Schneider Joshua P, Nakamura Kanna, Margetis Dionisios
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA.
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062408. doi: 10.1103/PhysRevE.89.062408. Epub 2014 Jun 19.
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 effects in facet motion with fully continuum approaches. We propose a resolution of this issue via connecting, through a jump condition, the continuum-scale surface chemical potential away from the facet, characterized by variations of the continuum surface free energy, with a chemical potential originating from the decay of atomic steps on top of the facet. The proposed condition accounts for step flow inside a discrete boundary layer near the facet. To validate this approach, we implement in a radial geometry a hybrid discrete-continuum scheme in which the continuum theory is coupled with only a few, minimally three, steps in diffusion-limited kinetics with conical initial data.
