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Widely-used complex plane analysis of impedance data is insufficiently sensitive to characterize fully the bulk properties of YSZ single crystal. Instead, more extensive data analysis is needed which uses a combination of parallel, admittance-based formalisms and series, impedance-based formalisms. Bulk electrical properties are measured at higher frequencies and contain contributions from both long range conduction and local dielectric relaxation. At lower frequencies, electrode–sample contact impedances are measured and are included in full equivalent circuit analysis. The impedance of YSZ crystal of composition 8 mol% Y2O3 in the (110) orientation, with Pt electrodes, was measured over the temperature range 150–750◦C and frequency range 0.01 Hz-3 MHz. Full data analysis required (i) a parallel constant phase element (CPE)–resistance (R) combination to model the electrode response, (ii) a series R-C element to represent local reorientation of defect dipoles and (iii) a R-C-CPE element to represent long range oxide-ion conduction; (ii) and (iii) together model the bulk response. The dielectric element underpins all discussions about defect structure and properties of YSZ but has not been included previously in analysis of impedance data. The new equivalent circuit that is proposed should allow better separation of bulk and grain boundary impedances of YSZ ceramics.

Although the constant phase element (CPE) parameters have been found to vary with DC bias voltage in electrochemical impedance spectroscopy measurement, to date, the CPE parameters are assumed to be constant within the voltage window in cyclic voltammetry (CV) simulation. This leads to failure in predicting the voltammetric response of a double layer in some cases. In this study, the voltage-dependent CPE and ohmic parameters are used to simulate the capacitive current. The results show good agreement with the experimental measurements of commercial electrical double layer capacitors. The model is extended to predict the response of a system involving both Faradaic and capacitive currents by combining the conventional physicochemical transport model with circuit analysis to include effects of the resistances and CPE. To accurately predict the entire CV responses, a modified Randles circuit with an additional resistance connected in series with the CPE is proposed to be an equivalent circuit of the system. Furthermore, the closed-form analytical solution of the time-domain response of CPE under CV conditions is also derived and presented to gain better understanding of the CPE response. Using the derived equation, CV can serve as an alternative approach for determining the CPE parameters.

The power-energy performance of supercapacitors is usually visualized by the Ragone plot of (gravimetric or volumetric) energy density vs power density. The energy is commonly computed from E = CV2/2, and the power from P = E/Δt, which assume RC-based models. In this study, we investigate the energy-power profiles of two commercial supercapacitors discharged with three different types of loads: (i) constant current, (ii) constant power, and (iii) constant resistive load. The energy is computed as per the definition from the time-integral of its instantaneous power, i.e. with p(t) = i(t) v(t). In doing so, we do not assume any specific model a priori, and we highlight the fact that supercapacitor performance depends on the type of load it supplies. We also model the experimental Ragone plot using a fractional-order model composed of a resistance and a constant phase element, and show its superiority over the standard RC model.

A method is disclosed for analysis of the impedance behavior of electrochemical impedance circuits or the Transfer Function for input-output systems, utilizing the symmetry of the phase angle response with the Log of the frequency to allow for determination of the lower frequency half of the impedance response over Log frequency based only on information from the upper half response. The underlying analytical basis for the symmetry of the phase angle and the methods for applying this analysis are applicable to simple R-C circuits, Randle circuits, Constant Phase Element (CPE)-Randles and coating model circuits. Symmetric functions describing the derivative of the phase angle, θ, with respect to the Log of the frequency can be used to determine the circuit elements requiring only the high frequency information. Only knowledge of the high frequency-based response is needed to know how the low frequency range behaves. Capturing high frequency impedance can be done in a few seconds compared with many hours of experimental effort to obtain low frequency behavior, to allow for continuous monitoring of polarization resistance with only a few seconds of data capture required. The method is applicable to numerous sensor applications across a range of disciplines including corrosion focused industries, battery technology and bioelectrochemical fields, and applicable to other Transfer Function analyses that include such as dielectric relaxation and complex modulus.

Various materials display a constant phase impedance, Z proportional to [i omega](-u), over a wide frequency range. In this paper, we show that this behavior is a natural consequence of charge transport in the macroscopic limit, and that in contrast to the common belief, no assumptions on the "relaxation functions" are required. Our unifying view of the constant-phase-element (CPE) is then employed for analyzing impedance spectra that were recorded during the aging of LixFePO4 cells. We find and explain a significant correlation between their capacity loss and changes in the exponent (u) of the CPE describing cathodic Li-intercalation. Changes in u with the state of charge are also discussed. CPE exponents are shown to be valuable performance indicators for Li-ion batteries. (C) The Author(s) 2015. Published by ECS. All rights reserved.

