Entropy Of Oxygen Research Articles

Thermodynamic analysis of metal oxides, metal peroxides and metal hydrides

The standard entropy differences between metal oxides (metal peroxides) and metal elements Δ S were roughly expressed by the following equation, |Δ S | ∝ Rln|Δ V |, R: gas constant, Δ V : volume differences below 10 cm 3 /molO 2 , which is similar to the relation of metal hydrides. It was presumed that the entropy of oxygen in the metal oxides and the metal peroxides, together with the entropy of hydrogen in the metal hydrides can be controlled by the thermodynamics of ideal gas. Those volume differences were increased by increasing of the work function based on the small ion binding properties. However, the absolute values of the standard enthalpy differences |Δ H | had large values at Δ V of -22 to 8 cm 3 /molO 2 . The thermodynamic stabilities which are the absolute values of the standard enthalpy differences decreased in the order, metal oxides > metal peroxides > metal hydrides. • The relation between standard entropy and volume differences Δ S, Δ V was analyzed. • |Δ S | linearly increased with ln|Δ V | below 2⊡3⊡ • The slope was approximately gas constant R. • |Δ H | had large values at Δ V of -22 to 8cm 3 /molO 2 ,Δ H standard enthalpy differences. • |Δ H | decreased in the order, metal oxides > metal peroxides > metal hydrides.

Crystal structure and oxygen nonstoichiometry of the third-order Ruddlesden-Popper phase Pr4(Ni0.9Co0.1)3O10-δ

Crystal structure and thermal expansion of the third-order Ruddlesden-Popper phase Pr4Ni2.7Co0.3O10-δ (PNCO) were determined by high temperature X-ray powder diffraction (HT-XRD) and Rietveld analysis in the temperature range 25–600 ​°C in air. The thermal expansion coefficient (TEC) of PNCO is smaller compared with first-order Ruddlesden-Popper phases and in excellent agreement with values of common electrolytes of solid oxide cells. HT-XRD, thermogravimetry, and differential scanning calorimetry showed a reversible phase transition at 600–650 ​°C. A single monoclinic (P21/a) phase occurs at 25–600 ​°C, while a mixture of monoclinic and tetragonal (I4/mmm) phases is found at 650–900 ​°C. The oxygen nonstoichiometry was determined by thermogravimetry as a function of temperature (300 ​≤ ​T/°C ​≤ ​900) and oxygen partial pressure (8.3 ​× ​10−4 ​≤ ​pO2/bar ​≤ ​8.3 ​× ​10−1). Data of the oxygen nonstoichiometry were further evaluated with respect to the partial molar enthalpy and entropy of oxygen, and the thermodynamic factor of oxygen.

Impact of oxygen content on preferred localization of p- and n-type carriers in La0.5Sr0.5Fe1-xMnxO3-δ.

The oxygen content in La0.5Sr0.5Fe1-xMnxO3-δ, measured by coulometric titration in a wide range of oxygen partial pressure at various temperatures, was used for defect chemistry analysis. The obtained data were well approximated by a model assuming defect formation in La0.5Sr0.5Fe1-xMnxO3-δvia Fe3+ and Mn3+ oxidation reactions and charge disproportionation on Fe3+ and Mn3+ ions. The partial molar enthalpy and entropy of oxygen in La0.5Sr0.5Fe1-xMnxO3-δ obtained by statistical thermodynamic calculations were found to be in satisfactory agreement with those obtained using the Gibbs-Helmholtz equations, thus further confirming the adequacy of the model. The impact of manganese substitution on defect equilibrium in La0.5Sr0.5Fe1-xMnxO3-δ was shown to be attributed to a lower enthalpy of Mn3+ oxidation reaction (vs. for the oxidation of Fe3+) and the charge disproportionation reaction on Mn3+ (vs. for that on Fe3+). The former makes Mn4+ ions more resistant to reduction than Fe4+. The latter favors the presence of Mn2+, Mn3+, and Mn4+ ions in oxides in comparable concentrations. The distribution of charge carriers over iron and manganese ions was determined as a function of oxygen content in La0.5Sr0.5Fe1-xMnxO3-δ.

