I would like to thank Jeffrey Krimmel for technical support using the Rayleigh cluster. The combination of open circuit voltage (OCV) measurement and quantitative fitting of impedance spectra yields electrochemical information at.
Defect Chemistry and Electrical Properties of Acceptor- Doped CeriaDoped Ceria
This is called the constant oxygen vacancy approximation.7 From (1.3) and (1.5) the electron concentration becomes. In the ionic regime of doped cerium, the total conductivity (essentially equal to the ionic conductivity) is independent of oxygen partial pressure.
Three Systems
For the space charge system, system II, each layer is divided into two space charge (SC) regions and a grain interior (GI) region as shown in Figure 1.1(b). For systems without space charge, systems I and III, the microstructure can be neglected and the entire electrolyte can be treated as a single crystal as shown in Figure 1.1(a) and 1.1(c).
Fundamentals of Impedance Spectroscopy
A similar analogy can be drawn between the other of the Bode-Bode graph, θ vs.sf, and the infrared spectrum. One of the most important subcircuits is the parallel connection of a resistor R and a Constant Phase ElementQ, such as one of the three shown in Figure 1.5.
Basic Equations
The third fundamental equation is that due to Poisson, which relates the sum of the charges in the system, P. These can be formulated in terms of the fluxes at the electrolyte|electrode interfaces, which are fixed by the values of the electrochemical potential at the respective interfaces and in the respective gas phase chambers.
Steady-State Solution under Open Circuit Conditions
As discussed above, the measured cell voltage can be expressed as (2.79) and (2.83) based on the ionic and electronic properties of the system. As discussed above, if the electrodes are assumed to be reversible with respect to electrons, the voltage is determined by the difference in reduced electrochemical potential of the electronic species.
Small-Signal Impedance Solution
It is worth noting that the high-frequency limit of the “high-frequency sub-circuit” in Figure 2.7(c) is the same as the alternating current. At the high-frequency limit, all capacitors are effectively shorted, creating the circuit shown in Figure 2.15(a). At the low-frequency limit, all capacitors are effectively open, creating the circuit shown in Figure 2.15(b).
Comparison of Empirical Equivalent Circuit Modeling and the Physical Equivalent Circuit Modelingand the Physical Equivalent Circuit Modeling
For the circuit in Figure 2.9(c): If there is no position dependence of the circuit elements, the impedance can be obtained analytically when the discrete elements become continuous or the number of elements N becomes infinite. It is shown above that the log-normal concentration distribution in Figure 2.9(c) yields the depressed arc. Alternatively, the two GI and GB arcs in Figure 2.19 can be modeled traditionally with the equivalent circuit RGIQGI −RGBQGB.
Experiments
The schematic experimental setup is shown in Figure 3.2(a) for systems I and II, and in Figure 3.2(b) for system III. In view of the small amplitude of the applied voltage and the small sample size relative to the overall flow rate and dimensions of the experimental apparatus, it is safely assumed that the gas composition is undisturbed by the impedance measurement. The oxygen partial pressure in the anode chamber was calculated assuming thermodynamic equilibrium between O2, H2 and H2O.
System I
The oxygen partial pressure dependence of the total electrical conductivity of SDC15 (as determined by the high-frequency cross section) at and 650 ◦C is shown in . While in the previous discussion, the electronic resistance Reon or the electronic conductivity σeon was obtained from the high-frequency intersection with the real axis of the impedance. The electron defect concentration, Figure 3.8(a), behaves as expected based on the defect chemistry model.
System II
The total conductivity of the sample in system I is four times that of the sample in system II at 600 ◦C, i.e., the operating temperature of the fuel cell. The impedance calculation, i.e., the solution of the matrix equation (2.137), was obtained using the direct sparse matrix solver SuperLU 3.0.63 The fitting was performed by the Levenberg-Marquardt program levmar 2.1.3.18 Both SuperLU and levmar were included in the program main written in C. In other words, 100 random numbers obeying the lognormal distribution were generated for the mean value of 0.46 V. The serial layer width was kept the same for all layers.
System III
A comparison of the experimental and fitted spectrum is given in Figure 3.16 when the H2 concentration is “100%” with 3% H2O saturation at the anode and the oxygen partial pressure is 0.21 atm at the cathode. The partial pressure of oxygen at the anode|electrolyte interface, pO2(0), is higher when the partial pressure of oxygen in the anode chamber, pO2(a), is higher. The oxygen potential profile across the sample is shown in Figure 3.25 at 600 ◦C when the H2 concentration is “100 %” with 3% H2O saturation at the anode and the oxygen partial pressure is 0.21 atm at the cathode.
Discussions
Under reducing conditions, the space charge potential decreases with decreasing oxygen partial pressures, as shown in Figure 3.18, and the values of the space charge potentials are comparable to those obtained under oxidizing conditions. Since the SDC15 measured here behaves as a pure ionic conductor at moderate oxygen partial pressures, it is likely that the electrochemical reduction of O2 in the Pt|SDC15|Pt system occurs by a similar mechanism to that in the Pt|YSZ|Pt system. 2 suggests that the electrode reactions are related to the electronic conductivity of mixed-conducting ceria, which shows exactly the same dependence on oxygen partial pressure.
