Crystal Structure of Ca₂Na₂(CO₃)₃ (Shortite)

Abstract

Ca₂Na₂(CO₃)₃ crystallizes in the orthorhombic unit cell a = 4.947(1) Å, b = 11.032(2) Å, and c = 7.108(1) Å at 25 °C with two formula weights in space-group Amm2. The structure has been redetermined, corrected, and refined to R_w = 0.025, R = 0.020 using 684 “observed” x-ray reflections from a single crystal. Corrections were made for absorption and isotropic extinction. In the extinction refinements, r refined to 0.00017(1) cm. The structure consists of Ca₂NaCO₃ layers interleaved with Na(CO₃)₂ layers. The Ca ion is coordinated strongly to nine oxygens, including three CO₃ edges, with Ca … O distances varying from 2.401(2) Å to 2.576(2) Å. One Na ion is coordinated strongly to eight oxygens, including two CO₃ edges, with Na … O distances from 2.429(2) Å to 2.605(1) Å. The other Na ion is coordinated strongly to six oxygens, including one CO₃ edge, at 2.296(1) Å to 2.414 Å, and weakly to a seventh at 3.050(3) Å. One CO₃ group is coordinated to seven cations, the other is coordinated to eight. The CO₃ groups have seemingly maximized their edge sharing with Ca ions rather than Na ions.

1. Introduction

As part of a program of studies [1, 2]¹ to obtain precise structural parameters on calcium carbonates, calcium carbonate hydrates, calcium phosphates, and related compounds, we have reinvestigated the crystal structure of Ca₂Na₂(CO₃)₃, which exists in nature as the mineral shortite. The structural features in these compounds are important in the consideration of possible epitaxial, syntaxial. and substitutional solid solution relationships in the major inorganic phases found in vivo.

Shortite was first found [3] in a matrix of montmorillonite clay which also contains pyrite (FeS₂), calcite (CaCO₃), and a carbonate of magnesium in crystals which were too small to be identified. Massive deposits of the commercially important mineral trona (Na₂CO₃ · NaHCO₃ · H₂O) are also found in the vicinity. A crystal structure for shortite has been reported by Wickman [4], who suggested atomic positions on the basis of refractive indices, spatial considerations, and the intensities of the 0kl reflections. We found this structure to contain one incorrect feature. The corrected structure of shortite is reported here.

2. Data Collection and Structure Refinement

The crystal used in the data collection is an approximate sphere, radius 0.112(4) mm, ground from a shortite fragment from mineral sample 105807, National Museum of Natural History, Smithsonian Institution, Washington, D.C. (sample supplied by J. S. White, Jr.). The sphere was mounted on the goniometer head in our usual way [2].

• formula (ideal): Ca₂Na₂(CO₃)₃

• cell: orthorhombic

  • a = 4.947(1) Å
  • b = 11.032(2) Å
  • c = 7.108(1) Å
• volume =387.9 ų

  • space-group Amm2;
  • cell contents 2[Ca₂Na₂(CO₃)₃]
  • reciprocal lattice extinctions: k + l = 2n + 1 for hkl;
  • calculated density 2.620 g · cm⁻³;
  • observed density 2.629 g · cm⁻³ [3].

The procedure given in reference [2] was followed in the collection and processing of data with the following exceptions. The θ–2θ scans were carried out at 2°/min. Each background was counted for 20 s. 1659 reflections were collected from the hkl and hkl octants and were merged into a unique set of 711, of which 684 are “observed” and 27 are “unobserved.” The R factor between observed equivalent reflections was 0.01. No absorption corrections were made because the maximum error in an intensity due to absorption is 0.8 percent. For Ca₂Na₂(CO₃)₃, μ(Mo) = 15.7 cm⁻¹. The Picker² hardware dropped the least significant digit during the data collection so that the standard deviations from counting statistics, and consequently our assessment of whether a given reflection is observed or unobserved, is only marginally correct. This affects very few reflections in the present case because the sample scattered strongly and nearly all reflections were unequivocally “observed” (modified hardware was used in later investigations). σ(F) was defined as F/10 for F < 10; 1 for 10 < F < 43; and F/43 for F > 43, where F_max was 211; weights in the least-squares refinements were 1/σ². Wickman’s structure [4] for Ca₂Na₂(CO₃)₃ would not refine to a residual, R_w, below 0.3. Examination of the Patterson function and an F₀ electron density Fourier synthesis phased from structure factor calculations using the positions of the Ca and Na ions suggested new positions for the C(1) and O(1) atoms. This structure was refined isotropically to R_w = 0.056, R = 0.050, and anisotropically to R_w= 0.030, R = 0.023 and then to R_w = 0.025, R = 0.020 with refinement on the isotropic extinction parameter, r, in addition to the previously varied parameters. The least-squares program RFINE written by Finger [5] was used. Only observed reflections were used in these refinements. The scattering factors for the neutral atoms were taken from Cromer and Mann [6]. No corrections for anomalous dispersion were made. The final value of r is 0.00017(1) cm where $F^2=F_{\text{ unc }}^2{(1+\beta r|F_{\text{ unc }}{|}^2)}^{1/2}$ and F_unc is the structure factor uncorrected for extinction. The notation is that of Zachariasen [7]; here r may be related to the average domain size if the crystal is of type II where the extinction is assumed to be governed by spherical domains. The z coordinate of Ca was set equal to zero to define the origin along c. In the final cycle, the average shift/error was 0.01 and the standard deviation of an observation of unit weight,

