On Minimum Size of Nanoparticle when Difference Disappears between Solid and Liquid Phases

Based on the model of a nanocrystal as a rectangular parallelepiped with variable surface shape, the expressions for the melting point T_m and the temperature of the crystallization start T_N < T_m and for specific (per atom) jumps of the entropy Δs, the latent heat Δh = T_m Δs, and the volume Δv are derived for the crystal-to-liquid phase transition. The dependence of these functions on the number of atoms N and on the nanoparticle shape is investigated. It is shown that at the certain size N₀, the functions Δs, Δh, and Δv become equal to zero and a hysteresis between the melting point and a temperature of crystallization start disappears: T_N(N₀) = T_m(N₀). In such a cluster, the physical difference between phases vanishes. This size for nanocopper lies within an interval of N₀ = 49...309 and increases when the nanoparticle shape deviates from the shape of most stable energy.