Evolution of Topology during Simulated Sintering of Powder Compacts

Abstract

Topological features were calculated for three‐dimensional microstructures simulated using a computer model. A method in which the material is divided into small volume elements (SVE method) was developed to measure topological features such as numbers of coordinating faces, edges, and corners on the computer‐generated microstructures. New relationships between different types of topological features of special interest in ceramics were derived based on the computer simulation statistics. These relationships enabled us to calculate the topological properties of a two‐phase system in which one phase has no internal boundaries, such as the pore, liquid, or glass phases in polyerystalline ceramics. Computer simulations allowed averaging those features statistically from large sample sizes, which can be difficult to do in practice. Dependence of topological features, such as the number of coordinating pores around a grain, on particle size distribution and sintered density of the system was studied. Results show that the number of coordinating faces is proportional to the square of particle size, and the number of edges per face is smaller for a wider particle size distribution. Equations are derived to describe the dependence of the number of coordinating faces and number of edges per face on grain size. The simulation shows that closed pores form at a lower sintered density for a wider particle size distribution.