Vacancy ordering in substoichiometric zirconium carbide: A review

Abstract

Zirconium carbide has a wide range of substoichiometry facilitated by varying numbers of carbon vacancies. Most experimental studies consider a solid solution of carbon and vacancies without long-range ordering of vacancies. However, theoretical studies predict several superstructural long-range ordered phases to be stable at low temperatures, and these predictions have been validated by experimental fabrication in some cases. The thermophysical properties of zirconium carbide are, therefore, affected not only by the number of carbon vacancies, but their arrangement, which increases the potential of its use as a tuneable ceramic in various applications in aerospace and nuclear industries. This review summarizes the experimental and theoretical studies exploring the longrange ordered zirconium carbides including the known crystal structures, the mechanism for vacancy ordering, and the presently available information on the thermophysical properties. Explanations for the infrequent experimental observations of ordered zirconium carbides are also discussed considering fabrication temperatures, vacancy diffusion, and the effects of impurities, which may be helpful for future synthesis. While our understanding of vacancy ordering in zirconium carbide has vastly improved in recent years, there remain significant knowledge gaps. Areas where more experimental and theoretical studies are needed for further understanding are highlighted.

Combined First-Principles and Experimental Investigation into the Reactivity of Codeposited Chromium–Carbon under Pressure

“…It is at least 248 meV atom –1 above the hull over the pressure range calculated. Cr 2 C ( Fd 3̅ m ) is an ordered supercell of the NaCl-type structure that has been observed experimentally in the metal-rich side of the Zr–C and Ti–C systems. − This phase begins 96 meV atom –1 above the hull at 0 GPa, which is lower energy than stoichiometric CrC ( Fm 3̅ m ), but it increases to 184 meV atom –1 above the hull at 30 GPa. This behavior is consistent with the stability of the Zr 2 C ( Fd 3̅ m ) phase in the substoichiometric NaCl-type Zr–C system, where Zr 2 C is initially stable relative to fully stoichiometric ZrC and decreases in stability with increasing pressure .…”

“…One explanation is that a large substoichiometry at the carbon site could have a significant influence on the enthalpy of the phase. Indeed, this is a common observation in many other TMCs that have been studied experimentally and computationally, with vacancy concentrations of up to 50% being typical in ZrC and TiC. − ,, …”

“…Indeed, this is a common observation in many other TMCs that have been studied experimentally and computationally, with vacancy concentrations of up to 50% being typical in ZrC and TiC. [61][62][63][64][65]69,70 We adopted a simple approach wherein 2 × 2 × 2 supercell structures of CrC (1−x) (Fm3̅ m) were generated with random concentrations and configurations of vacancies at the carbon site, before being relaxed using high-throughput DFT at pressures of 0 and 20 GPa (see the Methods section for more details). The results of these calculations are plotted in Figure 5.…”

First‐Principles Investigation of Phase Stability in Substoichiometric Zirconium Carbide under High Pressure

“…Although these ordered phases appear to lie on the convex hull, only the $$Fd\bar{3}m$$ Zr 2 C ordered phase has been consistently identified through experiment. [ 40,42–49 ] There are a few proposed reasons for why Zr 2 C is the only ordered phase that can be reliably synthesized, including the possibility that the disordered phases are kinetically “frozen in” during quenching from high temperature synthesis at higher values of x , or that the Zr 2 C structure simply outcompetes the other predicted structures, whether that be thermodynamically or kinetically. [ 49 ]…”

“…Although these ordered phases appear to lie on the convex hull, only the Fd 3m Zr 2 C ordered phase has been consistently identified through experiment. [40,[42][43][44][45][46][47][48][49] There are a few proposed reasons for why Zr 2 C is the only ordered phase that can be reliably synthesized, including the possibility that the disordered phases are kinetically "frozen in" during quenching from high temperature synthesis at higher values of x, or that the Zr 2 C structure simply outcompetes the other predicted structures, whether that be thermodynamically or kinetically. [49] Figure 2 shows that by 25 GPa, the mixing enthalpy of the Zr 2 C structure has become positive, and therefore is no longer on the convex hull.…”