# Problem related to the calculation of elastic constant with VASP5.4.4

I am using VASP5.4.4 to calculate the mechanical properties of the cubic phase SnTe. The structure can be found in the materials project website.

In detail, I use the following INCAR to calculate the elastic constants of the primitive cell (2 atoms) and the conventional cell (8 atoms) of SnTe.

System:
ISTART=0                       !startjob: 0-new 1-cont 2-samecut
ICHARG=2                       !charge: 1-file 2-atom 10-const
ENCUT=400                      !energy cutoff in eV
EDIFF=1E-5                     !stopping-criterion for electronic upd.
#NELM=300                      !nr. of electronic steps
ISMEAR=0                       !part. occupancies: -5 Blochl -4-tet -1-fermi 0-gaus 0 MP
SIGMA=0.05                     !broadening in eV -4-tet -1-fermi 0-gaus

Dynamic:
PREC=Accurate
ISIF=3
IBRION=6
NFREE=4
POTIM=0.015
SYMPREC=1E-8


The results for the two cells is shown below:

Primitive cell ($$\alpha=\beta=\gamma=60^\circ$$;$$a=b=c$$;2 atoms):

TOTAL ELASTIC MODULI (kBar)
Direction    XX          YY          ZZ          XY          YZ          ZX
--------------------------------------------------------------------------------
XX         754.4756    162.3949    290.3213     -0.0000   -180.9152     -0.0000
YY         162.3949    754.4756    290.3213     -0.0000    180.9152     -0.0000
ZZ         290.3213    290.3213    626.5492     -0.0000      0.0000     -0.0000
XY          -0.0000     -0.0000     -0.0000    296.0404     -0.0000   -180.9152
YZ        -180.9152    180.9152      0.0000     -0.0000    423.9667     -0.0000
ZX          -0.0000     -0.0000     -0.0000   -180.9152     -0.0000    423.9667
--------------------------------------------------------------------------------


Conventional cell ($$\alpha=\beta=\gamma=90^\circ$$;$$a=b=c$$;8 atoms):

 Direction    XX          YY          ZZ          XY          YZ          ZX
--------------------------------------------------------------------------------
XX        1140.9524     43.2055     43.2055      0.0000      0.0000     -0.0000
YY          43.2055   1140.9524     43.2055      0.0000      0.0000      0.0000
ZZ          43.2055     43.2055   1140.9524      0.0000      0.0000     -0.0000
XY           0.0000      0.0000      0.0000    164.8906      0.0000      0.0000
YZ           0.0000      0.0000      0.0000     -0.0000    164.8906     -0.0000
ZX          -0.0000      0.0000     -0.0000      0.0000     -0.0000    164.8906
--------------------------------------------------------------------------------

• Why the results of the primitive cell are different from the conventional cell? They are both cubic phase SnTe.

• For the cubic phase system, there are only four independent elastic constants. It seems that the results of the conventional cell are correct. However, the results of the primitive cell are like the trigonal system because there are six independent elastic constants. What am I missing here?

Conventional cell is the unit cell where the symmetry is properly defined whereas, primitive cell may not always indicate the actual symmetry. For example, FCC is a proper conventional unit cell but its primitive cell looks like a rhombohedron. Again, the lattice parameters of both cells are different (From materials project- conventional = 6.417 angstrom, primitive = 4.537 angstrom). A quick google search would show the lattice parameter of SnTe to be in the range of 6.302–6.327 angstrom. Distance between the atoms can directly affect the elastic property. Hence, the difference in the elastic constant values. It would be better to consider the conventional unit cell for calculation (as it has both symmetry and lattice parameter closer to the experimental value).

Hope it helps.

• I agree with you about the symmetry arguments. But I think the distance between the atoms is the same in primitive cell and conventional cell.
– Jack
Nov 26 '20 at 21:58
• My mistake. I think it should be the bonding characteristics i.e the influence of other atoms on a particular atom (different for conventional and primitive unit cell because of the numbers of atoms present in them) will affect the elastic property. Nov 28 '20 at 10:53

Based on symmetry of the simulation cell, vasp algorithm distort the unit cell. Distortion change the energetics and stress of unit cell which in turn gives us stress strain relationship,further algorithm uses this relation for calculating elastic constants. As your simulation box symmetry is different, you are getting different distortion which is resulting in two different results. Its always good to use conventional cell for calculating elastic constants. Let me discuss on more thing that, we often encounter discrepency in results while using IBRION=6 , I suggest you to stick with more conventional way of using strain-energy relation for calculating elastic constants.

• What's the difference or relationship between both cells?
– Jack
Nov 28 '20 at 14:53
• Just think about equivalent distorsion required by primitive cell and conventional cell based on symmetry. Inspire of focussing on Vasp, think why fcc should have 3 independent elastic constant while other symmetry don't have. Nov 29 '20 at 18:14