A Refinement of the Crystal Structure of Na₂CO₃ · H₂O

Abstract

The crystal structure of synthetic Na₂CO₃·H₂O has been refined using 1231 unique x-ray diffraction data collected by the peak height method on a diffractometer. R = 0.034. The unit cell is a = 6.474(2), b= 10.724(3) and c = 5.259(2) Å with z = 4 and space group P2₁ab. The calculated density is the same as the observed density, 2.26 g·cm⁻³. The structure contains sheets of ${\text{CO}}_3^{2-}$ ions bonded to Na⁺ ions and water molecules roughly halfway between the sheets. Each ${\text{CO}}_3^{2-}$ bonds edgewise to both Na⁺ ions. The Na⁺ ions have irregular but similar coordinations of seven neighbors. Each water molecule is bonded to both Na⁺ ions and forms hydrogen bonds to both neighboring ${\text{CO}}_3^{2-}$ layers.

1. Introduction

The crystal structure of Na ₂CO₃ · H₂O was determined except for the hydrogen positions, by Harper [1]¹ in 1936 using qualitative estimates of the x-ray intensities. In our program of studies on coordination in hydrated carbonates [2] and phosphates [3], we have refined Harper’s structure for Na₂CO₃ · H₂O using new x-ray data. Na₂CO₃ · H₂O is the mineral thermonatrite and often occurs with Na₂CO₃ · 10H₂O (natron) and Na₂CO₃ · NaHCO₃ · 2H₂O (trona) [4, 5, 6].

2. Determination of the Structure

Formula: Na₂ CO₃·H₂O. Unit cell: Orthorhombic with a = 6.472(2) Å, b = 10.724(3) Å, c = 5.259(2) Å at 24 °C as calculated from three pairs of 2θ values of axial reflections from a single crystal and observed on a diffractometer. The standard deviations of the cell parameters are in parentheses and are estimates based on experience with the technique. Cell volume: 365.1 ų. Wavelength used: 0.710688 Å (Mo Kα). Filter: 0.025 mm Nb. Space Group: P2₁ab. Cell contents in formula Wts: 4. Equivalent positions: x, y, z; 1/2 + x, − y, − z; 1/2 + x, 1/2−y, z; x, 1/2 + y, − z. Reciprocal lattice extinctions: h0l, h ≠ 2n; hk0, k ≠ 2n. Observed density: 2.255 g·cm⁻³ [7]. Calculated density: 2.256 g · cm⁻³. Habit: Fragment from plate. Size of crystal: ~ 0.35 mm max. ~ 0.05 mm min. Origin: Evaporation of aqueous solution at 60°C. Linear absorption coefficient: 4.37 cm⁻¹. Absorption corrections: None applied. Maximum error in any intensity from absorption is ~ 10 percent. Number of reflections: 2189 were collected from 2 octants and merged into a unique set of 1231 of which 1132 are “observed” reflections and 99 are less than 2σ above background and are “unobserved”. Maximum sin θ/λ for data: 0.904 Å ⁻¹. Method used to estimate data: peak height measurement [8] with a single crystal diffractometer [9] and some peak heights standardized against θ/2θ scans. Scattering factors: Na, C, O, for neutral atoms given in reference [10]; H from reference [11]. Least-squares refinements: Full-matrix, with Σ(w|| F_o| −|F_c||)² minimized. Refinements include unobserved reflections for which the calculated intensities are more than 2σ above background. Least-squares weights: 1/σ² normalized so that maximum weight is 1. Definitions: 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 where P = counts at the peak position, B_L and B_H= background counts at lower and higher 2θ respectively, T= time spent counting peak, T_B = time spent counting each background, AF = attenuator · factor, LP = Lorentz polarization correction.

$$\begin{gathered} R_w={\left(\sum {\left(w\Vert F_{\text{o}}|-|F_{\text{c}}\Vert \right)}^2/\sum {\left(w\left|F_{\text{o}}\right|\right)}^2\right)}^{1/2} \\ R=\left(\sum \Vert F_{\text{o}}|-|F_{\text{c}}\Vert \right)/\sum \left|F_{\text{o}}\right|· \end{gathered}$$

Final R_w: 0.029. Final R: 0.032. Average shift/error for last cycle: 0.015. Thermal parameters: anisotropic with form

$$\text{exp}\left(-1/4(a^{*2}{B}_{11}{h}^2+b^{*2}{B}_{22}{k}^2+c^{*2}{B}_{33}{l}^2+2a^{*}{b}^{*}{B}_{12}hk+2a^{*}{c}^{*}{B}_{13}hl+2b^{*}{c}^{*}{B}_{23}kl\right).$$

