Thermodynamic properties of ZrC are calculated up to the melting point ($T^{\mathrm{melt}}\approx 3700\text{K}$), using density functional theory (DFT) to obtain the fully anharmonic vibrational contribution, and including electronic excitations. A significant improvement is found in comparison to results calculated within the quasiharmonic approximation. The calculated thermal expansion is in better agreement with experiment and the heat capacity reproduces rather closely a CALPHAD estimate. The calculations are presented as an application of a development of the upsampled thermodynamic integration using Langevin dynamics (UP-TILD) approach. This development, referred to here as two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD), is the inclusion of tailored interatomic potentials to characterize an intermediate reference state of anharmonic vibrations on a two-stage path of thermodynamic integration between the original DFT quasiharmonic free energy and the fully anharmonic DFT free energy. This approach greatly accelerates the convergence of the calculation, giving a factor of improvement in efficiency of $\sim 50$ in the present case compared to the original UP-TILD approach, and it can be applied to a wide range of materials.

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_x (x ≤ 1) phases was found to decrease with increasing oxygen concentration, which can be attributed to the different ionocovalent nature of the C–Zr and O–Zr bonds. The volume of the vacancy-ordered phases within the expected oxygen solubility limit is greater than the disordered phase of the same composition, which is explained in terms of the relative bond strengths surrounding different vacancy distributions.

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 long‐range 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.

The origin of vacancy ordering in ZrC _x 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.

Equitable access to high-quality higher education is in line with the United Nations Sustainable Development Goals 4, 5, and 10, which indicate that it is crucial for a future sustainable society. Globalisation and reductions in systemic barriers to university admission are creating increasingly diverse higher education classrooms, but traditional education methods may unfairly disadvantage some groups of students. Creating equity in access to high-quality education requires teaching approaches that are considerate of each student’s individual sociocultural context as it affects their educational attainment. Building on discipline-based education research (DBER) principles in science, technology, engineering, and mathematics (STEM) education, a modified holistic approach is proposed that primarily centres on students and tailors the teaching methods to the needs of the individuals and the dynamic of the whole class. This work demonstrates that educational attainment and student confidence was improved by applying an individual-centred teaching approach in a highly diverse undergraduate engineering classroom. Trials of this approach in a pilot classroom showed clear and consistent improvement over standard active learning approaches. Best practice guidelines for individual-centred teaching in STEM classrooms are provided. Further work is needed to examine the efficacy of this approach in a generalised setting, but the positive outcomes for student attainment are in line with existing research in the literature. The best practice guidelines presented herein may serve as a starting point for other educators to become more aware of the sociocultural needs of their individual students and classrooms, which may result in a move towards equity in STEM higher education.