Growth of clusters in a first-order phase transition

Abstract

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms wasρ=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁≈(1-ρ)³ w(t),c ₁≈ (1−ρ)⁴ Q _l w(t)^l(2≤l≤10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the “cluster partition functions”;t is the time; andw(t)=0.015(1+7.17t ^−1/3). The distribution of large clusters (l≥20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=−(d/dl) ψ[lnt+pϕ (l/t)], whereϕ is a function given by those authors andψ is defined byψ(x)=C _o e−x-C ₁ e ^−4x/3-C ₂ e ^−5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.