The structure was refined isotropically from Harper’s parameters using the x-ray 67 system [12] of computer programs to R_w= 0.065; the x parameter of Na(l) was fixed at x = 0. The structure was refined anisotropically to R_w = 0.044 and the hydrogens were found unambiguously as the two highest peaks in the difference synthesis in which the coefficients were weighted by the least squares weights. The two next highest peaks were less than 3/4 as high as the peaks assigned to hydrogens and were (a) halfway between C and 0(3) in the CO₃ group and (b) 0.7 A from 0(1) of the CO3 group. The hydrogens were included with variable positional parameters and fixed thermal parameters (B_H = 1 Ų) in the final refinement to R_w⁼ 0.029. The largest correlation coefficients are ~ 0.25 between the scale factor and the B₁₁ thermal parameters of the two Na ions and ~ 0.15 between these B₁₁ thermal parameters. Most correlation coefficients are less than 0.05.

The atomic parameters are given in table 1. The observed and calculated structure factors are given in table 2. The hydrogen positions obtained from the weighted difference synthesis and from the refinements differ by ~ 0.17 Å. “Calculated” hydrogen positions were derived by applying the geometry of free water (O−H = 0.958 A, ZH−O−H = 104.5°) with the constraint that the O−H … O angles be as near to linear as possible. These hydrogen positions differ from the other positions by about 0.3 Å. The three sets of hydrogen positions are compared in table 3. The distances and angles which involve hydrogen were obtained using the “calculated” hydrogen positions.

Table 1.

Atomic parameters of Na₂CO₃ · H₂O

Atom	X	y	z	$B_{11}^{*}$	B22	B33	B12	B13	B23
Na(1)	0.0000	0.1938(1)	0.1398(1)	1.40(3)	1.54(3)	1.36(3)	0.17(3)	0.17(3)	0.08(2)
Na(2)	.0651(2)	.0020(1)	− .3786(2)	1.44(3)	1.19(3)	1.76(3)	.31(2)	.25(3)	.09(3)
C	−.2151(3)	.2556(2)	.6025(3)	.45(6)	1.11(6)	1.17(5)	−.06(5)	−.05(5)	−.03(5)
O(1)	−.2010(3)	.1381(1)	.5457(3)	1.56(6)	0.72(5)	2.72(7)	.08(5)	−.15(6)	−.47(4)
O(2)	−.2027(3)	.3369(1)	.4267(2)	1.73(6)	1.27(5)	1.24(5)	−.05(5)	−.04(5)	.47(4)
O(3)	− .2398(3)	.2876(1)	−.1639(2)	1.42(6)	2.14(6)	0.90(4)	−.28(5)	.25(4)	−.32(4)
O(4)	.0325(3)	−.0296(1)	.0683(3)	1.64(7)	1.43(6)	1.92(6)	−.21(5)	−.25(5)	.39(4)

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

^*Thermal parameters are in Ų.

Table 2.

