A rate equation for atomic ordering in mean field theory. I. Uniform case

Abstract

A critical discussion is given of the kinetics of (dis)ordering in a simple system of Ising spins with respectively Glauber and Kawasaki types of stochastic processes. The question addressed is whether the rate is governed by the same free energy excess (in equilibrium) as assumed in frequently used rate equations. The authors focus for simplicity on uniform systems with long range interactions whose equilibria are well described by mean field theory. Such situations are realized in systems with effective spin interactions mediated by strain. They find that the rate equation can be expressed in terms of a Glauber or Kawasaki potential. Their analytical forms are found to be quite different from each other and also different from the equilibrium mean field energy. However, the predicted rate equations are not substantially different for most temperatures of interest.