JOURNAL OF RESEARCH of the N a tional Bureau of Standards - A. Physics and Chemi stry Vol. 75A No. 1, Janua ry - February 197 1

Refinement of the Crystal Structure of the Aragonite Phase of CaC0 3

B. Dickens and J. S. Bowen*

Institute for Materials Research National Bureau of Standards

Washington, D.C. 20234

(July 31, 1970)

Aragonit e (C aCO ,,) c rysta lli zes in th e unit ce ll a = 4.9598(5) /\ . 6 = 7.9641(9) A, and c= 5.7379(6) A at 25 °C with four form ula we ights in space-group Pmcn. The s tru cture has been re fin ed to N".= 0.024 . N= 0.040 using 765 x- ray reAection s from a s ingJe crysta l. Th e Ca ion is coordinat ed to nin e oxygens with Ca .. . ° dis tan ces III th e range 2.414(2) A to 2.653(1) A. Th e two un iqu e C- O di s ta nces in th e CO" group are 1.288(2) ;\ (on the mirror plan e) and 1. 283(1) A. T he two un iqu e O- C-o a ngles are 119.6(2)" (ac ross the mirror plane) and 120.13(8)". Th e d is tances a nd an gles in th e CO" "roup are not s ignifi ca ntl y d iffe rent a t the 95 pe rcent confidence leve l. "

Key word s; Calcium carbonat es; ca rbonates; crysta l s tructure; s in gle c rys t.al x- ray diffrac tion.

1. Introduction

Aragonite (CaCO:d is found in nature as a mineral and is a n important biomineral because of its prese nce in coral , clam shells, gall stones , and otolith s. It is iso­structural with the carbonates of large divalent cation s such as Ba, Sr, and Pb.

Aragonite is less stable than the calcite phase of CaCO~ at room temperature, transform s into calcite, and is denser than calci te_ Thus aragonite is a high pressure form of CaCO:J• More details are available in reference [1].1 Because of th e importance of aragonite, and because of the possibility of performing calcula­tion s on th e lattice energies of selected carbonates along th e lines suggested by Busing [2], we have col­lected ne w x-ray data from a single crys tal of aragonite and have refined the structure from the positions given in 1924 by Bragg [3].

2. Structure Determination

F ornwLa (ideal): CaCO:l (aragoniteo phase); Unit t:;eU: orthorhom~ic with a = 4.9598(5) A, b = 7.9641(9) A, c = 5.7379(6) A at 25 DC (calculated by least squares from 12 28 values observed on a diffractometer volume: 226.65 A:1; radiation, Mo(Ka l ), A= 0.70926 ;( monochrom ator: highly oriented graphite crystal; space·group: Pm cl1 ; conte nts 4(CaC03 ); reciprocal latti ce extin ction s, hkO: h + k = 211, + 1, hOL: L = 211 + 1; observed density , 2.947(2) g'cm -:3 [4J; calculated

*Rest:arch Assoc iate from the Ame rica n Den tal Assoc iation a l the Na tional Bureau of Standard s. Was hi nglon. D.C. 20234.

I Figun's, in b racket s indi n lk lilt:' lilt-rature rdt' rt ' llct'S at the end of th is pa per.

density , 2.944 g ' cm- 3 ; Crystal: mater ial available was heavily twinn ed; a s ma lJ wedge was th e larges t crys tal fragment found whi ch showed no evidence of twinning under optical and x·ray examination; thi s wedge was attached to' thin borate glass fiber with clear household ceme nt ; fiber a ttached to in sert in goniome ter head with epoxy cement ; origin of crystal, mineral sample #75538 from National Mu se um of Natural History , Smithsonian In s titute, Was hington , D.C. (S upplied by ]. S. White, Jr. ); linear absorption correcti ons made by 8 X 8 X 8 Gaussian quadrature using subroutin es written by C. W. Burnham [5 1 and adapted by B. Di ck· ens; maximum and minimum corrections for absorp­tion = 0.880 and 0.963 (tran smission factors). Intensity Data: number of re fl ec tions , 2356 collec ted from 3 octants and merged into a unique se t of 765 , of whic h 619 are "observed" and 146 are "unobserved"; un­observed reflections are those less than 2(T above background; maximum sin 8/A for data 0.907 A - I; meth od used to es timate data: 8-28 scan , scintillation counter ; diffractometer: Picker ~ 4·circle single-crystal diffractometer automated by PDP 8/1 computer through F ACS-l interface and adapted to include least sig­nificant digit of counts; Computation: setting programs , those of reference [6] as adapted by Picker Nuclear

