Computational study of configurational and vibrational contributions to the thermodynamics of substitutional alloys: The case ofNi3Al

We have developed a methodology to study the thermodynamics of order-disorder transformations in $n$-component substitutional alloys that combines nonequilibrium methods, which can efficiently compute free energies, with Monte Carlo simulations, in which configurational and vibrational degrees of freedom are simultaneously considered on an equal footing basis. Furthermore, with this methodology one can easily perform simulations in the canonical and in the isobaric-isothermal ensembles, which allow the investigation of the bulk volume effect. We have applied this methodology to calculate configurational and vibrational contributions to the entropy of the ${\text{Ni}}_{3}\text{Al}$ alloy as functions of temperature. The simulations show that when the volume of the system is kept constant, the vibrational entropy does not change upon transition while constant-pressure calculations indicate that the volume increase at the order-disorder transition causes a vibrational entropy increase of $0.08{k}_{B}/\text{atom}$. This is significant when compared to the configurational entropy increase of $0.27{k}_{B}/\text{atom}$. Our calculations also indicate that the inclusion of vibrations reduces in about 30% the order-disorder transition temperature determined solely considering the configurational degrees of freedom.