Observed and calculated structure factors for Na₂CO₃·H₂O^a

0, K, 0
2	250	237
4	421	462
6	556	561
8	105	113
10	119	119
12	48	45
14	50	60
16	60	52
18	47	40
1, K, 0
2	156	151
4	520	519
6	254	254
8	153	166
10	88	88
12	45	47
14	109	118
16	68	75
18	18	15
2, K, 0
0	39	37
2	843	802
4	542	529
6	283	286
8	128	128
10	311	318
12	30	31
14	34	35
16	44	49
18	35	31
3, K, 0
2	176	171
4	428	415
6	282	281
8	127	127
10	144	146
12	49	49
14	38	43
16	55	59
18	19	19
4, K, 0
2	345	339
4	236	223
6	285	274
8	233	228
10	52	52
12	97	99
14	52	54
16	30	25
18	52	46
5, K, 0
2	101	96
4	171	167
6	29	30
8	115	113
10	24	23
12	37	39
14	113	119
16	60	61
6, K, 0
0	86	76
2	303	296
4	199	192
6	70	68
8	130	129
10	126	125
12	50	52
14	47	48
16	13*	7
7, K, 0
2	87	87
4	143	142
6	127	127
8	52	53
10	86	88
12	25	19
14	12*	2
8, K, 0
0	163	158
2	148	148
4	40	42
6	61	61
8	134	134
10	80	79
12	70	72
14	34	34
9, K, 0
2	28	28
4	37	38
6	33	31
8	50	53
10	16	19
12	46	51
10, K, 0
0	83	88
2	86	90
4	66	68
6	12*	9
8	43	47
10	39	40
11, K, 0
2	36	39
4	29	32
6	43	48
0, K, 1
0	289	274
1	77	74
2	22	19
3	5*	3
4	211	192
5	264	268
6	200	192
7	159	157
8	360	365
9	186	185
10	118	123
11	9*	8
12	188	191
13	9*	9
14	85	88
15	32	36
16	57	55
17	13	9
18	28	31
19	13*	1
1, K, 1
0	5*	0
1	44	39
2	66	66
3	307	314
4	350	350
5	206	204
6	89	86
7	269	273
8	144	147
9	165	166
10	147	151
11	33	31
12	40	43
13	120	122
14	83	85
15	29	26
16	67	69
17	44	44
18	17	7
19	37	36
2, K, 1
0	604	603
1	444	449
2	299	309
3	326	329
4	275	270
5	28	27
6	103	101
7	80	80
8	94	91
9	125	125
10	205	206
11	61	64
12	51	53
13	55	61
14	86	82
15	34	29
16	32	33
17	48	42
18	92	88
19	39	35
3, K, 1
0	5*	0
1	187	184
2	126	125
3	292	291
4	182	177
5	129	127
6	62	61
7	223	224
8	94	97
9	71	70
10	93	96
11	91	94
12	17	14
13	88	88
14	90	93
15	35	38
16	75	78
17	45	43
18	12*	6
4, K, 1
0	368	374
1	61	62
2	28	27
3	25	23
4	125	121
5	128	126
6	183	182
7	105	103
8	194	191
9	111	110
10	116	114
11	28	28
12	130	127
13	16	11
14	61	63
15	16	20
16	55	53
17	33	32
18	13	14
5, K, 1
0	7*	0
1	127	126
2	45	48
3	29	28
4	153	151
5	219	221
6	102	102
7	67	65
8	76	74
9	108	111
10	90	89
11	62	57
12	48	48
13	49	50
14	28	32
15	45	41
17	25	23
6, K, 1
0	189	195
1	166	171
2	98	93
3	113	111
4	125	124
5	38	37
6	74	74
7	93	90
8	29	25
9	70	68
10	144	142
11	47	46
12	27	27
13	19	20
14	39	37
15	12*	8
16	38	41
7, K, 1
0	9*	0
1	108	111
2	54	53
3	46	44
4	41	40
5	110	109
6	69	68
7	62	63
8	23	23
9	12	11
10	20	21
11	67	70
12	32	30
13	12	10
14	51	53
15	39	42
8, K, 1
0	174	183
1	47	49
2	82	84
3	28	31
4	48	46
5	42	42
6	90	89
7	31	31
8	42	41
9	29	29
10	58	58
11	12*	12
12	43	44
13	12*	4
14	33	34
9, K, 1
0	12*	0
1	40	45
2	25	25
3	61	63
4	43	44
5	76	77
6	39	40
7	24	27
8	26	26
9	40	42
10	29	29
11	27	26
12	14	13
10, K, 1
0	67	74
1	44	49
2	35	36
3	35	36
4	52	55
5	24	26
6	16	15
7	47	49
8	46	48
9	42	43
11, K, 1
0	12*	0
1	36	36
2	14	15
3	13*	10
4	17	17
5	32	34
6	39	39
0, K, 2
0	350	337
1	117	135
2	143	141
3	152	166
