Refinement of the Crystal Structure of the Aragonite Phase of Caco3

Home , Aragonite

JOURNAL OF RESEAR CH of the N a tional Bureau of Standards - A. Physics and Chemistry Vol. 75A No. 1, January - 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)

Arago nit e (C aCO ,,) c ry stalli zes in th e unit cell 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 Pm cn. The structure has been re fin ed to N".= 0.024. N= 0.040 using 765 x- ray reAections from a sin gJe crystal. The Ca ion is coordinat ed to nin e oxygens with Ca .. . ° distances III the range 2.414(2) A to 2.653(1) A. The two un ique C- O di s ta nces in th e CO" group are 1.288(2) ;\ (o n the mirror plan e) and 1. 283(1) A. T he two un ique O- C-o a ngles are 119.6(2 )" (acro ss the mirror plane) and 120.1 3(8)". The dis tances a nd angles in th e CO" "roup are not signifi cantl y d iffe rent at the 95 pe rcent confidence level. "

Key word s; Calcium carbonates; carbonates; crystal s tructure; s in gle c rys t.al x- ray diffracti on.

1. Introduction density, 2.944 g ' cm- 3 ; Crystal: material available was heavily twinned; a s ma lJ wedge was th e largest crystal Aragonite (CaCO:d is found in nature as a mineral fragment found whi ch showed no evidence of twinning and is an important biomineral because of its presence under optical and x·ray examination; this wedge was in coral, clam shells, gall stones, and otoliths. It is iso attached to' thin borate glass fiber with clear household structural with the carbonates of large divalent cations cement ; fib er attached to in sert in go niometer head such as Ba, Sr, and Pb. with epoxy cement; origin of crystal, mineral sample Aragonite is less stable than the calcite phase of #75538 from National Museum of Natural History, CaCO ~ at room temperature, transform s into calcite, Smithsonian Institute, Was hington, D.C. (S upplied by and is denser than calcite_ Thus aragonite is a high ]. S. White, Jr.); linear absorption correcti ons made pressure form of CaCO:J• More details are available in by 8 X 8 X 8 Gaussian quadrature using subroutines reference [1].1 Because of the importance of aragonite, written by C. W. Burnham [5 1and adapted by B. Di ck· and because of the possibility of performing calcula ens; maximum and minimum corrections for absorp tion s on th e lattice energies of selected carbonates tion = 0.880 and 0.963 (transmi ssion factors). Intensity along th e lines suggested by Busing [2], we have col Data: number of re fl ections, 2356 collected from 3 lected ne w x-ray data from a sin gle crystal of aragonite octants and merged into a unique set of 765 , of which and have refined the structure from the positions given 619 are "observed" and 146 are "unobserved"; un in 1924 by Bragg [3]. observed reflections are those less than 2(T above background; maximum sin 8/A for data 0.907 A - I; 2. Structure Determination meth od used to estimate data: 8-28 scan, scintillation counter; diffractometer: Picker ~ 4·circle single-crystal

