Refinement of the Crystal Structure of the Aragonite Phase of CaCO₃

Abstract

Aragonite (CaCO₃) crystallizes in the unit cell a = 4.9598(5) Å, b = 7.9641(9) Å, and c = 5.7379(6) Å at 25 °C with four formula weights in space-group Pmcn. The structure has been refined to R_w = 0.024, R = 0.040 using 765 x-ray reflections from a single crystal. The Ca ion is coordinated to nine oxygens with Ca … O distances in the range 2.414(2) Å to 2.653(1) Å. The two unique C—O distances in the CO₃ group are 1.288(2) Å (on the mirror plane) and 1.283(1) Å. The two unique O—C—O angles are 119.6(2)° (across the mirror plane) and 120.13(8)°. The distances and angles in the CO₃ group are not significantly different at the 95 percent confidence level.

1. Introduction

Aragonite (CaCO₃) is found in nature as a mineral and is an important biomineral because of its presence in coral, clam shells, gallstones, and otoliths. It is isostructural with the carbonates of large divalent cations such as Ba, Sr, and Pb.

Aragonite is less stable than the calcite phase of CaCO₃ at room temperature, transforms into calcite, and is denser than calcite. Thus aragonite is a high pressure form of CaCO₃. More details are available in reference [1].¹ Because of the importance of aragonite, and because of the possibility of performing calculations on the lattice energies of selected carbonates along the lines suggested by Busing [2], we have collected new x-ray data from a single crystal of aragonite and have refined the structure from the positions given in 1924 by Bragg [3].

