First-principles prediction of point defect energies and concentrations in the tantalum and hafnium carbides

First-principles calculations are combined with a statistical-mechanical model to predict the equilibrium point-defect concentrations in the refractory carbides TaC and HfC as a function of temperature and chemical composition. Several different types of point defects (vacancies, interstitials, antisite atoms) and their clusters are treated in a unified manner. The defect concentrations either strictly follow or can be closely approximated by Arrhenius functions with parameters predicted by the model. The model is general and applicable to other carbides, nitrides, borides, or similar chemical compounds. Implications of this work for understanding the diffusion mechanisms in TaC and HfC are discussed.