F ornwLa (ideal): CaCO:l (aragoniteo phase); Unit diffractometer automated by PDP 8/1 computer through t:;eU: orthorhom~ic with a = 4.9598(5) A, b = 7.9641(9) F ACS-l interface and adapted to include least sig A, c = 5.7379(6) A at 25 DC (calculated by least squares nificant digit of counts; Computation: setting programs, from 12 28 values observed on a diffractometer those of reference [6] as adapted by Picker Nuclear volume: 226.65 A:1; radiation, Mo(Ka l ), A= 0.70926 ;( Corporation; 0 scan range: 1.4°+ 114.6 0.692, monochromator: highly oriented graphite crystal; ~", ~A = space·group: Pm cl1 ; contents 4(CaC03 ); reciprocal A= 0.70926 A; scan parameters: backgrounds counted lattice extinctions, hkO: h + k = 211, + 1, hOL: L= 211 + 1; at higher and lower 28 for 100 s each; {}-28 scan at observed density, 2.947(2) g'cm -:3 [4J; calculated . t Certain commercial equipment , in struments, or materials are ide ntified in this pape r III order to adequatel y specify the expe rim ental procedure. In no case does sti c h id ent ifi ca· *Rest:arch Associate from the Ame rica n Dental Association a l the Nati onal Bureau of ~io.n imply rt:commendat ion or endorsement by the National Bureau of S ta ndards, nor does Standard s. Wa s hi nglon. D.C. 20234. It Imply that the material or equipment id entified is necessarily the best ava ilable for th e I Figun's, in b rackets in di n lk lilt:' lilt-rature rdt' rt ' llct'S at the end of th is pa per. purpose. 27 0.25°/min for 28 from one background position to the full-matrix, with ! w(lFol-IFcl)2 minimized ; refin e other; attenuators: 00.25 mm thick layers of Nb, 2 layers ments include unobserved refl ections which calculate for first attenuator, 4 for second , 6 for third; scan range hi gher than 2cr above background; least-squares correction: table look-up method to obtain values weights: 1/cr 2 (F ) ; R".= [LW(!Fo 1- IFe I F/LW!Fo It ] 1/2, recommended in refere nce [7]; intensity data on paper R = !IIF ol - lFcl l/! lFol; thermal parameters have the tape, processed by program written by B. Di ckens fo r form exp [- 1/4(a*2 Bllh2 + b*2 B22 /,- 2 + c*2B :I:I / 2 Univac 1108 computer; this program contains adapta + 2a*b*BI 2hk + 2a*c*BI 3hl + 2b*c* B23 kl) ]. Most least tions of subroutines writte n for similar program by squares and electron density synthesis calculations F. A. Mauer (NBS), standard refl ection plotting routine were carried out with the X·ray 67 syste m [11] of and extinct refl ecti on editing routine from programs co mputing programs. by 1. M. Stewart, Uni vers ity of Mar yland, a nd uses a n Final R efinement: R".= 0.024; R = 0.040 , average intense sta ndard refl ection (at low 20 angle) measured shift/error for last cycle = 0.0017; standard deviation every 50 refl ectio ns to correct for any change in of an observati on of unit weight intensity of the primary x-ray beam. Counts in = [!w(Fo- Fc)2/(765-28) ] 1/2= 0.775. peak = 1 = P - (T/2TB ) (B L + B H ) , cr(I) = [P + (B L + B,_,) (T/(2TB ))2 ]l /t, F = [(A F )(LP) (l ) ]l /t, cr (F ) The structure was refin ed isotropically from the = (cr(l )/2) (LP/I) lit, LP = 2 sin 20(' /(cos 2 20/l/ +cos2 positions give n by Bragg to R/V= 0.031, R = 0.047, a nd 20c ), f3 = - 1. 58883 X 106 LA.2(cos2 20111 + cos4 20c ) then anisotropically to Rw= 0.024, R = 0.040. The low dA /d/J-] / [AP sin2 Oc(cos 2 20m + cos2 20e ) ] (for extin c value of R Ie supports the earlie r indications that the tion corrections, calculated at same time as absorption crystal used in the data collection is not twinned. The correcti on). P = count s at the peak position, B\. and highest peak in an electron density difference synthesis BH = background counts at lowe r and hi gher 20 respec calcul ated aft er ani sotropi c refi nement to Rw= 0.024 tively, T = time spend counting peak, Til = time spent corres"Po nded to about 1/3 of an electron and was about counting each background, AF = atte nuator factor, 0.95 A from C towards 0 (1). The largest correlation LP = Lore ntz-polarizati on correcti on, Oe = Bragg a ngle coeffi cients are 0.34-0.44 between the scale factor and for refl ection under consideration, 0 111 = Bragg angle the B II , B22 and B:l :l te mperature factors of Ca. for monochomator (= 6.005° here), A = transmi ssion Two cycles of least squares refin e ment in which factor in the a bsorption correction , /J- is the linear the isotropic secondary extinc tion parameter r in absorption coe ffi c i~ nt , ciA /ci/J- is in mm, V is the volume P = F 3nc/ O + f3r !FuncI 2 ) was varied [12] together of the unit cell in A3. Data merging program for equiva with all other un constrain ed parame ters resulted in no lent refl ections, written by B. Di cke ns for Uni vac 1108 change in Rw or R and gave a value of - 0.3(9) X 10- 8 computer ; in this program each set of equivalent re fl ec for the extinction para meter. There was no significant tions is treated as follows: Refl ections which were all change in the structural details or their standard devi a- I unobserved were averaged and given the largest in tions. Thus, we believe secondary extinction to be dividual standard deviation in the set. Unobserved negligible in our crystal of aragonite. Only the observed refl ections in the presence of at least one obser ved re refl ecti ons were used in these refi ne me nts. Three fl ection were discarded. O bserved refl ections which cycles of least squares refin e me nt in whi ch allowance occurred only once in the re fl ection li st subsequent to was made for the a nomalous scattering of Ca (values this ste p were copied unchanged but their standard take n from reference 10) gave an increase fro m 0.024 deviations were increased by a factor of three. Ob to 0.025 fo r RIO' R was unchanged. There were no served refl ections with magnitudes which agreed significant changes in the atomi c positions. within the counting statistics and re Hections with The atomi c parameters from the refin e me nts without magnitudes whose ratios fell within the range 0.95 to corrections for a nomalous dis persion are give n in 1.06 were averaged and give n as sta ndard deviatio n table 1. The observed and calcul ated struc ture factors the maximum of the standard deviation from counting are given in table 2. T he thermal para meters fro m the statistics and the standard deviation from the range refin eme nts whi ch included correcti ons for the estimate [8 , 9]. Under these circumstances, refl ections a nomalous scattering of Ca are Ca: 0.71(1), 0. 65(1), whose magnitudes did not pass the criteria were dis 0.650), 0.00, 0.00, - 0.01(1); C: 0 .67(5), 0.80(6), 0. 43(5), carded. If no members of a set of equivalent refl ections 0.00, 0.00, 0.08(5); 0(1): 1.45(5), 0.51(4), 1.01(5), 0.00, passed the criteria, the highest magnitude was taken 0.00, 0.04(5); 0(2): 0. 67(3), 0.98(3), 1.00(3), - 0.32(3), and the associated standard deviati on multiplied by - 0.02(3), - 0.09(3). O nl y those for Ca are significantly fi ve. The justifi cation for these arbitrary increases of different from the valu es in table 1. Di s tances and standard deviation is that, without some corroboration , angles referred to in the paper were calculated us in g every refl ecti on is suspect because of the possibilities the values in table 1. of multiple refl ection, including the " tail" of nearby intense refl ecti ons in its measureme nt, cha nge in 3. Description of the Structure intensity of x-ray beam during refl ection measurement, The structure of aragonite, the main points of which misalignment of crystal, etc. Since we usually measure are well known , is shown in fi gure 1. The Ca ions lie three sets of equivalent re fl ections with care the in pseudohexagonal layers parallel to (001) and the number of standard deviations increased in this way layer sequence is ABAB. The Ca layers are separated is very small. Scattering factors: those for the ne utral by CO:! groups which lie in two layers parallel to (001), atoms in reference [10] ; least-squares refine ments: and form columns parallel to [OOl]. 28 ------

