Scaling in Late Stage Spinodal Decomposition with Quenched Disorder

TL;DR

This paper investigates how quenched disorder affects late-stage spinodal decomposition, revealing specific scaling laws at zero temperature and complex temperature-dependent behavior at finite temperature.

Contribution

It introduces a mean field model with quenched disorder to analyze domain growth and structure factor scaling, connecting disorder amplitude to domain size scaling laws.

Findings

At zero temperature, domain size scales with disorder amplitude as R(t) = A^{-eta} f(t/A^{- ext{gamma}}).

The ratio β/γ equals the Lifshitz-Slyosov exponent, linking disorder effects to classical coarsening theory.

Finite temperature results show deviations from simple scaling, indicating temperature influences disorder-driven phase separation.

Abstract

We study the late stages of spinodal decomposition in a Ginzburg-Landau mean field model with quenched disorder. Random spatial dependence in the coupling constants is introduced to model the quenched disorder. The effect of the disorder on the scaling of the structure factor and on the domain growth is investigated in both the zero temperature limit and at finite temperature. In particular, we find that at zero temperature the domain size, $R(t)$, scales with the amplitude, $A$, of the quenched disorder as $R(t) = A^{-\beta} f(t/A^{-\gamma})$ with $\beta \simeq 1.0$ and $\gamma \simeq 3.0$ in two dimensions. We show that $\beta/\gamma = \alpha$, where $\alpha$ is the Lifshitz-Slyosov exponent. At finite temperature, this simple scaling is not observed and we suggest that the scaling also depends on temperature and $A$. We discuss these results in the context of Monte Carlo and cell dynamical models for phase separation in systems with quenched disorder, and propose that in a Monte Carlo simulation the concentration of impurities, $c$, is related to $A$ by $A \sim c^{1/d}$.