- Na2Mg3(SO4)3(OH)2(H2O)4 - Na₂Mg₃(SO₄)₃(OH)₂(H₂O)₄

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:	36		Cmc2_1
Lattice parameters (Å):	19.7351	7.2228		10.0284
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	36		Cmc2_1
Lattice parameters (Å):	10.2556	10.2556		9.5981
Angles (°):	90.0	90.0		140.17

Cell contents:

Number of atoms:	72
Number of atom types:	5
Chemical composition:	0

Atomic positions (theoretical):

Na:	0.2080	0.7400	0.7742
Mg:	0.2108	0.2108	0.9877
Mg:	0.4923	0.3323	0.2812
S:	0.4703	0.1477	0.9903
O:	0.2835	0.0805	0.9746
O:	0.6263	0.3135	0.8915
O:	0.4270	0.9771	0.9561
O:	0.5461	0.2171	0.1343
S:	0.2101	0.2101	0.6661
O:	0.0883	0.0883	0.5438
O:	0.3986	0.2760	0.6670
O:	0.0874	0.0874	0.7923
O:	0.2769	0.2769	0.1883
O:	0.4820	0.4820	0.9072
O:	0.2800	0.0389	0.3595
O:	0.0095	0.6513	0.1158
H:	0.1490	0.1490	0.2315
H:	0.4471	0.4471	0.4941
H:	0.9495	0.1348	0.3565
H:	0.9819	0.7042	0.9575
H:	0.0302	0.4582	0.5609
H:	0.1133	0.3934	0.6435
Na:	0.7920	0.2600	0.2742
Mg:	0.7892	0.7892	0.4877
Mg:	0.5077	0.6677	0.7812
S:	0.5297	0.8523	0.4903
O:	0.7165	0.9195	0.4746
O:	0.3737	0.6865	0.3915
O:	0.5730	0.0229	0.4561
O:	0.4539	0.7829	0.6343
S:	0.7899	0.7899	0.1661
O:	0.9117	0.9117	0.0438
O:	0.6014	0.7240	0.1670
O:	0.9126	0.9126	0.2923
O:	0.7231	0.7231	0.6883
O:	0.5180	0.5180	0.4072
O:	0.7200	0.9611	0.8595
O:	0.9905	0.3487	0.6158
H:	0.8510	0.8510	0.7315
H:	0.5529	0.5529	0.9941
H:	0.0505	0.8652	0.8565
H:	0.0181	0.2958	0.4575
H:	0.9698	0.5418	0.0609
H:	0.8867	0.6066	0.1435
Na:	0.2600	0.7920	0.2742
Mg:	0.6677	0.5077	0.7812
S:	0.8523	0.5297	0.4903
O:	0.9195	0.7165	0.4746
O:	0.6865	0.3737	0.3915
O:	0.0229	0.5730	0.4561
O:	0.7829	0.4539	0.6343
O:	0.7240	0.6014	0.1670
O:	0.9611	0.7200	0.8595
O:	0.3487	0.9905	0.6158
H:	0.8652	0.0505	0.8565
H:	0.2958	0.0181	0.4575
H:	0.5418	0.9698	0.0609
H:	0.6066	0.8867	0.1435
Na:	0.7400	0.2080	0.7742
Mg:	0.3323	0.4923	0.2812
S:	0.1477	0.4703	0.9903
O:	0.0805	0.2835	0.9746
O:	0.3135	0.6263	0.8915
O:	0.9771	0.4270	0.9561
O:	0.2171	0.5461	0.1343
O:	0.2760	0.3986	0.6670
O:	0.0389	0.2800	0.3595
O:	0.6513	0.0095	0.1158
H:	0.1348	0.9495	0.3565
H:	0.7042	0.9819	0.9575
H:	0.4582	0.0302	0.5609
H:	0.3934	0.1133	0.6435

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:	1.1020	-0.0845	0.0066
	-0.0489	1.0954	0.0435
	-0.0194	0.0107	1.2008
Eig. Value:	1.1542	1.0305	1.2134
Mg:	2.1536	-0.0553	-0.0462
	-0.0553	2.0209	-0.1278
	-0.0358	-0.0994	2.0854
Eig. Value:	2.1736	1.9152	2.1711
Mg:	1.9649	-0.0899	0.0565
	0.0807	2.1631	-0.0012
