Thermodynamic surface characteristics of liquid-metal nanodroplets at the vapor boundary

New relationships for the size-dependent surface tension σ(r), surface energy ū(r), the temperature T(r) of equilibrium between a liquid droplet and the surrounding vapor, and derivatives dσ/dT and dT/dr, which define spherical nanodroplets of liquid metals at the vapor boundary, are derived under the assumption that the two-phase (liquid nanodroplet-vapor) and three-phase (liquid nanodroplet-vapor-solid phase) equilibrium conditions are fulfilled. Consistent calculations of the aforementioned quantities are performed. The revealed dependences between the surface characteristics of nanodroplets of several metals and the calculation results are discussed.