Monte Carlo Potts Simulation of Grain Growth of Solid Grains Dispersed in a Liquid Matrix

Abstract

Liquid phase sintering is a process in which solid grains coexist with a liquid matrix. This process has important applications in processing of several engineering materials. Examples of these applications are high-speed metal cutting tools, alumina substrates for packaging silicon chips and barium titanate electrical capacitor. Grain growth in liquid phase sintered materials occurs by Ostwald ripening. The purpose of this paper is developing Monte Carlo Potts model to simulate Ostwald ripening in liquid-phase sintered materials. Ostwald ripening is simulated by treating two phases, solid grains dispersed in a liquid matrix as a two-dimensional square array of sites. Each site of the solid-phase grains (phase A) is given a random positive number between 1 and Q where Q=100 for all the simulation. The sites of the liquid phase (phase B) are assigned only one negative number, qB = -1. It is found that the grain growth is controlled byvolume diffusion for volume fraction of the solid grains ranging from 40% to 90%. The grain growth exponent has the value, n=3, in agreement with the theoretical value of Ostwald ripening.