Mirna Urquidi-Macdonald

Applications of Kramers—Kronig transforms in the analysis of electrochemical impedance data—III. Stability and linearity

Abstract The application of the Kramers—Kronig (K—K) transforms in the analysis of electrochemical impedance data is examined with reference to the conditions of stability and linearity. We show that for iron in 1 M H 2 SO 4 , with the impedance being measured using a frequency response analyzer, the K—K transforms are insensitive to violation of linearity but they are very sensitive to interfacial instability. Thus, we conclude that if a system is linear, stable, and causal and if the impedance is finite over the frequency domain, the impedance data will transform according to the K—K relationships. However, if experimental impedance data are found to transform the four conditions noted above are not necessarily satisfied, but if the impedance data do not transform, we can stipulate that all four conditions do not hold simultaneously. It can be shown that this is a direct consequence of the complex function (impedance, Z ) being analytical and hence obeying Cauchys integral. However, the converse of Cauchys theorem is not true; that is, if Z obeys Cauchys theorem is not necessarily analytical. We also discuss the “tails” and “singularity” problems that arise when numerically evaluating the K—K transforms. If these problems are not properly recognized, they may lead to the erroneous conclusion that the K—K transforms cannot be used to validate impedance data when the imaginary component does not tend to zero as the frequency tends to zero or infinity.

Application of Kramers‐Kronig Transforms in the Analysis of Electrochemical Impedance Data II . Transformations in the Complex Plane

Algorithms have been developed to apply the Kramers-Kronig transforms in the analysis of experimental electrochemical impedance data. The application of these algorithms is illustrated by transforming calculated impedance data for an electrical equivalent circuit, by transforming experimental data for TiO/sub 2-/coated carbon steel in HCl/KCl solution at 25/sup 0/C, and by analyzing data for an aluminum alloy in 4M KOH at 60/sup 0/C. These transforms, coupled with statistical techniques, provide a powerful means of evaluating the validity of impedance data with respect to spurious errors that are present in either the real or imaginary component, and with respect to system stability.

Application of Kramers‐Kronig Transforms in the Analysis of Electrochemical Systems I . Polarization Resistance

A Kramers‐Kronig transform that is useful for validating electrochemical and corrosion impedance data is employed to calculate the polarization resistance from the frequency‐dependent imaginary component. Applications of the transform in the analysis of experimental impedance data for carbon steel in solution at ambient temperature and for aluminum and Al‐0.1P‐0.1In‐0.2‐Ga‐0.01Tl alloy in solution at 25°C are discussed.

A coupled environment model for stress corrosion cracking in sensitized type 304 stainless steel in LWR environments

Abstract A physico-electrochemical model has been developed to describe intergranular stress corrosion cracking (IGSCC) in sensitized Type 304 stainless steel (SS) in simulated light water reactor (LWR) environments. This model differs from previously reported models in that the internal and external environments are coupled by the need to conserve charge in the system. Thus, solution of Laplaces equation for the external environment, assuming that oxygen reduction on the external surfaces consumes the positive current emanating from the crack mouth, yields a boundary condition for solving Laplaces equation for the internal crack environment. Metal dissolution at the crack tip is described by the slip dissolution model, with the frequency of rupture of the passive film being a strong function of the stress intensity factor. The reduction of oxygen on the external surfaces is described in terms of a general Butler-Volmer equation that incorporates mass transport and charge transport phenomena. In this way, the model incorporates the effects of oxygen concentration, flow rate, and the conductivity of the external environment as well as accounting for the effect of stress on crack growth.

A simplified method for estimating corrosion cavity growth rates

A simplified method is proposed for calculating corrosion cavity propagation rates. This method is based on an assumption that if the rate of an electrode reaction depends (in an explicit form) only on the potential, the pit growth rate depends only on the concentration of those species that determine the potential distribution near the metal within the cavity. The advantage of this method is that it permits one to predict the rates of cavity propagation without knowing various parameters, such as the equilibrium constants of some chemical reactions and diffusion coefficients of species that are present at relatively low concentrations near the electrode surface. The analytical expressions for calculating propagation rates of cylindrical and hemispherical pits are compared with available experimental data. The influence of aggressive anions on the pit propagation rate has been investigated. It is shown that transport processes in the internal environment do, in the general case, influence the kinetics of metal corrosion.