$${[\Sigma W{\left(F_0-F_c\right)}^2/(711-50)]}^{1/2},$$

was 0.45.

The highest peaks in an electron density difference synthesis calculated at R = 0.03 corresponded to about 0.1 of an electron. The largest correlation coefficients are 0.42–0.44 between the scale factor and the B₁₁, B₂₂, and B₃₃ temperature factors of Ca and 0.64 between the extinction parameter and the scale factor. All other correlation coefficients are less than 0.28.

The atomic parameters are given in table 1. All atoms but O(2) lie in special positions; the Wyckoff symbol and symmetry of these positions are given in table 1. The observed and calculated structure factors, uncorrected for extinction, are given in table 2.

Table 1.

Atomic parameters of Ca₂Na₂(CO₃)₃

Atoms	(a)	x	y	z	B11*	B22	B33	B12	B13	B23
Ca	e, m, 4	0.5	0.21659(4)	0.0	0.65(1)	0.48(1)	0.58(1)			−0.01(1)
Na(l)	a, mm, 2	0.0	0.0	0.9263(3)	1.27(6)	0.97(5)	1.54(6)
Na(2)	b, mm, 2	0.5	0.0	0.6122(3)	1.15(5)	0.69(5)	1.15(5)
C(l)	d, m, 4	0.0	0.2961(2)	0.1697(3)	0.57(6)	0.84(7)	0.64(5)			−0.04(5)
O(1)	d, m, 4	0.0	0.1985(2)	0.0742(3)	1.08(6)	1.35(7)	1.44(7)			−0.81(6)
O(2)	f, 1, 8	0.2261(3)	0.3456(1)	0.2152(2)	0.59(4)	1.02(4)	1.08(4)	−0.19(3)	−0.04(3)	−0.02(3)
C(2)	b, mm, 2	0.5	0.0	0.2253(5)	1.1(1)	0.58(8)	0.64(9)
O(3)	b, mm, 2	0.5	0.0	0.0415(4)	1.7(1)	0.60(7)	0.61(7)
O(4)	e, m, 4	0.5	0.1013(2)	0.3111(3)	2.10(7)	0.57(5)	0.99(6)			−0.23(5)

Figures in parentheses are standard errors in last significant figure quoted, and were computed in the final cycle of full-matrix least-squares refinement.

^aWyckoff symbol, site symmetry, and multiplicity of site in space-group Amm2.

^*Thermal parameters have the form exp (−1/4 (a*²B₁₁h² + b*²B₂₂k² + c*²B₃₃l² + 2a*b*B₁₂hk + 2a*c*B₁₃hl + 2b*c*B₁₃kl)).

Table 2.

Observed and calculated structure factors for Ca₂Na₂(CO₃)₃ (shortite)

