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

Abstract

NaCl‐type carbides of the early transition metals can exhibit a substantial sub‐stoichiometry at the carbon site, impacting a host of bulk properties that depend upon carbon concentration including melting points, mechanical and elastic properties, and superconducting transition temperatures. Unfortunately, control over vacancies remains challenging with current preparation methods, motivating the search for new synthetic approaches that will allow for the prescription of specific vacancy configurations. Here, density functional theory is augmented with alloy cluster expansion to examine the structure and zero kelvin enthalpy of millions of structures across composition and pressure space. The results are used to examine how extreme pressures might be used to access novel ordered and disordered phases of ZrC, many of which have been calculated to be thermodynamically stable yet remain synthetically elusive. High pressure is shown to significantly reduce sub‐stoichiometry and drive the system toward fully stoichiometric ZrC. They examine the root of these changes and find that pressure exerts an influence over the distribution and abundance of specific nearest‐neighbor vacancy pairs. These results suggest that pressure is a powerful tool for the control of vacancies, and can offer a new synthetic handle on the bulk properties exhibited in this industrially important class of materials.

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

“…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 . Thus, our calculations are seemingly at odds with the experimental observation of this phase.…”

“…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. − ,, …”

“…This behavior is consistent with the stability of the Zr 2 C (Fd3̅ 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. 65 Thus, our calculations are seemingly at odds with the experimental observation of this 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. [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.…”