High–temperature phase chemistry of the system Gd–Pd–O

Anisothermal sectionof the phase diagram for the system Gd–Pd–O at 1223 K has been established by equilibrationof samples and phase identification after quenching by optical and scanning electron microscopy, X–ray powder diffraction, and energy dispersive spectroscopy. Three ternary oxides Gd₄PdO₇,Gd₂PdO₄ and Gd₂Pd₂O₅ were identified. Liquid alloys, the four inter–metallic compounds and Pd–rich solid solutionwere found to be inequilibrium with Gd₂O₃.

Based on the phase relations, four solid–state cells were designed to measure the Gibbs energies of formation of the three ternary oxides in the temperature range from 920 to 1320 K. Although three cells are sufficient to obtain the properties of the three compounds, the fourth cell was deployed to cross check the data. An advanced version of the solid–state cell incorporating a buffer electrode with yttria–stabilized zirconia solid electrolyte and pure oxygen gas at a pressure of 0.1 MPa as the reference electrode was used for high–temperature thermodynamic measurements. The standard Gibbs energy of formation of the inter–oxide compounds from their component binary oxides can be represented by the following equations:

Gd₄PdO₇(s) : Δ_f(ox)G⁰/J mol^–1 = –25,030 + 0.33T (±140), Gd₂PdO₄(s) : Δf(ox)_f(ox)G⁰/J mol^–1 = –25,350 + 0.84T (±135), Gd₂Pd₂O₅(s) : Δf(ox)_f(ox)G⁰/J mol^–1 = –48,700 + 0.38T (±270)

Based on the thermodynamic information, isothermal chemical potential diagrams and isobaric phase diagrams for the system Gd–Pd–O are developed.     

System Cu-Rh-O: Phase diagram and thermodynamic properties of ternary oxides CuRhO2 and CuRh2O4

An isothermal section of the phase diagram for the system Cu-Rh-O at 1273 K has been established by equilibration of samples representing eighteen different compositions, and phase identification after quenching by optical and scanning electron microscopy (SEM), X-ray diffraction (XRD), and energy dispersive analysis of X-rays (EDX). In addition to the binary oxides Cu₂O, CuO, and Rh₂O₃, two ternary oxides CuRhO₂ and CuRh₂O₄ were identified. Both the ternary oxides were in equilibrium with metallic Rh. There was no evidence of the oxide Cu₂Rh₂O₅ reported in the literature. Solid alloys were found to be in equilibrium with Cu₂O. Based on the phase relations, two solid-state cells were designed to measure the Gibbs energies of formation of the two ternary oxides. Yttria-stabilized zirconia was used as the solid electrolyte, and an equimolar mixture of Rh+Rh₂O₃ as the reference electrode. The reference electrode was selected to generate a small electromotive force (emf), and thus minimize polarization of the three-phase electrode. When the driving force for oxygen transport through the solid electrolyte is small, electrochemical flux of oxygen from the high oxygen potential electrode to the low potential electrode is negligible. The measurements were conducted in the temperature range from 900 to 1300 K. The thermodynamic data can be represented by the following equations: {fx741-1} where Δ_f(ox) G ^o is the standard Gibbs energy of formation of the interoxide compounds from their component binary oxides. Based on the thermodynamic information, chemical potential diagrams for the system Cu-Rh-O were developed.     

Phase equilibria in the system Sm–Rh–O and thermodynamic and thermal studies on SmRhO3

Using isothermal equilibration, phase relations are established in the system Sm–Rh–O at 1273 K. SmRhO₃ with GdFeO₃-type perovskite structure is found to be the only ternary phase. Solid-state electrochemical cells, containing calcia-stabilized zirconia as an electrolyte, are used to measure the thermodynamic properties of SmRhO₃ formed from their binary component oxides Rh₂O₃ (ortho) and Sm₂O₃ (C-type and B-type) in two different temperature ranges. Results suggest that C-type Sm₂O₃ with cubic structure transforms to B-type Sm₂O₃ with monoclinic structure at 1110 K. The standard Gibbs energy of transformation is $ \Delta_{\text{tr}} G^{\text{o}} ( \pm 87)/{\text{J}}\,{\text{mol}}^{ - 1} = 3763 - 3.39\,(T/{\text{K}}) $ . Standard Gibbs energy of formation of SmRhO₃ from binary component oxides Rh₂O₃ and Sm₂O₃ with B-type rare earth oxide structure can be expressed as $ \Delta_{\text{f(ox)}} G^{\text{o}} ( \pm 75)/{\text{J}}\,{\text{mol}}^{ - 1} = - 64230 + 6.97(T/{\text{K}}) $ . The decomposition temperature of SmRhO₃ estimated from the extrapolation of electrochemical data is 1665 (±2) K in air and 1773 (±3) K in pure oxygen. Temperature-composition diagrams at constant oxygen pressures are constructed for the system Sm–Rh–O. Employing the thermodynamic data for SmRhO₃ from emf measurement and auxiliary data for other phases from the literature, oxygen potential-composition phase diagram and 3-D chemical potential diagram for the system Sm–Rh–O at 1273 K are developed.     

