Grain growth in polycrystalline materials.
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Polycrystalline materials consist of a compact aggregate 
of crystal grains with different orientations of the 
crystal lattice. The grains appear and grow when, 
for example, a liquid metal starts solidifying. The
boundaries between the grains are thin but of finite 
thickness. Due to the disordered orientations within 
the grain interfaces, these boundaries are the main
sites for fractures in the material.  

In this project we will numerically study a phase-field 
model of grain growth. Each phase field represents a 
crystallographic orientation of the material. We evolve 
the kinetic equations of the phase fields and can thus 
study the evolution of grains in the material. An isotropic 
version of the grain growth model is described in [1].

The model can furthermore be extended to include 
anisotropy that depends on the angle between the grain's 
crystallographic direction and the grain boundary 
direction. This allows us to account for the symmetry 
of the crystal lattice.


[1] Long-Qing Chen and Wei Yang, "Computer simulation 
of the domain dynamics of a quenched system with a 
large number of nonconserved order parameters: 
The grain-growth kinetics", Physical Review B vol. 50 
pp. 15752-15756 (1994).