stress report

[Dipankar Saha]

What does the [n x n] matrix (eV/ angs.³)signify...in stress report??
How come this is dependent on the k-point selection?

[zh]

Strongly suggest you to first understand the definition and concept of stress tensor:
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/stress.cfm
http://www.colorado.edu/MCEN/MCEN5023/chap_03.pdf
http://en.wikipedia.org/wiki/Cauchy_stress_tensor

The unit in eV/ angs^.3 for stress tensor can be easily converted to GPa, bar, and so on.

The calculated values for the stress tensor could be strongly dependent on the size of k-point mesh. Usually one has to do a convergence test for the size of k-point mesh before the production run.
You can refer to the following article:
O. Beckstein, J. E. Klepeis, G. L. W. Hart, and O. Pankratov, First-principles elastic constants and electronic structure of α−Pt2Si and PtSi
http://dx.doi.org/10.1103/PhysRevB.63.134112

[Dipankar Saha]

Thanks a lot  Zh.... for your reply and all those details...!! 

[Dipankar Saha]

So whatever that I have got... as per that... stress report is showing the Cauchy stress tensor (considering small deformations)... in which an infinitesimally small cube has been assumed around any internal point ('p').  Under static equilibrium...only nine stress components are need to describe the stress at 'p', ....and these nine components are eventually forming a 3x3 matrix (which is actually the stress tensor).
 
Is it correct....??
If yes..then I would like to ask you...

1) In the stress report that we get from ATK analysis....where the 'p' is taken? Is it any where within the material?

2) What is the "sign rule" followed for the individual elements of the 3x3 matrix ?
(Is it due to the positive or negative direction of the normal to a surface...../ or, due to the direction of the force of the internal traction?)

3) At static equilibrium, if the shear stresses across the diagonal normal stress elements are to be equal....
then can I ignore a small difference between sigma_xy and sigma_yx ...which are coming as  -1.14057696e-16 and -1.15893803e-16 eV/angs³ ... and consider them as equal ?

[zh]

For the queries about the basics of stress tensor, it is better to find out the answer in textbook by yourself. Otherwise, a simple answer here cannot help you to capture the whole background of stress tensor, strain,  pressure, and elastic constant and so on. 

1. The pressure  is usually taken as the average of sigma_ii (i=1,2, 3, i.e., xx, yy, zz), i.e., the diagonal terms.    
2. You can do a simple test calculation: calculate the stress tensor for  a cubic structure  at two different volumes (one is much smaller the equilibrium volume, and the other is much larger than the equilibrium volume). From the reported values including sign at these two different volume, you can get the "sign rule" for the definition of stress tensor used in the ATK.
3. At the equilibrium state of a given pressure, the non-diagonal terms are usually close to zero (i.e., very small value) and they can be neglected.

[Dipankar Saha]

Thank you Zh for those answers ....

Instead of beating around the bush... I always appreciate the specific answers for the specific questions....

Anyways back to the business...

In your reply (1) ... you said something different what I didn't ask for.... :p  / Anyhow I got the essence.... what you tried to mean....

Now, one last question regarding this topic....

i) Why 'eV' in "eV/ Angs^3" ...??

[zh]

The use of "eV/Ang^3" for stress tensor in output is just to be consistent with the default units of energy and length used in the code. No special reasons. As I said, one can easily convert eV/Ang^3 to GPa, bar, Pa, N/m^2, and so on.

Did you try  to convert "eV/Ang^3" into GPa?  Please try it by yourself!!!
1 eV/Angstrom3 = 160.2176487 GPa
http://greif.geo.berkeley.edu/~driver/conversions.html
http://www.unitconversion.org/unit_converter/pressure.html

[Dipankar Saha]

Thanks....