Oxygen potentials,Gibbs' energies and phase relations in the Cu-Cr-O system

Thermodynamic properties of ternary compounds, cuprous and cupric chromites (CuCro₂, CuCr₂O₄), and oxygen potentials corresponding to three three-phase regions in the Cu-Cr-O system have been measured in the temperature range 900 to 1350 K using a solid state galvanic cell incorporating calcia-stabilized zirconia. Cuprous chromite was found to be nearly stoichiometric. The compositions of non-stoichiometric cupric chromite saturated with CuO and Cr₂O₃ have been determined using electron microprobe and energy dispersive X-ray analysis. The results of this study resolve discrepancies in Gibbs' energies of cuprous and cupric chromites reported in the literature. A ternary phase diagram for the Cu-Cr-O system at 1150 K and phase relations in air for the Cu₂O-CuO-Cr₂O₃ system as a function of temperature have been derived based on the new thermodynamic data. The phase diagram given in the literature is found to be inaccurate.     

Microstructure and phase transformation of zirconia-based ternary oxides for thermal barrier coating applications

Five dopant oxides, Sc₂O₃, Yb₂O₃, CeO₂, Ta₂O₅, and Nb₂O₅, were incorporated into 7YSZ to create ternary zirconia-based oxides with varying oxygen vacancies and substitutional defects. These ternary oxides were consolidated using a high-temperature sintering process. The resulting bulk oxides were subjected to microstructural study using scanning electron microscopy (SEM), X-ray diffraction (XRD), and differential scanning calorimetry (DSC). The results show that the microstructures of the ternary zirconia-based oxides are determined by the amount of oxygen vacancies in the system, the dopant cation radius, and atomic mass. Increasing the number of oxygen vacancies in the lattice by the addition of trivalent dopant as well as the use of larger cations promotes the stabilization of the high-temperature cubic phase. The tetravalent cation, on the other hand, has the effect of retaining tetragonal phase to room temperature without the influence of oxygen vacancy. The addition of pentavalent oxide leads to the formation of monoclinic phase upon cooling.     

Computer calculations of phase diagrams

The thermodynamic route of establishing phase diagrams is a relatively recent activity, considering that till about the fifties most phase diagrams were determined by the measurement of certain physical property or quantitative microscopy using light optics or x-ray diffraction. The thermodynamic formalism used by Kaufman and Bernstein is explained and illustrated with examples of the development of hypothetical binary phase diagrams. The calculation of ternary phase diagrams can begin with the binary phase diagram data as a first approximation. However, to calculate a reasonably accurate ternary phase diagram a certain amount of ternary solution data is necessary. Various empirical equations have been proposed in the literature to express ternary thermodynamic data. Calculation of simple ternary isothermal sections is illustrated with the examples of Mo-V-W and Cd-Sn-Pb systems. The numerical techniques which involve the differentiation of thermodynamic parameters with respect to composition get more involved with the number of components becoming 3 or more. A simpler approach has been applied recently to find the minimum position on the Gibbs free energy surface.     

Thermodynamics of Na2O-SiO2 melts

The thermodynamic properties of Na₂O-SiO₂ solid (942-1285 K) and liquid (1103-1719 K, 19.5-61.8 mol % Na₂O) silicates were studied by Knudsen cell mass spectrometry. To determine the activities of the constituent oxides, these were reduced to volatile suboxides directly in effusion cells. Mass spectra of the saturated vapor over Na₂O-SiO₂ showed the presence of the Na⁺, Na₂O⁺, NaO⁺, O ₂ ⁺ , TaO⁺, TaO ₂ ⁺ , NbO⁺, NbO₂, MoO⁺, MoO ₂ ⁺ , MoO ₃ ⁺ , and NiO⁺ ions resulting from the ionization of the Na, Na₂O, NaO, NaO₂,O₂, TaO, TaO₂, NbO, NbO₂, MoO, MoO₂, MoO₃, and NiO molecules. The activities calculated by two different procedures were found to coincide within the experimental error. The enthalpies and Gibbs energies of formation of sodium silicates were shown to be extremely low. The formation of solid orthoand metasilicates is accompanied by a decrease in entropy, in contrast to the other sodium silicates. Sodium orthosilicate has the lowest enthalpy and Gibbs energy. A thermodynamic model for Na₂O-SiO₂ melts is proposed which relies on associated solution theory and takes into account silica polymerization. The model describes the composition and temperature dependences of the activities of the constituent oxides in the melt with an accuracy no worse than the experimental error (2-3%). The model, in combination with the thermodynamic functions of formation of all the intermediate solid phases, was used to calculate phase equilibria in the Na₂O-SiO₂ system. The results agree well with the experimental data obtained by physicochemical methods.     

