Modeling of grain-boundary diffusion under nonstationary heating conditions

Abstract

Grain boundary diffusion appreciably affects the physicomechanical and chemical properties of constructional materials. Experimental studies show that transfer processes run more intensively in materials with a larger area of internal boundaries. For these materials, the temperature required for diffusion activation is reduced. Much attention is paid to grain-boundary diffusion in such areas as materials science, physics and chemistry of metals, and metal science. However, there are practically no published works where the diffusion along the grain boundaries and phases under non-isothermal conditions has been studied. This work presents a two-dimensional model of alloying element redistribution from the amorphous coating into the substrate. The substrate is represented by alternating grains with a clear selection of the triple junction. The areas adjacent to the grain boundaries are clearly selected in the model and have a finite thickness. Different ratios between the grain sizes and the boundaries widths relate to diffusion in micro- and nanocrystalline materials. The redistribution of the alloying element is initiated by one or several thermal pulses associated with the action of the electron beam. It is taken into account when the heat part of the problem has been formulated that the typical scales of the heat and diffusion processes are essentially different. The diffusion problem takes into account the temperature dependence of the diffusion coefficients in the volume of grains and along the boundaries between them. The problem was solved numerically. Varying the parameters of the model, it was found by that the ratio of activation energies in the phases has the greatest influence on the diffusant distribution. Pulsed treatment compared to treatment with constant heating results in slower leads to a slow down of diffusion along the grain boundaries. The simulation results are qualitatively consistent with the data found in the literature.