Mathematical Sciences

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17 May 2018

Topological defects in 2D orientation-field based phase-field models

Presented By Dr. Tamás Pusztai (Wigner Research Centre for Physics, Hungary)

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Abstract: 

Orientation-field based phase-field models serve as a versatile tool to study polycrystalline solidification. In this approach, instead of assigning a separate phase field to each constituent grain, a single scalar (in 2D) or quaternion (in 3D) field is introduced to describe the local crystallographic orientation, i.e., the polycrystalline structure. This not only results in higher efficiency by decreasing the number of fields in numerical simulations, but also allows for the appearance of orientational disorder within the grains. This comes, however, at a price. The circular nature of the 2D orientation variable may cause different problems in modelling. A recently studied example is the appearance of topological defects on grain boundaries in 2D grain coarsening simulations. These defects are the direct consequence of the order parameter space of the scalar orientation field being non-simply connected. Unfortunately, these defects lack a clear physical picture behind, furthermore, their associated singularity cause problems in numerical simulations, such as the pinning of the grain boundaries. By proposing two new orientation fields with simply connected order parameter spaces we have constructed two new phase-field models that are free of these topological defects and the numerical problems they induce.