A Level-Set Method for the Evolution of Faceted Crystals

A level-set formulation for the motion of faceted interfaces is presented. The evolving surface of a crystal is represented as the zero-level of a phase function. The crystal is identified by its orientation and facet speeds. Accuracy is tested on a single crystal by comparison with the exact evolution. The method is extended to study the evolution of a polycrystal. Numerical examples in two and three dimensions are presented.

[1]  S. Osher,et al.  THE WULFF SHAPE AS THE ASYMPTOTIC LIMIT OF A GROWING CRYSTALLINE INTERFACE , 1997 .

[2]  F. C. Frank,et al.  On the Kinematic Theory of Crystal Growth and Dissolution Processes, II , 1972 .

[3]  Thijssen,et al.  Dynamic scaling in polycrystalline growth. , 1992, Physical review. B, Condensed matter.

[4]  Pierpaolo Soravia.  Generalized motion of a front propagating along its normal direction: a differential games approach , 1994 .

[5]  John W. Cahn,et al.  Linking anisotropic sharp and diffuse surface motion laws via gradient flows , 1994 .

[6]  A. J. Dammers,et al.  Two-Dimensional Computer Modelling of Polycrystalline Film Growth , 1991 .

[7]  S. Osher,et al.  Motion of multiple junctions: a level set approach , 1994 .

[8]  James A. Sethian,et al.  Theory, algorithms, and applications of level set methods for propagating interfaces , 1996, Acta Numerica.

[9]  E. Rouy,et al.  A viscosity solutions approach to shape-from-shading , 1992 .

[10]  W. Carter,et al.  Vector-valued phase field model for crystallization and grain boundary formation , 1998 .

[11]  J. Taylor,et al.  Overview No. 98 I—Geometric models of crystal growth , 1992 .

[12]  John S. Wettlaufer,et al.  A geometric model for anisotropic crystal growth , 1994 .

[13]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[14]  Philips Research Reports , 1946, Nature.

[15]  S. Osher,et al.  The Geometry of Wulff Crystal Shapes and Its Relations with Riemann Problems , 1998 .

[16]  Chen,et al.  Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics. , 1994, Physical review. B, Condensed matter.

[17]  John W. Cahn,et al.  Diffuse interfaces with sharp corners and facets: phase field models with strongly anisotropic surfaces , 1998 .

[18]  A. Harten,et al.  The artificial compression method for computation of shocks and contact discontinuities: III. Self , 1978 .

[19]  M. A. Jaswon.  A Review of the Theory , 1984 .

[20]  A. Harten,et al.  The artificial compression method for computation of shocks and contact discontinuities. I - Single conservation laws , 1977 .

[21]  Wheeler,et al.  Phase-field models for anisotropic interfaces. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.