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 nx1. At still a lower frequency nx2 the cooperative ion hopping dispersion takes over. The independent ion hopping frequency n0 of the coupling model is calculated from the parameters characterizing the cooperative ion hopping dispersion. It is found for all ionic conductors that nx1@n0, and n0 always fall inside the frequency region nx1.n.nx2. The empirical results leads to a qualitative theory for the origin of the NCL, which gives physical meanings of the two crossover frequencies nx1 and nx2, as well as explaining the role of the independent hopping frequency n0, 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.