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Bode plots, corrected for Ohmic resistance, logarithmic plots of the imaginary component of the impedance, and effective capacitance plots are shown to be useful complements to the more traditionally used complex-plane and Bode representations for electrochemical impedance data. The graphical methods are illustrated by synthetic data and by experimental data associated with corrosion in saline environments. Bode plots are shown, in particular, to be confounded by the influence of electrolyte resistance. The plots proposed here provide useful guides to model development for both reactive and blocking systems. The logarithmic plots of the imaginary component of the impedance and effective capacitance plots are useful for all impedance data, and the correction for Ohmic resistance in Bode plots is useful when the solution resistance is not negligible. 12 Graphical methods provide the first step toward interpretation and evaluation of impedance data. A number of authors have described graphical methods based on a deterministic model for a given process. Mott-Shottky plots of 1/C sc 2 as a function of potential are used to obtain flatband potentials and doping levels characteristic of semiconducting systems.1 A graphical method was reported by Tribollet et al. that can be used to extract Schmidt numbers from experimental data in which the convective diffusion impedance dominates.2 The technique accounts for the finite value of the Schmidt number. Graphical methods in terms of a dimensionless frequency scaled by rotation speed are commonly used for the interpretation of electrohydrodynamic impedance measurements.3 Jansen and Orazem describe a graphical superposition of impedance data collected at different temperatures that reveals the influence of a single dominant activation-energy controlled process in solid-state systems.4 When a specific model is not postulated, typically two types of graphical representations are used: complex-impedance-plane plots, often called Nyquist plots, and Bode plots. [5][6][7] The Bode representation consists of the logarithm of impedance magnitude and the phase angle, both plotted as a function of frequency on a logarithmic scale. These types of representation have become the standard in impedance analysis for any complex quantity, e.g., admittance, complex capacitance, and electrohydrodynamic impedance, as well as electrochemical impedance.The object of this work is to demonstrate the limitations of the usual methods for representing impedance data and to suggest some useful alternatives. The proposed graphical methods are illustrated both by synthetic data and by experimental data associated with corrosion of a magnesium alloy AZ91 in saline environments. Synthetic DataThe methods for graphical representation and interpretation of electrochemical impedance are presented here for data characteristic of active and blocking electrodes. The classification of active systems is represented by a Randles circuit, as presented in Fig. 1a. The classification of blocking systems is represented ...

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The corrosion behavior of pure magnesium in sodium sulfate solutions was investigated using voltammetry and electrochemical impedance spectroscopy with a rotating disk electrode. The analysis of impedance data obtained at the corrosion potential was consistent with the hypothesis that Mg corrosion is controlled by the presence of a very thin oxide film, probably MgO, and that the dissolution occurs at film-free spots only. This hypothesis was substantiated both by the superposition of the EIS diagrams, obtained for different immersion times and for two Na 2 SO 4 concentrations once normalized, and by use of scanning electrochemical microscopy in the ac mode to sense the local conductivity of the material. On the basis of the electrochemical results, a model was proposed to describe magnesium corrosion at the open-circuit potential. Simulation of the impedance diagrams was in good agreement with the experimental results.

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 ͑CPE͒ but can be considered to be only an apparent CPE because the CPE exponent ␣ is a function of frequency.

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID : 2418To link to this article : URL : http://dx.Geometry-induced current and potential distributions modify the global impedance response of a disk electrode subject to faradaic reactions. The problem was treated for both linear and Tafel kinetic regimes. The apparent capacity of a disk electrode embedded in an insulating plane was shown to vary considerably with frequency. At frequencies above the characteristic frequency for the faradaic reaction, the global impedance response has a quasi-constant-phase element ͑CPE͒ character, but with a CPE coefficient ␣ that is a function of both dimensionless frequency K and dimensionless current density J. For small values of J, ␣ approached unity, whereas, for larger values of J, ␣ reached values near 0.78. The calculated values of ␣ are typical of those obtained in impedance measurements on disk electrodes. For determining the interfacial capacitance, the influence of current and potential distributions on the impedance response cannot be neglected, even if the apparent CPE exponent ␣ has values close to unity. Several methods taken from the literature were tested to determine their suitability for extracting interfacial capacitance values from impedance data on disk electrodes. The best results were obtained using a formula which accounted for both ohmic and charge-transfer resistances.

