- TRABZONITE - Ca₄[Si₃O₉(OH)]OH

Theoretical atomic positions. Lattice parameters fixed as in AMCSD

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:	40		Ama2
Lattice parameters (Å):	20.5805	10.3240		9.1053
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	40		Ama2
Lattice parameters (Å):	20.5460	6.8906		6.8906
Angles (°):	97.43	90		90

Cell contents:

Number of atoms:	80
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Ca:	0.3538	0.1606	0.9608
Ca:	0.3627	0.5341	0.3455
Ca:	0.2500	0.8607	0.6199
Ca:	0.5000	0.6233	0.6233
Ca:	0.2500	0.7819	0.1150
Ca:	0.5000	0.2159	0.2159
Si:	0.3730	0.6402	0.8759
Si:	0.4964	0.1172	0.6885
Si:	0.3740	0.0521	0.4472
O:	0.4748	0.5684	0.2832
O:	0.4642	0.1877	0.8937
O:	0.4418	0.9863	0.5475
O:	0.4471	0.7103	0.9501
O:	0.3896	0.1927	0.2861
O:	0.3372	0.5116	0.0217
O:	0.3305	0.8647	0.3756
O:	0.3279	0.8290	0.8616
O:	0.3876	0.5167	0.6652
O:	0.3324	0.1852	0.6236
O:	0.2500	0.1225	0.0891
O:	0.2500	0.5352	0.4341
H:	0.3530	0.3280	0.6457
H:	0.2500	0.2267	0.1988
H:	0.2500	0.4268	0.5122
Ca:	0.6462	0.9608	0.1606
Ca:	0.6373	0.3455	0.5341
Ca:	0.7500	0.6199	0.8607
Ca:	0.7500	0.1150	0.7819
Si:	0.6270	0.8759	0.6402
Si:	0.5036	0.6885	0.1172
Si:	0.6260	0.4472	0.0521
O:	0.5252	0.2832	0.5684
O:	0.5358	0.8937	0.1877
O:	0.5582	0.5475	0.9863
O:	0.5529	0.9501	0.7103
O:	0.6104	0.2861	0.1927
O:	0.6628	0.0217	0.5116
O:	0.6695	0.3756	0.8647
O:	0.6721	0.8616	0.8290
O:	0.6124	0.6652	0.5167
O:	0.6676	0.6236	0.1852
O:	0.7500	0.0891	0.1225
O:	0.7500	0.4341	0.5352
H:	0.6470	0.6457	0.3280
H:	0.7500	0.1988	0.2267
H:	0.7500	0.5122	0.4268
Ca:	0.8538	0.9608	0.1606
Ca:	0.8627	0.3455	0.5341
Ca:	0.0000	0.6233	0.6233
Ca:	0.0000	0.2159	0.2159
Si:	0.8730	0.8759	0.6402
Si:	0.9964	0.6885	0.1172
Si:	0.8740	0.4472	0.0521
O:	0.9748	0.2832	0.5684
O:	0.9642	0.8937	0.1877
O:	0.9418	0.5475	0.9863
O:	0.9471	0.9501	0.7103
O:	0.8896	0.2861	0.1927
O:	0.8372	0.0217	0.5116
O:	0.8305	0.3756	0.8647
O:	0.8279	0.8616	0.8290
O:	0.8876	0.6652	0.5167
O:	0.8324	0.6236	0.1852
H:	0.8530	0.6457	0.3280
Ca:	0.1462	0.1606	0.9608
Ca:	0.1373	0.5341	0.3455
Si:	0.1270	0.6402	0.8759
Si:	0.0036	0.1172	0.6885
Si:	0.1260	0.0521	0.4472
O:	0.0252	0.5684	0.2832
O:	0.0358	0.1877	0.8937
O:	0.0582	0.9863	0.5475
O:	0.0529	0.7103	0.9501
