Preface. Preface to the First Edition. Contributors. Contributors to the First Edition. Chapter 1. Fundamentals of Impedance Spectroscopy (J.Ross Macdonald and William B. Johnson). 1.1. Background, Basic Definitions, and History. 1.1.1 The Importance of Interfaces. 1.1.2 The Basic Impedance Spectroscopy Experiment. 1.1.3 Response to a Small-Signal Stimulus in the Frequency Domain. 1.1.4 Impedance-Related Functions. 1.1.5 Early History. 1.2. Advantages and Limitations. 1.2.1 Differences Between Solid State and Aqueous Electrochemistry. 1.3. Elementary Analysis of Impedance Spectra. 1.3.1 Physical Models for Equivalent Circuit Elements. 1.3.2 Simple RC Circuits. 1.3.3 Analysis of Single Impedance Arcs. 1.4. Selected Applications of IS. Chapter 2. Theory (Ian D. Raistrick, Donald R. Franceschetti, and J. Ross Macdonald). 2.1. The Electrical Analogs of Physical and Chemical Processes. 2.1.1 Introduction. 2.1.2 The Electrical Properties of Bulk Homogeneous Phases. 2.1.2.1 Introduction. 2.1.2.2 Dielectric Relaxation in Materials with a Single Time Constant. 2.1.2.3 Distributions of Relaxation Times. 2.1.2.4 Conductivity and Diffusion in Electrolytes. 2.1.2.5 Conductivity and Diffusion-a Statistical Description. 2.1.2.6 Migration in the Absence of Concentration Gradients. 2.1.2.7 Transport in Disordered Media. 2.1.3 Mass and Charge Transport in the Presence of Concentration Gradients. 2.1.3.1 Diffusion. 2.1.3.2 Mixed Electronic-Ionic Conductors. 2.1.3.3 Concentration Polarization. 2.1.4 Interfaces and Boundary Conditions. 2.1.4.1 Reversible and Irreversible Interfaces. 2.1.4.2 Polarizable Electrodes. 2.1.4.3 Adsorption at the Electrode-Electrolyte Interface. 2.1.4.4 Charge Transfer at the Electrode-Electrolyte Interface. 2.1.5 Grain Boundary Effects. 2.1.6 Current Distribution, Porous and Rough Electrodes- the Effect of Geometry. 2.1.6.1 Current Distribution Problems. 2.1.6.2 Rough and Porous Electrodes. 2.2. Physical and Electrochemical Models. 2.2.1 The Modeling of Electrochemical Systems. 2.2.2 Equivalent Circuits. 2.2.2.1 Unification of Immitance Responses. 2.2.2.2 Distributed Circuit Elements. 2.2.2.3 Ambiguous Circuits. 2.2.3 Modeling Results. 2.2.3.1 Introduction. 2.2.3.2 Supported Situations. 2.2.3.3 Unsupported Situations: Theoretical Models. 2.2.3.4 Unsupported Situations: Equivalent Network Models. 2.2.3.5 Unsupported Situations: Empirical and Semiempirical Models. Chapter 3. Measuring Techniques and Data Analysis. 3.1. Impedance Measurement Techniques (Michael C. H. McKubre and Digby D. Macdonald). 3.1.1 Introduction. 3.1.2 Frequency Domain Methods. 3.1.2.1 Audio Frequency Bridges. 3.1.2.2 Transformer Ratio Arm Bridges. 3.1.2.3 Berberian-Cole Bridge. 3.1.2.4 Considerations of Potentiostatic Control. 3.1.2.5 Oscilloscopic Methods for Direct Measurement. 3.1.2.6 Phase-Sensitive Detection for Direct Measurement. 3.1.2.7 Automated Frequency Response Analysis. 3.1.2.8 Automated Impedance Analyzers. 3.1.2.9 The Use of Kramers-Kronig Transforms. 3.1.2.10 Spectrum Analyzers. 3.1.3 Time Domain Methods. 3.1.3.1 Introduction. 3.1.3.2 Analog-to-Digital (A/D) Conversion. 