Numerical model for the effect of grain boundaries on the total amount diffused

The effect of grain boundary regions on the total amount diffused during an exchange experiment has been numerically modeled. The total amount diffused increases when the grain size is decreased, and when the ratio of the grain boundary and lattice diffusion coefficients increases. Grain boundary migration increases the total amount diffused during part of the processing time. The numerical calculations have shown that when lattice diffusion distance is larger than the grain size. Hart's equation is a satisfactory approximation for calculating the apparent diffusion coefficient value.