Melting enthalpy depression of nanocrystals based on surface effect

Abstract

Takagi was the first to demonstrate that ultrafine metallic particles melt below their corresponding bulk melting temperature in 1954 [1]. Now it is known that the melting temperatures of all nanocrystals, including metals [2, 3], semiconductors [4, 5] and organic nanocrystals [6, 7], depend on their size and this has been explained in terms of various models related to interface energy [8]. This size effect is experimentally also observed on the melting enthalpy [2, 6]. However, none of the above models can interpret sizedependent melting enthalpy of nanocrystals directly [8]. Knowledge of thermodynamic parameter are important for complete understanding of melting transition of nanocrystals and will deepen our insight into the size effect on melting. Therefore, a direct consideration on the size-dependence of melting enthalpy is needed. In this contribution, a simple physical model for the size-dependent melting enthalpy of nanocrystals in terms of the effect of bond number and bond energy of surface atoms of nanocrystals and that of the corresponding liquids on the internal energy of the system is developed. Combining with Mott’s expression for the vibrational entropy of melting for metallic crystals, size-dependent melting temperature of metallic nanocrystals is also predicted. The model predictions correspond well to the latest experimental results of indium nanocrystals. We consider that size-dependent melting enthalpy H (r ) is additive where r denotes radius of nanoparticles and nanowires, or half thickness of thin films,