Thermodynamic quantities and defect formation in solid solution La0.49Sr0.5−xBaxFeO3−δ

The key factors determining the applicability of mixed-conducting oxides in energy-related technologies refer to the stability to reduction and the level of oxygen ionic and electronic transport, both determined by partial molar enthalpy and entropy of oxygen in the oxide. Therefore, any information about the thermodynamic properties of the oxide has an important predictive value.The chemical potential of oxygen in La0.49Sr0.5−xBaxFeO3−δ relative to the standard state in the gas phase, ΔμO, was calculated using experimental data on oxygen content in oxides depending on the partial pressure of oxygen, pO2, and temperature. The partial molar enthalpy, ΔH¯O, and partial molar entropy, ΔS¯O, of oxygen were determined as functions of (3−δ) from ΔμO data using the Gibbs-Helmholtz equation. The previously proposed defect equilibrium model assuming the presence of unavailable oxygen vacancies in barium-containing oxides was successfully verified. Thermodynamic quantities ΔH¯O and ΔS¯O, obtained by statistical thermodynamic calculation based on this model were found to be in a reasonable agreement with those obtained with the Gibbs-Helmholtz equation. The performed calculations allowed enhancing the accuracy of the defect equilibrium model parameters.

Thermodynamics of oxygen in CaMnO3 − δ

The experimental data for equilibrium oxygen con- tent were used in order to extract increments of partial molar thermodynamic functions of oxygen with changes of oxygen stoichiometry in calcium manganite CaMnO3−δ .I t is shown that along with the oxygen exchange reaction, thermal exci- tation of Mn 4+ cations plays an important role in equilibration of charged manganese species that appear in response to the loss of oxygen at heating. The interrelation of partial molar enthalpy and entropy of oxygen with electron and ion defect formation parameters is obtained in approximation of the point defect model. The nearly linear changes of oxygen partial molar enthalpy are shown to directly reflect thermally driven changes in concentration of Mn 3+ cations.

Oxygen nonstoichiometry, crystal and defect structure of the double perovskite GdBaCo1.8Fe0.2O6 − δ

Crystal structure of the double perovskite GdBaCo1.8Fe0.2O6−δ was investigated by means of “in situ” X-ray diffraction at temperatures between 25 and 800°C in air. Pmmm–P4/mmm phase transition was found to occur in GdBaCo1.8Fe0.2O6−δ at 515°C. The results of oxygen nonstoichiometry, δ, measured as a function of oxygen partial pressure, pO2, in temperature range 700≤T, °C≤1025 by means of thermogravimetric technique are presented for this double perovskite. Partial molar enthalpy and entropy of oxygen in the GdBaCo1.8Fe0.2O6−δ structure were calculated. Both thermodynamic properties were shown to increase dramatically in the vicinity of the oxygen nonstoichiometry value equal to 1. The pO2 dependences of oxygen nonstoichiometry were found to have inflections when the oxygen content of GdBaCo1.8Fe0.2O6−δ is equal to 5.0 exactly.The analysis of the defect structure of the double perovskite GdBaCo1.8Fe0.2O6−δ was carried out using the model based on the simple cubic perovskite GdCoO3 as a reference state. Equilibrium constants of the appropriate defects reactions were, therefore, determined. As a consequence, concentrations of all defect species defined within the framework of the model proposed were calculated as functions of temperature and oxygen nonstoichiometry. Oxygen vacancies were shown to be formed during pO2 diminution in gas environment in the layers of GdBaCo1.8Fe0.2O6−δ crystal lattice where they are ordered until oxygen nonstoichiometry of the oxide becomes equal to unity afterwards oxygen vacancies are formed randomly in oxygen polyhedrons.