Solid oxide cell (SOC) performance is limited by various processes. One way to investigate these processes is by electrochemical impedance spectroscopy. In order to quantify and characterize the processes, an equivalent circuit can be used to model the SOC impedance spectra (IS). Unfortunately, the optimal equivalent circuit is often unknown and to complicate matters further, several processes contribute to the SOC impedance - making detailed process characterization difficult. In this work we analyze and model a series of IS measured during steam electrolysis operation of an SOC. During testing, degradation is only observed in the Ni/YSZ electrode and not in the electrolyte or the LSM/YSZ electrode. A batch fit of the differences between the IS shows that a modified Gerischer element provides a better fit to the Ni/YSZ electrode impedance than the frequently used RQ element - albeit neither equivalent circuit provides a perfect fit. However, modeling with the Gerischer element indicates that the Ni/YSZ electrode performance decrease, relates to an electrochemical reaction resistance increase at the electrode triple phase boundaries.

Measured electrochemical impedance spectra of porous electrodes comprised of redox-active ruthenium oxide and inert niobium hydroxide are compared with the results of structurally consistent mathematical models describing coupled processes of electron transport in the solid matrix, ion transport in the electrolyte, proton transport within the ruthenium oxide particles, and redox reaction on particle surfaces. Addition of moderate amounts of niobium to crystalline ruthenium oxide is found to improve the frequency response due to enhanced intraparticle proton transport. However, excessive niobium reduces ion and electron transport through the electrode thickness, reducing the available capacitance. Thus, an optimum composition is needed to achieve the best balance in transport properties. Near this optimum, the intraparticle proton transport undergoes a transition from a constant phase element (CPE) response for Ru-rich materials to a classical Warburg diffusion response for Nb-rich compositions. The CPE regime is analyzed in detail to identify fractal-like structures as well as alternative radial distributions of intraparticle proton diffusivity consistent with measured response. The models involving variations in radial diffusivity appear most probable and have nearly exponential decreases in radial diffusivity with distance from particle surfaces similar to a Debye distribution of charge carriers in an electric double layer.

Impedance spectra of carbon steel in the presence of 1-hydroxy-ethane-1,1-diphosphonic acid (HEDP) has been investigated in neutral solutions. The aim of the measurements was to study the effect of HEDP on the carbon steel corrosion as a function of inhibitor concentration. An optimal inhibitor concentration was found. A two-time constant equivalent circuit model including a constant phase element was consistent with experimental data in the frequency range studied. The system parameters, obtained by a nonlinear fit procedure are discussed in terms of the model used. Inhibitor efficiencies derived from impedance data are compared with those obtained from polarization and weight loss measurements. Results of these investigations show that a low concentrations, HEDP inhibits carbon steel corrosion by a precipitation mechanism forming insoluble iron complexes and repairing the porous oxide layer formed n the metal surface. Increasing HEDP concentration beyond the optimal value decreases its inhibition efficiency due to the dissolution of the oxide layer.

To characterize electrical losses of fuel cells or batteries, impedance spectroscopy (IS) or current interruption (CI) can be used. Analysis and parameter determination of impedance data is widely used. The system under study is usually represented by an equivalent circuit from which the system parameters can be determined. However, the analysis of current‐interruption data is often carried out with too simple circuits, e.g., using pure exponential behavior, because analysis in the time domain (CI) is often much more awkward than analysis in the frequency domain (IS). A comparative study has been carried out on the analysis of a relatively ideal electrical circuit, containing a pure capacitor, and a more realistic circuit where the capacitor is replaced by a constant‐phase element. Equations describing the response in the frequency and time domain are presented. Emphasis is put upon the analysis of circuits containing a constant‐phase element because impedance measurements clearly indicate the presence of such an element in many types of experiments, and because there is only limited literature available describing the behavior in the time domain.

A normal power-law distribution of local resistivity with a uniform dielectric constant was found to be consistent with the constant-phase element CPE. An analytic expression, based on the power-law resistivity distribution, was found that relates CPE parameters to the physical properties of a film. This expression worked well for such diverse systems as aluminum oxides, oxides on stainless steel, and human skin. Good values for film thickness were obtained, even when previously proposed expressions could not be used or yielded incorrect results. The power-law model yields a CPE impedance behavior in an appropriate frequency range, defined by two characteristic frequencies. Ideal capacitive behavior is seen above the upper characteristic frequency and below the lower characteristic frequency. A symmetric CPE response between the characteristic frequencies can be obtained by adding a parallel resistive pathway.

