[Pw_forum] Free energy w.r.t. T and QHA

[degironc]

In order to calculate the static equilibrium one calculates the energy 
E(a) as a function
of the structural parameters (these can be just the lattice parameter  
for simple
elementary solids or include several internal coordinates for more 
complex solids
or surface coordinates if you look to surfaces) and search for the minimum.
This however does not contain in any way the effect of temperature, not 
even the
Zero-Point Energy.
In QHA you do the same thing. You calculate the free-energy, F(T,a), as 
a function
of the structural parameters and search for the minimum. This provides 
you with
a reasonable approximation of structural thermal effects (that is 
thermal expansion)
if you are well below melting point. You can the estimate thermal effect 
on vibrational,
elastic and electronic properties as well ... to the extent they are 
associated with the
stuctural change and not to "truly anharmonic effects" beyound QHA.

You may find interesting/clarifying to have a look to
M.Lazzeri, and S.deGironcoli, Phys. Rev. B65, 245402 (2002),"A first 
principles study of the thermal expansion of Be (1 0 1_bar 0)"
M.Lazzeri, and S.deGironcoli, Phys. Rev. Lett. 81, 2096 (1998), 
"Ab-Initio Study of Be (0001) Surface Thermal Expansion"

hope this helps,
 stefano

W. YU wrote:

>Dear PW users,
>
>I have found that any code capable of phonon
>calculation (including PWscf-phonon)) would calculate
>the curve of F as a function of T under the framework
>of qausi-harmonic approximation (QHA).
>
>My question is: Is this calculation (F as a function
>of T)of any real significance? Since under QHA, free
>energy F is a funciton of temperature T and volume V.
>In a real situation, the system volume would change
>with temperature T, so does the phonon spectrum. Thus,
>in calculation of F(T) curve, we need phonon spectrum
>at each specific T which is sure different under QHA.
>This is for sure not the practice done by any codes. F
>is simply calculated with only a specific set of
>spectra (usually the spectra at static equilibrium
>geometry). It is understandable if this sort of
>calculation neglects the thermal expansion, but we
>will end up with harmonic approxiation then.
>
>Yes, from my own experience, the changes of phonon
>spectrum are small w.r.t. volume, but at least in
>principle it should be accounted for.
>
>Anybody interested? plase give some comments,thanks!
>
>W. YU  
>
>
>
>
>
> 
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