- LINTISITE - Na₃LiTi₂(Si₂O₆)₂2H₂O

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:	15		C2/c
Lattice parameters (Å):	28.5830	8.6000		5.2100
Angles (°):	90	91.03		90

Symmetry (theoretical):

Space group:	15		C2/c
Lattice parameters (Å):	14.5565	14.5565		5.1125
Angles (°):	89.25	90.74		146.35

Cell contents:

Number of atoms:	60
Number of atom types:	6
Chemical composition:	0

Atomic positions (theoretical):

Na:	0.3530	0.0225	0.1132
Na:	0.3680	0.3680	0.7500
Li:	0.0062	0.0062	0.2500
Ti:	0.5707	0.2433	0.6246
Si:	0.6697	0.1424	0.2916
Si:	0.1906	0.0076	0.5388
O:	0.2292	0.7999	0.4429
O:	0.4781	0.0506	0.7480
O:	0.3753	0.1255	0.4810
O:	0.1653	0.0932	0.5114
O:	0.5586	0.2906	0.9379
O:	0.1434	0.9242	0.8251
O:	0.6213	0.2089	0.2896
O:	0.4363	0.3478	0.1237
H:	0.3518	0.2666	0.2589
H:	0.4800	0.3234	0.0722
Na:	0.0225	0.3530	0.3868
Ti:	0.2433	0.5707	0.8754
Si:	0.1424	0.6697	0.2084
Si:	0.0076	0.1906	0.9612
O:	0.7999	0.2292	0.0571
O:	0.0506	0.4781	0.7520
O:	0.1255	0.3753	0.0190
O:	0.0932	0.1653	0.9886
O:	0.2906	0.5586	0.5621
O:	0.9242	0.1434	0.6749
O:	0.2089	0.6213	0.2104
O:	0.3478	0.4363	0.3763
H:	0.2666	0.3518	0.2411
H:	0.3234	0.4800	0.4278
Na:	0.6470	0.9775	0.8868
Na:	0.6320	0.6320	0.2500
Li:	0.9938	0.9938	0.7500
Ti:	0.4293	0.7567	0.3754
Si:	0.3303	0.8576	0.7084
Si:	0.8094	0.9924	0.4612
O:	0.7708	0.2001	0.5571
O:	0.5219	0.9494	0.2520
O:	0.6247	0.8745	0.5190
O:	0.8347	0.9068	0.4886
O:	0.4414	0.7094	0.0621
O:	0.8566	0.0758	0.1749
O:	0.3787	0.7911	0.7104
O:	0.5637	0.6522	0.8763
H:	0.6482	0.7334	0.7411
H:	0.5200	0.6766	0.9278
Na:	0.9775	0.6470	0.6132
Ti:	0.7567	0.4293	0.1246
Si:	0.8576	0.3303	0.7916
Si:	0.9924	0.8094	0.0388
O:	0.2001	0.7708	0.9429
O:	0.9494	0.5219	0.2480
O:	0.8745	0.6247	0.9810
O:	0.9068	0.8347	0.0114
O:	0.7094	0.4414	0.4379
O:	0.0758	0.8566	0.3251
O:	0.7911	0.3787	0.7896
O:	0.6522	0.5637	0.6237
H:	0.7334	0.6482	0.7589
H:	0.6766	0.5200	0.5722

