Growth of clusters in a first-order phase transition

O. Penrose, Joel L. Lebowitz, J. Marro, M. H. Kalos, A. Sur

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


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 0.59 Tc, where Tc is the critical temperature, and the concentration of minority atoms was ρ=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 by c1≈(1-ρ)3w(t), c1≈ (1-ρ)4Qlw(t)l(2≤l≤10); where cl is the concentration of clusters of size l;Q2, ..., Q10 are known constants, the "cluster partition functions";t is the time; and w(t)=0.015(1+7.17 t-1/3). The distribution of large clusters (l≥20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov, cl,(t)=-(d/dl)ψ[lnt+p φ{symbol}(l/t)], where φ{symbol} is a function given by those authors and ψ is defined by ψ(x)=Coe-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.

Original languageEnglish (US)
Pages (from-to)243-267
Number of pages25
JournalJournal of Statistical Physics
Issue number3
StatePublished - Sep 1978

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Nucleation
  • cluster growth
  • phase separation


Dive into the research topics of 'Growth of clusters in a first-order phase transition'. Together they form a unique fingerprint.

Cite this