Kinetics of nucleation with decreasing rate of growth

•Formation of embryos with the slow rate of growth is considered analytically.•The form of spectrum of the embryos sizes is approximately derived.•The property of effective size for embryos with the slow rate of growth is shown.•The head and the asymptotic tail for the spectrum of the embryos sizes are determined.•Two basic initial approximations of iteration procedure are presented.

Extension of analytical description of the stage of nucleation to the case of the slow growth rates of the embryos growth has been constructed. The metastable phase consumption by the already formed embryos affects the nucleation rate which leads to the non-linear evolution. The power exponentials which are smaller than that for the diffusion growth are chosen as the model laws of the embryos growth. All main characteristics of the nucleation period including the form of the embryos sizes spectrum are found. Analytical description of nucleation in the closed systems as well as in the open systems with the metastable phase influx is presented. It is shown that the relative errors of this description are small.