  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, by
appropriately constraining the system, we were able to compute the
contributions to the vibrational entropy due to bond proportion, atomic size
mismatch, and bulk volume effects. We have applied this methodology to
calculate configurational and vibrational contributions to the entropy of the
Ni3Al alloy as functions of temperature. We found that the bond proportion
effect reduces the vibrational entropy at the order-disorder transition, while
the size mismatch and the bond proportion effects combined do not change the
vibrational entropy at the transition. We also found that the volume increase
at the order-disorder transition causes a vibrational entropy increase of 0.08
kB/atom, which is significant when compared to the configurational entropy
increase of 0.27 kB/atom. Our calculations indicate that the inclusion of
vibrations reduces in about 30 percent the order-disorder transition
temperature determined solely considering the configurational degrees of
freedom.
