The effect of oxygen impurities on the stability and structural properties of vacancy-ordered and -disordered ZrC_x

Abstract

First-principles calculations are used to explore vacancy ordering in zirconium carbide at various stoichiometries as affected by oxygen impurities. Atomic bonding and electronic charge distribution are linked to stability and volume trends as a function of O concentration.

Vacancy ordering in substoichiometric zirconium carbide: A review

“…Davey et al performed first-principles calculations at 0 K to confirm that the above empirical function did represent variations of the lattice parameter of the disordered solution phase with changing carbon and oxygen concentrations. 73 The lattice parameter increases with increasing vacancy concentration from stoichiometric ZrC to a maximum ∼ZrC 0.83 , 72 and decreases with further increases in vacancy concentration beyond this. Davey et al explain this trend in terms of the average vacancy volume possible in various vacancy configurations.…”

“…72 Davey et al used 0 K first-principles calculations to explore the effects on the stability of ordered superstructural phases compared to the disordered phase, by varying the oxygen and carbon vacancy concentrations in ordered structures and SQS, representing the disordered phase. 73 Typical experimental samples of zirconium F I G U R E 1 0 Ordering energy as a function of oxygen concentration in each ordered zirconium carbide phase at 0 K, adapted from Davey et al 73 A positive ordering energy indicates that the ordered phase is stable, and a negative ordering energy indicates that the disordered phase at the same composition is stable. The oxygen concentrations at which the ordering energy become negative may be considered to be lower bound approximations for destabilization of the ordered structures carbide may contain up to 10 at.% dissolved oxygen, 74 where the oxygen will preferentially enter vacant sites if they are available, otherwise displacing carbon.…”

“…The oxygen concentrations at which the ordering energy become negative may be considered to be lower bound approximations for destabilization of the ordered structures carbide may contain up to 10 at.% dissolved oxygen, 74 where the oxygen will preferentially enter vacant sites if they are available, otherwise displacing carbon. 73,75 The ordering energy (the difference between the formation energy of the disordered and ordered phases at the same composition) is defined using the formation energy of an ordered or disordered Zr x C y O z compound with respect to the pure elements, 𝑂 are the energies per atom of pure Zr, C, and O in their ground state structures (hcp, graphite, and dimer O 2 , respectively). The ordering energy of each ordered phase may therefore be defined as…”

“…where a positive ordering energy indicates that the ordered phase is stable, and a negative ordering energy indicates that the disordered phase is stable. The calculated ordering energy from Davey et al 73 is shown in Figure 10 for each stable ordered phase as a function of oxygen concentration. At 0 K, the presence of impurity-levels of oxygen in the lattice decreases the stability of the ordered superstructures.…”

“…Davey et al. used 0 K first‐principles calculations to explore the effects on the stability of ordered superstructural phases compared to the disordered phase, by varying the oxygen and carbon vacancy concentrations in ordered structures and SQS, representing the disordered phase 73 . Typical experimental samples of zirconium carbide may contain up to 10 at.% dissolved oxygen, 74 where the oxygen will preferentially enter vacant sites if they are available, otherwise displacing carbon 73,75 .…”