Kinetic model for nucleation in partitioning systems

The classical theory of nucleation is an interface-limited theory and cannot properly describe nucleation process when the concentrations of the initial and final phases are different. A new model for time-dependent homogeneous nucleation that takes account of the coupled fluxes of interfacial attachment and long-range diffusion is presented. Numerical solutions from this new model show that the time-dependent nucleation rates scale with the smaller mobility and that the steady-state rates, Is, and induction times, θ, frequently differ significantly from values predicted by the classical theory. Simple approximate analytical expressions for Is and θ are presented. The concentration of the region of the parent phase near sub-critical crystal clusters is shifted toward that of the new phase. This shift may explain the nanometer-sized microstructures frequently obtained on the devitrification of bulk and Al-rare-earth-transition metal glasses.