Thermodynamic Modeling of the Melting Behavior of Metallic Nanoparticles ‎Embedded in a Matrix

Melting temperature is one of the most important size-dependent properties in nanoparticles. The experimental ‎study of nanoparticle melting is so complicated. So, many mathematical models have been proposed to ‎predict the melting temperature of free and embedded nanoparticles. However, most of these models are based ‎solely on solid phase properties and does not take the properties of the liquid state into account. This causes ‎inaccuracies in the results of these models. Therefore, development of new models with more accuracy is ‎essential. Based on the calculation of Gibbs free energies of solid and liquid phases, in the present study, a ‎thermodynamic model is proposed to calculate the melting temperature of embedded nanoparticles. The ‎proposed model used to calculate the melting temperature of silver nanoparticles embedded in nickel matrix ‎and Pb nanoparticles embedded in Cu and Zn matrices. The results showed that in the studied systems, ‎reducing the particle size will increase the melting temperature of the nanoparticles. Comparing the calculated ‎results with the available experimental data as well as the results of the previous models confirms the higher ‎accuracy of the proposed model. In addition to the particle size, the effect of nanoparticle shape on the melting ‎temperature is investigated. The results showed that the change in melting temperature with the change in ‎nanoparticles shape is evident only in nanoparticles smaller than 10 nm.‎