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:	0.8497	0.0388	0.0246
	-0.0141	1.1359	0.0053
	-0.0125	-0.0167	1.1011
Eig. Value:	0.8490	1.1373	1.1004
Na:	1.3815	-0.0000	-0.0653
	-0.0000	1.0736	0.0000
	-0.0331	0.0000	1.0173
Eig. Value:	1.3880	1.0736	1.0107
Li:	1.3955	-0.0000	0.0273
	-0.0000	0.8917	0.0000
	0.0140	-0.0000	0.9850
Eig. Value:	1.3965	0.8917	0.9840
Ti:	3.4152	0.2770	0.3652
	-0.5607	4.7138	0.5156
	0.2748	-0.5486	5.8565
Eig. Value:	3.3597	4.7270	5.8988
Si:	3.0832	-0.7283	-0.1454
	-0.6339	3.8049	0.1184
	-0.1791	-0.2365	3.3692
Eig. Value:	2.6341	4.2162	3.4070
Si:	3.3775	0.6047	-0.0744
	0.3826	3.7878	-0.3175
	0.2769	0.3823	3.1918
Eig. Value:	3.0213	4.1247	3.2111
O:	-1.2461	-0.0158	0.0056
	0.0561	-1.8271	-0.7564
	0.0592	-0.7566	-2.3098
Eig. Value:	-1.2449	-1.2747	-2.8634
O:	-1.8568	1.0374	-0.2083
	1.3382	-2.7959	0.2267
	-0.2660	0.2519	-1.3716
Eig. Value:	-1.0362	-3.6517	-1.3364
O:	-1.9909	-1.3173	-0.3410
	-1.4452	-2.9554	-0.4640
	-0.3662	-0.4565	-1.3794
Eig. Value:	-1.0083	-4.0616	-1.2558
O:	-2.2635	-0.1172	-0.0314
	-0.0727	-1.5348	0.1528
	-0.1413	0.0905	-1.4279
Eig. Value:	-2.2816	-1.6128	-1.3319
O:	-1.4433	-0.2592	0.3968
	-0.2350	-1.7468	-1.0894
	0.3747	-1.2426	-3.6410
Eig. Value:	-1.7110	-0.9025	-4.2176
O:	-1.3805	-0.0773	-0.0024
	-0.1125	-1.9801	0.9800
	-0.0802	0.8098	-2.3325
Eig. Value:	-1.4326	-1.1917	-3.0689
O:	-2.1098	0.4410	0.1706
	0.5127	-1.5739	0.3209
	0.2175	0.3725	-2.1174
Eig. Value:	-2.3893	-1.1343	-2.2775
O:	-1.4306	-0.1816	0.1895
	-0.2379	-0.9825	0.1465
	0.2494	0.1443	-1.0547
Eig. Value:	-1.6297	-0.8654	-0.9728
H:	0.4888	0.0677	-0.0006
	0.1101	0.6472	-0.2380
	-0.0070	-0.2702	0.5812
Eig. Value:	0.4981	0.8828	0.3362
H:	1.1186	0.1828	-0.3297
	0.2686	0.3243	-0.0887
	-0.3908	-0.0733	0.5334
Eig. Value:	1.3459	0.2631	0.3673
Na:	0.8497	-0.0388	0.0246
	0.0141	1.1359	-0.0053
	-0.0125	0.0167	1.1011
Eig. Value:	0.8490	1.1373	1.1004
Ti:	3.4152	-0.2770	0.3652
	0.5607	4.7138	-0.5156
	0.2748	0.5486	5.8565
Eig. Value:	3.3597	4.7270	5.8988
Si:	3.0832	0.7283	-0.1454
	0.6339	3.8049	-0.1184
	-0.1791	0.2365	3.3692
Eig. Value:	2.6341	4.2162	3.4070
Si:	3.3775	-0.6047	-0.0744
	-0.3826	3.7878	0.3175
	0.2769	-0.3823	3.1918
Eig. Value:	3.0213	4.1247	3.2111
O:	-1.2461	0.0158	0.0056
	-0.0561	-1.8271	0.7564
	0.0592	0.7566	-2.3098
Eig. Value:	-1.2449	-1.2747	-2.8634
O:	-1.8568	-1.0374	-0.2083
	-1.3382	-2.7959	-0.2267
	-0.2660	-0.2519	-1.3716
Eig. Value:	-1.0362	-3.6517	-1.3364
O:	-1.9909	1.3173	-0.3410
	1.4452	-2.9554	0.4640
	-0.3662	0.4565	-1.3794
Eig. Value:	-1.0083	-4.0616	-1.2558
O:	-2.2635	0.1172	-0.0314
	0.0727	-1.5348	-0.1528
	-0.1413	-0.0905	-1.4279
Eig. Value:	-2.2816	-1.6128	-1.3319
O:	-1.4433	0.2592	0.3968
	0.2350	-1.7468	1.0894
	0.3747	1.2426	-3.6410
Eig. Value:	-1.7110	-0.9025	-4.2176
O:	-1.3805	0.0773	-0.0024
	0.1125	-1.9801	-0.9800
	-0.0802	-0.8098	-2.3325
Eig. Value:	-1.4326	-1.1917	-3.0689
O:	-2.1098	-0.4410	0.1706
	-0.5127	-1.5739	-0.3209
	0.2175	-0.3725	-2.1174
Eig. Value:	-2.3893	-1.1343	-2.2775
O:	-1.4306	0.1816	0.1895
	0.2379	-0.9825	-0.1465
	0.2494	-0.1443	-1.0547
Eig. Value:	-1.6297	-0.8654	-0.9728
H:	0.4888	-0.0677	-0.0006
	-0.1101	0.6472	0.2380
	-0.0070	0.2702	0.5812
Eig. Value:	0.4981	0.8828	0.3362
H:	1.1186	-0.1828	-0.3297
	-0.2686	0.3243	0.0887
	-0.3908	0.0733	0.5334
