[Pw_forum] about elastic constant

[Bipul Rakshit]

Dear Michael Mehl,
I am calculating elastic constant of Mg2Si (C11=126, C12=26, C44=48)
experimental.
Now using the formula by S. Q. Wang, H. Q. Ye, J. Phys. condense matter.
using all the three equation, i am getting, 109, 25, 47 (C11,  C12, C44)
respectively.

But using only Eq. (6) and (7) only, I am getting 121, 20, 47 GPa,
So can you please elaborate, whether, by using two equations, and by fitting
the graphs, is it correct to find all the three elastic constants?

On Fri, Jul 17, 2009 at 2:27 AM, Michael Mehl <rcjhawk at gmail.com> wrote:

> 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
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-- 
Bipul Rakshit
PhD Student,
Barkatullah University,
Bhopal 462026,
MP, India
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