Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Phase Transitions and Critical Phenomena

DY 31.9: Talk

Friday, March 30, 2012, 12:00–12:15, MA 004

On phase-field modeling with a highly anisotropic interfacial energy — •Michael Fleck, Leslie Mushongera, Denis Pilipenko, Kumar Ankit, and Heike Emmerich — Materials and Process Simulation, University of Bayreuth, Germany

The crystalline nature of solids results in the anisotropy of many thermophysical parameters. In particular, the interfacial energy between different phases is often found to be a function of the crystallographic orientation of the interface. We report on phase-field approaches that allow for anisotropies sufficiently high so that the interface develops facets as well as sharp corners due to missing crystallographic orientations. The latter implies the necessity of a regularization that enforces local equilibrium at the corners, to remove the ill-posednes of the phase field evolution equation. Two different anisotropic phase-field formulations are presented and discussed: The classical model that allows the interface to vary with orientation, and another more recent formulation that has a constant interface width. Further, we develop an explicit finite difference scheme that combines a two-step differentiation with a stagnation grid formulation. The presented numerical implementation is stable and accurate enough to account for odd crystal symmetries and high angle rotations of the initial crystalline orientation. Even in the case of highly anisotropic interfacial energies, both formulations show excellent agreement with the well-known Wulff construction of the equilibrium shape of a particle embedded in a matrix.