Oxygen nonstoichiometry and defect structure of the double perovskite GdBaCo 2O 6 − δ

The results of oxygen nonstoichiometry, δ, measured by means of coulometric technique as a function of oxygen partial pressure, p O 2, in temperature range 900 ≤ T °C ≤ 1050 are presented for GdBaCo 2O 6 − δ with double perovskite structure. Partial molar enthalpy and entropy of oxygen in GdBaCo 2O 6 − δ structure were calculated. Both thermodynamic properties were shown to increase dramatically in the vicinity of the oxygen nonstoichiometry value equal to 1. The p O 2 dependences of oxygen nonstoichiometry and the δ dependences of the partial molar properties were found to have inflections when the oxygen content of GdBaCo 2O 6 − δ is equal to 5.0 exactly. The modeling of the defect structure of the double perovskite GdBaCo 2O 6 − δ was carried out by considering different reference states. Only the model based on the cubic perovskite GdCoO 3 as a reference state was shown to fit the experimental data on oxygen nonstoichiometry of GdBaCo 2O 6 − δ good enough. Equilibrium constants of the appropriate defects reactions were, therefore, determined. Concentrations of all defect species defined within the framework of this model were calculated as functions of temperature and oxygen nonstoichiometry. Oxygen vacancies were shown to be formed during p O 2 diminution in gas environment in the layers of GdBaCo 2O 6 − δ crystal lattice where they are ordered until oxygen nonstoichiometry of the oxide becomes equal to unity afterwards oxygen vacancies are formed randomly in oxygen polyhedrons.

Defect equilibria and partial molar properties of (La,Sr)(Co,Fe)O 3− δ

The oxygen nonstoichiometry δ of La 1− x Sr x Co 1− y Fe y O 3− δ ( x = 0.6 and y = 0.2, 0.4) was investigated by thermogravimetry in the range 703 ≤ T/°C ≤ 903 and 1E−5 < pO 2/atm < 1. The oxygen deficit increases with increasing T and decreasing pO 2. Electronic conductivities σ were measured as a function of pO 2 in the range 1E−5 < pO 2/atm < 1 at 700 ≤ T/°C ≤ 900. At constant T, a p-type pO 2-dependence of σ is observed. Oxygen nonstoichiometry data are analyzed with regard to the enthalpy and entropy of oxidation Δ H ox θ and Δ S ox θ , as well as to the partial molar enthalpy and entropy of oxygen with respect to the standard state of oxygen ( pO 2 θ = 1 atm), ( h O − H O θ ) and ( s O − S O θ ), respectively. For 2.67 ≤ (3 − δ) ≤ 2.79, ( h O − H O θ ) decreases with increasing δ, while ( s O − S O θ ) is constant within the limits of error. Defect chemical modelling was performed by an ideal solution model under consideration of three different valence states for B-site ions (Co or Fe). The dependence of σ on δ is modelled, using calculated defect concentrations as functions of δ. Deviations from the ideal behaviour suggest an immobilization of n-type charge carriers by oxygen vacancies.

Oxygen potential of (Pu 0.91Am 0.09)O 2− x

Oxygen potentials of (Pu 0.91Am 0.09)O 2− x were measured by thermogravimetric analysis with H 2O/H 2 gas equilibrium and dilute O 2 gas at 1123 K, 1273 K and 1423 K. The oxygen potentials were extremely high from stoichiometry to O/M = 1.99 and were somewhat lower than those of AmO 2− x near stoichiometry. On the other hand, those below O/M = 1.96 were much lower than those of AmO 2− x . Valence state changes of Am and Pu in the oxide were assumed, and experimentally determined data were examined using the slope of the plot of oxygen partial pressure versus deviation from stoichiometry, the oxygen potential as a function of mean valence state of metal, activity coefficient of AmO 2− x and the partial molar enthalpy and entropy of oxygen. It was concluded through these examinations that aspects of the oxygen potential of (Pu 0.91Am 0.09)O 2− x could be interpreted by the present assumption and that several interactions between Am and Pu could exist.

