04* 112.5°

B2-04* 1.47 01-B2-OS 114.6

B2-OS 1.45 01-B2-OS* 110.8

B2-OS * 1.48 Os-B2-04* 104.6

Average 1.47 A Os-B2-OS* 108.4

04 *-B2-Os *105.2

Average 109.4 °

Crystal structure of meyerhofferite, CaBaOa(OHh . H20 337

at larger distances. Adjacent polyion-calcium strings are linked onlythrough hydrogen bonds (discussed below). The perfect cleavageparallel to (010) and the secondary cleavages parallel to (100) and (110),first noted by SCHALLER (1916), are satisfactorily explained by thestructure since these cleavages involve only the breaking of hydrogenbonds.

Table 4. Boron-oxygen bond lengths and bond angles for meyerhofferite(See Fig. 1)

B-O bonds Bond angles

B~-OaB~-OsB~-O~*B~-O~*

Average

Tetrahedron around B~

Oa-B~-OsOa-B~-O~*03-B~-0~*Os-B~-O~*Os-B;-O~*O~*-B;-O~*

1.48 A1.431.471.47

1.46 AAverage

(B-O bonds all :!:: 0.03 A)

B1-01-B2

B1-Oa-B~

B2-Os-B;

(All angles

* Hydroxyl oxygen.

Z. Kristallogr. Ed. 114, 5/6

110.7°103.4111.0109.7108.1114.0

109.5 °

120.5°121.5125.2

:!:: 1.5°)

22

CompoundAverage B-O length

I ReferenceTriangleI

Tetrahedron II

Colemanite 1.37 A

I

1.48 A CHRIST, CLARK andEVANS, 1958

CaB303(OH)5 . 2 HP 1.36 I 1.48 CLARK and CHRIST, 1959Inyoite 1.38 1.47 CLARK, 1959Borax 1.36 1.48 MORIMOTO,1956Metaboric acid 1.36 1.46 ZACHARIASEN, 1952Meyerhofferite 1.36 1.47 Present study


The principal interatomic distances and angles are listed in Tables 4to 8. For meyerhofferite the average B-O distance in the triangle is1.36 A, and in the two tetrahedra, 1.46 A and 1.47 A, respectively(Table 4). These results are in excellent agreement with the resultspreviously found in other borates, as is shown in Table 5. The differ-ence in distances between triangular B-O and tetrahedral B-O is by

Table 5. Oomparison of average boron-oxygen bond lengths for meyerhofferite andother borates

now well established. On the basis of the present study no significancecan be attached to the variation of individual B- 0 bond lengthswithin the tetrahedra or triangle. The O-B-O bond angles appearreasonable, the average for the two tetrahedra being 109.4 ° and109.5°, respectively. The sum of the three O-B-O angles in thetriangle is exactly 360.0°, indicating that within limits of error theboron lies strictly in the plane of the triangle. The same finding hasbeen made for the other members of this series. The variation in bondangles within the triangle and within the tetrahedra is believed to bereal, the distortion probably representing accommodation of thepolyion to its surroundings in the crystal.

For oxygens bonded to the same boron, the average 0-0 separationis 2.35 A in the triangle and 2.39 A in each of the two tetrahedra(Table 6). It had been suggested previously (CLARKand CHRIST. 1959)that in the borates of this series the 0-0 separation is a little larger,on the average, in the tetrahedra than in th etriangle. This difference isto be expected because the B- 0 distances in the tetrahedra areappreciably larger than those in the triangle. For an equilateraltriangle with an average B-O length of 1.36 A (Table 4), and aregular tetrahedron with an average B-O length of 1.465 A (Table 4),

the calculated 0-0 separations are 2.36 A and 2.39 A, respectively,

in excellent agreement with those found.

Crystal structure of meyerhofferite, CaBaOa(OH)5 . H20 339

Table 6. Oxygen-oxygen distances in meyerhofferite for oxygensbonded to the same boron

(See Fig. 1)

Triangle around B1

01-02*01-0aO2*-Oa

Average =

2.37 A2.382.31

2.35A

Tetrahedron around B~

Oa-05 2.40 AOa-O~* 2.32Oa-O~* 2.4305-0~* 2.3705-0~* 2.35O~*-O~* 2.47

Average = 2.39 A

Tetrahedron around B2

01-04* 2.44 A01-05 2.4501-09 * 2.42

05-04 *2.32

05-09 * 2.38

04*-09* 2.35

Average = 2.39 A

(All 0-0 bonds ::l: 0.025 A)

* Hydroxyl oxygen.

From Fig. 1 it is seen that the polyion is based on a six-memberedboron-oxygen ring, containing the successively linked atoms Bv OvB2, 05' B~, 03' The plane defined by the three boron atoms obeys theequation (in perpendicular form):

0.0267x - 0.8253y + 0.5640z - 0.0660 = O.

Oxygen 05 lies very nearly in this plane, 01 is 0.16 A above the plane,and the largest deviation occurs for 03 which lies 0.30 A below theplane. The ring is therefore nearly planar. As might be expected fromthe presence of both triangularly and tetrahedrally coordinated boronin the same ring, there is considerable departure from the shape of aregular hexagon.

