Explanation of mechanical and electrical relaxation due to mobile ions in a superionic glass over the range 1 Hz–20 GHz by the coupling theory

Abstract

The observation of mechanical relaxation due to the motion of fast cations in a superionic AgI-rich borate glass has recently been extended by several groups to ten decades in relaxation time by a combination of Brillouin scattering, ultrasonic attenuation, and low-frequency dynamic mechanical measurements. The relaxation time was found to have an almost Arrhenius temperature dependence. The relaxation function is highly nonexponential at lower temperatures or frequencies, but narrows dramatically to exponential relaxation in the gigahertz range. Electrical relaxations due to the same mobile ions have been studied over eight decades by a combination of electric modulus and dc conductivity data. In this work, the coupling theory of relaxation is shown to provide an explanation for all the available mechanical and electrical relaxation data. In particular, the mechanical loss moduli as a function of temperature at 19 GHz, 5 MHz, and 110 Hz can be accurately reproduced both in peak position and shape using values of the primitive relaxation time ${\ensuremath{\tau}}_{0}$ and coupling parameter n obtained from the electrical relaxation data and a narrow distribution of energy barriers for mechanical relaxation which is not present in electrical relaxation.