Kinetics of crystalline configurations: I. General theory; Kinetics of homogeneous short range order

Abstract

A simple and exact way of coarse graining the master equation for a Markov process in configuration space is shown to exist. The coarse grained master equation is applied to the Ising model of a homogeneous binary interstitial alloy and to a “magnetic” Ising model. Using an approximation analogous to the quasi-chemical approximation, for both models the macroscopic rate equations for the establishment of short range order and the Fokker-Planck equation governing the fluctuations are derived.