I computed the miscibility gaps of the Cr-Mo alloy system with and without vibrational contributions. The vibrational entropy is considered by using the length dependence transferable force constants approach. The result (1720 K) without vibrational effect is large different from the one with vibrational effect (1150 K). I am wondering how does the result compare to that if one used the (rather basic but straighforward) formula Delta F = Delta <E> average - TS(ideal mixing) (SchM-CM-6n et al., Phys. Chem. Chem. Phys. 8:1778 (2006) for the free energy difference between the (disordered) alloy phases. Is the result obtained by ATAT taken more into account the configurational entropy? Thanks very much in advance.
Sorry I don’t see this formula in the paper and, actually, I don’t understand how it could work (the S(ideal) term seems out of place).
In any case, it looks like a perturbative expression, valid for small differences in free energies (but I need to see the exact formula to be sure!).
Thanks for your quick response. The aboved question was given by other people and I also donot see the exact formula in the reference. Let me check it and sorry for the inconvenience.
I have one more question and I wish it would not take you much time.
Concerning the semi-grand canonical MC simulations employed to compute the miscibility gap of the Cr-Mo system, the chemical potential difference <mu> is specified as: <mu>=<mu>Cr - <mu>Mo. I am wondering whether <mu>Cr and <mu>Mo should depend on the overall composition of the system. After all, their difference is supposed to correspond to the energy required to swap the atoms, and the energy of e.g. a Cr atom inside a Cr-Mo alloy will noticeably depend on the actual (local) concentration of Cr and Mo atoms.
I have double checked the formula of the ideal mixing and the exat form is:
S(ideal mixing) = -R[xln(x)+(1-x)ln(1-x)], where R = 8.31451 (J/mol*K) is the universal gas constant. The delta E mentioned aboved is the total energy of the solid solution state averaged over all minima belonging to this state and it seems that the phase diagram is obtained by means of the so-called convex hull method. I wonder if this ideal entropy mixing refers to the configuration entropy and only work in the case where the atomic radius of the system are equal to each other. On the other hand, the method (ATAT) we employed here taken into account the configuration entropy and vibrational entropy and is much suitable for the system where the vibrational entropy is significant.The vibrational entropy is quite large in my case, I was wondering if this large effect could be attributed to the large mismatch in the atomic radius between the Cr (atomic radius: 1.249 Ang.) and Mo (atomic radius: 1.363 Ang.) atoms which results in the atomic relaxation because the relaxed volumes of all the configurations that used to fit the cluster expansion do show a positive deviation from the vergard law. By the way, do you have any ideas how to get the entropy from the output of the Monte Carlo simulation. Thanks.