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 T_m 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 T_m 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, T_m(R⁻¹) and E(R⁻¹) dependences are characterized by different values of the slope coefficients : K_T > 1 whereas K_E < 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 T_m, 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 R_ch corresponding to a crossover from region I of mesoscopic NPs (R > R_ch) to region II of metal nanoclusters (R < R_ch). 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 N_ch varies in a wider range from 100 to 500 atoms as N_ch is proportional to \( {R}_{\mathrm{ch}}^3 \). In range II, noticeable fluctuations and non-scalable behavior of T_m 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.