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 pare ntheses are sta ndard e rro rs in last s ignificant fi g ure quoted , and were computed in the final cyc le of full· matrix least· sq ua res re fi nem ent. *The rmal para meters are in "\'.

F tGU HE I . A stereoscopic il/ustratioll of the crysta l strucw re of a.ragonite (C a CO ,,).

A uniq ue set of at oms is labeled. The ori gin of the crystallographic coor(linale system is ma rk ed by *.

3.1 . The Co Ion Environments therefore do not preclud e trigo nali ty of the CO :! group. Because th e oxyge ns in the CO:1 group have very similar The Ca ion lies on the mirror plane at x = 1/4. Its environments, little devia ti on fro m trigonality is ex environment is shown in fi gure 2 and summari zed in pected. The CO :! group is non planar however. The table 3. The coordination of nine oxygens to Ca consists carbon atom is 0.026(4) Ao ut of the plane of th e oxygen of three CO:1 edges, 0 (1, 2), O(l t, 2t) and 0 (2tV, 2 V) atoms in the CO :! group in aragonite. This dis placement and th ree apexes, O(lll , 2 11 , 2111 ). The apparent thermal is approximately seven times the standard deviati on and motion of Ca is almost isotropic (table 1, fi g. 2). is clearl y signifi cant. The di spl aceme nt is towards Correcti ons as given by Busing and Levy [1 3] to the nearest Ca layer and is presum ably a result of obtain the m ean separation between atoms from the polarizati on of each oxygen atom by the three bonded observed atomi c positional and thermal parameters Ca ions. If the di s placement were caused by Ca . . . C were calculated using a program written by Finger [1 2j. interacti ons, the C atom wo uld not move towards the These corrections are included in tables 3 and 4. Ca layer.

