Melting heat of a nanoparticle

Expressions for the melting point $(T_m)$, freezing temperature $(T_N<T_m)$, entropy change per atom $(\Delta s)$, latent heat $(\Delta h=T_m\Delta s)$, and volume change $(\Delta v)$ for the solid-liquid phase transition are derived from a model of a nanocrystal in the form of a parallelepiped with a variable shape of the surface. These quantities are studied as a function of the number of atoms $(N)$ and the shape of the nanoparticle. Calculations carried out for copper nanoparticles show good agreement with the results of computational experiments. It is shown that functions $\Delta s$, $\Delta h$, and $\Delta v$ vanish in a certain range of cluster dimension $N_0$ and a hysteresis between the melting point and freezing temperature disappears, $T_N(N_0)=T_m(N_0)$. In such a cluster, the phases become physically identical. For nanocopper, this dimension falls into the range $N_0$ = 49–309 and grows when the shape of the nanoparticle deviates from the energetically most favorable one.