	-0.0601	0.0468	2.1775
Eig. Value:	1.9647	2.1464	2.1942
S:	3.6603	-0.3037	-0.0580
	0.0102	3.4001	0.0683
	0.0751	-0.1373	3.3044
Eig. Value:	3.7275	3.3506	3.2868
O:	-2.2913	-0.2086	-0.1351
	-0.3377	-1.1621	-0.1244
	-0.1887	-0.0678	-0.9629
Eig. Value:	-2.3767	-1.1178	-0.9219
O:	-1.1174	-0.0072	0.0366
	-0.0699	-1.6910	0.6440
	0.0541	0.6581	-1.5604
Eig. Value:	-1.1148	-2.2830	-0.9710
O:	-1.7341	0.6657	-0.0777
	0.6013	-1.5514	-0.1784
	-0.0602	-0.0965	-1.0504
Eig. Value:	-2.2840	-0.8752	-1.1768
O:	-1.1224	0.0605	-0.0717
	0.0179	-1.1358	-0.4614
	-0.0352	-0.3976	-2.0422
Eig. Value:	-1.1393	-0.9465	-2.2145
S:	3.3153	0.1473	0.0031
	0.1483	3.6629	0.0042
	-0.0544	-0.1493	3.5273
Eig. Value:	3.2610	3.7445	3.5001
O:	-0.9469	-0.2455	-0.2050
	-0.2449	-1.5283	-0.5641
	-0.2014	-0.5554	-1.6270
Eig. Value:	-0.8573	-1.0270	-2.2179
O:	-2.3115	-0.2515	-0.0610
	-0.2084	-1.2644	-0.0719
	0.0437	-0.0449	-1.0453
Eig. Value:	-2.3601	-1.2325	-1.0286
O:	-1.1028	-0.2359	0.1467
	-0.2384	-1.6701	0.4031
	0.1619	0.4458	-1.9924
Eig. Value:	-1.0168	-1.4074	-2.3411
O:	-1.3002	-0.1043	0.0230
	-0.1029	-1.5441	0.0643
	-0.0066	-0.0179	-1.3560
Eig. Value:	-1.2621	-1.5848	-1.3534
O:	-1.2662	-0.0198	-0.0037
	-0.0170	-1.3141	-0.0083
	0.0164	0.0457	-1.3679
Eig. Value:	-1.2599	-1.3132	-1.3750
O:	-1.0527	-0.0074	-0.3137
	-0.0843	-1.1623	0.0499
	-0.2124	0.1144	-1.2952
Eig. Value:	-0.8612	-1.1788	-1.4703
O:	-1.6178	0.3174	0.2750
	0.3068	-0.8758	0.0153
	0.1093	-0.0187	-1.3249
Eig. Value:	-1.8010	-0.7543	-1.2632
H:	0.4149	0.2117	-0.0684
	0.2111	0.9203	-0.1885
	-0.0230	-0.0638	0.3747
Eig. Value:	0.3381	1.0248	0.3470
H:	0.3834	0.0199	-0.0404
	0.0197	0.4306	-0.1099
	-0.0279	-0.0768	0.4962
Eig. Value:	0.3762	0.3634	0.5706
H:	0.5268	0.0466	-0.1337
	-0.0415	0.8097	-0.0071
	-0.1179	0.0187	0.4737
Eig. Value:	0.6288	0.8098	0.3716
H:	0.5217	-0.0477	0.3278
	-0.0771	0.4354	-0.2405
	0.3083	-0.1847	1.0335
Eig. Value:	0.3383	0.4073	1.2450
H:	0.9668	-0.5397	0.5412
	-0.3092	0.5515	-0.2659
	0.2857	-0.2428	0.5524
Eig. Value:	1.4844	0.2861	0.3002
H:	1.2532	0.0494	0.1994
	-0.1574	0.3126	0.0066
	0.2240	0.0285	0.4690
Eig. Value:	1.3090	0.3022	0.4236
Na:	1.1020	-0.0845	-0.0066
	-0.0489	1.0954	-0.0435
	0.0194	-0.0107	1.2008
Eig. Value:	1.1542	1.0305	1.2134
Mg:	2.1536	-0.0553	0.0462
	-0.0553	2.0209	0.1278
	0.0358	0.0994	2.0854
Eig. Value:	2.1736	1.9152	2.1711
Mg:	1.9649	-0.0899	-0.0565
	0.0807	2.1631	0.0012
	0.0601	-0.0468	2.1775
Eig. Value:	1.9647	2.1464	2.1942
S:	3.6603	-0.3037	0.0580
	0.0102	3.4001	-0.0683
	-0.0751	0.1373	3.3044
