On the effects of elastic stress on the motion of fully faceted interfaces.

Abstract In this paper we develop conditions that govern the evolution of a fully faceted interface separating elastic phases. To focus attention on the effects of elastic stress, we restrict attention to interface-controlled kinetics, neglecting bulk transport; and to avoid geometric complications, we limit our discussion to two space-dimensions. We consider a theory in which the orientations present on the evolving particle are not necessarily those given by the Wulff shape: we allow for metastable crystallographic orientations as well as stable orientations. We find that elastic stress affects the velocity of a facet through the average value of the normal component of the jump in configurational stress (Eshelby stress) over the facet. Within our theory singularities in stress induced by the presence of corners do not influence the velocity of the facet. We discuss the nucleation of facets from corners; the resulting nucleation condition is shown to be independent of elastic stress. We also develop equations governing the equilibrium shape of a faceted particle in the presence of elastic stress.

[1]  Morton E. Gurtin,et al.  The nature of configurational forces , 1995 .

[2]  R. Kohn,et al.  Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature , 2014, 1407.5942.

[3]  Jean E. Taylor,et al.  Modeling crystal growth in a diffusion field using fully faceted interfaces , 1994 .

[4]  Conyers Herring,et al.  Some Theorems on the Free Energies of Crystal Surfaces , 1951 .

[5]  Sigurd B. Angenent,et al.  Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface , 1989 .

[6]  M. Gurtin,et al.  The thermodynamics of evolving interfaces far from equilibrium , 1996 .

[7]  J. D. Eshelby.  The elastic energy-momentum tensor , 1975 .

[8]  Kaushik Bhattacharya,et al.  Kinetics of phase boundaries with edges andjunctions , 1998 .

[9]  Pedro M. Girao,et al.  Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature: approaches based on the object-oriented paradigm , 1995, 1407.5943.

[10]  M. Gurtin.  Thermomechanics of Evolving Phase Boundaries in the Plane , 1993 .

[11]  J. Taylor,et al.  Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces , 1995 .

[12]  J. Taylor,et al.  II—mean curvature and weighted mean curvature , 1992 .

[13]  Morton E. Gurtin,et al.  Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces , 1995 .