72 A.1 The partial molar entropy of reduction of cerium oxide (units of J/K/mol . oxygen vacancies) obtained from the work of Panlener et al.[1]. 106 A.2 The partial molar enthalpy of reduction of cerium oxide (units of kJ/mol . oxygen vacancies) obtained from the work of Blumenthal et al.[2].
Big picture
Storing solar energy in chemical bonds
Furthermore, a number of non-stoichiometric oxides are known for their high temperature stability, excellent surface activity for oxygen exchange and bulk oxygen diffusion in other applications such as solid oxide fuel cells, sensors of oxygen and oxygen storage catalysts. The combination of all these properties makes a strong case for thermochemical water splitting based on the redox behavior of non-stoichiometric oxides.
Thermochemical water splitting using CeO 2−δ
A similar reaction scheme can be constructed for the splitting of carbon dioxide (CO2), which generates carbon monoxide (CO) at temperatures high enough to inhibit carbon formation. The feasibility of a ceria-based thermochemical process for water splitting has been successfully demonstrated.
Motivation and outline
The non-stoichiometry, δ, is a function of oxygen partial pressure, pO2, and temperature, T, and is related to the enthalpy and entropy of reduction. The all-electron wave function provides a complete description of the system and can be used to extract the thermodynamic properties across all length scales.
Background
Our computational study aims to isolate and focus on the thermodynamics of intrinsic oxygen vacancies in series relevant to thermochemical cycles. A step in this direction was made for the LixFePO4 system[41] by showing that the inclusion of electronic entropy via a cluster expansion approach yields a phase diagram whose topology is in qualitative agreement with experiments.
Methodology
- First principles calculations
- Cluster expansion : configurational degrees of freedom
- Lattice Monte Carlo simulations : thermodynamic properties . 16
- First principles calculations
- Cluster expansion
- Monte Carlo simulations
When this was observed, the energy of the structure was calculated from first principles and included in the cluster expansion to reduce extraction. This is the first first-principles study of the high-temperature phase diagram of ceria.
Conclusions
The first of the two steps is a high-temperature endothermic reaction involving the liberation of oxygen in bulk. The objective of this work is to demonstrate the versatility of this latter method, electrical conductivity relaxation (ECR), to study the effect of gas temperature and atmosphere on DChem and kS. In a relaxation experiment, one analyzes the transient behavior in the reequilibration process after a step change in the pO2 of the surrounding gas.
Theory
- Electrical conductivity relaxation
- Defect chemistry and conductivity of SDC15
- Chemical diffusion coefficient
- Surface reaction rate constant
Formally, the idle concentration in equation 3.29 is that at the surface, but in the absence of detailed knowledge of the surface characteristics, cV can be 'reasonably' approximated by the bulk value[87]. Furthermore, due to the equivalence between charge and mass transport across the interface, this electrochemically determined response constant is identical to the surface response constant obtained from ECR measurements[88]. In view of the many methods available to determine the surface reaction constant, it is not surprising that there are several experimental reports with which the values measured here can be compared.
Experimental and analytical procedure
Experimental methods
The composition of the polished samples was confirmed by electron probe microanalysis (EPMA) (JEOL JXA-8200, carbon-coated samples, CePO4 and SmPO4 used as reference standards). The integrity of the contacts was ensured by sputtering a 100 nm layer of gold on the four contact regions (208HR, Cressington, UK) and then applying an additional layer of gold by brushing (Fuel Cell Materials, Lot #5C149). The magnitude of the surface reaction rate constant was increased in some cases (to improve the accuracy of the diffusion coefficient measurement) by applying a layer of Pt nanoparticles on the sample surface.
Analysis of relaxation data
A comparison between input and output Dchem and kS values provides an estimate of the errors and guidance on the preferred analysis approach, a two-parameter or a single-parameter adjustment. Clearly, few errors are introduced into DChem, despite the risk of overfitting the data using the two-parameter expression. However, in the case of kS, the improved accuracy when using the single parameter fit at small L˜ motivates the identification of the correct formalism.
