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Thorium was a part of energy infrastructure in the 19th century due to the refractory and electronic properties of its dioxide. It will be a part of future energy infrastructure as the most abundant energy reserve based on nuclear fission. This paper discusses the solid-state chemistry of the monoxides and related rocksalt phases of thorium and the rare earths, both at atmospheric and at high pressure. The existence of solid thorium monoxide was first suggested more than 100 years ago; however, it was never obtained in bulk and has been studied mostly theoretically. Monoxides of lanthanides from Eu to Ho are ferromagnetic semiconductors sought for spintronics and were studied in thin films. La to Sm metallic monoxides were synthesized in bulk at pressures below 5 GPa. Recently, ThO formation in thin films has been reported and the stability of bulk ThO at high pressure was theoretically predicted based on first principles computations at 0 K. New ab initio computations were performed accounting for temperature effects up to 1000 K using lattice dynamics in the quasi-harmonic approximation. New computational results confirm the stabilization of pure ThO above 30 GPa and suggest the possibility of high-pressure synthesis of (Th,Nd)O at 1000 K and 5 GPa. 

The melting point is a fundamental property that is time-consuming to measure or compute, thus hindering high-throughput analyses of melting relations and phase diagrams over large sets of candidate compounds. To address this, we build a machine learning model, trained on a database of ∼10,000 compounds, that can predict the melting temperature in a fraction of a second. The model, made publicly available online, features graph neural network and residual neural network architectures. We demonstrate the model’s usefulness in diverse applications. For the purpose of materials design and discovery, we show that it can quickly discover novel multicomponent materials with high melting points. These predictions are confirmed by density functional theory calculations and experimentally validated. In an application to planetary science and geology, we employ the model to analyze the melting temperatures of ∼4,800 minerals to uncover correlations relevant to the study of mineral evolution. 

Among transition metal carbides and nitrides, zirconium, and hafnium compounds are the most stable and have the highest melting temperatures. Here we review published data on phases and phase equilibria in Hf-Zr-C-N-O system, from experiment and ab initio computations with focus on rocksalt Zr and Hf carbides and nitrides, their solid solutions and oxygen solubility limits. The systematic experimental studies on phase equilibria and thermodynamics were performed mainly 40–60 years ago, mostly for binary systems of Zr and Hf with C and N. Since then, synthesis of several oxynitrides was reported in the fluorite-derivative type of structures, of orthorhombic and cubic higher nitrides Zr3N4 and Hf3N4. An ever-increasing stream of data is provided by ab initio computations, and one of the testable predictions is that the rocksalt HfC0.75N0.22 phase would have the highest known melting temperature. Experimental data on melting temperatures of hafnium carbonitrides are absent, but minimum in heat capacity and maximum in hardness were reported for Hf(C,N) solid solutions. New methods, such as electrical pulse heating and laser melting, can fill the gaps in experimental data and validate ab initio predictions. 

Abstract Structure and thermodynamics of pure cubic ZrO₂and HfO₂were 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 automatedab initiomolecular 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 ZrO₂and 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 ZrO₂and 61 ± 10 kJ/mol for HfO₂, compared with 54 ± 2 and 52 ± 2 kJ/mol from computation. Volumetric thermal expansion for cubic ZrO₂and HfO₂are 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 HfO₂and ZrO₂, volume change on melting, and thermal expansion of the liquid to 3127 °C. Computed oxygen diffusion coefficients indicate that above 2400 °C pure ZrO₂is an excellent oxygen conductor, perhaps even better than YSZ.