We study nucleation and growth in systems with two distinct stable phases for both homogeneous and heterogeneous nucleation. Mean-field theories are developed that predict the fraction of material in each of the two stable phases as a function of time in any dimension d. Exact solutions for homogeneous and heterogeneous nucleation for d=1 are obtained and compared with the mean-field results. In the case of homogeneous nucleation in one dimension, we find an anomalous power-law correction to the leading-order asymptotic behavior for large times. The power-law exponent is a continuously varying function of the nucleation rates. Finally, Monte Carlo simulations show that the mean-field theories are surprisingly accurate for d=2.

• Received 19 May 1989

DOI:https://doi.org/10.1103/PhysRevB.40.8967