4	129	125
5	58	56
6	132	132
7	75	72
8	111	115
9	53	54
10	135	141
11	11	17
12	23	24
13	9*	10
14	10*	1
15	74	71
16	19	19
17	106	106
18	26	28
1, K, 2
0	13	0
1	556	601
2	113	113
3	427	440
4	27	20
5	495	504
6	121	123
7	113	113
8	47	49
9	124	123
10	77	82
11	149	149
12	47	48
13	22	16
14	41	43
15	67	68
16	47	50
17	39	36
18	12*	5
2, K, 2
0	133	134
1	319	331
2	174	177
3	222	227
4	228	233
5	167	166
6	72	72
7	206	205
8	36	39
9	267	265
10	74	76
11	74	72
12	37	39
13	41	38
14	30	31
15	26	25
16	21	22
17	35	35
18	13*	15
3, K, 2
0	6	0
1	389	402
2	88	90
3	119	122
4	57	55
5	377	388
6	41	41
7	164	165
8	59	60
9	130	129
10	65	68
11	99	98
12	25	26
13	78	81
14	41	43
15	58	58
16	46	49
17	12*	1
18	12*	0
4, K, 2
0	210	209
1	115	117
2	91	90
3	91	87
4	55	55
5	58	55
6	86	84
7	120	117
8	72	71
9	82	85
10	92	93
11	25	18
12	19	19
13	16	16
14	14	15
15	69	66
16	13	13
17	71	72
5, K, 2
0	7*	0
1	171	178
2	34	34
3	334	340
4	18	19
5	135	134
6	92	92
7	143	141
8	13	14
9	90	89
10	42	45
11	50	52
12	38	38
13	71	72
14	25	27
15	12*	14
16	28	30
17	45	46
6, K, 2
0	61	61
1	139	143
2	74	76
3	85	84
4	81	81
5	80	81
6	24	22
7	65	65
8	27	29
9	137	136
10	46	46
11	49	48
12	23	24
13	55	54
14	24	26
15	27	25
16	17	17
7, K, 2
0	8*	0
1	91	95
2	24	25
3	105	109
4	37	37
5	69	67
6	10*	7
7	127	127
8	35	36
9	58	58
10	35	35
11	11*	10
12	11*	3
13	66	68
14	20	23
15	20	18
8, K, 2
0	97	102
1	32	33
2	33	34
3	41	42
4	13	12
5	35	37
6	36	35
7	98	98
8	24	24
9	51	52
10	33	34
11	42	41
12	12*	10
13	17	17
9, K, 2
0	10*	0
1	19	18
2	10*	5
3	104	107
4	16	14
5	29	31
6	42	43
7	57	57
8	11*	3
9	49	53
10	13	13
11	21	19
10, K, 2
0	30	31
1	66	72
2	30	33
3	37	41
4	22	22
5	40	44
6	12*	10
7	12*	7
8	17	15
9	38	41
11, K, 2
0	12*	0
1	24	25
2	12*	4
3	31	34
4	18	18
5	13*	11
0, K, 3
0	279	278
1	35	35
2	458	469
3	88	86
4	168	170
5	208	214
6	15	13
7	118	121
8	209	203
9	205	205
10	33	27
11	26	30
12	122	120
13	10*	0
14	27	30
15	11*	5
16	21	23
17	53	53
18	41	42
1, K, 3
0	6*	0
1	88	87
2	148	153
3	238	242
4	182	188
5	41	48
6	168	173
7	181	185
8	77	80
9	125	128
10	22	20
11	59	58
12	47	47
13	104	103
14	50	51
15	43	43
16	16	18
17	54	53
18	22	22
2, K, 3
0	211	215
1	120	122
2	179	186
3	146	148
4	70	71
5	10	9
6	120	120
7	157	162
8	153	159
9	35	35
10	36	38
11	17	13
12	20	19
13	53	60
14	90	91
15	50	46
16	36	38
17	67	66
18	30	26
3, K, 3
0	8*	0
1	196	198
2	94	93
3	172	175
4	144	148
5	104	103
6	173	178
7	144	148
8	63	65
9	82	83
10	31	32
11	67	68
12	66	66
13	71	71
14	28	29
15	54	53
16	12*	8
17	45	42
4, K, 3
0	237	237
1	54	54
2	220	220
3	26	22
4	149	153
5	127	131
6	84	86
7	77	77
8	103	99
9	137	136
10	106	109
11	35	38
12	75	72
13	15	12
14	36	37
15	12*	8
16	33	33
17	54	52
5, K, 3
0	7*	0
1	43	43
2	102	106
3	111	111
4	88	89
5	114	119
6	78	79
7	74	75
8	31	31
9	89	92
10	25	26
11	61	57
12	30	31
13	57	57
14	29	32
15	33	32
16	28	31
6, K, 3
0	133	138
1	64	66
2	47	47
3	66	70
4	27	27
5	27	27
6	101	106
7	116	115
8	23	25
9	40	39
10	39	39
11	25	20
12	29	29
13	27	31
14	37	37
