- CRISTOBALITE X-I - SiO₂

2x1x1 super structure. The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) at 10GPa.

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:	Theo 14		Theo P2_1/n
Lattice parameters (Å):	6.7500	4.0633		6.8344
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	Theo 14		Theo P2_1/n
Lattice parameters (Å):	12.8731	3.8829		6.6716
Angles (°):	x	x		x

Cell contents:

Number of atoms:	48
Number of atom types:	2
Chemical composition:	0

Atomic positions (theoretical):

Si:	0.2508	0.0002	0.5013
Si:	0.9959	0.4984	0.0008
Si:	0.1787	0.9983	0.1178
Si:	0.0697	0.5021	0.3759
Si:	0.3209	0.0021	0.8831
Si:	0.4325	0.5006	0.6255
Si:	0.1358	0.4969	0.7584
Si:	0.3632	0.5050	0.2441
O:	0.1660	0.2247	0.3323
O:	0.0822	0.7325	0.1664
O:	0.3355	0.7743	0.6703
O:	0.4183	0.2599	0.8346
O:	0.2336	0.2345	0.7120
O:	0.0223	0.7200	0.7949
O:	0.2660	0.7656	0.2897
O:	0.4767	0.2794	0.2056
O:	0.1517	0.7314	0.5458
O:	0.1027	0.2538	0.9567
O:	0.3501	0.2688	0.4569
O:	0.3961	0.7446	0.0439
O:	0.2114	0.7614	0.9210
O:	0.0439	0.2813	0.5813
O:	0.2882	0.2385	0.0808
O:	0.4549	0.7269	0.4164
Si:	0.7458	0.0019	0.5004
Si:	0.5008	0.4992	0.0012
Si:	0.6812	0.9959	0.1184
Si:	0.5670	0.4996	0.3753
Si:	0.8192	0.9974	0.8748
Si:	0.9308	0.5047	0.6174
Si:	0.6359	0.4938	0.7570
Si:	0.8852	0.0043	0.2589
O:	0.6647	0.2332	0.3306
O:	0.5834	0.7400	0.1675
O:	0.8331	0.7666	0.6659
O:	0.9155	0.2682	0.8306
O:	0.7328	0.2327	0.7090
O:	0.5233	0.7198	0.7959
O:	0.7721	0.7810	0.2951
O:	0.9824	0.2669	0.2099
O:	0.6485	0.7319	0.5441
O:	0.6054	0.2527	0.9577
O:	0.8536	0.2489	0.4567
O:	0.8997	0.7679	0.0450
O:	0.7121	0.7514	0.9187
O:	0.5444	0.2728	0.5844
O:	0.7939	0.2191	0.0814
O:	0.9623	0.7491	0.4196

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):

