  The Hugoniot of Ni3Al with L12 structure is calculated with an equation of
state (EOS) based on a cluster expansion and variation method from first
principles. It is found that an order-disorder transition occurs at a shock
pressure of 205GPa, corresponding to 3750K in temperature. On the other hand,
an unexpected high melting temperature about 6955K is obtained at the same
pressure, which is completely different from the case at ambient pressure where
the melting point is slightly lower than the order-disorder transition
temperature, implying the high pressure phase diagram has its own
characteristics. The present work also demonstrates the configurational
contribution is more important than electronic excitations in alloys and
mineral crystals within a large range of temperature, and an EOS model based on
CVM is necessary for high pressure metallurgy and theoretical Earth model.
