Mathematical modelling of the mechanical alloying kinetics

Abstract

A rigorous mathematical model, based on the modified iso-concentration contour migration method, has been developed to predict the kinetics of diffusive intermixing in a binary miscible system in the course of mechanical alloying (MA). The present model considers the variation of diffusion coefficient with composition, and interface shift due to both interdiffusion and mechanical deformation. Comparison of the kinetics predicted by the present model with the relevant experimental data from Cu-Ni and Cu-Zn shows that the effective mass transport operative in MA attains a rate intermediate between that for volume or grain boundary diffusion. An effective temperature for diffusion (T_eff) has been proposed to simulate the observed alloying kinetics. T_eff is a function of composition but is not related to the adiabatic temperature rise at the point of ball-powder collision. Finally, the ratio of Teff to the corresponding liquidus temperature for all the composition studied lies between 0.4 and 0.5.