Phase diagram study and thermodynamic assessment of the Y2O3-YF3 system

The phase diagram of the Y₂O₃-YF₃ system up to 1973 K was investigated using a classical equilibration/quenching experiment and differential thermal analysis (DTA). Equilibrium phases were confirmed by electron probe microanalysis (EPMA) and X-ray diffraction (XRD) phase analysis. For the very first time, the entire range of the phase diagram of yttrium oxy-fluoride system up to 1973 K was experimentally determined. Cubic-Y₂O₃ phase dissolves more than 5 mol% of YF₃ at 1973 K. The melting points of YOF and vernier phases are found to be higher than 1973 K and their steep liquidus in the YF₃-rich region are determined. Based on new experimental phase diagram data and thermodynamic property data in the literature, the Y₂O₃-YF₃ system was thermodynamically modeled by the CALculation of PHAse Diagram (CALPHAD) method. As applications of the thermodynamic database, metastable solubilities of YF₃ in Y₂O₃ during plasma etching process were calculated.     

Critical evaluation and thermodynamic optimization of the Li-O,and Li2O-SiO2 systems

A critical evaluation and thermodynamic optimization of all available experimental data of the Li-O and Li₂O-SiO₂ systems were performed to obtain one set of consistent Gibbs energy functions for all phases in the systems. The obtained Gibbs energy functions can reproduce all available and reliable experimental data from 298 K to above liquidus temperatures at one atm total pressure. It is the first time, to the best of our knowledge that the Gibbs energy of stoichiometric phases like Li₂O, Li₄SiO₄, Li₂SiO₃, and Li₂Si₂O₅ was comprehensively evaluated and optimized. The liquid oxide solution was modeled using the Modified Quasichemical Model to describe its thermodynamic behavior accurately considering the short range ordering. Discrepancies observed in the metastable liquid immiscibility and the liquidus in the SiO₂-rich region of the Li₂O-SiO₂ system was resolved. The phase diagram and thermodynamic data of all the solid and liquid phases were well reproduced within experimental error limits.     

Phase diagram study and thermodynamic modeling of the MgO-Y2O3-MgF2-YF3 system

The phase diagram of the MgO-Y₂O₃-MgF₂-YF₃ system (Mg,Y//O,F reciprocal system) at 1273–1773 K was investigated for the very first time using a classical equilibrium/quenching and differential thermal analysis (DTA) experiments followed by electron probe microanalysis (EPMA) and X-ray diffraction (XRD) phase analyses. No ternary or quaternary crystalline phase was found, and the eutectic reactions in the reciprocal system were identified. The overall phase diagram of the reciprocal system was also calculated based on the thermodynamic modeling using the CALculation of PHAse Diagram (CALPHAD) method.     

Coupled experimental phase diagram study and thermodynamic optimization of the Li2O–MgO–SiO2 system

A coupled key phase diagram study and critical evaluation and optimization of all available experimental data of the Li₂O–MgO–SiO₂ system was performed to obtain a set of Gibbs energy functions to reproduce all the reliable phase equilibria and thermodynamic data. Differential scanning calorimetry measurements and equilibration/quenching experiments were performed in the Li₂SiO₃–MgO and Li₄SiO₄–Mg₂SiO₄ sections, respectively, using sealed Pt capsules to prevent the volatile loss of Li. According to the present experimental results, Li₂MgSiO₄ is the only compound present in the Li₄SiO₄–Mg₂SiO₄ isopleth, which shows a peritectic melting at 1465 ± 6°C (1738 ± 6 K). The Modified Quasichemical Model, which considers short‐range ordering in the melt, was employed to describe the thermodynamic properties of the liquid phase. The Li₄SiO₄–Li₂MgSiO₄ and Mg₂SiO₄‐rich solid solutions were modeled using the Compound Energy Formalism.     