The inhibition performance of some furan derivatives, namely, methyl 2-furoate, ethyl 2-furoate, and amyl 2-furoate on mild steel in normal hydrochloric acid medium (1 M HCl) at 25°C, was studied by weight loss, potentiodynamic polarization, electrochemical impedance spectroscopy (EIS), and electrochemical frequency modulation measurements (EFM). Furan derivatives inhibit the acidic corrosion even at very low concentrations, reaching a value of inhibition efficiency up to 93% at a concentration of 20 mM. The results obtained from the different corrosion evaluation techniques are in good agreement. Polarization curves indicate that the studied furan derivatives are mixed-type inhibitors. Data obtained from EIS measurements were analyzed to model the corrosion inhibition process through an appropriate equivalent circuit model. A constant phase element has been used. The adsorption of furan derivatives on the steel surface in 1 M HCl solution was found to obey Langmuir's adsorption isotherm with a negative value of the free energy of adsorption ΔG° ads+ Molecular dynamics simulations were carried out to establish the inhibition mechanism.

Cu electrochemical mechanical planarization (ECMP) has been investigated as an alternative technology to Cu chemical mechanical planarization (CMP). The influence of pH and a complexing agent on the surface quality and Cu removal rate during ECMP is studied on blanket Cu-coated wafers to understand discrepancies in surface quality between low pH ECMP electrolytes and CMP slurries containing 5-phenyl-1-H-tetrazole. The results show that surface roughness increases following Cu ECMP relative to Cu CMP, probably due to the introduction of pad porosity. The surface quality improves as the pH is increased from 3 to 6, suggesting that the formation of some Cu oxide may be desirable, although this decreases the Cu removal rate. The surface quality also improves with the substitution of a less aggressive complexing agent (glycine) for oxalic acid. Measurements by electrochemical impedance spectroscopy suggest that the passive film formed with an applied anodic potential during ECMP is thicker than that which forms during CMP at the open-circuit potential. Impedance measurements show that the trend in surface quality with pH is not always consistent with a previously reported correlation with the degree to which the constant phase element approaches an ideal capacitor.

The films forming on pure chromium and Alloy C22 in aqueous borate buffer were investigated with potential polarization scans, electrochemical impedance spectroscopy, and Mott-Schottky analysis. The capacitances of both films were frequency dependent, and a constant phase element (CPE) best described the frequency dispersion. Cathodic polarization scans were used to assess the accuracy of flatband potential values calculated from Mott-Schottky tests using different models to extract an effective capacitance from a CPE. It was found that using effective capacitances calculated with an expression developed by Brug et al. [J. Electroanal. Chem., 176, 275 (1984)] led to flatband potentials that closely agreed with cathodic polarization scans. Both films were found to be n-type, and flatband potentials of -1.217 and -0.617 V vs standard hydrogen electrode were found for Cr and Alloy C22, respectively.

A procedure is proposed for using the Mott-Schottky approximation to obtain the electronic properties (flatband potential and charge carrier density) of passive films that are modeled by equivalent circuits that contain a constant phase element (CPE) rather than a capacitor. Capacitances are calculated from the equivalent circuit containing a CPE using expressions developed by Hsu and Mansfeld [Corrosion, 57, 747 (2001)], and Brug et al. [J. Electroanal. Chem., 176, 275 (1984)]. Both expressions calculate similar flatband potentials for Ti and Ni, but the charge carrier densities are significantly different. The approach is applied to the analyses of passive films formed on titanium in 0.1 M H 2 SO 4 and nickel in 1 M NaOH. The passive film formed on Ti was found to be n-type, have a flatband potential of -330 mV vs a sat. Ag/AgCl reference electrode, and a charge carrier density of 1.4 X 10 21 cm -3 . The film formed on Ni was p-type, had a flatband potential of 100 mV, and a charge carrier density of 3 × 10 21 cm -3 .

