The study of grains growth during a phase and structural transformations has essential importance for materials science and engineering. The existing Kolmogorov theory covers growth of grains on the assumptions of the geometric similarity of particles, their convex shape and uniform geometric distribution in space. The statistical theory is presented in the work, allowing to analyze the transformations kinetics in the case that the grains have arbitrary shapes and the arbitrary distribution of the linear growth rate on their surfaces. The case study of modeling of the growth of grains with disk and rod morphology is demonstrated
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