Thermodynamic modeling of the K2O-Al2O3 and K2O-MgO-Al2O3 systems with emphasis on β- and βʹʹ-aluminas

A critical evaluation and thermodynamic modeling study including key phase diagram experiments was performed to investigate the K₂O-Al₂O₃ and K₂O-MgO-Al₂O₃ systems. For the first time, potassium β- and β??-alumina solid solutions were described using the Compound Energy Formalism with accurate cation distributions in their sublattices. From the new experimental results, the stability of potassium β??-alumina was assured up to 1600?°C. A large discrepancy reported in the literature, the eutectic temperature between KAlO₂ and β-alumina in the K₂O-Al₂O₃ system, was resolved. A set of self-consistent Gibbs energy functions for all stable phases in the K₂O-MgO-Al₂O₃ system was obtained. As a result, any phase diagram sections and thermodynamic properties of the K₂O-MgO-Al₂O₃ system can be calculated from the optimized Gibbs energy functions. In particular, the cation distribution in the β- and β??-alumina solid solutions is calculated depending on the non-stoichiometry of solution and temperature.     

Experimental investigation of the phase relations in the SiO2-Dy2O3-CaO ternary system

This paper reports on the experimental investigation of the phase relations in the CaO-SiO₂-Dy₂O₃ system. CaO-SiO₂-Dy₂O₃ slags were equilibrated at 1773 and 1873 K for 86400 s in Ar and then quenched in water to determine the phase relations of the system. The composition of the equilibrated phases was measured by EPMA-WDS and XRD. The presence of ternary compounds and the solid solution and liquid regions were determined to construct the isothermal sections at 1773 and 1873 K of the ternary phase diagram. The data from this work will support further investigations on the feasibility to recover REEs through pyrometallurgical processing.     

Heterostructural phase diagram of Ga2O3–based solid solution with Al2O3

Ga₂O₃, which is emerging as semiconductor material due to the ultra-wide bandgap, has tunability in bandgap and lattice constant by alloying Al. However, successful control of alloying phase is still challenging due to its heterostructural nature and rich polymorphs. Here, we identified the thermodynamic phase diagram of heterostructural (Al_xGa_1-x)₂O₃ alloy. Using density-functional theory (DFT) calculations and regular solution model, we calculated the Gibbs-free energy of mixing of heterostructural polymorphs. Based on the calculation, we show the phase diagram of (Al_xGa_1-x)₂O₃ alloy system with a markedly increased metastability than the isostructural alloy, which can make a vast phase space for homogeneous single-phase alloys. We also investigated the correlation between the bandgap and lattice constant within these systems using hybrid DFT calculations, which can guide the device design of Ga₂O₃ power electronics.     

Critical evaluation and thermodynamic optimization of the Na2O–FeO–Fe2O3–Al2O3–SiO2 system

A critical assessment and thermodynamic optimization of phase diagrams and thermodynamic properties of the entire Na₂O–FeO–Fe₂O₃–Al₂O₃–SiO₂ system were carried out at 1 atm total pressure. A set of optimized model parameters obtained for all phases present in this system reproduces available and reliable thermodynamic property and phase equilibrium data within experimental error limits from 298 K to above liquidus temperatures for all compositions and oxygen partial pressures from metallic Fe saturation to 1 atm. The Gibbs energy of liquid solution was described based on the Modified Quasichemical Model considering the possible formation of NaAlO₂ and NaFeO₂ associates in the liquid state. The solid solutions wüstite, spinel, feldspar, nepheline, carnegieite, mullite, corundum, clino-pyroxene, meta-oxides and Na-β″-alumina were treated within the framework of Compound Energy Formalism. The database of model parameters can be used to calculate any thermodynamic property and phase diagram section of the present system.     

Thermochemistry of BaSm2O4 and thermodynamic assessment of the BaO–Sm2O3 system

The BaO–Sm₂O₃ system is of interest for the optimization of synthesis of electroceramics. The only systematic experimental study of phase equilibria in the system was performed more than 40 years ago. The reported experimental values of the enthalpy of formation of BaSm₂O₄ are in conflict, and the reported compound Ba₃Sm₄O₉ has never been confirmed. In this work we synthesized BaSm₂O₄ by solid‐state reaction and determined its heat capacity, enthalpy of formation, and phase transitions by differential scanning calorimetry, high‐temperature oxide melt solution calorimetry and ultra‐high‐temperature differential thermal analysis, respectively. We confirmed the existence of Ba₃Sm₄O₉ and its apparent stability from 1873 to 2273 K by X‐ray diffraction on quenched laser‐melted samples but were not able to obtain single‐phase material for calorimetric measurements. The CALPHAD method was used to assess phase equilibria in the BaO–Sm₂O₃ system, using both available literature data and our new measurements. A self‐consistent thermodynamic database and the calculated phase diagram of the BaO–Sm₂O₃ system are provided. This work can be used to model and thus to understand the relationships among composition, temperature, and microstructure for multicomponent systems with BaO and Sm₂O₃.     

