The temperature dependence of grain boundary free energy of solids

The grain boundary free energy of solids at elevated temperatures has been rarely reported because of the difficulty in determining it from the existing methods. In the present work, a theoretical model for the temperature-dependent grain boundary energy is proposed via an analytical approach from the energy view by relating its temperature dependence to that of specific heat at constant pressure. The accuracy of the model is validated on metals and ceramics. The study shows that the grain boundary energy first remains approximately constant and then decreases almost linearly as temperature changes from 0 K to melting point. Phase transformation can reduce the grain boundary energy. As an example of application, the "brittleness parameter" of solids at elevated temperatures is characterized quantitatively for the first time. The ductility of metals increases rapidly with temperature. The brittleness of ceramics almost holds up to the melting point.