PEDRA, Parallel Electrical Dielectric Response Analysis, is my legacy. PEDRA is an approach aimed at identifying dielectric responses that the collected impedance data can support. PEDRA alone maybe sufficient to achieve correlation between EIS characterization and in-service performance. If not alone, PEDRA will be useful to identify number and types of responses prior using the traditional Equivalent Circuit Model, ECM, approach. Either way, it is hoped that seeing impedance spectroscopy from a different vantage point contributes to the popularity, usefulness, and the industrial community acceptance of this powerful technique toward technical engineering endeavors.
Back Story
I am a Materials Engineer with a BS in Material Science with over 30 years of experience with Electrical Impedance Spectroscopy (EIS). During the 1970 and 80s, I was employed at Teledyne Wah Chang, a Zr, Ti, Hf, V materials producer, in Albany, Oregon USA. At that time there was considerable interest in improving the service life of Zr Nuclear Fuel cladding. Surface Science techniques were gaining interest, however, I was using primarily autoclave tests and optical microscopy to understand both uniform and nodular oxide growth on Zircaloy. This was part of a larger endeavor to achieve longer fuel cycles for PWR or BWR fuel cores.
During that time, I listened to a talk promoting EIS by Digby MacDonald. Intrigued with the versatility, flexibility and moderate cost, we purchase a system and invited Digby to our lab. Under his direction we began collecting data using an x/y plotter and an oscilloscope. We calculated the impedance response from lissou figures. Reporting results were limited to plotting Nyquist and Bode Plots.
Then came software applications to fit the impedance data to equivalent circuit models (ECMs). The first ECMs were Randles models describing steady state corrosion. The data I was collecting on high impedance oxide films (>10^10 ohms) was quite different than the low impedance corrosion applications. The available software at the time was not sufficient to either characterize or correlate measurements to in-service behavior. My search for a solution began.
PEDRA Approach
The concept of EIS spectra containing dielectric responses rather than relaxation responses, was inspired by visit with A K Jonscher concerning his book: Dielectric Relaxation in Solids, 1983. In the preface, Dr Jonscher stated “The quest for understanding the laws of nature constitutes one of man’s most basic urges and lies at the origin of all discovery. Another is the urge to harness the discoveries to practical ends which is the mainspring of technology”. I was bitten by the phrase "to harness discoveries to practical ends". What if EIS is more about identifying 'dielectric responses' than fitting data to an envisioned physical model?
September 1991 I started work at Atomic Energy of Canada Limited (now Canadian Nuclear Labs). In the summer of 1995, the PEDRA application was created, using WaveMetrics IGOR PRO as a development tool. In 1996, we used Atomic Force Microscopy, AFM, to correlate of the power law term, n, with the fractal quality of the oxide surface. In May 2003, using FIBS and TEM, the fractal term was correlated to the observed oxide porosity within the barrier oxide film (see the slide shown above). During this stage of development an extensive amount of data was collected both in laboratory tests and on removed CANDU pressure tubes in a Hot Cell facility. However, in spite of these efforts, a concise method to relate the multi-parameter results to in-service behaviour eluded us. In May 2004 the EIS was abandoned.
In September 2012 I retired but continued to refine the PEDRA approach on data that had been previously collected. I was granted permission from CNL to published results on removed pressure tube results in 2013, yet I still had difficulty communicating multi-parameter results to in-service behavior. In February 2016, I stumbled on the idea of using a "SpecView" Gaussian line graph I used to fit the data, could be used to display results as overlay graphs. Using overlay the Gaussian presentation multiple data sets could be visually compared with each other on a signal graph.
PEDRA Revision 9.0
2013 to 2024 I compared the PEDRA application to other commercial impedance software, reviewed published work and had conversations with software developers and EIS users. In February 2025, convinced that the PEDRA offered value to the EIS technique, I employed byte physics, Physics Software Development, to revise and improve PEDRA.
The result is PEDRA 9.0 2025. Version 9.0, although quite capable, is not a finished product but is an offering to the EIS community to improve upon. It has a simple user interface, has three methods of importing data files, ability to handle multiple data files, determines initial parameter values from the data plot, has an option to set variable constraints, an user interactive iterative hold-release curve fitting method, overlay "SpecView" plots of results, open software architecture and inherent powerful computational and graphs capability (IGOR PRO).
The central Expandable Equivalent Circuit Model, EECM, describes individual dielectric response that can be supported by the data (currently up to four responses can be included). There are two types of EECMs, 1) an independent (parallel current paths), series R-CPE dielectric elements (Debye form) and 2) dependent (cascading R current paths) series R-CPE elements (Randle form).
In addition to the central EECM, there are the three common recognized high or low frequency boundary contributions: 1) high frequency, high current inductance (e.g. low impedance batteries and super-capacitors), 2) high frequency, low current capacitance (e.g. high impedance polymer and oxide barrier films), and 3) low frequency, inductance (moderate impedance charge polarization, steady state active dissolution). The first two are implemented in the PEDRA 9.0.1.