Size dependence of the bulk modulus of Si nanocrystals

Abstract

This study investigates the effect of size on bulk modulus and its related parameters, including melting temperature and mass density based on the ratio number of surface atoms to that of its internal. The equation of bulk modulus in the bulk state B(∞) is modified to include the related size-dependent parameters without any adjustable parameter, and is applied to Si nanocrystals. The bulk modulus B(r) decreases from 9.8 × 1010 N m2 for the bulk state to 5.93 × 1010 N m2 for a 5 nm diameter of Si nanoparticles. An inherent relation between bulk modulus and change of the lattice parameter in nanocrystals obtained from the variation in the surface to volume ratio, this leads to increase in the mean bond length. The effect of mass density and melting temperature on bulk modulus are also discussed. Calculated results for bulk modulus are verified by experimental as well as the available computer simulation data.