Symmetry lowering and surface elasticity effects on Young’s modulus and Poisson’s ratio of nanofilms

Abstract

Physical and mechanical properties of nanosized materials and structures are strongly affected by surface effects. In this paper, a self-consistent theoretical scheme for describing the elastic properties of nanofilms was proposed. The Young’s modulus, biaxial modulus and Poisson’s ratio of nanofilms were obtained analytically with considerations of symmetry lowering, surface elasticity, elastic parameter splitting and additional elastic coefficient. Applications of present theory to elastic systems such as Si nanofilm Young’s modulus, Cu nanofilm biaxial modulus and Poisson’s ratio yield good agreement with previous calculated results. We found that Young’s modulus and Poisson’s ratio were split due to symmetry lowering, and this splitting confirms the symmetry lowering. For a nanofilm with a given thickness, Young’s modulus and biaxial modulus increase with surface elastic coefficients increase except $c_{{12}}^{{\alpha ,s}}$. The larger positive $c_{{12}}^{{\alpha ,s}}$ drives Young’s modulus towards smaller abnormally. The present study in this paper is envisaged to provide useful insights for the design and application of nanofilm-based devices.