3.1.3.3 Computer Interfacing. 3.1.3.4 Digital Signal Processing. 3.1.4 Conclusions. 3.2. Commercially Available Impedance Measurement Systems (Brian Sayers). 3.2.1 Electrochemical Impedance Measurement Systems. 3.2.1.1 System Configuration. 3.2.1.2 Why Use a Potentiostat? 3.2.1.3 Measurements Using 2, 3 or 4-Terminal Techniques. 3.2.1.4 Measurement Resolution and Accuracy. 3.2.1.5 Single Sine and FFT Measurement Techniques. 3.2.1.6 Multielectrode Techniques. 3.2.1.7 Effects of Connections and Input Impedance. 3.2.1.8 Verification of Measurement Performance. 3.2.1.9 Floating Measurement Techniques. 3.2.1.10 Multichannel Techniques. 3.2.2 Materials Impedance Measurement Systems. 3.2.2.1 System Configuration. 3.2.2.2 Measurement of Low Impedance Materials. 3.2.2.3 Measurement of High Impedance Materials. 3.2.2.4 Reference Techniques. 3.2.2.5 Normalization Techniques. 3.2.2.6 High Voltage Measurement Techniques. 3.2.2.7 Temperature Control. 3.2.2.8 Sample Holder Considerations. 3.3. Data Analysis (J. Ross Macdonald). 3.3.1 Data Presentation and Adjustment. 3.3.1.1 Previous Approaches. 3.3.1.2 Three-Dimensional Perspective Plotting. 3.3.1.3 Treatment of Anomalies. 3.3.2 Data Analysis Methods. 3.3.2.1 Simple Methods. 3.3.2.2 Complex Nonlinear Least Squares. 3.3.2.3 Weighting. 3.3.2.4 Which Impedance-Related Function to Fit? 3.3.2.5 The Question of "What to Fit" Revisited. 3.3.2.6 Deconvolution Approaches. 3.3.2.7 Examples of CNLS Fitting. 3.3.2.8 Summary and Simple Characterization Example. Chapter 4. Applications of Impedance Spectroscopy. 4.1. Characterization of Materials (N. Bonanos, B. C. H. Steele, and E. P. Butler). 4.1.1 Microstructural Models for Impedance Spectra of Materials. 4.1.1.1 Introduction. 4.1.1.2 Layer Models. 4.1.1.3 Effective Medium Models. 4.1.1.4 Modeling of Composite Electrodes. 4.1.2 Experimental Techniques. 4.1.2.1 Introduction. 4.1.2.2 Measurement Systems. 4.1.2.3 Sample Preparation-Electrodes. 4.1.2.4 Problems Associated With the Measurement of Electrode Properties. 4.1.3 Interpretation of the Impedance Spectra of Ionic Conductors and Interfaces. 4.1.3.1 Introduction. 4.1.3.2 Characterization of Grain Boundaries by IS. 4.1.3.3 Characterization of Two-Phase Dispersions by IS. 4.1.3.4 Impedance Spectra of Unusual Two-phase Systems. 4.1.3.5 Impedance Spectra of Composite Electrodes. 4.1.3.6 Closing Remarks. 4.2. Characterization of the Electrical Response of High Resistivity Ionic and Dielectric Solid Materials by Immittance Spectroscopy (J. Ross Macdonald). 4.2.1 Introduction. 4.2.2 Types of Dispersive Response Models: Strengths and Weaknesses. 4.2.2.1 Overview. 4.2.2.2 Variable-slope Models. 4.2.2.3 Composite Models. 4.2.3 Illustration of Typical Data Fitting Results for an Ionic Conductor. 4.3. Solid State Devices (William B. Johnson and Wayne L. Worrell). 4.3.1 Electrolyte-Insulator-Semiconductor (EIS) Sensors. 4.3.2 Solid Electrolyte Chemical Sensors. 4.3.3 Photoelectrochemical Solar Cells. 4.3.4 Impedance Response of Electrochromic Materials and Devices (Gunnar A. Niklasson, Anna Karin Johsson, and Maria Stromme). 4.3.4.1 Introduction. 