Temperature dependent phase stability of Ti(C_1−xN_x) solid solutions using first-principles calculations

We investigated lattice dynamic and temperature-dependent thermodynamic phase stabilities of Ti(C_1−xN_x) solid solutions using first-principles calculations within the quasi-harmonic approximation. Phonon dispersion and density of states were obtained by the finite-element method. Special quasi-random structures were used to mimic the random distribution of carbon and nitrogen atoms in the sublattice of Ti(C_1−xN_x). The reliability of the models and calculations were obtained by comparing the structural and elastic properties of Ti(C_1−xN_x) with previous results. The random mixing of carbon and nitrogen atoms had a minor effect on the elastic properties, but greatly influenced the dynamic stability. Thermodynamic phase stability was investigated using the formation energy of the solid solutions. The phonon density of states with the quasi-harmonic approximation yielded accurate formation energies at various temperatures. Nitrogen-rich phases showed noticeable changes in thermodynamic stability with increasing temperature, and their phase stability decreased quickly in comparison with the carbon-rich phases. Our results provide fundamental insights into Ti(CN) solid solutions that will help underpin the use and production of Ti(CN) materials.