Abstract:
Different approaches to the determination of temperature are considered. Thermodynamic consideration of
clusters takes into account not only the energy of thermal motion of atoms, but also the potential energy of
interaction of atoms in the cluster, including the energy of configuration excitation. The thermodynamic
determination of the temperature of clusters is more complete and accurate. Thermodynamic consideration of
clusters, taking into account their total internal energy and entropy, allows us to describe many processes
occurring during structural transitions, and gives a deeper and more detailed understanding of the physics of
phase transitions in clusters. In this paper we review various models of the melting temperature of
nanoparticles and propose a quantum-statistical analysis of the melting of nanoparticles. To explain the
change in the melting temperature of nanoobjects, the most widely used thermodynamic approach is based on
taking into account the increasing role of surface energy with a decrease in the characteristic size. The
dependence of the melting temperature of metal nanoparticles on size is also explained on the basis of the
criteria proposed by Lindemann. According to Lindemann's ideas, the crystal melts when the root-meansquare
displacement of atoms in the crystal becomes larger than the fraction of intraatomic distances. The
molecular dynamics method allows one to study structural transitions, thermodynamic parameters, transport
properties, and electronic states in complex systems. The increasing computing power of computers
constantly expands the range of possible applications of the molecular dynamics method. At present, the
behavior of quite complex systems containing tens of thousands of atoms is successfully modeled. With the
help of nonequilibrium statistical thermodynamics, a connection was found between the microscopic
(quantum) processes of interaction of primary fields (the parameters of which can be controlled and varied
over a wide range) with the macroscopic characteristics of the physical object. In all cases, the size
dependence of the melting temperature of nanoparticles is determined.