0,0,L
2	514	529	188
4	515	519	965
6	211	211	55
8	177	175	833
10	251	261	30
12	161	159	891
0,1,L
1	299	297	888
3	600	607	975
5	100	97	12
7	125	125	212
9	41	39	944
11	17*	22	245
0,2,L
0	481	529	500
2	408	405	101
4	490	496	970
6	390	393	38
8	191	192	939
10	236	241	877
12	189	191	949
0,3,L
1	397	396	830
3	772	816	138
5	196	194	69
7	367	375	937
9	146	147	903
11	173	174	935
0,4,L
0	466	506	0
2	836	892	27
4	71	63	948
6	131	126	859
8	196	195	43
10	74	70	887
12	128	126	22
0,5,L
1	780	813	931
3	497	499	998
5	348	357	70
7	88	82	836
9	131	133	33
11	147	144	934
0,6,L
0	495	506	0
2	380	372	819
4	250	239	198
6	319	324	918
8	104	104	153
10	111	106	808
12	90	92	959
0,7,L
1	522	516	97
3	287	280	40
5	293	291	35
7	230	227	894
9	352	354	937
11	130	127	992
0,8,L
0	190	194	0
2	85	72	197
4	42	34	140
6	98	98	51
8	7*	4	17
10	124	124	752
0,9,L
1	427	422	55
3	478	493	905
5	325	325	36
7	83	85	99
9	206	207	959
11	41	43	26
0,10,L
0	459	469	0
2	311	308	13
4	144	147	764
6	176	174	857
8	63	66	217
10	72	69	906
0,11,L
1	175	179	924
3	169	171	123
5	178	180	945
7	259	261	939
9	120	121	983
0,12,L
0	43	35	500
2	243	244	500
4	171	163	26
6	251	252	971
8	121	124	50
10	179	177	830
0,13,L
1	180	183	841
3	156	155	958
5	125	121	922
7	122	123	63
9	79	73	808
0,14,L
0	404	408	0
2	267	265	62
4	246	247	918
6	138	136	70
8	165	164	954
0,15,L
1	85	86	914
3	41	36	801
5	124	122	170
7	124	121	31
0,16,L
0	182	188	500
2	84	85	913
4	248	249	971
6	228	226	11
0,17,L
1	68	69	856
3	165	159	109
5	24*	27	110
0,18,L
0	230	227	0
2	131	132	975
4	153	152	983
0,19,L
1	125	121	944
3	223	223	985
0,20,L
0	127	116	0
1,0,L
0	607	638	500
2	421	418	938
4	561	569	82
6	434	442	946
8	340	346	958
10	240	244	44
12	99	95	861
1,1,L
1	364	361	815
3	311	300	932
5	276	276	71
7	178	176	148
9	66	60	860
11	50	46	95
1,2,L
0	124	98	500
2	764	830	874
4	530	538	908
6	280	282	946
8	233	233	997
10	175	178	975
12	142	145	981
1,3,L
1	365	376	30
3	286	274	821
5	323	323	803
7	210	214	972
9	145	140	979
11	133	137	18
1,4,L
0	307	307	500
2	497	498	123
4	284	281	6
6	165	161	47
8	306	310	943
10	115	116	8
12	48	41	943
1,5,L
1	280	275	939
3	217	215	934
5	625	639	10
7	274	275	16
9	126	128	27
11	164	161	911
1,6,L
0	252	243	0
2	284	282	788
4	140	127	907
6	115	114	906
8	49	41	986
10	95	90	944
12	99	96	950
1,7,L
1	446	451	992
3	287	280	939
5	330	333	839
7	310	313	974
9	194	192	972
11	213	211	983
1,8,L
0	231	238	500
2	294	296	788
4	186	188	819
6	29	26	895
8	42	40	110
10	16*	16	136
1,9,L
1	217	214	78
3	367	371	979
5	318	319	9
7	262	267	38
9	176	173	929
11	111	113	919
1,10,L
0	217	216	500
2	50	35	3
4	216	219	90
6	161	155	957
8	161	162	930
10	150	148	99
1,11,L
1	326	329	971
3	117	109	26
5	131	134	885
7	179	170	875
9	137	135	973
1,12,L
0	63	56	0
2	289	293	891
4	241	243	932
6	153	154	939
8	162	162	978
10	136	136	982
1,13,L
1	90	86	11
3	123	123	42
5	192	192	101
7	18*	21	843
9	74	74	950
1,14,L
0	191	191	500
2	274	270	53
4	202	202	6
6	141	140	998
8	249	248	952
1,15,L
1	38	33	86
3	71	62	36
5	148	144	34
7	23*	33	154
1,16,L
0	185	185	0
2	221	221	924
4	161	157	991
6	184	186	934
1,17,L
1	102	97	30
3	37	36	854
5	110	111	809
1,18,L
0	235	239	500
2	144	140	85
4	132	130	53
1,19,L
1	122	119	92
3	137	136	961
2,0,L
0	1047	1186	0
2	841	875	7
4	289	290	190
6	357	361	883
8	142	143	77
10	178	175	927
12	211	214	967
2,1,L
1	403	382	129
3	435	435	848
5	154	156	104
7	144	149	888
9	62	64	935
11	55	54	906
2,2,L
0	154	91	500
2	498	497	19
4	311	315	29
6	375	377	987
8	176	180	8
10	243	240	844
12	204	208	971
2,3,L
1	554	546	150
3	125	125	100
