Cage decay, near constant loss, and crossover to cooperative ion motion in ionic conductors: Insight from experimental data

Experimental frequency-dependent conductivity relaxation spectra of a number of molten, glassy, and crystalline ionic conductors that show both the presence of the near constant loss (NCL) and the cooperative ion hopping contribution are analyzed. On decreasing frequency, the NCL appears first but terminates at some frequency νₓ₁. At still a lower frequency νₓ₂ the cooperative ion hopping dispersion takes over. The independent ion hopping frequency ν₀ of the coupling model is calculated from the parameters characterizing the cooperative ion hopping dispersion. It is found for all ionic conductors that νₓ₁ν₀, and ν₀ always fall inside the frequency region νₓ₁>ν>νₓ₂. The empirical results leads to a qualitative theory for the origin of the NCL, which gives physical meanings of the two crossover frequencies νₓ₁ and νₓ₂, as well as explaining the role of the independent hopping frequency ν₀, in determining them. The weak temperature dependence of the NCL has been recaptured by the qualitative theory. An improved understanding is gained of the evolution of the ion dynamics from early times when the cages decay very slowly with time, giving rise to the near constant loss, to long times when ions move cooperatively, leading finally to dc conductivity.