3.2. The C03 Group 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 details of the CO :1 group and its environment the CO:1 group being coordinated slightly more strongly are given in table 4 and shown in fi gure 3. The positions to Ca as judged from the Ca .. . 0 distances. How reported by Bragg [3] give C- O di stances of 1.26 Aan d ever , this stronger coordination of 0 (2) to Ca wo uld 1.30 A, and O- C - O angles of 117°, 11 7° and 12r, also suggest that C - 0 (2) should be longer than C- O(1). which, under the circum stances, are all close to those This is not the case. The average value of the C- O reported here. The C - 0 distances aT!n () - C - 0 di stances is 1.286 A. This agrees well with the C- O angles reported here fo r the CO:! group do nUL diffe r di stances of 1.283(2) A reported [1 4]for calcite in which from each other significantly at the 95 percent confi 32 symmetry is forced on the C0 3 group by space dence level; th e same is true for the O-C-O angles. In group R3c. If the apparent thermal moti ons of the view of th e possibility of unknown systemati c error , nec atoms in the CO:! group are attributed to thermal essaril y excluded from the calculati ons, our results motion rather than to sli ght positional disorder , there 29 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 Similarly, 0(1) may be undergoing some additional or less perpendicular to the edge coordination to Ca. wagging out of the C03 layer.

TABLE 4. The C03 group and its environment w TABLE 3. The Ca environment in aragonite (CaC03 ) aragonite (CaC03 )

Atoms Di ~ tance , *Lower *Noncorrelaled Atoms Distance, A Lower Riding A raw bound [13J motion [1 3J or angle, deg. bound [l3J model [1 3]

Ca,O(l") 2.414(2) 2.414 2.423 C,O(1) 1.288(2) A 1.289 A 1.295 A Ca, 0 (2", 2' '' ) 2.445(1) 2.445 2.454 C,0(2) 1.283(1) 1.284 1.288 Ca, 0(2, 2') 2.520(1) 2.520 2.527 0(1), 0(2) 2.229(1) Ca, 0(2''', 2') 2.544(1) 2.544 2.551 0(2), 0(2') 2.219(2) Ca, 0(1, I') 2.653(1) 2.653 2.660 0(1), C, 0(2) 120.13(8t

0(2), C, 0(2') 119.6(2) 0 In all tables of interatomic distances and angles, the figures in 0(1), Ca' 2.414(2) A parentheses are standard deviations in the last digit and were cal· 0(1), (Ca ", Calli ) 2.653(1) culated from the standard deviations in the atomic positional paramo 0(2), Ca 2.445(1) eters and the un it cell parameters. 0(2), Ca" 2.520(1) *Mean separation between atoms when allowance is made for 0(2), Ca'" 2.544(1) th ermal motion. 30 'Table 2. Observed and calculated structure factors for aragonite (caC03)