Corporation; 0 scan range: 1.4°+ 114.6 ~", ~A = 0.692,

A = 0.70926 A; scan parameters: backgrounds counted at higher and lower 28 for 100 s each; {}-28 scan at

27

. t Certa in commercial equipment , instru ments , or mate rials are ide nt ified in th is pape r III orde r to adequatel y specify the expe rim ental procedure. In no case does sti c h ident ifi ca· ~io.n imply rt:commendat ion or endorsement by the Nationa l Bureau of S ta nda rds, nor does It Imply that the materia l or equipment identified is necessarily the bes t ava ilable for th e purpose.

0.25°/min for 28 from one background position to the other; attenuator s: 00.25 mm thick layers of N b, 2 layers for firs t a tte nuator, 4 for seco nd , 6 for third ; scan range correction : table look-up method to obtain values recommended in refere nce [7]; intensity data on paper tape, processed by program written by B. Dickens for Univac 1108 computer ; this program contains adapta­tions of subroutines writte n for similar program by F. A. Mauer (NBS), standard reflection plotting routine and extinct re fl ection editing routine from programs by 1. M. Stewart , Uni vers ity of Mar yland , a nd uses a n intense s ta ndard re fl ec tion (at low 20 angle) measured every 50 refl ec tio ns to correct for any change in intensity of the primary x-ray beam. Counts in peak = 1 = P - (T/2TB ) (B L + B H ) , cr(I) = [P + (B L

+ B,_, ) (T/(2 TB ))2 ]l /t, F = [(A F )( LP ) (l ) ]l /t, cr (F ) = (cr(l )/2) (LP/I) lit, LP = 2 s in 20(' /(cos 2 20/l/ +cos2

20c ), f3 = - 1. 58883 X 106 LA.2(cos2 20111 + cos4 20c )

dA /d/J-] / [AP sin 2 Oc(cos 2 20m + cos2 20e ) ] (for extin c­tion correc tions, calculated at same time as absorption correc tion). P = count s a t th e peak pos ition , B\. and BH = background counts at lowe r an d hi gher 20 respec­tively , T = time spend counting peak , Til = time spent countin g each background , AF = atte nuator factor , LP = Lore ntz-polariza ti on correcti on, Oe = Bragg a ngle for refl ection under consideration, 0111 = Bragg angle for monochomator (= 6.005° here), A = transmi ss ion fac tor in the a bsorption correction , /J- is the lin ear absorption coeffici~nt , ciA /ci/J- is in mm , V is the volume of the unit cell in A3. Data merging program for equi va­lent re fl ections, written by B. Dicke ns for Univac 1108 computer ; in this program each se t of equivalent re fl ec­tions is treated a s follows : R efl ections which were all unobserved were averaged and given the larges t in­dividual standard deviation in the se t. Unobserved re fl ections in the presence of at leas t one obser ved re­flection were di scarded. O bserved refl ections which occurred only once in the re fl ection li st subsequent to thi s ste p were copied unchanged but their standard deviation s were increased by a factor of three. Ob­served refl ections with magnitudes which agreed within the counting s tatistics and re Hections with magnitudes whose ratios fell within the range 0.95 to 1.06 were averaged and given as sta ndard deviation the maximum of the standard deviation from counting statis tics and the standard devia tion fro m the range es timate [8 , 9]. Under these circumstances, refl ections whose magnitudes did not pass the crite ria were dis­carded. If no members of a set of equivalent refl ections passed the criteri a, the highest magnitude was taken and the associa ted standard deviation multiplied by fi ve. Th e justifi cation for these arbitrary increases of standard deviation is th at , without some corroboration , every re fl ecti on is suspect because of the possibilities of multiple re fl ection, including the " tail" of nearby intense r e fl ections in its measureme nt , cha nge in intensity of x-ray beam du ring re fl ection measurement , misalignment of c rystal , etc. Since we usually measure three se ts of equivalent re fl ections with care the number of standard deviations increased in this way is very small. Scattering factors: those for the ne utral atoms in reference [10]; least-squares refine ments:

