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С. В. Шевченко
«Формирование микроструктуры поликристаллических материалов и статистика распределения зёрен по их средним размерам: возможность описания на основе уравнения коагуляции Смолуховского »
371–388 (2015)

PACS numbers: 05.10.Ln, 61.43.Gt, 61.72.-y, 64.60.De, 68.55.jm, 81.07.Wx, 81.10.Jt

A brief analysis for commonly used approaches to explaining an experimentally derived grain-size distribution functions (i.e. microstructural homogeneity) in polycrystalline solids is presented. Paper reports progress in exploring the problem by utilizing of a model based on the Smoluchowski theory for coagulation. The basic idea consists of the usage of exact solutions for the Smoluchowski equations as a source of kinetics and asymptotic behaviour for grain-size distribution functions during amorphous alloy crystallization, normal grain growth, and recrystallization. Grain-size distribution functions for several limiting cases are simulated with using both the coagulation equation solutions and the direct Monte Carlo method study of nucleation and growth in the solid state. As shown, such a simulation results in realistic microstructures and grain-size distributions.