U , K " , 0; u7 45 O. K , 9 "> '63 365 10 46 42 (, lA6 -1 AU 1 f1 57 47 3.K , ;> 4 "t ,. 2u3 -202 4 • ., . 7 42 -43 1<, , ;,: . 0 o 28. ~ 175 - 1r.0:;; 2f.,;> - 2!:lB I P. * - ~ 7 1 58 1 5 7 11 30 * _ 30 5 -7 .. d - 52 59 -72 7 89 A4 54 - 5 1 .... IJ - 01 ;>1. 14 70 64 7 'IS 319 1 , K.R A 156 - 1S7 1 20 -12.:> 6 u7 45 I b l 154 hi -09 48 -48 ;:>57 - 25(' 8 129 -12 7 1 t.3 -I If, C!':1U - 289 '"' ;:>;:l* - 28 147 -1 50 A 4A 53 q 65 - 6q :> . K,7 206 204 7 ;:l4* - l A il ... 16 .J I">;) 146 2~8 263 12A - 131 149 4S h 30S - 357 " j I n .\ - 1 0 9 27* -16 g 4 7 - 4~ 181 -t A7 1 0 146 1 48 74 - 73 8 ;:>7* lA I") 2 .)4 2.36 .\ 4U 41 23* -1 iB AS o , K, 6 1.32 I;>? ., cul.lo - ebfl 1 n 11."1 11 0 '+8 -44 1 ~ '+2 40 117 11 0 1 1 4 6 4? 34 2fl 360 360 9 1 n4 -1 62 7 4b 43 t. 1Ql 191 224 2 1 3 ,un 299 1 0 1 .. 0 1~ 2 11 f., f. - 6b 5 57 - 52 11 150 -157 2 147 - 2 0 1 2 1(,0 1 'is ?5? - :;053 1 q* -25 to up, - 2A ,., 0 1 Sri ., ';)7. 23 H 54 .39 J\ 2Fo* 2u lA6 174 7,K, "'i 1 2 2 b ~ 28 ~ 1 ;,.> I nu 98 27* 0 12 25. 3 ~ 143 146 13 39 ~'" 72 6f, 200 204 9 .. ~ -34 h ;) lj + -11 9 73 - 67 I n on -ItS 29. 32 1~ .. 2 2 0 1"\ 1<00 9 69 46 - 311 13 1 H~ -17R 4 36 27 1?9 - ,3~ lAq 198 3,K . 7 1 0 lu ll -1 0 1 ."li n . ~4 1 0 27* 25 91 79 11 5 -11 ::0 5 AD 8 1 2.K , ~ 116 - lIP 194 _196 11 ~8 * - 3b M 1"';;> -1 ~2 11 77 - 83 F"I(.1 60 f>7 31* 2p, 0 , K , I n . .. . 5 O,K o1 0 1 . K ,4 6 135 133 27. - 2 A 23* -21 1 1 n7 llU 1 2 I.::: U -11 7 71 - 53 2Q .. - .:>1 7 85 - 89 33 ;:>9 ;:>7* - 22 9 19P _ 19A 2 119 120 4 . ... , 8 5,K . 4 47 4.3 29* 37 Fl2 -77 c.d 21 qf., 96 4b - 36 n W.. RS 8 28* 37 46 _50 A 146 152 1 0 2 :h 9 3 ;>4. 19 4 , ~ , .) ;:>43 241 201 - 203 136 I ~q 47L - 469 2;:>4 - ;:>2 3 11 qO - A7 u3 4f, 1 09 -11 0 r.. 22 t:': .... o 272 1 nr: 97 92 - 88 4-;::0 ~1 2.)u 228 20;1 - 199 61 f,5 126 l ;:>q 2.:< . A 79 - fl7 .::1.. 1 0 9 1 3217 211 .2u" 17 4q 30 4F1 _ Ul'> 47 46 , ... .. 31 1 , K. 0 l'B I Rq 1 145 14S 21- _ 2 u 3 , K, , 1;8 -70 -17 71 <;II. - 87 43 37 47 - 4"> 152 - 151 73 P.O uO 72 7 1:> (, - 1~6 " n * - f, 2 95 93 H 177 l An I An -1 AO 9 :;OQ. 2f, 0:: 2* 26 ;::09* 1 0 1 0 1 1 02 p. 178 - 170 4f, 25 3 0 * -I F. .kO 324 ~ 21;> 208 ~ 4 - 61 t 57 -160 .3 29. 0 9 ;>2* I? 5.3 - 5;> 4 1A 423 h <.. 2 * 2 (. l'?~ -1 £6 26* .39 q ?M * - 9 4 1 0 4 -9R 1 26 1?4 73 -75 4 "'1 63 404 477 2.1 * 17 4 9(' .'19 1 0 f,4 Ii? FH\ - 83 72 76 :."I.K ,A oJ 7 2u B4 - 88 1 11 13q - t31i 1 0 1 ;.) 3 151 11. 11 ..... 106 49 45 ;:>22 - 221i 5 126 - 129 11 ;>6* 21 63 -70 1 02 - 99 R ll~ -111 4. " . 9 8 2b* - 14 7 , K . 0 8 , K . O 11 79 Bu 11 ~I'>. -l U 131 -1 29 I n 4;> -U4 6 43 3 \? 38 - A 4 97 1 O~ 59 57 1 ~9 122 9 c.~ . 9 178 -1 75 (, , 1( . 2 J. 2 '-I U 3j 1::0 ;> ,, * 11 2 1 6 - 2 12 11 l U4 -l n 7 7 131 -132 t:~ 2 9* 12 5 53 5? 