- ZIRCONIUM DIOXIDE - ZrO₂

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints), starting from a rutile-type structure.

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):	4.7840	4.7840		3.1790
Angles (°):	90.0	90.0		90.0

Cell contents:

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

Atomic positions (theoretical):

Zr:	0.0000	0.0000	0.0000
Zr:	0.5000	0.5000	0.5000
O:	0.3054	0.3054	0.0000
O:	0.1946	0.8054	0.5000
O:	0.6946	0.6946	0.0000
O:	0.8054	0.1946	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	106	106	106	106	5.814e+36 0.0	4.360e+36 0.0	1.017e+37 0.0
5	Eu	151	151	151	151
6	Eu	249	249	249	249
7	Eu	249	314	314	249
8	Eu	339	339	339	339
9	A2g	339	369	369	339
10	A2u	374	374	374	374
11	Eg	455	455	455	534
12	Eg	534	534	534	534	8.798e+40 27.9	9.348e+40 29.7	1.815e+41 57.6
13	B1u	534	534	534	549	8.798e+40 27.9	1.485e+41 47.1	2.364e+41 75.1
14	Eu	549	549	549	599
15	Eu	599	599	599	599
16	A1g	599	691	691	691
17	B2g	691	846	846	794	2.186e+41 69.4	9.642e+40 30.6	3.150e+41 100.0
18		858	858	858	858	8.059e+38 0.3	1.108e+39 0.4	1.914e+39 0.6

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