The temperature-dependent surface energy of ceramic single crystals

Knowledge of the surface energy of ceramic single crystals at elevated temperatures is of fundamental importance. However, it is very hard to obtain this quantity from the existing experiments, simulations, and theories. In the present work, following the Orowan-Polanyi and Gilman models’ principles, two theoretical models for the temperature-dependent surface energy of the ceramic single crystals are proposed based on the authors’ previous studies on the temperature-dependent ideal tensile strength of solids. Thus established models relate the temperature dependence of the surface energy to these of the specific heat at constant pressure, Young's modulus, and coefficient of the linear thermal expansion. The temperature-dependent surface energies of α-Al₂O₃ and β-Si₃N₄ are calculated and agree well with the experimental data. The study shows that the surface energy firstly remains approximately constant and then decreases linearly as temperature increases from 0 K to melting point. However, it has stronger temperature dependence than Young's modulus, that is, surface energy decreases more rapidly with increasing temperature.