28

full-matrix , with ! w(lFol-IFcl)2 minimized ; refin e­ments include unobserved re fl ec tions which calculate higher than 2cr above background ; least-squares weights : 1/cr2 (F ) ; R".= [LW(!Fo 1- IFe I F/LW!Fo I t ] 1/2,

R = !IIF ol - lFcl l/! lFol; thermal parameters have the form exp [- 1/4(a*2 Bllh 2 + b*2B22 /,-2 + c*2B :I:I / 2 + 2a*b*BI 2hk + 2a*c*BI 3hl + 2b*c*B23 kl) ]. Most least squares and electron density synthesis calculations were carri ed out with the X·ray 67 sys te m [11] of co mputing programs.

Final R efinement: R".= 0.024; R = 0.040 , average shift/e rror for last cycle = 0.0017; standard deviation of an observation of unit we ight

= [!w(Fo- Fc)2/(765-28) ] 1/2= 0.775.

The structure was refined isotro pically from the positions given by Bragg to R/V= 0.031, R = 0.047, a nd then anisotropically to Rw = 0.024, R = 0.040. The low value of R Ie supports the earlie r indi cations that the crys tal used in the data collection is not twinned. The highes t peak in an electron density difference synthesis calcula ted aft er ani sotropi c refinement to Rw= 0.024 corres"Ponded to about 1/3 of an electron and was about 0.95 A from C towards 0 (1). The largest correlation coeffi cients are 0.34-0.44 between the scale factor and the B II , B22 and B:l :l te mperature fac tors of Ca.

Two cycles of least squares r efine ment in which the isotropic secondary extinc tion parameter r in P = F 3nc/ O + f3r !FuncI 2 ) was varied [12] together with all other un cons tra ined parame ters res ulted in no change in Rw or R and gave a value of - 0.3(9 ) X 10- 8

for the extinction para meter. There was no significant change in the structural de tails or their standard devia- I

tions. Thus, we believe secondary extinction to be negligible in our crystal of aragonite. Only the observed re fl ections were used in these refi ne me nts. Three cycles of leas t squares re fine me nt in whi ch allowance was made for the a nomalous scatte ring of Ca (values take n from refere nce 10) gave an increase fro m 0.024 to 0.025 fo r RIO' R was unchanged. There were no significant changes in the a tomi c pos itions.

The atomi c parameters from the refin e me nts witho ut corrections for a nomalous dis persion ar e given in table 1. The observed and calculated struc ture fac tors are given in table 2. T he thermal para meters fro m the refin eme nts which included correcti ons for the a nomalous scattering of Ca are Ca: 0.71(1), 0.65(1), 0.650), 0.00, 0.00, - 0.01(1); C: 0 .67(5), 0.80(6), 0.43(5), 0.00, 0.00, 0.08(5); 0(1): 1.45(5), 0.51(4), 1.01(5), 0.00, 0.00, 0.04(5); 0(2): 0.67(3), 0.98(3) , 1.00(3), - 0.32(3), - 0 .02(3), - 0.09(3) . O nl y those for Ca are s ignifica ntly different from the valu es in table 1. Dis tances and angles referred to in the paper were calculated us in g the values in table 1.

3. Description of the Structure

The structure of aragonite, the main points of which are well known , is shown in fi gure 1. The Ca ions lie in pseudohexagonal layers parallel to (001) and the layer sequence is ABAB. The Ca layers are separated by CO:! groups which lie in two layers parallel to (001), and form columns parallel to [OOl].

