-    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: 
Number of atom types: 
Chemical composition: 

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: 

Size:

  
Nx:  Ny:  Nz:    
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.

Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
 
Choose the polarization of the lasers.
I ∥ 
I ⊥ 
I Total 

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 ⊥  I Total 
You can define the size of the supercell for the visualization of the vibration.
Nx: 
Ny: 
Nz: 
Normalized
Raw
Options for intensity.