Description and analysis of electrical relaxation data for ionically conducting glasses and melts

doi:10.1016/S0167-2738(97)00462-1

Solid State Ionics

Volume 105, Issues 1–4, 1 January 1998, Pages 175-183

https://doi.org/10.1016/S0167-2738(97)00462-1 Get rights and content

Abstract

In recent years there has arisen considerable controversy and some confusion with regard to analysis and interpretation of electrical relaxation data for ionically conducting glasses and melts. For example, there are questions as to whether the data are better described using the electric modulus formalism with a KWW distribution of relaxation times or by using a Jonscher power law fit to the frequency dependent electrical conductivity. This topic is reviewed and discussed, with some emphasis placed on the degree to which information on the electrical relaxation mechanisms and the microscopic sources of nonexponential relaxation can be extracted from data presentation and analysis using the electric modulus formalism with a well behaved electric field relaxation function.

Introduction

In recent years there have arisen some controversies with regard to the empirical analysis and interpretation of electrical relaxation data for ionically-conducting glasses and melts. This relaxational behavior is generally presumed to be due to the motions of ions which give rise at long times or low frequencies to the dc electrical conductivity σ [1]. For example, there are questions as to whether the data are better analyzed using the electric modulus M* formalism or by focussing on the frequency dependence of the real part of the complex conductivity σ′ 1, 2, 3, 4, 5, 6. In the present paper, which may be considered in part as something of a sequel to two earlier papers by the present author 1, 7, a number of these issues are addressed and discussed.

Section snippets

Formalisms for description of electrical relaxation data

Electrical relaxation measurements in ionically conducting glasses and melts are usually carried out in the frequency domain. Typically one measures either the parallel conductance G and capacitance C of the sample using an admittance bridge or the magnitude of the sample impedance |Z| and the phase angle δ between the input and output signals using an impedance meter. These results may then be expressed in terms of the real parts of the complex permittivity ε′ and of the complex conductivity σ

Analysis of electrical relaxation data

Although actual electrical relaxation data for ionically-conducting glasses and melts can be expressed in any of the four formats in , , , , analysis of such data in recent years has tended to focus on the frequency dependence of either σ′ or of M* 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Examples of the frequency dependence of these quantities are shown in Fig. 1, Fig. 2 in the forms of a log σ′ vs. log f plot (f=ω/2π=frequency) and of a complex plane plot of M″ vs. M′ for a Na₂O–3SiO₂ glass at

Low temperature/high frequency relaxation

As evident from Fig. 1 and as discussed in several recent papers 1, 4, 8, 11, 24, 25, 26, the Jonscher expression, Eq. (14), for the frequency dependence of σ′ fails to give a good account of the data at high frequencies and/or low temperatures. Rather, at high frequencies and/or low temperatures σ′ tends to exhibit roughly an ω¹ frequency dependence, leading Nowick and coworkers [24] to suggest an augmented form of the Jonscher equation $σ′=σ+Aω^{n} +A′ω$ In Fig. 3 is shown a fit of the Na₂O–3SiO₂

Microscopic source of nonexponential electrical relaxation

One of the advantages of the KWW analysis of electrical relaxation is that it produces a well behaved electric field relaxation function φ(t) and mean relaxation time 〈τ〉 which can be compared with relaxation functions and times for other properties of the same material. For example, a comparison of 〈τ〉 with 〈τ_s〉, the mean shear stress relaxation time due to viscous flow, leads to the so-called decoupling index, R_τ=〈τ_s〉/〈τ〉, for ionically-conducting melts 1, 27. A long standing question which

Conclusions

The main aim of the present paper is to present and review some arguments that the use of the electric modulus M* in analysis of electrical relaxation in ionically-conducting glasses and melts is both legitimate and useful. With regard to the utility aspect, we have noted that complex plane M″ vs. M′ plots provide a clear indication of the presence of a second, weak, high frequency/low temperature relaxation process in addition to the relaxation process generally attributed to motions of the

Acknowledgements

The author would like to thank Kia L. Ngai for numerous helpful discussions.

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Description and analysis of electrical relaxation data for ionically conducting glasses and melts

Abstract

Introduction

Section snippets

Formalisms for description of electrical relaxation data

Analysis of electrical relaxation data

Low temperature/high frequency relaxation

Microscopic source of nonexponential electrical relaxation

Conclusions

Acknowledgements

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

Polymer

J. Phys. Chem. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Non-Cryst. Solids

Phys. Rev. Lett.

Phys. Rev.