Derivation of a relation between the activation energies of ionic conductivity in the glassy and molten states of glass-forming ionic conductors: an application to silver iodide–silver selenate

Abstract

In the glassy state of glass-forming ionic conductors, the temperature dependence of dc conductivity σ is Arrhenius with a constant activation energy, E σ ,. High above the glass transition temperature where σ is approaching a level of 1 Ω −1 cm −1 and the corresponding conductivity relaxation times τ σ are of the order of 1 ps, the apparent activation energy of σ, E a, is significantly smaller than E σ . In a previous study it was shown that the ratio, E a/ E σ , is nearly equal to the fractional exponent, β, of the Kohlrausch–Williams–Watts function, exp[−( t/ τ KWW) β ], which is a characteristic of the nonexponential conductivity relaxation of ionic conductors. In this work we show that this correlation between activation energies in the glassy and the molten states follows from results of the coupling model. Experimental data of C. Cramer and M. Buscher have given conductivity relaxation spectra over a broad frequency range for a fast ion conducting 0.48(AgI) 2–0.52Ag 2SeO 4 composition below and above the glass transition temperature T g. We have analyzed the glassy state conductivity relaxation data by using the electric modulus formalism as well as by direct consideration of the ac conductivity. After the removal of a contribution to the ac conductivity that is proportional to ω 1.0, where ω is the angular frequency, the data in both representations are well fitted by the appropriate Fourier transform of Φ(t)= exp [−(t/τ KWW ) β] , with β=0.51. With this value of β, we found that the product, βE σ , is about the same as E a within experimental error. This agreement provides support for the correlation, E a/ E σ ≈ β, which was previously established for glass-forming ionic conductors with decoupling indices, R τ , that vary over twelve orders of magnitude, as well as for several crystalline ionic conductors.