Coarsening in polycrystalline material using quaternions.

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 ∼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 (∼0.42) when the grain boundary energy follows the misorientation-dependent, phenomenological Read-Shockley formula.