Numerical Simulation of Anisotropic Shrinkage in a 2D Compact of Elongated Particles

Microstructural evolution during simple solid-state sintering of two-dimensional compacts of elongated particles packed in different arrangements was simulated using a kinetic, Monte Carlo model. The model used simulates curvature-driven grain growth, pore migration by surface diffusion, vacancy formation, diffusion along grain boundaries, and annihilation. Only the shape of the particles was anisotropic; all other extensive thermodynamic and kinetic properties such as surface energies and diffusivities were isotropic. We verified our model by simulating sintering in the analytically tractable cases of simple-packed and close-packed, elongated particles and comparing the shrinkage rate anisotropies with those predicted analytically. Once our model was verified, we used it to simulate sintering in a powder compact of aligned, elongated particles of arbitrary size and shape to gain an understanding of differential shrinkage. Anisotropic shrinkage occurred in all compacts with aligned, elongated particles. However, the direction of higher shrinkage was in some cases along the direction of elongation and in other cases in the perpendicular direction, depending on the details of the powder compact. In compacts of simple-packed, mono-sized, elongated particles, shrinkage was higher in the direction of elongation. In compacts of close-packed, mono-sized, elongated particles and of elongated particles with a size and shape distribution, the shrinkage was lower in the direction of elongation. The results of these simulations are analyzed, and the implication of these results is discussed.