Thermodynamic Modeling of the MgO–Al2O3–CrO–Cr2O3 System

A complete critical evaluation and thermodynamic modeling of the phase diagrams and thermodynamic properties of the MgO–Al₂O₃–CrO–Cr₂O₃ system at 1 bar total pressure are presented. Optimized equations for the thermodynamic properties of all phases are obtained which reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25°C to above the liquidus temperatures at all compositions and oxygen partial pressures. The optimized thermodynamic properties and phase diagrams are believed to be the best estimates presently available. The database of the model parameters can be used along with software for Gibbs energy minimization in order to calculate any type of phase diagram section.     

Optimization of the Thermodynamic Properties and Phase Diagrams of the Na2O–SiO2 and K2O–SiO2 Systems

Available thermodynamic and phase diagram data have been evaluated for all phases in the Na₂O-SiO₂ and K₂O-SiO₂ systems at 1 bar pressure from 298 K to above the liq-uidus temperatures. All reliable thermodynamic and phase diagram data have been simultaneously optimized in order to obtain one set of model equations for the Gibbs energies of all phases as functions of temperature and composition. The thermodynamic properties and phase diagrams calculated from these parameters are self-consistent. The modified quasi-chemical model was used to represent the Gibbs energies of the molten slag phases.     

Thermodynamic Modeling of the Isomorphous Phase Diagrams in the Al2O3–Cr2O3 and V2O3–Cr2O3 Systems

The phase diagrams in the Al₂O₃–Cr₂O₃ and V₂O₃–Cr₂O₃ systems have been assessed by thermodynamic modeling with existing data from the literature. While the regular and subregular solution models were used in the Al₂O₃–Cr₂O₃ system to represent the Gibbs free energies of the liquid and solid phases, respectively, the regular solution model was applied to both phases in the V₂O₃–Cr₂O₃ system. By using the liquidus, solidus, and/or miscibility gap data, the interaction parameters of the liquid and solid phases were optimized through a multiple linear regression method. The phase diagrams calculated from these models are in good agreement with experimental data. Also, the solid miscibility gap and chemical spinodal in the V₂O₃–Cr₂O₃ system were estimated.     

Activities in Li2O-, Na2O, and K2O-SiO2 Solutions

Activities of alkali metal oxides and silica are calculated for regions of the Li₂O-SiO₂, Na₂O-SiO₂, and K₂O-SiO₂ phase diagrams where volatility, cell potential, and thermodynamic data are available. For the high-silica composition regions, activities are calculated from the stable phase diagrams and assumptions based on sub-regular solution behavior. These data permit estimates of the phase boundaries for the metastable two-liquid regions in the Li₂O and Na₂O systems which may be compared with experiment. An estimate is also made of the critical point for K₂O-SiO₂ to determine whether metastable phase separation in this system will be experimentally obtainable.     

Assessment of the CaO-Al2O3 System

A thermodynamic assessment of the quasi-binary system CaO-Al₂O₃ has been made using a computerized CALPHAD (calculation of phase diagrams) technique. The actual optimization was carried out with a computer program for the optimization of parameters in thermodynamic models called PARROT. The liquid phase is described by a simple two-sublattice subregular solution model with Ca²⁺ and Al³⁺ as cationic species and O^2- as anionic species. All solid phases are treated as stoichiometric compounds. A consistent set of parameters describing the system is presented, and numerous comparisons with experimental data are made. There is a lack of accurate data in the high-alumina part of the system, and the importance of a better knowledge of the CaO·6Al₂O₃ phase is stressed.     

Solid Solutions in Antiferroelectric Region of the System PbHfO3-PbTiO3-PbSnO3-PbNO2O6

Dielectric, ferroelectric, and piezoelectric properties were investigated for compositions in the high-lead hafnate region of the system PbHfO₃-PbTiO₃-PbSnO₃-PbNO₂O₆. Phase diagrams were prepared that show the existence of a ferroelectric-to-antiferroelectric phase transition with increasing temperature. Five phases were shown to exist in the portion of the system investigated two ferroelectric phases, two antiferroelectric phases, and one paraelectric phase. Ferroelectric-antiferroelectric phase transitions induced by temperature, electric field, and pressure were investigated. The highest spontaneous polarization measured was approximately 25 μcoul per cm².     

