Interface evolution in phase transformation ruled by nucleation and growth

An analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations in 2D and 3D space and the latter nucleation and growth on flat solid substrate. The theory is formulated for the general case of spatially correlated nuclei, arbitrary nucleation rate and power growth law of nuclei. In the case of heterogeneous nucleation, spheroidal nuclei have been assumed and the dependence of the kinetics on contact angle investigated. The validity of the present approach is deemed through comparison with experimental data from literature which also comprise oxide growth by ALD (Atomic Layer Deposition) metal electrodeposition at solid substrate and alloy recrystallization.