Native Defects in α-Mo₂C: Insights from First-Principles Calculations

Molybdenum carbide is a promising material for replacing the hydrogenation catalysts used in industry. It has been synthesized using different sources of molybdenum oxides and carbon, such as molybdenum heptamolybdate, molybdenum oxides, glucose, alkanes, and toluene. Nonstoichiometric material is produced, normally forming carbon vacancies or molybdenum vacancies, depending on the synthetic route. An approach for calculating the Helmholtz free energy of vacancy formation has been proposed, taking as reference the carbon and molybdenum atomic energies in the solid. The Helmholtz free energy for the carbon and molybdenum vacancies for different temperatures has been calculated. The results show that at 650 K, 9.6% of molybdenum vacancies and 10.2% of carbon vacancies exist. For temperatures below 610 K, the concentration of molybdenum vacancies is larger than that of carbon vacancies. The electron localization function (ELF) has been calculated for both defective materials, showing that the carbon vacancy presented trapped electrons forming a network that extends throughout the crystal with nearly homogeneous density. For the molybdenum vacancies, the electron density is completely depleted, leading to an electron-deficient site. The Lewis acid and base sites formed upon the presence of vacancies must be of real importance for understanding the catalytic properties of such materials. The presence of both vacancies is predicted to exist at a temperature of about 620 K.