A general approach to grain growth driven by energy density differences

Abstract

A general approach to grain growth driven by energy density differences among the grains, associated with curvature and/or extraneous driving forces (e.g. external fields) is developed. A mean field approximation leads to the definition of a threshold energy density, E ∗ , which depends on moments of the current distributions of grain diameters, a, and grain energy densities, E, such that the rate of change, da/ dt, of the diameter of a grain is proportional to ( E ∗–E ). When curvature effects are negligible, the kinetic equations can be solved analytically to obtain the average grain diameter < a> and the diameter distribution as a function of time. A scaling regime is reached for (and only for) power law distributions of E, with a power law kinetics < a>∝ t μ . The combined effects of curvature and extraneous driving forces were studied numerically. The rate of growth and the width of the grain diameter distribution change when compared to pure curvature growth, the sign of the change depending on the initial energy density and diameter distributions.