2016/06/29 by Joshua P. Schneider, Schneider, Joshua P., Paul N. Patrone +3
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Block Copolymer Self-Assembly #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Theoretical and Computational Physics #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.1606.09272
openalex publication_date 2016/06/29 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28
Starting with a many-atom master equation of a kinetic, restricted solid-on-solid (KRSOS) model with external material deposition, we investigate nonlinear aspects of the passage to a mesoscale description for a crystal surface in 1+1 dimensions. This latter description focuses on the motion of an atomic line defect (i.e. a step), which is defined via appropriate statistical average over KRSOS microstates. Near thermodynamic equilibrium and for low enough supersaturation, we show that this mesoscale picture is reasonably faithful to the Burton-Cabrera-Frank (BCF) step-flow model. More specifically, we invoke a maximum principle in conjunction with asymptotic error estimates to derive the elements of the BCF model: (i) a diffusion equation for the density of adsorbed adatoms; (ii) a step velocity law; and (iii) a linear relation for the mass flux of adatoms at the step. In this vein, we also provide a criterion by which the adatom flux remains linear in supersaturation, suggesting a range of non-equilibrium conditions under which the BCF model remains valid. Lastly, we make use of kinetic Monte Carlo simulations to numerically study effects that drive the system to higher supersaturations -- e.g. deposition of material onto the surface from above. Using these results, we describe empirical corrections to the BCF model that amount to a nonlinear relation for the adatom flux at the step edge.