A semi-analytical method for quantifying the size-dependent elasticity of nanostructures

In this paper, a semi-analytical method is developed to compute the elastic stiffness of nanostructures such as nanowires, nanotubes and nanofilms. Compared with existing methods for such computations, this new method is more accurate and significantly reduces the computational time. It is based on the Taylor series expansion of an interatomic potential about the relaxed state of a nanostructure and implicitly accounts for the effects of shape, size and surface of the nanostructures. To analyze the applicability and accuracy of this method, as a case study, calculations are carried out to quantify the size dependence of the elastic moduli of nanofilms and nanowires with [0 0 1], [1 1 0] and [1 1 1] crystallographic growth orientations for groups 10 and 11 transition metals (Cu, Ni, Pd and Ag). The results are in excellent agreement with data in the literature and reveal consistent trends among the materials analyzed.