Oxygen nonstoichiometry ( δ) of TiO 2−δ-revisited

Oxygen nonstoichiometry ( δ ) of “undoped” polycrystalline TiO 2− δ has been measured as a function of oxygen partial pressure in the widest ever examined range of 10 - 18 ⩽ P O 2 / atm ⩽ 10 - 1 at elevated temperatures (1073⩽ T/K⩽1473) by thermogravimetry and coulometric titrometry combined and compared with all the reported values. Isothermal variation of nonstoichiometry against P O 2 is explained with a defect model involving quadruply ionized titanium interstitials, electrons, holes, and unidentified acceptors which may be background impurity acceptors or cation vacancies. The equilibrium constants for intrinsic electronic excitation reaction and redox reaction are determined from the nonstoichiometry measured and compared exhaustively with all the reported values. The relative partial molar enthalpy and entropy of oxygen are evaluated as functions of nonstoichiometry and the inner workings of their variations discussed.

Oxygen Nonstoichiometry, Conductivity, and Seebeck Coefficient of La 0.3Sr 0.7Fe 1− xGa xO 2.65+ δ Perovskites

The total electrical conductivity and the Seebeck coefficient of perovskite phases La 0.3Sr 0.7Fe 1− x Ga x O 2.65+ δ ( x=0–0.4) were determined as functions of oxygen nonstoichiometry in the temperature range 650–950°C at oxygen partial pressures varying from 10 −4 to 0.5 atm. Doping with gallium was found to decrease oxygen content, p-type electronic conduction and mobility of electron holes. The results on the oxygen nonstoichiometry and electrical properties clearly show that the role of gallium cations in the lattice is not passive, as it could be expected from the constant oxidation state of Ga 3+. The nonstoichiometry dependencies of the partial molar enthalpy and entropy of oxygen in La 0.3Sr 0.7(Fe,Ga)O 2.65+ δ are indicative of local inhomogeneities, such as local lattice distortions or defect clusters, induced by gallium incorporation. Due to B-site cation disorder, this effect may be responsible for suppressing long-range ordering of oxygen vacancies and for enhanced stability of the perovskite phases at low oxygen pressures, confirmed by high-temperature X-ray diffraction and Seebeck coefficient data. The values of the electron–hole mobility in La 0.3Sr 0.7(Fe,Ga)O 2.65+ δ , which increases with temperature, suggest a small-polaron conduction mechanism.

Nonstoichiometry (δ) and High-Temperature Thermodynamic Properties of (Mg0.22Mn0.07Fe0.71)3−δO4 Ferrite Spinel

Nonstoichiometry of (Mg0.22Mn0.07Fe0.71)3−δO4 ferrite has been measured in the temperature range of 1000×1200°C as a function of oxygen activity (aO2) using a solid state coulometric titration technique. At a given temperature, the nonstoichiometry (δ) was found to vary with the oxygen activity as δ=[V]0 · a2/3O2 −[I]0·a−2/3O2 where [V]0 and [I]0 are constants. This aO2-dependence of δ was explained in terms of Frenkel disorder, i.e., cation vacancy and interstitial. From the temperature dependence of the defect constants ([V]0 and [I]0) and the oxygen activity for the stoichiometric composition (δ=0), thermodynamic quantities such as enthalpies for the defect formation reactions and relative partial molar enthalpy and entropy of oxygen were calculated.

Thermodynamic data of the perovskite-type LaMnO3±x and La0.7Sr0.3MnO3±x by a solid-state electrochemical technique

A solid-state electrochemical technique was employed to study the thermodynamic properties of some nonstoichiometric undoped and 30% Sr-doped LaMnO3 perovskites over the temperature range 1073–1373 K. The equilibrium pressures of oxygen and the relative partial free energies, enthalpies and entropies of oxygen in LaMnO3±x and La0.7Sr0.3MnO3±x were determined as a function of temperature and oxygen nonstoichiometry.

