- ANATASE - TiO₂

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:	141		I4_1/amd
Lattice parameters (Å):	3.7842	3.7842		9.5146
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	141		I4_1/amd
Lattice parameters (Å):	5.3148	5.3148		5.3148
Angles (°):	138.6	138.6		60.0

Cell contents:

Number of atoms:	6
Number of atom types:	2
Chemical composition:	0

Atomic positions (theoretical):

Ti:	0.0000	0.0000	0.0000
O:	0.2106	0.2106	0.0000
Ti:	0.7500	0.2500	0.5000
O:	0.9606	0.4606	0.5000
O:	0.5394	0.0394	0.5000
O:	0.7894	0.7894	0.0000

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	Eg	191	191	191	191	2.157e+41 14.9	2.955e+41 20.4	5.111e+41 35.3
5	Eg	191	191	191	191	2.139e+41 14.8	2.952e+41 20.4	5.092e+41 35.2
6	Eg	215	215	215	215	4.356e+41 30.1	6.000e+41 41.5	1.036e+42 71.6
7	Eg	215	215	215	215	4.403e+41 30.4	6.044e+41 41.8	1.045e+42 72.2
8	Eu	299	299	299	299	1.721e+38 0.0	2.106e+38 0.0	3.827e+38 0.0
9	Eu	299	368	368	299	1.037e+38 0.0	1.166e+38 0.0	2.203e+38 0.0
10	B1g	417	417	417	417	3.361e+41 23.2	2.521e+41 17.4	5.881e+41 40.7
11	A2u	446	446	446	552	3.697e+37 0.0	1.624e+37 0.0	5.321e+37 0.0
12	Eu	552	552	552	552	1.329e+38 0.0	1.663e+38 0.0	2.992e+38 0.0
13	Eu	552	558	558	558	2.275e+37 0.0	2.559e+37 0.0	4.834e+37 0.0
14	A1g	558	565	565	565	9.543e+41 66.0	1.340e+41 9.3	1.088e+42 75.2
15	B1g	565	586	586	586	2.541e+41 17.6	1.906e+41 13.2	4.447e+41 30.7
16	B2u	586	720	720	720
17	Eg	720	720	720	720	6.087e+41 42.1	8.373e+41 57.9	1.446e+42 100.0
18	Eg	720	927	927	786	6.093e+41 42.1	8.375e+41 57.9	1.447e+42 100.0

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