Partial Molar Entropy Of Oxygen Research Articles

Oxygen Nonstoichiometry and Thermodynamic Explanation of Large Oxygen‐Deficient Ruddlesden–Popper Oxides LaxSr3−xFe2O7−δ

The oxygen nonstoichiometry of large oxygen‐deficient Ruddlesden–Popper oxides LaxSr3−xFe2O7−δ (LSFO7‐x) (x = 0, 0.25, 0.5) was measured by the high‐temperature gravimetry and the coulometric titration. In the composition series, the P(O2) dependencies exhibited typical plateaus at δ = (2−[])/2. Meanwhile, La0.5Sr2.5Fe2O7−δ showed the smallest oxygen nonstoichiometry and was the most thermochemically stable compound against P(O2), temperature, and the La content. Based on the defect equilibrium model and the statistical thermodynamic calculation derived oxygen nonstoichiometric data, the substitution of La for Sr‐site can promote the forward reaction of oxygen incorporation, the backward reaction of the disproportionation of the charge carriers, and oxygen redistribution between the O1 and O3 sites, resulting in the reduction of oxygen‐deficient and the lower decomposition P(O2). The obtained thermodynamic quantities of the partial molar enthalpy of oxygen, , and the partial molar entropy of oxygen, , calculated from the statistical thermodynamic calculation are in good agreement with those using the Gibbs–Helmholtz equation.

Oxygen nonstoichiometry and thermodynamic quantities in the Ruddlesden–Popper oxides LaxSr3 − xFe2O7 − δ

Oxygen nonstoichiometry in the Ruddlesden–Popper type oxides LaxSr3−xFe2O7−δ (x=0, 0.25 and 0.5) was determined by means of the high temperature gravimetry and the coulometric titration. The measurements were carried out in the temperature range between 773 and 1073K and the P(O2) range between 10−40 and 1bar. The P(O2) dependencies of the oxygen nonstoichiometry exhibited typical plateaus at δ~1.0 for Sr3Fe2O7−δ, δ~0.875 for La0.25Sr2.75Fe2O7−δ and δ~0.75 for La0.5Sr2.5Fe2O7−δ, where the average oxidation state of iron is 3+. In the LaxSr3−xFe2O7−δ series, La0.5Sr2.5Fe2O7−δ showed the smallest oxygen nonstoichiometry and was the most thermochemically stable compound against on P(O2), temperature, and the La content. Thermodynamic quantities of the partial molar enthalpy of oxygen, hO−hO°, and the partial molar entropy of oxygen, sO−sO°, were calculated from measured nonstoichiometric data. The behavior of oxygen nonstoichiometry and thermodynamic quantities indicates that the ideal-solution-like defect formation is established (La,Sr)3Fe2O7 in the oxygen deficient region.

Oxygen nonstoichiometry, the defect equilibrium model and thermodynamic quantities of the Ruddlesden-Popper oxide Sr3Fe2O(7-δ).

Oxygen nonstoichiometry of the Ruddlesden-Popper oxide Sr3Fe2O7-δ was measured at intermediate temperatures (773-1073 K) by coulometric titration and high temperature gravimetry. The oxygen nonstoichiometric behavior was analyzed using the defect equilibrium model with localized electrons. From the defect chemical analysis, estimated oxygen vacancy concentration at the O3 sites increases and at the O1 sites decreases with the increasing temperature. This characteristic behavior is considered to be caused by the redistribution of oxygen and vacancies between the O1 and O3 sites. The obtained thermodynamic quantities of the partial molar enthalpy of oxygen, h(O) - h°(O), and the partial molar entropy of oxygen, s(O) - s°(O), calculated from the Gibbs-Helmholtz equation are in good agreement with those from the statistical thermodynamic calculation based on the defect equilibrium model, indicating that the proposed defect equilibrium model is reasonable.

