Analytical Model for Studying Bulk Modulus Variation in Free Standing Nanostructures Based on Their Size and Shape

Abstract

In the present study, a unified model is proposed to determine the shape and size impact on the bulk modulus of nanostructures. The dependence of bulk modulus of nanostructure on the melting temperature is considered to obtain the expression of bulk modulus in terms of size, shape, packing fraction and surface to volume coordination number ratio. The Bulk modulus variation with respect to size of the nanomaterial is studied for nanostructures of Si, Al, Au, Ag, Cu, Ni and Pt. The model helps to determine the bulk modulus variation in spherical, tetrahedral, octahedral, hexahedral nanoparticles, cylindrical, triangular, square and hexagonal cross-section nanowires and thin nanofilms. It is noted that with change in shape of the nanomaterial, the ratio of surface atoms to total atoms in it changes and drastic variation in bulk modulus of nanostructure is noticed. The model computed results so obtained are depicted in figures with the simulated data of previous workers to compare the results obtained. The bulk modulus is found to drop with size reduction and good consistency is observed between the compared results that help to judge the suitability of the present model theory.