- WEGSCHEIDERITE - Na₅CO₃(HCO₃)₃

Crystal Structure

Because of the translational symmetry all the calculations are performed in the primitive unit cell and not in the conventional unit cell. The following information regarding the structure is given with respect to this primitive unit cell, which sometimes can take an unintuitive shape.

Symmetry (experimental):

Space group:	2		P-1
Lattice parameters (Å):	3.4762	10.0393		15.5969
Angles (°):	107.770	95.589		95.028

Symmetry (theoretical):

Space group:	2		P-1
Lattice parameters (Å):	3.2921	9.7992		15.2507
Angles (°):	107.48	95.25		94.98

Cell contents:

Number of atoms:	48
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Na:	0.7835	0.6720	0.0463
Na:	0.8081	0.1781	0.0954
Na:	0.1809	0.7154	0.2762
Na:	0.4086	0.2126	0.3025
Na:	0.7699	0.7483	0.4767
C:	0.4132	0.4748	0.1388
C:	0.1368	0.4681	0.3770
C:	0.2405	0.9335	0.1300
C:	0.7562	0.9956	0.3804
O:	0.2753	0.5543	0.0956
O:	0.3686	0.3401	0.1099
O:	0.6216	0.5414	0.2223
O:	0.9326	0.3825	0.3024
O:	0.1823	0.6022	0.3948
O:	0.3078	0.4079	0.4342
O:	0.3197	0.8487	0.0561
O:	0.2989	0.0687	0.1528
O:	0.0735	0.8739	0.1885
O:	0.8804	0.0614	0.3254
O:	0.7422	0.8619	0.3633
O:	0.6426	0.0751	0.4574
H:	0.7417	0.4670	0.2537
H:	0.5000	0.5000	0.5000
H:	0.9875	0.9547	0.2446
H:	0.5000	0.0000	0.5000
Na:	0.2165	0.3280	0.9537
Na:	0.1919	0.8219	0.9046
Na:	0.8191	0.2846	0.7238
Na:	0.5914	0.7874	0.6975
Na:	0.2301	0.2517	0.5233
C:	0.5868	0.5252	0.8612
C:	0.8632	0.5319	0.6230
C:	0.7595	0.0665	0.8700
C:	0.2438	0.0044	0.6196
O:	0.7247	0.4457	0.9044
O:	0.6314	0.6599	0.8901
O:	0.3784	0.4586	0.7777
O:	0.0674	0.6175	0.6976
O:	0.8177	0.3978	0.6052
O:	0.6922	0.5921	0.5658
O:	0.6803	0.1513	0.9439
O:	0.7011	0.9313	0.8472
O:	0.9265	0.1261	0.8115
O:	0.1196	0.9386	0.6746
O:	0.2578	0.1381	0.6367
O:	0.3574	0.9249	0.5426
H:	0.2583	0.5330	0.7463
H:	0.0125	0.0453	0.7554

Atom type

We have listed here the reduced coordinates of all the atoms in the primitive unit cell.
It is enough to know only the position of the atoms from the assymetrical unit cell and then use the symmetry to build the whole crystal structure.

Visualization of the crystal structure:

You can define the size of the supercell to be displayed in the jmol panel as integer translations along the three crystallographic axis.
Please note that the structure is represented using the primitive cell, and not the conventional one.

Dielectric Properties

We define:

The Born effective charges, also called dynamical charges, are tensors that correspond to the energy derivative with respect to atomic displacements and electric fields or, equivalently, to the change in atomic force due to an electric field: The sum of the Born effective charges of all nuclei in one cell must vanish, element by element, along each of the three directions of the space.
The dielectric tensors are the energy derivative with respect to two electric fields. They also relate the induced polarization to the external electric field.

Born effective charges (Z):