Eig. Value:	1.3459	0.2631	0.3673
Na:	0.8497	0.0388	0.0246
	-0.0141	1.1359	0.0053
	-0.0125	-0.0167	1.1011
Eig. Value:	0.8490	1.1373	1.1004
Na:	1.3815	-0.0000	-0.0653
	-0.0000	1.0736	0.0000
	-0.0331	0.0000	1.0173
Eig. Value:	1.3880	1.0736	1.0107
Li:	1.3955	-0.0000	0.0273
	-0.0000	0.8917	0.0000
	0.0140	0.0000	0.9850
Eig. Value:	1.3965	0.8917	0.9840
Ti:	3.4152	0.2770	0.3652
	-0.5607	4.7138	0.5156
	0.2748	-0.5486	5.8565
Eig. Value:	3.3597	4.7270	5.8988
Si:	3.0832	-0.7283	-0.1454
	-0.6339	3.8049	0.1184
	-0.1791	-0.2365	3.3692
Eig. Value:	2.6341	4.2162	3.4070
Si:	3.3775	0.6047	-0.0744
	0.3826	3.7878	-0.3175
	0.2769	0.3823	3.1918
Eig. Value:	3.0213	4.1247	3.2111
O:	-1.2461	-0.0158	0.0056
	0.0561	-1.8271	-0.7564
	0.0592	-0.7566	-2.3098
Eig. Value:	-1.2449	-1.2747	-2.8634
O:	-1.8568	1.0374	-0.2083
	1.3382	-2.7959	0.2267
	-0.2660	0.2519	-1.3716
Eig. Value:	-1.0362	-3.6517	-1.3364
O:	-1.9909	-1.3173	-0.3410
	-1.4452	-2.9554	-0.4640
	-0.3662	-0.4565	-1.3794
Eig. Value:	-1.0083	-4.0616	-1.2558
O:	-2.2635	-0.1172	-0.0314
	-0.0727	-1.5348	0.1528
	-0.1413	0.0905	-1.4279
Eig. Value:	-2.2816	-1.6128	-1.3319
O:	-1.4433	-0.2592	0.3968
	-0.2350	-1.7468	-1.0894
	0.3747	-1.2426	-3.6410
Eig. Value:	-1.7110	-0.9025	-4.2176
O:	-1.3805	-0.0773	-0.0024
	-0.1125	-1.9801	0.9800
	-0.0802	0.8098	-2.3325
Eig. Value:	-1.4326	-1.1917	-3.0689
O:	-2.1098	0.4410	0.1706
	0.5127	-1.5739	0.3209
	0.2175	0.3725	-2.1174
Eig. Value:	-2.3893	-1.1343	-2.2775
O:	-1.4306	-0.1816	0.1895
	-0.2379	-0.9825	0.1465
	0.2494	0.1443	-1.0547
Eig. Value:	-1.6297	-0.8654	-0.9728
H:	0.4888	0.0677	-0.0006
	0.1101	0.6472	-0.2380
	-0.0070	-0.2702	0.5812
Eig. Value:	0.4981	0.8828	0.3362
H:	1.1186	0.1828	-0.3297
	0.2686	0.3243	-0.0887
	-0.3908	-0.0733	0.5334
Eig. Value:	1.3459	0.2631	0.3673
Na:	0.8497	-0.0388	0.0246
	0.0141	1.1359	-0.0053
	-0.0125	0.0167	1.1011
Eig. Value:	0.8490	1.1373	1.1004
Ti:	3.4152	-0.2770	0.3652
	0.5607	4.7138	-0.5156
	0.2748	0.5486	5.8565
Eig. Value:	3.3597	4.7270	5.8988
Si:	3.0832	0.7283	-0.1454
	0.6339	3.8049	-0.1184
	-0.1791	0.2365	3.3692
Eig. Value:	2.6341	4.2162	3.4070
Si:	3.3775	-0.6047	-0.0744
	-0.3826	3.7878	0.3175
	0.2769	-0.3823	3.1918
Eig. Value:	3.0213	4.1247	3.2111
O:	-1.2461	0.0158	0.0056
	-0.0561	-1.8271	0.7564
	0.0592	0.7566	-2.3098
Eig. Value:	-1.2449	-1.2747	-2.8634
O:	-1.8568	-1.0374	-0.2083
	-1.3382	-2.7959	-0.2267
	-0.2660	-0.2519	-1.3716
Eig. Value:	-1.0362	-3.6517	-1.3364
O:	-1.9909	1.3173	-0.3410
	1.4452	-2.9554	0.4640
	-0.3662	0.4565	-1.3794
Eig. Value:	-1.0083	-4.0616	-1.2558
O:	-2.2635	0.1172	-0.0314
	0.0727	-1.5348	-0.1528
	-0.1413	-0.0905	-1.4279
Eig. Value:	-2.2816	-1.6128	-1.3319
O:	-1.4433	0.2592	0.3968
	0.2350	-1.7468	1.0894
	0.3747	1.2426	-3.6410
Eig. Value:	-1.7110	-0.9025	-4.2176
O:	-1.3805	0.0773	-0.0024
	0.1125	-1.9801	-0.9800
	-0.0802	-0.8098	-2.3325
Eig. Value:	-1.4326	-1.1917	-3.0689
O:	-2.1098	-0.4410	0.1706
	-0.5127	-1.5739	-0.3209
	0.2175	-0.3725	-2.1174
Eig. Value:	-2.3893	-1.1343	-2.2775
O:	-1.4306	0.1816	0.1895
	0.2379	-0.9825	-0.1465
	0.2494	-0.1443	-1.0547
Eig. Value:	-1.6297	-0.8654	-0.9728
H:	0.4888	-0.0677	-0.0006
	-0.1101	0.6472	0.2380
	-0.0070	0.2702	0.5812
Eig. Value:	0.4981	0.8828	0.3362
H:	1.1186	-0.1828	-0.3297
	-0.2686	0.3243	0.0887
	-0.3908	0.0733	0.5334
Eig. Value:	1.3459	0.2631	0.3673