Grain Growth with Size-Dependent or Statistically Distributed Mobility

Abstract

Conventional grain growth is rate-limited by the mobility of grain boundary. To describe similar phenomena limited by the mobility of other grain junctions, we have developed a general theory allowing for size-dependent mobility and its statistical variance. We obtained analytic solutions for the steady-state size distribution and the growth exponent, defined as (grain size)n ~ time, down to n=1, which arises when the mobility of three-grain lines is rate-limiting. When the mobility of four-grain junctions is rate-limiting, exponential growth and a bifurcating size distribution result. These solutions manifest a general trend: The size distribution narrows with increasing n. Yet experimentally the opposite trend has been observed recently, which can only be reproduced in simulation if the mobility distribution is made at lease bimodal, with one mode being immobile or nearly immobile. The latter can be realized in slow grain growth below the temperature of mobility transition.