------- --- ----

TABLE 1. Atomic parameters in aragonite (C aC0 3)

Atoms x y z /3" * B" B"" B'2 B", B 2:l

Ca 0.25000 0.58507(5) 0.25974(6) 0.664(9) 0.599(9) 0.601(9) 0.0000 0.0000 - 0.01(1) C .25000 .2386(2) .4148(3) .75(5) .85(5) .46(5) .0000 .0000 .07(5) 0(1) .25000 .0770(2) .4043(2) 1.50(5) .54(4) 1.04(4) .0000 .0000 .03(4) 0 (2) .4737(2) .3196(1) .4131(2) 0.71 (3) 1.03(3) 1.02(3) - 0.32(3) - .02(3) - .09(3)

Figures in pa re nth eses are sta nd a rd e rro rs in last s ignifi cant fi g ure quoted , and were computed in the final cyc le of full · matri x leas t· sq ua res re fi nem ent.

*Th e rma l pa ra mete rs are in "\' .

F tGU HE I . A stereoscopic il/ustratio ll of the crys ta l strucw re of a.ragonite (Ca CO ,,).

A un iq ue set of at oms is label ed. The origin of the c rysta llographic coor(linale sys tem is ma rked by *.

3.1 . The Co Ion Environments

Th e Ca ion lies on the mirror plane at x = 1/4. Its environme nt is shown in fi gure 2 and summari zed in table 3. The coordin a tion of nin e oxygens to Ca con sis ts of three CO:1 edges , 0 (1 , 2), O(l t, 2 t) and 0 (2tV, 2V) and th ree apexes , O(lll , 211 , 2111 ). The appare nt thermal motion of Ca is almost isotropic (table 1, fi g. 2).

Corrections as given by Busing and Le vy [13] to obtain the m ean separation between atoms from the observed atomi c positional and thermal parame ters were calculated using a program written by Finger [12j. These corrections are included in tables 3 and 4.

3.2. The C03 Group

Th e details of the CO :1 group and its environment are given in table 4 and shown in fi gure 3. Th e positions re ported by Bragg [3] give C- O di stances of 1.26 A and 1.30 A, and O- C - O angles of 117°, 117° and 12r, whic h, unde r the circ um stances, are all close to those re ported here. The C - 0 di s ta nces aT!n () - C - 0 angles reported here fo r the CO:! group do nUL diffe r from each other significa ntly a t the 95 percent confi­de nce level; th e same is true for the O-C-O a ngles. In view of th e possibility of unknown systemati c error , nec­essaril y excluded from the calculations, our results

therefore do not preclud e trigonali ty of the C O :! group. Beca use th e oxyge ns in the CO:1 group have very similar e nvironments , little de via tion fro m trigonality is ex­pected. The CO :! group is non planar however. The carbon atom is 0.026(4) A out of the plane of th e oxygen a toms in the CO :! group in aragonite. This dis place me nt is a pproximately seven times the standard devia ti on and is clearl y s ignificant. Th e di spl ace me nt is towards th e nearest Ca layer and is presumably a result of polarization of each oxygen atom by the three bonded Ca ions. If the di s placement we re caused by Ca . . . C interactions, the C atom would not move towards the Ca layer.

29

The difference in the O- C- O angles, 119.6° and 120.13°, if real , is consistent with the 0(2, 21) edge of the CO:1 group being coordinated slightly more strongly to Ca as judged from the Ca .. . 0 distances. How­e ver , thi s s tronger coordination of 0 (2) to Ca would also sugges t that C - 0 (2) should be longer than C- O(1). This is not the case. The a verage value of the C- O di sta nces is 1.286 A. Thi s agrees well with th e C- O di stan ces of 1.283(2) A re ported [14]for calcite in whic h 32 symme try is forced on the C0 3 gro up by space­group R3c. If the a pparent thermal moti ons of the a toms in the C O:! group are attributed to thermal motion rather than to slight positional disorder , there

OJ OJ

FIGURE: 2. The Ca environment in aragonite (CaCO,,).

FIGURE: 3. Th.e CO" group environment in aragon.ite (CaCO,,).

