Order to disorder phase transformation at high temperatures is attributed to the increased entropy of the disordered phase. For most materials increase in configurational entropy (Sconf) of disordered state is sufficient to explain order-disorder phase transformation. Difference in vibrational entropy (Svib) of ordered and disordered phases (∆Svib(o→do)) is largely ignored as it is miniscule as compared to ∆Sconf(o→do). For order-disorder phase transformation in Ni3Al, in addition to the increase in Sconf to a maximum of 0.562 kB per atom of disordered phase, experimental studies using neutron diffraction have found increase in vibrational entropy (Svib) of 0.2 kB per atom.[1] Several studies have attempted to explain such unusual behavior, using range of computational methods.[2,3] The most recent and authoritative first-principles study by van de Walle et al.[4] reported a nominal ∆Svib(o→do) by considering disordered Ni3Al as a random solid solution. This leaves a several decades old experimental observation still unexplained.
In this study I explore the possibility of partial clustering of Al, as a source of large ∆Svib(o→do). Periodically repeating supercells were used to represent Ni3Al as ordered, solid-solution, and with partial Al clusters. Solid-solution is modeled using special quasi-random structure (SQS).[5] Partial clustering is achieved by swapping Ni atoms with Al atoms so that number of Al-Al bonds increases. First-principles density functional theory (DFT) based computation as implemented in Vienna Ab Initio Simulation Package (VASP)[6] was used to calculate energy and forces. Phonopy[7] was used to calculate vibrational entropy, within quasi-harmonic approximation. I employed the pair approximation of the cluster variation method (CVM)[8] to estimate the Sconf of partially and fully disordered supercells of Ni3Al.
We show that Ni3Al with Al clusters is both thermodynamically and dynamically stable. ∆Svib(o→do) of the system containing Al clusters is higher than that of fully disordered. Our results suggest that experimentally observed increased vibrational entropy of disordered system could be due to the presence of Al clusters.

References:
1 Fultz, B., Anthony, L., Nagel, L.J., Nicklow, R.M. and Spooner, S., 1995. Phonon densities of states and vibrational entropies of ordered and disordered Ni 3 Al. Physical Review B, 52(5), p.3315.
2 Althoff, J.D., Morgan, D., de Fontaine, D., Asta, M., Foiles, S.M. and Johnson, D.D., 1997. Vibrational spectra in ordered and disordered Ni 3 Al. Physical Review B, 56(10), p.R5705.
3 Ravelo, R., Aguilar, J., Baskes, M., Angelo, J.E., Fultz, B. and Holian, B.L., 1998. Free energy and vibrational entropy difference between ordered and disordered Ni 3 Al. Physical Review B, 57(2), p.862.
4 Van de Walle, A., Ceder, G. and Waghmare, U.V., 1998. First-principles computation of the vibrational entropy of ordered and disordered Ni 3 Al. Physical review letters, 80(22), p.4911.
5 Zunger, A., Wei, S.H., Ferreira, L.G. and Bernard, J.E., 1990. Special quasirandom structures. Physical Review Letters, 65(3), p.353.
6 Kresse, G. and Furthmüller, J., 2001. Vienna ab-initio simulation package (vasp). Vienna: Vienna University.
7 Togo, A. and Tanaka, I., 2015. First principles phonon calculations in materials science. Scripta Materialia, 108, pp.1-5.
8 Kikuchi, R., 1951. A theory of cooperative phenomena. Physical review, 81(6), p.988.