Nearly constant loss or constant loss in ionically conducting glasses: A physically realizable approach

Conductivity exhibiting power-law frequency response with an exponent of un ity leads to frequency-independent dielectric loss. Such constant-loss (CL) behavior is not physically realizable over a nonzero frequency range, and approximate expressions that have been used to represent it are inconsisten t with the Kronig-Kramers relations. Response models are proposed and inves tigated that do satisfy these relations and can lead to very close approxim ation to CL over many frequency decades, as often observed at low temperatu res in ionic conductors such as glasses. Apparent CL response is shown to a rise from the series connection of a constant-phase complex-power-law eleme nt (CPE), with exponent delta (0 < delta <1), and a frequency-independent d ielectric constant, epsilon (U). Two physically disparate situations can le ad to such a series connection. The first involves bulk CPE response in ser ies with an electrode-related, double-layer blocking capacitance involving a dielectric constant epsilon (S). Then, apparent CL behavior may be associ ated with localized ionic motion in the bulk of the material. The second (m irror-image) situation involves CPE response associated with ionic motion i n or at an electrode in series with a capacitance such as the bulk high-fre quency-limiting total dielectric constant epsilon (infinity) or the pure-di electric quantity epsilon (D infinity). The present model is used to simult aneously fit both the real and imaginary parts of data derived from measure ments on a sodium-trisilicate glass at 122 K. This data set exhibits power- law nearly constant loss for epsilon (')(omega) and apparent CL for epsilon (')(omega). The magnitude of the CL closely satisfies a simple equation in volving only delta and epsilon (U). Further, for the electrode-power-law si tuation, estimated values of limiting-high-frequency dielectric constants t urn out to be more consistent with bulk values established at much higher t emperatures where nearly constant loss is no longer a dominant part of the response. Data at -0.5 degreesC are also analyzed with a more complicated c omposite model, one that is a generalization of both of the above approache s, and nearly constant loss bulk, not electrode, power-law effects in both epsilon (')(omega) and epsilon (')(omega) are isolated and quantified. For this data set it is shown that electrode effects are important at both ends of the frequency range. (C) 2001 American Institute of Physics.