Role of chemical potential in relaxation of faceted crystal structure.

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.