Summary and Conclusions
In the second pathway, hydrogen desorption occurs directly on the oxide surface, which then electrochemically reacts with oxygen, giving off electrons that are then transported through the oxide to Pt. That is, we propose that the electrochemical reaction occurs directly on the ceria surface (ie, that ceria is electrochemically active) and that the reaction is limited by the rate of removal of electrons from the reaction sites (ie, electron conductivity). Accordingly, cerium is believed to be electrochemically active for hydrogen oxidation, the reaction occurring directly on the ceria surface and limited by the rate of electron removal from the reaction sites.
Grain Interior Capacitance
Grain Boundary Capacitance
Interfacial Capacitance
Chemical Capacitance
The impedance of the general electrode|MIEC|electrode system shown in Figure 2.13(a) of the main text can be estimated by reformulating the circuit from one consisting of R and C to one consisting of elements of arbitrary resistance in Figure D.1 . ZA and ZB are the terminal impedances corresponding to the total impedance of the electrode|MIEC in rails 1 and 2 respectively. Z1 and Z2 are the impedances on tracks 1 and 2 respectively while Z3 is the resistance between tracks 1 and 2.
Introduction
The surface area of the amorphous product ranged from 65 to 104 m2/g and no other characterization of the airgel was presented. In addition, there are reports that mesopores in these materials can be blocked by the deposition of metallic catalyst particles.106 These features can impede the diffusion of the reactants and byproduct gases and prevent effective catalysis. The synthesis process is completed within hours and it is possible, by appropriate heat treatment, to control the crystallite size of the fluorite phase comprising the solid network, as well as the pore structure of the airgel.
Experimental
Cerium is likely to occur in the 4+ oxidation state at all stages of sample preparation, regardless of sample color. Grain/particle size measurements were performed by applying the Scherrer equation to the FWHM of the (111) peak, after accounting for instrument broadening using silicon as a standard. The surface area was calculated using the BET method.110 The pore size distribution was determined by applying the BJH method111 to the desorption branch of the isotherm.
Results and Discussion
The airgel exhibits an adsorption isotherm of type IV (IUPAC classification) with a marked hysteresis loop of H1 type (Figure E.5a). The narrowness of the pore diameter distribution, which has a maximum at 21.2 nm, is further evident in Figure E.6a. Moreover, the pores are randomly connected in a three-dimensional network (Figure E.5), which is further expected to promote gas diffusion through the airgel structure.
Conclusions
Acknowledgements
Undoped and Mg-doped La2Zr2O7 with a pyrochlore structure were prepared by the combined EDTA-citrate complexation method. An isotope effect under atmospheres containing H2O- or D2O- was observed, indicating that protons (or deuterons) are mobile species. The isotope effect was discussed on the basis of a mechanical transition state statistical theory.
Introduction
Based on the ionic radius and electronegativity, we expect the solubility of Mg on the Zr site to be higher than Y and Ca. In this study, proton conduction of grain interior and grain boundaries of undoped and Mg-doped La2Zr2O7 was investigated. The conductivity isotope effect under H2O- or D2O-containing atmospheres was discussed on the basis of a statistical mechanical transition state theory.
Experimental
The instrument broadening was approximated by the FWHM of (111) peak of Si powders around 100 um. The particle sizes of the sample powders were calculated by Scherrer method using FWHMs of (222) peak. The specific surface area was measured by nitrogen adsorption at 77 K using the BET (Brunauer-Emmett-Teller) equation.
Results and Discussion
From (F.4), the ratio of the isotope rate constants can be expressed as. where the vibrational partition function, assuming harmonic oscillators, is exclusive of zero-point energy. where ki is the force constant that is the same for the two isotopes, and µ is the reduced mass of the harmonic oscillator. The effects of dopant amount on conductivity are shown in Figure F.7(a) and Figure F.7(b) for the grain interior and the specific grain boundary, respectively. The relationship between the activation energies of the internal conductivity of the grains and the lattice constants is also plotted in Figure F.3.
Conclusions
This is probably caused by the structural and compositional difference at the grain boundary between the undoped and doped samples. On the other hand, for the doped sample, the dopant generally tends to be enriched around the grain boundary region, so both the structure and composition can be very different from the undoped sample. Simply, the grain boundary phase of the doped sample is not as conductive as that of the undoped sample.
Acknowledgments
Treatment of the impedance of mixed conductors - equivalent circuit model and explicit approximate solutions. Impedance spectroscopy as a tool for chemical and electrochemical analysis of mixed conductors: A case study of ceria. Journal of the American Ceramic Society. Analysis of the proportionality constant that correlates the mean intercept length with the mean grain size.
