Three-Dimensional Grain Growth Model Using the Phase Field Approach

Overview

Grain growth occurs due to thermally activated atomic jumps across grain boundaries. The driving force for grain growth is the reduction in the grain boundary area. This website gives a summary of three-dimensional grain growth computer modeling using Phase Field and Monte Carlo techniques.

A Monte Carlo model is used for simulating curvature-driven grain growth. Initially a domain with certain dimensions is used. Each point in the domain is assigned a random number between one and the total number of grain orientations. Each point is chosen randomly and the change in energy is due to switching the grain orientation number to another random number between one and the total number of grain orientations which result in computer-simulated grain growth.

In a Phase Field model, a polycrystalline microstructure is described by many orientation field variables, called order parameters, which describe the orientation of grains. It can have an infinite number of grain orientations. However, coalescence can occur because only a finite number of grain orientations can be modeled in a computer simulation. Grain coalescence is two or more grain, which have the same combination of order parameters, become one large grain due to the limited number of order parameters to represent each grain.