Thermodynamic Properties and Phase Diagram for the System MoO2–TiO2

The activity of molybdenum dioxide (MoO2) in the MoO2–TiO2 solid solutions was measured at 1600 K using a solid-state cell incorporating yttria-doped thoria as the electrolyte. For two compositions, the emf was also measured as a function of temperature. The cell was designed such that the emf is directly related to the activity of MoO2 in the solid solution. The results show monotonic variation of activity with composition, suggesting a complete range of solid solutions between the end members and the occurrence of MoO2 with a tetragonal structure at 1600 K. A large positive deviation from Raoult's law was found. Excess Gibbs energy of mixing is an asymmetric function of composition and can be represented by the subregular solution model of Hardy as follows.The temperature dependence of the emf for two compositions is reasonably consistent with ideal entropy of mixing. A miscibility gap is indicated at a lower temperature with the critical point characterized by Tc (K)=1560 and . Recent studies indicate that MoO2 undergoes a transition from a monoclinic to tetragonal structure at 1533 K with a transition entropy of 9.91 J·(mol·K)−1. The solid solubility of TiO2 with rutile structure in MoO2 with a monoclinic structure is negligible. These features give rise to a eutectoid reaction at 1412 K. The topology of the computed phase diagram differs significantly from that suggested by Pejryd.

Thermodynamic activities in the Pb(Zr1-XTiX)O-3 solid solution at 1373 K

Although Pb(Zr1-XTiX)O-3 solid solution is the cornerstone of the piezoelectric ceramics, there is no information in the literature on thermodynamic activities of the component phases in the solid solution. Using inter-crystalline ion exchange equilibria between Pb(Zr1-XTiX)O-3 solid solution with cubic perovskite structure and (Zr1-YTiY)O-2 solid solutions with monoclinic and tetragonal structures, activities of PbTiO3 and PbZrO3 in the perovskite solid solution have been derived at 1373 K using the modified Gibbs-Duhem integration technique of Jacob and Jeffes. Tie-lines from the cubic solid solution are skewed towards the ZrO2 corner. Activities in the zirconia-rich (Zr1-YTiY)02 solid solutions are taken from a recent emf study. The results for the perovskite solid solution at 1373 K can be represented by a sub-regular solution model: Delta G(E.M) (J mol(-1)) = X-PbTiO3 X-PbZrO3(5280X(PbTiO3) - 1980X(PbZrO3)) where Delta G(E.M) is the excess Gibbs energy of mixing of the cubic solid solution and Xi represents the mole fraction of component i. There is a significant positive deviation from ideality for PbTiO3-rich compositions and mild negative deviation near the PbZrO3 corner. The cubic solid solution is intrinsically stable against composition fluctuations at temperatures down to 840 K. The results contrast sharply with the recent calorimetric data on enthalpy of mixing which signal instability of the cubic perovskite solid solution. (C) 2007 Elsevier B.V. All rights reserved.

Metal-spinel-corundum three phase equilibria in the system Ni-Cr-Al-O at 1373 K

The tie-lines representing the inter-crystalline ion exchange equilibria between the NiCr2O4-NiAl2O4 spinet solid solution and Cr2O3-Al2O3 corundum solid solution are determined by electron microprobe andEDAX pointcountanalysis of the oxide phases equilibrated with metallic Ni at 1373 K. The component activities in the spinet solid solution are derived from the tie-lines and thermodynamic data for Cr2O3-Al2O3 solid solution available in the literature. The Gibbs energy of mixing of the spinet solid solution calculated from the experimental data is discussed in relation to the values derived from the cation distribution models which assume random mixing of cations on both tetrahedral and octahedral sites. Positive deviation from the models is observed indicating significant positive enthalpy contribution arising form the size mismatch between Al+3 and Ni+2 ions on the tetrahedral site and Al+3, Ni+2 and Cr+3 on the octahedral site. Variation of the oxygen potential for threephase equilibrium involving metallic nickel, spinet solid solution and corundum solid solution is computed as a function of composition of the solid solutions at 1373 K. The oxygen potential exhibits a minimum at aluminum cationic fraction eta(Al)/(eta(Al) + eta(Cr)) = 0.524 in the oxide solid solutions.

