Nanosize lattice-structured-based model dependence to calculate melting temperature and other related thermodynamical parameters in metallic nanoparticles

A lattice volume-based model is derived to calculate the nanosize-dependent melting temperature of solids T(r) in the simplest form of T(r) = T(infinity) x (Delta V(r)/Delta V-c), where T(infinity), Delta V(r), Delta V-c are bulk melting temperature, nanosize dependence in the lattice volume change and its maximum change in which at, the solids are melted at zero Kelvin. The equation is applicable to calculate the nanosize dependence of melting temperature for the nanoscale size down to the material's critical radius of 1.2 nm. Accordingly, the nanosize dependence melting temperature calculations for the entire range from that of the bulk state down to the critical size for Au nanoparticles are confirmed with those of the experimental data. This model confirms well to 10 nm size particles and less where other models are not, the size range in which the solids have its most sensitive dependence of thermodynamic, mechanic, and optoelectronic properties. The model also confirms the nanosize dependence reported in experimental data for Ag, Al, Bi, In, Pb, and Cu particles. Equations to calculate nanosize dependence of cohesive energy, Debye temperature, vibrational entropy, and enthalpy of melting for metallic particles are accordingly modified and applied on Au and Cu nanoscale sizes.