Molecular dynamics study of equilibrium concentration profiles and the gradient energy coefficient in Cu-Pb nanodroplets

Atomistic simulations were used to equilibrate the concentration profiles in 5.3 nm liquid droplets for an embedded atom method model of Cu-Pb. The strong tendency of Pb to surface segregate establishes a nonuniform profile, which decays over a length comparable to the particle radius. With the free energy vs composition determined from separate Monte Carlo simulations, the composition profile can be analyzed in terms of the Cahn-Hilliard diffuse interface model and the gradient energy coefficient, κ, can be obtained. Results from three different temperatures indicate that κ lies in the range 1.0–1.4×10⁻¹⁰ J∕m. In addition to the gradient energy coefficient, various aspects of phase equilibria at the nanoscale have been investigated. The critical point of the liquid-liquid miscibility was found to decrease by ≈50 K for the 5.3 nm particle size, the melting point of pure Cu is suppressed by ≈110 K, and the liquidus slope is shallower than that of the bulk system.