Role of entropy in the stability of cobalt titanates

The standard molar Gibbs free energy of formation of Co2TiO4, CoTiO3,and CoTi2O5 as a function of temperature over an extended range (900 to 1675) K was measured using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte, with CoO as reference electrode and appropriate working electrodes. For the formation of the three compounds from their component oxides CoO with rock-salt and TiO2 with rutile structure, the Gibbs free energy changes are given by:Delta(f)G degrees((ox))(Co2TiO4) +/- 104/(J . mol(-1)) = -18865 - 4.108 (T/K)Delta(f)G degrees((ox))(CoTiO3) +/- 56/(J . mol(-1)) = -19627 + 2.542 (T/K) Delta(f)G degrees((ox))(CoTi2O5) +/- 52/(J . mol(-1)) = -6223 - 6.933 (T/K) Accurate values for enthalpy and entropy of formation were derived. The compounds Co2TiO4 with spinel structure and CoTi2O5 with pseudo-brookite structure were found to be entropy stabilized. The relatively high entropy of these compounds arises from the mixing of cations on specific crystallographic sites. The stoichiometry of CoTiO3 was confirmed by inert gas fusion analysis for oxygen. Because of partial oxidation of cobalt in air, the composition corresponding to the compound Co2TiO4 falls inside a two-phase field containing the spinet solid solution Co2TiO4-Co3O4 and CoTiO3. The spinel solid solution becomes progressively enriched in Co3O4 with decreasing temperature. (c) 2010 Elsevier Ltd. All rights reserved.

Chemical potentials of oxygen for fayalite-quartz-lron and fayalite-quartz-magnetite equilibria

The oxygen potentials corresponding to fayalite-quartz-iron (FQI) and fayalite-quartz-magnetite (FQM) equilibria have been determined using solid-state galvanic cells: Pt,Fe + Fe2SiO4 + SiO2/(Y2O3)ZrO2/Fe + \r"FeO,\l"Pt and Pt, Fe3O4 + Fe2SiO4 + SiO2/(Y2O3)ZrO2/Ni + NiO, Pt in the temperature ranges 900 to 1400 K and 1080 to 1340 K, respectively. The cells are written such that the right-hand electrodes are positive. Silica used in this study had the quartz structure. The emf of both cells was found to be reversible and to vary linearly with temperature. From the emf, Gibbs energy changes were deduced for the reactions: 0.106Fe (s) + 2Fe0.947O (r.s.) + SiO2 (qz) → Fe2SiO4 (ol) δG‡= -39,140+ 15.59T(± 150) J mol-1 and 3Fe2SiO4 (ol) + O2 (g) → 2Fe3O4 (sp) + 3SiO2 (qz) δG‡ = -471,750 + 160.06 T±} 1100) J mol-1 The “third-law≓ analysis of fayalite-quartz-wustite and fayalite-quartz-magnetite equilibria gives value for δH‡298 as -35.22 (±0.1) and -528.10 (±0.1) kJ mol-1, respectively, independent of temperature. The Gibbs energy of formation of the spinel form of Fe2SiO4 is derived by com-bining the present results on FQI equilibrium with the high-pressure data on olivine to spinel transformation of Fe2SiO4.

Activities in liquid Ga-Te alloys at 1120 k

The activity of gallium in liquid Ga-Te alloys has been measured at 1120 K using a solid state galvanic cell incorporating yttria-stabilized thoria as the solid electrolyte. The cell can be schematically represented as (−) W,Re,Ga(1)+Ga2O3(s)|(Y2O3) ThO2|Ga-Te(1) + Ga2O3(s), Re, W (+) The activity of tellurium was derived by Gibbs-Duhem integration. The activity of gallium shows negative deviation from Raoult's law for XGa < 0.6 and positive deviation from ideality for XGa > 0.6. The activity of gallium was constant in the composition range 0.73 < XGa < 0.89, indicating liquid state immiscibility in this region. The Gibbs energy of mixing and the concentration-concentration structure factor at long wavelength limit show a minimum at XGa ≈ 0.4, suggesting strong interactions in the liquid phase with formation of ‘Ga2Te3‘-type complexes

