Computational modeling of phase connectivity in solid-liquid phase microstructures during grain growth

A Monte Carlo simulation method for modeling grain growth of solid particles in a liquid phase was developed to analyze the connectivity of a solid phase in a solid-liquid system on a two or three dimensional lattice. The mean size, contiguity and connectivity of the solid particles were analyzed as a function of the fraction of solid phase (f(S)) and interface energy (gamma(SL)) between solid and liquid phases. The differences between results from 2D and 3D simulations were also examined. The connectivity increased with increasing f(S) and Y-SL, 3D simulations producing a much larger connectivity than 2D simulations. The unrealistically low values obtained from 2D simulations proved that 3D simulation is necessary for a reliable analysis of phase connectivity. The connectivity results from 3D simulations could be divided into two groups; in the first group, the microstructures were close to 100% connectivity, while in the second group, the connectivity decreased. This decrease was caused by grain growth, lowering of f(S) and gamma(SL) and increasing of the distance from the edge plane. A plot of connectivity vs. contiguity indicated that there was a critical value of contiguity (approximately 5%) above which close to 100% connectivity could be maintained, and below which the connectivity decreased approximately linearly. Our computational method may be applied to the design of microstructures of materials containing solid and liquid phases when a particular connectivity is desired.