Eig. Value:	3.7275	3.3506	3.2868
O:	-2.2913	-0.2086	0.1351
	-0.3377	-1.1621	0.1244
	0.1887	0.0678	-0.9629
Eig. Value:	-2.3767	-1.1178	-0.9219
O:	-1.1174	-0.0072	-0.0366
	-0.0699	-1.6910	-0.6440
	-0.0541	-0.6581	-1.5604
Eig. Value:	-1.1148	-2.2830	-0.9710
O:	-1.7341	0.6657	0.0777
	0.6013	-1.5514	0.1784
	0.0602	0.0965	-1.0504
Eig. Value:	-2.2840	-0.8752	-1.1768
O:	-1.1224	0.0605	0.0717
	0.0179	-1.1358	0.4614
	0.0352	0.3976	-2.0422
Eig. Value:	-1.1393	-0.9465	-2.2145
S:	3.3153	0.1473	-0.0031
	0.1483	3.6629	-0.0042
	0.0544	0.1493	3.5273
Eig. Value:	3.2610	3.7445	3.5001
O:	-0.9469	-0.2455	0.2050
	-0.2449	-1.5283	0.5641
	0.2014	0.5554	-1.6270
Eig. Value:	-0.8573	-1.0270	-2.2179
O:	-2.3115	-0.2515	0.0610
	-0.2084	-1.2644	0.0719
	-0.0437	0.0449	-1.0453
Eig. Value:	-2.3601	-1.2325	-1.0286
O:	-1.1028	-0.2359	-0.1467
	-0.2384	-1.6701	-0.4031
	-0.1619	-0.4458	-1.9924
Eig. Value:	-1.0168	-1.4074	-2.3411
O:	-1.3002	-0.1043	-0.0230
	-0.1029	-1.5441	-0.0643
	0.0066	0.0179	-1.3560
Eig. Value:	-1.2621	-1.5848	-1.3534
O:	-1.2662	-0.0198	0.0037
	-0.0170	-1.3141	0.0083
	-0.0164	-0.0457	-1.3679
Eig. Value:	-1.2599	-1.3132	-1.3750
O:	-1.0527	-0.0074	0.3137
	-0.0843	-1.1623	-0.0499
	0.2124	-0.1144	-1.2952
Eig. Value:	-0.8612	-1.1788	-1.4703
O:	-1.6178	0.3174	-0.2750
	0.3068	-0.8758	-0.0153
	-0.1093	0.0187	-1.3249
Eig. Value:	-1.8010	-0.7543	-1.2632
H:	0.4149	0.2117	0.0684
	0.2111	0.9203	0.1885
	0.0230	0.0638	0.3747
Eig. Value:	0.3381	1.0248	0.3470
H:	0.3834	0.0199	0.0404
	0.0197	0.4306	0.1099
	0.0279	0.0768	0.4962
Eig. Value:	0.3762	0.3634	0.5706
H:	0.5268	0.0466	0.1337
	-0.0415	0.8097	0.0071
	0.1179	-0.0187	0.4737
Eig. Value:	0.6288	0.8098	0.3716
H:	0.5217	-0.0477	-0.3278
	-0.0771	0.4354	0.2405
	-0.3083	0.1847	1.0335
Eig. Value:	0.3383	0.4073	1.2450
H:	0.9668	-0.5397	-0.5412
	-0.3092	0.5515	0.2659
	-0.2857	0.2428	0.5524
Eig. Value:	1.4844	0.2861	0.3002
H:	1.2532	0.0494	-0.1994
	-0.1574	0.3126	-0.0066
	-0.2240	-0.0285	0.4690
Eig. Value:	1.3090	0.3022	0.4236
Na:	1.1649	0.0266	-0.0225
	-0.0093	1.0325	-0.0377
	-0.0217	0.0043	1.2007
Eig. Value:	1.1544	1.0305	1.2132
Mg:	2.0515	0.1829	0.0449
	0.0133	2.0764	-0.0352
	-0.0759	0.0026	2.1774
Eig. Value:	1.9650	2.1465	2.1937
S:	3.6998	0.0577	-0.0891
	-0.2569	3.3587	-0.0160
	0.1451	0.0563	3.3049
Eig. Value:	3.7278	3.3479	3.2876
O:	-1.5585	0.5366	-0.0219
	0.6680	-1.8918	0.1803
	-0.1011	0.1743	-0.9635
Eig. Value:	-1.1190	-2.3727	-0.9221
O:	-1.3138	-0.3049	-0.3826
	-0.2419	-1.4935	-0.5165
	-0.3796	-0.5398	-1.5604