Structure, oxygen stoichiometry and electrical conductivity in the system Sr-Ce-Fe-O

The perovskite type oxides of the system Sr-Ce-Fe-O were prepared by mixing and thermal treatment in air. Microstructure and phase composition were determined by scanning electron microscopy and X-ray diffraction. Besides the pure SrCeO 3 and SrFeO 3 − x a solid solution range of Sr 1 − y Ce y FeO 3 − x was observed between y = 0.01 ÷ 0.2. This solid solution is the active phase responsible for high oxygen exchange and electrical conductivity as required for cathode materials of high-temperature electrochemical cells. The oxygen exchange and oxygen deficiency x were measured by solid electrolyte coulometry. From pO 2- T- x diagrams the partial molar enthalpies and entropies of oxygen were calculated for the air-oxidized states of the solid solution and of the two-phase region: ΔH o of the two-phase material 0.8 SrCeO 3 − 0.2 SrFeO 3 − x is − 23 to − 29 kJ mol −1 and ΔS o is − 3 to − 8 J mol −1 K −1. For the solid solution Sr 0.9Ce 0.1FeO 3 − x the values depend on x: ΔH o increases from − 33.5 to − 28.4 kJ mol −1 and ΔS o increases from − 10 to + 20 J mol −1 K −1 in the range 0.24 < x < 0.36. The dc electrical conductivity of the monophase material Sr 1 − y Ce y FeO 3 − x show a maximum near 500 °C at y c e = 0.05 mol (80 S cm −1, E a = 0.088 eV). The conductivity is of p-type in the region of higher oxygen partial pressures and n-type at reducing conditions.

Oxygen Nonstoichiometry of (Nd2/3Ce1/3)4(Ba2/3Nd1/3)4Cu6O16+x

The equilibrium oxygen content of (Nd2/3Ce1/3)4(Ba2/3 Nd1/3)4Cu6O16+x was measured by coulomeric titration in the temperature range 550-820°C and at oxygen pressures between 10-3 and 1 atm. From the results, the partial molar enthalpy and entropy of oxygen were calculated as functions of the oxygen content. The data were explained based on a point defects model and the equilibrium constants of the redox and charge disproportionation reactions involved were derived. A phase transition near the point x ≈ 1.83, which nominally corresponds to one trivalent copper cation per elementary unit, was observed.

Variation of the partial thermodynamic properties of oxygen with composition in YBa2Cu3O7−δ

The variation of equilibrium oxygen potential with oxygen concentration inYBa2Cu3O7-δhas been measured in the temperature range of 773 to 1223 K. For temperatures up to 1073 K, the oxygen content of theYBa2Cu3O7-δsample, held in a stabilized-zirconia crucible, was altered by coulometric titration. The compound was in contact with the electrolyte, permitting direct exchange of oxygen ions. For measurements above 1073 K, the oxide was contained in a magnesia crucible placed inside a closed silica tube. The oxygen potential in the gas phase above the 123 compound was controlled and measured by a solid-state cell based on yttria-stabilized zirconia, which served both as a pump and sensor. Pure oxygen at a pressure of 1.01 × 105 Pa was used as the reference electrode. The oxygen pressure over the sample was varied from 10-1 to 105 Pa. The oxygen concentrations of the sample equilibrated with pure oxygen at 1.01 × 105 Pa at different temperatures were determined after quenching in liquid nitrogen by hydrogen reduction at 1223 K. The plot of chemical potential of oxygen as a function of oxygen non-stoichiometry shows an inflexion at δ ∼ 0.375 at 873 K. Data at 773 K indicate tendency for phase separation at lower temperatures. The partial enthalpy and entropy of oxygen derived from the temperature dependence of electromotive force (emf ) exhibit variation with composition. The partial enthalpy for °= 0.3, 0.4, and 0.5 also appears to be temperature dependent. The results are discussed in comparison with the data reported in the literature. An expression for the integral free energy of formation of YBa2Cu3O6.5 is evaluated based on measurements reported in the literature. By integration of the partial Gibbs’ energy of oxygen obtained in this study, the variation of integral property with oxygen concentration is obtained at 873 K.

