- EUCRYPTITE - LiAlSiO₄

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from an experimental structure similar to the one reported 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:	146		R3
Lattice parameters (Å):	13.5320	13.5320		9.0440
Angles (°):	90	90		120

Symmetry (theoretical):

Space group:	146		R3
Lattice parameters (Å):	8.1867	8.1867		8.1867
Angles (°):	107.84	107.84		107.84

Cell contents:

Number of atoms:	42
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Li:	0.2317	0.4559	0.0613
Li:	0.7727	0.5423	0.9407
Si:	0.2802	0.0994	0.8698
Al:	0.7208	0.9004	0.1331
Si:	0.7938	0.3857	0.5701
Al:	0.2077	0.6145	0.4317
O:	0.3525	0.6511	0.3187
O:	0.6667	0.3522	0.6844
O:	0.6718	0.9448	0.6095
O:	0.3131	0.0416	0.3765
O:	0.9640	0.2821	0.9532
O:	0.0381	0.7279	0.0625
O:	0.5848	0.9084	0.2580
O:	0.4063	0.0891	0.7529
Li:	0.4559	0.0613	0.2317
Li:	0.5423	0.9407	0.7727
Si:	0.0994	0.8698	0.2802
Al:	0.9004	0.1331	0.7208
Si:	0.3857	0.5701	0.7938
Al:	0.6145	0.4317	0.2077
O:	0.6511	0.3187	0.3525
O:	0.3522	0.6844	0.6667
O:	0.9448	0.6095	0.6718
O:	0.0416	0.3765	0.3131
O:	0.2821	0.9532	0.9640
O:	0.7279	0.0625	0.0381
O:	0.9084	0.2580	0.5848
O:	0.0891	0.7529	0.4063
Li:	0.0613	0.2317	0.4559
Li:	0.9407	0.7727	0.5423
Si:	0.8698	0.2802	0.0994
Al:	0.1331	0.7208	0.9004
Si:	0.5701	0.7938	0.3857
Al:	0.4317	0.2077	0.6145
O:	0.3187	0.3525	0.6511
O:	0.6844	0.6667	0.3522
O:	0.6095	0.6718	0.9448
O:	0.3765	0.3131	0.0416
O:	0.9532	0.9640	0.2821
O:	0.0625	0.0381	0.7279
O:	0.2580	0.5848	0.9084
O:	0.7529	0.4063	0.0891

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):

