liquid-drop model. Where: σsv=solid-vapor interface energy σlv=liquid-vapor interface energy Hf=Bulk heat of fusion ρs=density of solid ρl=density of liquid d=diameter of nanoparticle Liquid shell nucleation model The liquid shell nucleation model (LSN) predicts that a surface layer of atoms melts prior to the bulk of the particle. The melting temperature of a nanoparticle is a function of its radius of curvature according to the LSN. Large nanoparticles melt at greater temperatures as a result of their larger radius of curvature. The model calculates melting conditions as a function of two competing order parameters using Landau potentials. One order parameter represents a solid nanoparticle, while the other represents the liquid phase. Each of the order parameters is a function of particle radius. The parabolic Landau potentials for the liquid and solid phases are calculated at a given temperature, with the lesser Landau a potential assumed to be the equilibrium state at any point in the particle. In the temperature range of surface melting, the results show that the Landau curve of the ordered state is favored near the center of the particle while the Landau curve of the disordered state is smaller near the surface of the particle. The Landau curves intersect at a specific radius from the center of the particle. The distinct intersection of the potentials means the LSN predicts a sharp, unmoving interface between the solid and liquid phases at a given temperature. The exact thickness of the liquid layer at a given temperature is the equilibrium point between the competing Landau potentials. Equation 5 gives the condition at which an entire nanoparticle melts according to the LSN model. Where: d0=atomic diameter Liquid nucleation and growth model The liquid nucleation and growth model (LNG) treats nanoparticle melting as a surface initiated process. The surface melts initially, and the liquid-solid interface quickly advances through the entire nanoparticle. The LNG defines melting conditions through the Gibbs-Duhem relations, yielding a melting temperature function dependent on the interfacial energies between the solid and liquid phases, volumes and surface areas of each phase, and size of the nanoparticle. The model calculations show that the liquid phase forms at lower temperatures for smaller nanoparticles. Once the liquid phase forms, the free energy conditions quickly change and favor melting. Equation 6 gives the melting conditions for a spherical nanoparticle according to the LNG model. Bond-order-length-strength (BOLS) model The bond-order-length-strength (BOLS) model employs an atomistic approach