Numerical comparison of usual Arrhenius-type equations for modeling ionic transport in solids

Abstract

The primary objective of this work is to draw attention to the inherent differences between Arrhenius-type equations used for modeling ionic conductivity in solids. The used methodology comprises a comparison between the two most used Arrhenius-type equations by generating data applying one equation and fitting them by using the other equation. Data are generated in different conditions by varying input parameters such as the extent of the temperature range and the average temperature of this range, as well as the pre-exponential term and activation energy of the Arrhenius-type equation. The fitting procedure is performed by plotting the generated data based on the linearized form of those equations followed by the linear fitting. The results show a substantial difference between the activation energy value of those equations, which is mainly dependent on the average temperature of the range. In contrast with the widely held perception that differences in the activation energy of both equations usually can be neglected, this work reveals that relative differences between activation energy of these equations are usually significant. These relative differences are often around 10% and may reach over 15% depending on a combination of intrinsic and extrinsic input parameters such as low activation energy and high-temperature of measurement, respectively. An analytical equation that expresses the relative difference between activation energy calculated from both equations is also presented and discussed.

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Acknowledgments

The author acknowledges the São Paulo State Foundation (FAPESP) for its support of this work under CEPID (grant number 2013/07793-6). Also, the author thanks Brazil’s National Council for Scientific and Technological Development (CNPq) and Brazil’s Federal Agency for the Support and Improvement of Higher Education (CAPES) for doctoral scholarships granted in Brazil (grant number 140456/2014-7) and France (grant number 88881.132930/2016-01), respectively. The author is also in debt with his professors, Ana Candida M. Rodrigues, Dulcina Maria P. F. de Souza, and Edgar D. Zanotto for the first reminding about the differences between the two equations. In particular, the author gratefully acknowledges Jean-Louis Souquet for his useful comments in the theoretical background of this work and Norma Maria Pereira Machado, who made relevant suggestions.

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Correspondence to Rafael Bianchini Nuernberg.

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Nuernberg, R.B. Numerical comparison of usual Arrhenius-type equations for modeling ionic transport in solids. Ionics 26, 2405–2412 (2020). https://doi.org/10.1007/s11581-019-03243-7

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Keywords

  • Ionic conductivity
  • Arrhenius-type equations
  • Activation energy