  The path probability method (PPM), which is a natural extension of the
cluster variation method (CVM) to a time domain, has been employed in a
relaxation process of atomic configurations in alloy systems. Although the
vacancy mechanism is the main atomic migration process in an alloy system, most
studies of PPM have used the spin flipping mechanism (or the direct exchange
mechanism) because of the huge computational burden imposed by the vacancy
mechanism. In this paper the computational problem is circumvented by treating
various path variables in the PPM as cluster probabilities in the CVM, and the
vacancy mechanism is explicitly taken into account in the theoretical
framework. The method is employed to explore the relaxation process in a Ni3Al
ordered phase within the tetrahedron approximation, and the effect of vacancy
concentration is investigated.
