Deterministic and Stochastic Dynamics in Spinodal Decomposition of a Binary System

Abstract

A model for diffusion and phase separation, which takes into account hyperbolic relaxation of the solute diffusion flux, is developed. Such a ‘hyperbolic model’ provides analysis of ‘hyperbolic evolution’ of patterns in spinodal decomposition in systems supercooled below critical temperature. Analytical results for the hyperbolic model of spinodal decomposition are summarized in comparison with outcomes of classic Cahn−Hilliard theory. Numeric modelling shows that the hyperbolic evolution leads to sharper boundary between two structures of a decomposed system in comparison with prediction of parabolic equation given by the theory of Cahn and Hilliard. Considering phase separation processes in stochastic systems with a field-dependent mobility and an internal multiplicative noise, we study dynamics of spinodal decomposition for parabolic and hyperbolic models separately. It is that the domain growth law is generalized when internal fluctuations are introduced into the model. A mean field approach is carried out in order to obtain the stationary probability, bifurcation and phase diagrams displaying re-entrant phase transitions. We relate our approach to entropy-driven phase-transitions theory.

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