Defect chemistry and physical properties of Ln0.5Sr0.5FeO3 (Ln: La, Pr)

A defect chemical model for the behavior of acceptor and donor-doped LaFeO3 as a function of oxygen pressure is proposed. The nonstoichiometric deviation is calculated as a function of oxygen partial pressure, pO2, at different temperatures. The defect structure of complex oxides is described within the point defects approach.The results show that the conductivity is dependent on pO2 and temperature. Thermoelectric power values indicate clearly the nature of the dominant specie in charge transport. Stability regimes and compensation mechanisms at various oxygen partial pressures and temperatures are proposed. This model also examines the charge compensation mechanisms that dominate under the different regimes.From equilibrium constants, partial molar enthalpy and partial molar entropy of oxygen in Ln0.5Sr0.5Fe O3−δ (Ln: La, Pr) are estimated.

Thermodynamic quantities and defect equilibrium in La 2−xSr xNiO 4+δ

In order to elucidate the relation between thermodynamic quantities, the defect structure, and the defect equilibrium in La 2− x Sr x NiO 4+ δ , statistical thermodynamic calculation is carried out and calculated results are compared to those obtained from experimental data. Partial molar enthalpy of oxygen and partial molar entropy of oxygen are obtained from δ- P(O 2)– T relation by using Gibbs–Helmholtz equation. Statistical thermodynamic model is derived from defect equilibrium models proposed before by authors, localized electron model and delocalized electron model which could well explain the variation of oxygen content of La 2− x Sr x NiO 4+ δ . Although assumed defect species and their equilibrium are different, the results of thermodynamic calculation by localized electron model and delocalized electron model show minor difference. Calculated results by the both models agree with the thermodynamic quantities obtained from oxygen nonstoichiometry of La 2− x Sr x NiO 4+ δ .

Oxygen nonstoichiometry and defect structure of perovskite-type oxides in the La–Sr–Co–(Fe, Ni)–O systems

Oxygen nonstoichiometry of La 1− x Sr x Co 1− y Me y O 3− δ (Me = Ni, Fe) has been studied as a function of temperature and oxygen partial pressure (1 to 10 −3 atm) by TGA. The defect structure of complex oxides was described within the point defects approach by fitting the parameters of theoretical equations log ( P O 2 ) = f ( δ ) to the set of experimental data. Partial molar enthalpy and partial molar entropy of oxygen in La 1− x Sr x Co 1− y Me y O 3− δ (Me = Ni, Fe) were calculated.

Theoretical oxygen potential change of quaternary solid solution, A y2+B z3+U 1− y− zO 2+ x, by configurational entropy calculation

The change of oxygen potential, Δ G ̄ O 2 , for the solid solutions of general formula A y 2+B z 3+U 1− y− z O 2+ x was studied by the method of configurational entropy calculation for cations and cation complexes. A part of Mg atoms (fraction m) were assumed to occupy the interstitial 4 b sites of the solid solution, and the number of ways of arranging the free ions and intra-cation complexes was calculated followed by differentiation of the logarithm of this number with respect to oxygen non-stoichiometry to obtain partial molar entropy of oxygen. As the complexes, ( A 2+ U 5+), ( A 2+2 U 5+) and (B 3+U 5+) were assumed to be formed. For the first two complexes, an average composition (A 2+ αU 5+) was defined, and for (B 3+U 5+) a fraction, β, of B 3+ was considered to form the complex. The O/M ratio (M=A+B+U) which gave the steepest change of Δ G ̄ O 2 was calculated. Below this O/M ratio to 2− y−(1− β) z/2, the solid solution possibly satisfied the relation m= X/(2 y), where X=− x. In the region where this relation held, the solid solution was supposed to be oxygen stoichiometric.

Defect Chemistry of La2−xSrxCuO4−δ: Oxygen Nonstoichiometry and Thermodynamic Stability

