Carrier Concentrations and Relaxation Spectroscopy: New Information From Scaling Properties of Conductivity Spectra in Ionically Conducting Glasses
ABSTRACT A new kind of scaling analysis for the conductivity spectra of glasses without any arbitrary parameters is presented. By applying this method to sodium borate glasses of different compositions, we find strong indications for the existence of a universal ionic relaxation process as well as for a strong electrolyte behavior. Our results enable us to show that the often used electric modulus formalism is misleading when relaxation mechanisms on a microscopic level are concerned. A more meaningful discussion can be based on the log-log dependence of the conductivity on frequency.
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- "It is obvious that, we do not follow fitting at all (yet it could be done to define all the related parameters in w or T, etc., for better extrapolations): We solve the equations at some points for σ(w) and mimic the empirical data and try to make predictions. Below are the results with the parameters given in Tables I, II and III for doped Si , sodium borate glasses  and mixed alkali glasses , respectively. Various discussions about the model are given in further sections and Appendix; and, it may be worth to brief the underlying currents in several temperature regimes here: We have mainly displacement and polarization currents at small temperatures; T<E A /k B where E A is Arrhenius (activation) energy. "
ABSTRACT: We obtain the frequency and temperature dependence of the conductivity for (disordered) solids, where the temperature dependence is defined in terms of the related thermodynamic state function in exponential (or power law, etc.) forms. The model is applied to n-type Si with various donor and acceptor impurities and several concentrations at T about 0 Kelvin and sodium borate glasses and mixed alkalis with various compositions (x) in all at T about 500 Kelvin. The results are found in good agreement with experiments.
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ABSTRACT: We propose two different models for the ion transport in ion conducting glasses. The starting point of our first model is a many-particle Fokker-Planck equation for the distribution function of the ions. The ions interact with each other and with the glass particles. The interaction with the glass is modelled by stochastic, time independent potentials. This distribution function is the solution of a Vlasov-Fokker-Planck equation. Additionally we calculate the diffusion coefficient of the charge center in the framework of an effective two-particle model. We find that the conductivity of the system depends in a non-linear way on the concentrations of the different ions and on their composition ratio. Although these calculations differ from the mixed alkali effect, the analytical results give a possible explanation for the weak mixed alkali effect. Our second model includes the dynamics of the ions as well as the dynamics of the glass structures. The linear response to an external electrical field and the dynamic structure factors of the glass are calculated in the framework of the Keldysh technique. There is a strong coupling of the two-particle Green’s functions and the one-particle Green’s functions. The Green’s functions are approximated by perturbation theory up to second order. Because of different scattering processes, the lifetimes of the one-particle states are finite and depend on the concentrations and on the composition ratios of the different ingredients. The analytically calculated conductivity depends in a non-linear way on the concentrations of the alkali ions, which fits very well to the experimental data for low concentrations. The calculated conductivity of mixed alkali glasses shows a mixed alkali effect, which is also in qualitative accordance with the experimental results. Additionally, our model predicts a nonlinear dependence of the conductivity of mixed anion glasses on the composition ratio.
Article: Conductivity spectroscopy[Show abstract] [Hide abstract]
ABSTRACT: In the area of conductivity spectroscopy, key technical advances include the measurement of spatially resolved conductivities and progress in the development of femtosecond terahertz pulse spectroscopy. Conductivity spectroscopy and quasielastic neutron scattering have been successfully combined to tackle problems in the microdynamics of polymeric and crystalline materials. In the interpretation of conductivity spectra of glassy electrolytes and glass forming melts, interest is shifting from power laws to scaling laws.Current Opinion in Solid State and Materials Science 08/1997; 2(4-2):483-490. DOI:10.1016/S1359-0286(97)80094-0 · 7.17 Impact Factor