15	26	23
7, K, 3
0	9*	0
1	108	111
2	43	45
3	29	27
4	78	80
5	74	75
6	73	74
7	78	78
8	36	38
9	25	23
10	16	15
11	48	52
12	38	40
13	18	14
14	16	15
8, K, 3
0	104	110
1	50	53
2	30	26
3	22	24
4	77	80
5	57	60
6	40	42
7	29	29
8	27	25
9	51	52
10	73	76
11	19	21
12	15	12
9, K, 3
0	11*	0
1	25	27
2	32	33
3	72	72
4	33	34
5	53	55
6	24	25
7	16	14
8	12*	5
9	45	47
10	29	30
10, K, 3
0	33	36
1	20	23
2	20	20
3	30	34
4	22	22
5	23	26
6	37	40
7	56	60
8	23	24
11, K, 3
0	12*	0
1	40	42
2	22	23
0, K, 4
0	495	490
1	18	16
2	54	56
3	81	79
4	283	289
5	14	19
6	150	147
7	168	174
8	23	20
9	13	14
10	142	148
11	10*	5
12	67	64
13	74	79
14	11*	3
15	11*	1
16	69	65
17	38	38
1, K, 4
1	121	120
2	111	116
3	137	140
4	150	152
5	69	74
6	107	109
7	156	165
8	33	32
9	81	86
10	38	40
11	30	31
12	60	63
13	30	28
14	46	47
15	29	28
16	16	17
17	13*	15
2, K, 4
0	205	201
1	163	162
2	177	182
3	49	53
4	82	80
5	107	111
6	214	220
7	26	25
8	74	75
9	54	53
10	138	134
11	91	94
12	21	23
13	35	40
14	69	69
15	11*	3
16	29	37
17	50	51
3, K, 4
1	77	79
2	128	135
3	180	186
4	164	169
5	25	29
6	83	86
7	113	119
8	28	33
9	67	71
10	29	28
11	12	10
12	28	31
13	16	15
14	28	28
15	31	31
16	12*	11
4, K, 4
0	250	246
1	19	19
2	163	168
3	57	60
4	175	178
5	13	16
6	64	62
7	120	123
8	105	103
9	13	11
10	66	70
11	12	9
12	74	73
13	53	56
14	23	20
15	12*	10
16	43	41
5, K, 4
1	87	89
2	24	24
3	30	29
4	61	59
5	68	71
6	52	53
7	98	100
8	43	43
9	48	51
10	41	45
11	28	30
12	42	44
13	24	22
14	51	52
15	13*	13
6, K, 4
0	14	17
1	83	84
2	131	132
3	44	44
4	57	58
5	62	66
6	72	74
7	38	39
8	96	98
9	62	61
10	45	44
11	42	45
12	34	34
13	16	16
14	59	60
7, K, 4
1	37	37
2	57	58
3	102	104
4	80	84
5	11	10
6	51	52
7	41	43
8	25	29
9	29	31
10	18	17
11	12*	10
12	13	9
13	17	16
8, K, 4
0	43	44
1	18	19
2	92	96
3	32	36
4	52	54
5	11*	9
6	36	38
7	55	58
8	66	67
9	12*	12
10	20	17
11	15	12
9, K, 4
1	46	48
2	17	17
3	25	24
4	22	20
5	38	41
6	15	12
7	33	33
8	26	25
9	19	19
10, K, 4
0	49	57
1	30	31
2	44	46
3	23	22
4	38	43
5	28	32
0, K, 5
0	147	146
1	57	44
2	11	12
3	35	38
4	101	102
5	18	15
6	27	28
7	64	61
8	95	89
9	9*	4
10	10*	6
11	57	58
12	87	82
13	17	18
14	12	11
15	29	32
16	41	35
1, K, 5
1	123	127
2	68	73
3	249	249
4	97	101
5	81	82
6	37	38
7	101	99
8	27	25
9	45	45
10	37	35
11	29	34
12	11	15
13	47	50
14	33	34
15	29	27
16	14	13
2, K, 5
0	121	118
1	187	189
2	166	168
3	96	98
4	35	35
5	37	36
6	54	55
7	118	119
8	50	53
9	71	70
10	67	61
11	54	52
12	11*	8
13	21	22
14	73	67
15	12*	1
16	13*	14
3, K, 5
1	71	71
2	32	37
3	170	170
4	52	56
5	50	49
6	11	12
7	111	111
8	42	43
9	17	17
10	20	15
11	73	76
12	25	29
13	47	49
14	38	39
15	25	24
4, K, 5
0	125	124
1	39	37
2	51	51
3	40	43
4	72	73
5	16	14
5	16	14
5	16	14
7	61	61
7	61	61
7	61	61
9	34	34
10	27	26
11	43	44
12	72	68
13	28	27
14	12*	1
15	19	20
5, K, 5
1	107	109
2	48	51
3	120	121
4	59	62
5	112	115
6	41	41
7	15	17
8	10*	6
9	36	37
10	28	27
11	14	12
12	14	10
13	12*	13
14	19	18
6, K, 5
0	95	97
1	98	100
2	65	65
3	46	47
4	56	58
5	32	32
6	46	48