Theoretical Distribution Functions for the Breakdown of Passive Films

Theoretical distribution functions for the critical voltage (V/sub c/) and induction time (t/sub ind/) for the breakdown of passive films in aqueous systems containing aggressive anions are derived. The variations of these distributions with the parameter ..cap alpha..(dependence of the film/solution interfacial potential on applied voltage), halide activity and pH are explored by numerical analysis. The theoretical distribution functions are found to closely mimic the experimentally determined distributions in V/sub c/ and t/sub ind/ for the breakdown of passive films of Fe-17 Cr in 3.5% NaCl solution of 30/sup 0/C, as reported by Shibata. The findings support the hypothesis that cation vacancy diffusivity is an important property in determining the susceptibility of passive films to breakdown under anodic polarization conditions.

Development of fast algorithms for estimating stress corrosion crack growth rate

A simplified method is proposed for modeling the chemistry and potential distribution in a stress corrosion crack in sensitized stainless steel in boiling water reactor (BWR) coolant environments. The model is based on an assumption that only those species that are present in the largest concentrations in the crevice determine the potential distribution down the crack. The advantage of this method is that it permits simplification of the mathematics and allows predictions to be made of the potential and concentration distributions without knowing various parameters, such as the equilibrium constants for homogeneous chemical reactions in the cavity and diffusion coefficients of species that are present at relatively low concentrations near the crack tip. In some important cases, analytical expressions can be obtained for the pH, potential near the crack tip, and crack propagation rate. The conditions for which the potential on the crack flanks and that in the vicinity of the crack tip coincide with the free corrosion potential in the local environment, and hence, for which there exists a balance between rates of the local anodic and cathodic partial processes, are determined. The impact of the potential drop in the external environment on the potential and concentration distributions down the crack and on the crack propagation rate is also investigated. Excellent agreement is obtained between calculated and measured crack growth rates.

Distribution functions for the breakdown of passive films

A deterministic treatment is presented of the statistical nature of the breakdown of passive films on metal surfaces, in which it is assumed that breakdown sites on the surface are normally distributed in terms of the cation vacancy diffusivity (D) or log D. This analysis, which is based on the point defect model for the breakdown of passive films, predicts normal or near-normal distributions in the breakdown voltage, depending upon whether it is log D or D that is normally distributed. The model also yields distribution functions for the induction time that mimic the highly asymmetric form exhibited by experimental data. By using values for D, log D and their associated standard deviations, determined from the distributions in the breakdown voltage, the point defect model is able to account quantitatively for the experimentally observed distributions in the induction time for the breakdown of passive films on Fe-17Cr in 3.5% NaCl solution at 30°C, as reported by Shibata[1].

Evaluation of Alloy Anodes for Aluminum‐Air Batteries II . Delineation of Anodic and Cathodic Partial Reactions

The design, calibration, and operation of a source/collector electrochemical cell for delineating anodic and cathodic partial currents for reactive metals in aqueous media is described. This cell has been used to measure the hydrogen evolution current on aluminum and aluminum alloys in 4M KOH at 25/sup 0/, 50/sup 0/, and 80/sup 0/C over a wide range of potential. These data were then combined with the total current to calculate the anodic partial current as a function of potential. The data show that aluminum is a passive metal in 4M KOH at 25/sup 0/ and 50/sup 0/C, but that at 80/sup 0/C it undergoes transpassive dissolution over the entire potential range that is accessible.

Electrochemical Impedance Spectroscopic Study of Passive Zirconium I. High-Temperature, Deaerated Aqueous Solutions

The development of deterministic models for predicting the accumulation of corrosion damage to zirconium and Zircaloys in pressurized water reactor (PWR) coolant environments requires the acquisition of values for various model parameters. In the present work, the point defect model (PDM) was further developed to account for the properties of passive films comprising hydride barrier layers and porous oxide outer layers that form on zirconium and Zircaloys in high-temperature, hydrogenated aqueous solutions. The model parameter values were extracted from electrochemical impedance spectroscopic data for zirconium in hydrogenated, borate buffer solution [0.1 M B(OH) 3 + 0.001 M LiOH, pH 6.94] at 250°C by optimization. The results indicate that the corrosion resistance of zirconium in high-temperature, hydrogenated aqueous solutions is dominated by the outer layer, as was found to be the case for nonhydrogenated solutions where a defective oxide barrier layer forms. The impedance model based on the PDM provides a good account of the growth of the bi-layer passive films described above, and the extracted model parameter values might be used, for example, for predicting the accumulation of general corrosion damage to Zircaloy fuel cladding in PWR operating environments.