Entropic contributions to entropy

[paulfons]

I have a couple of phases that I would like to compare the relative stability of with respect to pressure. I plan to do so via the enthalpy. I have calculated the change in enthalpy H as a function of applied pressure for each phase without problem using Vasp. I have also calculated the thermal properties using phonopy-qha (quasi harmonic approximation) to solve for Cp at equilibrium. I am planning to add the phonon related enthalpic contributions by adding the int(Cp dT) to calculate delta H. I can calculate from a Maxwell relation that (dCp/dP)T is -T(d^2 V/dT^2)P, but while I have calculated the expansion coefficient using phonopy-qha, it is not as trivial to calculate the second derivative of the coefficient of expansion with respect to temperature. Looking at the term, it seems likely to be small. I am curious if anyone has experience with this and would it be fair to assume that Cp is pressure independent to 10 kB or so? Thanks for any advice in advance.