Internal electrode resistance plays a role affecting the power capability of electric double-layer capacitors. Capacitor cells made of activated carbon cloth are analyzed using ac impedance spectroscopy. To reduce the internal resistance, carbon nanotubes (CNTs) are grafted on the carbon cloth via sputtering catalyst seeding, followed by chemical vapor deposition with CH 4 . The impedance spectra of the assembled capacitor cells showed that the internal resistance of the electrodes was significantly reduced from 0.9 to 0 Ω. In addition to the increase in the electronic conductivity, the introduction of CNTs also enhanced the utilization factor of the carbon electrode, thus leading to a more efficient double-layer formation inside carbon micropores. Constant phase element analysis of the capacitive behavior in micropores showed that the deviation from ideality was less significant for the carbon cloth grafted with CNTs. This developed CNT-grafting technique significantly promoted the power performance of carbon cloth by enhancing the transport of both electrons and ions in the assembled capacitor cells. At a current density as high as 150 mA cm -2 , a capacitance loss of only 7% (compared to the ultimate value) was obtained for the CNT-grafted carbon cloth.

International audience; Two numerical methods were used to calculate the influence of geometry-induced current and potential distributions on the impedance response of an ideally polarized disk electrode. A coherent notation is proposed for local and global impedance which accounts for global, local, local interfacial, and both global and local ohmic impedances. The local and ohmic impedances are shown to provide insight into the frequency dispersion associated with the geometry of disk electrodes. The high-frequency global impedance response has the appearance of a constant-phase element CPE but can be considered to be only an apparent CPE because the CPE exponent is a function of frequency.

Erratum: The Apparent Constant-Phase-Element Behavior of an Ideally Polarized Blocking Electrode. A Global and Local Impedance Analysis [J. Electrochem. Soc., 154, C81 (2007)] Vicky Mei-Wen Huang, Vincent Vivier, Mark E. Orazem, Nadine Pebere, and Bernard Tribollet Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, USA UPR15 du CNRS, Laboratoire Interfaces et Systemes Electrochimiques, Universite Pierre et Marie Curie, 75252 Paris, France CIRIMAT, UMR CNRS 5085, ENSIACET, 31077 Toulouse Cedex 04, France

A detailed analysis from both numerical calculations and experimental results is presented for the local electrochemical impedance spectroscopy (LEIS) measurements of a disk electrode, which accounted for the placement of the LEIS probe above the electrode surface. The calculations for an electrode with a local constant phase element behavior were in excellent agreement with experimental observations for a stainless steel electrode in a Na 2 SO 4 /NaCl (pH 4) electrolyte. Measurement of the local impedance at two positions above the electrode surface allowed estimations of the local interfacial impedance and the local ohmic impedance, which were in excellent agreement with the simulations. The results demonstrate that the local impedance measurement itself cannot be used to estimate the surface area sampled by the LEIS probe. The area sampled must be determined instead by the probe geometry.

In this study, the electrical conductivity of undoped nanocrystalline thin films of cerium dioxide was studied by impedance spectroscopy in the temperature range from room temperature to 350°C in different atmospheres. Two types of films were studied: sample 1, a strongly oriented columnar film (thickness 75 nm); and sample 4, a less oriented 125 nm thick film. Except in one case, the impedance response of thin films, incorporated in the Pt/(n-100)Si/CeO 2-x /Pt multilayer structure, consisted of a single relaxation time. Conductivity and dielectric properties of both types of films were derived from an equivalent circuit consisting of a resistance in parallel with a constant phase element. The conductivity of CeO 2-x thin films was thermally activated with activation energies from ∼0.3 to ∼ 0.5 eV, and did not depend on the type of film. The absolute value of conductivity of the less oriented film (sample 4) was found to be two to three orders of magnitude higher than that of the highly oriented film (sample 1).

In this paper we report on the corrosion behavior of Ti 3 GeC 2 and Ti 2 AlN in a 1 M NaOH solution, investigated by electrochemical impedance spectroscopy (EIS), polarization, and (-potential measurements. The EIS results for Ti 3 GeC 2 and some results for Ti 2 AlN could be fitted to a complex equivalent circuit, where the double layer is represented by a constant phase element. The passive film is represented by a polarization resistance in series with a parallel connection of a resistance of the passive film (R pf ) and its capacitance (C pf ). In both cases passive layers were formed. Based on the ζ-potential measurements, we conclude that the passivating layer that forms on Ti 3 GeC 2 , over a wide pH range, is most likely GeO 2 -based, while the one formed on Ti 2 AlN is most likely Al 2 O 3 -based and/or TiO 2 -based.

