Object-Oriented Design and Implementation of a Monte Carlo Algorithm for Simulation of Grain Growth

The Monte Carlo (MC) method has been widely adapted to model grain growth under various situations. There were several implementations of the MC technique frequently appearing in literature to simulate normal grain growth of single-phase materials. Probably due to the design and implementation methodology, which was procedural, these implementations did not fully reflect the physics of grain boundary movement in grain growth. Therefore the grain growth kinetics obtained may be deviated from reality and was in disagreement with theoretical predictions.

In this work, a two-dimensional computer program for the MC grain growth simulation was developed using the object-oriented programming technique. The microstructure of materials was modeled as a network of topologically connected grains, and the microstructure evolution was realized as the grain boundary movements using the MC methods. The grain was defined as a group of adjacent material points with same orientations. The material point was the smallest object with various static and dynamic attributes such as geometric coordinates, orientation, the amount of bulk energies, etc. A piece of continuum material was mapped onto a lattice composed of a large number of such material points. The implementation for simulating grain boundary movement was based on the fundamental idea that grain growth is a free energy reduction process through the elimination of grain boundaries. In every step of the simulations, a minimum-energy state of the material lattice should be achieved. This was done by randomly selecting points located at grain boundaries and flipping the points to neighboring grains, attempting to cause largest reduction in total boundary energy. If the total boundary energy rises due to the flipping attempts, the old orientations of the points were recovered. In each step of the simulations, all the material points at grain boundaries were attempted exactly once.

It had been rigidly shown in theory that if the assumption of self-similarity is satisfied, then the grain growth of an ideal single-phase material should follow a parabolic law. The simulations using the above algorithm generated time-invariant scaled grain size distribution and grain shape distribution for the isotropic normal grain growth. The kinetics of the microstructure evolution in agreement with the theory prediction was reproduced. Furthermore, grain growth with various models for the anisotropic grain boundary energy potential was simulated using the above MC algorithm. Self-similarity of grain shapes was observed in all cases. The parabolic growth law observed in the isotropic case remains unchanged, and the degree of anisotropy affects the grain growth rate only. These results further validated the theoretical work on self-similarity and grain growth kinetics.

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