5	202	201	79
7	159	158	831
9	300	298	923
11	69	76	47
2,4,L
0	844	914	0
2	430	422	120
4	356	362	876
6	114	116	208
8	177	175	910
10	115	119	52
12	63	59	943
2,5,L
1	617	634	952
3	398	401	972
5	355	358	69
7	76	72	788
9	150	149	15
11	118	122	943
2,6,L
0	95	56	500
2	251	251	61
4	270	275	971
6	205	206	58
8	90	84	808
10	102	102	4
2,7,L
1	305	314	933
3	528	540	97
5	73	72	874
7	361	362	945
9	204	204	938
11	200	198	938
2,8,L
0	125	122	0
2	73	72	764
4	42	34	14
6	95	93	79
8	9*	12	234
10	112	108	763
2,9,L
1	319	325	936
3	489	503	979
5	144	142	983
7	206	208	36
9	98	98	981
11	107	106	923
2,10,L
0	658	691	0
2	155	141	207
4	144	142	950
6	83	75	105
8	77	74	231
10	126	123	60
2,11,L
1	168	168	3
3	93	92	91
5	213	214	977
7	203	201	928
9	152	150	970
2,12,L
0	176	181	500
2	127	124	73
4	234	233	956
6	215	214	35
8	109	106	943
2,13,L
1	145	145	61
3	180	182	775
5	236	239	12
7	44	43	823
9	74	73	53
2,14,L
0	288	289	0
2	311	313	27
4	161	162	950
6	136	137	984
8	161	160	10
2,15,L
1	112	115	826
3	53	51	55
5	77	74	236
7	74	68	45
2,16,L
0	39	39	500
2	218	221	927
4	165	160	53
6	258	256	944
2,17,L
1	74	71	83
3	78	71	62
5	57	51	57
2,18,L
0	191	190	0
2	147	147	969
4	132	131	999
2,19,L
1	141	140	61
3,0,L
0	578	578	500
2	148	149	13
4	456	454	32
6	303	308	982
8	314	317	929
10	245	249	59
12	90	86	814
3,1,L
1	133	131	926
3	221	218	990
5	157	154	61
7	162	163	114
9	33	28	805
11	43	40	187
3,2,L
0	121	96	0
2	491	501	877
4	428	432	915
6	223	222	963
8	210	209	978
10	167	169	989
12	124	122	970
3,3,L
1	274	275	939
3	185	181	950
5	268	268	764
7	247	248	986
9	79	78	998
11	148	146	986
3,4,L
0	120	116	500
2	382	382	77
4	191	185	64
6	152	151	974
8	260	259	968
10	91	93	967
3,5,L
1	199	198	948
3	187	184	946
5	488	495	5
7	244	246	16
9	115	114	22
11	151	148	913
3,6,L
0	70	62	0
2	275	273	846
4	51	36	15
6	144	144	870
8	57	49	820
10	83	79	877
3,7,L
1	388	389	33
3	215	217	889
5	294	297	887
7	228	229	970
9	207	208	966
11	171	170	997
3,8,L
0	178	185	500
2	230	233	801
4	125	124	824
6	33	33	861
8	49	42	117
10	8*	10	128
3,9,L
1	227	228	98
3	275	280	952
5	317	317	15
7	201	200	36
9	182	183	934
3,10,L
0	97	93	500
2	112	114	951
4	182	183	133
6	164	162	916
8	146	141	975
10	108	103	80
3,11,L
1	271	274	956
3	128	128	45
5	112	112	866
7	164	164	895
9	108	109	975
3,12,L
0	36	27	0
2	277	282	901
4	188	189	949
6	155	155	922
8	151	149	995
3,13,L
1	78	82	902
3	150	152	71
5	123	119	107
7	56	51	952
3,14,L
0	207	207	500
2	216	214	62
4	200	203	988
6	123	124	24
8	228	225	938
3,15,L
1	20*	21	993
3	68	63	60
5	134	130	34
7	22*	26	189
3,16,L
0	199	205	0
2	159	161	930
4	167	169	968
6	151	149	960
3,17,L
1	83	80	973
3	41	38	991
5	105	103	776
3,18,L
0	213	212	500
2	129	127	80
4,0,L
0	975	1033	0
2	276	273	112
4	291	294	957
6	176	176	31
8	143	136	866
10	200	200	15
4,1,L
1	130	133	882
3	259	261	957
5	27	24	970
7	69	65	200
9	18*	16	911
11	8*	17	777
4,2,L
0	243	234	500
2	222	218	61
4	289	294	975
6	276	281	24
8	147	148	950
10	191	191	882
4,3,L
1	159	166	900
3	383	386	126
5	70	68	83
7	250	252	935
9	118	118	914
11	137	134	938
4,4,L
0	319	313	0
2	402	405	25
4	80	81	950
6	100	102	905
8	146	145	30
10	72	64	906
4,5,L
1	393	400	937
3	319	322	989
5	233	234	63
7	84	83	873
9	120	120	13
11	114	116	937
4,6,L
0	217	216	0
2	180	184	839
4	136	132	171
6	209	207	921
8	76	77	132
10	86	78	815
4,7,L
1	296	296	66
3	228	229	35
5	211	208	28
7	182	182	905
9	272	270	939
4,8,L
0	90	80	0
2	40	47	198
4	17*	17	112
6	72	69	45
8	0*	1	813
10	98	92	756
4,9,L
1	279	280	40
3	330	331	917
5	246	247	31
7	74	75	48
9	173	170	961
4,10,L