Activity–Composition Relations in NiAl2O4─MnAl2O4 Solid Solutions and Stabilities of NiAl2O4 and MnAl2O4 at 1300° and 1400°C

Activities of NiO were measured in the oxide and spinel solutions of the system MnO–NiO–Al₂O₃ at 1300° and 1400° C with the aim of deriving information on the thermodynamic properties of the spinel phases. Synthetic samples in selected phase assemblages of the system were equilibrated with metallic nickel and a gas phase of known oxygen partial pressures at a total pressure of 1 atm. The data on NiO activities and directions of conjugation lines between coexisting oxide and spinel phases were used to establish the activity–composition relations in spinel solid solutions at 1300° and 1400°C. The MnAl₂O₄–NiAl₂O₄ solid solutions exhibit considerable negative deviations from ideality at these temperatures. The free energy of formation of MnAl₂O₄ from its oxide components (MnO + Al₂O₃) at 1300° and 1400°C is calculated to be −24.97 and −26.56 kJ. mol⁻¹, respectively. The activities determined in the stoichiometric spinel solid solutions are more negative as compared with those predicted from cation distribution models.     

Thermodynamics of the Y-Ba-Cu-C-O-H System: Application to the Organometallic Chemical Vapor Deposition of the YBa2Cu3O7−x Phase

A calculational thermodynamic investigation of the chemical vapor deposition (CVD) of YBa₂Cu₃O_{7− x} from organometallic precursors has been performed, based on the minimization of the Gibbs energy of the Y-Ba-Cu-C-O-H chemical system. Thermodynamic data for the participating compounds were selected after a critical assessment of the available thermochemical information and are self-consistent with an accepted phase diagram. The results are presented in CVD diagrams which illustrate the influence of the most commonly used operating conditions of temperature, pressure, and initial gas composition on the formation of stable phases.     

Phase Diagrams for the Systems MgCl2-MgF2, CaCl2-MgF2, and NaCl-MgF2

Equilibrium phase diagrams for the systems MgCl₂-MgF₂, CaCl₂-MgF₂ and NaCl-MgF₂ were determined by differential thermal analysis, thermal analysis, and temperature-composition equilibrium techniques. Simple eutectics were observed at 78.0±0.5 mol% MgCl₂ and 628°±2°C in the MgCl₂-MgF₂ system, at 87.5±0.5 mol% CaCl₂ and 694°±2°C in the CaCl₂-MgF₂ system, and at 95.5±0.5 mol% NaCl and 786°±3°C in the NaCl-MgF₂ system. The phase diagrams determined for these systems were compared with phase diagrams that were computed using Temkin's model. The phase diagrams of the CaCl₂-MgF₂ and NaCl-MgF₂ systems were also compared with diagrams that were computed using the expression suggested by Flood et al. for reciprocal systems. The experimentally determined and computed phase diagrams agreed for the MgCl₂-MgF₂ system but not for the CaCl₂-MgF₂ and NaCl-MgF₂ systems.     

Thermodynamic Evaluation for the Y2O3–BaO–CuOx System

The thermodynamic data for the Y₂O₃–BaO–Cu₂O–CuO quaternary system were optimized from measured thermodynamic data. A two-sublattice model for ionic solution was used to express the Gibbs free energy of the liquid phase, and a two-sublattice regular solution model was used for the nonstoichiometric YBa₂Cu₃O_6+δ superconducting compound. The optimized thermodynamic data were used to calculate the phase diagrams of the Cu₂O–CuO binary system and the CuO _x –Y₂Cu₂O₅ and CuO _x –BaCuO₂ quasi-binary systems. The results were in good agreement with reported measured data. The liquidus projection and isothermal and vertical sections of the Y₂O₃–BaO-CuO _x quasi-ternary system were calculated. The effect of oxygen pressure on some reaction temperatures was predicted by calculating them at various oxygen pressures, and the oxygen contents (6 +δ) in YBa₂Cu₃O_6+δ were calculated at various temperatures and oxygen pressures. The results were compared with experimental data.     

Thermodynamic Calculation of the ZrO2–YO1.5–MgO System

A thermodynamic evaluation of the ZrO₂-MgO system has been developed and combined with previous assessments of the ZrO₂–YO_1.5 and YO_1.5–MgO systems to describe the ZrO₂–YO_1.5-MgO Systems to describe the ZrO₂–YO_1.5-MgO system by means of Bonnier's equation. The calculated results are shown by isothermal and vertical sections, a projection of the liquidus surfaces, and the reaction scheme. Comparisons between calculated and experimental diagrams demonstrate that the calculations satisfactorily account for most of the available experimental data.     

