Small power-law dependence of ionic conductivity and diffusional dimensionality in β-alumina

O. Kamishima, Y. Iwai, J. Kawamura

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)


    AC conductivity σ(ω) of single crystals of Ag β-alumina and Na β-alumina has been studied in the temperature range from approximately 100 K to room temperature. The DC regime of σ(ω), which had a close relation to the ion dynamics for the long-range diffusion, was found to have the small power-law dependence σ(ω) ∝ ωn with frequency exponent n = 0.11-0.15, not σ(ω) ∝ ω0 = const. In higher frequencies, the σ(ω) was monotonically increasing with Log-frequency and was put into Jonscher's universal law (σ(ω) ∝ ω0.6). The β-alumina is an ideal two-dimensional super ionic conductor. Its low-dimensionality and the scaling theory for a random walk enable us to understand the small power-law dependence of ionic conductivity. We suggested that a "scale-invariance" would hold true behind the super ionic conduction in the self-similarity point of view.

    Original languageEnglish
    Pages (from-to)89-95
    Number of pages7
    JournalSolid State Ionics
    Publication statusPublished - 2015 Nov 15


    • Fractal
    • Power-law conductivity
    • Scale-invariance
    • Super ionic conductor
    • β-Alumina

    ASJC Scopus subject areas

    • Chemistry(all)
    • Materials Science(all)
    • Condensed Matter Physics


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