[Wien] possible pressure-induced transition(find DeltaG)

[Víctor Luaña Cabal]

On Thu, Mar 13, 2014 at 09:43:02PM -0700, MAHDI SALMANI HIRMAND wrote:
> Dear Prof. Blaha,
> I am studying possible pressure-induced transition for some compounds.
> stefaan guide me how i can calculate Gibbs energy and find the pressure.
> 
> He told me "you can easily calculated the enthalpy H=E+PV using
> case.eosfit and case.eosfitb. Repeat for the second phase, and see
> at which pressure the two enthalpy curves intersect."  > > i did it
> but the two enthalpy > curves are almost the same and it is difficult
> finding the position > which two enthalpy curves intersect.  > usually
> in paper they find difference of enthalpy energy from two phases and >
> therefore the pressure which in it DeltaG or DeltaH=0

This is appraching a tutorial. Mr. X, can you help me to do my
homework? I'm solving this difficult problem and there are not authomatic
tools. What can I do.

Answer: Try to learn a little.

QUESTION: how i can calculate Gibbs energy and find the pressure?

ASUMPTION: Do you already have The E(V) curve por several volumes.

POINTS: 1) In highly symmetrical phases the volume is directly related
to a lattice parameter and all internal positions of the atoms are fixed
by symmetry. Crystalographers would say the atoms are occupying Wykoff
positions of multiplicity 1.

2) In less symmetric phases there are other degrees of freedom. Let
us call them $\vec{x}$. If you have some formation on crystallography
(and the problem you are asking for is a crystallography problem). in
that systems you must solve the problem

$E(V) = \min_{\vec{x}}^{V=V_0} E(V,\vec{x})$

and build a table of E versus V. In all points keeping the SAME
crystallographic structure The same solid state phase.

Then introducing the effect of pressure is trivial. You decide it. If
p=10 GPa the Gibbs energy is:

G(p) = E(V) + pV

To reflect all the thermodynamic variables that influence the problem:

$G(p,T) = E(V(\vec{x})) + pV(\vec{x}) - TS(\vec{x})$

If you are interested in pressure-driven phase transitions you can assume
T=0~K. Of course, thermal effects are important. Peter Debje (Debye if
you follow the way he decided to write his name when travaling to US)
dis reseach on that and you can study the result of his research and
learn a little more looking for the seminal paper of the GIBBS code.
In fact, using the gibbs code you can transform the E(V) data in a
G(p,T) estimation. If you have the more complete E(V) + vibronic spectra
($\vec{x}$) you can use the gibbs2 code, ...