Defect Structure and Thermodynamic Properties of the Wustite Phase (Fe1‐yO)

The defect structure model in the wustite phase is considered involving the 4:l cluster as a basic defect structure unit. Interactions between defects are considered in terms of the Debye‐Hückel theory for strong electrolytes. It has been shown that the available data on wustite nonstoichiometry fit well the 4:l cluster model. Above 1173 K the degree of ionization of the cluster is −5. The equilibrium constant of the cluster formation determined in this work is Kc= [((VFe)4Fei)5−][h]5 [FeFe]−6[Vi]−1PO2−3/2f6±= 1.07 × 10−14 exp[396.7 (kJ)/RT]. The equilibrium constant is quite consistent with such thermodynamic parameters as partial molar enthalpy and entropy of oxygen in Fe1‐yO within the entire stability range of the wustite phase.

Nonstoichiometry of the perovskite-type oxides La 1− xSr xCoO 3−δ

In order to clarify the extent of oxygen nonstoichiometry and defect equilibrium in the oxide solid solution La 1− x Sr x CoO 3− δ ( x = 0, 0.1, 0.2, 0.3, 0.5, and 0.7), thermogravimetric measurements were made in the range 10 −5 ≤ P( O 2) atm ≤ 1 and 300 ≤ T °C ≤ 1000 , where the solid solution was stable as a single-phase perovskite-type oxide. The nonstoichiometry, δ, increases with decreasing P(O 2), increasing Sr content, x, and increasing temperature, T. At temperatures below 800°C, δ of LaCoO 3−δ could not be detected. For La 0.3Sr 0.7CoO 3−δ, a large δ was observed at temperatures as low as 300°C. The observed δ for each La 1− x Sr x CoO 3−δ ranges between 0 and values slightly in excess of x 2 . Using the Gibbs-Helmholtz equation, the partial molar enthalpy and entropy of oxygen, ( h O - h O°) and ( s O - s O°) respectively, were calculated as a function of x and δ. The value of ( h O - h O°) decreases linearly with increasing δ. The δ dependence of ( s O - s O°) is determined by the configurational entropy of V ·· O and O x O on the oxygen sublattice, while no noticeable contribution was detected from the configurational entropy due to electronic states. This is consistent with the metallic character of the electronic conduction in La 1− x Sr x CoO 3−δ.

Thermochemistry of rare-earth-metal-alkaline-earth-metal-copper oxide superconductors

Enthalpies of formation of the perovskite-related oxides La/sub 2/CuO/sub 4/, La/sub 1.85/Sr/sub 0.15/CuO/sub 4/, and YBa/sub 2/Cu/sub 3/O/sub y/(y = 6.25, 6.47, 6.69, and 6.93) have been determined at 298.15 K by solution calorimetry. Room-temperature stabilities of these compounds have been assessed in terms of the parent binary oxides and of the oxygen content. High-temperature (to 900/degree/C) thermal behavior of YBa/sub 2/Cu/sub 3/O/sub y/ has been used to determine thermodynamic properties (partial molal enthalpy, free energy, and entropy of oxygen) of this material in order to characterize the quenched state in relation to the high-temperature equilibrium state. The thermochemistry of oxygen has been used to interpret the relationship between the oxygen partial pressure and the defect chemistry in the nonstoichiometric phase of YBa/sub 2/Cu/sub 3/O/sub y/. The relevance of the defect chemistry to conductivity is discussed. 34 references, 2 tables.

On defect clustering in the wustite phase

Defect structure in highly nonstoichiometric ferrous oxide has been discussed in terms of defect thermodynamics based on mass action law. It has been shown that the best agreement between theory and experiment is obtained under the assumption that 4:1 clusters, suggested by Cheetham and Catlow, are the predominant defects in the wustite phase. The ionization degree of these extended defects increases with increasing temperature, reaching a maximum value at 1573 K. Relative partial enthalpy and entropy of oxygen in Fe 1− y O were evaluated.