Phase equilibria of SiO2–Ce2O3–CaO-25 wt %Al2O3 system at 1673 K–1773 K

The utilization of rare earth resources, especially secondary resources (e.g., RE-oxide system slag), has been limited by the lack of thermodynamic information. In order to supplement and improve the thermodynamic data related to rare earth, the equilibrium experiments of SiO₂–Ce₂O₃–CaO-25 wt %Al₂O₃ system phase diagram was carried out at 1673 K and 1773 K by the high-temperature isothermal equilibration/quenching technique in current paper. The composition of seven phase regions were determined by FE-SEM, XRD, EPMA and XRF analysis on the samples obtained by high temperature equilibrium technology at 1673 K and 1773 K, including the primary crystal regions of three compounds (C₂AS, 2CaO·SiO₂, CaO·2Ce₂O₃·3SiO₂) and three three-phase coexistence regions (L + C₂AS + 2CaO·SiO₂, L + C₂AS + CaO·2Ce₂O₃·3SiO₂, L + CaO·2Ce₂O₃·3SiO₂+CeAl₁₁O₁₈) and a liquid region. The phase relations and isotherms of SiO₂–Ce₂O₃–CaO-25 wt %Al₂O₃ system obtained in current work are beneficial to the recycling of rare earth resources containing cerium.     

Combined experimental and computational investigation of thermodynamics and phase equilibria in the CaO–TiO2 system

Phase relations in the CaO–TiO₂ system are of considerable interest in geology, metallurgy, and ceramics. Despite a number of studies of phase equilibria in the CaO–TiO₂ system, there are still some open questions regarding the stability of intermediate compounds. In this work, a series of specimens with different CaO:TiO₂ ratios were prepared by solid‐state reaction. The heat capacities of Ca₃Ti₂O₇ and Ca₄Ti₃O₁₀ from 300 to 1073 K were measured by differential scanning calorimetry and their formation enthalpies from the component oxides at 298 K were measured by high temperature oxide melt solution calorimetry. Using phase diagram information and thermodynamic data from the literature and the present measurements, thermodynamic optimization of the CaO–TiO₂ system was carried out by the CALPHAD technique. The phase diagram and the thermodynamic properties of the CaO–TiO₂ system were calculated using the obtained thermodynamic database, which clarify the stable and metastable phase equilibria of the system. The thermodynamic stability of the various compounds was discussed.     

Pseudo Phase Diagram and Microwave Dielectric Properties of Li2O–MgO–TiO2 Ternary System

Li₂O–MgO–TiO₂ ternary system is an important microwave dielectric ceramic material with excellent properties and prospect in both scientific research and application. A phase diagram of the Li₂O–MgO–TiO₂ ternary system was established in this article, based on earlier research results and our present work. Microwave dielectric properties with compositions in different regions of the phase diagram have been analyzed. We found that the 0.33 Li₂MgTi₃O₈–0.67 Li₂TiO₃ ceramics sintered at 1200°C exhibited excellent dielectric properties: Q × f value = 80 476 GHz (at 7.681 GHz), ε_r = 24.7, τ_f = +3.2 ppm/°C. We also designed two ceramic systems in the Li‐rich region of the Li₂O–MgO–TiO₂ ternary system, which received little attention in the past decades, because many excellent single‐phase ceramics, such as Li₂MgTiO₄, Li₂MgTi₃O₈ and MgTiO₃, have been found in the Ti‐rich region. The ceramic systems have low sintering temperatures but also relatively poor dielectric properties.     

