Surface Cauchy-Born analysis of surface stress effects on metallic nanowires

Abstract

We present a surface Cauchy-Born approach to modeling FCC metals with nanometer scale dimensions for which surface stresses contribute significantly to the overall mechanical response. The model is based on an extension of the traditional Cauchy-Born theory in which a surface energy term that is obtained from the underlying crystal structure and governing interatomic potential is used to augment the bulk energy. By doing so, solutions to three-dimensional nanomechanical boundary value problems can be found within the framework of traditional nonlinear finite element methods. The major purpose of this work is to utilize the surface Cauchy-Born model to determine surface stress effects on the minimum energy configurations of single crystal gold nanowires using embedded atom potentials on wire sizes ranging in length from $6\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}280\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with square cross sectional lengths ranging from $6\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}35\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The numerical examples clearly demonstrate that other factors beside surface area to volume ratio and total surface energy minimization, such as geometry and the percentage of transverse surface area, are critical in determining the minimum energy configurations of nanowires under the influence of surface stresses.