In a previous tutorial, we have calculated the elastic properties of TiO2 compound using an indirect way through 4 steps (How to calculate the Elastic Constants of TiO2 in tetragonal structure). In this tutorial, we will use a new task developed in the new version of 2025.  


There are 2 ways to use this new task: 

1- Perturbation theory

2- Finite displacement 


1- Perturbation theory: DFPT 

TiO2-LDA.cell

#TiO2.cell
%BLOCK LATTICE_ABC
 4.552678  4.552678  2.916623
90.000000 90.000000 90.000000
%ENDBLOCK LATTICE_ABC

%BLOCK POSITIONS_FRAC
O    0.304078   0.304078  -0.000000
O    0.804078   0.195922   0.500000
O    0.195922   0.804078   0.500000
O    0.695922   0.695922  -0.000000
Ti   0.000000   0.000000   0.000000
Ti   0.500000   0.500000   0.500000
%ENDBLOCK POSITIONS_FRAC

%block species_pot
   NCP19
%endblock species_pot

symmetry_generate

kpoint_mp_grid 4 4 4


TiO2-LDA.param

#TiO2.param
 task             : geom opt
#task             : elastic
 cutoff_energy    : 1000 eV
 xc_functional    : LDA_PW
 max_scf_cycles   : 100
 opt_strategy     : memory
 num_dump_cycles  : 0

elec_energy_tol   : 1.0E-9 eV
geom_force_tol    : 1.0E-3 eV/ang
#continuation      : default


Steps of calculation

Task 1: Perform a variable cell geometry optimization. Test the kinetic energy cut-off and k-point grid such that the force is converged to within the default geom_force_tol value. 

$ mpirun -np 4 castep.mpi TiO2-LDA

Task 2: Make the following modification to the param file

#task             : geom opt
 task             : elastic
 ........
 .........
continuation      : default


The continuation option used in the param file means that the optimized structure is read from the check file and there is no need to update the cell file which still contains the old structure.

This calculation is tested with LDA_PW xc-functional and there are some queries with the PBE xc-functional on the rutile compound. 

$ mpirun -np 4 castep.mpi TiO2-LDA


We got the following elastic constants from the file TiO2-LDA.elastic

===============================================================================
           Elastic Constants Tensor (Frozen Ion) (GPa)
  -------------------------------------------------------------------------------
     339.156774   174.252050   174.043905     0.000000     0.000000
0.000000
     174.252050   339.156774   174.043905     0.000000     0.000000
0.000000
     174.043905   174.043905   530.753440     0.000000     0.000000
0.000000
       0.000000     0.000000     0.000000   151.088284     0.000000
0.000000
       0.000000     0.000000     0.000000     0.000000   151.088284
0.000000
       0.000000     0.000000     0.000000     0.000000     0.000000
227.078481
  ===============================================================================


1- Finite displacement

TiO2-PBE.cell

#TiO2.cell
%BLOCK LATTICE_ABC
 4.552678  4.552678  2.916623
90.000000 90.000000 90.000000
%ENDBLOCK LATTICE_ABC

%BLOCK POSITIONS_FRAC
O    0.304078   0.304078  -0.000000
O    0.804078   0.195922   0.500000
O    0.195922   0.804078   0.500000
O    0.695922   0.695922  -0.000000
Ti   0.000000   0.000000   0.000000
Ti   0.500000   0.500000   0.500000
%ENDBLOCK POSITIONS_FRAC

%block species_pot
   NCP19
%endblock species_pot

symmetry_generate

kpoint_mp_grid 8 8 12


TiO2-PBE.param

#TiO2.param
 task             : geom opt
# task             : elastic
 cutoff_energy    : 1000 eV
 xc_functional    : PBE
 max_scf_cycles   : 100
 opt_strategy     : memory
 num_dump_cycles  : 0
 fine_grid_scale  : 4.0

elec_energy_tol   : 1.0E-9 eV
geom_force_tol    : 4.0E-3 eV/Ang
#elastic_method    : FINITEDISPLACEMENT
WRITE_CELL_STRUCTURE    : true


Steps of calculation

Task 1: Perform a variable cell geometry optimization. Test the kinetic energy cut-off and k-point grid such that the force is converged to within the default geom_force_tol value. 

$ mpirun -np 4 castep.mpi TiO2-PBE

Task 2: Make the following modification to the param file

# task             : geom opt
 task             : elastic
 .....
 .....
elastic_method    : FINITEDISPLACEMENT


Since the continuation option is not used in the param file means that we need to use the optimized structure in the cell file as follows:

$ mv TiO2.cell TiO2_old.cell
$ cp TiO2_out.cell TiO2.cell

 

Which gives the following content of the TiO2.cell 

#TiO2.cell
#8x8x12
%block lattice_abc
    4.64430546629963 4.64430546629963 2.96566885567127
   90.0             90.0             90.0
%endblock lattice_abc

%BLOCK positions_frac
   O                0.305199369651207       0.305199369651207       0.000000000000000
   O               -0.305199369651207      -0.305199369651207       0.000000000000000
   O                0.805199369651207       0.194800630348793       0.500000000000000
   O               -0.805199369651207      -0.194800630348793       0.500000000000000
   Ti               0.000000000000000       0.000000000000000       0.000000000000000
   Ti               0.500000000000000       0.500000000000000       0.500000000000000
%ENDBLOCK positions_frac

%block species_pot
#   NCP19
O  O_NCP19_PBE_OTF.usp
Ti Ti_NCP19_PBE_OTF.usp
%endblock species_pot

symmetry_generate

kpoint_mp_grid 8 8 12

%block phonon_kpoint_list
0 0 0
%endblock phonon_kpoint_list

 


$ mpirun -np 4 castep.mpi TiO2-PBE

 

We got the following elastic constants from the file TiO2-PBE.elastic

===============================================================================
           Elastic Constants Tensor (GPa)
  -------------------------------------------------------------------------------
     338.699402   173.646861   173.435554     0.000000     0.000000
0.000000
     173.646861   338.699402   173.435554     0.000000     0.000000
0.000000
     173.435554   173.435554   530.112817     0.000000     0.000000
0.000000
       0.000000     0.000000     0.000000   150.926612     0.000000
0.000000
       0.000000     0.000000     0.000000     0.000000   150.926612
0.000000
       0.000000     0.000000     0.000000     0.000000     0.000000
226.667229
  ===============================================================================

 

Reference:  You can compare the results with the following