Size-dependent melting: Numerical calculations of the phonon spectrum
  In order to clarify the relationship between the phonon spectra of nanoparticles and their melting temperature, we studied in detail the size-dependent low energy vibration modes. A minimum model with atoms on a lattice and harmonic potentials for neighboring atoms is used to reveal a general behavior. By calculating the phonon spectra for a series of nanoparticles of two lattice types in different sizes, we found that density of low energy modes increases as the size of nanoparticles decreases, and this density increasing causes decreasing of melting temperature. Size-dependent behavior of the phonon spectra accounts for typical properties of surface-premelting and irregular melting temperature on fine scales. These results show that our minimum model captures main physics of nanoparticles. Therefore, more physical characteristics for nanoparticles of certain types can be given by phonons and microscopic potential models. 
Kai Kang, Shaojing Qin, and Chuilin Wang