Si:	3.8189	0.0809	-0.0248
	0.3060	3.7796	-0.0221
	0.0465	0.0006	3.9743
Eig. Value:	3.9937	3.6042	3.9749
Si:	3.8381	-0.0656	-0.0081
	-0.2236	3.4081	0.1775
	0.0241	0.0393	3.9075
Eig. Value:	3.8722	3.3440	3.9375
Si:	3.8677	0.0498	0.0016
	0.0624	3.7551	-0.1487
	-0.0293	-0.0435	3.9464
Eig. Value:	3.8713	3.7018	3.9961
Si:	3.8773	-0.0826	-0.0142
	-0.2519	3.4196	0.2078
	0.0232	0.0501	3.9131
Eig. Value:	3.9007	3.3382	3.9711
Si:	3.8500	0.0314	0.0049
	0.0467	3.7662	-0.1363
	-0.0288	-0.0364	3.9444
Eig. Value:	3.8530	3.7231	3.9845
Si:	3.8785	-0.0566	-0.0109
	-0.2100	3.1425	-0.0002
	0.0294	0.0001	3.9329
Eig. Value:	3.8994	3.1191	3.9354
Si:	3.8899	-0.0208	0.0224
	0.0117	3.4418	-0.0215
	-0.0223	-0.0005	3.9863
Eig. Value:	3.8899	3.4415	3.9865
Si:	3.8806	-0.0118	0.0144
	0.0348	3.4098	0.0026
	-0.0212	0.0108	3.9695
Eig. Value:	3.8807	3.4094	3.9697
O:	-1.9106	0.5024	-0.0326
	0.5065	-1.8743	-0.1757
	-0.0350	-0.1464	-2.0011
Eig. Value:	-2.4165	-1.3572	-2.0123
O:	-1.9305	-0.4992	0.0376
	-0.4933	-1.8488	0.1861
	-0.0464	0.1010	-1.9902
Eig. Value:	-2.4093	-1.3724	-1.9878
O:	-1.9099	0.5122	-0.0308
	0.5704	-1.8871	-0.1615
	-0.0213	-0.1456	-2.0063
Eig. Value:	-2.4580	-1.3325	-2.0128
O:	-1.9190	-0.5651	0.0388
	-0.5375	-1.8179	0.1915
	-0.0412	0.1175	-1.9820
Eig. Value:	-2.4457	-1.2953	-1.9779
O:	-1.9289	0.5003	0.0460
	0.5262	-1.8624	-0.1671
	-0.0265	-0.0996	-2.0013
Eig. Value:	-2.4328	-1.3682	-1.9917
O:	-1.9577	0.0286	-0.0046
	0.0323	-1.3532	-0.0183
	0.0031	-0.0595	-1.9500
Eig. Value:	-1.9594	-1.3492	-1.9523
O:	-1.9307	0.4933	0.0420
	0.5211	-1.8623	-0.1669
	-0.0365	-0.1002	-1.9976
Eig. Value:	-2.4255	-1.3733	-1.9917
O:	-1.9512	0.0265	-0.0056
	0.0075	-1.3214	-0.0344
	-0.0024	-0.0802	-1.9391
Eig. Value:	-1.9524	-1.3157	-1.9437
O:	-1.9081	-0.5586	-0.0215
	-0.5262	-1.8011	0.1489
	-0.0217	0.1575	-1.9886
Eig. Value:	-2.4178	-1.2861	-1.9939
O:	-1.9440	0.4245	-0.0010
	0.3692	-1.8396	0.4556
	0.0738	0.3906	-1.9443
Eig. Value:	-2.4548	-1.2926	-1.9804
O:	-1.9005	-0.5650	-0.0211
	-0.5780	-1.8110	0.1398
	-0.0280	0.1649	-1.9870
Eig. Value:	-2.4454	-1.2596	-1.9935
O:	-1.9392	0.4314	-0.0076
	0.3940	-1.8359	0.4236
	0.0669	0.3889	-1.9516
Eig. Value:	-2.4563	-1.2953	-1.9752
O:	-1.9504	-0.3871	-0.0155
	-0.3896	-1.8933	-0.4421
	0.0622	-0.3488	-1.9606
Eig. Value:	-2.4674	-1.3582	-1.9788
O:	-1.9567	0.0267	-0.0095
	0.0181	-1.3502	-0.0165
	-0.0023	-0.0597	-1.9432
Eig. Value:	-1.9590	-1.3469	-1.9442
O:	-1.9489	-0.3871	-0.0143
	-0.3961	-1.8907	-0.4458
	0.0661	-0.3507	-1.9638
Eig. Value:	-2.4696	-1.3517	-1.9821
O:	-1.9502	0.0707	-0.0026
	0.0649	-1.3214	0.0309
	-0.0066	-0.0081	-1.9318
Eig. Value:	-1.9587	-1.3140	-1.9308