2. Structure Determination

Formula (ideal): CaCO₃ (aragonite phase); Unit Cell: orthorhombic with a = 4.9598(5) Å, b = 7.9641(9) Å, c = 5.7379(6) Å at 25 °C (calculated by least squares from 12 2θ values observed on a diffractometer; volume: 226.65 ų; radiation, Mo(K_α1), λ = 0.70926 Å; monochromator: highly oriented graphite crystal; space-group: Pmcn; contents 4(CaCO₃); reciprocal lattice extinctions, hk0: h + k = 2n + 1, h0l: l = 2n + 1; observed density, 2.947(2) g · cm⁻³ [4]; calculated density, 2.944 g · cm⁻³; Crystal: material available was heavily twinned; a small wedge was the largest crystal fragment found which showed no evidence of twinning under optical and x-ray examination; this wedge was attached to thin borate glass fiber with clear household cement; fiber attached to insert in goniometer head with epoxy cement; origin of crystal, mineral sample #75538 from National Museum of Natural History, Smithsonian Institute, Washington, D.C. (Supplied by J. S. White, Jr.); linear absorption corrections made by 8 × 8 × 8 Gaussian quadrature using subroutines written by C. W. Burnham [5] and adapted by B. Dickens; maximum and minimum corrections for absorption = 0.880 and 0.963 (transmission factors). Intensity Data: number of reflections, 2356 collected from 3 octants and merged into a unique set of 765, of which 619 are “observed” and 146 are “unobserved”; unobserved reflections are those less than 2σ above background; maximum sin θ/λ for data 0.907 Å⁻¹; method used to estimate data: θ–2θ scan, scintillation counter; diffractometer: Picker² 4-circle single-crystal diffractometer automated by PDP 8/I computer through FACS–1 interface and adapted to include least significant digit of counts; Computation: setting programs, those of reference [6] as adapted by Picker Nuclear Corporation; scan range: ${1.4}^{°}+114.6\frac{\Delta \text{λ}}{\text{λ}}$, Δλ = 0.692, λ = 0.70926 Å; scan parameters: backgrounds counted at higher and lower 2θ for 100 s each; θ–2θ scan at 0.25°/min for 2θ from one background position to the other; attenuators: 00.25 mm thick layers of Nb, 2 layers for first attenuator, 4 for second, 6 for third; scan range correction: table look-up method to obtain values recommended in reference [7]; intensity data on paper tape, processed by program written by B. Dickens for Univac 1108 computer; this program contains adaptations of subroutines written for similar program by F. A. Mauer (NBS), standard reflection plotting routine and extinct reflection editing routine from programs by J. M. Stewart, University of Maryland, and uses an intense standard reflection (at low 2θ angle) measured every 50 reflections to correct for any change in intensity of the primary x-ray beam. Counts in peak = I = P - (T/2T_B) (B_L + B_H), σ(I) = [P + (B_L + B_H) (T/(2T_B))²]^1/2, F = [(AF)(LP)(I)]^1/2, σ(F) = (σ(I)/2) (LP/I)^1/2, LP = 2 sin 2θ_c/(cos² 2θ_m + cos² 2θ_c), β = −1.58883 × 10⁶[λ²(cos² 2θ_m + cos⁴ 2θ_c) dA/dμ]/[AV² sin² θ_c(cos² 2θ_m + cos² 2θ_c)] (for extinction corrections, calculated at same time as absorption correction). P = counts at the peak position, B_L and B_H = background counts at lower and higher 2θ respectively, T = time spend counting peak, T_B = time spent counting each background, AF = attenuator factor, LP = Lorentz-polarization correction, θ_c = Bragg angle for reflection under consideration, θ_m = Bragg angle for monochomator (= 6.005° here), A = transmission factor in the absorption correction, μ is the linear absorption coefficient, dA/dμ is in mm, V is the volume of the unit cell in ų. Data merging program for equivalent reflections, written by B. Dickens for Univac 1108 computer; in this program each set of equivalent reflections is treated as follows: Reflections which were all unobserved were averaged and given the largest individual standard deviation in the set. Unobserved reflections in the presence of at least one observed reflection were discarded. Observed reflections which occurred only once in the reflection list subsequent to this step were copied unchanged but their standard deviations were increased by a factor of three. Observed reflections with magnitudes which agreed within the counting statistics and reflections with magnitudes whose ratios fell within the range 0.95 to 1.06 were averaged and given as standard deviation the maximum of the standard deviation from counting statistics and the standard deviation from the range estimate [8, 9]. Under these circumstances, reflections whose magnitudes did not pass the criteria were discarded. If no members of a set of equivalent reflections passed the criteria, the highest magnitude was taken and the associated standard deviation multiplied by five. The justification for these arbitrary increases of standard deviation is that, without some corroboration, every reflection is suspect because of the possibilities of multiple reflection, including the “tail” of nearby intense reflections in its measurement, change in intensity of x-ray beam during reflection measurement, misalignment of crystal, etc. Since we usually measure three sets of equivalent reflections with care the number of standard deviations increased in this way is very small. Scattering factors: those for the neutral atoms in reference [10]; least-squares refinements: full-matrix, with Σw(|F₀| − |F_c|)² minimized; refinements include unobserved reflections which calculate higher than 2σ above background; least-squares weights: 1/σ²(F); R_w = [Σw(|F₀| − |F_c|)²/Σw|F₀|²]^1/2, R = Σ||F₀| − |F_c||/Σ|F₀|; thermal parameters have the form exp [− 1/4(a*²B₁₁h² + b*²B₂₂k² + c*²B33l² + 2a*b*B₁₂hk + 2a*c*B₁₃hl + 2b*c*B₂₃kl)]. Most least squares and electron density synthesis calculations were carried out with the X-ray 67 system [11] of computing programs.

Final Refinement: R_w = 0.024; R = 0.040, average shift/error for last cycle =0.0017; standard deviation of an observation of unit weight = [Σw(F₀ − F_c)²/(765 − 28)]^1/2 = 0.775.

The structure was refined isotropically from the positions given by Bragg to R_w = 0.031, R = 0.047, and then anisotropically to R_w = 0.024, R = 0.040. The low value of R_w supports the earlier indications that the crystal used in the data collection is not twinned. The highest peak in an electron density difference synthesis calculated after anisotropic refinement to R_w= 0.024 corresponded to about 1/3 of an electron and was about 0.95 Å from C towards O(1). The largest correlation coefficients are 0.34–0.44 between the scale factor and the B₁₁, B₂₂ and B₃₃ temperature factors of Ca.

