Abstract

Nanowires and ultra-thin films have wide applications in the quickly developed nanotechnology and nanoscience. The surface-to-bulk ratio in nanowires and ultra-thin films is much larger than that in conventional bulk materials. The higher surface-to-bulk ratio makes the Young’s modulus become a size-dependent property at the nanometer scale, which is seemingly contradictory to the conventional continuum elasticity. Investigating and understanding the underlying mechanism of the size-dependent elastic properties in nanomaterials is of both academic and practical significance. In this work, both theoretical modeling and virtual experiments have been made on this issue. A nanoelement built with stress-free bulk lattice constant(s), undergoes an initial relaxation, during which its morphology changes and energy reduces. With different definitions of surfaces and edges, two models for a nanomaterial – a nanowire or an ultra-thin film – are derived based on the same thermodynamics framework. Model I treats surfaces to be two-dimensional and edges to be one-dimensional, wile model II treats surfaces and edges to be three-dimensional. Under external loading, the initially relaxed state is taken as the reference. Experimentally, relaxation and tension/compression tests in different loading directions have been conducted on SiC, Si and Cu crystalline nanowires with different cross-sectional sizes and ultra-thin films with different thicknesses by Molecular Dynamics (MD) simulations. This systematic study successfully illustrates the intrinsic mechanism of the size-dependent Young’s modulus in nanomaterials and the proposed methodology facilitate characterizing mechanical properties of nanomaterials to some extent when continuum concepts, such as, surface energy and surface elastic constants, are used.