0	312	315	0
2	200	199	25
4	81	78	220
6	129	124	879
8	49	46	180
4,11,L
1	131	140	945
3	130	130	87
5	143	146	950
7	206	198	945
9	105	102	980
4,12,L
0	62	66	500
2	194	192	3
4	130	129	18
6	207	201	971
8	101	100	47
4,13,L
1	121	122	862
3	113	113	953
5	98	99	928
7	98	97	57
4,14,L
0	306	309	0
2	208	206	53
4	191	194	928
6	121	118	47
4,15,L
1	59	56	924
3	37	28	823
5	94	91	178
4,16,L
0	148	154	500
2	75	84	937
4	198	198	971
4,17,L
1	52	57	875
3	126	122	99
5,0,L
0	158	151	500
2	287	298	964
4	265	267	92
6	282	281	925
8	244	245	986
10	154	151	14
5,1,L
1	129	123	783
3	103	102	857
5	177	174	59
7	74	71	177
9	64	59	908
5,2,L
0	43	39	0
2	363	371	900
4	245	245	947
6	197	197	936
8	178	177	1
10	128	130	967
5,3,L
1	231	233	72
3	138	142	790
5	188	190	892
7	103	103	976
9	134	130	966
5,4,L
0	219	223	500
2	175	173	138
4	204	202	975
6	111	111	80
8	208	209	919
10	108	109	37
5,5,L
1	151	154	997
3	139	140	932
5	352	357	999
7	190	189	15
9	102	103	7
5,6,L
0	158	166	0
2	83	75	767
4	122	121	896
6	51	54	21
8	38	37	182
5,7,L
1	253	258	961
3	199	202	998
5	208	211	839
7	263	263	986
9	109	108	979
5,8,L
0	94	96	500
2	142	138	792
4	97	93	845
6	19*	16	932
8	22*	26	50
5,9,L
1	143	146	9
3	238	243	999
5	194	192	986
7	215	212	22
5,10,L
0	168	169	500
2	17*	9	184
4	165	163	20
6	90	85	27
8	137	134	897
5,11,L
1	207	207	992
3	86	87	992
5	108	108	931
7	112	110	883
5,12,L
0	78	80	0
2	175	175	903
4	180	186	941
6	104	106	964
5,13,L
1	88	89	86
3	62	65	960
5	163	157	93
5,14,L
0	117	122	500
2	209	206	24
4	139	141	25
5,15,L
1	17*	22	89
3	39	35	31
5,16,L
0	100	105	0
2	191	194	939
6,0,L
0	409	417	0
2	304	300	21
4	125	125	57
6	194	196	926
8	99	102	31
6,1,L
1	91	89	73
3	137	136	867
5	77	70	92
7	56	49	896
9	43	41	948
6,2,L
0	124	126	500
2	212	210	19
4	165	165	5
6	218	219	984
8	111	115	4
6,3,L
1	160	159	87
3	110	112	61
5	101	96	62
7	100	95	863
9	166	168	928
6,4,L
0	323	320	0
2	166	165	81
4	161	162	907
6	72	72	87
8	106	105	928
6,5,L
1	248	250	963
3	222	223	976
5	192	186	61
7	60	64	860
9	111	116	992
6,6,L
0	50	19	500
2	53	49	134
4	120	119	975
6	107	103	40
8	46	46	858
6,7,L
1	181	184	952
3	273	271	66
5	74	76	970
7	206	208	942
6,8,L
0	36	26	0
2	37	36	194
4	8*	8	72
6	55	50	41
8	9*	4	930
6,9,L
1	183	187	953
3	270	267	981
5	114	114	996
7	132	133	10
6,10,L
0	322	321	0
2	91	86	160
4	85	85	946
6	55	59	61
6,11,L
1	108	112	987
3	89	85	42
5	127	129	968
6,12,L
0	141	142	500
2	97	96	58
4	145	144	956
6,13,L
1	91	85	56
3	94	94	796
6,14,L
0	204	198	0
2	182	181	27
7,0,L
0	254	254	500
2	77	80	13
4	252	254	988
6	142	144	25
8	202	200	909
7,1,L
1	19*	20	122
3	86	82	24
5	49	45	5
7	94	88	73
7,2,L
0	98	100	0
2	194	195	909
4	207	208	945
6	124	125	977
7,3,L
1	127	132	905
3	115	114	31
5	132	130	772
7	177	173	999
7,4,L
0	48	47	500
2	181	179	17
4	101	97	84
6	105	107	927
7,5,L
1	119	123	997
3	103	109	950
5	235	233	986
7	158	151	16
7,6,L
0	19*	7	500
2	142	142	904
4	37	31	247
6	101	100	860
7,7,L
1	219	215	55
3	113	119	874
5	194	197	938
7,8,L
0	80	78	500
2	99	100	820
4	42	38	871
6	23*	24	851
7,9,L
1	161	161	86
3	132	138	923
5	210	204	11
7,10,L
0	0*	3	500
2	119	118	939
4	102	97	150
7,11,L
1	141	143	951
3	96	101	42
7,12,L
0	17*	14	0
2	175	177	918
8,0,L
0	341	337	0
2	145	144	70
4	135	138	959
8,1,L
1	48	44	938
3	85	81	952
5	19*	15	124
8,2,L
0	140	145	500
2	122	125	40
4	134	132	973
8,3,L
1	83	80	942
3	149	144	85
5	19*	11	994
8,4,L
0	161	155	0
2	145	138	29
4	75	74	957
8,5,L
1	165	163	952
3	172	168	995
8,6,L
0	51	42	0
2	69	68	877
4	54	50	98
8,7,L
1	136	140	10
3	157	150	28
8,8,L
0	8*	3	500
2	21*	26	214