Hydrothermal phase equilibria studies in Ln2O3H2O systems and synthesis of cubic lanthanide oxides

Phase diagrams for the systems Ln₂O₃H₂O (Ln = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu and Y) studied at 5000 to 10,000 psi and temperature range of 200–900°C, show that Ln(OH)₃ hexagonal and LnOOH monoclinic are the only stable phases from Nd to Ho. The cubic oxide phase (CLn₂O₃) is stable for systems of Er, Tm, Yb and Lu, with no evidence of its equilibrium in the systems of lighter lanthanides. Using strong acids, HNO₃ and HCOOH, as mineralisers the cubic oxides could be stabilised from Eu down to Lu. Solid solution phases of CeO₂Y₂O₃ and Eu₂O₃Y₂O₃ have also been synthesised with HNO₃ as mineraliser, since these compounds have promising use as solid electrolyte and phosphor materials respectively.     

Thermodynamic Assessment of EuCl<Subscript>3</Subscript>–MgCl<Subscript>2</Subscript> and EuCl<Subscript>3</Subscript>–BaCl<Subscript>2</Subscript> Systems

Using the CALPHAD technique, an assessment of the binary EuCl₃–MgCl₂ and EuCl₃–BaCl₂ systems has been carried out in this study. The modified quasi-chemical model was defined to describe the Gibbs energies of the liquid phases, and the model parameters were optimized from the experimental phase diagram data. The phase diagrams and enthalpies of mixing of the EuCl₃–MgCl₂ and EuCl₃–BaCl₂ systems were calculated. The calculated results by the present method agree well with the experimental data. The Gibbs energies of formation of Mg₃Eu₂Cl₁₂, Ba₃Eu₂Cl₁₂, and Ba₂Eu₃Cl₁₃ from the pure components were predicted.     

Effect of Eu<Subscript>2</Subscript>O<Subscript>3</Subscript> doping on the crystallization behavior of BaO-Bi<Subscript>2</Subscript>O<Subscript>3</Subscript>-B<Subscript>2</Subscript>O<Subscript>3</Subscript> glasses

We gave studied the crystallization behavior of 30BaO · 25Bi₂O₃ · 45B₂O₃ glasses doped with Eu₂O₃ to different levels. At a Eu₂O₃ content of 7 mol % or higher, the glasses undergo volume crystallization. The only precipitating phase is a solid solution between europium and bismuth oxides. With increasing europium concentration in the glass, the structure of the crystallites changes from cubic to rhombohedral. We have investigated the morphology, physicochemical properties, and luminescence spectra of the glasses and glass-ceramics.     

Thermodynamic analysis and crystal-chemical modeling of the defect structure of calcium iron garnets

This paper presents detailed analysis of the phase equilibria and thermodynamic stability of CaO, Fe₂O₃, Gd₂O₃, Nd₂O₃, Pr₂O₃, ZrO₂, NiO, and ThO₂, and detect formation during high-temperature synthesis of gadolinium (yttrium) calcium and zirconium calcium iron garnets doped with praseodymium, neodymium, nickel, cerium, thorium, and other oxides. The origin of point defects in each garnet is discussed. Crystal-chemical modeling indicates that all calcium-containing garnets are nonstoichiometric, but differ in the origin of non-stoichiometry, δ. The values of δ are shown to correlate with the activation energy for oxygen-ion conduction determined by emf measurements on solid electrolytes. The mechanisms of formation of different garnets from binary oxides are compared.     