Na:	0.9856	-0.0738	0.0669
	-0.0176	1.0777	0.0207
	0.0088	0.1107	1.1483
Eig. Value:	0.9475	1.0761	1.1880
Na:	0.9918	0.0453	-0.0189
	0.0033	1.2174	-0.0314
	0.0014	-0.0075	1.1399
Eig. Value:	0.9889	1.2249	1.1353
Na:	0.9844	0.0003	-0.0529
	-0.0117	1.2190	0.0844
	0.0001	0.0732	1.0043
Eig. Value:	1.0045	1.2455	0.9576
Na:	0.9892	0.0380	-0.0107
	-0.0020	1.2710	0.1035
	-0.0075	0.0437	0.9205
Eig. Value:	0.9902	1.2867	0.9039
Na:	0.9831	-0.0341	0.0202
	0.0073	1.2689	0.0861
	-0.0034	0.0684	0.9969
Eig. Value:	0.9916	1.2897	0.9676
C:	1.0786	-0.3994	0.9797
	-0.4559	2.5688	-0.1435
	0.9161	0.1416	2.4147
Eig. Value:	0.5163	2.5368	3.0090
C:	1.1588	-0.2223	1.1094
	-0.2105	2.2783	-0.0374
	1.0800	-0.0712	2.4901
Eig. Value:	0.5281	2.2655	3.1335
C:	1.0987	0.3415	-0.9643
	0.2379	2.4153	0.2508
	-1.0211	0.1143	2.5097
Eig. Value:	0.5248	2.4754	3.0236
C:	1.1266	0.1191	-1.1366
	0.1108	2.3038	-0.1354
	-1.0442	-0.1636	2.4553
Eig. Value:	0.5136	2.2611	3.1110
O:	-0.9984	0.4205	-0.3629
	0.3881	-1.6646	0.5443
	-0.3022	0.4153	-1.2750
Eig. Value:	-0.7633	-2.2117	-0.9629
O:	-0.7839	0.0684	-0.1129
	0.0515	-1.8563	-0.3369
	-0.1087	-0.4306	-1.1490
Eig. Value:	-0.7227	-2.0246	-1.0419
O:	-1.0391	0.2959	-0.7155
	0.2030	-1.0457	0.2056
	-0.7882	0.3475	-2.0261
Eig. Value:	-0.6118	-0.9782	-2.5210
O:	-1.1315	0.0865	-0.7215
	0.0649	-1.2038	-0.1031
	-0.7651	0.0431	-1.9727
Eig. Value:	-0.6856	-1.2162	-2.4063
O:	-0.7829	0.0440	-0.1470
	0.0187	-1.8654	-0.2025
	-0.1337	-0.1750	-1.0070
Eig. Value:	-0.7043	-1.9051	-1.0460
O:	-1.0931	0.1522	-0.8356
	0.2679	-1.2062	0.3872
	-0.7882	0.1872	-2.0160
Eig. Value:	-0.6181	-1.1176	-2.5797
O:	-0.9618	0.1271	0.4313
	0.1414	-1.1002	-0.4498
	0.4656	-0.3837	-1.8955
Eig. Value:	-0.7758	-0.9386	-2.2430
O:	-0.7853	-0.1101	0.1132
	-0.0302	-1.9613	-0.2157
	0.1151	-0.2802	-1.0440
Eig. Value:	-0.7212	-2.0253	-1.0441
O:	-1.0398	-0.1693	0.7612
	-0.2432	-1.0653	0.3076
	0.7554	0.1943	-1.8818
Eig. Value:	-0.5874	-0.9945	-2.4051
O:	-1.0505	-0.2134	0.6641
	-0.2553	-1.3691	0.4272
	0.6222	0.3351	-1.8232
Eig. Value:	-0.6861	-1.1726	-2.3842
O:	-0.7868	0.0454	0.1788
	0.0356	-1.8362	-0.2003
	0.1405	-0.1679	-0.9928
Eig. Value:	-0.6972	-1.8795	-1.0391
O:	-1.1582	-0.1888	0.8398
	-0.0810	-1.1341	0.0341
	0.8418	0.2761	-2.0563
Eig. Value:	-0.6512	-1.1087	-2.5886
H:	0.7555	-0.6411	0.4221
	-0.3906	0.8664	-0.5113
	0.5442	-1.0332	1.0027
Eig. Value:	0.3915	0.1491	2.0840
H:	0.7555	0.4332	0.8124
	0.1002	0.2526	0.1659
	0.7102	0.7696	1.8330
Eig. Value:	0.3635	0.1137	2.3640
H:	0.6946	-0.3299	-0.6415
	-0.0906	0.2479	0.1251
	-0.5767	0.5818	1.5432
Eig. Value:	0.3787	0.1472	1.9597