The labels refer to atoms in table 4.

seems to be oscillation within the C03 layer, i.e., more or less perpendicular to the edge coordination to Ca.

TABLE 3. The Ca environment in aragonite (CaC03 )

Atoms Di~tance , *Lower *Noncorrela led A raw bound [13J motion [1 3J

Ca,O(l") 2.414(2) 2.414 2.423 Ca, 0 (2", 2' '' ) 2.445(1) 2.445 2.454 Ca, 0(2 , 2') 2.520(1) 2.520 2.527 Ca, 0(2' '', 2') 2.544(1) 2.544 2.551 Ca, 0(1, I') 2.653(1) 2.653 2.660

In all tables of interatomic distances and angles , the figures in parentheses are standard deviations in the last digit and were cal· culated from the standard deviations in the atomic positional paramo eters and the un it cell parameters.

*Mean separat ion between atom s when allowance is made for th ermal mot ion.

30

Similarly, 0(1) may be undergoing some additional wagging out of the C03 layer.

TABLE 4. The C03 group and its environment w aragonite (CaC03 )

Atoms Distan ce, A Lower Riding or angle, deg. bound [l3J model [13]

C,O(1) 1.288(2) A 1.289 A 1.295 A C,0(2) 1.283(1) 1.284 1.288 0(1) , 0(2) 2.229(1) 0(2) , 0(2') 2.219(2) 0(1), C, 0(2) 120.13(8t 0(2), C, 0(2') 119.6(2) 0

0(1), Ca' 2.414(2) A 0(1), (Ca ", Cal li ) 2.653(1) 0(2), Ca 2.445(1) 0(2), Ca" 2.520(1) 0(2), Ca'" 2.544(1)

c.:l .....

'Table 2. Observed and calculated structure factors for aragon ite (caC0 3)

U , K " ,

.... IJ - 01 C!':1U - 289

h 30 S - 35 7 ., cul.lo - ebfl

1 0 1 .. 0 1~ 2

1 2 2 b ~ 28~ 1~ .. 2 2 0

0 , K , I

c.d 21 47 L - 469 .b~ - 344

0; u7 45 2f.,;> - 2!:lB

;>1. 14 '"' ;:>;:l* - 28 " j I n .\ - 1 0 9

1 n 11."1 11 0 11 f., f. - 6b 1 ;,.> I nu 98 1"\ 1<00 9 69

n . .. . 5

qf., 96 2;:>4 - ;:>2 3 1.". \34

6::04 -055 a 2M, - 2 Hb 2.)u 228 20 ;1 - 199

47 46 , ... .. 31 uO 72 7 1:> (, - 1~6

.kO 324 ~ 21;> 208 73 -7 5 4 "'1 63

1 0 1 ;.) 3 151 11. 11 ..... 106 11 79 Bu 11 ~I'>. -l U J. 2 '-I U 3j 1::0 ;> ,, * 11 1.1 o U -77 114 1 0 1 - 159,

U, K . ;.

2U b - 2 1 u ~ t7 558 ~ .Jy -~01

'I ud - 6'1 ~ ,:!.) d 234

16 * - 3 344 346

<;. 1 95 i1 b~ 57 'J ::;,5 - 61

lU 1j,!. -124 1\ ~ 7 -59 1.? 1 ,tu -lj4 13 :,n 4-11 114 /0 -b9

U , K. , ,)

~l -So 4 .... 1 1489

J. 7 * 23 j 7 * - 1 .... iJ .30 1 ~ * 1n

-, 21. 21 h IJ.2 - 113 'J .::1 * lJ

1 U <::.:.U - 222 1 1 ~) j -31 12 1c.o 121 1.1 ;,: 7. -11

(j . ~ , ..

