Thermodynamic Modeling of the FeO–Fe2O3–MgO–SiO2 System

The liquid and solid phases in the FeO–Fe₂O₃–MgO–SiO₂ system are of importance in ceramics, metallurgy, and petrology. A complete critical evaluation and thermodynamic modeling of the phase diagrams and thermodynamic properties of this system are presented. Optimized equations for the thermodynamic properties of all phases are obtained that 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 with software for Gibbs energy minimization to calculate any type of phase diagram section.     

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.     

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.     

Phase Relations and Lattice Constants in the MgO-Al2O3-Ga2O3 System at 1550°C

Phase relations and lattice constants in the MgO–Al₂O₃–Ga₂O₃ system at 1550°C have been determined experimentally. In a large part of this system, only a nonstoichiometric spinel is stable. Compositions as extreme as 12.5 mol% MgO–20.5 mol% Ga₂O₃–67 mol% Al₂O₃ for a homogeneous spinel are possible. In the bordering phase diagrams of MgO–Al₂O₃ and MgO–Ga₂O₃, the composition of the spinel is as high as 63 mol% Al₂O₃ or Ga₂O₃, respectively. The contributions of all simple ionic exchange reactions on the lattice constant of the spinel have been deduced from X-ray diffractometry data.     

High-Temperature Neutron Diffraction of the AlN–Al2O3–Y2O3 System

The importance of aluminum nitride (AlN) stems from its application in microelectronics as a substrate material due to high thermal conductivity, high electrical resistance, mechanical strength and hardness, thermal durability, and chemical stability. Yttria (Y₂O₃) is the best additive for AlN sintering. AlN densifies by a liquid-phase mechanism, where the surface oxide, Al₂O₃, reacts with Y₂O₃ to form an Y-Al-O-N liquid that promotes particle rearrangement and densification. Construction of the phase relations in this multicomponent system is essential for optimizing the properties of AlN. The ternary phase diagram of the AlN–Al₂O₃–Y₂O₃ was developed by Gibbs energy minimization using interpolation procedures based on modeling the binary subsystems. This paper aims at testing the resultant understanding experimentally at selected compositions using in situ high-temperature neutron diffractometry. These experimental results agree with the thermodynamic calculations of AlN–Al₂O₃–Y₂O₃. The ternary phase diagram has been constructed for the first time in this work. High-temperature neutron diffractometry has permitted real time measurement of the reactions involved in this ternary system, especially to determine the temperature range for each reaction, which would have been difficult to establish by other means.     

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.     

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.     

Phase Equilibria in the KNbO3-SrNb2O6 and KNbO3-BaNb2O6 Systems

Phase equilibrium studies of the KnbO₂-SrNb₂O₆ system revealed that tetragonal tungsten bronze-type solid solutions extend from 59 to 87 mol% SrNb₂O₆. The solid solution field has a relatively flat liquidus peaking at 1486°C and 78 mol% SrNb₂O₆. In contrast, solid solutions are limited to 67 to 75 mol% BaNb₂O₆ in the KnbO₃-BaNb₂O₆ system, with peritectic decomposition occurring at the 75 mol% solid-solution limit. The diagrams establish conditions for perfecting the growth and stoichiometry of potassium-strontium and potassium-barium niobate electrooptic crystals. Dielectric and crystallographic properties of crystals grown in these systems are presented, and the phase relations are compared to previous work in the sodium-barium niobate system.     

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.     

The Bi2O3–Nb2O5–NiO Phase Diagram

The Bi₂O₃–Nb₂O₅–NiO phase diagram at 1100°C was determined by means of solid-state synthesis, X-ray diffraction, and scanning electron microscopy. A ternary eutectic with a melting point below 1100°C was found to exist in the field between NiO, Bi₂O₃, and the end-member of the δBi₂O₃–Nb₂O₅ solid solution. The existence of the previously reported Bi₃Ni₂NbO₉ phase was disproved. A pyrochlore homogeneity range around Bi_1.5Ni_0.67Nb_1.33O_6.25 was determined together with all the phase relations in this phase diagram.     

Phase Relations in the System Al2O3–B2O3–Nd2O3

The phase relations at a temperature below "subsolidus" in the system Al₂O₃–B₂O₃–Nd₂O₃ are reported. Specimens were prepared from various compositions of Al₂O₃, B₂O₃, and Nd₂O₃ of purity 99.5%, 99.99%, and 99.9%, respectively, and fired at 1100°C. There are six binary compounds and one ternary compound in this system. The ternary compound, NdAl₃(BO₃)₄ (NAB), has a phase transition at 950°C ± 15°C. The high-temperature form of NAB has a second harmonic generation (SHG) efficiency of KH₂PO₄ (KDP) of the order of magnitude of the form which has been used as a good self-activated laser material, and the low-temperature form of NAB has no SHG efficiency.     

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.     

