Dear Zahir Muhammad 

Have a nice time and good day

You should mention some details about your studied samples to help you.

Generally, you can use a hydrostatic piston or compressor of known pressure. 

Good luck

Regards

Dear Dr. Ahmed Saeed Hassanien; thank you for your reply. I am doing DFT calculation using VASP basically I want to check the variation in variations of band gap

(Eg) and the energy difference (DE) between deformed and undeformed the monolayers as functions of uniform strain. I want to check the change in Eg with the increasing compressive strain for both PBE and HSE06 techniques of vasp.

Dear Zahir,

I don't know VASP but it should be fairly straightforward. All you have to do is apply the strain (by reducing the lattice constants by a fixed percentage), perform a fixed-cell geometry optimisation (to relax the ionic positions), and compute the stress at the end. That gives you the stress-strain relationship for this particular strain, so all you do is repeat over the strain range you're interested in. A few things to watch out for:

a) Depending on the sign convention used by the code, your computed stress will probably be minus the stress you want -- you want the external stress that, when applied, would give this strain, but most codes will give you the internal stress that arises from the cell itself when you strain it;

b) If your system passes through a phase transition at these pressures/strains then you probably won't capture that correctly. As a first step, you can slightly perturb the atomic positions, so that the forces aren't zero by symmetry, and this will allow spontaneous symmetry-breaking. This would capture transitions like the ferroelectric distortions in SrTiO3 etc. In general, however, you would need to do a separate E-P or E-V plot  for each phase, to determine where the transitions are.

Hope that helps,

Phil Hasnip 

Thank you Dr. Phil Hasnip for your interesting informative answer I understand your answer and I will to do it.  

Philip James Hasnip thanks for your reply to this query.

my queries are:-

1. Can we change only one lattice direction? i.e. say 'a' only?

2. I saw published data of band-gap variation versus strain (tensile and compressive strain). That means for each such variation of a and b directions of same percentage, the band-gaps(PBE) were calculated?

3. Is it essential to get Strain-Stress relations ship? and by the way How to get the stress value after changing the lattice constants? [like you said fixed cell optimisation. do we need to do a static run after optimisation, in VASP?]

Regards

SK M Like I said, I don't know much about VASP but I'll try my best.

1. Yes, changing one (or some) of the lattice parameters should be fine.

2. Usually people plot this for isotropic strain, unless they're actually interested in deformation potentials

3. It's not essential, but it gives you a good energy-volume/energy-strain curve that you can check. It's hard to determine that you've done everything correctly for the eigenvalues, but for the total energy you can usually find other studies to check.

As for how to get the stress, I don't know. In my own code (CASTEP) I'd just set "calculate_stress : true" in the input .param file, but I've no idea how VASP does it, I'm afraid.

Thanks a lot Philip James Hasnip . Just after writing to you i have checked my lattice match values for a hetero structure [perovskite-charge transport layer]. i found that the mismatch is different in a and b directions (most cases it will be so, unless cubic lattice). my intention is to only observe PBE bandgap variation, CBM and VBM positions of 2D material in the structure. Now i am bit worried what other factors that might influence the charge transport due to this mismatch. Any thoughts based on your experience?

Thank you.