Jürgen Fleig

The grain boundary impedance of random microstructures: numerical simulations and implications for the analysis of experimental data

Abstract The grain boundary impedance of polycrystalline materials is usually analyzed in terms of a simplified microstructure composed of cubic-shaped grains. In order to investigate the validity of such a “brick layer model”, impedance spectra of polycrystals with computer-generated microstructures (two-dimensional Voronoi diagrams) have been simulated. These calculations showed that the current density in polycrystals can be rather inhomogeneous and that the so-called grain boundary impedance depends on the bulk conductivity. Nevertheless, the corresponding grain boundary resistances, capacitances and relaxation frequencies are frequently close to the values expected from a brick layer model. The impact of these calculations on the analysis of grain boundary impedances caused by space charge depletion layers is discussed. It is shown in how far impedance parameters yield reliable space charge potentials. Measurements on polycrystalline SrTiO3 illustrate the suggested approach. In the quantitative analysis of these experiments, capacitances have been calculated from constant phase elements.

Quantitative Comparison of Mixed Conducting SOFC Cathode Materials by Means of Thin Film Model Electrodes

Geometrically well-defined model electrodes have been employed to unambiguously elucidate the individual resistive and capacitive processes of various solid oxide fuel cell cathodes by means of impedance spectroscopy. The measurements were performed on dense, thin film-type microelectrodes of La 1-x Sr x Co 1-y Fe y O 3-δ and related perovskite-type materials prepared by pulsed laser deposition and photolithography. It was found that the substitution of the A-site cation La in La 1-x Sr x Co 1-y Fe y O 3-δ by Sm and especially by Ba leads to a strong enhancement of the surface exchange kinetics, whereas a variation of the Co/Fe ratio between 0 and 1 has only little effect on this quantity at temperatures around 750°C. Furthermore, it has been studied how the electrochemical activation effect, i.e., the strong reduction of the surface exchange resistance after application of a large dc bias, depends on composition.

The polarization of mixed conducting SOFC cathodes: Effects of surface reaction coefficient, ionic conductivity and geometry

Multi-dimensional finite element simulations of current distributions in mixed ionic and electronic conducting cathodes (MIEC) are presented for the case that the cathodic oxygen incorporation into an electrolyte takes place through the bulk of the electrode. The effects of the ionic conductivity and the surface reaction coefficient on the overall process are analyzed. Depending on these material parameters different parts of the cathode are involved in the oxide ion transport to the electrolyte (from a very small region close to the three phase boundary for a fast surface reaction up to the entire cathode for a very slow surface reaction). The calculations also reveal which combinations of ionic conductivity and surface reaction coefficient are appropriate to achieve acceptable polarization resistances. The influence of the particle size is discussed and interpolation formulae are given to estimate the cathodic polarization in porous MIECs.

The geometry dependence of the polarization resistance of Sr-doped LaMnO3 microelectrodes on yttria-stabilized zirconia

Abstract Impedance spectroscopic studies and I–V measurements are performed at Sr-doped LaMnO3 (LSM) microelectrodes in order to elucidate the mechanism of the oxygen-reduction reaction on yttria-stabilized zirconia. The geometry dependence of the polarization resistance was investigated by systematic variations of the microelectrodes size and thickness. The relation between the resistance and the electrode geometry turns out to be bias-dependent: in the cathodic regime and close to equilibrium, the resistance is proportional to the inverse electrode area. Moreover, measurements without bias revealed an almost linear dependence of the resistance on the electrode thickness. This suggests that the relevant oxygen reduction path involves the transport of oxide ions through the bulk of the LSM cathode. In the anodic regime, however, the resistance becomes proportional to the inverse three-phase boundary length and, hence, a mechanism involving the LSM surface is most probable with a step close to the three-phase boundary being rate limiting. Experiments performed on LSM microelectrodes with thin alumina “discs” beneath the LSM to partly block the oxygen ion transport through the bulk of the electrode support this interpretation.

Relationship between Cation Segregation and the Electrochemical Oxygen Reduction Kinetics of La0.6Sr0.4CoO3−δ Thin Film Electrodes

Pulsed laser deposited La 0.6 Sr 0.4 CoO 3―δ (LSC) thin film electrodes on yttria stabilized zirconia (YSZ) single crystals were investigated by impedance spectroscopy, time of flight secondary ion mass spectrometry (ToF-SIMS) and inductively coupled plasma optical emission spectrometry (ICP-OES). Effects caused by different film deposition temperatures, thermal annealing and chemical etching were studied. Correlations between changes in electrode polarization resistance of oxygen reduction and surface composition were found. At high deposition temperatures and after thermal annealing an inhomogeneous cation distribution was detected in the surface-near region, most manifest in a significant Sr enrichment at the surface. An activating effect of chemical etching of LSC is described, which can lower the polarization resistance by orders of magnitude. Chemistry behind this activation and thermal degradation was analyzed by ToF-SIMS and ICP-OES measurements of in-situ etched LSC films. The latter allow quantitative depth resolved compositional analysis with nominally sub nm resolution. High resolution scanning electron microscopy images illustrate the accompanying changes in surface morphology. All measurements suggest that stoichiometric LSC surfaces intrinsically exhibit very high activity towards oxygen reduction.

Comparison, Selection, and Parameterization of Electrical Battery Models for Automotive Applications

This paper describes the comparison and parameterization process of dynamic battery models for cell and system simulation. Three commonly used equivalent circuit battery models are parameterized using a numeric optimization method and basic electrical tests with a lithium-ion polymer battery cell. The maximum model performance is investigated, and the parameterized models are compared regarding the parameterization effort and the model accuracy. For the model with the best tradeoff between the parametrization effort and the model accuracy, a reasonable simplification of the parameterization process is presented. This model is parameterized with the simplified parameterization process and, finally, validated by using a current profile obtained from an electric vehicle simulation performing a real-life driving cycle.

Space charge conduction: Simple analytical solutions for ionic and mixed conductors and application to nanocrystalline ceria

In this paper we present a set of simple analytical solutions for the parallel and the serial contributions of space charge zones to the overall conduction in bicrystals and (brick layered) ceramics for a variety of situations. The different situations are characterized by signs of the space charge potential, by different charge numbers of the carriers and by the presence or absence of acceptor or donor dopants. We can give solutions for arbitrary charge numbers as long as we restrict to sufficiently high space charge potentials and can presuppose equilibrium for the mobile carriers. A recent analysis of impedance measurements of nanocrystalline ceria based on a space charge model is briefly mentioned as a specific example, as it reflects the occurrence of highly n-conducting accumulation layers in addition to strongly blocking oxygen vacancy depletion layers.

Role of space charge in the grain boundary blocking effect in doped zirconia

Abstract Although the presence of siliceous phases is a major cause of the grain boundary blocking effect in doped zirconia (ZrO 2 ), the grain boundary resistivity also appears to be significantly influenced by space charges. The ionic transport across the grain boundaries occurs solely through direct grain-to-grain contacts which are themselves blocking in nature. Such a blocking effect can be consistently accounted for by the oxygen vacancy depletion in the grain boundary space charge layer. The Al 2 O 3 addition markedly modified the grain boundary properties, which are also consistently explained by the space charge effect.

Tensile Lattice Strain Accelerates Oxygen Surface Exchange and Diffusion in La1–xSrxCoO3−δ Thin Films

The influence of lattice strain on the oxygen exchange kinetics and diffusion in oxides was investigated on (100) epitaxial La1–xSrxCoO3−δ (LSC) thin films grown by pulsed laser deposition. Planar tensile and compressively strained LSC films were obtained on single-crystalline SrTiO3 and LaAlO3. 18O isotope exchange depth profiling with ToF-SIMS was employed to simultaneously measure the tracer surface exchange coefficient k* and the tracer diffusion coefficient D* in the temperature range 280–475 °C. In accordance with recent theoretical findings, much faster surface exchange (∼4 times) and diffusion (∼10 times) were observed for the tensile strained films compared to the compressively strained films in the entire temperature range. The same strain effect—tensile strain leading to higher k* and D*—was found for different LSC compositions (x = 0.2 and x = 0.4) and for surface-etched films. The temperature dependence of k* and D* is discussed with respect to the contributions of strain states, formation enthalpy of oxygen vacancies, and vacancy mobility at different temperatures. Our findings point toward the control of oxygen surface exchange and diffusion kinetics by means of lattice strain in existing mixed conducting oxides for energy conversion applications.

The impedance of ceramics with highly resistive grain boundaries: validity and limits of the brick layer model

Impedance spectroscopy is an important tool to investigate the electrical properties of grain boundaries. For the analysis of the impedance spectra cubic grains, laterally homogeneous grain boundaries and identical properties of all grain boundaries are usually assumed (brick layer model). However, in real ceramics these assumptions are generally violated. Using the finite element method we calculated the impedance of several polycrystals exhibiting highly resistive grain boundaries with microstructures and grain boundary properties deviating from the simple brick layer model. Detours around highly resistive regions (e.g. due to high grain boundary density or enhanced grain boundary resistivity) can play an important role and lead to grain-boundary semicircles depending on bulk properties and even to additional semicircles. Conditions are discussed within which the brick layer model allows for a reasonable evaluation of the spectra.