Equilibrium and kinetic shapes of grains in polycrystals

Abstract

The equilibrium crystal shape is a convex shape bound by the lowest energy interfaces. In many polycrystalline microstructures created by grain growth, the observed distribution of grain boundary planes appears to be dominated at low driving forces (after long grain growth times) by the planes present in the equilibrium crystal shape. However, at earlier stages of grain growth, it is expected that kinetic effects will play an important role in grain boundary motion and morphology. Analogous to the equilibrium crystal shape, the kinetic crystal shape of seed crystals growing from a liquid at higher supersaturations is bound by the slowest growing orientations. This study presents an equivalent construction for grain boundaries in polycrystals and uses it to determine the kinetic crystal shape for strontium titanate as a function of temperature. Relative grain boundary mobilities for strontium titanate for the low energy crystallographic orientations from seeded polycrystal experiments are used to calculate the kinetic crystal shapes as a function of temperature and annealing atmosphere. The kinetic crystal shapes are then compared to the morphologies and orientations of the interfaces of the growing seed crystals, and to the equilibrium crystal shapes, as well.The conclusions are that (1) the kinetic crystal shape is extremely anisotropic and displays significant transitions as a function of temperature that do not mirror changes in equilibrium crystal shape, (2) the kinetic shapes observed in the microstructures are dominated by the growing side of the interface (single crystal) and not by the dissolving side (polycrystalline matrix), and (3) faster growing orientations break up into macroscopic facets composed of slower growing orientations. The implications for grain growth underscore the applicability of crystal growth models to grain growth in polycrystals. In particular, in strontium titanate, the anisotropy of the grain boundary mobility as represented in the kinetic crystal shape is expected to be reduced from five macroscopic parameters to two (interface normal) allowing for incorporation of growth rate anisotropy in simulations of microstructure evolution at the earliest stages of grain growth, i.e. at the highest driving forces.