7	55	56
8	18	16
9	34	33
10	63	59
11	47	48
12	18	13
13	29	28
7, K, 5
1	36	37
2	13	14
3	34	36
4	11	9
5	56	56
6	11*	4
7	50	51
8	28	30
9	31	33
10	12*	6
11	51	53
8, K, 5
0	59	60
1	19	19
2	57	59
3	28	30
4	30	32
5	16	17
6	41	42
7	31	33
8	26	23
9	34	34
9, K, 5
1	40	41
2	17	14
3	31	30
4	22	20
5	49	53
6	22	22
6	22	22
0, K, 6
0	27	25
1	95	92
2	78	78
3	54	53
4	9*	4
5	39	37
6	21	25
7	60	62
8	73	70
9	20	21
10	88	82
11	11*	14
12	68	67
13	47	42
14	46	44
15	26	20
1, K, 6
1	93	90
2	55	53
3	13	17
4	29	31
5	124	119
6	74	71
7	63	62
8	58	63
9	51	51
10	48	49
11	79	79
12	34	32
13	33	35
14	38	36
2, K, 6
0	33	28
1	63	59
2	84	78
3	24	24
4	51	53
5	23	20
6	10*	9
7	71	66
8	12	11
9	36	33
10	41	39
11	63	61
12	53	51
13	32	29
14	32	31
3, K, 6
1	62	61
2	16	12
3	108	109
4	22	20
5	82	80
6	53	53
7	31	30
8	57	60
9	54	51
10	35	37
11	55	55
12	32	34
13	28	23
14	44	41
4, K, 6
0	79	77
1	71	68
2	66	66
3	39	37
4	19	13
5	42	40
6	26	26
7	33	34
8	59	56
9	30	30
10	67	62
11	16	12
12	51	51
13	37	34
5, K, 6
1	46	46
2	52	52
3	53	49
4	44	44
5	41	41
6	57	55
7	79	79
8	28	32
9	34	35
10	33	34
11	40	42
12	18	16
6, K, 6
0	25	24
1	34	33
2	56	54
3	37	35
4	24	25
5	15	13
6	13*	8
7	33	32
8	12*	5
9	34	36
10	32	32
11	30	30
7, K, 6
1	11*	8
2	18	15
3	79	79
4	38	39
5	11*	5
6	23	23
7	29	30
8	29	29
9	30	31
8, K, 6
0	77	76
1	28	28
2	40	41
3	16	15
4	20	21
5	30	28
6	19	17
7	18	15
9, K, 6
1	30	31
2	26	27
0, K, 7
0	90	88
1	27	29
2	168	156
3	17	11
4	49	47
5	43	37
6	11*	11
7	50	45
8	69	64
9	41	35
10	11*	1
11	38	34
12	13*	9
13	43	39
1, K, 7
1	43	42
2	56	55
3	59	56
4	55	55
5	39	37
6	69	65
7	56	57
8	11*	7
9	25	21
10	14	12
11	25	24
12	39	39
13	30	27
2, K, 7
0	93	88
1	10*	10
2	51	44
3	20	14
4	33	29
5	42	39
6	44	42
7	33	28
8	62	58
9	29	26
10	39	37
11	38	33
12	25	24
3, K, 7
1	46	46
2	68	67
3	24	24
4	75	74
5	64	63
6	69	65
7	26	26
8	21	21
9	32	31
10	18	15
11	34	34
12	33	29
4, K, 7
0	81	78
1	21	21
2	107	101
3	30	27
4	49	46
5	37	32
6	22	22
7	40	36
8	35	34
9	33	28
10	41	40
11	32	30
5, K, 7
1	32	34
2	20	17
3	42	41
4	11*	4
5	11*	9
6	43	42
7	43	43
8	12*	10
9	13*	12
10	30	25
6, K, 7
0	82	80
1	14	9
2	11*	5
3	24	21
4	16	12
5	39	36
6	48	45
7	28	23
8	19	17
7, K, 7
1	28	27
2	36	37
3	23	24
4	49	48
5	38	37
6	38	37
0, K, 8
0	19	9
1	11*	7
2	11*	4
3	45	40
4	57	53
5	60	57
6	11*	0
7	60	56
8	20	16
9	20	15
10	48	47
1, K, 8
1	11*	9
2	38	38
3	40	39
4	38	38
5	27	26
6	45	41
7	37	36
8	18	19
9	39	38
10	24	22
2, K, 8
0	76	73
1	72	65
2	34	32
3	66	62
4	16	11
5	58	53
6	72	67
7	18	16
8	26	24
9	13*	12
3, K, 8
1	11*	2
2	25	23
3	42	39
4	12*	11
5	25	23
6	39	37
7	38	36
8	15	18
9	31	32
4, K, 8
0	11*	7
1	16	14
2	34	30
3	38	35
4	48	44
5	48	45
6	14	13
7	49	43
8	32	28
5, K, 8
1	16	13
2	27	27
3	26	26
4	38	37
5	33	32
6	25	20
6, K, 8
0	13*	11
1	54	51
2	42	40
3	42	40
0, K, 9
0	70	61
1	22	14
2	13	11
3	21	17
4	84	76
5	28	24
6	19	13
1, K, 9
1	20	16
2	13*	9
3	58	50
4	24	22
5	25	21
6	26	27
2, K, 9
0	21	19
1	44	42
2	68	62
3	13*	6
4	27	24
5	25	23
3, K, 9
1	20	12
	15	11
	35	31