Standard free energy change of formation per unit volume: a new parameter for evaluating nucleation and growth of oxides, sulphides, carbides and nitrides

 The present paper introduces a thermodynamic parameter, the standard free energy changes of formation of oxide, sulphide, carbide and nitride per unit volume, as a criterion for comparing the formation tendency of these compounds. The diagrams for the standard free energy change of formation of common oxides, sulphides, carbides and nitrides per unit volume vs temperature have been calculated and established based on the available thermodynamic data. It is believed that these diagrams can provide better explanations to some oxidation phenomena including the effects of reactive elements on the selective oxidation of Cr₂O₃ and Al₂O₃. Received: 12 September 1997 / Accepted: 16 September 1997     

Phase equilibria in the CaF2-Al2O3-CaO system

Computations of phase equilibria in the CaF₂-Al₂O₃-CaO system have been carried out on the basis of experimentally found thermodynamic properties of all intermediate phases and melts. Coordinates of the phase equilibrium boundaries were determined by solving a system of equations expressing equality of chemical potentials of the components in coexisting phases. The nature and quantity of the coexisting phases were established by a search for the Gibbs energy minimum of the system. All the phases of the CaF₂-Al₂O₃-CaO system were taken into consideration. Calculated phase diagrams of the CaO-CaF₂, CaO-Al₂O₃ and CaF₂-Al₂O₃ binary subsystems are in good agreement with the data available in the literature. Isotherms of the CaF₂-Al₂O₃-CaO system were calculated at 1600, 1650, 1723 and 1773 K. A wide region of liquid separation into two phases is observed in the system. One phase is composed of practically pure CaF₂ with additions of several mol% of CaO and Al₂O₃, and the other consists of 50 to 65 mol% of CaF₂ only. Eleven invariant points of the CaF₂-Al₂O₃-CaO system include seven ternary eutectics, two ternary peritectics and two points of four-phase monotectic transition. The primary fields of crystallization of all the phases are alongated toward the CaF₂ apex, the CaO field being the widest and the 3CaO·Al₂O₃ field the narrowest. Seven junctions of the CaF₂-Al₂O₃-CaO phase diagram were represented. Computed saturation lines of CaF₂-Al₂O₃-CaO melt with CaO, Al₂O₃, CaO·6Al₂O₃ and CaO·2Al₂O₃, and also the positions of a number of characteristic points, agree well with the experimental data available. The present calculations reveal a number of details and peculiarities of the constitution of the CaF₂-Al₂O₃-CaO phase diagram.     

Equilibrium relationships in the systems Li-Co-O and Li-Ni-O

A knowledge of equilibrium relationships in the systems Li-Co-O and Li-Ni-O was of interest because of the possibility of using Li-doped oxides as electrode materials in the fused carbonate fuel cell. Equilibrium relationships in air in the former system were investigated using a thermobalance and an isobaric ternary phase diagram was constructed which shows that Co₃O₄ co-exists with a CoO rich solid solution phase and an Li₂O.Co₂O₃ rich solid solution phase at 860° C. Because of the difficulty of obtaining complete reaction, equilibrium in the system Li-Ni-O was investigated primarily by X-ray examination of fired specimens. It was found that after leaching out unreacted Li₂CO₃, all the mixtures lay along the join NiO-LiNiO₂ in the ternary phase diagram, indicating that in the presence of Li₂O oxidation of NiO was occurring. Results were presented to show the effects of composition and heat treatment on the electrical conductivities of selected mixtures.     

Solid-state phase equilibria and thermodynamic properties of ternary compounds in the Tl-Sb-S system

The Tl-Sb-S system has been studied in the composition region Tl₂S-Sb₂S₃-S using differential thermal analysis, X-ray diffraction, and emf measurements on thallium concentration cells at temperatures from 300 to 390 K, and the 300-K isothermal section of its phase diagram has been mapped out. The existence of the ternary compounds TlSb₅S₈, TlSb₃S₅, TlSbS₃, TlSbS₂, Tl₃SbS₄, and Tl₃SbS₃ has been confirmed, and the position of the phase fields involving these compounds has been accurately determined. Using emf data, we have evaluated the partial molar functions (D[`(G)]\Delta \bar G , D[`(H)]\Delta \bar H , D[`(S)]\Delta \bar S ) of the thallium in the alloys studied, the standard thermodynamic functions of formation of the ternary compounds, and their standard entropies.     