Multicomponent Glasses of GeO2 and Sb2O3 with Bi2O3, T12O, andlor PbO

Previous studies on glass formation involving GeO₂ with Bi₂O₃, TI₂O, and PbO were extended by the use of Sb₂O₃. Wide areas of glass formation occur in the systems GeO₂-PbO-Sb₂O₃ and GeO₂-Bi₂O₃-Sb₂O₃ at all but the lowest GeO₂ contents; the region of single-phase glasses in the system GeO₂-Tl₂O-Sb₂O₃ is severely restricted. Glasses were examined by powder X-ray diffraction, differential thermal analysis, thermomechanical analysis, and Archimedes'technique to obtain glass transition and crystallization exotherm temperatures, thermal expansion coefficients, and densities; these properties are presented in diagrams for the GeO₂-Sb₂O₃ binary and for two ternary systems. Based on calculated values of Δ_o,the waveleneth for zero material dispersion. and dM/dΔ . the material disiersion slope at Δ_o, compositions in these systems may be useful for the construction of ultralow-loss optical waveguides in the 3 to 4 μm region.     

The System Al2O3-Cr2O3-Sio2

Liquidus phase equilibrium data are presented for the system Al₂O₃-Cr₂O₃-SiO₂. The liquidus diagram is dominated by a large, high-temperature, two-liquid region overlying the primary phase field of corundum solid solution. Other important features are a narrow field for mullite solid solution, a very small cristobalite field, and a ternary eutectic at 1580°C. The eutectic liquid (6Al₂O₃-ICr₂O₃-93SiO₂) coexists with a mullite solid solution (61Al₂O₃-10Cr₂O₃-29SiO₂), a corundum solid solution (19Al₂O₃-81Cr₂O₃), and cristobalite (SO₂). Diagrams are presented to show courses of fractional crystallization, courses of equilibrium crystallization, and phase relations on isothermal planes at 1800°, 1700°, and 1575°C. Tie lines were sketched to indicate the composition of coexisting mullite and corundum solid solution phases.     

Vaporization Studies of the La2O3–Ga2O3 System

The vaporization of the samples of the compositions Ga₂O₃+ LaGaO₃, LaGaO₃+ La₄Ga₂O₉, and La₄Ga₂O₉+ La₂O₃ was investigated using Knudsen effusion mass spectrometry in the temperature range 1494–1937 K. The partial pressures of the gaseous species O₂, Ga, GaO, Ga₂O, and LaO were determined over the samples investigated. The equilibrium partial pressures were used for the calculation of the thermodynamic activities of the components at 1700 K. Gibbs energies of formation of LaGaO₃( s ) and La₄Ga₂O₉( s ) at 1700 K from the component oxides were derived from the thermodynamic activities as −46.4 ± 4.7 and −99.2 ± 7.9 kJ·mol⁻¹, respectively. The results were compared with the literature data obtained using other methods.     

Thermodynamics of CuAlO2 and CuAl2O4 and Phase Equilibria in the System Cu2O-CuO-Al2O3

The standard Gibbs free energies of formation of CuAlO₂ and CuAl₂O₄ were determined in the range 700° to 1100°C, using emf measurements on the galvanic cells (1) Pt,CuO +] Cu₂O/CaO-ZrO₂/O₂,Pt; (2) Pt,Cu +] CuAlO₂+] Al₂O₃/CaO-ZrO₂/ Cu +] Cu₂O,Pt; and (3) Pt,CuAl₂O₄+] CuAlO₂+]Al₂O₃/CaO-ZrO₂/O₂,Pt. The results are compared with published information on the stability of these compounds. The entropy of transformation of CuO from tenorite to the rock-salt structure is evaluated from the present results and from earlier studies on the entropy of formation of spinels from oxides of the rock-salt and corundum structures. The temperatures corresponding to 3-phase equilibria in the system Cu₂O-CuO-Al₂O₃ at specified O₂ pressures calculated from the present results are discussed in reference to available phase diagrams.     

Phase Equilibria and Ionic Conductivity in the System ZrO2−Yb2O3−Y2O3

The phase equilibria in the zirconia-rich part of the system ZrO₂−Yb₂O₃−Y₂O₃ were determined at 1200°, 1400°, and 1650°C. The stabilizing effects of Yb₂O₃ and Y₂O₃ were found to be quite similar with <10 mol% of either being necessary to fully stabilize the cubic fluorite-structure phase at 1200°C. The two binary ordered phases, Zr₃Yb₄O₁₂ and Zr₃Y₄O₁₂, are completely miscible at 1200°C. These were the only binary or ternary phases detected. The ionic conductivities of ternary specimens in this system were measured using the complex impedance analysis technique. For a given level of total dopant, the substitution of Yb₂O₃ for Y₂O₃ gives only minor increases in specimen conductivity.     

Thermochemistry of Glasses in the Y2O3-Al2O3-SiO2 System

Enthalpies of drop solution in molten 2PbO-B₂O₃ at 1078 K were measured for glasses along the 2YAlO₃-3SiO₂ and return ½Y₃Al₅O₁₂-3SiO₂ joins. The onset glass transition temperature increases slightly with increasing silica content and Y/Al. Enthalpies of mixing were calculated on the basis of amorphous end members. Strongly negative heats of mixing support the absence of miscibility gaps except possibly for very high silica content, consistent with experimental phase analyses, which indicate much narrower miscibility gaps compared with the phase diagrams calculated on the basis of previous data and the CALPHAD formalism.