Coarsening in polycrystalline material using quaternions

Abstract

We develop a phase field model to study the phenomenon of recrystallization and grain coarsening in polycrystalline material. A unique feature of our model is that it can time-evolve the actual orientation field of a material, expressed in terms of quaternions, a four-dimensional non-conserved vector field. The quaternions evolve in time following a Langevin dynamics. The free energy that drives the evolution contains bulk energy for various preferred grain types and anisotropic grain boundary energy. As a proof of principle for the new formalism we show that the average grain size (L) follows the usual L similar to t(1/2) scaling law when the grain boundary energy is independent of the misorientation angle between neighboring grains, whereas the scaling exponent is less (similar to 0.42) when the grain boundary energy follows the misorientation-dependent, phenomenological Read-Shockley formula.