" l u2 t OJ 1 3 ... 0 334 '" ~::;,3 ~ Sl ."\:.. 1 5 0 4 l oU - 16 0

t) .. ' 6

140<., - 5Ub !\ fl - B3 ;:>~* - 1 3

In(, -113 111 1 11

!:i l - ,+7 .2 1 t. 2 1 0

35 ~ I.~h 14'+

83 1 " - 42 11 4 0

G. I>. , 7

R'-4 -92 ;:l 1A14 174 .. r.4 bY

I<. 2">7 251 .. , :>4 F 16

:>..,* -14 U?! 37

10<, -t93 ;>q* 37

In A7 - 90

I: . .. . !:i

" 1 ~., 135 74 - 82

? 1:>3 123 \ 1n:> lu8

.. In" - 104 S ;::0"'. 20 r. If. r, -1 57 7 f,.. -64

<; 1 -~1

?! f, . -26

O. K , 9

70 64 147 -1 50 27* -1 6 '+8 -44

5 57 - 52 27* 0 46 - 311

O,K o1 0

4b - 36 1 09 -11 0

88 - 85 j 58 - 52

1 , K. 0

~ 4 - 61 404 477

49 45 131 -1 29 2 1 6 - 2 12

11 2 2* - 5 13 93 72

1.K,1

423 421 I bO 153

j 51 -49 175 168 300 -~OO

20* 33 192 -187

88 - 92 2 1* 13

10 34 - 20 11 185 1 8 7 Ie 4 9 -44 13 9 1 B9 14 47 39

1,1< . 2

471 454 407 -4 0 4-

16* -7 476 -!.I.71

16* -1 0' 214 - ;>17 1~3 -156 1 8 1 185

4 4 -42 2 41 2 4 2

lU 24* -4 11 lOB 1.04 12 8b 84-13 113 -1 0q 14 :30* 17

1. K.3

5 1 0 -!'iOS l u 1 -95

27 - 25 4 83 -82

Columns are K, lOF

"> '63 365 I P. * - ~

7 'IS 319 A 4A 53 g 4 7 -4~

1 ~ '+2 40 11 150 -1 57 12 25. 3 13 1 H~ -17 R

1 . K ,4

n W.. RS <!Yn 2A7

84 - A2 'I '163 365

61 f,5 l'B I Rq

" n * - f,

t 57 -1 60 2.1 * 17

;:>22 - 221i I n 4;> -U4 11 l U4 -l n 7 1;:> 2S . 7 1 3 1 01 q7

t,K,5

;:>57 2UCI 32 2S 2n* -14 2 n * 0

~ l A - 21fl 2;> . -~1

1 ~i\ -1 (-,2 2~* 4 2.'* 6

I n 4., -34 11 153 152 12 47 45

1':( , 6

n 6n 60 2 1 * - 2.3 36 31.1-

::037 - <3q 1.1- .' - 3C1 ~q - 31 5u -56 dr. 74 23* - 15

q 1 5;> 152 1 :1 3A 3~

1 t 27.

1. 1( ,7

1 14~ -1 4~ ;:> bR - 97 " .33 15

gu - 96 1 j'l 14 0 ;l .,. -9

fiR 9 0 A 97 95 Q ?s* -7

0' lOF

c

10 46 42

1 , K.R

18 1 -t A7 117 11 0

2 147 - 2 0 ~ 143 146 4 36 27 5 AD 8 1 6 135 133 7 85 - 89 8 28* 37 9 III -111

I , K , 9

1 145 14S 2 95 93 .3 29 . 0 4 9(' .'19 5 126 - 129 6 43 3 7 131 -132

l, K 01 0

o 47 42 go:; - 98 63 66

llA - 119

;> . K.O

469 - 494 477 - 466 151 146 615 635

8 2 1* 4 10 7t -71 1 2 205 - 20 1 14 119 -117

2 , 1( .1

264 254 653 659 :?53 - 247 :>70 272 tl7 119

51 50 7 ~O - 85

2 56 - 253 49 - 55

10 227 - 230 11 47 54 1 2 2A* 2A 13 28 * 14 14 t46 144

2 . K , 2

5 1 5 513 12 3 1 20 141 142

6 1 - 58 ? 34 - 237 189 - 194

(, lA6 -1 AU 7 158 1 5 7 A 156 - 1S7 q 65 - 6q

1 0 146 1 48 1 1 4 6 4? 1 2 1(,0 1 'is

13 39 ~'"