Two cycles of least squares refinement in which the isotropic secondary extinction parameter r in $F^2=F_{\text{ unc }}^2/$(1 + βr|F_unc|²) was varied [12] together with all other unconstrained parameters resulted in no change in R_w or R and gave a value of −0.3(9) × 10⁻⁸ for the extinction parameter. There was no significant change in the structural details or their standard deviations. Thus, we believe secondary extinction to be negligible in our crystal of aragonite. Only the observed reflections were used in these refinements. Three cycles of least squares refinement in which allowance was made for the anomalous scattering of Ca (values taken from reference 10) gave an increase from 0.024 to 0.025 for R_w. R was unchanged. There were no significant changes in the atomic positions.

The atomic parameters from the refinements without corrections for anomalous dispersion are given in table 1. The observed and calculated structure factors are given in table 2. The thermal parameters from the refinements which included corrections for the anomalous scattering of Ca are Ca: 0.71(1), 0.65(1), 0.65(1), 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). Only those for Ca are significantly different from the values in table 1. Distances and angles referred to in the paper were calculated using the values in table 1.

Table 1.

Atomic parameters in aragonite (CaCO₃)

Atoms	x	y	z	B11*	B22	B33	B12	B13	B23
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)
O(1)	.25000	.0770(2)	.4043(2)	1.50(5)	.54(4)	1.04(4)	.0000	.0000	.03(4)
O(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 parentheses are standard errors in last significant figure quoted, and were computed in the final cycle of full-matrix least-squares refinement.

^*Thermal parameters are in Ų.

Table 2.

Observed and calculated structure factors for aragonite (CaCO₃)

