Atomistic calculations of elastic properties of metallic fcc crystal surfaces

Abstract

Elastic properties of crystal surfaces are useful in understanding mechanical properties of nanostructures. This paper presents a fully nonlinear treatment of surface stress and surface elastic constants. A method for the determination of surface elastic properties from atomistic simulations is developed. This method is illustrated with examples of several crystal faces of some fcc metals modeled with embedded atom potentials. The key finding in this study is the importance of accounting for the additional relaxations of atoms at the crystal surface due to strain. Although these relaxations do not affect the values of surface stress ͑as had been determined in previous works͒, they have a profound effect on the surface elastic constants. Failure to account for these relaxations can lead to values of elastic constants that are incorrect not only in magnitude but also in sign. A possible method for the experimental determination of the surface elastic constants is outlined.

The renaissance of continuum mechanics

“…Note that the applicability of the conventional continuum beam models in the mechanics of nanotubes and nanorods has been previously discussed by Harik (2001). However, these models may not be able to capture the kaleidoscopic size-dependent phenomena that have been widely observed, either numerically or experimentally, in nanomaterials/ nanostructures (Shenoy, 2005;Chen et al, 2006). In such cases, generalized (or enriched) continuum mechanics models, such as nonlocal theory (Wang, 2005), gradient theory , surface theory (Duan et al, 2008;Chen, 2011), and other high-order theories may need to be adopted.…”

Thermo-coupled Surface Cauchy–Born theory: An engineering finite element approach to modeling of nanowire thermomechanical response

“…This stress formulation is different from the conventional definition of a 2 × 2 surface stress (Shenoy, 2005) which includes only tangential terms. Similarly, the surface spatial modulus, D T , can be defined as…”

Determinations of both length scale and surface elastic parameters for fcc metals

“…In the present research, differing from previous methods (by definitions), we used a very simple method, energy variational method, to derive out the surface/interface theory, which is same as the commonly used Shuttleworth's version of the surface/interface theory [24,28].…”

“…Maede and Vanderbilt [26] and Needs [27] studied the surface stresses of semiconductor element and metal element by using ab initio calculations. Shenoy [28] studied the surface constitutive relation and derived the surface elastic constants, and he obtained the formulas of the surface elastic parameters. Mi et al [29] and Pahlevani and Shodja [30] investigated the surface stress and the surface elastic parameters through molecular dynamics (MD) simulation.…”