Growth of clusters in a first-order phase transition

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 was=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 byc₁(1-)³w(t),c₁ (1–)⁴Q_lw(t)^l(2l10); wherec_l is the concentration of clusters of sizel;Q₂,...,Q₁₀ 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 (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c_l,(t)=–(d/dl)[lnt+p(l/t)], where is a function given by those authors and is defined by(x)=C_oe–x-C₁e^–4x/3-C₂e^–5x/3;C₀,C₁,C₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.