^aThe columns are k, 10F_o, 10F_c, “Unobserved” reflections are marked by · F_o and F_c are on an absolute scale.

Table 3.

The hydrogen positions in Na₂CO₃·H₂O

Atom	Weighted difference synthesis			Least squares refinements			Calculated*
	X	y	Z	X	y	z	X	y	z
H(l)	0.12	−0.07	0.14	0.11	−0.06	0.15	0.134	−0.056	0.190
H(2)	−.08	−.08	.14	−.10	−.08	.12	−.077	− .089	.084

^*Assuming the geometry of free water with O—H = 0.958 Å and ∠ H—O—H = 104.5°, and making the O—H … O hydrogen bonds as linear as possible.

3. Description of the Structure

The structure (fig. 1) contains CO₃ anions whose planes are almost perpendicular to a and which form sheets at x ~ 0.25 and x ~ 0.75. Because the C atoms lie close to the planes of the a glides, they form columns along a at y= 0.25, z ~ 0.60. Two adjacent CO₃ groups in a column are held together by both being ionically bonded to four Na ions and hydrogen bonded by one water molecule. The four Na ions and the water molecule form a pentagon roughly halfway between the CO₃ sheets. Adjacent CO3 groups in a given sheet are linked by the Na ions that lie above and below the sheet.

Figure 1.

A stereoscopic illustration of Na₂CO₃ · H₂0 viewed along a. The origin of the unit cell is marked by the asterisk.

3.1. The Carbonate Anion and Invironment

The dimensions in the CO3 anion are given in table 4 and the environment is detailed in table 4 and figure 2. The CO₃ group is nearly trigonal. As can be seen in figures 1 and 2, O(2) is the only oxygen which is not hydrogen bonded, being instead ionically bonded to four Na ions. The absence of hydrogen bonding to O(2) may account for the observation that the C—O(2) bond is apparently the shortest of the three. O(1) is coordinated to three Na ions and is the acceptor in the hydrogen bond O(1) … H(l)—O(4) from the water molecule. O(3) is bonded strongly to two Na ions and more weakly (2.822 Å) to a third Na(2). O(3) is the acceptor in the hydrogen bond O(3) … H(2)−O(4) from the water molecule.

Table 4.

The CO₃ group

Atoms	Distances, Å, or angle, deg.
C, O(l)	1 299(3)
C,O(2)	1.274(2)
C, O(3)	1. 285(2)
O(1), O(2)	2 223(2)
O(1) O(3)	2 229(2)
O(2), O(3)	2 230(2)
O(l), C, O(2)	119.6(2)
O(1), C, O(3)	119.2(2)
O(2), C, O(3)	121.2(2)
O(1), Na(l)	2 570(2)
O(1), Na(2)	2 293(2)
O(1), Na(2′)	2.307(2)
O(1), O(4)	2 907(2)
O(1), H(l)	1 96
O(2), Na(l)	2 521(2)
O(2), Na(l′)	2.468(2)
O(2), Na(2′)	2.508(2)
O(2), Na(2)	2 491(2)
O(3). Na(l)	2 444(2)
O(3), Na(l′)	2.330(2)
O(3), Na(2)	2 822(2)
O(3) O(4)	2. 685(2)
O(3), H(2)	1.74

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. The primes refer to atoms in figure 2.

Figure 2.

The carbonate group environment in Na₂CO₃·H₂O. The primes refer to atoms in table 4.

Since the planes of the CO₃ groups are all essentially perpendicular to a, this is expected to be the direction of lowest refractive index, as was found by Harper [1]. Later workers [13, 14] apparently did not permute the refractive indexes when they permuted the unit cell axes to fit crystallographic convention.

