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A continuum theory is used to predict scaling laws for the morphologicalrelaxation of crystal surfaces in two independent space dimensions. The goal isto unify previously disconnected experimental observations of decaying surfaceprofiles. The continuum description is derived from the motion of interactingatomic steps. For isotropic diffusion of adatoms across each terrace, inducedadatom fluxes transverse and parallel to step edges obey different laws,yielding a tensor mobility for the continuum surface flux. The partialdifferential equation (PDE) for the height profile expresses an interplay ofstep energetics and kinetics, and aspect ratio of surface topography thatplausibly unifies observations of decaying bidirectional surface corrugations.The PDE reduces to known evolution equations for axisymmetric mounds andone-dimensional periodic corrugations.

Unified continuum approach to crystal surface morphological relaxation