Gibbs free energies of formation of ZnAl2O4 and ZnCr2O4

The standard free energies of formation of zinc aluminate and chromite were determined by measuring the oxygen potential over a solid CuZn alloy, containing 10 at.−% Zn, in equilibrium with ZnO, ZnAl2O4+Al2O3(χ) and ZnCr2O4+Cr2O3, in the temperature range 700–900°C. The oxygen potential was monitored by means of a solid oxide galvanic cell in which a Y2O3 ThO2 pellet was sandwiched between a CaOZrO2 crucible and tube. The temperature dependence of the free energies of formation of the interoxidic compounds can be represented by the equations, The heat of formation of the spinels calculated from the measurements by the “Second Law method” is found to be in good agreement with calorimetrically determined values. Using an empirical correlation for the entropy of formation of cubic spinel phases from oxides with rock-salt and corundum structures and the measured high temperature cation distribution in ZnAl2O4, the entropy of transformation of ZnO from wurtzite to rock-salt structure is evaluated.

The standard molar Gibbs energy of formation of YbPt3 and LuPt3 intermetallics

The standard molar Gibbs energies of formation of YbPt3 and LuPt3 intermetallic compounds have been measured in the temperature range 880 K to 1100 K using the solid-state cells:View the MathML source and View the MathML source The trifluoride of Yb is not stable in equilibrium with Yb or YbPt3. The results can be expressed by the equations: View the MathML source View the MathML source The standard molar Gibbs energy of formation of LuPt3 is −41.1 kJ · mol−1 more negative than that for YbPt3 at 1000 K. Ytterbium is divalent in the pure metal and trivalent in the intermetallic YbPt3. The energy required for the promotion of divalent Yb to the trivalent state is responsible for the less negative ΔfGmo of YbPt3. The enthalpies of formation of the two intermetallics are in reasonable agreement with Miedema's model. Because of the extraordinary stability of these compounds it is possible to reduce oxides of Yb and Lu with hydrogen in the presence of platinum at View the MathML source. The equilibrium chemical potential of oxygen corresponding to the reduction of Yb2O3 and Lu2O3 by hydrogen in the presence of platinum is presented in the form of an Ellingham diagram.

Gibbs Energy of Formation of MnO: Measurement and Assessment

Based on the measurements of Alcock and Zador, Grundy et al. estimated an uncertainty of the order of +/- 5 kJ mol(-1) for the standard Gibbs energy of formation of MnO in a recent assessment. Since the evaluation of thermodynamic data for the higher oxides Mn3O4, Mn2O3, and MnO2 depends on values for MnO, a redetermination of its Gibbs energy of formation was undertaken in the temperature range from 875 to 1300 K using a solid-state electrochemical cell incorporating yttria-doped thoria (YDT) as the solid electrolyte and Fe + Fe1-delta O as the reference electrode. The cell can be presented as Pt, Mn + MnO/YDT/Fe + Fe1+delta O, Pt Since the metals Fe and Mn undergo phase transitions in the temperature range of measurement, the reversible emf of the cell is represented by the three linear segments. Combining the emf with the oxygen potential for the reference electrode, the standard Gibbs energy of formation of MnO from alpha-Mn and gaseous diatomic oxygen in the temperature range from 875 to 980 K is obtained as: Delta G(f)(o)/Jmol(-1)(+/- 250) = -385624 + 73.071T From 980 to 1300 K the Gibbs energy of formation of MnO from beta-Mn and oxygen gas is given by: Delta G(f)(o)/Jmol(-1)(+/- 250) = -387850 + 75.36T The new data are in excellent agreement with the earlier measurements of Alcock and Zador. Grundy et al. incorrectly analyzed the data of Alcock and Zador showing relatively large difference (+/- 5 kJ mol(-1)) in Gibbs energies of MnO from their two cells with Fe + Fe1-delta O and Ni + NiO as reference electrodes. Thermodynamic data for MnO is reassessed in the light of the new measurements. A table of refined thermodynamic data for MnO from 298.15 to 2000 K is presented.

