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Grooving of a grain boundary by evaporation–condensation below the roughening transition
grain boundary evaporation–condensation below roughening transition
2015/10/16
The development of surface grooves at grain boundaries that intersect a planar surface is analyzed for the case that the evolution occurs below the thermodynamic roughening transition by evaporation–c...
CONTINUUM DESCRIPTIONS OF CRYSTAL SURFACE EVOLUTION
CONTINUUM DESCRIPTIONS CRYSTAL SURFACE EVOLUTION
2015/10/16
It is well known that liquid surfaces evolve in shape due to the effect of surface tension, which drives configurations towards lower energy. The breakup of an initially cylindrical fluid thread into ...
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...
Continuum Theory of Nanostructure Decay Via a Microscale Condition
Continuum Theory Nanostructure Decay Microscale Condition
2015/10/16
The morphological relaxation of faceted crystal surfaces is studied via a continuum approach. Our formulation includes (i) an evolution equation for the surface slope that describes step line tension,...
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...
We study macroscopic aspects of crystal surface relaxation in 2+1 dimensions by accounting for nearequilibrium kinetics of transparent steps at the nanoscale. For slowly varying step geometries, we sh...
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...
A stochastic step flow model with growth in 1+1 dimensions
stochastic step flow model growth 1+1 dimensions
2015/10/16
Mathematical implications of adding Gaussian white noise to the Burton– Cabrera–Frank model for N terraces (‘gaps’) on a crystal surface are studied under external material deposition for large N. The...
Small fluctuations in epitaxial growth via conservative noise
Small fluctuations epitaxial growth conservative noise
2015/10/16
We study the combined effect of growth (material deposition from above) and nearest-neighbor entropic and force-dipole interactions in a stochastically perturbed system of N line defects (steps) on a ...
Homogenization of composite vicinal surfaces: Evolution laws in 1+1 dimensions
Crystal surface Burton–Cabrera–Frank (BCF) model Line defects Diffusion Macroscopic limit Multiscale expansion
2015/10/16
We apply classical homogenization to derive macroscopic relaxation laws for crystal surfaces with distinct inhomogeneities at the microscale. The proposed method relies on a formal multiscale expansio...
From atoms to steps:The microscopic origins of crystal evolution
Burton–Cabrera–Frank theory Solid-on-solid model Non-equilibrium statistical mechanics
2015/10/16
The Burton–Cabrera–Frank (BCF) theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect t...
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...
Mechanism of Hollow Nanoparticle Formation Due to Shape Fluctuations
Hollow Nanoparticle Formation Shape Fluctuations
2015/10/16
Shape fluctuations in nanoparticles strongly influence their stability. Here, we introduce a quantitative model of such shape fluctuations and apply this model to the important case of Pt-shell/transi...
On solutions of Maxwell’s equations with dipole sources over a thin conducting film
solutions of Maxwell’s equations dipole sources conducting film
2015/10/16
We derive and interpret solutions of time-harmonic Maxwell’s equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. Graphene sheet, lying between two unbo...