- WOLLASTONITE - CaSiO₃

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):	4.1942	3.8737		3.7388
Angles (°):	90.1	95.2		103.4

Symmetry (theoretical):

Space group:	2		P-1
Lattice parameters (Å):	7.9223	7.3056		7.0841
Angles (°):	90.1	95.5		103.4

Cell contents:

Number of atoms:	30
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Ca:	0.2001	0.4234	0.7627
Ca:	0.2062	0.9305	0.7661
Ca:	0.5058	0.7508	0.5295
Si:	0.1864	0.3870	0.2686
Si:	0.1873	0.9555	0.2687
Si:	0.3977	0.7228	0.0584
O:	0.3026	0.4624	0.4635
O:	0.3016	0.9380	0.4643
O:	0.5721	0.7673	0.1998
O:	0.9842	0.3706	0.2609
O:	0.9838	0.8703	0.2583
O:	0.4010	0.7249	0.8334
O:	0.2251	0.1805	0.2286
O:	0.2746	0.8716	0.0965
O:	0.2744	0.5131	0.0953
Ca:	0.7999	0.5766	0.2373
Ca:	0.7938	0.0695	0.2339
Ca:	0.4942	0.2492	0.4705
Si:	0.8136	0.6130	0.7314
Si:	0.8127	0.0445	0.7313
Si:	0.6023	0.2772	0.9416
O:	0.6974	0.5376	0.5365
O:	0.6984	0.0620	0.5357
O:	0.4279	0.2327	0.8002
O:	0.0158	0.6294	0.7391
O:	0.0162	0.1297	0.7417
O:	0.5990	0.2751	0.1666
O:	0.7749	0.8195	0.7714
O:	0.7254	0.1284	0.9035
O:	0.7256	0.4869	0.9047

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):