The oxygen nonstoichiometry of La2−xSrxCuO4−δ(x=0–0.3) was measured as a function of Sr content, temperature (400–1000°C), and oxygen partial pressure (P(O2)= 1–1×10−10atm) using high-temperature gravimetry and coulometric titration. The oxygen nonstoichiometry ranges from oxygen excess to oxygen deficiency one depending onP(O2) and the Sr content,x. Oxygen excess was observed for specimens withxless than 0.05. The dependence of oxygen excess nonstoichiometry on oxygen partial pressures was found to be explained by a model with interstitial oxygen as a predominant defect. In oxygen-deficient regions, partial molar enthalpy and partial molar entropy of oxygen were calculated from the nonstoichiometry data. It was revealed from the variation in partial molar enthalpy that a strong interaction between the oxygen and its vacancy exists in oxygen-deficient La2−xSrxCuO4−δ. The experimentally obtained partial molar entropy of oxygen was compared with those calculated assuming a so-called metal model, a hopping conduction model, and a narrow band conduction model, where the increase in oxygen vacancies hardly influences the carrier concentration, the holes generated by oxidation of the specimen are trapped by Cu ions, and the holes generated are itinerant, respectively. The variation in partial molar entropy of oxygen could be explained well by either the hopping model or the narrow band conduction model. The oxygen partial pressures required for the decomposition of La2−xSrxCuO4−δwere also measured through the nonstoichiometry measurement. Discontinuity was observed in the dependence of oxygen partial pressures for decomposition on Sr content betweenx=0.05 and 0.10, suggesting an abrupt variation in the thermodynamic behavior of La2−xSrxCuO4−δwith the Sr content in this region.

Thermoelectric power of tetragonal ZrO2

Thermoelectric power data were determined for undoped and 1 at% Ti-doped TZP specimens within the temperature range 922 to 1076 K and the oxygen partial pressure range between 10−16 Pa and 100 kPa. The observed pressure and temperature dependences are related to the variation in the partial molar entropy of oxygen in the gas phase. The transported entropy of oxygen ions S∗O−2 in the solid electrolyte is estimated to be 15 JK−1 mol−1.

Calculation of oxygen potential change of irradiated UO 2 and UO 2—PuO 2 mixed oxide fuels using the intra-cation complex model

The oxygen potential change of irradiated uranium dioxide and urania-plutonia mixed oxide fuels, which is caused by the formation of solid solutions of some fission product metals with the fuel oxides, was calculated using the intra-cation complex model. It assumes weak-bound complexes between the cations of relatively positive and negative charges with respect to U 4+. Partial molar entropy of oxygen, Δ S ̄ O 2 , was derived by differentiating the logarithm of the number of ways of arranging the cationic defects and complexes over the cation sublattices. The fission product metals which dissolve into the fuel matrix were classified into +2, +3 and +4 valence state ion groups, and their effect on Δ G ̄ O 2 was clarified in the equations of Δ G ̄ O 2 representation. Comparison of the calculated results with the Δ G ̄ O 2 values for irradiated fuels as well as for the fuels containing some fission product simulant cations revealed that agreement was good, showing that the Δ G ̄ O 2 change on irradiation can be expressed as a function of M 3+ fraction.

Composition and oxygen potential of cubic fluorite-type solid solution EuyU1−yO2+x () and rhombohedral Eu6UO12+x' (x'< 0)

A fluorite-type solid solution, EuyU1−yO2+x, was formed in single phase up to y = 0.51 when heated in vacuum at 1400°C. Between y = 0.51 and 0.80, a two-phase mixture of fluorite and rhombohedral phases exists. The rhombohedral phase was of single phase in a range y = 0.8–0.9. The change of lattice parameter and x value in the fcc solid solution were determined as a function of y value in EuyU1−yO2+x. The crystal structure of the nonstoichiometric Eu6UO11.41 is the same as RE6UO12 (R3, Z = 3) with Bartram's atom parameters. The measured oxygen potentials (ΔḠO2) for fcc EuyU1−yO2+x (y = 0.1 and 0.3) are not only much higher than those of the solid solutions of the other rare-earth elements, but are also shifted to the lower x side yielding a nearly vertical change of ΔḠO2 in the hypostoichiometric range (x < 0). As a result, the partial molar entropy of oxygen (ΔSO2) and enthalphy (ΔHO2) are significantly different from those of the solid solutions of the other rare-earth elements. ΔḠO2, ΔSO2 and ΔHO2 for rhombohedral Eu0.8571U0.1429O1.7143+x (x < 0) were measured and discussed.

