J S Wettlaufer et al 1994 J. Phys. A: Math. Gen. 27 5957 doi:10.1088/0305-4470/27/17/027
J S Wettlaufer, M Jackson and M Elbaum
Show affiliationsEquilibrium crystal shapes are defined uniquely by the Wulff construction. The classical kinematic theory of crystal growth, due mainly to Frank and Chernov, provides a mathematically equivalent prescription for the limiting growth shape. To connect these two well studied states, we derive a local geometric growth model and examine the transient shape evolution of an equilibrium form containing both facets and rough regions. Our model is appropriate to the weakly driven growth of a two-dimensional single crystal with n-gonal symmetry and arbitrary closed initial shape. The model links disparate kinetic processes determined by the local interfacial structure to the isotropic growth drive, and reproduces the experimentally observed transition from a partly rounded equilibrium shape to a highly faceted crystal which we term 'global kinetic faceting'. We solve for the transient shape dynamics globally, and locally, and in the latter case present a curvature evolution equation valid for any local growth law. Both approaches show that, during kinetic faceting, rough orientations grow out of existence with decreasing curvature.
68.35.B- Structure of clean surfaces (and surface reconstruction)
53A10 Minimal surfaces, surfaces with prescribed mean curvature (See also 49Q05, 49Q10, 53C42)
Issue 17 (7 September 1994)
J S Wettlaufer et al 1994 J. Phys. A: Math. Gen. 27 5957
Rebecca A. Koopmann et al. 2001 ApJS 135 125
T Joshua Pfefer et al 2009 Phys. Med. Biol. 54 6867
V M Hannen et al 2003 Class. Quantum Grav. 20 S261
Héctor G. Arce and Alyssa A. Goodman 2001 ApJ 554 132
Jennifer J. Birriel et al 1998 ApJ 507 L75
R. Demarco et al. 2007 ApJ 663 164
F Bentosela et al 1999 J. Phys. A: Math. Gen. 32 3029
E Çetinórgü et al 2006 J. Phys. D: Appl. Phys. 39 5245
Aleksandr B Shvartsburg 2000 Phys.-Usp. 43 1201