Stochastic Models of Defects' Clusterization in Solids

Kinetic approach to modelling of phase transition in solids at their fluctuation stage, as well as to creation of mathematical models cluster formation of vacancy and impurity nature, is discussed. The model interacting spherical Brownian particles with alternating masses (in result of fluctuation changes of physical parameters of simulated system) is used. The description of Brownian motion is made in terms of equation of the mathematical physics (Fokker-Planck-Kolmogorov, Boltzmann, Smolukhovsky-Kramers) and equivalent equation of stochastic analog (the stochastic differential equation Ito) /SDE/. The Ito SDE, which has been earlier used for simulation of non-equilibrium physico-chemical processes in gases and plasmas, are formulated now for microdynamics of large particle ensembles. Distribution of clusters in accordance width their sizes, resulting from stochastic fluctuations of the thermodynamic potential of the “cluster-lattice- vacancies' flow ” system is determined. The action of external and self-consistent forces arising in the considered system is taken into account as well.