Power law behaviour of a.c. conductivities

conductivities in glasses have long been found to obey a power law, 

The exponent value of 0.6 in Jonscher regime is considered to arise by the ion-ion interactions, usually of the coulombic type. During the process of the hopping of the ions, even separate hopping events may have a broad distribution of relaxation times, and this effect can manifest as stretching of the relaxation times. Ngai s coupling model accounts for stretched exponential relaxation and considers it as a consequence of 

conductivity activation energy is often designated as E , Eq, E, Ejc and (0) in the literature and all are equivalent. We have used Ej as preferred description in this book although in chapter 6, has been used to make it known that it is an activation barrier. But otherwise represents the primitive activation barrier observed in a.c. measurements. 

There have been several attempts made to correlate p to other conductivity parameters like Edc and inter-carrier-ion distance /. Martin has been successful in correlating p with distance d, which varies as where C is the concentration of carrier ions. In general, p is found to decrease monotonically with increasing concentration. This is in 

CdO and smaller amounts of CdCU, YF3 and LaFs). The modulus relaxation spectrum has been fitted to stretched exponential function and it has been found that p has a roughly constant value in the glassy state and above Tg, it decreases rapidly. Since decoupling index also decreases rapidly above the glass transition temperature, it is suggestive of an implicit relation between and / . It is also noted that Rr Tg itself is inversely correlated to the corresponding p values and P decreases linearly with log at Tg (also see Hunt, 1994) 

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