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Continuum approach to self-similarity and scaling in morphological relaxation of a crystal with a facet
Continuum approach self-similarity and scaling morphological relaxation crystal with a facet
2015/10/16
The morphological relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition temperature is studied analytically for diffusion-limited sDLd and attachment-detachme...
CONTINUUM RELAXATION OF INTERACTING STEPS ON CRYSTAL SURFACES IN 2+1 DIMENSIONS
crystal surface epitaxial growth morphological evolution Burton–Cabrera–Frank model Ehrlich–Schwoebel barrier entropic interactions elastic dipole interactions step chemical potential continuum limit surface mobility
2015/10/16
We study the relaxation of crystal surfaces in 2+1 dimensions via the motion ofinteracting atomic steps. The goal is the rigorous derivation of the continuum limit. The starting point is a discrete sc...
Unified continuum approach to crystal surface morphological relaxation
Unified continuum approach crystal surface morphological relaxation
2015/10/16
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. Our goal is to unify previously disconnected experimental o...
Anisotropic diffusion in continuum relaxation of stepped crystal surfaces
Anisotropic diffusion continuum relaxation stepped crystal surfaces
2015/10/16
We study the continuum limit in 2+1 dimensions of nanoscale anisotropic diffusion processes on crystal surfaces relaxing to become flat below roughening. Our main result is a continuum law for the sur...
ELECTROMIGRATION IN MACROSCOPIC RELAXATION OF STEPPED SURFACES
epitaxial relaxation crystal facet Burton–Cabrera–Frank model electromigration desorption surface diffusion step chemical potential macroscopic limit variational principle
2015/10/16
We study the effect of an external electric field E on macroscopic relaxation laws for crystal surfaces in 2 + 1 dimensions. We derive a nonlinear, fourth-order partial differential equation (PDE) for...
Role of chemical potential in relaxation of faceted crystal structure
chemical potential relaxation faceted crystal structure
2015/10/16
Below the roughening transition, crystal surfaces have macroscopic plateaus, facets, whose evolution is driven by the microscale dynamics of steps. A long-standing puzzle was how to reconcile discrete...
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
Mittag-Leer Functions Complete Monotonicity Laplace Transform Fractional Di erential Equations
2011/7/27
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics.