The Ngai coupling model of relaxation: Generalizations, alternatives, and their use in the analysis of non-Arrhenius conductivity in glassy, fast-ionic materials
The ionic conductivity of glassy, fast-ion-conducting materials can show non-Arrhenius behavior and approach saturation at sufficiently high temperatures [J. Kincs and S. W. Martin, Phys. Rev. Lett. 76, 20 (1996)]. The Ngai coupling model was soon applied to explain some of these observations [K. L. Ngai and A. K. Rizos, Phys. Rev. Lett. 76, 1296 (1996)], but detailed examination and generalization of the coupling model suggested the consideration of a related, yet different, approach, the cutoff model. Although both the coupling and cutoff models involve a shortest nonzero response time, τ c , and lead to single-relaxation-time Debye response at limiting short times and high frequencies, they involve different physical interpretations of their low- and high-frequency response functions. These differences are discussed; the predictions of both models in the frequency and time domains are compared; and the utility of both models is evaluated for explaining the non-Arrhenius conductivity behavior associated with the dispersed frequency response of z AgI +(1−z)[0.525 Ag 2 S+0.475B 2 S 3 :SiS 2 ] glass for z=0 and 0.4. The cutoff approach, using simulation rather than direct data fitting, yielded semiquantitative agreement with the data, but similar analysis using the coupling model led to poor results. The coupling model leads to an appreciable slope discontinuity at the τ c transition point between its two separate response parts, while the cutoff model shows no such discontinuity because it involves only a single response equation with a smooth transition at τ c to limiting single-relaxation-time response. The greater simplicity, utility, and generality of the cutoff model suggest that it should be the favored choice for analyzing high-conductivity data exhibiting non-Arrhenius behavior