Refinement of the thermodynamic properties of ruthenium dioxide and osmium dioxide

The standard Gibbs energies of formation of RuO2 and OsO2 at high temperature have been determined with high precision, using a novel apparatus that incorporates a buffer electrode between the reference and working electrodes, The buffer electrode absorbs the electrochemical flux of oxygen through the solid electrolyte from the electrode with higher oxygen chemical potential to the electrode with lower oxygen potential, The buffer electrode prevents polarization of the measuring electrode and ensures accurate data, The standard Gibbs energies of formation (Delta(f)G degrees) of RuO2, in the temperature range of 900-1500 K, and OsO2, in the range of 900-1200 K, can be represented by the equations Delta(f)G degrees(RuO2)(J/mol) = -324 720 + 354.21T - 23.490T In T Delta(f)G degrees(OsO2)(J/mol) = -304 740 + 318.80T - 18.444T In T where the temperature T is given in Kelvin and the deviation of the measurement is +/- 80 J/mol, The high-temperature heat ;capacities of RuO2 and OsO2 are measured using differential scanning calorimetry. The information for both the low- and high-temperature heat rapacity of RuO2 is coupled with the Delta(f)G degrees data obtained in this study to evaluate the standard enthalpy of formation of RuO2 at 298.15 K (Delta(f)H degrees(298.15K)). The low-temperature heat capacity of OsO2 has not been measured: therefore, the standard enthalpy and entropy of formation of OsO2 at 298.15 K (Delta(f)H degrees(298.15K) and S degrees(298.15K), respectively) are derived simultaneously through an optimization procedure from the high-temperature heat capacity and the Gibbs energy of formation. Both Delta fH degrees(298.15K) and S degrees(298.15K) are treated as variables in the optimization routine, For RuO2, the standard enthalpy of formation at 298.15 K is Delta fH degrees(298.15K) (RuO2) -313.52 +/- 0.08 kJ/mol, and that for OsO2 is Delta(f)H degrees(298.15K) (OSO2) = -295.96 +/- 0.08 kJ/mol. The standard entropy of OsO2 at 298.15 K that has been obtained from the optimization is given as S degrees(298.15K) (OsO2) = 49.8 +/- 0.2 J (mol K)(-1).

Phase relations and thermodynamic properties of compounds in the pseudobinary system BaO-Y2O3

The coexisting phases in the pseudobinary system BaO-Y2O3 have been identified by equilibrating samples containing different amounts of component oxides at 1173, 1273 and 1373 K. Only two ternary oxides, BaY2O4 and Ba3Y4O9, have been found to be stable in the temperature range of investigation. Solid state galvanic cells: Pt, O2+BaO+BaF2double vertical barBaF2+2mol%Al2O3double vertical barBaF2+BaY2O4+Y2O3+O2, Pt and Pt, O2+BaO+BaF2double vertical barBaF2+2mol% Al2O3double vertical barBaF2+BaY2O4+Ba3Y4O9+O2, Pt have been employed for determining the Gibbs' energies of formation of BaY2O4 and Ba3Y4O9 from the component oxides in the range 850 to 1250 K. A composite solid electrolyte incorporating Al2O3-dispersed BaF2 was used in the cells. To prevent interaction between the Al2O3 powder and electrode materials, the solid electrolyte was coated with pure BaF2. The Gibbs' energies of formation of BaY2O4 and Ba3Y4O9 from component oxides are given by: Δf0 (BaY2O4, s)=−128,310+5.211T (±580) J mol−1, (850less-than-or-equals, slantTless-than-or-equals, slant1250 K) and ΔGfo(Ba3Y4O9, s)= −317,490 −24.704T (±1100) J mol−1, (850less-than-or-equals, slantTless-than-or-equals, slant1250 K).

