TUTORIAL ON ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY

David C. Silverman

Table of Contents

Corrosion Rate Estimation

1. Curve-fit the impedance spectrum using an appropriate model bearing in mind that the constant phase element should be used until proven it is not needed.
2. Estimate the polarization resistance from fitted curve applying the expression   .    This term should be calculated from the model.
3. Curve-fit a small amplitude (~20mV) DC polarization curve to Butler-Volmer type equation to obtain the proportionality constant, B which is related to the anodic and cathodic Tafel slopes. If the Tafel slopes cannot be estimated, then assume a reasonable value for B (e.g. often 0.015 to 0.03V will suffice). Note that the polarization resistance estimated by this technique should be comparable to that estimated from the impedance spectrum.
4. Calculate the corrosion current from:   .
5. Use an appropriate equivalent weight of the alloy to convert from current density, the units of Icorr, to mass loss.

Curve-fitting of the impedance spectrum can be accomplished by using the models discussed in this tutorial as a starting point. Alternatively, software is commercially available to enable appropriate curve-fitting. The assumption is made in this tutorial that the zero frequency resistance has been estimated properly. A small amplitude DC polarization curve can be generated by following the procedure in ASTM G59 “Conducting Potentiodynamic Polarization Resistance Measurements”. A scan rate of 0.1 mV/s can be used and still have a scan generated within a couple of minutes.

This figure shows a result in which the fit to the Butler Volmer type of equation is reasonable. The curve-fit was done by adjusting the anodic Tafel slope, the cathodic Tafel slope, and the polarization resistance. Assuming one anodic and one cathodic reaction and the corrosion potential far removed from the equilibrium potential, the constant B can be estimated from the equation   .    where ba and bc are the anodic and cathodic Tafel slopes. Note that the assumption of one anodic and one cathodic reaction with no reverse reaction is just that, an assumption which should be verified in every case.

The complicating factor is that sometimes experimental artifacts can prevent a fit that can produce appropriate values. This figure shows a polarization resistance result where electrical interference affected the current output. Tafel slope values estimated from the curve were not reasonable. Interestingly, the polarization resistance estimated from this type of curve-fit has often been found to be reasonable even when the Tafel slopes are not. As mentioned above, the value of B can often be assumed to lie between 0.015V and 0.03V when the Tafel slopes are not reasonable or cannot be estimated.

The following table shows the type of agreement that can be achieved between corrosion rates estimated from mass loss and those estimated from electrochemical impedance spectroscopy. The fluid was a complex waste stream and the alloy was carbon steel. The impedance spectra were similar to that shown above and that shown in the section entitled Pseudoinductance . The agreement between the mass loss and impedance results strongly suggests that the resistance assumed to be the polarization resistance from the models was, indeed, the polarization resistance. The results have been extracted from D. C. Silverman, Electrochimica Acta, 38, 2075 (1993).



Time-averaged Corrosion Rate for Waste Samples (mm/y)
Impedance	Mass Loss
0.36	0.30
0.44	0.38
0.12	0.30
8.5	7.4
1.6	1.8
0.15	0.19
0.30	0.43


Additional discussion and examples of predicting corrosion rates from electrochemical impedance spectroscopy can be found in D. C. Silverman and J. E. Carrico, "Electrochemical Impedance Technique - A Practical Tool For Corrosion Prediction", Corrosion, Vol. 44, No. 5, p. 280 (1988) ¹    (517k), D. C. Silverman, "Rapid Corrosion Screening in Poorly Defined Systems by Electrochemical Impedance Technique", Corrosion, Vol. 46, No. 7, p. 589 (1990) ¹    (569k), and D. C. Silverman, "Corrosion Prediction from Circuit Models - Application to Evaluation of Corrosion Inhibitors", in Electrochemical Impedance: Analysis and Interpretation (J. R. Scully, D. C. Silverman, and M. W. Kendig, ed.), ASTM STP 1188, p. 192, American Society for Testing and Materials, Philadelphia, PA, 1993.

An order of magnitude rule of thumb relating the polarization resistance to corrosion rate calculated in mpy is shown in the following table. These numbers were generated using a Tafel constant of 0.025V. As an example of accuracy, in the case of iron with a valence of 2, the corrosion rates in mpy are about twice the number shown.



Order of Magnitude Estimates of Corrosion Rates
Polarization Resistance (ohm-cm2)	Corrosion Rate mpy
10	103
102	102
103	10
104	1
105	10-1
106	10-2
107	10-3
Corrosion rates are usually determined by extrapolation for polarization resistances greater than 104 ohm-cm2

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David C. Silverman, Ph.D. - Primary Consultant
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