From atoms to steps: The microscopic origins of crystal evolution

SURFACE SCIENCE

卷:625

Article

Patrone, Paul N.^1,2  Einstein, T. L.^3,4  Margetis, Dionisios^5,6,7 

[1] NIST, Ctr Nanoscale Sci & Technol, Gaithersburg, MD 20899 USA

[2] Univ Minnesota, Inst Math & Applicat, Minneapolis, MN 55455 USA

[3] Univ Maryland, Dept Phys, College Pk, MD 20742 USA

[4] Univ Maryland, Condensed Matter Theory Ctr, College Pk, MD 20742 USA

[5] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[6] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

[7] Univ Maryland, Ctr Sci Computat & Math Modeling, College Pk, MD 20742 USA

关键词: Burton-Cabrera-Frank theory;    Solid-on-solid model;    Non-equilibrium statistical mechanics;   

DOI  :  10.1016/j.susc.2014.02.015

来源: Elsevier

【 摘 要 】

The Burton-Cabrera-Frank (BCF) theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as composed of staircase-like structures of steps separating terraces. Adsorbed atoms (adatoms), which are represented by a continuous density, diffuse on terraces, and steps move by absorbing or emitting these adatoms. Here we shed light on the microscopic origins of the BCF theory by deriving a simple, one-dimensional (1D) version of the theory from an atomistic, kinetic restricted solid-on-solid (KRSOS) model without external material deposition. We define the time-dependent adatom density and step position as appropriate ensemble averages in the KRSOS model, thereby exposing the non-equilibrium statistical mechanics origins of the BCF theory. Our analysis reveals that the BCF theory is valid in a low adatom-density regime, much in the same way that an ideal gas approximation applies to dilute gasses. We find conditions under which the surface remains in a low-density regime and discuss the microscopic origin of corrections to the BCF model. Published by Elsevier B.V.

【 授权许可】

Free