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Heat capacities and enthalpies of formation of BaGd₂O₄were determined by high‐temperature differential scanning calorimetry and high‐temperature oxide melt solution calorimetry, respectively. Thermodynamic stability of BaLn₂O₄compounds increases with decreasing Ln³⁺ionic radius. Previously reported data on BaNd₂O₄and BaSm₂O₄corroborate this trend. Missing data for compounds in BaO–Ln₂O₃(Ln = La, Pr, Eu, Er) systems were estimated from established relations, thermodynamic assessment was performed, and binary phase diagrams were calculated.

 

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. 

Densities of liquid oxide melts with melting temperatures above 2000 °C are required to establish mixing models in the liquid state for thermodynamic modeling and advanced additive manufacturing and laser welding of ceramics. Accurate measurements of molten rare earth oxide density were recently reported from experiments with an electrostatic levitator on board the International Space Station. In this work, we present an approach to terrestrial measurements of density and thermal expansion of liquid oxides from high-speed videography using an aero-acoustic levitator with laser heating and machine vision algorithms. The following density values for liquid oxides at melting temperature were obtained: Y2O3 4.6 ± 0.15; Yb2O3 8.4 ± 0.2; Zr0.9Y0.1O1.95 4.7 ± 0.2; Zr0.95Y0.05O1.975 4.9 ± 0.2; HfO2 8.2 ± 0.3 g/cm3. The accuracy of density and thermal expansion measurements can be improved by employing backlight illumination, spectropyrometry and a multi-emitter acoustic levitator. 

Phase transformations in multicomponent rare earth sesquioxides were studied by splat quenching from the melt, high temperature differential thermal analysis and synchrotron X-ray diffraction on laser-heated samples. Three compositions were prepared by the solution combustion method: (La,Sm,Dy,Er,RE)2O3, where all oxides are in equimolar ratios and RE is Nd or Gd or Y. After annealing at 800 °C, all powders contained mainly a phase of C-type bixbyite structure. After laser melting, all samples were quenched in a single-phase monoclinic B-type structure. Thermal analysis indicated three reversible phase transitions in the range 1900–2400 °C, assigned as transformations into A, H, and X rare earth sesquioxides structure types. Unit cell volumes and volume changes on C-B, B-A, and H-X transformations were measured by X-ray diffraction and consistent with the trend in pure rare earth sesquioxides. The formation of single-phase solid solutions was predicted by Calphad calculations. The melting point was determined for the (La,Sm,Dy,Er,Nd)2O3 sample as 2456 ± 12 °C, which is higher than for any of constituent oxides. An increase in melting temperature is probably related to nonideal mixing in the solid and/or the melt and prompts future investigation of the liquidus surface in Sm2O3-Dy2O3, Sm2O3-Er2O3, and Dy2O3-Er2O3 systems. 

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.