Constant-Phase Elements (CPE) are often used to fit impedance data arising from a broad range of experimental systems. Four approaches were used to interpret CPE parameters associated with the impedance response of human skin and two metal oxides in terms of characteristic frequencies and film thickness. The values obtained with each approach were compared against independent measurements. The power-law model developed recently by Hirschorn et al. 1,2 provided the most reliable interpretation for systems with a normal distribution of properties. Readers are cautioned that the CPE parameter Q does not provide an accurate value for capacitance, even when the CPE exponent α is greater than 0.9.Electrical circuits invoking constant-phase elements (CPE) are often used to fit impedance data arising from a broad range of experimental systems. The impedance for a film-covered electrode showing CPE behavior may be expressed in terms of ohmic resistance R e , a parallel resistance R || , and CPE parameters α and Q aswhere f is the frequency in units of Hz. When α = 1, the system is described by a single time-constant, and the parameter Q has units of capacitance; otherwise, Q has units of s α / cm 2 or F/s (1−α) cm 2 . 3 Under conditions that (2πf ) α R || Q 1,

The corrosion behavior of as-cast magnesium alloys ͑AM50, AZ91, and AZ91Si͒ was investigated in a 0.1 M sodium sulfate solution at the corrosion potential (E corr ) using electrochemical impedance spectroscopy. Transmission electron microscopy was used to analyze the corrosion product layer, and phase shifting interferometric microscopy was carried out to characterize the reactivity of intermetallic particles. Due to its microstructure, the AM50 alloy presented uniform corrosion during immersion, whereas corrosion of the AZ91 alloys began in the grain body and progressively spread to the eutectic areas. For the AZ91 alloys, the dissolution of the ␣-eutectic phase led to a strong aluminum enrichment of the corrosion product layer and, when a threshold was reached in the level of Al 2 O 3 in the magnesium oxide ͑or hydroxide͒ layer, a change of phenomenology occurred in the impedance diagrams. In addition, electrochemical results revealed that an increase of silicon concentration for the AZ91 alloys decreased the corrosion resistance. This was attributed to an increase of the number of Mg 2 Si particles, accelerating the dissolution of eutectic areas.In the automotive industry, magnesium-aluminum-zinc and magnesium-aluminum-manganese alloys are popular, in particular, the AZ91 and AM50 alloys. The corrosion resistance of magnesiumaluminum alloys has been partly explained in terms of increased passivity by incorporation of aluminum, which stabilizes the magnesium oxide layer even though the layer is thinner when the amount of Al is increased. 1,2 Nevertheless, in the aerospace industry, the use of magnesium alloys ͑Mg-Al with rare-earth elements͒ is limited due to their poor mechanical properties and low corrosion resistance. 3 The primary reason for the low corrosion resistance of magnesium alloys is the internal galvanic attack caused by alloying or impurity elements. Therefore, inclusions of metals with a low hydrogen overvoltage constitute efficient cathodes for magnesium and cause severe galvanic corrosion. 4,5 Fe, Cu, and Ni form particles which are highly cathodic in comparison with the Mg matrix. Ni and Cu are usually at low levels in alloys from primary production. Fe is the most troublesome element in the alloys. 5 The addition of manganese to Mg-Al alloys induces the formation of Al-Mn-Fe particles, and the corrosion resistance of the alloys can be improved by decreasing the galvanic potential difference between the intermetallic particles and the surrounding matrix. More precisely, Lunder et al. 6 showed that the corrosion resistance of the alloys was dependent on the Fe/Mn ratio in the materials and thus in the particles. In fact, the kinetics of the cathodic reaction were strongly influenced by the amount of Mn in the particles.According to Daloz et al.,7 the presence of zinc strongly influences the potential of both matrix and precipitate and thus also has beneficial effects on the corrosion resistance of Mg-Al alloys.For high temperature applications, Mg-Al-Si alloys are used. Silicon hardly dissolve...