High temperature stability of oxysulfides containing Ce3+ and Y3+ ions

Standard Gibbs energies of formation of oxysulfides of cerium and yttrium from their respective oxedes were determined using solid oxide galvanic cells incorporating calcia-stabilized zirconia as the electrolyte in the temperature range 870–1120 K. The sulfur potential over the electrode containing the oxide and oxysulfide was fixed by a buffer mixture of Ag + Ag2S. A small amount of CaH2 was added to the buffer to generate an equilibrium ratio of H2S and H2 species in a closed system containing the buffer and the electrode. The sulfur potential is transmitted to the electrode via the gas phase. The results can be summarized by the equations 2left angle bracketCeO2right-pointing angle bracket+1/2(S2)→left angle bracketCe2O2Sright-pointing angle bracket+(O2) ΔG°=430600−109·7T(±400)J mol−1 left angle bracketY2O3right-pointing angle bracket+1/2(S2)→left angle bracketY2O2Sright-pointing angle bracket+1/2(O2) ΔG°=114780−1·45T(±200)J mol−1 The values are compared with data reported in the literature. The stability field diagram for the Ce---O---S system has been developed using the results of this study for Ce2O2S and data for other phases from the literature.

Compatibility of RuO2 electrodes with PZT ceramics

Because of its high electrical conductivity and good diffusion barrier properties ruthenium dioxide (RuO2) is a good electrode material for use with ferroelectric lead zirconate-titanate (PZT) solid solutions. Under certain conditions, RuO2 can react with PZT to form lead ruthenate (Pb2Ru2O6.5) during processing at elevated temperatures resulting in lead depletion from PZT. The standard Gibbs energies of formation of RuO2 and Pb2Ru2O6.5 and activities of components of the PZT solid solution have been determined recently. Using this data along with older thermodynamic information on PbZrO3 and PbTiO3, the stability domain of Pb2Ru2O6.5 is computed as a function of PZT composition, temperature and oxygen partial pressure in the gas phase. The results show PbZrO3-rich compositions are more prone to react with RuO2 at all temperatures. Increasing temperature and decreasing oxygen partial pressure suppress the reaction. Graphically displayed are the reaction zones as a function of oxygen partial pressure and PZT composition at temperatures 973, 1173 and 1373 K.

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).

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

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.

Use of metastable equilibria for determination of Gibbs energy of solids

Attempts are made to measure activities of both components of a binary alloy (A�B) at 650 K using a solid-state galvanic cell incorporating a new composite solid electrolyte. Since the ionic conductivity of the composite solid electrolyte is three orders of magnitude higher than that of pure CaF2, the cell can be operated at lower temperatures. The alloy phase is equilibrated in separate experiments with flourides of each component and fluorine potential is measured. The mixture of the alloy (A�B) and the fluoride of the more reactive component (BF2) is stable, while (A�B) + AF2 mixture is metastable, Factors governing the possible use of metastable equilibria have been elucidated in this study. In the Co�Ni system, where the difference in Gibbs energies of formation of the fluorides is 21.4 kJ/mol, emf of the cell with metastable phases at the electrode is constant for periods ranging from 90 to 160 ks depending on alloy composition. Subsequently, the emf decreases because of the onset of the displacement reaction. In the Ni�Mn system, measurement of the activity of Ni using metastable equilibria is not fully successful at 650 K because of the large driving force for the displacement reaction (208.8 kJ/mol). Critical factors in the application of metastable equilibria are the driving force for displacement reaction and diffusion coefficients in both the alloy and fluoride solid solution.

Thermodynamic Properties of Niobium Oxides

Thermodynamic properties of three oxides of niobium have been measured using solid state electrochemical cells incorporating yttria-doped thoria (YDT) as the electrolyte in the temperature range T = (1000 to 1300) K. The standard Gibbs energies of formation of NbO, NbO2, and NbO2.422 from the elements can be expressed as: Delta(f)G(NbO)(o) +/- 547/J . mol(-1) = -414 986 + 86.861(T/K) Delta(f)G(NbO2)(o) +/- 548/J . mol(-1) = -779 864 + 164.438(T/K) Delta(f)G(NbO2.422)(o) +/- 775/J . mol(-1) = -911 045 + 197.932(T/K) The results are discussed in comparison with thermodynamic data reported in the literature. The new results refine data for NbO and NbO2 presented in standard data compilations. There are no data in thermodynamic compilations for NbO2.422 (Nb12O29). In the absence of the heat capacity and enthalpy of formation measurements, only the Gibbs energy of formation of NbO2.422 can be assessed. The free energy of formation of stoichiometric Nb2O5 is evaluated on the basis of measurements on NbO2.422 and information available in the literature on phase boundary compositions and isothermal variation of nonstoichiometric parameter with oxygen potential for Nb2O5-x. The results suggest a minor revision of data for Nb2O5. A minimum in the Gibbs energy of mixing for the system Nb-O occurs in the nonstoichiometric domain of Nb2O5-x with x = 0.036.