2.K , ~

33 ;:>9 46 _50 I H* 10

.39 1 - ,9:\ ') 38 -44

126 l ;:>q 21- _ 2 u

H 177 l An

9 ;>2* I? 1 0 f,4 Ii? 11 ;>6* 21 \? 38 - A t:~ 2 9* 12

2 , K , 4

o 3 .'8 -"3h lA. A q4 - "'Ii

116 -117 ~ 17b 1 A? S 1('7 - 16A h it 6 1 17 7 11'>3 1 f,,;:> F'. 1 32 12q 9 24 * 3

1 0 127 - 1;>Q 11 54 ">1'> 12 1 .35 - l~ n

2,K , 5

201 - :>0:> 290 ;::OQ2 1 23 122 165 1 6 U

22 * 1 n ?3 * 17

132 120 l A2 - l AO

46 ~7

t o 15 0 -1 "i0 11 A9 - 9r. 12 4A ')7

2 . K . 6

230 ;)~n

50 UA 1 55 , ">7 Ins , nc;

7 2 _ 1'>9 75 6."\

£> 343 - "\46 7 55 - ''is

;>4* -1 62 - 71

1 f1 57 47 11 30 * _ 30

:> . K,7

34 2fl ?5? - :;053

72 6f, 1?9 - ,3~ 116 - lIP

27 . - 2 A ;:>7* - 22

A 146 152 o 2A * 23

1 0 1'+9 147

2.:< . A

I An -1 AO 5.3 - 5;> FH\ - 83 63 -7 0

4 97 1 O~ 5 53 5?

113 117 46 -46

A AS AU

2 . K , 9

5 0 - 50 56 ~? 3 7 - A

156 153 7 2 65

f" 59 - 5 1

2.K, I n

106 1 0!:i 44 37

~ 51 39

:,\ • ..:. 0

1 191 -1 9n 31A - ,23

l eu 33 7 34 ?;:> o ;>2"> ?2q

11 " q 24 l"'i 1 0 1 -1 02

3.1< ol

2!:i'" -;:lsq ;> 06 -;> 0 1

, 5 1 _ 4h l A* 4

2QO 2AA 65 - SA

172 1 flq ~4 4~

4 5 - 3q 1 n 54 6:'\ 11 J44 -1 4 f> 1::0 27* 1 3 D 1 0 1 - 8A

3.K , ;>

1 20 -12.:> 206 204

74 - 73 360 360

1 q* -25 20 0 204 lAq 198 194 _196

23 * -21 9 19P _ 19A

1 0 2 :h 9 11 qO - A7 12 47 -'+7 13 1 0!" A3

3 , K , ,

4 1A 423 72 76

1 02 - 99 59 57

22 1 _ 224 21 * 3

268 - 266 8 45 -4? q ;:l4 . - A

l n 47 - 3A-11 179 184 12 ';JA * - 2

3 . K,4

3A 33 Hift -169

20 * lA 3 0 5 - 303

74 -77 191 - 191

59 56 179 179

A 6n - 59 9 I B9 lA6

1 0 46 4(' 11 A7 A6 12 2A- . 15

3 , K. <;,

1 195 -197 40 33 21 * -1 9 71 - 72

220 21:5 4q 47

15U 146 A 26 * 23 q 2 4* - 2 0

1 0 25 * -4 11 120 -12 3

3.1", F.

6 4 - 64 AA 85 23 * - 27

2 0 3 204

,. 4 "t 5 -7

u7 45 ;:l4* - l A ;:>7* lA

1 n4 -1 62

6 7 8 9

to up, - 2A

3,K . 7

1 1 n7 llU 2 119 12 0 3 ;>4. 19

u3 4f, t "i0 -150

;:>r.. 22 79 - fl7 1;8 -70

9 :;OQ. 2f,

:."I.K ,A

1 ~9 122 A2 - p.o:;;

'i1 43 l~ti - 136

::09 -1 2 ou - A;>

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10 I.:>A 1 29 11 !:il 56 1 2 ' f') . 23

U. K . 2:

lA9 -lin lA7 11'9

2u3 -202 .. d - 52

I b l 154 il ... 16

I") 2 .)4 2.36 7 4b 43 ,., 0 1 Sri 9 .. ~ -34

1 0 lu ll -1 0 1 11 ~8 * - 3b 1 2 I.::: U -11 7

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.. 4 -314 t:': .... o 272

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11 9 176 Ibj

30 - 12A

4R - 192

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89 10 0 0 11 49 -"

4 , K . ...