O:	0.1104	0.1927	0.2861
O:	0.1628	0.5116	0.0217
O:	0.1695	0.8647	0.3756
O:	0.1721	0.8290	0.8616
O:	0.1124	0.5167	0.6652
O:	0.1676	0.1852	0.6236
H:	0.1470	0.3280	0.6457

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:	2.1757	0.2186	-0.0374
	0.1539	2.3780	0.0282
	-0.0352	-0.0371	2.3341
Eig. Value:	2.0618	2.4920	2.3340
Ca:	2.1437	0.0501	-0.0972
	-0.0707	2.4519	-0.0627
	-0.0835	-0.0784	2.2663
Eig. Value:	2.0907	2.4768	2.2943
Ca:	2.5984	0.0000	0.0000
	0.0000	2.2441	-0.1736
	-0.0000	-0.0130	2.0591
Eig. Value:	2.5984	2.2830	2.0202
Ca:	2.1675	0.1591	0.0000
	0.1614	2.5075	-0.0000
	-0.0000	-0.0000	2.3084
Eig. Value:	2.1039	2.5711	2.3084
Ca:	2.4806	-0.0000	0.0000
	0.0000	1.9920	-0.0470
	0.0000	-0.1097	2.1804
Eig. Value:	2.4806	1.9637	2.2087
Ca:	2.0892	0.0775	0.0000
	0.0221	2.3956	-0.0000
	0.0000	-0.0000	2.2635
Eig. Value:	2.0813	2.4035	2.2635
Si:	3.0209	-0.1323	-0.0944
	-0.2490	2.7247	-0.0292
	-0.1198	-0.1286	2.8961
Eig. Value:	3.1323	2.5855	2.9238
Si:	3.1411	-0.0817	-0.0703
	-0.0417	2.9287	-0.1407
	-0.1906	0.0835	2.9620
Eig. Value:	3.2159	2.9634	2.8525
Si:	2.9252	-0.0618	0.2869
	-0.0878	2.9092	0.0878
	0.2199	-0.0139	2.8813
Eig. Value:	3.1614	2.9270	2.6273
O:	-1.6301	-0.2790	0.0576
	-0.2891	-2.1774	0.0886
	0.0001	0.2175	-1.4724
Eig. Value:	-1.5232	-2.3254	-1.4314
O:	-1.6367	-0.1418	0.1934
	-0.1401	-1.5945	0.4319
	0.2467	0.4089	-1.9499
Eig. Value:	-1.5379	-1.3157	-2.3275
O:	-2.2284	0.4126	-0.5798
	0.4370	-1.3855	0.1013
	-0.4566	0.0432	-1.5774
Eig. Value:	-2.6475	-1.1355	-1.4084
O:	-2.4422	0.3981	-0.6231
	0.3676	-1.4496	0.3443
	-0.5856	0.3403	-1.4977
Eig. Value:	-2.9059	-1.3801	-1.1035
O:	-1.5076	-0.1243	-0.0307
	-0.1487	-2.3181	0.1153
	-0.0074	0.1659	-1.5285
Eig. Value:	-1.4534	-2.3626	-1.5381
O:	-1.4926	-0.2292	0.1426
	-0.1830	-2.2604	0.1572
	0.2465	0.0776	-1.6467
Eig. Value:	-1.3469	-2.3508	-1.7021
O:	-1.7659	-0.2127	-0.3824
	-0.1796	-1.5951	-0.1664
	-0.3824	-0.2304	-1.9724
Eig. Value:	-1.4493	-1.5192	-2.3649
O:	-1.7990	0.3136	0.2565
	0.3194	-1.9395	-0.2756
	0.1919	-0.2088	-1.7335
Eig. Value:	-1.5311	-2.3652	-1.5757
O:	-1.4673	-0.1533	-0.0661
	-0.2146	-1.6932	0.1782
	-0.0632	0.1293	-2.4473
Eig. Value:	-1.3483	-1.7812	-2.4782
O:	-1.3522	-0.2332	-0.0008
	-0.2830	-1.4830	-0.2138
