-    HAFNIUM DIOXIDE     -    HfO2

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):  4.7736  4.7736  3.1603 
Angles (°):  90.0  90.0  90.0 

Cell contents: 

Number of atoms: 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Hf:  0.0000  0.0000  0.0000 
O:  0.3048  0.3048  0.0000 
Hf:  0.5000  0.5000  0.5000 
O:  0.1952  0.8048  0.5000 
O:  0.6952  0.6952  0.0000 
O:  0.8048  0.1952  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
111
111
111
111
5
B1g
114
114
114
114
2.096e+37
0.0
1.572e+37
0.0
3.668e+37
0.0
6
Eu
234
234
234
234
7
Eu
234
241
241
234
8
Eu
252
252
252
252
9
Eu
252
347
347
252
10
A2g
386
386
386
386
11
A2u
415
415
415
531
12
B1u
531
531
531
551
13
Eg
551
551
551
551
4.961e+40
26.8
5.271e+40
28.5
1.023e+41
55.3
14
Eg
551
551
551
593
4.961e+40
26.8
8.372e+40
45.2
1.333e+41
72.0
15
Eu
593
593
593
593
16
Eu
593
717
717
717
17
A1g
717
814
814
741
1.307e+41
70.6
5.434e+40
29.4
1.851e+41
100.0
18
B2g
872
872
872
872
1.625e+39
0.9
2.235e+39
1.2
3.860e+39
2.1
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.