  The equation of state (EOS) of alloys at high pressures is generalized with
the cluster expansion method. It is shown that this provides a more accurate
description. The low temperature EOSs of Ni-Al alloys on FCC and BCC lattices
are obtained with density functional calculations, and the results are in good
agreement with experiments. The merits of the generalized EOS model are
confirmed by comparison with the mixing model. In addition, the FCC phase
diagram of the Ni-Al system is calculated by cluster variation method (CVM)
with both spin-polarized and non-spin-polarized effective cluster interactions
(ECI). The influence of magnetic energy on the phase stability is analyzed. A
long-standing discrepancy between ab initio formation enthalpies and
experimental data is addressed by defining a better reference state. This aids
both evaluation of an ab initio phase diagram and understanding the
thermodynamic behaviors of alloys and compounds. For the first time the
high-pressure behavior of order-disorder transition is investigated by ab
initio calculations. It is found that order-disorder temperatures follow the
Simon melting equation. This may be instructive for experimental and
theoretical research on the effect of an order-disorder transition on shock
Hugoniots.
