2007/09/17 by Dionisios Margetis, Margetis, Dionisios, Russel E. Caflisch +1
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Material Dynamics and Properties #Materials Science (cond-mat.mtrl-sci) #Theoretical and Computational Physics #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.0709.2726
openalex publication_date 2007/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson type formula and the associated step stiffness as a function of the step edge orientation angle, theta. Basic ingredients of the model are: (i) the diffusion of point defects (``adatoms'') on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a mean-field approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, \tbe(θ), is determined via perturbations of the kinetic steady state for small edge Peclet number, P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, \tbe is found to satisfy \tbe =O(θ-1) for O(P1/3)