- RUTILE - TiO₂

Experimental structure. Atomic position and lattice parameters 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:	136		P4_2/mnm
Lattice parameters (Å):	4.5870	4.5870		2.9540
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	136		P4_2/mnm
Lattice parameters (Å):	4.5870	4.5870		2.9540
Angles (°):	90.0	90.0		90.0

Cell contents:

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

Atomic positions (theoretical):

Ti:	0.0000	0.0000	0.0000
Ti:	0.5000	0.5000	0.5000
O:	0.2984	0.2984	0.0000
O:	0.7016	0.7016	0.0000
O:	0.2016	0.7984	0.5000
O:	0.7984	0.2016	0.5000

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	B1u	134	134	134	134
5	B1g	181	181	181	181	5.530e+39 0.2	4.148e+39 0.1	9.678e+39 0.3
6	A2u	211	211	211	257
7	E1u	257	257	257	257
8	E1u	257	380	380	413
9	B1u	413	413	413	421
10	E1g	421	421	421	421	5.061e+41 16.7	8.541e+41 28.2	1.360e+42 44.8
11	E1g	421	421	421	426	5.061e+41 16.7	5.377e+41 17.7	1.044e+42 34.4
12	E1u	426	426	426	426
13	E1u	426	426	426	426
14	A2g	426	465	465	501
15	E1u	501	501	501	501
16	E1u	501	565	565	565
17	A1g	565	809	809	733	2.126e+42 70.1	9.069e+41 29.9	3.033e+42 100.0
18	B2g	809	826	826	809	2.358e+39 0.1	3.242e+39 0.1	5.600e+39 0.2

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