elastic constants of hcp structure

[skaram]

Hi,
i m trying to calculate the elastic constants (C11, C12, C13, C33, C44) of TiB2(hcp structure), so i can calculate the bulk modulus. I used five different deformations (from some papers), which i imposed on the equilibrium lattice of the unit cell. For each situation i applied 6 deformations (-3%, -2%, -1%, 1%, 2%, 3%) to the right coordinates and vectors and i calculated the energies using IBRION=2 (relax ions) & ISIF=4 (keep cell volume unchanged) . Then i used a 3rd order polynomial fit in order to determine the values needed for the calculation of the elastic constants. The problem is that the values of the calculated elastic constants differ a lot from previous published work and are probably wrong. Am i doing something wrong in the procedure of relaxing the structures or there is a problem in the whole procedure that i am using?
Thank you in advance,
Stelios K

[metosa]

I think you should use finer mesh.

i.e. 3%, -2.9%, -2.8%, -2.7%.....

also for elastic region, you should try -2% +2%

[forsdan]

At first stage the size of the mesh is not the most important thing to check. First please make sure that you perform the cell deformation correctly. Secondly, you shouldn't allow the cell shape to change during relaxation since the shape is defined by the deformations. So for each deformation please only relax the internal degrees of freedom by putting ISIF = 2 in combination with IBRION = 2. In addition please make sure that you are converting the elastic cost per volume correctly from eV/Angstroms^3 into Pa (or bar). Finally you can then start to consider using a finer mesh.

Depending on the specific deformation you're using you can have deviations from the second-order elastic-energy behavior in form of contributions being fourth order of the strain. So I would recommend to use a higher order for the polynomial fit (at least four). (If these contributions are of the third order only, the fourth-order term in the fit will be zero anyway.)

When you are comparing to other values, please notice that DFT results for the elastic constants can differ both from the experimental values as well as between different exchange-correlation-functionals (e.g. LDA vs GGA). So if possible first compare to other DFT data which have been extracted using the same parameters as you have used. Then you can go on and compare to experimental data.

Hope this helps.

Best regards,
/Dan Fors








<span class='smallblacktext'>[ Edited Wed Dec 30 2009, 12:06AM ]</span>

[skaram]

Hi,
well thank you for your replies. I did as you said, using the right value for ISIF and creating a finer mesh for deformations: -2% to 2% with a 0.2% step. The results were quite good for the elastic constants. The only problem as it seems is that the resulting value for C12 is negative. Is there a physical explanation for this, or is it again because there is something wrong in my calculations? I also calculated the bulk and elastic modulus for the above calculated elastic contants and the results were 275 GPa for bulk and 815 GPa for the elastic modulus.

P.S. i am using a USPP/LDA standard potentials.
Thank you again,
Stelios K