- BROOKITE - TiO₂

Theoretical atomic positions and lattice parameters at experimental volum from 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:	61		Pbca
Lattice parameters (Å):	9.1740	5.4490		5.1380
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	61		Pbca
Lattice parameters (Å):	9.1696	5.4410		5.1480
Angles (°):	90.0	90.0		90.0

Cell contents:

Number of atoms:	24
Number of atom types:	2
Chemical composition:	0

Atomic positions (theoretical):

Ti:	0.1289	0.0984	0.8622
O:	0.0114	0.1473	0.1824
O:	0.2292	0.1081	0.5343
Ti:	0.3711	0.9016	0.3622
O:	0.4886	0.8527	0.6824
O:	0.2708	0.8919	0.0343
Ti:	0.8711	0.5984	0.6378
O:	0.9886	0.6473	0.3176
O:	0.7708	0.6081	0.9657
Ti:	0.6289	0.4016	0.1378
O:	0.5114	0.3527	0.8176
O:	0.7292	0.3919	0.4657
Ti:	0.8711	0.9016	0.1378
O:	0.9886	0.8527	0.8176
O:	0.7708	0.8919	0.4657
Ti:	0.6289	0.0984	0.6378
O:	0.5114	0.1473	0.3176
O:	0.7292	0.1081	0.9657
Ti:	0.1289	0.4016	0.3622
O:	0.0114	0.3527	0.6824
O:	0.2292	0.3919	0.0343
Ti:	0.3711	0.5984	0.8622
O:	0.4886	0.6473	0.1824
O:	0.2708	0.6081	0.5343

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.

Powder Raman

Powder Raman spectrum

The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm^-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.

Choose the polarization of the lasers.

I ∥

I ⊥

I Total

Horizontal:

Xmin:
Xmax:

Vertical:

Ymin:
Ymax:

Data about the phonon modes

Frequency of the transverse (TO) and longitudinal (LO) phonon modes in the zone-center. The longitudinal modes are computed along the three cartesian directions. You can visualize the atomic displacement pattern corresponding to each phonon by clicking on the appropriate cell in the table below.

1	ac	0	0	0	0
2	ac	0	0	0	0
3	ac	0	0	0	0
4	A1g	126	126	126	126	1.838e+41 6.8	1.151e+41 4.2	2.988e+41 11.0
5	B3g	127	127	127	127	2.571e+41 9.5	3.535e+41 13.0	6.106e+41 22.5
6	Au	128	128	128	128
7	A1g	144	144	144	144	1.978e+42 72.9	7.358e+41 27.1	2.713e+42 100.0
8	B1g	156	156	156	156	4.871e+40 1.8	6.698e+40 2.5	1.157e+41 4.3
9	B2u	159	159	159	159
10	B2g	165	165	165	165	3.073e+40 1.1	4.225e+40 1.6	7.297e+40 2.7
11	B2u	175	175	176	175
12	B3u	184	187	184	184
13	A1g	196	196	196	196	2.415e+39 0.1	3.032e+38 0.0	2.718e+39 0.1
14	B1u	205	205	205	212
15	B3g	212	212	212	213	2.966e+40 1.1	4.078e+40 1.5	7.045e+40 2.6
16	B2g	213	213	213	219	3.759e+40 1.4	5.168e+40 1.9	8.927e+40 3.3
17	B1u	223	223	223	227
18	B2u	227	227	229	229
19	B3u	229	235	235	235
20	A1g	235	237	237	237	5.855e+41 21.6	2.893e+41 10.7	8.747e+41 32.2
21	B1g	237	241	241	241	2.716e+40 1.0	3.734e+40 1.4	6.450e+40 2.4
22	Au	241	279	279	279
23	Au	279	279	279	279
24	B3g	279	280	280	280	1.085e+40 0.4	1.492e+40 0.5	2.577e+40 0.9
25	B1u	280	282	282	282
26	B2g	282	290	290	290	2.745e+41 10.1	3.774e+41 13.9	6.519e+41 24.0
27	Au	290	305	305	294
28	B3g	305	310	315	305	7.140e+41 26.3	9.818e+41 36.2	1.696e+42 62.5
29	B2g	315	315	316	315	9.837e+40 3.6	1.353e+41 5.0	2.336e+41 8.6
30	Ag	316	316	317	317	8.685e+38 0.0	3.833e+38 0.0	1.252e+39 0.0
31	Ag	317	317	321	321	1.480e+41 5.5	6.531e+40 2.4	2.133e+41 7.9
32	B1g	321	321	332	332	1.880e+41 6.9	2.585e+41 9.5	4.466e+41 16.5
33	B3u	332	341	342	342
34	B3u	342	346	346	346
35	Au	346	356	353	356
36	B1g	356	362	356	362	3.998e+41 14.7	5.497e+41 20.3	9.495e+41 35.0
37	B2g	362	370	362	364	4.359e+40 1.6	5.994e+40 2.2	1.035e+41 3.8
38	B2u	370	374	374	370
39	Au	376	376	376	376
40	B1u	377	377	377	384
41	B1g	384	384	384	398	3.822e+40 1.4	5.256e+40 1.9	9.078e+40 3.3
42	B3u	398	402	398	402
43	B2u	402	410	410	410
44	A1g	410	414	414	414	1.584e+41 5.8	1.149e+41 4.2	2.733e+41 10.1
45	B3g	414	434	434	434	6.497e+40 2.4	8.934e+40 3.3	1.543e+41 5.7
46	B3g	434	438	443	434	3.311e+40 1.2	4.552e+40 1.7	7.863e+40 2.9
47	B3u	443	444	444	443
48	B1g	444	452	452	444	4.306e+41 15.9	5.921e+41 21.8	1.023e+42 37.7
49	B2g	452	467	467	452	1.101e+41 4.1	1.514e+41 5.6	2.614e+41 9.6
50	B1g	467	470	470	467	6.392e+37 0.0	8.789e+37 0.0	1.518e+38 0.0
51	Au	470	470	470	470
52	B1u	470	477	471	477
53	A1g	477	483	477	483	4.650e+40 1.7	3.231e+40 1.2	7.881e+40 2.9
54	B2u	483	487	488	488
55	B3g	488	488	491	491	2.724e+41 10.0	3.745e+41 13.8	6.469e+41 23.8
56	B2g	491	491	502	491	9.140e+38 0.0	1.257e+39 0.0	2.171e+39 0.1
57	B3u	502	512	512	502
58	B3g	512	520	520	512	1.229e+40 0.5	1.690e+40 0.6	2.919e+40 1.1
59	B1u	520	536	536	536
60	A1g	536	542	537	542	1.133e+42 41.8	2.061e+41 7.6	1.340e+42 49.4
61	Au	542	559	542	559
62	B1g	559	574	559	574	2.767e+41 10.2	3.804e+41 14.0	6.571e+41 24.2
63	B2u	574	599	599	599
64	B2g	599	622	622	622	2.069e+41 7.6	2.844e+41 10.5	4.913e+41 18.1
65	A1g	622	632	632	632	1.658e+42 61.1	3.446e+41 12.7	2.002e+42 73.8
66	Au	632	645	644	645
67	B2u	645	740	740	740
68	B1g	740	784	784	759	2.062e+39 0.1	2.835e+39 0.1	4.897e+39 0.2
69	B3g	784	786	794	784	3.653e+40 1.3	5.023e+40 1.9	8.676e+40 3.2
70	B2g	794	794	806	794	2.072e+37 0.0	2.849e+37 0.0	4.920e+37 0.0
71	B3u	806	833	809	806
72	B1u	833	836	833	844

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