	0.0104	-0.2648	-2.2225
Eig. Value:	-1.1293	-1.6298	-2.2986
O:	-1.7166	0.0000	-0.0000
	0.0000	-1.2056	-0.0792
	0.0000	-0.1028	-1.2173
Eig. Value:	-1.7166	-1.1203	-1.3026
O:	-1.6955	-0.0000	0.0000
	-0.0000	-1.1232	-0.0966
	-0.0000	-0.1047	-1.4066
Eig. Value:	-1.6955	-1.0911	-1.4387
H:	0.4979	0.2807	0.3967
	0.3017	0.7613	0.6277
	0.5651	0.7954	1.2739
Eig. Value:	0.3117	0.2359	1.9855
H:	0.4130	-0.0000	0.0000
	-0.0000	0.3709	0.0371
	-0.0000	0.0616	0.3300
Eig. Value:	0.4130	0.4039	0.2970
H:	0.4979	-0.0000	-0.0000
	0.0000	0.3039	0.0471
	-0.0000	0.0192	0.3519
Eig. Value:	0.4979	0.2870	0.3688
Ca:	2.1757	0.2186	0.0374
	0.1539	2.3780	-0.0282
	0.0352	0.0371	2.3341
Eig. Value:	2.0618	2.4920	2.3340
Ca:	2.1437	0.0501	0.0972
	-0.0707	2.4519	0.0627
	0.0835	0.0784	2.2663
Eig. Value:	2.0907	2.4768	2.2943
Ca:	2.5984	0.0000	-0.0000
	0.0000	2.2441	0.1736
	0.0000	0.0130	2.0591
Eig. Value:	2.5984	2.2830	2.0202
Ca:	2.4806	-0.0000	-0.0000
	0.0000	1.9920	0.0470
	-0.0000	0.1097	2.1804
Eig. Value:	2.4806	1.9637	2.2087
Si:	3.0209	-0.1323	0.0944
	-0.2490	2.7247	0.0292
	0.1198	0.1286	2.8961
Eig. Value:	3.1323	2.5855	2.9238
Si:	3.1411	-0.0817	0.0703
	-0.0417	2.9287	0.1407
	0.1906	-0.0835	2.9620
Eig. Value:	3.2159	2.9634	2.8525
Si:	2.9252	-0.0618	-0.2869
	-0.0878	2.9092	-0.0878
	-0.2199	0.0139	2.8813
Eig. Value:	3.1614	2.9270	2.6273
O:	-1.6301	-0.2790	-0.0576
	-0.2891	-2.1774	-0.0886
	-0.0001	-0.2175	-1.4724
Eig. Value:	-1.5232	-2.3254	-1.4314
O:	-1.6367	-0.1418	-0.1934
	-0.1401	-1.5945	-0.4319
	-0.2467	-0.4089	-1.9499
Eig. Value:	-1.5379	-1.3157	-2.3275
O:	-2.2284	0.4126	0.5798
	0.4370	-1.3855	-0.1013
	0.4566	-0.0432	-1.5774
Eig. Value:	-2.6475	-1.1355	-1.4084
O:	-2.4422	0.3981	0.6231
	0.3676	-1.4496	-0.3443
	0.5856	-0.3403	-1.4977
Eig. Value:	-2.9059	-1.3801	-1.1035
O:	-1.5076	-0.1243	0.0307
	-0.1487	-2.3181	-0.1153
	0.0074	-0.1659	-1.5285
Eig. Value:	-1.4534	-2.3626	-1.5381
O:	-1.4926	-0.2292	-0.1426
	-0.1830	-2.2604	-0.1572
	-0.2465	-0.0776	-1.6467
Eig. Value:	-1.3469	-2.3508	-1.7021
O:	-1.7659	-0.2127	0.3824
	-0.1796	-1.5951	0.1664
	0.3824	0.2304	-1.9724
Eig. Value:	-1.4493	-1.5192	-2.3649
O:	-1.7990	0.3136	-0.2565
	0.3194	-1.9395	0.2756
	-0.1919	0.2088	-1.7335
Eig. Value:	-1.5311	-2.3652	-1.5757
