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

Abstract

The origin of vacancy ordering in ZrCx is explained considering structure geometry, electronic charge distribution, and atomic bonding features, and linked to stability and volume trends in the vacancy-ordered and -disordered zirconium carbides.

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

“…A positive IpCOHP indicates that the pair bond has a greater antibonding character (is repulsive). The average IpCOHP for each bond type reveals that the bonding in pristine zirconium carbide is dominated by the rst nearest neighbour (1nn) C-Zr bond, in agreement with Xie et al 18 and Davey et al 19 The 1nn Zr-Zr bond and second nearest neighbour (2nn) C-C bonds also provide smaller but nite bonding contributions. The bonding strength of the other bond types, and those at further distances, are all negligibly small.…”

“…The ground state energy at 0 K was determined via non-spinpolarised density functional theory (DFT) calculations in the same procedure as Davey et al, 19 using the Projector Augmented Wave (PAW) method 34,35 in the GPU implementation 36,37 of the Vienna Ab initio Soware Package (VASP). [38][39][40] The cutoff energy and k-point Monkhorst-Pack mesh 41 density were chosen as 700 eV and at least 15 000 k-points per supercell to ensure good convergence of all energy calculations.…”

“…The formation energy of stoichiometric ZrC and the ordered ZrC x phases without any oxygen impurities are consistent with other rst-principles studies. [15][16][17][18][19] The formation energies in Table 2 show that in all cases of oxygen defect types (ii) and (iii), the structures containing oxygen are more stable than the pure structure and the oxygen defect formation energy is negative. This increased stability may explain why processing ZrC x to fully remove oxygen (such as by carbothermal or methanothermal reduction) is so challenging.…”

“…For all structures, the octahedral site (defect type (ii) or (iii)) is most favourable for the oxygen atom, where the vacant octahedral site (defect type (iii)) is preferred if vacancies are present, in agreement with experimental observations from Réjasse et al 30 As the oxygen defect formation energy is negative for all the cases of defect types (ii)- (iv), several different defective structures may coexist in a real bulk crystal, although only the most stable octahedral defects are considered further in this work. 19 The O-Zr bond is primarily characterised by partial hybridisation of the Zr d-electrons and the O p-electrons between À8 eV and À5 eV below the Fermi energy which obviously enhances the binding of the system. The extent of the orbital hybridisation from the density of states once again suggests that the O-Zr bond is more ionic than the C-Zr bond.…”

“…A theoretical phase diagram from Gusev and Rempel 14 determined by the Order Parameter Functional (OPF) method predicted the stability of several ordered zirconium carbide subphases below 1200 K. Zhang et al 15,16 used the Cluster Expansion (CE) method, and Yu et al 17 and Xie et al 18 used the USPEX evolutionary algorithm, to obtain the theoretical convex hull of stable phases at 0 K. All predicted several ordered subphases that are stable compared to the vacancy-disordered phase, but disagreeing upon which phases are stable. In recent work, Davey et al 19 considered the most stable reported structures and claried the sub-stoichiometric ordered phases at 0 K to be Zr 7 C 6 (R 3), Zr 4 C 3 (C2/c), Zr 3 C 2 (Fddd), and Zr 2 C (Fd 3m). De Novion and Maurice 8 rst proposed that the long-range ordering of carbon vacancies was driven by short-range preferences for the arrangement of vacancies, which was conrmed by Razumovskiy et al, 20,21 and Zhang et al, 15 who demonstrated that there was a preference for vacancy pairs to be at third nearest neighbour distances, and that in all stable ordered phases vacancy pairs avoid the second nearest neighbour separation completely.…”