Description and analysis of electrical relaxation data for ionically conducting glasses and melts
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 equationIn 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 〈τs〉, the mean shear stress relaxation time due to viscous flow, leads to the so-called decoupling index, Rτ=〈τs〉/〈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.
References (36)
J. Non-Cryst. Solids
(1994)J. Non-Cryst. Solids
(1991)J. Non-Cryst. Solids
(1994)- et al.
J. Non-Cryst. Solids
(1994) - et al.
J. Non-Cryst. Solids
(1995) J. Non-Cryst. Solids
(1996)- et al.
J. Non-Cryst. Solids
(1994) - et al.
Polymer
(1997) - et al.
J. Phys. Chem. Solids
(1994) - et al.
J. Non-Cryst. Solids
(1994)
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.
Cited by (120)
Variation in the dielectric and magnetic characteristics of multiferroic LuFeO<inf>3</inf> as a result of cobalt substitution at Fe sites
2023, Journal of Alloys and CompoundsUniversal properties of relaxation and diffusion in complex materials: Originating from fundamental physics with rich applications
2023, Progress in Materials ScienceImpedance spectroscopy and DFT/TD-DFT studies of diyttrium trioxide for optoelectronic fields
2023, Journal of Rare EarthsThe universal and anomalous properties of the dynamics of ions in liquid, glassy, and crystalline ionic conductors
2023, Journal of Non-Crystalline Solids: XElectrical conductivity and relaxation in lithium-doped barium vanadate glasses investigated by impedance spectroscopy
2023, Journal of Physics and Chemistry of Solids