O:	-1.4673	-0.1533	0.0661
	-0.2146	-1.6932	-0.1782
	0.0632	-0.1293	-2.4473
Eig. Value:	-1.3483	-1.7812	-2.4782
O:	-1.3522	-0.2332	0.0008
	-0.2830	-1.4830	0.2138
	-0.0104	0.2648	-2.2225
Eig. Value:	-1.1293	-1.6298	-2.2986
O:	-1.7166	0.0000	0.0000
	0.0000	-1.2056	0.0792
	-0.0000	0.1028	-1.2173
Eig. Value:	-1.7166	-1.1203	-1.3026
O:	-1.6955	-0.0000	-0.0000
	-0.0000	-1.1232	0.0966
	0.0000	0.1047	-1.4066
Eig. Value:	-1.6955	-1.0911	-1.4387
H:	0.4979	0.2807	-0.3967
	0.3017	0.7613	-0.6277
	-0.5651	-0.7954	1.2739
Eig. Value:	0.3117	0.2359	1.9855
H:	0.4130	-0.0000	-0.0000
	-0.0000	0.3709	-0.0371
	0.0000	-0.0616	0.3300
Eig. Value:	0.4130	0.4039	0.2970
H:	0.4979	-0.0000	0.0000
	0.0000	0.3039	-0.0471
	0.0000	-0.0192	0.3519
Eig. Value:	0.4979	0.2870	0.3688
Ca:	2.1757	-0.2186	-0.0374
	-0.1539	2.3780	-0.0282
	-0.0352	0.0371	2.3341
Eig. Value:	2.0618	2.4920	2.3340
Ca:	2.1437	-0.0501	-0.0972
	0.0707	2.4519	0.0627
	-0.0835	0.0784	2.2663
Eig. Value:	2.0907	2.4768	2.2943
Ca:	2.1675	-0.1591	-0.0000
	-0.1614	2.5075	0.0000
	0.0000	-0.0000	2.3084
Eig. Value:	2.1039	2.5711	2.3084
Ca:	2.0892	-0.0775	0.0000
	-0.0221	2.3956	0.0000
	0.0000	0.0000	2.2635
Eig. Value:	2.0813	2.4035	2.2635
Si:	3.0209	0.1323	-0.0944
	0.2490	2.7247	0.0292
	-0.1198	0.1286	2.8961
Eig. Value:	3.1323	2.5855	2.9238
Si:	3.1411	0.0817	-0.0703
	0.0417	2.9287	0.1407
	-0.1906	-0.0835	2.9620
Eig. Value:	3.2159	2.9634	2.8525
Si:	2.9252	0.0618	0.2869
	0.0878	2.9092	-0.0878
	0.2199	0.0139	2.8813
Eig. Value:	3.1614	2.9270	2.6273
O:	-1.6302	0.2790	0.0576
	0.2892	-2.1774	-0.0886
	0.0001	-0.2175	-1.4724
Eig. Value:	-1.5232	-2.3254	-1.4314
O:	-1.6365	0.1418	0.1934
	0.1401	-1.5945	-0.4319
	0.2467	-0.4089	-1.9499
Eig. Value:	-1.5378	-1.3157	-2.3275
O:	-2.2282	-0.4126	-0.5798
	-0.4370	-1.3855	-0.1013
	-0.4565	-0.0432	-1.5774
Eig. Value:	-2.6474	-1.1354	-1.4084
O:	-2.4420	-0.3981	-0.6231
	-0.3675	-1.4496	-0.3443
	-0.5855	-0.3403	-1.4977
Eig. Value:	-2.9058	-1.3801	-1.1035
O:	-1.5075	0.1243	-0.0307
	0.1487	-2.3181	-0.1153
	-0.0074	-0.1659	-1.5285
Eig. Value:	-1.4534	-2.3626	-1.5381
O:	-1.4928	0.2292	0.1426
	0.1830	-2.2604	-0.1572
	0.2465	-0.0776	-1.6467
Eig. Value:	-1.3470	-2.3508	-1.7022
O:	-1.7657	0.2127	-0.3824
	0.1795	-1.5951	0.1664
