Nonmetal ordering in TiC1−xNx: Ground-state structure and the effects of finite temperature

The TiC1−xNx system has long been prized in industry because of its desirable thermodynamic and hardness characteristics. Previous studies have not produced comprehensive results describing the ordering tendencies of TiC1−xNx at any temperature. We apply the mixed-basis cluster expansion and Monte Carlo methods to the problem and find a fascinating array of ground-state structures occurring at precise nitrogen-concentration intervals of x=1/16 and related to each other by simple 201 quasisuperlattice motifs. Thermodynamic Monte Carlo results indicate that the critical ordering temperatures at all concentrations are well below room temperature. Short-range ordering develops at T 800 K and exhibits the characteristic motifs of the predicted ground-state structures. Bulk modulus optimization is not feasible since this quantity shows little sensitivity to atomic configuration.