Quick search Find article
Quick search
Find article

A geometric model for anisotropic crystal growth

J S Wettlaufer, M Jackson and M Elbaum

Show affiliations


Equilibrium 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.


PACS

81.10.Aj Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation

68.35.B- Structure of clean surfaces (and surface reconstruction)

68.35.Ct Interface structure and roughness

MSC

53A10 Minimal surfaces, surfaces with prescribed mean curvature (See also 49Q05, 49Q10, 53C42)

74N05 Crystals

Subjects

Surfaces, interfaces and thin films

Condensed matter: structural, mechanical & thermal

Dates

Issue 17 (7 September 1994)



View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.