22 1 _ 224 A2 - p.o:;; i ll l o U -17(' 1'.2 54 10 £ 9* - 2P. 1 24 -1 22 247 ?3 ~ 1.1 o U -77 11 2 2* - 5 1;:> 2S. 7 113 117 21 * 3 'i1 43 11 ~7* -20 11 I -117 ;) O~ 2 I n 177 -172 47 ~? 114 1 0 1 - 159, t) .. ' 6 13 93 72 1 3 1 01 q7 l, K 01 0 2 , K , 4 46 -46 268 - 266 l~ti - 136 12 ,;2 9~ " ? ~ * -11 5 , K , 5 2~ * 5 27* 20 5 0 - SU A AS AU 8 45 -4? ::09 -1 2 97 9 7 29* - 11 n l Al - 17;> U, K . ;. 140<., - 5Ub 1.K,1 t,K,5 o 47 42 o 3 .'8 -"3h q ;:l4 . - A ou - A;> 4 , j(, ,14 5 " . ,U 1 177 177 23* 7 171 167 !\fl - B3 go:; - 98 lA. A 2 . K , 9 l n 47 - 3A- 10:;;1 - 153 62 67 4 12r. - 1 2 3 8 ,1(, J 2U b - 2 1 u ;:>~* - 1 3 423 421 ;:>57 2UCI 63 66 q4 - "'Ii 11 179 184 Q6 9 1, d 1;,;.1 11 9 4':" -45 39 - 2q 7 "i - (,2 7,K .l ~ t7 558 In(, -113 I bO 153 32 2S llA - 119 116 -117 5 0 - 50 12 ';JA * - 2 1 1I~ 176 2 71 2 7~ 43 - 3 0 141 - 13<;1 'f.," - '-. ~ .Jy - ~01 111 1 11 j 51 -49 2n* -14 ~ 17b 1 A? 56 ~? ~ . K . q Ibj GI,j. lib 149 -14 0 bF, 60 124 - 12h 147 - 1 U~ 'I ud - 6'1 !:i l - ,+7 175 168 2 n * 0 ;> . K.O S 1('7 - 16A 3 7 - A 3 . K,4 '0'35 30 l.'J... -144 25* -4 Sq - 92 103 - 92 2 7* -1 n ~ ,:!.) d 234 .2 1 t. 2 1 0 300 - ~OO ~ l A - 21fl h it 6 1 17 156 153 143 - 147 1~3 - 12A U~ -136 11 8 -1 21 47 -43 41 - 37 4 142 -1 4;> c.:l 16* - 3 35 20* 33 2;> . - ~1 469 - 494 7 11'>3 1 f,,;:> 7 2 65 3A 33 ~9 -911 5 ,7 4R 11 :>p,* 0 8 28* 1 5 1 0 1 04 101 43 41 "'i 28* 13 ..... 344 346 ~ I.~h 14'+ 192 -187 1 ~i\ -1(-,2 477 - 466 F'. 1 32 12q f" 59 - 5 1 Hift -169 44 3 5 b l ~l - 192 9 2 7* - s 1 71 175 n 2A* 1 n <;. 1 95 83 88 - 92 2~* 4 151 146 9 24* 3 20 * lA 7R -7U 7 .H -7 5 . k. .1 h'l( ,3 55 -41 i1 b ~ 57 1 " - 42 2 1* 13 2.'* 6 615 635 1 0 127 - 1;>Q 2.K, I n 3 0 5 - 303 ~9 9? ri ~d - 3!> 5 , K,6 97 105 A, K " 'J ::;,5 - 61 11 4 0 10 34 - 20 I n 4., -34 8 2 1* 4 11 54 ">1'> 74 -77 9 0 1 - SU 2 ?.... 225 3q 23 13 41 11 lU 1j,!. -124 11 185 1 8 7 11 153 152 10 7t -71 12 1.35 - l~ n 106 1 0!:i 191 - 191 4 , K, n 10 0 0 89 :>1<. -1 0 48 41 9 ,Q -1 02 127 -I?? 1\ ~ 7 -59 G. I>. , 7 Ie 4 9 -44 12 47 45 1 2 205 - 20 1 44 37 59 56 11 49 \ "> 0 - 5 7 36 1 9 ~., 2~* ? 7,K. 2 <)0 4;> 1.? 1 ,tu -lj4 13 9 1 B9 14 119 -117 2,K , 5 ~ 51 39 179 179 onB 675 -" 11:\ 1 19 25* 30 ;::OUI -19 , A5 _ FIg 13 :,n 4-11 R'-4 -92 14 47 39 1':( , 6 A 6n - 59 ~9 39 4 , K . ... 1,:.,4 -lb1 190 -189 j~ - ~A 25* -10 29* -3~ 114 /0 -b9 ;:l 1A14 174 2 , 1( .1 201 - :>0:> :,\ • ..:. 0 9 I B9 lA6 1 <;2 -145 ;>;\. - j 27* - 2 7 67 r.4 82 82 92 qn .. r.4 bY 1,1< . 2 n 6n 60 290 ;::OQ2 1 0 46 4(' 2f,8 - 275 (j 3 74 131 - 134 53 - 5 4 In* -17 44 - 39 S 40 25 U , K. , ,) 0 I<. 2">7 251 2 1 * - 2.3 264 254 1 23 122 1 191 -1 9n 11 A7 A6 1 6 -171 1 15 -177 ~ Al - 76 5 1 -49 t U"i 107 18 4 179 .., :>4 F 16 471 454 36 31.1- 653 659 1 65 1 6 U 31A - ,23 12 2A- . 