Columns are l, 10F₀, 10F_c and phase in millicycles. “Unobserved” reflections are marked by *. The F_c values do not include corrections for extinction. F₀ and F_c are on an absolute scale.

3. Description of the Structure

The structure of Ca₂Na₂(CO₃)₃ is shown in figures 1 and 2. There are Ca₂NaCO₃ layers at x = 0.5 and Na(CO₃)₂ layers at x = 0. The CO₃ group containing C(2), O(3), O(4), and O(4′) lies on the mirror at x = 0.5 and is a member simultaneously of three cation-anion chains in which cations are coordinated to edges and opposite apexes of the CO₃ group. One CaCO₃ chain runs parallel to [011], one runs parallel to [011], and one NaCO₃ chain runs parallel to [001]. Similar cation-anion chains are present in the barytocalcite phase of BaCa(CO₃)₂ [8]. The bonding of the apex of the CO₃ group in the NaCO₃ chain to Na is weak, however. The CO₃ group containing C(1), O(1), O(2), and O(2′), which is on the mirror at x = 0 and has its plane parallel to (011) or (011), forms NaCO₃ chains like those cation-anion chains at x = 0.5. The two oxygens O(2) and O(2′), which lie above and below the mirror, provide bonding with cations in neighboring Ca₂Na(CO₃) layers. Each Na at x = 0 is common to two chains. The CO₃ groups have seemingly oriented themselves to maximize edge coordination to Ca; each CO₃ group is bonded edgewise to two Ca ions and one Na ion. Preferential edge coordination of CO₃ to Ca is in accord with Ca exerting the largest electrostatic attraction on the CO₃ group and is consistent with the Ca coordinations in CaCO₃ · 6H₂O [1], CaNa₂(CO₃)₂ · 5H₂O [9], and CaNa₂(CO₃)₂ · 2H₂O [9].

Figure 1. The crystal structure of Ca₂Na₂(CO₃)₃, shortite, viewed along a.

The origin of the coordinate system is marked by *.

Figure 2.

As in figure 1 but viewed along c.

There is a void in the structure centered at about 0, 0.5, 0.8 (figs. 1 and 2). If the ionic radius of the oxygen in the CO₃ groups is assumed to be 1.4 Å, this void is about 2.2–2.5 Å in diameter. Because it has both cations and anions in its surface, it is unlikely that it would be occupied, except perhaps by an inert gas atom.

3.1. The Calcium Ion Environment

The Ca ion lies on a mirror plane at x = 0.5. Its environment is shown in figure 3 and summarized in table 3. The coordination contains three CO₃ edges, O(1^I, 2^I), O(1, 2) and O(3. 4), and three CO₃ apexes, O(2^II), O(2^III) and O(4^I). The Ca … O distances indicate strong ionic bonding from Ca to all these oxygen atoms and are in the normal range. Strong coordination to nine neighboring oxygens is rare for Ca and is possible here because of the small O … O separation (~2.2 Å) in the edge of the CO₃ group. A large coordination number for Ca is favored by the Ca … O interaction being the strongest electrostatic attraction in the crystal. The Ca ions are about 4 Å apart in the structure; the shortest Ca … Na distance, with associated weaker electrostatic repulsion than Ca … Ca, is about 3.5 Å.

Figure 3. The Ca and Na environments in Ca₂Na₂(CO₃)₃.

The primes refer to atoms in tables 3 and 4.

Table 3.

The calcium environment in Ca₂Na₂(CO₃)₃

Atoms	Distance
	Å
Ca, O(4)	2.401(2)
Ca, O(3)	2.411(1)
Ca, O(2, 2I, 2II, 2III)	2.508(1)
Ca, O(1, lI)	2.543(1)
Ca, O(4I)	2.576(2)

In all tables of interatomic distances and angles, the quantities in parentheses are standard errors in the last significant figure and were computed from the standard errors in the atomic positional parameters and in the cell parameters. They include contributions from the variance co-variance matrix. The atom labels refer to atoms in figure 3.

