A temperature-dependent surface free energy model for solid single crystals

A temperature-dependent theoretical model for the surface free energy of the solid single crystals is established. This model relates the surface free energy at the elevated temperatures to that at the reference temperature, the temperature-dependent specific heat at constant pressure and coefficient of the linear thermal expansion, the heat of phase transition, the melting heat, and the vapor heat. As examples, the surface free energies of Fe, Cu, Al, Ni, and Pb from 0 K to melting points are calculated and are in reasonable agreement with these from Tyson's theories and the experimental results. This model has obvious advantages compared to Tyson's semi-empirical equations from the aspect of physical meaning, applicable condition, and accuracy. The study shows that the surface free energy of the solid single crystals firstly remains approximately constant and then decreases linearly as temperature increases from 0 K to melting point.