	-0.3824	0.2304	-1.9724
Eig. Value:	-1.4493	-1.5192	-2.3648
O:	-1.7990	-0.3136	0.2565
	-0.3194	-1.9395	0.2756
	0.1919	0.2088	-1.7335
Eig. Value:	-1.5311	-2.3652	-1.5757
O:	-1.4674	0.1533	-0.0661
	0.2146	-1.6932	-0.1782
	-0.0632	-0.1293	-2.4473
Eig. Value:	-1.3484	-1.7812	-2.4782
O:	-1.3522	0.2332	-0.0008
	0.2830	-1.4830	0.2138
	0.0104	0.2648	-2.2225
Eig. Value:	-1.1293	-1.6299	-2.2986
H:	0.4979	-0.2807	0.3967
	-0.3017	0.7613	-0.6277
	0.5651	-0.7954	1.2739
Eig. Value:	0.3117	0.2359	1.9855
Ca:	2.1757	-0.2186	0.0374
	-0.1539	2.3780	0.0282
	0.0352	-0.0371	2.3341
Eig. Value:	2.0618	2.4920	2.3340
Ca:	2.1437	-0.0501	0.0972
	0.0707	2.4519	-0.0627
	0.0835	-0.0784	2.2663
Eig. Value:	2.0907	2.4768	2.2943
Si:	3.0209	0.1323	0.0944
	0.2490	2.7247	-0.0292
	0.1198	-0.1286	2.8961
Eig. Value:	3.1323	2.5855	2.9238
Si:	3.1411	0.0817	0.0703
	0.0417	2.9287	-0.1407
	0.1906	0.0835	2.9620
Eig. Value:	3.2159	2.9634	2.8525
Si:	2.9252	0.0618	-0.2869
	0.0878	2.9092	0.0878
	-0.2199	-0.0139	2.8813
Eig. Value:	3.1614	2.9270	2.6273
O:	-1.6302	0.2790	-0.0576
	0.2892	-2.1774	0.0886
	-0.0001	0.2175	-1.4724
Eig. Value:	-1.5232	-2.3254	-1.4314
O:	-1.6365	0.1418	-0.1934
	0.1401	-1.5945	0.4319
	-0.2467	0.4089	-1.9499
Eig. Value:	-1.5378	-1.3157	-2.3275
O:	-2.2282	-0.4126	0.5798
	-0.4370	-1.3855	0.1013
	0.4565	0.0432	-1.5774
Eig. Value:	-2.6474	-1.1354	-1.4084
O:	-2.4420	-0.3981	0.6231
	-0.3675	-1.4496	0.3443
	0.5855	0.3403	-1.4977
Eig. Value:	-2.9058	-1.3801	-1.1035
O:	-1.5075	0.1243	0.0307
	0.1487	-2.3181	0.1153
	0.0074	0.1659	-1.5285
Eig. Value:	-1.4534	-2.3626	-1.5381
O:	-1.4928	0.2292	-0.1426
	0.1830	-2.2604	0.1572
	-0.2465	0.0776	-1.6467
Eig. Value:	-1.3470	-2.3508	-1.7022
O:	-1.7657	0.2127	0.3824
	0.1795	-1.5951	-0.1664
	0.3824	-0.2304	-1.9724
Eig. Value:	-1.4493	-1.5192	-2.3648
O:	-1.7990	-0.3136	-0.2565
	-0.3194	-1.9395	-0.2756
	-0.1919	-0.2088	-1.7335
Eig. Value:	-1.5311	-2.3652	-1.5757
O:	-1.4674	0.1533	0.0661
	0.2146	-1.6932	0.1782
	0.0632	0.1293	-2.4473
Eig. Value:	-1.3484	-1.7812	-2.4782
O:	-1.3522	0.2332	0.0008
	0.2830	-1.4830	-0.2138
	-0.0104	-0.2648	-2.2225
Eig. Value:	-1.1293	-1.6299	-2.2986
H:	0.4979	-0.2807	-0.3967
	-0.3017	0.7613	0.6277
	-0.5651	0.7954	1.2739
Eig. Value:	0.3117	0.2359	1.9855