Structure and thermodynamics of pure cubic ZrO₂ and HfO₂ were studied computationally and experimentally from their tetragonal to cubic transition temperatures (2311 and 2530 °C) to their melting points (2710 and 2800 °C). Computations were performed using automated ab initio molecular dynamics techniques. High temperature synchrotron X-ray diffraction on laser heated aerodynamically levitated samples provided experimental data on volume change during tetragonal-to-cubic phase transformation (0.55 ± 0.09% for ZrO₂ and 0.87 ± 0.08% for HfO₂), density and thermal expansion. Fusion enthalpies were measured using drop and catch calorimetry on laser heated levitated samples as 55 ± 7 kJ/mol for ZrO₂ and 61 ± 10 kJ/mol for HfO₂, compared with 54 ± 2 and 52 ± 2 kJ/mol from computation. Volumetric thermal expansion for cubic ZrO₂ and HfO₂ are similar and reach (4 ± 1)·10⁻⁵/K from experiment and (5 ± 1)·10⁻⁵/K from computation. An agreement with experiment renders confidence in values obtained exclusively from computation: namely heat capacity of cubic HfO₂ and ZrO₂, volume change on melting, and thermal expansion of the liquid to 3127 °C. Computed oxygen diffusion coefficients indicate that above 2400 °C pure ZrO₂ is an excellent oxygen conductor, perhaps even better than YSZ.

The oxidation of boride and carbide-based ultra-high-temperature ceramics is the primary limiting factor for their use as aerodynamic surfaces. Understanding the behaviour of the oxides that can result from oxidation of metal borides and carbides at very high temperatures is essential to optimise and tailor the performance of these materials; yet experimental thermodynamic and structural data for refractory oxides above 2000°C are mostly absent. The following techniques that can be applied to fill this gap are discussed: (i) commercial ultra-high-temperature differential thermal analysis for investigation of phase transformations and melting in inert environments to 2500°C, (ii) a combination of laser heating with a splittable nozzle aerodynamic levitator for splat quenching and drop calorimetry from temperatures limited only by sample evaporation, (iii) synchrotron X-ray and neutron diffraction on laser-heated aerodynamically levitated oxide samples for in situ observation of phase transformations in variable atmospheres, refinement of high-temperature structures and thermal expansion. Recent experimental findings include anomalous thermal expansion of the defect fluorite phase of YSZ, thermodynamics of pyrochlore–fluorite transformation from high-temperature structure refinements, and measurement of thermal expansion to the melting temperatures and fusion enthalpies of Zr, Hf, La, Yb and Lu oxides. These methods provide temperatures, enthalpies and volume change for phase transformations above 2000°C, which are required for thermodynamic assessments and calculation of phase diagrams of multicomponent systems.