Jump relaxation in solid electrolytes

The field of enthalpy relaxation is reviewed. Current phenomenologies for dealing with the non-linear and non-exponential character of enthalpy relaxation are presented, and their successes and shortcomings are discussed. Qualitative experimental data and quantitative parameterizations are summarized, and some directions for future research are suggested.

Enthalpy relaxation and recovery in amorphous materials

The distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous Cole–Davidson distribution function. In order to make the comparison between the two distribution functions, a simple empirical relationship between the Cole–Davidson and Williams–Watts parameters was determined which may be used to compare data analyzed using the two fitting functions. Although the relaxation functions are similar to each other, the distribution functions are quite dissimilar. The Cole–Davidson distribution shows a sharp long time cutoff, while the Williams–Watts distribution decays approximately exponentially at long times. Finally, several useful relations between relaxation and distribution functions are summarized or derived, and the limitations of deriving distribution functions from relaxation functions are discussed.

Detailed comparison of the Williams–Watts and Cole–Davidson functions

For six glass forming substances of very different kinds the volumes of cooperatively rearranging regions (CRR) and the corresponding correlation lengths are calculated using parameters obtained by Moynihan et al. from thermograms and formulas from a fluctuation theory of glass transition. The correlation lengths range from 0.7 nm for a crown glass up to 2.2 nm for a lubricant oil. The CRR contains between 35 and 290 strongly interacting particles. The consequences of such wide correlations are discussed with respect to the relations between the dynamic glass transition, the freezing-in process, and the structure of glasses.

The size of cooperatively rearranging regions at the glass transition

A method was developed to determine the kinetic parameters controlling structural relaxation in the glass transition region from data acquired during continuous heating or cooling. The nonexponential character of the relaxation is accounted for by assuming an equilibrium isothermal relaxation function of the form exp [−(t/Toe)s], where Toe is a relaxation time and 0<β1. The data are linearized using the method of Narayanaswamy, and the continuous temperature variation during heating or cooling is dealt with by invoking the superposition principle. The analysis yields the kinetic parameters A, the relaxation-time preexponential term; Δh★, the relaxation-time activation enthalpy; x, a term describing the relative effects of temperature and structure on the rate of relaxation; and β. The method was applied to analysis of the variation of the enthalpy of vitreous B2O3 during rate heating through the transition region following rate cooling through the same region at a variety of rates.

Analysis of Structural Relaxation in Glass Using Rate Heating Data

The empirical dielectric decay function ϕ(t)= exp –(t/τ0)β, 0 0, but significant corrections may have to be applied for β >0.5 and log ωτ0 < 0.

S. B. Dev

Papers

Further considerations of non symmetrical dielectric relaxation behaviour arising from a simple empirical decay function