Theories and Models of Ion Diffusion

  • Junko Habasaki
  • Carlos León
  • K. L. Ngai
Chapter
First Online:
Part of the Topics in Applied Physics book series (TAP, volume 132)

Abstract

This chapter describes some models that are often used in trying to understand experimental data and fundamental questions in ion diffusion in ionically conducting materials. The basics of linear response theory are introduced first, with the definition of the linear response function, the Kramers-Kronig relations, and the Fluctuation-Dissipation theorem. A second section is devoted to present the Debye model and several other phenomenological descriptions of dielectric relaxation in materials whose electrical response is dominated by bound charges. This helps to understand the conductivity relaxation that occurs in materials with mobile charges like ionic conductors, and to introduce the so called conductivity formalism and electric modulus formalism for the analysis of experimental data of ion diffusion dynamics. A simple model of ion hopping is introduced that accounts for the thermally activated behavior often found in ionic conductivity data. The relationship between non-Debye relaxation and non-Gaussianity of the dynamics in the real space is also discussed in this chapter. Finally, three different models for ion diffusion are described in some detail. These are the Random Barrier Model, the MIGRATION concept, and the Coupling Model.

Keywords

Dielectric Relaxation Mean Square Displacement Electric Modulus Wait Time Distribution Linear Response Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Junko Habasaki
    • 1
  • Carlos León
    • 2
  • K. L. Ngai
    • 3
  1. 1.Tokyo Institute of TechnologyYokohamaJapan
  2. 2.Facultad de FisicaUniversidad Complutense MadridMadridSpain
  3. 3.IPCFCNRPisaItaly

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