Stability and structural properties of vacancy-ordered and -disordered ZrC_x

Vacancy-ordered superstructural phases of zirconium carbide have been intermittently observed at low temperatures for over 50 years. However, little is known about these ordered phases as they have proven to be challenging to fabricate experimentally, although theoretical predictions suggest that they should be significantly more stable than the more-observed vacancy-disordered solid solution ZrCx (x ≤ 1) phase at low temperatures. The stability and structural properties of the vacancy-ordered and vacancy-disordered phases are investigated using first-principles calculations. The stability of the ordered superstructural phases is related to the driving force from the relative instability of certain vacancy configurations, which are preferred or avoided in ordered structures. The trend of the vacancy ordering and the underlying mechanisms of the relative instability are explained in terms of the geometry of the crystal structures and the electronic charge distribution and atomic bonding features.