Subsolidus Phase Relations in the Systems M2 +O–M2+O–V2O5(M+ = Li, Na, K, Rb, Cs; M2+ = Mg, Ca)

Subsolidus phase relations in the M₂O(M₂CO₃)–MgO–V₂O₅ and M₂O(M₂CO₃)–CaO–V₂O₅ (M = Li, Na, K, Rb, Cs) systems are studied. Twenty mixed vanadates are obtained, of which Rb₂CaV₂O₇, Cs₂CaV₂O₇, LiMg₄(VO₄)₃, RbCaVO₄, and CsCaVO₄ are identified for the first time. Structural data are summarized for all of the mixed vanadates: the space group and lattice parameters are indicated for 14 compounds (for 6 compounds, such data are obtained for the first time), and I and d data are presented for 8 compounds. Partial series of Ca₃(VO₄)₂-based solid solutions with the general formula Ca_{3 – x} M_2x (VO₄)₂ (M = Na, K, Rb, Cs) are identified in the range 0 < x 0.14. Six phase diagrams (M⁺ = Li, Rb, Cs; M²⁺ = Mg, Ca) are investigated and are compared with the phase diagrams of the other ternary systems in question. The key features of the ternary phase diagrams and, hence, the reactivity of the constituent oxides are shown to vary systematically in going from Li₂O to Cs₂O and from MgO to SrO, which is interpreted in terms of the variation in the ionic radius of the alkali and alkaline-earth metals.     

Alloy-oxide equilibria in the system Pt-Rh-O

The composition of Pt-Rh alloys that co-exist with Rh₂O₃ in air have been identified by experiment at 1273 K. The isothermal sections of the phase diagram for the ternary system Pt-Rh-O at 973 K and 1273 K have been computed based on experimentally determined phase relations and recent thermodynamic measurements on Pt_1−X Rh _X alloys and Rh₂O₃. The composition dependence of the oxygen partial pressure for the oxidation of Pt_1−X Rh _X alloys at different temperatures, and temperature for the oxidation of the alloys in air are computed. The diagrams provide quantitative information for optimization of the composition of Pt_1−X Rh _X alloys for high temperature application in oxidizing atmospheres.     

Thermodynamic properties of ternary phases in the Cu-Tl-Se system

The Cu-Tl-Se system has been studied at temperatures from 300 to 420 K using emf measurements with Cu₄RbCl₃I₂ as a Cu+ ion conducting solid electrolyte. The emf data have been used to map out the subsolidus phase diagram of the Cu-Tl-Se system in the composition region Tl₂Se-CuTlSe-CuSe-Se. We have calculated the partial molar thermodynamic functions of the copper in the alloys and the standard thermodynamic functions of formation and standard entropies of the ternary compounds CuTlSe₂, CuTlSe, and Cu₂TlSe₂. The results confirm that the thermodynamic properties of copper-containing ternary systems can be studied using the approach in question even when they contain an element (thallium in this study) located to the left of copper in the electrochemical series.     

Phase Equilibria in Systems Involving the Rare-Earth Oxides. Part I. Polymorphism of the Oxides of the Trivalent Rare-Earth Ions

The polymorphic relationships of the pure rare-earth oxides have been reinvestigated using X-ray diffraction methods for identification of phases. The oxides of the trivalent rare earth ions crystallize in three different types: A, B, and C. Each oxide has only one truly stable polymorph: La₂O₃, Ce₂O₃, Pr₂O₃, and Nd₂O₃ belong to the A type; Sm₂O₃, Eu₂O₃, and Gd₂O₃ to the B type; Tb₂O₃, Dy₂O₃, Ho₂O₃, Er₂O₃, Tm₂O₃, Yb₂O₃, and Lu₂O₃ to the C type. In addition Nd₂O₃, Sm₂O₃, Eu₂O₃, and Gd₂O₃ have low-temperature, apparently metastable, C-type polymorphs. The low-temperature form inverts irreversibly to the stable form at increasingly higher temperatures for decreasing cation radius.     

Studies on the interactions of metal oxides and Na2 SO4 at 1100 and 1200 K in oxygen

The interaction of different metal oxides such as Co₃O₄, NiO, Al₂O₃, Cr₂O₃, Fe₂O₃ and SiO₂ with Na₂SO₄ at a temperature of 1100 and 1200 K in flowing oxygen has been studied. The thermogravimetric studies for each system were carried out as a function of Na₂SO₄ in the mixture. The presence of different constituents in the reaction products were identified by X-ray diffraction analysis and the morphologies of the reaction products were characterized using metallography and scanning electron microscopy (SEM). The formation of products was also investigated by thermodynamic computation of free energies of the reactions and the study of relevant equilibrium phase diagrams. The soluble species in the aqueous solutions of the reaction products were determined quantitatively using atomic absorption spectrophotometry. The high temperature interaction products usually contain a 3-phase structure namely, Na₂O·M₂O _x , M₂O _x and metal sulphide and/or metal sulphate. The formation of Na₂O·M₂O _x depends upon the solid state solubility of metal oxide in the molten salt at high temperatures. Under limited solubility conditions Na₂O·M₂O _x is invariably formed, but as soon as this condition is relaxed the oxide. M₂O _x , precipitates and forms a separate phase.