Thermodynamic properties of LaFeO3-delta and LaFe12O19

The standard Gibbs energies of formation of lanthanum orthoferrite (LaFeO3-delta) and hexaferrite (LaFe12O19)were determined using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte and pure oxygen gas at ambient pressure as the reference electrode. From emf of the solid-state cell, the Gibbs energy of formation of nonstoichiometric orthoferrite (LaFeO3-delta) is obtained. To derive values for the stoichiometric phase, variation of the oxygen nonstoichiometric parameter with oxygen partial pressure was measured using thermogravimetry under controlled gas mixtures. The results obtained for LaFeO3 and LaFe12O19 can be summarized by the following equations, which represent the formation of ternary oxides from their component binary oxides: 1/2 La2O3 + 1/2 Fe2O3 -> LaFeO3: Delta G degrees (LaFeO3) (+/- 450) (J mol(-1)) = -62920 - 2.12T (K), and 1/2 La2O3 + 9/2Fe(2)O(3) + Fe3O4 -> LaFe12O19; Delta G degrees (LaFe12O19) (+/- 200) (J mol(-1)) = -103900 + 21.25T (K). These data are discussed critically in comparison with thermodynamic values reported in the literature from a variety of measurements. The values obtained in this study are consistent with calorimetric entropy and enthalpy of formation of the perovskite phase and with some of the Gibbs energy measurements reported in the literature. For the lanthanum hexaferrite (LaFe12O19) there are no prior thermodynamic measurements for comparison. (c) 2011 Elsevier B.V. All rights reserved.

Thermodynamic properties of the calcium ferrites CaFe2O4 and Ca2Fe2O5

The chemical potentials of CaO in the two-phase fields Fe2O3 + CaFe2O4 and CaFe2O4 + Ca2Fe2O5 of the pseudobinary system CaO - Fe2O3 have been measured in the temperature range from 975 to 1275 K, relative to pure CaO as the reference state, using solid state galvanic cells incorporating single-crystal CaF2 as the solid electrolyte. The cell was operated under pure oxygen at ambient pressure. The standard Gibbs energies of formation of calcium ferrites, CaFe2O4 and Ca2Fe2O5, were derived from the reversible emfs. The results can be summarized by the following equations:CaO + Fe2O3 --> CaFe2O4;Delta G degrees = - 37,480 + 1.16 T (+/- 250) J/mol 2 CaO + Fe2O3 --> Ca2Fe2O5;Delta G degrees = - 45, 280 - 13.51 T (+/- 275) J/mol These values are compared with thermodynamic data reported in the literature. The results of this study are in excellent agreement with heat capacity data, and in reasonable agreement with earlier measurements of enthalpy and Gibbs energy of formation, but suggest significant revision of enthalpies of formation of calcium ferrites given in current thermodynamic compilations.

Systematic trends in structural and thermodynamic properties of ternary oxides in the systems Ln-Pd-O (Ln = lanthanide element)

Isothermal sections of the phase diagrams for the systems Ln-Pd-O (Ln = lanthanide element) at 1223 K indicate the presence of two inter-oxide compounds Ln(4)PdO(7) and Ln(2)Pd(2)O(5) for Ln = La, Pr, Nd, Sm, three compounds Ln(4)PdO(7), Ln(2)PdO(4) and Ln(2)Pd(2)O(5) for Ln = Eu, Gd and only one compound of Ln(2)Pd(2)O(5) for Ln = Tb to Ho. The lattice parameters of the compounds Ln(4)PdO(7), Ln(2)PdO(4) and Ln(2)Pd(2)O(5) show systematic nonlinear variation with atomic number. The unit cell volumes decrease with increasing atomic number. The standard Gibbs energies, enthalpies and entropies of formation of the ternary oxides from their component binary oxides (Ln(2)O(3) and PdO) have been measured recently using an advanced version of the solid-state electrochemical cell. The Gibbs energies and enthalpies of formation become less negative with increasing atomic number of Ln. For all the three compounds, the variation in Gibbs energy and enthalpy of formation with atomic number is markedly non-linear. The decrease in stability with atomic number is most pronounced for Ln(2)Pd(2)O(5), followed by Ln(4)PdO(7) and Ln(2)PdO(4). This is probably related to the repulsion between Pd2+ ions on the opposite phases Of O-8 cubes in Ln(2)Pd(2)O(5), and the presence of Ln-filled O-8 cubes that share three faces with each other in Ln4PdO7. The values for entropy of formation of all the ternary oxides from their component binary oxides are relatively small. Although the entropies of formation show some scatter, the average value for Ln = La, Pr, Nd is more negative than the average value for the other lanthanide elements. From this difference, an average value for the structure transformation entropy of Ln(2)O(3) from C-type to A-type is estimated as 0.87 J.mol(-1).K-1. The standard Gibbs energies of formation of these ternary oxides from elements at 1223 K are presented as a function of lanthanide atomic number. By invoking the Neumann-Kopp rule for heat capacity, thermodynamic properties of the inter-oxide compounds at 298.15 K are estimated. (C) 2002 Elsevier Science Ltd. All rights reserved.