4.3.4.2 Materials. 4.3.4.3 Experimental Techniques. 4.3.4.4 Experimental Results on Single Materials. 4.3.4.5 Experimental Results on Electrochromic Devices. 4.3.4.6 Conclusions and Outlook. 4.3.5 Time-Resolved Photocurrent Generation (Albert Goossens). 4.3.5.1 Introduction-Semiconductors. 4.3.5.2 Steady-State Photocurrents. 4.3.5.3 Time-of-Flight. 4.3.5.4 Intensity-Modulated Photocurrent Spectroscopy. 4.3.5.5 Final Remarks. 4.4. Corrosion of Materials (Digby D. Macdonald and Michael C. H. McKubre). 4.4.1 Introduction. 4.4.2 Fundamentals. 4.4.3 Measurement of Corrosion Rate. 4.4.4 Harmonic Analysis. 4.4.5 Kramer-Kronig Transforms. 4.4.6 Corrosion Mechanisms. 4.4.6.1 Active Dissolution. 4.4.6.2 Active-Passive Transition. 4.4.6.3 The Passive State. 4.4.7 Point Defect Model of the Passive State (Digby D. Macdonald). 4.4.7.1 Introduction. 4.4.7.2 Point Defect Model. 4.4.7.3 Electrochemical Impedance Spectroscopy. 4.4.7.4 Bilayer Passive Films. 4.4.8 Equivalent Circuit Analysis (Digby D. Macdonald and Michael C. H. McKubre). 4.4.8.1 Coatings. 4.4.9 Other Impedance Techniques. 4.4.9.1 Electrochemical Hydrodynamic Impedance (EHI). 4.4.9.2 Fracture Transfer Function (FTF). 4.4.9.3 Electrochemical Mechanical Impedance. 4.5. Electrochemical Power Sources. 4.5.1 Special Aspects of Impedance Modeling of Power Sources (Evgenij Barsoukov). 4.5.1.1 Intrinsic Relation Between Impedance Properties and Power Sources Performance. 4.5.1.2 Linear Time-Domain Modeling Based on Impedance Models, Laplace Transform. 4.5.1.3 Expressing Model Parameters in Electrical Terms, Limiting Resistances and Capacitances of Distributed Elements. 4.5.1.4 Discretization of Distributed Elements, Augmenting Equivalent Circuits. 4.5.1.5 Nonlinear Time-Domain Modeling of Power Sources Based on Impedance Models. 4.5.1.6 Special Kinds of Impedance Measurement Possible with Power Sources-Passive Load Excitation and Load Interrupt. 4.5.2 Batteries (Evgenij Barsoukov). 4.5.2.1 Generic Approach to Battery Impedance Modeling. 4.5.2.2 Lead Acid Batteries. 4.5.2.3 Nickel Cadmium Batteries. 4.5.2.4 Nickel Metal-hydride Batteries. 4.5.2.5 Li-ion Batteries. 4.5.3 Impedance Behavior of Electrochemical Supercapacitors and Porous Electrodes (Brian E. Conway). 4.5.3.1 Introduction. 4.5.3.2 The Time Factor in Capacitance Charge or Discharge. 4.5.3.3 Nyquist (or Argand) Complex-Plane Plots for Representation of Impedance Behavior. 4.5.3.4 Bode Plots of Impedance Parameters for Capacitors. 4.5.3.5 Hierarchy of Equivalent Circuits and Representation of Electrochemical Capacitor Behavior. 4.5.3.6 Impedance and Voltammetry Behavior of Brush Electrode Models of Porous Electrodes. 4.5.3.7 Impedance Behavior of Supercapacitors Based on Pseudocapacitance. 4.5.3.8 Deviations of Double-layer Capacitance from Ideal Behavior: Representation by a Constant-phase Element (CPE). 4.5.4 Fuel Cells (Norbert Wagner). 4.5.4.1 Introduction. 4.5.4.2 Alkaline Fuel Cells (AFC). 4.5.4.3 Polymer Electrolyte Fuel Cells (PEFC). 4.5.4.4 Solid Oxide Fuel Cells (SOFC). Appendix. Abbreviations and Definitions of Models. References. Index.