Li:	1.0200	0.0568	0.0048
	0.0411	0.9883	0.0424
	-0.0407	0.0038	1.0421
Eig. Value:	1.0558	0.9440	1.0507
Li:	1.0449	0.0133	-0.0060
	0.0237	0.9680	-0.0252
	0.0217	-0.0047	1.0495
Eig. Value:	1.0462	0.9607	1.0554
Si:	3.0465	-0.2425	0.2160
	-0.1054	3.1004	0.0772
	-0.1297	0.1375	3.1265
Eig. Value:	2.8572	3.2735	3.1427
Al:	2.5690	-0.2240	0.2303
	-0.0985	2.7252	0.1039
	-0.1457	0.1743	2.7480
Eig. Value:	2.4275	2.8997	2.7150
Si:	2.8428	-0.0078	0.1574
	-0.1791	3.2271	-0.0905
	0.0435	0.1896	3.1053
Eig. Value:	2.7842	3.2541	3.1370
Al:	2.4454	-0.0238	0.1881
	-0.1861	2.8098	-0.1458
	0.0700	0.2092	2.7151
Eig. Value:	2.3667	2.8380	2.7656
O:	-1.4469	-0.4717	-0.2835
	-0.4127	-1.9082	-0.4132
	-0.2022	-0.4246	-1.7251
Eig. Value:	-1.1785	-2.4848	-1.4168
O:	-1.4605	-0.5057	-0.2177
	-0.4502	-2.1102	-0.2978
	-0.1459	-0.3004	-1.5323
Eig. Value:	-1.2055	-2.4907	-1.4068
O:	-1.2798	-0.1857	0.1325
	-0.1950	-1.4660	0.1256
	0.0786	0.1327	-2.3127
Eig. Value:	-1.1606	-1.5490	-2.3489
O:	-1.2794	-0.1770	-0.0094
	-0.1884	-1.4517	-0.1269
	-0.0324	-0.1434	-2.3096
Eig. Value:	-1.1608	-1.5471	-2.3327
O:	-1.3684	-0.4388	0.1669
	-0.4726	-2.1773	0.3359
	0.1245	0.3279	-1.5610
Eig. Value:	-1.1636	-2.5193	-1.4239
O:	-1.3758	-0.3952	0.2586
	-0.4379	-1.9852	0.4430
	0.1982	0.4510	-1.7623
Eig. Value:	-1.1644	-2.5264	-1.4326
O:	-1.5201	0.0473	0.0045
	0.0847	-2.2087	0.0129
	0.0451	0.0297	-1.2926
Eig. Value:	-1.5170	-2.2153	-1.2891
O:	-1.5536	-0.1996	-0.0105
	-0.1778	-2.1956	0.0063
	0.0535	0.0421	-1.2909
Eig. Value:	-1.5032	-2.2479	-1.2890
Li:	0.9539	-0.0029	0.0343
	-0.0186	1.0545	-0.0253
	0.0237	0.0333	1.0421
Eig. Value:	0.9440	1.0558	1.0507
Li:	0.9712	0.0189	-0.0189
	0.0293	1.0417	0.0178
	-0.0149	-0.0165	1.0495
Eig. Value:	0.9607	1.0462	1.0554
Si:	3.2376	-0.0049	-0.0411
	0.1322	2.9094	-0.2257
	0.1840	0.0436	3.1265
Eig. Value:	3.2735	2.8572	3.1427
Al:	2.8258	-0.0497	-0.0252
	0.0757	2.4684	-0.2514
	0.2238	0.0391	2.7480
Eig. Value:	2.8997	2.4275	2.7150
Si:	3.2119	-0.0340	-0.1570
	-0.2053	2.8580	-0.0910
	0.1425	-0.1325	3.1053
Eig. Value:	3.2541	2.7842	3.1370
Al:	2.8096	-0.0242	-0.2203
	-0.1865	2.4456	-0.0900
	0.1462	-0.1652	2.7151
Eig. Value:	2.8380	2.3667	2.7656
O:	-1.4099	0.3913	-0.2161
	0.4503	-1.9452	0.4521
	-0.2666	0.3874	-1.7251
Eig. Value:	-1.1785	-2.4848	-1.4168
O:	-1.5338	0.4925	-0.1490
	0.5481	-2.0369	0.3375
	-0.1872	0.2766	-1.5323
Eig. Value:	-1.2055	-2.4907	-1.4068
O:	-1.2546	0.1804	0.0426
	0.1711	-1.4912	-0.1775
	0.0756	-0.1344	-2.3127
Eig. Value:	-1.1606	-1.5490	-2.3489
O:	-1.2504	0.1717	-0.1052
	0.1602	-1.4807	0.0716
	-0.1080	0.0998	-2.3096
Eig. Value:	-1.1608	-1.5471	-2.3327
O:	-1.5805	0.5950	0.2074
	0.5612	-1.9653	-0.3125
	0.2217	-0.2718	-1.5610
Eig. Value:	-1.1636	-2.5193	-1.4239
O:	-1.4721	0.4935	0.2543
	0.4508	-1.8889	-0.4454
	0.2915	-0.3972	-1.7623
Eig. Value:	-1.1644	-2.5264	-1.4326
O:	-2.0937	0.2465	0.0090
	0.2838	-1.6351	-0.0103
	0.0032	-0.0540	-1.2926
Eig. Value:	-2.2153	-1.5170	-1.2891
O:	-1.8717	0.3615	0.0106
	0.3833	-1.8776	0.0059
	0.0097	-0.0674	-1.2909
Eig. Value:	-1.5032	-2.2479	-1.2890
Li:	1.0386	-0.0303	-0.0391
	-0.0461	0.9697	-0.0170
	0.0170	-0.0371	1.0421
Eig. Value:	1.0558	0.9440	1.0507
Li:	1.0032	-0.0478	0.0249
	-0.0374	1.0097	0.0074
	-0.0068	0.0212	1.0495
Eig. Value:	0.9607	1.0462	1.0554
Si:	2.9363	0.0418	-0.1749
	0.1788	3.2106	0.1485
	-0.0542	-0.1811	3.1265
Eig. Value:	2.8572	3.2735	3.1427
Al:	2.5465	0.0856	-0.2051
	0.2110	2.7477	0.1476
	-0.0781	-0.2133	2.7480
Eig. Value:	2.4275	2.8997	2.7150
Si:	3.0501	0.2987	-0.0003
	0.1275	3.0198	0.1815
	-0.1860	-0.0571	3.1053
Eig. Value:	3.2541	2.7842	3.1370
Al:	2.6278	0.2914	0.0322
	0.1291	2.6274	0.2358
	-0.2162	-0.0440	2.7151
Eig. Value:	2.8380	2.3667	2.7656
O:	-2.1758	-0.0082	0.4996
	0.0508	-1.1793	-0.0389
	0.4688	0.0372	-1.7251
Eig. Value:	-2.4848	-1.1785	-1.4168
O:	-2.3617	-0.0701	0.3668
	-0.0146	-1.2090	-0.0397
	0.3331	0.0238	-1.5323
Eig. Value:	-2.4907	-1.2055	-1.4068
O:	-1.5843	0.0192	-0.1750
	0.0099	-1.1615	0.0519
	-0.1542	0.0017	-2.3127
Eig. Value:	-1.5490	-1.1606	-2.3489
O:	-1.5668	0.0225	0.1146
	0.0110	-1.1642	0.0553
	0.1404	0.0436	-2.3096
Eig. Value:	-1.5471	-1.1608	-2.3327
O:	-2.3698	-0.1055	-0.3744
	-0.1393	-1.1760	-0.0234
	-0.3462	-0.0561	-1.5610
Eig. Value:	-2.5193	-1.1636	-1.4239
O:	-2.1936	-0.0342	-0.5129
	-0.0770	-1.1674	0.0025
	-0.4897	-0.0538	-1.7623
Eig. Value:	-2.5264	-1.1644	-1.4326
O:	-1.9793	-0.3499	-0.0134
	-0.3125	-1.7494	-0.0026
	-0.0483	0.0242	-1.2926
Eig. Value:	-2.2153	-1.5170	-1.2891
O:	-2.1986	-0.1945	-0.0002
	-0.1727	-1.5507	-0.0122
	-0.0632	0.0253	-1.2909
Eig. Value:	-2.2479	-1.5032	-1.2890