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Theoretical calculations predict several long-range ordered sub-stoichiometric zirconium carbide phases to be stable at low temperature, rather than a random (disordered solution) distribution of vacancies. However, experimental synthesis of vacancy-ordered phases is extremely challenging and not all predicted phases have been experimentally observed. It has been hypothesised that the inevitable oxygen contamination in experimental samples may affect the vacancy ordering. In this work, the stability and structural properties of the vacancy-ordered and vacancy-disordered phases are investigated as a function of oxygen defect concentration using first-principles calculations. The observed trends are explained in terms of changes to the local bonding in the presence of varying amounts of oxygen and vacancies. It is found that the relative stability of the ordered phases (compared to the disordered phase at the same composition) decreases as oxygen concentration increases, and some vacancy-ordered phases are destabilised by the level of oxygen impurities found in experimental samples. This suggests that oxygen contamination is a contributing factor to the challenge of synthesising ordered zirconium carbides, and gives insight that may assist fabrication in the future. The volume of all ZrC

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.