Impedance spectroscopy : theory, experiment, and applications

In the last decades we have seen the discovery of many new solid state electrolytes (SSEs) with a considerable increase in ionic conductivities, making them potentially useful in rechargeable Li and Li-ion batteries with enhanced safety characteristics.[1–4] These SSEs may also enable the use of Li metal anodes, thus contributing to substantially increasing the energy density and specific energies of batteries.[5] Most recently, a novel class of low-cost, lightweight SSEs, Liantiperovskites, having structures similar to perovskites ABO3 (cubic, Pm-3m), but with inverted charge Li3AB, were introduced with a remarkable combination of very low processing temperatures and high ionic conductivities at near-room temperatures.[6,7] In Li3AB, A is oxygen (O) and B is a halogen (X), such as Cl or Br.[8] Unfortunately, multiple theoretical and experimental follow-up studies on Liantiperovskites reported a wide range of conductivities,[9–12] creating a controversy surrounding the true conductivity of this class of SSEs. Furthermore, density functional theory (DFT)based phase diagram calculations indicate that at least some members in the Li-antiperovskite family (e.g., Li3OCl) may be thermodynamically unstable, decomposing to Li2O and LiCl.[10] Interestingly, lithium halide hydroxides (Li2OHX) also adopt the Li3AB structure.[13] Unlike Li3OCl salt, where six Li atoms occupy the vertices of the Li6O octahedral, in Li2OHX the vertices are occupied by four lithium atoms leaving two other sites vacant.[14] The presence of these two vacancies may be expected to enhance Li+ diffusion and lead to higher conductivities. On the other hand, H in Li2OHCl sits at the oxygen atom in the center of the octahedral,[11] and may potentially block the diffusion of Li+, thus reducing ionic conductivity.[13] Morphological parameters also affect the conductivities of Li-antiperovskites. A cubic crystal lattice favors faster Li+ diffusion and thus may be preferred over lower symmetry phases.[15] Li2OHX is extremely Li-halide hydroxides (Li2OHX) and Li-oxyhalides (Li3OX) have emerged as new classes of low-cost, lightweight solid state electrolytes (SSE) showing promising Li-ion conductivities. The similarity in the lattice parameters between them, careless synthesis, and insufficient rigor in characterization often lead to erroneous interpretations of their compositions. Finally, moisture remaining in the synthesis or cell assembling environment and variability in the equivalent circuit models additionally contribute to significant errors in their properties. Thus, there remains a controversy about the real values of Li-ion conductivities in such SSEs. Here an ultra-fast synthesis and comprehensive material characterization is utilized to report on the ionic conductivities of contaminant-free Li2+xOH1−xCl (x=0-0.7), and Li2OHBr not exceeding 10-4 S cm-1 at 110 °C. Using powerful combination of experimental and numerical approaches, it is demonstrated that the presence of H in these SSEs yields significantly higher Li+ -ionic conductivity. Born-Oppenheimer molecular dynamics simulations show excellent agreement with experimental results and reveal an unexpected mechanism for faster Li+ transport. It involves rotation of a short OH-group in SSEs, which opens lower-energy pathways for the formation of Frenkel defects and highly-correlated Li+ jumps. These findings will reduce the existing confusions and show new avenues for tuning SSE compositions for further improved Li-ion conductivities. Ion Conductivities