3.2. The Na Ion Environments

There are two crystallographically distinct Na ions in the crystal structure. Na(2) and Ca lie in the same plane perpendicular to [100]. Na(1) lies halfway between the planes containing Na(2) and Ca. Both Na ions lie at the intersections of mirror planes.

Na(1) is coordinated (fig. 3 and table 4) to eight oxygen atoms, of which O(2^III, 2^IV) and O(2^V, 2^VI) are CO₃ edges. All the Na(1) … O distances are within the normal range and indicate strong ionic bonding. The coordination is similar to that of (i) the Caion CaNa₂(CO₃)₂ · 5H₂O [9], where the oxygens not in shared edges are in water molecules, and (ii) the Ca(1) ion in Ca₅(PO₄)₂SiO₄ [10].

Table 4.

The sodium environments in Ca₂Na₂(CO₃)₃

Atoms	Distance
	Å
Na(1), O(1, lI)	2.429(2)
Na(1), O(2III, 2IV, 2V, 2VI)	2.530(2)
Na(1), O(3,3I)	2.605(1)
Na(2), O(2II, 2III, 2VI, 2VII)	2.296(1)
Na(2), O(4, 4I)	2.414(3)
Na(2), O(3)	3.050(3)

The atom labels refer to atoms in figure 3.

Na(2) is bonded strongly to six oxygen atoms (table 4) essentially arranged in a square pyramid with a CO₃ shared edge O(4, 4^I) centered about the apex position (fig. 3). The environment of Na(2) is completed by O(3), which is, however, 3.050 Å away and thus bonded relatively weakly to Na(2). The geometry of strong coordination for Na(2) is like that of Na(2) in Na₂CO₃ · H₂O [11].

3.3. The CO₃ Groups and Their Environments

The dimensions of the CO₃ groups are given in table 5. The C(1) CO₃ group is nearly trigonal with an average C – O distance of 1.282 Å; the C(2) CO₃ group appears to be significantly non-trigonal, but with an average C – O distance of 1.283 Å. The average C – O distances compare well with 1.283(2) Å in calcite (CaCO₃) [12], 1.285 Å in aragpnite (CaCO₃) [2], 1.286 Å in Na₂CO₃ · H₂O [11], 1.288 Å in CaNa₂ (CO₃)₂ · 5H₂O [9], 1.286 Å in CaNa₂ (CO₃)₂ · 2H₂O [9], and 1.286 Å in CaCO₃ · 6H₂O [1]. All these distances are uncorrected for thermal motion.

Table 5.

The Carbonate Anions and Their Environments Ca₂Na₂(CO₃)₃

Atoms	Distance. Å, or angle deg.
C(l), O(1)	1.273(3) Å
C(l), O(2, 2I)	1.286(2)
O(1), O(2, 2I)	2.211(2)
O(2), O(2I)	2.238(2)
O(1), C(1), O(2, 2I)	119.6(1)°
O(2), C(1), O(2I)	120.9(2)
C(2), O(3)	1.306(4) Å
C(2), O(4, 4I)	1.273(3)
C(3), O(4, 4I)	2.218(3)
O(4), O(4I)	2.235(4)
O(3), C(2), O(4, 4I)	118.7(2)°
O(4), C(2), O(4I)	122.7(3)
O(1), Na(lI)	2.429(2) Å
O(1), Ca, CaI	2.543(1)
O(2), Na(2)	2.296(1)
O(2), CaII	2.508(1)
O(2), CaIII	2.508(1)
O(2), Na(l)	2.530(2)
O(2), O(2II)	2.709(2)
O(3), Ca	2.411(1)
O(3), CaIV	2.411(1)
O(3), Na(1), Na(1I)	2.605(1)
O(3), Na(2)	3.050(3)
O(4), CaII	2.401(2)
O(4), Na(2)	2.414(3)
O(4), Ca	2.576(2)

The atom labels refer to atoms in figure 4.

