Modelling of high-temperature order-disorder phase transitions of non-stoichiometric MoC and TiC from first principles.

High-temperature order-disorder phase transitions play an important role in determining the structure and physical and chemical properties of non-stoichiometric transition metal carbides. Due to the large number of possible carbon vacancy arrangements, it is difficult to study these systems with first-principles calculations. Here, we construct a simple atomistic potential capable of accurately reproducing the energetics of the carbon vacancy arrangements in cubic MoC and TiC obtained from density functional theory calculations. We show that this potential can be applied to correctly predict the transition temperatures between the ordered and disordered states in Monte Carlo simulations on large supercells and reveal the extend of local order in the disordered phases of MoC and TiC that show interesting physical and chemical properties. We find that even the high-temperature disordered phase exhibit a relatively high degree of local order as indicated by the relatively small change in the root mean square number of C atom neighbours of Mo/Ti compared to the ordered phase (from 3.0 to 3.1-3.2). This atomistic potential enables the study of how the structure of these carbides can be tuned through the synthesis temperature to control the properties of carbide materials that are related to the degree of disorder in the system such as catalytic activity and electrical conductivity and play an important role in applications of these carbides. Fundamentally, the successful modelling of these carbides suggests that despite the presence of metallic, covalent and ionic interactions, bonding in carbides can be modelled by simple and physically intuitive interatomic potentials.