A unified bond energy model for size-dependent melting temperature of freestanding and embedded nanomaterials

Abstract

The bond energy (BE) model is a simple and practical model that has been developed to predict the melting temperature of nanomaterials. The model contains a material parameter, whose value is assumed to be 0.5 or 0.75. However, the exact value of the material parameter is not known. Available experimental data reveal that 0.5 or 0.75 are not suitable for all materials. In this research, a unified BE model has been developed to calculate the melting temperature of freestanding and embedded nanoparticles. In addition, using the available experimental data, a semi-empirical relationship has been proposed to estimate the value of the material parameter as a function of atomic distances. The results show that for freestanding nanoparticles the value of the material parameter can vary between 0.1 and 1.6. It is also found that the material parameter for embedded nanoparticles correlated with the lattice parameter mismatch between the nanoparticle and the matrix. The results show that if lattice parameter mismatch is less than 11.5%, the material parameter of freestanding and embedded nanoparticles are equal, but increasing lattice parameter mismatch, increases the material parameter of embedded nanoparticles. In addition to the melting temperature of nanoparticles, the proposed model was successfully used to calculate the melting temperature of nanowires.