Protons Enhance Conductivities in Lithium Halide Hydroxide/Lithium Oxyhalide Solid Electrolytes by Forming Rotating Hydroxy Groups

Na ion- Conducting Ceramic as Solid Electrolyte for Rechargeable Seawater Batteries

The isothermal decay at 25 °C of the optical absorption bands in irradiated LiF TLD‐100 single crystals has been compared with the decay, under the same conditions, of thermoluminescence (TL) and dielectric loss. The decay of the 380‐nm band can be described by a third‐order process suggesting that this band is directly related to free Mg‐vacancy dipoles, which cluster during aging to form trimers. When compared with recent measurements which indicate that the TL peaks 2 and 3 are not related to the Mg dipoles [G. C. Taylor and E. Lilley, J. Phys. D 15, 1243, 1253 (1982)] the present results infer that the 380‐nm band is not directly related to these TL peaks either, in contrast to earlier conclusions [J. H. Jackson and A. M. Harris, Phys. Lett. 29A, 423 (1969)]. This assertion receives some support from pulse annealing measurements and from x‐ray‐induced luminescence spectra. In particular, the latter results reveal that the spectrum consists of several overlapping bands, the relative intensities of whic...

Optical absorption and luminescence in lithium fluoride TLD‐100

The optical spectroscopy of Mn2+ ions both in dipolar form and forming Suzuki‐phase precipitates has been studied in NaCl by photostimulated luminescence at room and liquid nitrogen temperatures An analysis of the positions of the crystal field transitions shows that the 10 Dq value is slightly higher (about 7%) in the Suzuki than in the dipolar phase while the covalency is the same in both cases Such analysis allows us to estimate the value fσ−fπ=48% from the optical data which is in agreement with the EPR data for [MnCl6]4− clusters Moreover, an intense band peaking at 231 nm which disappears when the dipolar phase is formed has been ascertained to be associated with the Suzuki phase This band has been assigned to the double excitation 6A1(S) +6A1(S) → 4T1(G)+[4A1(G), 4E(G)]; that is consistent with the existence of Mn2+ ions in close positions in the Suzuki phase

Optical spectroscopy of Mn2+ ions in solid solution and Suzuki phase in NaCl single crystals

Measurements of conductance and capacitance are made on polycrystalline β″-alumina over a range of frequencies from 10 to 107 Hz and temperatures from −130 to 400 °C. The results are analyzed using complex impedance plots which exhibited a bulk and grain boundary component. Above 220 °C the resistance of the grains exceeded that of the grain boundaries. The activation energy for bulk conductivity is found to be 0.18 eV. The low-temperature results indicated that the grain boundary impedance is being short-circuited either by easy paths through the grain boundaries and/or by some very low impedance boundaries leading to conduction, through preferred grains and grain boundaries.

Bulk and Grain Boundary Ionic Conductivity in Polycrystalline β″- Alumina

The anion displacements and the lattice energy have been calculated as a function of divalent ion radius for the 6 NaCl · MCl2 structure and compared with experimental results. The calcualtions are in agreement with the experimental observation that the 6 NaCl · MCl2 phases tend to form with (r++/r+) < 1.2 but not at larger values.



Die Ionenversetzungen und die Gitterenergie werden fur verschiedene Werte des Ionenradius fur den Fall der 6 NaCl · MCl2-Struktur berechnet und mit experimentellen Resultaten verglichen. Die Rechnungen sind in ubereinstimmung mit der experimentellen Beobachtung, das 6 NaCl · MCl2-Phasen allgemein dann auftreten, wenn (r++/r+) < 1,2, aber nicht fur grosere Werte.

