Corrections to late-stage behavior in spinodal decomposition: Lifshitz-Slyozov scaling and Monte Carlo simulations.

Abstract

The Lifshitz-Slyozov theory of the late stages of diffusion-limited spinodal decomposition (Ostwald ripening) is generalized to apply for arbitrary volume fractions of the two phases. Corrections to the asymptotic R(t)\ensuremath{\sim}${t}^{1/3}$ scaling are considered; they are due to excess transport in interfaces and are therefore of relative order ${R}^{\mathrm{\ensuremath{-}}1}$(t), where R(t) is the average domain size. That the asymptotic exponent (1/3) has not been observed in Monte Carlo simulations of Ising models can be attributed to such corrections. Further simulations of the square-lattice Ising model are performed: The results are consistent with the generalization of the Lifshitz-Slyozov theory. The recent work of Mazenko et al. that proposes instead R(t)\ensuremath{\sim}logt is criticized.