Diffusion growth of flat interface of a second phase controlled by the homogeneous nucleation

Kinetics of layer-by-layer growth of a second phase controlled by the homogeneous creation of clusters due to chemical reaction at the phase boundary is studied theoretically. The velocity ay which the infinite boundary between phases moves is determined in both the reaction- and diffusion-limited cases. The velocity is proportional to J1/3 and J1/2 (J is the nucleation rate), respectively. For a small specimen the velocity is shown to be proportional to J in both cases