Calculation of the effective diffusion coefficients in the nanostructured twophase media by Monte-Carlo method

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Yu. О. Lyashenko
V. V. Morozovych
О. Yu. Liashenko


Various functional materials have inhomogeneous structure with essentially different diffusion kinetics in their subsystems. The importance of determining the effective diffusivity may be crucial while considering nanocrystalline materials. In nanocrystalline materials volume fractions of grains (crystallites) and interfaces, which are formed between these grains are comparable, so the effective diffusivities of inhomogeneous media depend on diffusivities of each phases in the arbitrary proportion.
The Lattice Monte Carlo method was used to calculate the effective diffusivity in the nanostructured systems, which consist of two-phase zones with different morphology. Our Monte Carlo calculations show that the effective diffusion coefficient depends on the volume fraction of phases in the two-phase zone and on the morphological type of the two-phase structure. It was shown that the effective diffusivity depends on whether a highly or lowly permeable phase is incorporated into the matrix of another phase. It enables to obtain the fork like interval for the effective diffusivities between branches corresponding to the parallel and serial phase connections and between branches corresponding to the configurations, in which particles of one phase are incorporated in the matrix of another phase. It was also shown that for the inhomogeneous two-phase zone the effective diffusion coefficient has intermediate value at any volume fraction of phases.

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Mathematical and Calculation Physics


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