Thermal Conductivity of Molten Li2O–B2O3 and K2O–B2O3 Systems

Using the transient hot‐wire method, the thermal conductivity properties of the molten Li₂O–B₂O₃ and K₂O–B₂O₃ systems were measured. The thermal conductivity increases with decreasing the temperature due to the borate structure change. In addition, calculations of the one‐dimensional Debye temperature and the phonon mean free paths as a function of temperature of the alkali borate systems were made. At a fixed temperature of 1273 K, the effect of the alkali oxide concentration on the thermal conductivity was evaluated. Within a range of 10–30 mol% Li₂O (or K₂O), a positive relationship between the thermal conductivity and 4‐coordinate boron was obtained. However, below 10 mol% Li₂O (or K₂O), the change in the intermediate‐range order of the borate structure had a more dominant effect on the thermal conductivity. Finally, the effect of cations on the thermal conductivity in the various molten R₂O–B₂O₃ (R=Li, Na and K) systems was considered. Depending on the type of cation, the change in the ionization potential had an effect on the thermal conductivity and also resulted in a change in the bond strength.     

Thermodynamic modeling of the CaO-SiO2-ZrO2 system coupled with key phase diagram experiments

Thermodynamic modeling coupled with key phase diagram experiments of the ternary CaO-SiO₂-ZrO₂ system was carried out. The isothermal phase diagram of the CaO-SiO₂-ZrO₂ system at 1873 K was established by using a classical phase equilibration and quenching technique followed by EPMA phase analysis. The Gibbs energy of each phase was optimized through critical evaluation of all available thermodynamic properties and phase diagram data in literature with new experimental data. The discrepancies between experimental phase diagram data and possible errors in the existing thermodynamic data were resolved in this study.     

Adjacent relations of primary phase fields and invariant reactions of the system CaO-SiO2-Nb2O5-La2O3

The adjacent relation of primary phase fields and corresponding invariant reactions of the system CaO-SiO₂-Nb₂O₅-La₂O₃ are of great importance for the study on its phase diagram. In the present work, the phase equilibrium in the high w(La₂O₃) region of CaO-SiO₂-Nb₂O₅-La₂O₃ system was studied by thermodynamic equilibrium experiment. The adjacent relation of primary phase fields was determined and represented in the form of adjacent tetrahedrons. The Alkemade Rule applicable to quaternary phase diagram was deduced, which can be used to infer the liquidus temperature trend on univariant curves. The rule was then used to determine the possible temperature range of invariant reactions corresponding to the adjacent tetrahedron in CaO-SiO₂-Nb₂O₅-La₂O₃ system, and the result was shown in the form of Schairer diagram. Finally, the reaction types of five invariant points were determined according to the Lever Rule for quaternary phase diagram, including: ① L₁+CaO·3SiO₂·2La₂O₃→CaO·SiO₂+SiO₂+La₂O₃·Nb₂O₅, ② L₂→CaO·SiO₂+La₂O₃·Nb₂O₅+SiO₂+CaO·Nb₂O₅, ③ L₃+CaO·3SiO₂·2La₂O₃+2CaO·Nb₂O₅→10CaO·6SiO₂·Nb₂O₅+La₂O₃·Nb₂O₅, ④ L₄+10CaO·6SiO₂·Nb₂O₅→CaO·SiO₂+2CaO·Nb₂O₅+La₂O₃·Nb₂O₅, ⑤ L₅+2CaO·Nb₂O₅→CaO·Nb₂O₅+La₂O₃·Nb₂O₅+CaO·SiO₂.     

Isothermal section of CaO-SiO2-La2O3 system within specific region at 1673–1473 K

So far, the relevant phase equilibrium relations and the type of equilibrium phase fields in the CaO-SiO₂-La₂O₃ basic slag system phase diagram are still unknown, which restricts the smelting process and application in materials of rare earth elements. In the current work, phase equilibrium relations within specific region of CaO-SiO₂-La₂O₃ system at 1673–1473?K were studied experimentally by using the thermodynamic equilibrium experiment followed by X-ray diffraction (XRD), scanning electron microscope (SEM), and energy dispersive spectrometer (EDS). According to the experimental results, the existence of ternary compound CaO·3SiO₂·2La₂O₃ was determined, it is confirmed to be a solution solid phase. The sub-solidus phase relations between different solid phases were also determined. Finally, the isothermal sections of CaO-SiO₂-La₂O₃ system within specific region at 1673?K, 1573?K and 1473?K were obtained, respectively. The experimental results can not only enrich the phase diagram information of silicate system, but also have practical significance for the application of rare earth in materials.