Origin of constant loss in ionic conductors

We have analyzed the constant loss contribution to the ac conductivity in the frequency range 10 Hz-1 MHz and temperatures down to 8 K, for two Li ionic conductors, one crystalline (Li0.18La0.61TiO3) and the other glassy (61SiO(2). 35Li(2)O . 3Al(2)O(3).P2O5). As temperature is increased a crossover is observed from a nearly constant loss to a fractional power law frequency dependence of the ac conductivity. At any fixed frequency omega, this crossover occurs at a temperature T such that omega approximate to nu (0) exp(-E-m/k(B)T), where nu (0) is the attempt frequency and E-m is identified with the barrier for Li+ ions to leave their wells.