Temperature-dependent stable phase domains of Zr–C–N (Zr–ZrC–ZrC0.96–Zr(C1−xNx)−ZrN, x = 0.1–0.9) systems from ab initio calculations and experimental results

Abstract

Despite the importance of ZrC, ZrN, and their intermediate solid solutions, the temperature-dependent phase stability of the Zr–C–N system has not previously been determined precisely. This work reports these phase stabilities determined experimentally and using ab initio calculations within the quasi-harmonic approximation. Special quasi-random structure models and supercell models with random substitution were used to mimic the random atomic distribution of C and N in the sublattice of Zr(C1−xNx) solid solutions. The results indicated that volume and high-temperature entropy changes are important to determine the free energy of the solid solutions and that moderate temperatures (∼1500–2000 K) were needed to synthesize Zr(C1−xNx) solid solutions. The calculated stable phase domains were then successfully produced. Our results clarify the synthesis and stable phase prediction of the Zr–C–N system under certain external conditions, and they will help broaden the applicability of ZrC, ZrN, and their solid solution phases.