Eig. Value:	-1.1159	-2.2805	-0.9713
O:	-2.2767	-0.0494	0.0494
	0.0085	-1.0012	0.1890
	0.0159	0.1124	-1.0502
Eig. Value:	-2.2781	-0.8730	-1.1771
O:	-1.1649	-0.0376	0.2413
	0.0058	-1.0897	0.4007
	0.2278	0.3277	-2.0423
Eig. Value:	-1.1361	-0.9459	-2.2149
O:	-1.6555	0.5754	-0.0002
	0.5322	-1.9183	0.0927
	0.0625	0.0070	-1.0450
Eig. Value:	-1.2339	-2.3564	-1.0285
O:	-1.0477	-0.0856	-0.2748
	-0.0095	-1.1602	0.1635
	-0.2364	0.0480	-1.2957
Eig. Value:	-0.8563	-1.1774	-1.4699
O:	-1.6226	0.3027	0.2014
	0.3131	-0.8714	-0.1880
	0.0956	-0.0556	-1.3248
Eig. Value:	-1.8018	-0.7535	-1.2634
H:	0.6402	0.0947	-0.0981
	0.1831	0.6959	0.0912
	-0.1029	0.0612	0.4738
Eig. Value:	0.6288	0.8098	0.3713
H:	0.5478	-0.0463	0.4061
	-0.0167	0.4095	-0.0254
	0.3548	-0.0558	1.0333
Eig. Value:	0.3383	0.4074	1.2450
H:	1.2135	-0.0126	0.5855
	-0.2433	0.3047	-0.1428
	0.3750	0.0030	0.5524
Eig. Value:	1.4840	0.2863	0.3003
H:	0.9224	-0.5577	0.1497
	-0.3496	0.6454	-0.1331
	0.1534	-0.1652	0.4690
Eig. Value:	1.3110	0.3022	0.4236
Na:	1.1649	0.0266	0.0225
	-0.0093	1.0325	0.0377
	0.0217	-0.0043	1.2007
Eig. Value:	1.1544	1.0305	1.2132
Mg:	2.0515	0.1829	-0.0449
	0.0133	2.0764	0.0352
	0.0759	-0.0026	2.1774
Eig. Value:	1.9650	2.1465	2.1937
S:	3.6998	0.0577	0.0891
	-0.2569	3.3587	0.0160
	-0.1451	-0.0563	3.3049
Eig. Value:	3.7278	3.3479	3.2876
O:	-1.5585	0.5366	0.0219
	0.6680	-1.8918	-0.1803
	0.1011	-0.1743	-0.9635
Eig. Value:	-1.1190	-2.3727	-0.9221
O:	-1.3138	-0.3049	0.3826
	-0.2419	-1.4935	0.5165
	0.3796	0.5398	-1.5604
Eig. Value:	-1.1159	-2.2805	-0.9713
O:	-2.2767	-0.0494	-0.0494
	0.0085	-1.0012	-0.1890
	-0.0159	-0.1124	-1.0502
Eig. Value:	-2.2781	-0.8730	-1.1771
O:	-1.1649	-0.0376	-0.2413
	0.0058	-1.0897	-0.4007
	-0.2278	-0.3277	-2.0423
Eig. Value:	-1.1361	-0.9459	-2.2149
O:	-1.6555	0.5754	0.0002
	0.5322	-1.9183	-0.0927
	-0.0625	-0.0070	-1.0450
Eig. Value:	-1.2339	-2.3564	-1.0285
O:	-1.0477	-0.0856	0.2748
	-0.0095	-1.1602	-0.1635
	0.2364	-0.0480	-1.2957
Eig. Value:	-0.8563	-1.1774	-1.4699
O:	-1.6226	0.3027	-0.2014
	0.3131	-0.8714	0.1880
	-0.0956	0.0556	-1.3248
Eig. Value:	-1.8018	-0.7535	-1.2634
H:	0.6402	0.0947	0.0981
	0.1831	0.6959	-0.0912
	0.1029	-0.0612	0.4738
Eig. Value:	0.6288	0.8098	0.3713
H:	0.5478	-0.0463	-0.4061
	-0.0167	0.4095	0.0254
	-0.3548	0.0558	1.0333
Eig. Value:	0.3383	0.4074	1.2450
H:	1.2135	-0.0126	-0.5855
	-0.2433	0.3047	0.1428
	-0.3750	-0.0030	0.5524
Eig. Value:	1.4840	0.2863	0.3003
H:	0.9224	-0.5577	-0.1497
	-0.3496	0.6454	0.1331
	-0.1534	0.1652	0.4690
Eig. Value:	1.3110	0.3022	0.4236