-    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: 


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.

Parameters of the Calculation 

All the calculations have been done using the ABINIT software. This is a list of the most representative parameteres used during the Raman calculation.

Number of electronic bands: 26
   grid: 4 4 8 
   number of shifts: 
   shifts: 0.5 0.5 0.5 
Kinetic energy cut-off: 38 Ha  [=1034.0408 eV ]
eXchange-Correlation functional: LDA pw90 

Hf:  hafnium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 1 local 
O:  oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local