Modeling the cohesive energy and melting point of nanoparticles by their average coordination number

We present a relation between the average coordination number and the cohesive energy for nanoparticles that shows that the ratio of nanoparticles cohesive energy to the bulk value is equal to the ratio of the nanoparticles average coordination number to that of the bulk. We consider the effect of lattice and surface packing factors on the average coordination numbers of the atoms in the nanoparticle. The melting temperature of nanoparticles has been calculated from the obtained relation for cohesive energy, and predictions for the cohesive energy and melting temperature of the nanoparticles have been compared with other theoretical models and available experimental data and the results of molecular dynamics simulations.