15 10 116 1 1 F. 05 61i ~ -1 0 94 93 21< 26* - 23 8 ,K, :>i ~l -So :>..,* -14 407 -4 0 4- ::037 - <3q :?53 - 247 22* 1 n l eu 33 I? 2?5 2 17 2 u j - 207 I n u :> 25 h 2B* -1 0 116 116 4 .... 1 1489 U?! 37 16* -7 1.1- .' - 3C1 :>70 272 ?3* 17 7 34 ?;:> 3 , K. <;, 1.)0 -1 31 11 1 /..1 160 h'i( ,4 130 1 22 4- (J -I '"' J. 7 * 23 10<, -t93 476 -!.I.71 ~q - 31 tl7 119 132 120 o ;>2"> ?2q 4 . K. 1 6 o::~.. 21 5.K ,7 1 28 -1 27 1 20 1 1 "> j ;>q * 7 * - 1 37 1 6* -1 0' 5u -56 51 50 l A2 - l AO 11 " q 24 1 1 95 -197 7 ~2 - 91 :0 . .. , ~ 170 -173 47 -42 ?R ' 1 q. 4 .... iJ .30 In A7 - 90 214 - ;>17 dr. 74 7 ~ O - 85 46 ~ 7 l"'i 1 0 1 -1 02 40 33 l u Y 165 1 20 -1 22 2"''' -31 9 0 A7 1~3 -156 2 56 - 253 t o 150 -1 "i0 21 * -1 9 2f,,6 - 26A 1 ~ * 1n 23* - 15 .::4 * 4 0 2 '1 '25 ~O -44 ;::0 Hn -77 7.K , .3 ?8. 17 -, 21. 21 I: . .. . !:i 1 8 1 185 q 1 5;> 1 52 49 - 55 11 A9 - 9r. 3.1< ol 71 - 72 1 06 -11 1 lU I ll) 94 1 2 ...... - 2 1 U 3 49 34 .... 4-7 - 50 h IJ.2 - 113 4 4 -42 1 :1 3A 3~ 10 227 - 230 12 4A ')7 220 21:5 4 33"i - 340 - 54 101 -97 t 004 107 228 21 1 8.t< ,4 'J .::1 * lJ " 1 ~. , 135 2 41 2 4 2 1 t 27. 11 47 54 2!:i'" -;:lsq 4q 47 5 A6 93 4 , K ' n ... ~"li', - 232 90 91 7.' -7r. 43 37 1 U <::.:.U - 222 74 - 82 lU 24* -4 1 2 2A* 2A 2 . K . 6 ;> 06 -;> 0 1 15U 146 6 ~5 2 f, ;> 1. -11 4S 5 F, l U:'\ 105 86 - 82 1 00 qf, 1 1 ~) j -31 ? 1:>3 123 11 lOB 1.04 1. 1( ,7 13 28* 14 , 5 1 _ 4h A 26* 23 7 '7 37 r. .3:;,9 - 357 11 ? -1 09 0:> 70 7 Sf" 79 .36 26 ('3 Sq 12 1c.o 121 \ 1n:> lu8 12 8b 84- 14 t46 144 230 ;)~n l A* 4 q 2 4* - 2 0 8 736 ;:>37 .:;)6 -bO ... Ion - j8 11 .\ 79 97 - 94 :> AO 7 A 1.1 ;,: 7. -11 .. In" - 104 13 113 -1 0q 1 14~ -1 4~ 50 UA 2QO 2AA 1 0 25* -4 9 "> 0 -4 3 jo - 21 7 I n4 101 5,K ,A 2r.* n 28* 1 30" 1 0:; S ;::0"'. 20 14 :30* 17 ;:> bR - 97 2 . K , 2 1 55 , ">7 65 - SA 11 120 -123 10 I.:>A 1 29 "0 - 8n !"'I C"; ,<, -5~ 157 -1 5 1 (j . ~ , .. r. If. r, -157 " .33 15 Ins , nc; 172 1 flq 11 !:il 56 . < 7 9 G 1p. :'1 lBb 1 08 - 1 66 n,i< ,5 49 - ?3 7 f,.. -64 1. K.3 gu - 96 5 1 5 513 7 2 _ 1'>9 ~4 4~ 3.1", F. 1 2 ' f') . 23 .7 -39 I n ? h . 1 93 93 " l u2 t OJ <; 1 - ~1 1 j'l 14 0 123 1 20 75 6."\ 4 5 - 3q '"0 ,.2 1 \ Ql 80 89 - 9 .' 7,K ,14 1 3 ... 0 334 ?! f, . -26 5 1 0 -!'iOS ;l .,. -9 141 142 £> 343 - "\46 1 n 54 6:'\ 6 4 - 64 U. K . 2: < 7. 3 0 1 ",08 1 07" lh!'\ 1(,f, '" ~::;,3 ~ Sl l u 1 -95 fiR 9 0 6 1 - 58 7 55 - ''is 11 J44 -1 4 f> AA 85 i\ l u b 1 0~ S." ,.3 4 30* 26 4 9 42 50 52 ."\:.. 1 5 0 27 - 25 A 97 95 ? 34 - 237 ;>4* -1 1::0 27* 1 3 23* - 27 lA9 -lin " ~ 7 .7 11f, l1q Al - 7.3 4 l oU - 160 Q 189 - 194 2 0 3 204 lA7 11'9 4 83 -82 ?s* -7 62 - 71 D 1 0 1 - 8A I 2 1' - 21~ ~? 20 25_ 1