Design of temperature-compensated reference electrodes for non-isothermal galvanic sensors

The criterion for the design of a temperature-compensated reference electrode for non-isothermal galvanic sensors is deduced from the basic flux equations of irreversible thermodynamics. It is shown that when the Seebeck coefficient of the non-isothermal cell using a solid oxygen ion-conducting electrolyte under pure oxygen is equal to the relative partial molar entropy of oxygen in the reference electrode divided by 4 F, then the EMF of the non-isothermal cell is the same as that of an isothermal cell with the same electrodes operating at the higher temperature. By measuring the temperature of the melt alone and the EMF of the non-isothermal galvanic sensor, one can derive the chemical potential or the concentration of oxygen in a corrosive medium. The theory is experimentally checked using sensors for oxygen in liquid copper constructed with various metal+oxide electrodes and fully stabilised (CaO)ZrO 2 as the electrolyte. To satisfy the exact condition for temperature compensation it is often necessary to have the metal or oxide as a solid solution in the reference electrode.

Vaporization study on vanadium-oxygen solid solution by mass spectrometric method.

The vapor pressures over vanadium-oxygen solid solution (0.001≦O/V≦0.145) were measured by mass-spectrometric method in the temperature range of 1,855–2,117K. The main vapor species were observed to be V(g) and VO(g). The vapor pressure of V(g) is higher than that of VO(g) over the solid solutions with all O/V ratios except for O/V=0.145. The vapor pressure of V(g) is nearly independent of O/V ratio. The vapor pressure of VO(g) decreases with decreasing O/V ratio. The oxygen partial pressure was calculated as a function of temperature and O/V ratio from the vapor pressures of V(g) and VO(g), from which the partial molar enthalpy and entropy of oxygen in the solid solution were determined. The partial molar enthalpy of oxygen was observed to be independent of composition, suggesting the presence of very weak interaction between interstitial oxygens. The compositional dependence of the partial molar entropy of oxygen can be explained by assuming the occupation of the octahedral site in bcc vanadium lattice ...

Oxygen pressures over LaMnO 3+x

Equilibrium oxygen partial pressures over non-stoichiometric lanthanum manganite, LaMnO 3+x, have been determined by a gravimetric method at 1188–1370 K. Relative partial molar free energy, entropy and enthalpy of solution of oxygen in this phase were derived. The variation of the relative partial molar entropy of oxygen with the composition in the non-stoichiometric LaMnO 3+x phase was calculated and discussed in relation to the metal vacancy model.

ChemInform Abstract: THERMODYNAMIC STUDIES ON THE ADDITION OF MOLECULAR OXYGEN TO COBALT(II) COMPLEXES. PART 1. THE COBALT(II)‐ETHYLENEDIAMINE‐OXYGEN SYSTEM IN AQUEOUS SOLUTION AT 25°C

AbstractMittels polarographischer Sauerstoffanalyse, pH‐Metrie und Spektrophotometrie wird die Gleichgewichtskonstante für die Bildung des doppeIt‐verbrückten Dicobaltkomplexes (I) in l mol dm′3 KCl bei 25°C bestimmt.

Vaporization study on the niobium-oxygen solid solution by mass-spectrometric method

The vapor pressures over the niobium-oxygen solid solution were measured by mass-spectrometric method in the temperature range 2091–2379 K. The main vapor species were observed to be NbO(g) and NbO 2(g). The solidus line of the niobium-oxygen solid solution and the solubility limit of oxygen in niobium metal at high temperatures were determined from the vaporization behavior. The partial pressure of oxygen was calculated as a function of temperature and O/Nb composition from the partial pressures of NbO(g) and NbO 2(g), from which the partial molar enthalpy and entropy of oxygen in the niobium-oxygen solid solution were determined. The compositional dependence of the partial pressure of oxygen was observed to obey the Henry's law at low oxygen concentrations in niobium metal less than about 5 a/o. The partial molar enthalpy in the oxygen concentration range between 1 and 5 a/o was observed to be nearly independent of composition, suggesting the presence of very weak interaction between interstitial oxygens. The compositional dependence of the partial molar entropy of oxygen in this low oxygen concentration range was explained by assuming the occupation of the octahedral sites in b.c.c. niobium lattice by the interstitial oxygens. The partial excess entropy of oxygen was compared with the value derived from the sum of the contributions from the volume expansion, vibrational and electronic heat capacity terms.

