The K Value Distribution of Liquid Phase Sintered Microstructures

A complex geometry of a powder compact in the three-dimensional multiple particle arrangement was generated by a Monte Carlo method, and the K value (a constant links the two-dimensional connectivity to the three-dimensional coordination number) distributions of liquid phase sintered systems, parameters linked the two-dimensional connectivity to the three-dimensional coordination number, were solved by the numerical computation. With this probability model, irregular packing of particles in three-dimensional space could be formulated with the variations of the particle size distribution. Unlike previous analytical models in which the grain boundary energy was set to a constant value, a relationship between the grain boundary energy and the misorientation angle between neighboring grains could be incorporated into this model in a probability manner. Simulation results indicate that the mean K value in the initial stage of liquid phase sintering increases with an increasing volume fraction of liquid phase, an increasing ratio of the mean base particle size to the mean additive particle size, and a decreasing standard deviation of the particle size distribution. The findings of the simulation are favorably compared with previous experimental observations on W-Ni-Fe alloys.