The environments of the CO₃ groups are shown in figure 4 and are summarized in table 5. All three edges of both CO₃ groups are coordinated, in both cases to two Ca ions and one Na ion in the same plane as the CO₃ group. All oxygen atoms are further coordinated: O(1) to Na(1) in the plane of the C(1) CO₃ group, O(2) to Ca and Na(2) both out of this plane. O(4) to Ca(1) in the plane of the C(2) CO₃ group, and O(3) to two Na(1) ions which are both out of this plane. Edge coordination of O(3, 4) and O(3, 4^I) to Ca is expected to decrease the O(3)–C(2)–O(4) and O(3)–C(2)–O(4^I) angles in accord with Pauling’s rule because the O(4, 4^I) edge of the same CO₃ group is coordinated with weaker electrostatic force to Na(2). This is in accord with the observed O–C–O angles of 118.7(2)° for the Ca coordinated edges and 122.7(4)°, for the Na coordinated edge. Similar effects would be expected in the other CO₃ group, where O(1, 2) and O(1, 2^I) are coordinated to Ca and O(2, 2^I) is coordinated to Na. Here the angles, 119.6(1) for the Ca coordinated edges and 120.9(2)° for the Na coordinated edge are in the right directions from 120°, but are more nearly equal, which suggests that the effect is more complex than this simple reasoning. The average of the distances Ca … O(3) and Ca … O(4) is 2.493 Å; that of the Ca … O(1) and Ca … O(2) distances is 2.526 Å. The difference of 0.03 Å between these average values may account for part of the difference in angles of the CO₃ groups because O(3) and O(4) are bonded more strongly to Ca and the O(3), C(2), O(4) angle would then be expected to be decreased more than the O(1), C(1), O(2) angle.

Figure 4. The environments of the CO₃ groups in Ca₂Na₂(CO₃)₃.

The primes refer to atoms in table 5.

In the absence of hydrogen bonding, the oxygens coordinated most strongly to cations may be expected to have the longest C – O bonds. This is qualitatively the case. Similar effects have been observed in Na₂CO₃ · H₂O [11], CaNa₂(CO₃)₂·5H₂O and CaNa₂(CO₃)₂·2H₂O [9] and in the PO₄ groups in Ca₇Mg₉(Ca, Mg)₂(PO₄)₁₂ [13]. In the C(1) CO₃ group in Ca₂Na₂(CO₃)₃, the bond distance C(1) – O(2) and the symmetrically equivalent distance C(1) – O(2^I) are slightly longer than C(1) – O(1). O(2) is coordinated to two Ca ions and two Na ions; O(1) is coordinated to one Ca ion and one Na ion. In the C(2) CO₃ group, C(2) – O(3) is appreciably longer than the two equivalent distances C(2) – O(4) and C(2) – O(4^I). O(3) is coordinated to two Ca ions and two Na ions; O(4) is coordinated to two Ca ions and one Na ion. The differences in the coordinations of O(3) and O(4) here do not appear large enough to explain the 0.035 Å difference in C – O bond lengths. The difference, 0.020 Å, in the bond lengths C(1) – O(2) and C(2) – O(3), may be partly explained by the fact that while the C(1) CO₃ group has two longer bonds, the C(2) CO₃ group has only one, which may therefore be expected to have approximately twice the extension due to the cation field that the C(1) – O(2) bonds have.

The C(1) atom in the C(1) CO₃ group is 0.012(3) Å out of the plane defined by the O(1), O(2), and O(2^I) atoms. This may be a result of perturbation of the sp² hybridization of the oxygen atoms by neighboring cations. The C(2) CO₃ group is planar by symmetry.

4. Discussion

The positions given by Wickman, (0.0, 0.226, 0.743) for C(1), (0.0, 0.325, 0.850) for O(1), and (0.230, 0.177, 0.690) for O(2), which are 0.57, 1.98, and 0.31 Å, respectively, from the positions given here, show that in his structure the C(1)O₃ group has been reflected along c through the plane z = 0.75, so that O(1) then juts out into the void instead of being on the void surface. The interatomic distances are reasonable in Wickman’s structure and the O … O repulsions are therefore approximately the same in the two models. In the structure reported here, however, O(1) is able to form stronger bonds to the two Ca ions above and below it along a, and to Na(1) in the same plane parallel to (100); this is probably the factor governing the orientation of the CO₃ group. The calculation of refractive indices in the way originally given by Bragg [14] assumes that only oxygen atoms have optical anisotropy and ignores all interatomic interactions. Thus, Wickman, following this procedure, was able to obtain qualitative agreement between observed and calculated values using a model in which the orientation of the C(1) CO₃ group relative to the (001) plane was ~35° instead of −31° 42′. The average orientations of C(1) CO₃ groups in the unit cell are about the same for the two models when one takes into account the symmetry operations. This agreement can be seen from table 6, which compares the observed indices with the values calculated for the two models using Bragg’s procedure. A much more suitable test of these models, which would produce better quantitative agreement with the observed values, would require consideration of dipole-dipole coupling terms and optical anisotropy of all atoms, especially Na, rather than just oxygens [15, 16]. As a further refinement, the dependence of the atomic optical anisotropy on the environment should be incorporated.

Table 6.

Refractive indices for shortite

Observed	Wickman’s model	Here	Orientation
1.531	1.515	1.502	c
1.555	1.545	1.541	a
1.570	1.555	1.554	b