[Pw_forum] about elastic constant

[Michael Mehl]

Bipul Rakshit wrote:

> Dear Michael Mehl,
> I have read the two papers
> http://cst-www.nrl.navy.mil/users/mehl/papers/cij453.pdf
> 
> and
> 
> Phys. Rev. B 47, 2493 (1993)
> ,
> But my question is, they have given only two equation, and our unknown 
> quantity are 3 (C11, C12, and C44). So can we find three unknown 
> quantity from two equations acuratelly.

C44 is computed directly.

C' = C11-C12, or maybe 1/2 (C11-C12).

For a cubic crystal, B = (C11 + 2 C12)/3.

That's three equations for three unknowns.

C44 and C' are computed as outlined in Wang's paper, my papers, and 
elsewhere.  The bulk modulus is obtained from

B = V E''(V),

and you can compute the second derivative of the energy by finding the 
energy at several volumes and either using one of the many 
equation-of-state fitting codes available, or via numerical differentiation.

--
Michael J. Mehl, Naval Research Laboratory, Washington DC
On Sabbatical at Duke University until 31 July 2009