0, K, 0
2	60	−61
4	298	−289
6	383	−357
8	264	−268
10	140	142
12	285	284
14	42	20
0, K, 1
1	28	21
2	472	−469
3	355	−344
4	654	−655
5	230	228
6	47	46
7	66	72
8	320	324
9	73	−75
10	153	151
11	79	80
12	40	33
13	80	−77
14	161	−159
0, K, 2
0	206	−210
1	577	558
2	409	−401
3	68	−69
4	238	234
5	16*	−3
6	344	346
7	91	95
8	62	57
9	55	−61
10	133	−124
11	57	−59
12	140	−134
13	58	48
14	76	−69
0, K, 3
1	51	−50
2	491	489
3	17*	23
4	17*	−1
5	30	30
6	19*	16
7	21*	21
8	112	−113
9	21*	0
10	230	−222
11	53	−31
12	126	121
13	27*	−11
0, K, 4
0	102	103
1	338	334
2	253	251
3	51	50
4	160	−160
5	47	45
6	262	−258
7	21*	14
8	22*	−28
9	103	−109
10	113	110
11	68	−66
12	100	98
13	69	69
0, K, 5
1	96	96
2	224	−223
3	133	134
4	283	−286
5	200	−199
6	23*	31
7	126	−126
8	212	208
9	61	63
10	113	108
11	26*	−10
12	28*	11
0, K, 6
0	499	−506
1	80	−83
2	22*	−13
3	106	−113
4	111	111
5	51	−47
6	214	210
7	39	35
8	136	144
9	80	83
10	89	−92
11	48	40
0, K, 7
1	89	−92
2	184	174
3	64	69
4	257	251
5	24*	16
6	25*	−14
7	43	37
8	195	−193
9	29*	37
10	87	−90
0, K, 8
0	138	135
1	79	−82
2	123	123
3	102	108
4	106	−104
5	25*	20
6	160	−157
7	64	−64
8	51	−51
9	30*	−26
0, K, 9
1	70	64
2	147	−150
3	27*	−16
4	48	−44
5	57	−52
6	27*	0
7	46	−38
0, K, 10
0	48	−36
1	109	−110
2	88	−85
3	58	−52
1, K, 0
1	54	−61
3	464	477
5	49	45
7	131	−129
9	216	−212
11	22*	−5
13	93	72
1, K, 1
1	423	421
2	160	153
3	51	−49
4	175	168
5	300	−300
6	20*	33
7	192	−187
8	88	−92
9	21*	13
10	34	−20
11	185	187
12	49	−44
13	91	89
14	47	39
1, K, 2
0	471	454
1	407	−404
2	16*	−7
3	476	−471
4	16*	−10
5	214	−217
6	153	−156
7	181	185
8	44	−42
9	241	242
10	24*	−4
11	108	104
12	86	84
13	113	−109
14	30*	17
1, K, 3
1	510	−505
2	101	−95
3	27	−25
4	83	−82
5	363	365
6	18*	−3
7	315	319
8	48	53
9	47	−43
10	42	40
11	150	−157
12	25*	3
13	188	−178
1, K, 4
0	96	85
1	290	287
2	84	−82
3	363	365
4	61	65
5	193	189
6	20*	−6
7	157	−160
8	23*	17
9	222	−226
10	42	−44
11	104	−107
12	25*	7
13	101	97
1, K, 5
1	257	249
2	32	25
3	20*	−14
4	20*	0
5	218	−216
6	22*	−31
7	158	−162
8	23*	4
9	23*	6
10	45	−34
11	153	152
12	47	45
1, K, 6
0	60	60
1	21*	−23
2	36	34
3	237	−239
4	43	−39
5	39	−31
6	54	−56
7	86	74
8	23*	−15
9	152	152
10	38	33
11	27*	5
1, K, 7
1	146	−142
2	88	−97
3	33	15
4	94	−96
5	139	140
6	23*	−9
7	88	90
8	97	95
9	25*	−7
10	46	42
1, K, 8
0	181	−187
1	117	110
2	47	−20
3	143	146
4	36	27
5	80	81
6	135	133
7	85	−89
8	28*	37
9	111	−111
1, K, 9
1	145	145
2	95	93
3	29*	0
4	96	89
5	126	−129
6	43	3
7	131	−132
1, K, 10
0	47	42
1	95	−98
2	63	66
3	118	−119
2, K, 0
0	469	−494
2	477	−466
4	151	146
6	615	635
8	21*	4
10	71	−71
12	205	−201
14	119	−117
2, K, 1
1	264	254
2	653	659
3	253	−247
4	270	272
5	117	119
6	51	50
7	90	−85
8	256	−253
9	49	−55
10	227	−230
