Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Continuum approach to self-similarity and scaling in morphological relaxation of a crystal with a facet
 

Summary: Continuum approach to self-similarity and scaling in morphological relaxation
of a crystal with a facet
Dionisios Margetis,1
Michael J. Aziz,2
and Howard A. Stone2
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2
Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Received 1 April 2004; revised manuscript received 5 October 2004; published 26 April 2005
The morphological relaxation of axisymmetric crystal surfaces with a single facet below the roughening
transition temperature is studied analytically for diffusion-limited DL and attachment-detachment-limited
ADL kinetics with inclusion of the Ehrlich-Schwoebel barrier. The slope profile F r,t , where r is the polar
distance and t is time, is described via a nonlinear, fourth-order partial differential equation PDE that
accounts for step line-tension energy g1 and step-step repulsive interaction energy g3; for ADL kinetics, an
effective surface diffusivity that depends on the step density is included. The PDE is derived directly from the
step-flow equations and, alternatively, via a continuum surface free energy. The facet evolution is treated as a
free-boundary problem where the interplay between g1 and g3 gives rise to a region of rapid variations of F, a
boundary layer, near the expanding facet. For long times and g3/g1 O 1 singular perturbation theory is
applied for self-similar shapes close to the facet. For DL kinetics and a class of axisymmetric shapes, a the
boundary-layer width varies as g3/g1

  

Source: Aziz, Michael J.- School of Engineering and Applied Sciences, Harvard University
Margetis, Dionisios - Institute for Physical Science and Technology & Department of Mathematics, University of Maryland at College Park

 

Collections: Materials Science; Mathematics; Physics