Experimental and Computational Characterization of Alloy--Spinel--Corundum Equilibrium in the System Fe--Co--Al--O at 1873K

The three-phase equilibrium between alloy, spinel solid solution and alpha -Al sub 2 O sub 3 in the Fe--Co--Al--O system at 1873k was fully characterized as a function of alloy composition using both experimental and computational methods. The equilibrium oxygen content of the liquid alloy was measured by suction sampling and inert gas fusion analysis. The O potential corresponding to the three-phase equilibrium was determined by emf measurements on a solid state galvanic cell incorporating (Y sub 2 O sub 3 )ThO sub 2 as the solid electrolyte and Cr + Cr sub 2 O sub 3 as the reference electrode. The equilibrium composition of the spinel phase formed at the interface between the alloy and alumina crucible was measured by electron probe microanalysis (EPMA). The experimental results were compared with the values computed using a thermodynamic model. The model used values for standard Gibbs energies of formation of pure end-member spinels and Gibbs energies of solution of gaseous O in liquid Fe and cobalt available in the literature. The activity--composition relationship in the spinel solid solution was computed using a cation distribution model. The variation of the activity coefficient of O with alloy composition in the Fe--Co--O system was estimated using both the quasichemical model of Jacob and Alcock and Wagner's model along with the correlations of Chiang and Chang and Kuo and Chang. The computed results of spinel composition and O potential are in excellent agreement with the experimental data. Graphs. 29 ref.--AA

Activities, concentration fluctuations and complexing in liquid Ca-Al alloys

Détermination de l'activité du calcium par la méthode d'effusion de Knudsen. Calcul, à partir de la distribution mesurée pour l'aluminium entre l'alliage et du fer pur, de l'activité de l'aluminium dans des alliages riches en calcium. Détermination en combinant les deux méthodes, des activités des deux composants et de l'énergie de Gibbs de mélange pour tout le domaine de composition. Calcul et analyse du facteur de structure concentration-concentration

Stability of CU(2)Ln(2)O(5) compounds - Comparison, assessment and systematics

Phase diagram studies show that at ambient pressure only one ternary oxide, Cu(2)Ln(2)O(5), is stable in the ternary systems Cu-Ln-O (Ln = Tb, Dy, Ho, Er, Tm, Yb, Lu) at high temperatures. The crystal structure of Cu(2)Ln(2)O(5) can be described as a zig-zag arrangement of one-dimensional Cu2O5 chains parallel to-the a-axis with Ln atoms occupying distorted octahedral sites between these chains. Four sets of emf measurements on Gibbs energy of formation of Cu(2)Ln(2)O(5) (Ln = Tb, Dy, Ho, Er, Tm, Yb, Lu; Y) from component binary oxides and one set of high-temperature solution calorimetric data on enthalpy of formation have been reported in the literature. Except for Cu2Y2O5, the measured values for the Gibbs energies of formation of all other Cu(2)Ln(2)O(5) compounds fall in a narrow band (+/-1 kJ mol(-1)) and indicate a regular increase in stability with decreasing ionic radius of the lanthanide ion. The values for the second law enthalpy of formation, derived from the temperature dependence of emf obtained in different studies, show larger differences, as high as 25 kJ mol(-1) for Cu2Tm2O5. Though associated with an uncertainty of +/-4 kJ mol(-1), the calorimetric measurements help to identify the best set of emf data. The trends in thermodynamic data correlate well with the global instability index (GII) based on the overall deviation from the valence sum rule. Low values for the index calculated from crystallographic information indicate higher stability. Higher values are indicative of the larger stress in the structure.

Trends in the stability of ternary oxides: Systems M-Pb-O (M = Ca, Sr, Ba)

Recent experimental investigations of phase equilibria and thermodynamic properties of the systems M-Pb-O, where M = Ca, Sr or Ba, indicate a regular increase in thermodynamic stability of ternary oxides, MPbO3 and M2PbO4, with increasing basicity of the oxide of the alkaline-earth metal. Number of stable interoxide compounds at 1100 K in the systems M-Pb-O (M = Mg, Ca, Sr, Ba) increases in unit increments from Mg to Ba. In this paper, experimentally determined standard Gibbs energies of formation of M2PbO4 (M = Ca, Sr, Ba) and MPbO3 (M = Sr, Ba) from their component binary monoxides and oxygen gas are combined with an estimated value for CaPbO3 to delineate systematic trends in thermodynamic stability of the ternary oxides. The trends are interpreted using concepts of tolerance factor and acid-base interactions. All the ternary oxides in these systems contain lead in the tetravalent state. The small Pb4+ ions polarize the surrounding oxygen ions and cause the formation of oxyanions which are acidic in character. Hence, the higher oxidation state of lead is stabilized in the presence of basic oxides of alkaline-earth group. A schematic subsolidus temperature-composition phase diagram is presented for the system BaO-PbO-O-2 to illustrate the change in oxidation states in binary and ternary oxides with temperature.

