Melting temperature and binding energy of metal nanoparticles: size dependences, interrelation between them, and some correlations with structural stability of nanoclusters

Size dependences of the melting temperature Tm and binding energy E, i.e., their dependences on the particle radius R, have been investigated by employing thermodynamics, a local coordination approximation for E as well as molecular dynamics. We have found that both quantities Tm and E decrease at decreasing the particle size and follow to the linear or close to linear dependence on the reciprocal particle radius R−1. However, Tm(R−1) and E(R−1) dependences are characterized by different values of the slope coefficients : KT > 1 whereas KE < 1. As a result, the binding energy does not take zero value even for the limiting case of smallest nanoclusters down to tetramers, trimer, and dimers. As for the melting temperature Tm, the linear dependence on R−1 should be relevant to mesoscopic metal nanoparticles (NPs) only consisting of at least several hundreds of atoms. A concept is put forward of a characteristic particle radius Rch corresponding to a crossover from region I of mesoscopic NPs (R > Rch) to region II of metal nanoclusters (R < Rch). This characteristic radius cannot be exactly determined. For metal NPs, including Au ones, it is of order of 1 nm, and the characteristic number of atoms Nch varies in a wider range from 100 to 500 atoms as Nch is proportional to ( {R}_{mathrm{ch}}^3 ). In range II, noticeable fluctuations and non-scalable behavior of Tm are reported. We believe that for nanoclusters (range II), the concepts of the phase transition and of the melting temperature lose their physical meaning. On the structural level, region II relates to statistical distributions of different isomers, their instabilities and corresponding structural transformations depending on temperature and particle size.