'1< Columns are K, lOF lOF F and Fare on an absolute scale. Reflections marked a re"unobserv ed" 0' c o c We thank W. E. Brown for helpful discussions and [S] Burnham, C. W. , Computation of absorption corrections and P. B. Kingsbury for technical help. The ORTEP pro· the significance of end effect. Am. Min., 51, 159- 167 (1966). gram of C. K. Johnson, Oak Ridge National Laboratory, [6] Busing, W. R., Ellison, R. D., Levy, H. A., King, S. 1'., and Roseberry, R. T., The Oak Ridge Laboratory Computer was used to draw the figures. This investigation was controlled X-ray Diffractometer. Oak Ridge National supported in part by research grant DE-00572 to the Laboratory Report ORNL 4143, January 1968. American Dental Association from the National Insti· [7] Alexander, L. E., and Smith, C. 5., Single crystal intensity tute of Dental Research, and is part of the dental measurements with the three circle counter diffractometer. research program conducted by the National Bureau Acta Cryst., 15, 983-1004 (1962). [8] Ibers, J. A., Estimates of the standard deviations of the ob of Standards in cooperation with the American Dental served structure factors and of the electron density from Association; the United States Army Medical Research intensity data. Acta Cryst., 9,652-654 (1956). and Development Command; the Dental Sciences [9] Tippett, L. H. C. , On the extreme individuals and the range' Division of the School of Aerospace Medicine, USAF; of samples taken from a normal population. Biometrika, 17, 364- 387 (1925). the National Institute of Dental Research; and the [10] International Tables for X-ray Crystallography, 3, p. 202. The Veterans Administration. 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 Mary 4. References land, Coll ege Park, Maryland 20742, December (1967). [12] Finger, L. W., Determination of cation distribution by least [I] Palache, C., Berman, H., and Frondel, c. , Dana's system of squares refinement of single crystal x-ray data. Carnegie mineralogy, vol. II, 7th ed., J. Wiley and Sons, N.Y. 1963, Institute of Washington Year Book, 67, 216- 217 (1969). 182- 193. [13] Busing, W. R., and Levy, H. A., The effect of thermal motion [2] Busing, W. R., An aid to the analysis of interionic and inter on the estimation of bond lengths from diffraction measure molecular forces in crystals. Abstract Ml. American Crystal ments. Acta Cryst., 17,142- 146 (1964). lographic Association winter meeting, Tucson, Arizona [14] Chessin, H., Hamilton, W. C., and Post, 8., Position and (1968). thermal parameters of oxygen atoms in calcite. Acta Cryst., [3] Bragg, W. L., The structure of aragonite. Proc. Roy. Soc. 18,689- 693 (1965). London, 105, 16- 39 (1924). r41 Reference [1J, page 184. (Paper 75Al-647)