3.2. The Sodium Environments

The two crystallographically distinct Na ions in the structure are in general positions. Their environments are shown in figure 3 and are given in table 5.

Figure 3.

The water and sodium environments in Na₂CO3·H₂O. The primes refer to atoms in tables 5 and 6.

Table 5.

The sodium environments

Atoms	Distance, Å
Na(l), O(1)	2.570(2) Å
Na(1), O(2)	2.521(2)
Na(l), O(3)	2.444(2)
Na(l), O(4)	2.434(2)
Na(1), O(2′)	2.468(2)
Na(l), O(3′)	2.330(2)
Na(l), O(4′)	3.669(2)
Na(2), O(4)	2.384(2) Å
Na(2), O(1′)	2.293(2)
Na(2), O(1″)	2.307(2)
Na(2), O (2″)	2.508(2)
Na(2), O(2‴)	2.491(2)
Na(2), O(4″)	2.936(2)
Na(2), O(3′)	2.822(2)

The primes refer to the atoms in figure 3.

Na(1) is bonded ionically to five oxygens from CO₃ groups, and strongly to one water oxygen. Four of the CO₃ oxygens, O(1), O(2′), O(3), O(3′), figure 3, define an approximate square about Na(1), and water oxygen O(4) forms the apex of a square pyramid. The fifth carbonate oxygen, O(2), is in the same CO3 group as O(1); the CO₃ group is therefore coordinated edgewise to Na(1). The position of O(2) is such that the coordination about Na(1) cannot be considered octahedral. The next oxygen in the direction of the octahedral apex is the water oxygen O(4′), which is relatively far (3.669 Å) from Na (1).

The coordination of Na(2) is similar to that of Na(1). Na(2) is slightly displaced from the center of an approximate square of carbonate oxygens, O(1′), O(2″), O(1″), O(2″ ′). The displacement is towards the strongly bonded water molecule 0(4), which is the apex of a square based pyramid (base down in figure 3). The coordination of Na(2) is completed by O(4″) (2.936 Å) which is the remaining apex of an approximate octahedron, and by O(3′) which is in the same CO₃ group as O(2″). Thus the CO₃ group is coordinated edgewise to Na(2) also, this time using O(2) and O(3) instead of O(1) and O(2), which are used to coordinate to Na(1). This edgewise coordination is shown in figure 2. The coordination to Na(2) comprises five carbonate oxygens and two water molecules instead of four carbonate oxygens and two water molecules as suggested by Harper [1] and noted by Wells [15].

3.3. The Water Environment

The water environment is given in table 6 and shown in figure 3. The water molecule is bonded to Na(1) and Na(2) with distances of 2.434 and 2.384 Å respectively, and forms hydrogen bonds to oxygens O(1) and O(3) of neighboring CO₃ groups. Na(1), Na(2), O(1), and O(3) are arranged approximately tetrahedrally about the water oxygen. The distortion of this tetrahedron is considerable as can be seen from the angles listed in table 6. The closest H … Na distance is H(1) … Na(2) = 2.42 Å, which is in the normal range.

Table 6.

The water environment

Atom	Distance Å or angle, deg.
O(4),Na(1)	2.434(2) Å
O(4),Na(2)	2.384(2)
O(4),Na(2′)	2.936(2)
O(4), O(1)	2.907(2)
O(4). O(3)	2.684(2)
H(1),O(l)	1.96
H(2), O(3)	1.74
Na(l), O(4),Na(2)	91.15(6)°
O(1), O(4),Na(1)	109.70(7)
O(1), O(4),Na(2)	133.83(9)
O(3), O(4),Na(l)	129.28(9)
O(3), O(4),Na(2)	110.29(7)
O(1), O(4), O(3)	88.12(6)
O(4),H(l),O(l)	168.
O(4),H(2), O(3)	167.

The prime refers to an atom in figure 3.

The calculated hydrogen positions in table 3 were obtained using the geometry of free water and imposing the condition that the O—H … O angles both be as linear_oas possible. Because H(2) … O(3) is shorter (1.74 Å) than H(1) … O(1) (1.96 Å) it is possible that the hydrogen bond O(4)—H(2) … O(3) is strictly linear. Assuming the same water geometry, the hydrogens would then be ≃0.14 Å away from the positions given in table 3 at 0.145, −0.046, 0.182 for H(1) and −0.065,−0.095,0.102 for H(2). The O(4)—H(1) … O(1) angle would then be 156°, and the H(1) … O(1) and H(2) … O(3) distances would be 2.01 A and 1.73 Å, respectively. The closest H Å Na distance would be H(1) … Na(2)=2.39 Å.