System Dy-Fe-O: thermodynamic properties of ternary oxides using Calvet calorimetry and solid-state electrochemical cell

The enthalpy increments and the standard molar Gibbs energies of formation-of DyFeO3(s) and Dy3Fe5O12(s) have been measured using a Calvet micro-calorimeter and a solid oxide galvanic cell, respectively. A co-operative phase transition, related to anti-ferromagnetic to paramagnetic transformation, is apparent. from the heat capacity data for DyFeO3 at similar to 648 K. A similar type of phase transition has been observed for Dy3Fe5O12 at similar to 560 K which is related to ferrimagnetic to paramagnetic transformation. Enthalpy increment data for DyFeO3(s) and Dy3Fe5O12(s), except in the vicinity of the second-order transition, can be represented by the following polynomial expressions:{H(0)m(T) - H(0)m(298.15 K)) (Jmol(-1)) (+/-1.1%) = -52754 + 142.9 x (T (K)) + 2.48 x 10(-3) x (T (K))(2) + 2.951 x 10(6) x (T (K))(-1); (298.15 less than or equal to T (K) less than or equal to 1000) for DyFeO3(s), and {H(0)m(T) - H(0)m(298.15 K)} (Jmol(-1)) (+/-1.2%) = -191048 + 545.0 x (T - (K)) + 2.0 x 10(-5) x (T (K))(2) + 8.513 x 10(6) x (T (K))(-1); (208.15 less than or equal to T (K) less than or equal to 1000)for Dy3Fe5O12(s). The reversible emfs of the solid-state electrochemical cells: (-)Pt/{DyFeO3(s) + Dy2O3(s) + Fe(s)}/YDT/CSZ//{Fe(s) + Fe0.95O(s)}/Pt(+) and (-)Pt/{Fe(s) + Fe0.95O(s)}//CSZ//{DyFeO3(s) + Dy3Fe5O12(s) + Fe3O4(s)}/Pt(+), were measured in the temperature range from 1021 to 1250 K and 1035 to 1250 K, respectively. The standard Gibbs energies of formation of solid DyFeO3 and Dy3Fe5O12 calculated by the least squares regression analysis of the data obtained in the present study, and data for Fe0.95O and Dy2O3 from the literature, are given by Delta(f)G(0)m(DyFeO3,s)(kJmol(-1))(+/-3.2)= -1339.9 + 0.2473 x (T(K)); (1021 less than or equal to T (K) less than or equal to 1548)and D(f)G(0)m(Dy3Fe5O12,s) (kJmol(-1)) (+/-3.5) = -4850.4 + 0.9846 x (T (K)); (1035 less than or equal to T (K) less than or equal to 1250) The uncertainty estimates for Delta(f)G(0)m include the standard deviation in the emf and uncertainty in the data taken from the literature. Based on the thermodynamic information, oxygen potential diagram and chemical potential diagrams for the system Dy-Fe-O were developed at 1250 K. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Gibbs energy of formation of lead zirconate

The Gibbs energy of formation of zirconia-saturated lead zirconate was determined by emf measurements on the solid state cells and at 800 to 1400 K. The results obtained differ significantly from those reported in the literature based on vapor-pressure measurements, using Knudsen effusion and transportation techniques and assuming that the vapor phase consisted entirely of monomeric PbO molecules. A reanalysis of the data obtained in the earlier vapor-pressure studies, using mass-spectrometric measurements on polymeric PbO species in the gas phase, gives Gibbs energies of formation of lead zirconate which are in better agreement with those obtained in this study. Recent electrochemical measurements using CaO-ZrO2 and PbF2 solid electrolytes are in good agreement with the present study. The results obtained in this study are also consistent with the phase diagram which shows decomposition of the zirconate to tetragonal zirconia and a liquid phase rich in PbO at 1843 K.