Early stages of spinodal decomposition for the Cahn-Hilliard-Cook model of phase separation

Abstract

A computer simulation using discretized space and time is employed to examine the early stages of phase separation as described by the Cahn-Hilliard-Cook equation (CHCE). The relative simplicity of this simulation provides a direct test of various mathematical treatments of the nonlinear term in the CHCE. In particular, the numerical results are used to ascertain the validity of the approximations inherent in the perturbative expansions of Grant, San Miguel, Vinals, and Gunton, and of Langer, Bar-on, and Miller. The time of validity of all approximations is shown to be logarithmically related to the strength of the thermal fluctuations. In addition, the effect of the initial state on the dynamical evolution of the order parameter is examined.