Si:	3.8661	0.0608	-0.0066
	0.2387	3.4656	-0.2181
	0.0260	-0.0468	3.9115
Eig. Value:	3.8951	3.3843	3.9639
Si:	3.8615	-0.0417	0.0042
	-0.1536	3.0877	0.3736
	0.0004	0.0775	3.8574
Eig. Value:	3.8626	3.0158	3.9282
Si:	3.8586	0.0131	0.0076
	-0.0029	3.4991	0.0654
	-0.0269	0.0232	3.9682
Eig. Value:	3.8580	3.4948	3.9731
Si:	3.8590	-0.0394	-0.0034
	-0.1837	3.1503	-0.0098
	0.0289	-0.0069	3.9291
Eig. Value:	3.8727	3.1331	3.9325
Si:	3.8453	0.0649	-0.0053
	0.2359	3.4465	-0.1986
	0.0251	-0.0442	3.9115
Eig. Value:	3.8813	3.3702	3.9518
Si:	3.8821	-0.0316	0.0020
	-0.0034	3.4693	-0.0540
	-0.0299	-0.0184	3.9684
Eig. Value:	3.8811	3.4659	3.9728
Si:	3.8706	-0.0260	-0.0072
	0.0042	3.4431	-0.0285
	-0.0266	-0.0083	3.9515
Eig. Value:	3.8677	3.4422	3.9554
Si:	3.8783	0.0296	0.0022
	0.0019	3.4821	0.0541
	-0.0283	0.0167	3.9690
Eig. Value:	3.8775	3.4788	3.9731
O:	-1.9026	0.5747	-0.0290
	0.6121	-1.8457	-0.1625
	-0.0166	-0.1583	-1.9972
Eig. Value:	-2.4869	-1.2564	-2.0022
O:	-1.9206	-0.5721	0.0395
	-0.6037	-1.8371	0.1729
	-0.0288	0.1115	-1.9890
Eig. Value:	-2.4889	-1.2752	-1.9826
O:	-1.9370	0.5031	0.0390
	0.5453	-1.8569	-0.1643
	-0.0394	-0.0926	-1.9936
Eig. Value:	-2.4400	-1.3571	-1.9905
O:	-1.8959	-0.5705	-0.0297
	-0.5592	-1.8390	0.1821
	-0.0255	0.1643	-1.9938
Eig. Value:	-2.4553	-1.2725	-2.0009
O:	-1.9349	0.5061	0.0320
	0.5509	-1.8661	-0.1692
	-0.0457	-0.0951	-1.9923
Eig. Value:	-2.4465	-1.3547	-1.9921
O:	-1.9506	0.0333	-0.0035
	0.0016	-1.3228	-0.0317
	-0.0040	-0.0767	-1.9378
Eig. Value:	-1.9516	-1.3175	-1.9420
O:	-1.9568	-0.0264	-0.0090
	-0.0299	-1.3599	0.0135
	0.0027	0.0592	-1.9473
Eig. Value:	-1.9584	-1.3563	-1.9493
O:	-1.9314	-0.4997	0.0414
	-0.5516	-1.8575	0.1658
	-0.0371	0.0969	-1.9952
Eig. Value:	-2.4404	-1.3534	-1.9904
O:	-1.8930	-0.5751	-0.0277
	-0.6052	-1.8408	0.1709
	-0.0341	0.1686	-1.9884
Eig. Value:	-2.4768	-1.2479	-1.9975
O:	-1.9344	0.4402	-0.0034
	0.4605	-1.8612	0.4354
	0.0581	0.3884	-1.9556
Eig. Value:	-2.5000	-1.2780	-1.9732
O:	-1.9451	-0.4328	0.0024
	-0.4305	-1.8617	-0.4614
	0.0671	-0.3877	-1.9408
Eig. Value:	-2.4909	-1.2791	-1.9776
O:	-1.8964	0.5683	-0.0311
	0.5548	-1.8365	-0.1815
	-0.0281	-0.1637	-1.9947
Eig. Value:	-2.4504	-1.2743	-2.0028
O:	-1.9372	-0.4339	0.0054
	-0.4362	-1.8614	-0.4684
	0.0707	-0.3901	-1.9502
Eig. Value:	-2.4951	-1.2719	-1.9818
O:	-1.9519	0.0748	-0.0012
	0.0777	-1.3253	0.0312
	-0.0027	-0.0066	-1.9347
Eig. Value:	-1.9615	-1.3159	-1.9345
O:	-1.9547	-0.0326	-0.0024
	-0.0274	-1.3605	0.0130
	0.0025	0.0582	-1.9488
Eig. Value:	-1.9568	-1.3569	-1.9504
O:	-1.9434	0.4340	0.0009
	0.4379	-1.8630	0.4628
	0.0664	0.3890	-1.9428
Eig. Value:	-2.4961	-1.2763	-1.9767