Anion Displacements and the Lattice Energy of the 6 NaCl · MCl2 Family of Structures

The morphologies of the precipitating phases in the systems NaClCdCl2, NaClMnCl2, NaClSrCl2, NaClBaCl2, and KClSrCl2 have been observed by optical and replica electron microscopy. Precipitates with a cubic structure and {100}ppt ∥ {100}matrix tend to be cubic or rectangular in shape, whereas the noncubic structures are needle-like.



Die geometrische Form der kristallisierenden Phasen in den Systemen NaClCdCl2, NaClMnCl2, NaClSrCl2, NaClBaCl2 und KClSrCl2, werden mittels Lichtmikroskopie und Abdruckelektronenmikroskopie untersucht. Phasen mit kubischer Struktur und {100}Ph ∥ {100}Matrix sind normalerweise kubischer oder jedenfalls rechtwinkliger Form, wahrend die nichtkubischen Strukturen nadelformig sind.

Morphology of Divalent Cation Precipitates in Alkali Halide Single Crystals

A detailed mechanism for the clustering of divalent impurity–cation vacancy dipoles in alkali halide single crystals is developed to extend the dimer-trimer mechanism proposed by Crawford. In the extended model the geometry of dimer and trimer configurations and the Suzuki precipitate structure (6 MX · NX2) are considered in conjunction with the electrostatic constraints to cluster formation. A number of parallel reaction paths leading to distinct cluster configurations are examined. Only one path appears to lead to the nucleation of precipitates of Suzuki phase. The kinetic equations for the initial decay of dipoles in the extended model reduce to three limiting cases and are compared with experimentally observed rate laws.



Es wird ein detaillierter Mechanismus fur die Klusterbildung von zweiwertigen Storstellen–Kationenleerstellen-Dipolen in Alkalihalogenid-Einkristallen entwickelt, um den von Crawford vorgeschlagenen Dimer-Trimer-Mechanismus zu erweitern. In dem erweiterten Modell wird die Geometrie der Dimer- und Trimer-Konfigurationen und die Suzuki-Prazipitatstruktur (6 MX · NX2) in Verbindung mit den elektrostatischen Zwangskraften fur die Klusterbildung betrachtet. Eine Anzahl von parallelen Reaktionswegen wird untersucht, die zu unterschiedlichen Klusterkonfigurationen fuhren. Nur ein Weg scheint zur Keimbildung von Prazipitaten der Suzukiphase zu fuhren. Die kinetischen Gleichungen fur den anfanglichen Zerfall der Dipole in dem erweiterten Modell reduzieren sich auf drei Grenzfalle und werden mit experimentell beobachteten Ratengleichungen verglichen.

Structural aspects of clustering reactions in alkali halides doped with divalent impurities

The importance of rapid cooling from high temperatures to retain a random dispersion of [M++V−] divalent cation impurity–vacancy pairs is demonstrated. For fully efficient quenches very thin crystals with relatively small broad face areas should be used. For crystals such as LiF TLD100 containing about 170 ppm Mg++ it is also necessary to quench into a liquid such as acetone. In many clustering studies in the past using large crystals, substantial clustering must have taken place during the quench.



Es wird der Einflus einer schnellen Abkuhlung von hohen Temperaturen auf die Erzielung einer statistischen Verteilung von divalenten [M++V−]-Kationenverunreinigungs–Leerstellenpaaren gezeigt. Fur ein vollstandig effizientes Abschrecken sollten sehr dunne Kristalle mit relativ geringen Abmessungen der breiten Flachen benutzt werden. Fur Kristalle wie LiF TLD 100, die etwa 170 ppm Mg++ enthalten, ist es ebenfalls notwendig, sie in einer Flussigkeit wie z. B. Azeton abzuschrecken. In einer Reihe von Untersuchungen der letzten Zeit uber Clusterbildung, die grose Kristalle benutzen, mus eine betrachtliche Clusterbildung wahrend des Abschreckens stattgefunden haben.

Rapid cooling of divalent cation doped alkali halide crystals

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