Synergistic use of thermogravimetric and electrochemical techniques for thermodynamic study of TiOx (1.67 <= x <= 2.0) at 1573 K

A thermodynamic study of the Ti-O system at 1573 K has been conducted using a combination of thermogravimetric and emf techniques. The results indicate that the variation of oxygen potential with the nonstoichiometric parameter delta in stability domain of TiO2-delta with rutile structure can be represented by the relation, Delta mu o(2) = -6RT In delta - 711970(+/-1600) J/mol. The corresponding relation between non-stoichiometric parameter delta and partial pressure of oxygen across the whole stability range of TiO2-delta at 1573 K is delta proportional to P-O2(-1/6). It is therefore evident that the oxygen deficient behavior of nonstoichiometric TiO2-delta is dominated by the presence of doubly charged oxygen vacancies and free electrons. The high-precision measurements enabled the resolution of oxygen potential steps corresponding to the different Magneli phases (Ti-n O2n-1) up to n = 15. Beyond this value of n, the oxygen potential steps were too small to be resolved. Based on composition of the Magneli phase in equilibrium with TiO2-delta, the maximum value of n is estimated to be 28. The chemical potential of titanium was derived as a function of composition using the Gibbs-Duhem relation. Gibbs energies of formation of the Magneli phases were derived from the chemical potentials of oxygen and titanium. The values of -2441.8(+/-5.8) kJ/mol for Ti4O7 and -1775.4(+/-4.3) kJ/mol for Ti3O5 Obtained in this study refine values of -2436.2(+/-26.1) kJ/mol and-1771.3(+/-6.9) kJ/mol, respectively, given in the JANAF thermochemical tables.

Thermodynamics of Cobalt (II, III) Oxide (Co3O4): Evidence of Phase Transition

The Gibbs' energy change for the reaction, 3CoO (r.s.)+1/2O2(g)→Co3O4(sp), has been measured between 730 and 1250 K using a solid state galvanic cell: Pt, CuO+Cu2O|(CaO)ZrO2|CoO+Co3O4,Pt. The emf of this cell varies nonlinearly with temperature between 1075 and 1150 K, indicating a second or higher order phase transition in Co3O4around 1120 (±20) K, associated with an entropy change of ∼43 Jmol-1K-1. The phase transition is accompanied by an anomalous increase in lattice parameter and electrical conductivity. The cubic spinel structure is retained during the transition, which is caused by the change in CO+3 ions from low spin to high spin state. The octahedral site preference energy of CO+3 ion in the high spin state has been evaluated as -24.8 kJ mol-1. This is more positive than the value for CO+2 ion (-32.9 kJ mol-1). The cation distribution therefore changes from normal to inverse side during the phase transition. The transformation is unique, coupling spin unpairing in CO+3 ion with cation rearrangement on the spinel lattice, DTA in pure oxygen revealed a small peak corresponding to the transition, which could be differentiated from the large peak due to decomposition. TGA showed that the stoichiometry of oxide is not significantly altered during the transition. The Gibbs' energy of formation of Co3O4 from CoO and O2 below and above phase transition can be represented by the equations:ΔG0=-205,685+170.79T(±200) J mol-1(730-1080 K) and ΔG0=-157,235+127.53T(±200) J mol-1(1150-1250 K).

The vapour pressures of barium and strontium

The vapour pressures of barium and strontium have been measured by continuous monitoring of the weight loss of Knudsen cells in the temperature range 700�1200 K. The results for strontium agree with those reported in the literature, but the vapour pressure of barium has been found to be considerably lower than the generally accepted value. The experimentally determined pressures are in good agreement with theoretical values obtained using the Gibbs-Bogoliubov first-order variational method.