In order to investigate the initial stage corrosion mechanism of a hot-dip-coated zinc surface, the corrosion characteristics of two spangle sectors, the shiny sector and the dull sector, were tested by electrochemical methods. Also, initial stage corrosion behaviors of microstructures were observed by using in situ electrochemical-atomic force microscope (EC-AFM). From the results of potentiodynamic polarization tests in 0.1 M NaOH, it was found that there were instabilities of passivation current densities around-0.55 V (vs. SCE), which seem to be related to unstable corrosion product films on the spangle sectors in the initial stage of corrosion. The constant phase element value calculated from electrochemical impedance spectroscopy confirmed that the film on the shiny sector is more stable than that on the dull. The in situ EC-AFM experiment in 0.01 M NaOH showed a lath-like structure, the characteristic microstructure of the dull sector that served for prior sites of ZnO/Zn(OH) 2 formation and pit occurrence. Also, the initial stage corrosion behavior, formation, pitting, and the early break down of corrosion product film were visualized by in situ AFM observation in distilled water.

Effects of crystal structure on the electrochemistry of boron-doped high temperature-high pressure (HTHP) diamond single crystals grown from a Ni-Fe-C melt are studied. On the {111}, {100}, and {311} faces, the linear and nonlinear electrochemical impedance measurements were performed and the rate of electron transfer for Fe(CN) 3-/4- 6 was evaluated. Like polycrystalline chemical vapor deposited films the HTHP electrodes equivalent circuit includes a constant phase element. The uncompensated acceptor concentration in the semiconductor diamond was determined from Mott-Schottky plots and amplitude-demodulation measurements and was found to vary in the range of 10 18 to 10 21 cm -3 . The difference in the electrochemical behavior of individual crystal faces is primarily attributed to different boron concentrations in the growth sectors associated with the faces.

Electrochemical impedance spectroscopy was used in the study of lithium insertion in a WO 3 film Spectra obtained at different potentials showed the characteristic shape of a diffusion process, with a Warburg regime at high frequencies and a capacitive branch at low frequencies arising from the charge storage associated with the intercalation of Li + . But the low frequency wing showed, as in many other reports, a pronounced dispersion which could not be accounted for solely by the diffusion capacitance. The possibility of an additional kinetic process was investigated. A number of models accounting for such effect were considered, including the constant phase element restricted diffusion model that differentiates diffusion from blocking effects and another model with fast and slow charging processes. The evolution of the impedance with charge-discharge cycles was considered as well It was found that a suitable interpretation of the experimental results is provided by a new model that considers the coupling of diffusion and the solid-state reaction whereby inserted ions are incorporated in fixed sites of the lattice. This model could be further elaborated on the basis of a diffusion and multiple trapping scheme, which provides an ordinary or Warburg diffusion region in the range of highest frequencies, and additional components at lower frequencies which reflect the kinetics of the ion immobilizing process and which in some cases show an anomalous diffusion pattern. This explanation was found consistent with the results of complementary techniques of measurement such as the electro-optical transfer function.

It is argued that a porous insertion electrode can be modeled, for purposes of ac impedance analysis, by a modified Randles equivalent circuit containing a generalized constant-phase-angle impedance in series with the double-layer capacitance. The impedance spectrum of the disintercalation system Li/sub 1//sup -/..integral..CoO/sub 2/ showed two time-dependent semicircles, indicating the need for a further modification of the equivalent circuit by a physical process tha could be represented by a resistor/capacitor combination. An adsorption process and a Li/sup +/-ion-electrolyte surface layer are each shown to refine to identically low R factors and to be represented by equivalent circuits that transform on into the other, each having circuit values with reasonable values for the physical processes represented. Time-dependent experiments could eliminate the adsorption models, and electron microscopy gave direct evidence for the surface-laye model; further indirect evidence came from constant-voltage experiments and the preparation of electrodes with greater electrode/electrolyte interface area. Although propylene carbonate appears to be kinetically stabl in contact with Li/sub 1//sup -/..integral..CoO/sub 2/ at potentials of up to 4.5V vs. lithium, mixtures of propylene carbonate with oxide particles having /chi/ = 0.34 produce thick polymer films.

A method to determine the equivalent circuit of a semiconductor/electrolyte/counterelectrode cell is presented. The electrical analog of the phenomenon leading to frequency dependent behavior has been taken to be a resistor in series with a capacitor. The case where a large number of RC elements are present has been determined in the following way. The values of the capacitances and time constants of these elements have been assumed to be distributed exponentially. For this distribution it follows that the equivalent circuit can be represented as a frequency dependent resistor in parallel with a frequency dependent capacitor. Expressions for the frequency dependent resistance and capacitance have been derived. The impedance and admittance responses of a large number of circuits have been simulated. The circuit which best represented an n-Fe/sub 2/O/sub 3/ (1% TiO/sub 2/)/1M NaOH/Pt cell was determined by comparing the simulated responses with the measured responses. 18 refs.