Clusters, Metastability, and Nucleation: Kinetics of First-Order Phase Transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperature T. For temperatures 0.59T~, 0.81To, and 0.89Tc, with density p of A atoms equal to that in the B-rich phase at coexistence, the density C~ of clusters of l A atoms approximately satisfies the following empirical formulas: C1 ~ w(1 p)a and C~ ,.~ (1 p)~Q,w ~ (2 ~< l ~< 10). Here w is a parameter and we define Q~ = ~K e-~K~, where the sum goes over all translationally nonequivalent /-particle clusters and E(K) is the energy of formation of the cluster K. For l > 10, Qz is not known exactly; so we use an extrapolation formula Q~ ~ AwZ~l -~ e x p ( b P ) , where w~ is the value of w at coexistence. The same formula (with w > w~) also fits the observed values of C~ (for small values of l) at densities greater than the coexistence density (for T = 0.59T~): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (and w therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a " sp inoda l " transition is found.