Ca:	2.2582	-0.0868	0.0133
	-0.0089	2.2833	0.1100
	0.0306	0.1224	2.2403
Eig. Value:	2.1263	2.3843	2.2711
Ca:	2.2560	0.0965	0.0701
	0.0101	2.2423	-0.0910
	0.0905	-0.0944	2.2171
Eig. Value:	2.3028	2.0831	2.3294
Ca:	2.2165	0.0072	0.0948
	0.0065	2.1888	0.0228
	0.0841	0.0220	2.2925
Eig. Value:	2.1559	2.1872	2.3548
Si:	3.0451	0.0765	-0.0152
	0.0241	3.2402	-0.1628
	0.0897	-0.1226	2.8078
Eig. Value:	3.0480	3.2889	2.7562
Si:	3.1526	-0.1190	-0.0803
	-0.0781	3.1770	0.1359
	0.0077	0.1411	2.8260
Eig. Value:	3.0778	3.2999	2.7779
Si:	2.9294	-0.0366	0.1677
	-0.0250	3.0375	0.0356
	-0.0850	-0.0224	3.0840
Eig. Value:	2.9112	3.0453	3.0944
O:	-1.5896	-0.0929	-0.2011
	-0.1362	-1.6336	-0.2182
	-0.3172	-0.1961	-2.0700
Eig. Value:	-1.4707	-1.5520	-2.2705
O:	-1.6795	0.0639	-0.2694
	0.1062	-1.5222	0.1073
	-0.3488	0.0349	-2.0788
Eig. Value:	-1.5498	-1.4692	-2.2615
O:	-1.9206	-0.1216	-0.4275
	-0.1222	-1.4950	-0.1025
	-0.2872	-0.0720	-1.7431
Eig. Value:	-2.2306	-1.4704	-1.4578
O:	-2.3015	-0.0412	-0.1090
	-0.0286	-1.5686	0.0019
	-0.1276	-0.0058	-1.2153
Eig. Value:	-2.3159	-1.5670	-1.2025
O:	-2.2446	-0.2881	-0.0724
	-0.2870	-1.7433	-0.0456
	-0.0759	-0.0419	-1.2555
Eig. Value:	-2.3819	-1.6127	-1.2488
O:	-1.4497	0.0150	0.1582
	0.0166	-1.4854	0.0444
	0.0998	0.0323	-2.3073
Eig. Value:	-1.4233	-1.4913	-2.3278
O:	-1.3898	0.3791	-0.0723
	0.3894	-2.9021	-0.0213
	-0.0422	-0.0053	-1.1157
Eig. Value:	-1.3150	-2.9941	-1.0984
O:	-1.9506	0.6086	0.4930
	0.7463	-1.6049	-0.4239
	0.5453	-0.3310	-1.8463
Eig. Value:	-2.8766	-1.0777	-1.4476
O:	-1.3320	-0.4606	0.2501
	-0.6133	-2.2140	0.6076
	0.3362	0.5388	-1.8357
Eig. Value:	-1.0773	-2.8687	-1.4357
Ca:	2.2582	-0.0868	0.0133
	-0.0089	2.2833	0.1100
	0.0306	0.1224	2.2403
Eig. Value:	2.1263	2.3843	2.2711
Ca:	2.2560	0.0965	0.0701
	0.0101	2.2423	-0.0910
	0.0905	-0.0944	2.2171
Eig. Value:	2.3028	2.0831	2.3294
Ca:	2.2165	0.0072	0.0948
	0.0065	2.1888	0.0228
	0.0841	0.0220	2.2925
Eig. Value:	2.1559	2.1872	2.3548
Si:	3.0451	0.0765	-0.0152
	0.0241	3.2402	-0.1628
	0.0897	-0.1226	2.8078
Eig. Value:	3.0480	3.2889	2.7562
Si:	3.1526	-0.1190	-0.0803
	-0.0781	3.1770	0.1359
	0.0077	0.1411	2.8260
Eig. Value:	3.0778	3.2999	2.7779
Si:	2.9294	-0.0366	0.1677
	-0.0250	3.0375	0.0356
	-0.0850	-0.0224	3.0840
Eig. Value:	2.9112	3.0453	3.0944
O:	-1.5896	-0.0929	-0.2011
	-0.1362	-1.6336	-0.2182
	-0.3172	-0.1961	-2.0700
Eig. Value:	-1.4707	-1.5520	-2.2705
O:	-1.6795	0.0639	-0.2694
	0.1062	-1.5222	0.1073
	-0.3488	0.0349	-2.0788
Eig. Value:	-1.5498	-1.4692	-2.2615
O:	-1.9206	-0.1216	-0.4275
	-0.1222	-1.4950	-0.1025
	-0.2872	-0.0720	-1.7431
Eig. Value:	-2.2306	-1.4704	-1.4578
O:	-2.3015	-0.0412	-0.1090
	-0.0286	-1.5686	0.0019
	-0.1276	-0.0058	-1.2153
Eig. Value:	-2.3159	-1.5670	-1.2025
O:	-2.2446	-0.2881	-0.0724
	-0.2870	-1.7433	-0.0456
	-0.0759	-0.0419	-1.2555
Eig. Value:	-2.3819	-1.6127	-1.2488
O:	-1.4497	0.0150	0.1582
	0.0166	-1.4854	0.0444
	0.0998	0.0323	-2.3073
Eig. Value:	-1.4233	-1.4913	-2.3278
O:	-1.3898	0.3791	-0.0723
	0.3894	-2.9021	-0.0213
	-0.0422	-0.0053	-1.1157
Eig. Value:	-1.3150	-2.9941	-1.0984
O:	-1.9506	0.6086	0.4930
	0.7463	-1.6049	-0.4239
	0.5453	-0.3310	-1.8463
Eig. Value:	-2.8766	-1.0777	-1.4476
O:	-1.3320	-0.4606	0.2501
	-0.6133	-2.2140	0.6076
	0.3362	0.5388	-1.8357
Eig. Value:	-1.0773	-2.8687	-1.4357