The average distance between borons in the same ring is 2.50 A(Table 7). The Ca-O distances are listed in Table 7. There are sixoxygens at an average distance of 2.41 A making an approximatelyoctahedral array about the Ca, and two oxygens making longer bondsof 2.51 A and 2.55 A; the average for all eight Ca-O bonds is 2.44 A.The two distances of closest approach for the calciums are 3.76 A and

3.89 A (Table 7).

22*


Table 7. Calcium-oxygen bond lengths, calcium-calcium and boron-boron inter-atomic distances in meyerhofferite

(See Fig. 2)

Ca-O bonds

Ca-04* 2.37 ACa-07** 2.40Ca-O;* 2.40Ca-06* 2.42Ca-()5 2.44

Ca-O~ 2.45

Average of six = 2.41 AAverage of eight = 2.44 A

Ca-O~* 2.55Ca-O; 2.51

Average of two = 2.53

(All Ca-O bonds :f:: 0.02 A)

Ca-Ca distances

Ca-Ca' (z = 0.756 cycles) 3.89 A

Ca-Ca' (z = - 0.244 cycles) 3.76 A(Ca-Ca distances :f:: 0.01 A)

B- B distances

B;-B; 2.43 AB;-B3 2.51B~-B3 2.56

Average = 2.50 A

(B-B distances :f:: 0.03 A)

* Hydroxyl oxygen.** Water oxygen.

Distances of less than 3.00 A between interpolyion oxygens, andbetween these oxygens and the water molecules, are consideredindicative of possible hydrogen bonding. There are eight such dis-tances, three between 2.70 A and 2.80 A, two between 2.80 A and2.90 A, and three between 2.90 A and 3.00 A (Table 8). Those inter-atomic distances considered to represent hydrogen bonds are shown bydashed lines in Fig. 1. The assignment of the proton donor atoms andthe proton acceptor atoms was carried out by first assuming that thetwo protons of the water molecule 07 are directed toward the centro-symmetrically-related atoms Os and O~, making bonds of length2.70 A and 2.84 A respectively. Since Os and O~ are centrosymmetricequivalents this means that each of these atoms receives one normaland one weak hydrogen bond from a water molecule. Having made

Crystal structure of meyerhofferite, CaBgOg(OH)5 . H20 341

this assignment, the remainderof the assignments immediatelyfoHow: 07 receives a hydrogenbond from O~ of length 2.78 A,

O~receives two very weak bondsof lengths 2.91 A and 2.94 Afrom O~ and O~, respectively,and O~ receives a bond from 04of length 2.79 A. The only ringoxygen involved in hydrogenbonding, O~, receives a bond from

06 of length 2.88 A. The remain-ing distance less than 3.00 A,that of 2.95 A between 07 and0;, is considered to be a van derWaals contact.

Table 8. Oxygen-oxygen distances inmeyerhofferite for oxygens not bonded

to the same boron(See Fig. 1)

(Only distances < 3.0 A listed)

07**-08* 2,70 A07**-0~* 2.780~*-09* 2.7907**-0~* 2.840~-06* 2.88O2*-08* 2.91O2*-09* 2.9407**-0; 2.95

(All 0-0 bonds:!: 0.025 A)

* Hydroxyl oxygen.

**Water oxygen.

Acknowledgments

We are grateful to several colleagues at the U.S. GeologicalSurvey for assistance in this study: the program used in the least-squares analysis was developed by D. E. ApPLEMAN and E. Mo-NASTERSKI; D. E. ApPLEMAN, H. T. EVANS, JR., and VINCENT LA-TORREprocessed many of the calculations; W. T. SCHALLERfurnishedthe crystals.

References

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A. D. BOOTH (1948), Fourier technique in x-ray organic structure analysis.University Press, Cambridge.

C. L. CHRIST (1953), Studies of borate minerals (II): X-ray crystallography ofinyoite and meyerhofferite; x-ray and morphological crystallography of2CaO. 3B20g . 9H20. Am. Mineral. 38, 912-918.

C. L. CHRIST (1959), Nature of the polyions contained in hydrated boratecrystals [abstract]. Program and Abstracts, American CrystallographicAssociation Annual Meeting, Ithaca, N. Y., p. 28.

C. L. CHRIST (1960), Crystal chemistry and systematic classification of hydratedborate minerals. Am. Mineral. 45, 334-340.

C. L. CHRIST and JOAN R. CLARK (1956), The structure of meyerhofferite,2CaO. 3B20g . 7H20, a pI crystal, determined by the direct method of

HAUPTMAN and KARLE. Acta Crystallogr. 9, 830.


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JOAN R. CLARK and C. L. CHRIST (1959), Studies of borate minerals (VIII):Tho orystal struoturo of CaB303(OHh . 2H20. Z. Kristallogr. 112, 213-233.

JOAN R. CLARK and C. L. CHRIST (1960), Hauptman-Karle phase determinationapplied to meyerhofferite. Z. Kristallogr. 114, 343-354.

HOWARD T. EVANS, JR. (1948), Relations among crystallographic elements.Am. Mineral. 33, 60-63.

JAMES A. IBERS (1957), New atomio form faotors for beryllium and boron. ActaCrystallogr. 10, 86.

International tables for x-ray crystallography (1952), vol. I. Kynooh Press,Birmingham.

J. KARLE and H. HAUPTMAN (1953), Application of statistical methods to thenaphthalene structure. Acta Crystallogr. 6, 473-476.

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