- TSCHERMAKITE - []Ca₂Mg₃Al₂Si₆Al₂O₂₂(OH)₂

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:	1	P1
Lattice parameters (Å):
Angles (°):

Symmetry (theoretical):

Space group:	1		P1
Lattice parameters (Å):	0.5292	0.5292		0.5292
Angles (°):	82.76	97.10		57.16

Cell contents:

Number of atoms:	41
Number of atom types:	6
Chemical composition:	0

Atomic positions (theoretical):

Mg:	0.0872	0.0872	0.5000
Al:	0.0969	0.0832	0.5021
Mg:	0.1788	0.1689	0.9995
Ca:	0.0114	0.9933	0.0068
Al:	0.2838	0.2734	0.5090
Al:	0.3746	0.7981	0.3141
O:	0.4694	0.8801	0.8330
O:	0.1952	0.9937	0.2050
O:	0.2782	0.0681	0.7488
O:	0.1117	0.8853	0.7119
O:	0.6276	0.8983	0.7891
O:	0.5134	0.7812	0.1464
O:	0.4660	0.7644	0.6268
H:	0.3199	0.6656	0.2748
Si:	0.2240	0.7903	0.7639
Si:	0.8077	0.3655	0.6967
O:	0.8823	0.4662	0.1800
O:	0.9825	0.1972	0.7909
O:	0.0574	0.2929	0.2498
O:	0.8906	0.1096	0.2874
O:	0.8768	0.6276	0.1911
O:	0.7870	0.4874	0.8871
O:	0.7858	0.4569	0.4042
H:	0.6681	0.3333	0.6957
Mg:	0.7872	0.2150	0.2283
Al:	0.9136	0.9108	0.5002
Ca:	0.8169	0.8271	0.9937
Si:	0.7043	0.7267	0.5004
Si:	0.6373	0.1922	0.6976
O:	0.5360	0.1187	0.1793
O:	0.8071	0.0166	0.7933
O:	0.7118	0.9462	0.2515
O:	0.3736	0.1289	0.1851
O:	0.5136	0.2198	0.8881
Si:	0.5410	0.2184	0.4053
Si:	0.1876	0.6319	0.2953
O:	0.1100	0.5350	0.8151
O:	0.0070	0.7993	0.2041
O:	0.9396	0.7129	0.7438
O:	0.1085	0.3781	0.7991
O:	0.2050	0.5046	0.1136

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):