11	47	54
12	28*	28
13	28*	14
14	146	144
2, K, 2
0	515	513
1	123	120
2	141	142
3	61	−58
4	234	−237
5	189	−194
6	186	−184
7	158	157
8	156	−157
9	65	−69
10	146	148
11	46	42
12	160	155
13	39	36
2, K, 3
1	33	29
2	46	−50
3	18*	10
4	391	−393
5	38	−44
6	126	129
7	21*	−24
8	177	180
9	22*	12
10	64	62
11	26*	21
12	38	−8
13	29*	12
2, K, 4
0	338	−336
1	18*	8
2	94	−86
3	116	−117
4	176	182
5	167	−168
6	116	117
7	163	162
8	132	129
9	24*	3
10	127	−129
11	54	56
12	135	−130
2, K, 5
1	201	−202
2	290	292
3	123	122
4	165	164
5	22*	10
6	23*	17
7	132	129
8	182	−180
9	46	37
10	150	−150
11	89	−96
12	48	27
2, K, 6
0	230	230
1	50	48
2	155	157
3	105	109
4	72	−69
5	75	63
6	343	−346
7	55	−55
8	24*	−1
9	62	−71
10	57	47
11	30*	−30
2, K, 7
1	34	26
2	252	−253
3	72	66
4	129	−133
5	116	−118
6	27*	−28
7	27*	−22
8	146	152
9	28*	23
10	149	147
2, K, 8
0	180	−180
1	53	−52
2	88	−83
3	63	−70
4	97	103
5	53	52
6	113	117
7	46	−46
8	85	84
2, K, 9
1	50	−50
2	56	52
3	37	−8
4	156	153
5	72	65
6	59	−51
2, K, 10
0	106	105
1	44	37
2	51	39
3, K, 0
1	191	−190
3	318	−323
5	19*	33
7	34	22
9	225	229
11	39	24
13	101	−102
3, K, 1
1	256	−259
2	206	−201
3	51	−46
4	18*	4
5	290	288
6	65	−58
7	172	169
8	44	43
9	45	−39
10	54	63
11	144	−146
12	27*	13
13	101	−88
3, K, 2
0	120	−122
1	206	204
2	74	−73
3	360	360
4	19*	−25
5	200	204
6	189	198
7	194	−196
8	23*	−21
9	198	−198
10	23*	9
11	90	−87
12	47	−47
13	105	83
3, K, 3
1	418	423
2	72	76
3	102	−99
4	59	57
5	221	−224
6	21*	3
7	268	−266
8	45	−42
9	24*	−8
10	47	−38
11	179	184
12	28*	−2
3, K, 4
0	38	33
1	168	−169
2	20*	18
3	305	−303
4	74	−77
5	191	−191
6	59	56
7	179	179
8	60	−59
9	189	186
10	46	46
11	87	86
12	28*	15
3, K, 5
1	195	−197
2	40	33
3	21*	−19
4	71	−72
5	220	213
6	49	47
7	154	146
8	26*	23
9	24*	−20
10	25*	−4
11	120	−123
3, K, 6
0	64	−64
1	88	85
2	23*	−27
3	203	204
4	41	39
5	24*	−7
6	47	45
7	24*	−18
8	27*	18
9	164	−162
10	48	−28
3, K, 7
1	107	114
2	119	120
3	24*	19
4	43	46
5	150	−150
6	26*	22
7	79	−87
8	68	−70
9	29*	26
3, K, 8
0	129	122
1	82	−85
2	51	43
3	136	−136
4	29	−12
5	94	−82
6	151	−153
7	96	94
3, K, 9
1	143	−147
2	89	−90
3	44	35
4	78	−74
5	89	92
4, K, 0
0	668	675
2	39	39
4	152	−145
6	268	−275
8	196	−171
10	116	116
12	225	217
4, K, 1
1	19*	4
2	266	−268
3	106	−111
4	335	−340
5	86	93
6	35	26
7	37	37
8	236	237
9	50	−43
10	128	129
11	51	56
12	30*	23
4, K, 2
0	189	−187
1	187	189
2	203	−202
3	48	−52
4	161	159
5	21*	16
6	234	236
7	46	43
8	61	58
9	45	−34
10	100	−101
11	28*	−36
12	120	−117
4, K, 3
1	44	−34
2	268	272
3	21*	10
4	77	71
5	22*	26
6	22*	2
7	37	20
8	112	−111
9	25*	0
10	184	−170
11	27*	−26
12	92	92
4, K, 4
0	121	119
1	175	176
2	169	163
3	35	30
4	123	−128
5	47	48
6	192	−192
7	31	−7
8	48	−38
9	81	−80
10	86	89
11	49	−46
4, K, 5
