Molecular dynamics simulation of melting of metal nanoparticles using temperature dependence of self-diffusion coefficient

Usually the melting of nanoparticles, including metal nanoclusters, is registered by a jump in the temperature dependence of the cohesive (potential) term in the particle specific (per atom) internal energy u. On the one hand, such an approach entirely corresponds to the basis thermodynamic definition of the phase transition of the 1-st order. On the other hand, this approach does not confirm directly that the nanoparticle is really transformed from the crystalline state to a liquid-like one. From this point of view, it is of interest to register the melting transition analyzing the temperature dependence of the self-diffusion coefficient D. In this work D has been found using formula <(Δr)²>=6Dt which follows from both the Fick diffusion equation and Einstein’s theory of Brownian motion. Here <(Δr)²> is the average square of the increment Δr of the radial coordinate r of an atom, t is the time. In Fig. 1 the dependence of lg(D) on the relative temperature ΔT=T-T_m is shown for Ni nanoparticles consisting of 500 atoms (T_m is the particle melting temperature found via the jump of u). An analogous dependence was found for Au nanoparticles. One can see that the jump of lg(D) in Fig. 1 corresponds in general to ΔT=0K. At the same time, the jump in question takes place as temperature T which is in about 25K lower than T_m.

Using the well-known formula D= D₀exp(-E/RT), we have evaluated the pre-exponential factor D₀ and the heat (energy) of activation E of diffusion (R is the molar gas constant). As one can see from the table, values of D₀ and E, corresponding to solid Ni nanoparticles, agree with those for the bulk Ni phase.