Mg:	1.9175	-0.0272	-0.0377
	0.0199	1.9955	0.0236
	-0.0410	-0.0007	2.0318
Eig. Value:	1.9052	1.9927	2.0468
Al:	3.1633	0.0827	0.0733
	0.0358	3.0261	-0.0267
	0.0635	0.0365	2.8600
Eig. Value:	3.1982	3.0062	2.8450
Mg:	1.8515	-0.0445	0.0424
	-0.0116	2.1799	-0.0185
	-0.0087	-0.0133	1.9737
Eig. Value:	1.8472	2.1837	1.9742
Ca:	2.4701	0.0342	-0.0006
	0.0054	2.0439	-0.0398
	0.0228	-0.0424	2.3078
Eig. Value:	2.4716	2.0366	2.3136
Al:	2.2589	0.2257	0.0154
	0.0451	2.8907	0.0881
	0.0598	0.0181	2.3904
Eig. Value:	2.2268	2.9251	2.3881
Al:	2.4472	0.2362	-0.0888
	0.0427	2.2443	0.0932
	-0.1108	0.1509	2.5872
Eig. Value:	2.5106	2.1220	2.6462
O:	-1.8898	0.0687	-0.1620
	0.0800	-1.7904	0.1484
	-0.1655	0.1591	-1.7002
Eig. Value:	-2.0632	-1.7607	-1.5565
O:	-2.1179	-0.0451	0.0315
	0.0036	-1.5642	-0.0213
	0.0443	-0.0225	-1.7890
Eig. Value:	-2.1228	-1.5610	-1.7873
O:	-1.2293	-0.0102	0.1069
	-0.0465	-1.5861	0.0003
	0.1056	0.0081	-1.4735
Eig. Value:	-1.1879	-1.5901	-1.5108
O:	-1.7748	-0.3075	0.0087
	-0.2136	-1.9714	-0.1485
	0.0345	-0.1764	-1.7080
Eig. Value:	-1.5206	-2.1839	-1.7497
O:	-1.5740	-0.3385	0.0224
	-0.2463	-1.5674	0.2176
	-0.0193	0.1879	-2.0707
Eig. Value:	-1.7972	-1.2522	-2.1627
O:	-1.5919	-0.1568	0.1730
	-0.0660	-1.6480	-0.3599
	0.1583	-0.3555	-1.9322
Eig. Value:	-1.6976	-1.2895	-2.1851
O:	-1.1978	-0.0461	-0.0431
	-0.0607	-2.6932	-0.0160
	-0.0245	-0.0414	-1.1815
Eig. Value:	-1.2220	-2.6957	-1.1548
H:	0.3483	0.0694	-0.0683
	0.0849	0.5744	-0.0276
	-0.0726	-0.0264	0.5026
Eig. Value:	0.3059	0.6190	0.5005
Si:	2.8873	-0.2343	-0.0677
	0.0121	3.7556	-0.0774
	-0.0876	0.0347	3.3259
Eig. Value:	2.8596	3.7699	3.3393
Si:	3.2128	-0.4020	-0.2372
	-0.0802	2.9151	-0.0324
	-0.2381	-0.2697	3.5292
Eig. Value:	3.2963	2.7037	3.6571
O:	-1.9404	-0.0670	-0.1825
	-0.0935	-1.7149	-0.1109
	-0.1930	-0.1309	-1.6041
Eig. Value:	-2.0682	-1.7015	-1.4896
O:	-2.2318	0.0869	0.0104
	-0.0299	-1.4157	0.0383
	0.0352	0.0575	-1.6707
Eig. Value:	-2.2336	-1.4058	-1.6789
O:	-1.1233	-0.0009	0.1333
	-0.0129	-1.5594	0.0019
	0.1358	-0.0010	-1.4419
Eig. Value:	-1.0741	-1.5596	-1.4910
O:	-1.8144	0.5070	-0.0129
	0.4902	-1.9967	0.2049
	-0.0408	0.2645	-1.5459
Eig. Value:	-1.3134	-2.4560	-1.5876
O:	-1.4285	0.4023	0.2119
	0.2964	-1.5394	-0.5836
	0.2129	-0.5954	-2.2845
Eig. Value:	-1.0668	-1.4760	-2.7096
O:	-1.4065	0.0590	0.2301
	-0.0485	-1.5932	0.7233
	0.2770	0.7727	-2.3929
Eig. Value:	-1.4361	-1.0836	-2.8729
O:	-1.1277	0.0272	-0.0429
	-0.0011	-3.0732	-0.0053
	-0.0150	0.0041	-1.0931
Eig. Value:	-1.1440	-3.0733	-1.0767
H:	0.2079	-0.0090	-0.0905
	-0.0149	0.5262	-0.0031
	-0.0994	0.0008	0.4713
Eig. Value:	0.1768	0.5268	0.5017
Mg:	1.9258	-0.0030	-0.0456
	0.0112	2.0330	0.0096
	-0.0441	-0.0020	2.0485
Eig. Value:	1.9110	2.0330	2.0633
Al:	3.1963	-0.0402	0.0240
	-0.0453	2.9156	-0.0643
	0.0750	-0.0066	2.8539
Eig. Value:	3.2110	2.9194	2.8355
Ca:	2.3372	0.0621	-0.0144
	0.0158	2.0443	0.0634
	-0.0242	0.0640	2.3092
Eig. Value:	2.3472	2.0241	2.3195
Si:	2.8324	0.1265	-0.0726
	-0.0367	3.8548	0.0744
	-0.0881	-0.0355	3.2921
Eig. Value:	2.8166	3.8572	3.3055
Si:	3.1405	0.4567	-0.2778
	0.1029	2.9074	0.0501
	-0.2970	0.2256	3.5929
Eig. Value:	3.2696	2.6388	3.7325
O:	-1.9035	0.0713	-0.1669
	0.0475	-1.7771	0.1107
	-0.1770	0.1270	-1.5854
Eig. Value:	-2.0236	-1.7589	-1.4836
O:	-2.1562	-0.0997	0.0748
	0.0052	-1.4181	-0.0715
	0.0881	-0.1048	-1.7139
Eig. Value:	-2.1720	-1.3879	-1.7283
O:	-1.8347	-0.5956	0.0218
	-0.5019	-1.9715	-0.1854
	0.0053	-0.2907	-1.5726
Eig. Value:	-1.2545	-2.4883	-1.6360
O:	-1.4522	-0.3785	0.2500
	-0.2885	-1.5657	0.5464
	0.2275	0.5717	-2.2505
Eig. Value:	-1.1227	-1.4676	-2.6781
O:	-1.3955	-0.0530	0.2084
	0.0264	-1.6264	-0.6968
	0.2484	-0.7304	-2.3866
Eig. Value:	-1.4386	-1.1300	-2.8400
Si:	2.8015	-0.1652	-0.0877
	-0.0444	3.5508	-0.1516
	-0.0802	0.0353	3.2675
Eig. Value:	2.7704	3.5724	3.2770
Si:	3.0768	-0.4243	-0.2439
	-0.1447	2.8608	-0.0516
	-0.2706	-0.2515	3.5268
Eig. Value:	3.2355	2.5847	3.6442
O:	-1.9975	-0.0992	-0.1812
	-0.0874	-1.7056	-0.1198
	-0.2126	-0.1587	-1.5950
Eig. Value:	-2.1255	-1.7014	-1.4713
O:	-2.2457	0.0918	0.0304
	0.0062	-1.4167	0.0704
	0.0613	0.0821	-1.6522
Eig. Value:	-2.2515	-1.3899	-1.6732
O:	-1.7861	0.4925	0.0159
	0.4557	-1.9641	0.1490
	0.0091	0.2417	-1.5542
Eig. Value:	-1.3118	-2.3825	-1.6101
O:	-1.4348	0.4081	0.2015
	0.3145	-1.5574	-0.5337
	0.1788	-0.5700	-2.2782
Eig. Value:	-1.0758	-1.5219	-2.6727
O:	-1.4210	0.0395	0.2384
	-0.0269	-1.6026	0.7321
	0.2670	0.7835	-2.3940
Eig. Value:	-1.4495	-1.0838	-2.8844