(j 3 74 1 15 -17 7

05 61i 2 u j - 207 1.) 0 -1 31

6 o::~.. 21 7 ~2 - 91

l u Y 165 .::4 * 4 0

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1 24 -1 22 177 -17 2

27* 20 29* - 11

171 167

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124 - 12h 103 - 92

41 - 37 43 41

1 71 175 55 -41 97 105

13 41 11

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25* -10 82 82 44 - 39

1 8 4 179 26* - 23

116 11 6 130 1 22 1 28 -1 27

47 -42

7.K , .3

228 21 1 43 37 86 - 82 .36 26 97 - 94 28* 1

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F and Fare on an abso lute scale. Reflections marked a re"unobs erv ed" o c

We thank W. E. Brown for helpful discussions and P. B. Kingsbury for technical help. The ORTEP pro· gram of C. K. Johnson, Oak Ridge National Laboratory, was used to draw the figures. This investigation was supported in part by research grant DE-00572 to the American Dental Association from the National Insti· tute of Dental Research, and is part of the dental research program conducted by the National Bureau of Standards in cooperation with the American Dental Association; the United States Army Medical Research and Development Command; the Dental Sciences Division of the School of Aerospace Medicine, USAF; the National Institute of Dental Research; and the Veterans Administration.

4. References

[I] Palache, C., Berman, H., and Frondel, c. , Dana's system of mineralogy, vol. II, 7th ed., J. Wiley and Sons, N.Y. 1963, 182- 193.

[2] Busing, W. R., An aid to the analysis of interionic and inter­molecular forces in crystals. Abstract Ml. American Crystal­lographic Association winter meeting, Tucson, Arizona (1968).

[3] Bragg, W. L., The structure of aragonite. Proc. Roy. Soc. London , 105, 16- 39 (1924).

r 41 Reference [1J, page 184.

32

[S] Burnham , C. W. , Computation of absorption corrections and the significance of end effect. Am. Min., 51, 159- 167 (1966).

[6] Busing, W. R., Ellison, R. D., Levy, H. A., King, S. 1'., and Roseberry, R. T., The Oak Ridge Laboratory Computer­controlled X-ray Diffractometer. Oak Ridge National Laboratory Report ORNL 4143 , January 1968.

[7] Alexander, L. E. , and Smith , C. 5. , Single crystal intensity measurements with the three circle counter diffractometer. Acta Cryst., 15, 983-1004 (1962).

[8] Ibers, J. A., Estimates of the standard deviations of the ob­served structure factors and of the electron density from intensity data. Acta Cryst., 9,652-654 (1956).

[9] Tippett, L. H. C. , On the extreme individuals and the range' of samples taken from a normal population. Biometrika, 17, 364- 387 (1925).

[10] International Tables for X-ray Crystallography, 3, p. 202. The Kynoch Press, Birmingham, England, 1962.

[II] Stewart, J. M., Editor. X-ray 67 program system for X-ray crystallography. Technical report 67- 58, University of Mary­land , College Park , Maryland 20742 , December (1967).

[12] Finger, L. W. , Determination of cation distribution by least squares refinement of single crystal x-ray data. Carnegie Institute of Washington Year Book, 67, 216- 217 (1969).

[13] Busing, W. R., and Levy , H. A., The effect of thermal motion on the estimation of bond lengths from diffraction measure­ments. Acta Cryst., 17,142- 146 (1964).

[14] Chessin, H., Hamilton , W. C., and Post, 8., Position and thermal parameters of oxygen atoms in calcite. Acta Cryst. , 18,689- 693 (1965).

(Paper 75Al-647)