1	83	74
2	175	−177
3	65	68
4	203	−207
5	130	−131
6	25*	21
7	92	−91
8	169	165
9	29*	40
10	110	94
4, K, 6
0	359	−357
1	58	−60
2	36	−21
3	98	−86
4	92	79
5	47	−38
6	190	182
7	27*	30
8	106	105
9	87	67
4, K, 7
1	61	−69
2	152	146
3	44	41
4	191	191
5	27*	23
6	29*	−11
7	30*	34
8	152	−152
4, K, 8
0	115	116
1	61	−53
2	100	97
3	96	91
4	94	−87
5	29*	10
6	124	−126
4, K, 9
1	62	54
2	111	−117
3	28*	−11
5, K, 0
1	48	−45
3	271	275
5	94	86
7	138	−144
9	135	−136
11	28*	0
5, K, 1
1	226	225
2	28	−10
3	50	−57
4	113	119
5	164	−161
6	23*	−3
7	131	−134
8	81	−76
9	42	−10
10	42	25
11	161	160
5, K, 2
0	221	225
1	206	−210
2	49	−54
3	235	−232
4	21*	−11
5	112	−109
6	43	−38
7	104	101
8	56	−58
9	183	186
10	26*	1
11	91	80
5, K, 3
1	213	−215
2	42	−43
3	59	−72
4	48	−48
5	258	263
6	23*	−1
7	224	213
8	54	39
9	73	−67
10	27*	25
11	77	−83
5, K, 4
0	88	83
1	193	195
2	92	−88
3	217	211
4	43	37
5	101	102
6	26*	39
7	84	−88
8	26*	−14
9	178	−175
10	29*	−28
5, K, 5
1	177	177
2	62	67
3	39	−29
4	43	−30
5	149	−140
6	25*	−4
7	118	−121
8	28*	15
9	27*	−5
5, K, 6
0	48	41
1	36	19
2	25*	30
3	190	−189
4	27*	−27
5	53	−54
6	51	−49
7	94	93
8	28*	−10
5, K, 7
1	120	−122
2	50	−44
3	49	34
4	101	−97
5	90	91
6	45	5
7	65	70
5, K, 8
0	168	−166
1	93	93
2	35	6
3	108	107
4	30*	26
6, K, 0
0	257	−256
2	128	−131
4	83	85
6	300	299
8	26*	24
10	60	−45
6, K, 1
1	47	43
2	243	241
3	56	−51
4	157	161
5	42	41
6	24*	17
7	47	−45
8	178	−170
9	28*	−9
10	139	−136
6, K, 2
0	205	210
1	23*	5
2	97	97
3	23*	7
4	126	−123
5	75	−62
6	141	−139
7	66	60
8	89	−92
9	47	−43
10	104	101
6, K, 3
1	39	23
2	98	−102
3	23*	2
4	201	−191
5	38	−28
6	67	64
7	26*	−17
8	105	107
9	27*	5
6, K, 4
0	170	−173
1	25*	−31
2	80	−77
3	47	−50
4	109	107
5	73	−76
6	103	105
7	86	79
8	83	79
9	26*	6
6, K, 5
1	89	−93
2	168	166
3	49	42
4	116	119
5	52	20
6	28*	6
7	89	84
8	129	−127
6, K, 6
0	186	174
1	29*	32
2	91	79
3	60	67
4	71	−53
5	29*	37
6	201	−203
6, K, 7
1	49	30
2	152	−151
3	46	25
4	104	−98
7, K, 0
1	124	−122
3	177	−172
5	27*	20
7	29*	−11
9	171	167
7, K, 1
1	124	−126
2	103	−92
3	41	−37
4	43	41
5	171	175
6	55	−41
7	97	105
8	41	11
7, K, 2
0	25*	−10
1	82	82
2	44	−39
3	184	179
4	26*	−23
5	116	116
6	130	122
7	128	−127
8	47	−42
7, K, 3
1	228	211
2	43	37
3	86	−82
4	36	26
5	97	−94
6	28*	1
7	157	−151
8	49	−23
7, K, 4
0	50	52
1	81	−73
2	25*	1
3	175	−165
4	54	−51
5	113	−116
6	49	45
7	132	122
7, K, 5
1	115	−112
2	31*	28
3	29*	−21
4	82	−77
5	136	139
7, K, 6
0	48	−46
1	73	80
2	30*	−16
3	126	124
8, K, 0
0	247	235
2	47	42
4	50	−54
6	181	−172
8, K, 1
1	26*	−5
2	147	−143
3	27*	−10
4	142	−142
5	28*	13
6	28*	10
8, K, 2
0	127	−122
1	50	42
2	85	−89
3	29*	−33
4	92	90
5	40	25
8, K, 3
1	40	−19
2	120	115
3	28*	2
4	90	87
5	28*	17
8, K, 4
0	100	96
1	63	59
2	80	78
3	30*	15

