 # Stress tensor

Hello dear siesters) I am trying to calculate mechincal properties using some strains. As I understood I must to create some strain-stress situations. Can you tell me more about this procedure may be some underwater rocks that are important? Plus can you help me in siesta out file there two tensor stresses (1 is matrix 6x1 Stress-tensor-Voight(kbar) and another is Stress tensor (static) - and it is very low in my calculation). What stress tensor should I use for extracting suitable stress components?

Hi - For the kind of thing you want to do you have to be areful with the scale, and, if you do variable-cell relaxations, with the stress tolerance. Remember that pressures that can be large in other contexts can be minute for electronic structure calculations. So, you need to set up strains that are small enough for linear elasticity to be still valid, but large enough so that the obtained pressures are not too small, and thereby affected by technical “noises”. kbar is a good scale in general.

The two tensors you find should be the same, just different units, and one is given as a 3x3 2-rank tensor and the other is give in the Voigt notation, (11), (22), (33), (12), (13), (23), since any decent rotation-free strain should be symmetric.

Dear “Eartacho” thank you for your answer it helped a lot. We will be working in this direction. But where should I take C44 components in this tensors?

If you are referring to the elastic tensor (C44 component), that is a fourth rank tensor obtained from the derivative of the stress w.r.t. strain. This is a second derivative, not accessible to Hellmann-Feynman theorem, and not coded into Siesta. It can be obtained by either DFPT or finite differences. The latter can be done by a bespoke steering of conventional DFT runs, by which one applies a set of small finte strains and computes the corresponding stresses. Knowing the symmetry of the crystal you will need a number of such runs to get the appropriate number of distinct components of the elastic tensor. If you only need the C44, one well chosen deformation (or a few to remove noise and higher order devitations) would suffice. There are utilities automatising this, but I am no expert on them.

Dear eartacho thanks for the answer, I approximately represent the whole process; the only question is which of the coefficients in the tensors will correspond to C44?

If I remember correctly, the index 4 in the Voigt notation corresponds to the element (12) in the strain or stress tensor (or 21). So, 44 would mean 12,12 in the 4-rank tensor