Results and discussion
Equilibrium conductivity
In this case, the scattering was assumed to originate from differences in grain boundary contributions to the total resistance. Due to the microstructure of the present samples, such an explanation is unlikely to be applicable in this work (since the grains are large enough that the grain boundary contribution is negligible, as discussed above). Nevertheless, it is conceivable that the low number density of grain boundaries in the materials studied here affects the bulk impurity levels and is likely to do so.
Relaxation behavior
Although DChem is slightly higher under the more oxidizing conditions of the CO/CO2 experiment, the dramatically improved relaxation rate is primarily a result of changes in kS. As described above, it was predicted, based on reported values of DChem and kS under H2/H2O/Ar mixtures, that SDC samples of the dimensions used here would be limited in surface response. Additional evidence for the major role of surface reaction kinetics in the relaxation behavior of SDC15 samples of moderate thickness (especially 1.72 mm) under reducing conditions is shown in Figure 3.9, in which the bare oxide profiles under H2-H2O - Ar and CO-CO2-Ar at 800 ◦C are compared.
Conclusions
However, the pO2 dependence of the oxygen transport properties, Dchem andkS, has not yet been investigated. We investigated the effect of 20 mol% Zr doping on the electrical conductivity and oxygen transport properties of CeO2−δ using electrical conductivity relaxation (ECR). In ECR, a step change in the oxygen activity of the surrounding gas phase causes the non-stoichiometry.
Defect chemistry of undoped ceria
The standard free energy change for this reaction, equivalent to the partial molar free energy of oxygen in CeO2−δ, can be related to pO2 as. The defective chemical reaction in Eq. 4.1 and the partial molar reaction in Eq. 4.9 are formally identical – both represent an infinitesimal change in the non-stoichiometry from δ to δ+ ∆δ. The difference arises from the fact that the defective chemical notation includes only sites that actively participate in the redox reaction.
Experimental procedure
It describes a chemical change from one non-stoichiometric structure to another infinitesimally different non-stoichiometric structure and thus embodies a configurational entropy change.
Results and discussion
Equilibrium conductivity
The conductivity of cerium oxide continues to increase with decreasing pO2, showing a clear increase in slope (from -1/5 to more than -1/4) around 10−19atm. The conductivity values were used in combination with published non-stoichiometric data for undoped cerium oxide and ZDC20 [1, 97] to estimate the electronic mobility, ue, of cerium oxide and ZDC at 800 ◦C. However, with a further decrease in pO2, the conductivity remains constant despite increasing non-stoichiometry, and the mobility is proportionally reduced (by a factor of 2.5).
Oxygen transport
As further proof of the strong dependence of DChem and kS on pO2 under oxidizing conditions, relaxation profiles around average pO2 of 10-1 and 10-3 atm are shown in the figure. The goal of our analysis is to check whether the observed trend in transport parameters is consistent with the behavior of the thermodynamic factor. This is understandable, since the thermodynamic factor provides a measure of the relative difficulty of reducing ceria.
Conclusions
The fundamental thermodynamic property underlying these applications is the oxygen non-stoichiometry (δ) and its variation with temperature and oxygen partial pressure. In this technique, the impedance response of the oxide is analyzed to extract a quantity called the chemical capacitance (Cchem)[110], which is subsequently related to the oxygen non-stoichiometry. In this work we determine the non-stoichiometry of cerium oxide thin films deposited on 8 mol% yttrium stabilized zirconium substrates (YSZ) using AC impedance spectroscopy.
Theory
Derivation of chemical capacitance
5.3, the total chemical capacity can be expressed in terms of the oxygen content and oxygen partial pressure of the surrounding gas:. 5.6) Finally, by expressing the volumetric oxygen concentration in terms of the non-stoichiometry, cO = (2−δ)/Vm, Eq. Physically, chemical capacity is a measure of the ease of reducibility of an oxide at a given non-stoichiometry.
From chemical capacitance to non-stoichiometry
Unlike dielectric capacitance, which scales with the surface area of the capacitor plates, chemical capacitance is a large quantity, scaling with volume. The term enclosed within the brackets can be known as the inverse of the thermodynamic factor[88]. A rigorous derivation of the impedance response of a MIEC starting with the fundamental transport equations and its relationship to Cchem is addressed elsewhere.