Columns are K, 10F_o, 10F_c. F_o and F_c are on an absolute scale. Reflections marked

^*are “unobserved”.

3. Description of the Structure

The structure of aragonite, the main points of which are well known, is shown in figure 1. The Ca ions lie in pseudohexagonal layers parallel to (001) and the layer sequence is ABAB. The Ca layers are separated by CO₃ groups which lie in two layers parallel to (001), and form columns parallel to [001].

Figure 1.

A stereoscopic illustration of the crystal structure of aragonite (CaCO₃).

A unique set of atoms is labeled. The origin of the crystallographic coordinate system is marked by *.

3.1. The Ca Ion Environments

The Ca ion lies on the mirror plane at x = 1/4. Its environment is shown in figure 2 and summarized in table 3. The coordination of nine oxygens to Ca consists of three CO₃ edges, O(1, 2), O(1^I, 2^I) and O(2^IV, 2^V) and three apexes, O(1^II, 2^II, 2^III). The apparent thermal motion of Ca is almost isotropic (table 1, fig. 2).

Figure 2.

The Ca environment in aragonite (CaCO₃).

Table 3.

The Ca environment in aragonite (CaCO₃)

Atoms	Distance,	*Lower	*Noncorrelaled
	Å raw	bound [13]	motion [13]
Ca, O(1II)	2.414(2)	2.414	2.423
Ca, O(2II, 2III)	2.445(1)	2.445	2.454
Ca, O(2, 2I)	2.520(1)	2.520	2.527
Ca, O(2IV,2V)	2.544(1)	2.544	2.551
Ca, O(1, 1I)	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 calculated from the standard deviations in the atomic positional parameters and the unit cell parameters.

^*Mean separation between atoms when allowance is made for thermal motion.

Corrections as given by Busing and Levy [13] to obtain the mean separation between atoms from the observed atomic positional and thermal parameters were calculated using a program written by Finger [12]. These corrections are included in tables 3 and 4.

Table 4.

The CO₃ group and its environment in aragonite (CaCO₃)

Atoms	Distance, Å or angle, deg.	Lower bound [13]	Riding model [13]
C, O(1)	1.288(2) Å	1.289 Å	1.295 Å
C, O(2)	1.283(1)	1.284	1.288
O(1), O(2)	2.229(1)
O(2), O(2I)	2.219(2)
O(1), C, O(2)	120.13(8)°
O(2), C, O(2I)	119.6(2)
O (1), CaV	2.414(2) Å
O (1), (CaII, CaIII)	2.653(1)
O(2), Ca	2.445(1)
O(2), CaII	2.520(1)
O(2), CaIV	2.544(1)

3.2. The CO₃ Group

The details of the CO₃ group and its environment are given in table 4 and shown in figure 3. The positions reported by Bragg [3] give C–O distances of 1.26 Å and 1.30 Å, and O–C–O angles of 117°, 117° and 127°, which, under the circumstances, are all close to those reported here. The C–O distances and O – C – O angles reported here for the CO₃ group do not differ from each other significantly at the 95 percent confidence level; the same is true for the O–C–O angles. In view of the possibility of unknown systematic error, necessarily excluded from the calculations, our results therefore do not preclude trigonality of the CO₃ group. Because the oxygens in the CO₃ group have very similar environments, little deviation from trigonality is expected. The CO₃ group is nonplanar however. The carbon atom is 0.026(4) Å out of the plane of the oxygen atoms in the CO₃ group in aragonite. This displacement is approximately seven times the standard deviation and is clearly significant. The displacement is towards the nearest Ca layer and is presumably a result of polarization of each oxygen atom by the three bonded Ca ions. If the displacement were caused by Ca … C interactions, the C atom would not move towards the Ca layer.

Figure 3.

The CO₃ group environment in aragonite (CaCO₃).

The labels refer to atoms in table 4.

The difference in the O–C–O angles, 119.6° and 120.13°, if real, is consistent with the O(2, 2^I) edge of the CO₃ group being coordinated slightly more strongly to Ca as judged from the Ca … O distances. However, this stronger coordination of O(2) to Ca would also suggest that C–O(2) should be longer than C–O(1). This is not the case. The average value of the C–O distances is 1.286 Å. This agrees well with the C–O distances of 1.283(2) A reported [14] for calcite in which 32 symmetry is forced on the CO₃ group by space-group $\text{R}\overline{3}\text{c}$. If the apparent thermal motions of the atoms in the CO₃ group are attributed to thermal motion rather than to slight positional disorder, there seems to be oscillation within the CO₃ layer, i.e., more or less perpendicular to the edge coordination to Ca. Similarly, O(1) may be undergoing some additional wagging out of the CO₃ layer.