Kinetics of a first-order phase transition: computer simulations and theory

We make a quantitative comparison between the predictions of the Becker-Döring equations and computer simulations on a model of a quenched binary A-B alloy. The atoms are confined to the vertices of a simple cubic lattice, interact through attractive nearest neighbor interactions, and move by interchanges of nearest neighbor pairs (Kawasaki dynamics). We study in particular the time evolution of the number of clusters of A atoms of each size, at four different concentrations: _A=0.035, 0.05, 0.075, and 0.1 atoms per lattice site. The temperature is 0.59 times the critical temperature. At this temperature the equilibrium concentration of A atoms in the B-rich phase is _A^eq=0.0145 atoms/lattice site. The coefficients entering the Becker-Döring equations are obtained by extrapolation from previously published low-density calculations, leaving the time scale as the only adjustable parameter. We find good agreement at the three lower densities. At 10% density the agreement is, as might be expected, less satisfactory but still fairly good-indicating a quite wide range of utility for the Becker-Döring equations.Supported in part by NSF Grant DMR81-14726 and DOE Contract DE-AC02-76ERO3077.