AC impedance spectroscopy
As a result, grain boundary arcs appear in the lower frequency part of the complex resistivity plot. The difference in the magnitude of the time constants dictates the degree of overlap between the semicircles. For an unknown material, the appropriateness of the equivalent circuit model can be assessed from various parameters such as geometry, grain size or electrode composition and by analyzing the resulting resistance spectrum.
Experimental methods
Sample preparation and characterization
Some of the films were deposited through an 8 mm × 8 mm mask, while the rest of the films were deposited on the entire substrate. Joint 2θ−ω X-ray diffraction examinations showed only (001) oriented peaks of YSZ16 and ceria substrate (Figure 5.2). The grain size of the polycrystalline films was measured to be 10 microns using scanning electron backscatter micrographs (Figure 5.4b).
Electrochemical measurements
Results and discussion
Impedance spectra and equivalent circuit modeling
The impedance spectra of the polycrystalline films were qualitatively identical (a quantitative comparison of the area-normalized surface reactance is precluded by the porous nature of the current Pt collector). The compensation resistance (Fig. 5.10b), after subtracting the pO2 independent contribution due to the YSZ substrate (obtained under reducing conditions), was found to correspond to the ohmic resistance of the ceria film. The smaller, high-frequency arc features were found to be independent of pO2.
Chemical capacitance
In all such cases, the total capacitance was verified to be unchanged upon installation. Both aliovalently doped oxides have in common a large external concentration of free moieties fixed by a trivalent dopant (Sm3+ in SDC15; under reducing conditions Pr exists as Pr3+ in PDC10). It has also been reported that the surface of SDC films is enriched in [Ce3+] compared to the bulk and that the enhancement is almost independent of temperature and oxygen partial pressure [119].
Non-stoichiometry from chemical capacitance
The thin-film non-stoichiometry starts to deviate slightly from the bulk values as the intermediate pO2 range is approached (>10−15 atm). Taking this contribution as cutoff and subtracting it from the total capacitance will actually exacerbate the discrepancy in the non-stoichiometry data. The non-stoichiometry of their LSC films was nearly two orders of magnitude larger than that of bulk LSC.
Summary
Since the non-stoichiometry of cerium is sensitive to both oxygen partial pressure and temperature, a practical alternative is to perform isothermal chemical cycling between a reducing gas mixture and steam[122]. The goal of this ongoing work is to characterize the oxygen transport of ceria and ZDC20 under realistic isothermal cycling conditions, using well-defined sample geometry and well-controlled pO2 changes. The conductivity of ceria shows a slope of -1/6, which implies that the point defects do not interact (Eq. 4.7).
![Table A.1: The partial molar entropy of reduction of ceria (units of J/K/mol of oxygen vacancies) obtained from the work of Panlener et al.[1].](https://thumb-ap.123doks.com/thumbv2/123dok/10417469.0/123.918.226.629.565.808/table-partial-entropy-reduction-oxygen-vacancies-obtained-panlener.webp)
Relaxation behavior
- Unit cell of ceria
- Illustration of a two step solar thermochemical cycle to split water and
- Plot of the convex hull of various defect structures
- Calculated phonon density of states for CeO 2−δ
- Effective cluster interactions vs cluster diameter
- Temperature oxygen non-stoichiometry plot for a constant µ Monte
- Calculated high temperature phase diagram of CeO 2−δ with and without
- Entropy of CeO 2−δ computed from Monte Carlo simulations
- Entropy of reduction as a function of δ from Monte Carlo simulations . 26
- Warren Cowley short range order parameters for vacancy pair clusters. 29
- Scanning electron micrograph of Pt catalyst particles sputtered on SDC15
- Illustration of data analytical procedures developed to extract D Chem
The thermodynamic function that describes the state of the system is the bulk potentialΩ, defined by. However, the oxygen concentration is the only independent quantity – the concentrations of the rest are fixed as a result of charge and site conservation. C.2, shows that the magnitude of the slope becomes more or less equal to ∆Sconf ig(δ) with decreasing δ.
![Figure 2.9: Entropy change associated with forming an oxygen vacancy (see Eqn. 2.11) as a function of nonstoichiometry compared with experiment[1].](https://thumb-ap.123doks.com/thumbv2/123dok/10417469.0/43.918.190.626.126.459/figure-entropy-associated-forming-function-nonstoichiometry-compared-experiment.webp)