Thermodynamic Study of the Liquid Cu&amp;ndash;O System

The phase relationships in the liquid Cu–O system were determined by the following three experimental techniques, (1) Water quenching of the samples in crucible, (2) Water quenching of the samples after suction into an alumina tube, (3) Emf measurements combined with the suction-water quenching.The cells used were as follows: Pt/Ni, NiO/ZrO2(+CaO)/O in Cu(1) or copper oxide (1)/LaCrO3/Pt, Pt/Ni, NiO/ZrO2(+CaO)/O in Cu(1)+copper oxide (s or 1)/LaCrO3/Pt.It was confirmed that the miscibility gap exists between liquid copper and liquid copper oxide and it seems to disappear at higher temperature than 1620 K.From emf measurements, the activities of oxygen and copper were calculated at 1573 K, and the standard free energies of formation of solid and liquid Cu2O were determined in the temperature range from 1370 to 1600 K . Relative partial molar entropy of oxygen in the liquid Cu–O system showed a minimum value at or close to the stoichiometric Cu2O composition.The oxygen potential-temperature-composition (P-T-X) diagram for the Cu–O binary system was determined from the results of this study.

An entropy meter based on the thermoelectric potential of a nonisothermal solid-electrolyte cell

The theory, design, and performance of a solid electrolyte twin thermocell for the direct determination of the partial molar entropy of oxygen in a single-phase or multiphase mixture are described. The difference between the Seebeck coefficients of the concentric thermocells is directly related to the difference in the partial molar entropy of oxygen in the electrodes of each thermocell. The measured potentials are sensitive to small deviations from equilibrium at the electrodes. Small electric disturbances caused by simultaneous potential measurements or oxygen fluxes caused by large oxygen potential gradients between the electrodes also disturb the thermoelectric potential. An accuracy of ±0.5 cal th K −1 mol −1 has been obtained by this method for the entropies of formation of NiO and NiAl 2O 4. This “entropy meter” may be used for the measurement of the entropies of formation of simple or complex oxides with significant residual contributions which cannot be detected by heat-capacity measurements.

Nonstoichiometry in uranium dioxide

Abstract Thermodynamic properties of uranium oxides with O/U atomic ratios between 2.04 and 2.34, principally in the nonstoichiometric UO 2+x single-phase region, were determined at temperatures in the range 500°C to 1100°C by electromotive force measurements with cells of the type Ni-NiO¦ZrO 2 (+CaO)¦uranium oxide. The relative partial molar free energies of oxygen for the single-phase region UO 2+x and the two two-phase coexisting regions UO 2+x -U 4 O 9−y and U 4 O 9 -U 3 O 8−z were obtained with adequate precision. Several statistical models for the defect structure of UO 2+x have been reviewed. The variation of the relative partial molar entropy of oxygen with composition in the UO 2+x phase was derived on the basis of the 2:2:2 defect complex model proposed from the neutron diffraction study of Willis. The entropies were computed to fit the experimental data assuming that the excess oxygen atoms entered into the fluorite structure in pairs and that the available sites for such oxygen pairs and U 5+ ions would be partially restricted for occupancy.

Studies on cubic magnesium uranate, Mg yU 1− yO 2+ x—I : Phase relations and crystal chemistry

Cubic magnesium uranate, Mg y U 1− y O 2+ x , was prepared by the reaction of the mixtures of MgUO 4, MgU 3O 10 and/or UO 2 in a stream of helium. The cubic region and the values of x and y in Mg y U 1− y O 2+ x were studied under various reaction conditions. Density measurements of this compound gave a strong support to a substitutional structure. The variation of lattice constant with composition was observed to follow a linear equation, a 0 = 5·4704−0·1170x−0·5677 y. Equilibrium oxygen pressure was found to increase with magnesium concentration. The results were discussed by modifying the equation to express partial molar entropy of oxygen given by Aronson and Clayton to valence control type Mg y U 1− y O 2+ x .