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The ac electrical characteristics of a 2-D square randomly filled RC network are shown to exhibit many features in common with those of a typical ionic conductor. These include the ‘universal’ power law frequency responses of ac conductivity and permittivity. It is suggested that a random network of ion conduction channels and insulating islands may provide a realistic model of the conduction paths within a bulk ionic conductor. DC ionic conductivity is identified with a resistive percolation path through the network and the higher frequency power law component with that of the random network of ac conducting linked capacitive and conductive regions. The dielectric loss peak associated with ionic conductors is also found to be a random R-C network characteristic. The effect of the insulating islands having a Debye-like capacitance is modelled and ZrO 2 12 mol% Y 2 O 3 data are presented which exhibit the effects predicted.

DC conductivity in ionic conductors is proportional to the hopping rate of the charge carriers. The hopping of the charge carriers can result in a dielectric loss peak and the DC conductivity is also proportional to the loss peak frequency. In the present study, the AC conductivity of 12 mol.% Y2O3 doped ZrO2 has been measured and the relationship between the hopping frequencies characteristic of the AC conductivities and dielectric loss peak frequencies has been examined. In addition, the peak frequencies in the complex impedance plane were also measured, to compare with the hopping frequencies. It has been demonstrated that two sample constants can be used to connect the three frequencies. It is suggested that the three frequencies are a consequence of a common phenomena and that all result from the hopping process of the charge carriers.

Measurements of the bulk ac electrical response of the fluorine ion conductor (1− x )CdF 2 x ErF 3 , x =0.15, are shown to be composed of separable dipolar dielectric and hopping conductive components. The dielectric component has a relaxation frequency of ∼4 kHz and power law, Cole–Davidson frequency dependencies of real and imaginary parts. The conductive component is frequency independent up to ∼100 kHz and decreases in a Drude fashion at higher frequencies. Ion hopping, characterised by a narrow exponential distribution of activation energies, is shown to generate the measured electrical responses. A model is proposed in which the dielectric component is identified with ions associated with immobile counter-ion or defect clusters and the conductive component with ions at lower activation energy sites between the clusters. It is found that a quantitative account of the conductivity can be obtained by assuming it to arise from a percolation fraction of the ions.

The magnitude of the entropy of activation for conduction in a variety of solid electrolytes has been estimated from data on ion hopping rates. In materials that show a disordering transition in the mobile ion sublattice, a correlation exists between the magnitudes of the enthalpy and entropy of activation obtained from conductivity data for the low temperature, ordered region. This correlation accounts for the Meyer-Neldel rule, an exponential correlation between conductivity pre-exponential factor and activation enthalpy observed in families of related materials. In the low temperature, ordered region of solid electrolyte behaviour, significant entropy terms give rise to enhanced ion hopping rates: it is proposed that this phenomenon be taken as an operational definition of “fast ion conduction”.

A relationship between the a.c. and d.c. components of ionic conductivity, established for single crystal Na β-alumina, is critically examined. Experimental evidence for a variety of other ionic conductors is reviewed and it is concluded that the relationship is of value for the analysis of the conductivities of ionic conductors in general. It is shown that it is possible to distinguish between conductors in which the mobile ion concentration is thermally activated and those for which it is temperature independent. This analysis reveals a decrease in mobile ion concentration in single crystal samples of Na β-alumina at low temperatures. The determination of ion hopping rates using a.c. conductivity measurements is discussed in detail and the results are compared with those obtained from mechanical relaxation studies.

Mechanical relaxations in single-crystal Na β-alumina were studied by measuring the attenuation of longitudinal ultrasonic waves propagating parallel to the conduction planes over the frequency range 50–240 MHz. Broad, thermally activated attenuation peaks were observed which were attributed to the motion of Na + ions in the conduction planes. These results are compared with literature data on (a) internal friction and (b) electrical relaxations. A combined Arrhenius plot of the relaxation times obtained from all measurements showed excellent agreement between the electrical and mechanical relaxation results. Least-squares analysis gave a prefactor of 1×10 13 Hz and an activation energy of 0.166 eV. However, there was some evidence of curvature in the data which, if confirmed would lead to a slightly smaller prefactor and activation energy. The difficulty of measuring electrical relaxations in solid electrolytes is pointed out and the possible validity of using the complex electric modulus formalism to obtain ion hopping frequencies is discussed.

The a.c. conductivity σ(ω) of ionic materials takes the form, σ(ω) = σ(0) + Aωn. The carrier hopping rate, ωp, is obtained from the new expression σ(0) = A ωpn and the carrier concentration is estimated from σ(0). The contribution of creation and migration terms to the activation energy for conduction may be determined from the thermal activation of σ(0) and ωp and the corresponding entropy terms quantified. Data have been analyzed for four widely different ionic materials: single crystal Na β-alumina, polycrystalline Li4SiO4, Ag7l4AsO4 glass and Ca(NO3)2/KNO3 glass and melt. For each, the carrier concentration and hopping rates have been obtained.

Estimates of the entropy of activation for conduction show that it is a major source of variation in the magnitude of the conductivity preexponential factor for a wide variety of solid electroytes. In some cases, the entropy is directly related to the activation energy and this relationship accounts for the observed Meyer-Neldel rule. The occurrence of curvature in Arrhenius plots of ionic conductivity, associated with disordering in the mobile ion sublattice, is a direct consequence of the large entropy of activation. The absence of such curvature in the data for various alkali β-aluminas is explained by the zero or small negative entropies of activation associated with the interstitialcy mechanisms of conduction.

Experimental and theoretical aspects of the measurement of ultrasonic attenuation in ionic conductors are reviewed. The conditions under which relaxation peaks associated with ion transport may be observed in ionically conducting solids are assessed and procedures given for extracting characteristic hopping frequencies. A review of literature data on various beta aluminas and Ag ion conducting glasses is given.

The low temperature ac conductivity of single crystal Na β-alumina, in the region of the bulk, intragranular response shows very non Debye-like behaviour. In the Z ∗ plane, a broadened asymmetric arc is observed. Plots of M ″ against frequency show broad, asymmetric peaks. Dispersions occur in plots of Y ′, Y ″, ϵ′ and ϵ″ against frequency. We use a simple equivalent circuit, comprising a frequency dependent admittance in parallel with a Debye-like parallel RC element, which models well the ac response of β-alumina in all four complex formalisms in terms of four independent parameters.

Power law dispersions in the bulk, intragranular, ac conductivity and permittivity of a non-ideal solid electrolyte are modelled by a frequency-dependent admittance in parallel with the R, C elements of a conventional equivalent circuit. Expressions are derived for imaginary parts of the complex impedance Z ″ and electric modulus M ″ for such a dispersive conductor. The dependance of the shapes of the Z ″ and M ″ versus frequency peaks on the equivalent-circuit parameters are illustrated. Z ″ and M ″ are predicted to peak at different frequencies. An analysis of Na β-alumina data is presented. It is shown that the hopping rate of ions in a solid electrolyte can be obtained from the functional form of Z ″ and M ″ peaks and the frequency separation of their peak maxima.