Ab initio investigation of Ti2Al(C,N) solid solutions

M(n+1)AX(n) phases (M: early transition metal, A: IIIA-or IVA-group element, X: carbon or nitrogen) are layered ternary compounds that possess both metal-and ceramic-like properties with numerous potential applications in bulk and thin film forms, particularly under high-temperature conditions. In this work, we use the cluster expansion formalism to investigate the energetics of C-N interactions across the entire Ti2AlC-Ti2AlN composition range. It is shown that there is a definite tendency for ordering in the C,N sublattice. However, the molar volume and bulk modulus of the ordered structures found along the Ti2AlC-Ti2AlN composition range show small deviations from the (linear) rule of mixing, indicating that despite the ordering tendencies, the C-N interactions are not strong and the solution becomes disordered at relatively low temperatures. Random solid solutions of Ti2AlC1-xNx are simulated using special quasirandom structures (SQS) with x = 0.25, 0.50, and 0.75. The thermodynamic properties of these structures are compared to those of the structures found to belong to the ground state through the cluster expansion approach. It is found that the structural properties of these approximations to random alloys do not deviate significantly from Vegard's law. The trend in the structural parameters of these SQS are found to agree well with available experimental data and the predictions of the bulk modulus suggest a very weak alloying effect-with respect to Vegard's law-on the elastic properties of Ti2AlC1-xNx.