Size effects in the elastic deformation behavior of metallic nanoparticles

In this work, the results of a series of molecular statics simulations to investigate the size dependence of the elastic properties of metallic nanoparticles are presented. The per-atom stiffness tensor was calculated from the derivative of the used embedded atom method potentials and, from it, lower order elastic parameters, such as the Young’s modulus or the Poisson ratio. The Young’s modulus decayed up to 30 % relative to the bulk values for 2.5 nm small particles, whereas the Poisson ratio showed an increase with decreasing particle size for most materials. Particles with a diameter of 30 nm approached the continuum values to around 1 %, marking the transition to continuum theory. The size-dependent Young’s modulus and several other material properties can be described by a simple algebraic function of the number of atoms per particle. By plotting the radial distribution of the local Young’s modulus within particles of different size, it is shown that only the outermost 2–3 atomic layers are responsible for the size-dependent change of elastic properties. Within these layers, the average atomic stiffness was found to decay linearly and independent of the particle size.