Phase Relations and Dielectric Properties in the Bi2O3–ZnO–Ta2O5 System

Dielectric properties and phase formation of Bi-based pyrochlore ceramics were evaluated for the Bi₂O₃–ZnO–Ta₂O₅ system. The compositional range r Bi₂(Zn_1/3Ta_2/3)₂O₇· (1− r )(Bi_3/2Zn_1/2)(Zn_1/2Ta_3/2)O₇ (0 ≤ r ≤ 1) in Bi₂O₃–ZnO–Ta₂O₅ was investigated to determine the relative solubility of BZT cubic (α-BZT, r = 0) and the pseudo-orthorhombic (β-BZT, r = 1) end members. It was found that extrinsic factors, such as kinetically limited phase formation and bismuth loss, contribute to apparent phase boundaries in addition to thermodynamic stability of each phase. Considering this, the locations of true phase boundaries were r < 0.30 and r ≥ 0.74 for α and β phases, respectively. Dielectric constants between 58 and 80 and low dielectric loss (tan δ < 0.003) were measured for the complete compositional range. The temperature coefficient of capacitance was controlled by composition, which was found to be <30 ppm/°C at the edge of β-phase solid solution. In addition to the excellent dielectric properties these materials can be sintered at low temperatures, which make Bi-based pyrochlores promising candidates for high-frequency electronic applications.     

Experimental Investigation and Thermodynamic Assessment of the Nd2O3–Y2O3 System

The phase relations in the Nd₂O₃–Y₂O₃ system were experimentally studied in the 1300°–1600°C range. X-ray diffraction, scanning electron microscopy, and electron probe microanalysis were applied to analyze the phase composition of annealed Nd₂O₃–Y₂O₃ mixtures with varying Y₂O₃ content. A thermodynamic assessment was conducted using the experimental data obtained. The excess Gibbs energies of the solution phases were described based on a simple substitutional solution model. A consistent set of optimized interaction parameters was derived for the Gibbs energy of the constituent phases, resulting in a good match between calculated and experimental data.     

Calculation of Phase Diagrams for the YO1.5—BaO—CuOx System

The thermodynamic data for the YO_1.5–BaO, BaO-CuO_x, and YO_1.5–CuO_x quasi-binary systems were optimized from experimental phase diagrams. They were used to calculate tentative phase diagrams for the YO_1.5–BaO—CuO_x quasi-ternary system. The equilibrim liquidus surface and the isothermal sections of the ternary system at 900°, 925°, 950°, 975°, and 1000°C were calculated. The isopleths containing YBa₂Cu₃O_7-δ were also calculated.     

Experimental Investigation and Thermodynamic Modeling of the ZrO2–SmO1.5 System

Phase equilibria of the ZrO₂–SmO_1.5 system have been studied by X-ray diffraction, scanning electron microscopy, and energy-dispersive X-ray spectroscopy. The compositions of phases in the tetragonal+fluorite, fluorite+pyrochlore, and fluorite+B-Sm₂O₃ two-phase fields have been determined for samples quenched from temperatures between 1400° and 1700°C. The heat content of the fluorite phase with 30 mol% SmO_1.5 and of the pyrochlore phase with 50 mol% SmO_1.5 has been measured in the temperature range 200°–1400°C using high-temperature drop calorimetry. The transition between pyrochlore and fluorite phases is clearly first order in the SmO_1.5-rich region, while no fluorite+pyrochlore two-phase region has been detected for the samples with ZrO₂ excess. Based on the obtained experimental results and literature data, the phase diagram and thermodynamic properties were optimized using the CALPHAD approach.     

The Ternary Systems BaO–TiO2–SnO2 and BaO-TiO2-ZrO2

An investigation of the ternary systems BaO-TiO₂-SnO₂ and BaO-TiO₂-ZrO₂ led to the discovery of two new compounds belonging to the system BaO-TiO₂. These compounds, Ba₂Ti₉-O₂₀ and Ba₂Ti₉O₂₀, are stabilized by minute additions of SnO₂ or ZrO₂. The known compound BaTi₂O₅ can be obtained only from the molten phase and decomposes below 1300°C. into Ba₂Ti₅O₁₂ and BaTiO₂. In these systems no ternary compounds are found. The ternary phase diagrams can be divided into regions with high and low dielectric losses, which are in accordance with the phase relations. Tables with crystallographic data of the new compounds are included.