ABINIT Discussion Forums

Dear colleagues,

My problem is the following: I've calculated the thermal expansion coefficient of SrO in NaCl phase. The shape of its behaviour with increasing T is adequate, but all the values are by 4 order of magnitude larger than usual (10^-5).

My rf calcs. (phonon freqs. - wj) are in a very good agreement with experiments and previous DFT calcs. Room temperature S and Cv are also in a very good agreement with exp. data.

To calc. the thermal expansion coefficient I used an equation (14) given in PRB 50, 17054 : (1/3B0)*SUM(gj*Cvj). It depends on B0 (equilibrium bulk modulus), gj (Grueneisen parameters) and Cvj (phonon contribution to the constant volume specific heat). For B0 I got close to previous results (it doesn't influence the results much). I gave it in J/Bohr^3. For gj I got the values between 2 and -4 (I have soft modes in NaCl phase). For gj I did finite difference of ln's, with freqs given in Ha and volumes in Bohr^3. Later I tried with freqs in Hz, but I got the same values. Cvj I got from equations (4) and (5) in PRB 68, 224304 : Cvj = k*exp(hbar*wj/k*T)*(hbar*wj/k*T * 1/(exp(hbar*wj/k*T)-1))^2. Boltzmann constant I gave in J/K, hbar in Js, T in K and wj in Hz.

Just to mention, when one uses expression (16) from PRB 50, 17054 for Cvj and explicitly does the T derivation, one gets the same formula as in PRB 68, 224304, except that an equilibrium volume V0 appears in the denominator besides B0 (so, its (1/3B0V0)...). But in this case, I think that units in the expression do not give K^-1 needed for the thermal expansion coefficient. But even including the volume here, the results are still 2 orders of magnitude too large. I think volume should be not here.

When all is summed up, I get the above problem. I just cannot find the source of it. I would appreciate any thought, criticism and ideas on this issue and my way of doing it.

Thank you all in advance!

Yours,
Igor Lukacevic

Hi Igor,

1) if you have soft modes, formally you should not be doing any thermodynamic integration (S, Cv, or the expansion coefficient...)
2) if this is not the problem, you probably have a missing conversion factor. More numerically, what is the difference between your curve and experiment? The Gruneisen parameters sound ok in magnitude, which leaves the Cvj - they should sum to Cv, correct? Is that the case? It looks strange that the Cvj have a factor of k out front. Transforming that to atomic units is tricky.

ciao

Matthieu

Hi Matthieu,

thanks for answering.

mverstra wrote:1) if you have soft modes, formally you should not be doing any thermodynamic integration (S, Cv, or the expansion coefficient...)

Why is it so? Is it because of the strongly negative Grun. parameters? Or some numerics in the expressions for them? But, then, how could I get a good results for Cv and S?

mverstra wrote:2) if this is not the problem, you probably have a missing conversion factor.

I'll check again, although I did that already I don't know how many times.

mverstra wrote:More numerically, what is the difference between your curve and experiment?

I don't know. I cannot find any exp. (or theor.) paper reporting this quantity.

mverstra wrote:The Gruneisen parameters sound ok in magnitude, which leaves the Cvj - they should sum to Cv, correct? Is that the case?

Correct. they sum up to Cv.

mverstra wrote:It looks strange that the Cvj have a factor of k out front.

How come it's strange? I looked at at least a dozen of papers reporting an expression for Cvj, and every one of them has a k in front.

mverstra wrote:Transforming that to atomic units is tricky.

Why atomic units? Shouldn't I be doing in SI system?


Igor

ilukacevic wrote:

mverstra wrote:More numerically, what is the difference between your curve and experiment?

I don't know. I cannot find any exp. (or theor.) paper reporting this quantity.

Sorry. Just found one on the web. Linear thermal exp. coeff. is 13.72x10^(-6) at around room temp. So, volumnic thermal coeef. would be about 3 times that, 41.16x10^(-6). And I get 0.364823

Igor

ilukacevic wrote:Why is it so? Is it because of the strongly negative Grun. parameters? Or some numerics in the expressions for them? But, then, how could I get a good results for Cv and S?

if you have imaginary modes the system is unstable - there is no way to attribute occupation statistics to negative energies, the instability should explode. Anaddb just ignores them, but this is incorrect formally. It could be that most of the Cv and S come from the other modes, but that would be luck.

ilukacevic wrote:How come it's strange? I looked at at least a dozen of papers reporting an expression for Cvj, and every one of them has a k in front.

Why atomic units? Shouldn't I be doing in SI system?

yes, I think it's fine. In SI it must be in J/K or something


Matthieu