H:	0.7734	0.7630	-0.5451
	0.4163	0.8948	-0.5845
	-0.6148	-1.2084	1.1950
Eig. Value:	0.3695	0.1162	2.3774
Na:	0.9856	-0.0738	0.0669
	-0.0176	1.0777	0.0207
	0.0088	0.1107	1.1483
Eig. Value:	0.9475	1.0761	1.1880
Na:	0.9918	0.0453	-0.0189
	0.0033	1.2174	-0.0314
	0.0014	-0.0075	1.1399
Eig. Value:	0.9889	1.2249	1.1353
Na:	0.9844	0.0003	-0.0529
	-0.0117	1.2190	0.0844
	0.0001	0.0732	1.0043
Eig. Value:	1.0045	1.2455	0.9576
Na:	0.9892	0.0380	-0.0107
	-0.0020	1.2710	0.1035
	-0.0075	0.0437	0.9205
Eig. Value:	0.9902	1.2867	0.9039
Na:	0.9831	-0.0341	0.0202
	0.0073	1.2689	0.0861
	-0.0034	0.0684	0.9969
Eig. Value:	0.9916	1.2897	0.9676
C:	1.0786	-0.3994	0.9797
	-0.4559	2.5688	-0.1435
	0.9161	0.1416	2.4147
Eig. Value:	0.5163	2.5368	3.0090
C:	1.1588	-0.2223	1.1094
	-0.2105	2.2783	-0.0374
	1.0800	-0.0712	2.4901
Eig. Value:	0.5281	2.2655	3.1335
C:	1.0987	0.3415	-0.9643
	0.2379	2.4153	0.2508
	-1.0211	0.1143	2.5097
Eig. Value:	0.5248	2.4754	3.0236
C:	1.1266	0.1191	-1.1366
	0.1108	2.3038	-0.1354
	-1.0442	-0.1636	2.4553
Eig. Value:	0.5136	2.2611	3.1110
O:	-0.9984	0.4205	-0.3629
	0.3881	-1.6646	0.5443
	-0.3022	0.4153	-1.2750
Eig. Value:	-0.7633	-2.2117	-0.9629
O:	-0.7839	0.0684	-0.1129
	0.0515	-1.8563	-0.3369
	-0.1087	-0.4306	-1.1490
Eig. Value:	-0.7227	-2.0246	-1.0419
O:	-1.0391	0.2959	-0.7155
	0.2030	-1.0457	0.2056
	-0.7882	0.3475	-2.0261
Eig. Value:	-0.6118	-0.9782	-2.5210
O:	-1.1315	0.0865	-0.7215
	0.0649	-1.2038	-0.1031
	-0.7651	0.0431	-1.9727
Eig. Value:	-0.6856	-1.2162	-2.4063
O:	-0.7829	0.0440	-0.1470
	0.0187	-1.8654	-0.2025
	-0.1337	-0.1750	-1.0070
Eig. Value:	-0.7043	-1.9051	-1.0460
O:	-1.0931	0.1522	-0.8356
	0.2679	-1.2062	0.3872
	-0.7882	0.1872	-2.0160
Eig. Value:	-0.6181	-1.1176	-2.5797
O:	-0.9618	0.1271	0.4313
	0.1414	-1.1002	-0.4498
	0.4656	-0.3837	-1.8955
Eig. Value:	-0.7758	-0.9386	-2.2430
O:	-0.7853	-0.1101	0.1132
	-0.0302	-1.9613	-0.2157
	0.1151	-0.2802	-1.0440
Eig. Value:	-0.7212	-2.0253	-1.0441
O:	-1.0398	-0.1693	0.7612
	-0.2432	-1.0653	0.3076
	0.7554	0.1943	-1.8818
Eig. Value:	-0.5874	-0.9945	-2.4051
O:	-1.0505	-0.2134	0.6641
	-0.2553	-1.3691	0.4272
	0.6222	0.3351	-1.8232
Eig. Value:	-0.6861	-1.1726	-2.3842
O:	-0.7868	0.0454	0.1788
	0.0356	-1.8362	-0.2003
	0.1405	-0.1679	-0.9928
Eig. Value:	-0.6972	-1.8795	-1.0391
O:	-1.1582	-0.1888	0.8398
	-0.0810	-1.1341	0.0341
	0.8418	0.2761	-2.0563
Eig. Value:	-0.6512	-1.1087	-2.5886
H:	0.7555	-0.6411	0.4221
	-0.3906	0.8664	-0.5113
	0.5442	-1.0332	1.0027
Eig. Value:	0.3915	0.1491	2.0840
H:	0.6946	-0.3299	-0.6415
	-0.0906	0.2479	0.1251
	-0.5767	0.5818	1.5432
Eig. Value:	0.3787	0.1472	1.9597