Orthonormal Scales in a Nyquist Diagram

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Orthonormal scales should be used for Nyquist impedance plots. The length from 0 to 1 along the imaginary axis should be equal to the length from 0 to 1 along the real axis. Otherwise, semicircle graphs are not semicircles and it becomes difficult to measure angles. This Demonstration presents two examples: the impedance for a Tafelian redox system and the Randles circuit with Warburg impedance. Orthonormal and non-orthonormal plots are compared (blue curves and scale: non-orthonormal scale; orange curves and scale: orthonormal scale).

Contributed by: Jean-Paul Diard and Claude Montella (February 2019)
(Bio-Logic SAS and Université Grenoble Alpes, LEPMI, Grenoble, France)
Open content licensed under CC BY-NC-SA


This Demonstration uses an orthonormal representation for the impedance of electrochemical systems. Two examples are dealt with, A and B.

A. equivalent circuit for a Tafelian electrochemical system with:


where is the angular frequency, is the charge transfer resistance and is the interfacial double-layer capacitance.

B. Randles circuit for the electrochemical (E) reaction occurring at the interface with a quiescent solution:


where is the Warburg parameter.


[1] J.-P. Diard, B. Le Gorrec and C. Montella, Cinétique electrochimique, Paris: Hermann, 1996.

[2] C. Montella, J.-P. Diard and B. Le Gorrec, Exercices de cinétique electrochimique, II Méthode d'impédance, Paris: Hermann, 2005.

[3] M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy, Hoboken, NJ: John Wiley & Sons, 2008.


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