JOURNAL OF MATERIALS SCIENCE 33 (1998) 4485 — 4490 Dynamic transport in ionic conductors A. K. JONSCHER Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK C. LE ON, J. SANTAMARIA Departmento de Fisica Aplicada III, Universidad Complutense, 28040 Madrid, Spain The experimental data for the dielectric response of certain ionically conducting ceramics obtained by Kuhn and coworkers were re-interpreted using the ‘‘universal’’ dielectric formalism and the results reveal the presence of two well defined processes with power law exponents of !0.6 to !0.7 for the high-temperature, low-frequency branch and !0.3 and less for the low-temperature, high-frequency branch. The physical significance of these results is discussed in terms of transport in strongly anisotropic materials. 1998 Kluwer Academic Publishers 1. Introduction The electrical and other properties of ionically con- ducting ceramics of composition Na — Fe Ti — O , with x"0.875, modified by soft chemistry extraction methods, to reduce the Na concentration with 0))0.44, were studied in considerable detail by Kuhn et al. [1] who also included data of the fre- quency dependence of transport parameters. In the present paper we are giving further detailed analysis of their dielectric data, using the ‘‘universal’’ dielectric response approach [2, 3] with a view to obtaining a better appreciation of the dynamics of ionic transport. We do this not only out of interest in the particular materials in question, but also from a more general standpoint, since we believe these data illustrate several points relevant to dynamic transport in ionic conductors. In particular, we note the fact that in many situ- ations the frequency dependence of the complex di- electric susceptibility ()" ()! " ()!i ()J(i) (1) follows the ‘‘universal’’ fractional power law, where is the angular frequency, is the ‘‘high-frequency’’ permittivity beyond which the losses become negli- gible, the exponent falls in the range 0(n(1, and Kramers—Kronig (KK) compatibility requires that ()/ ()"cot(n/2) (2) This means that logarithmic plots of () and () are parallel straight lines with slopes n!1. The alternating current conductivity is given by ()" (). We note that it is not necessary for the universal law to be applicable in all cases, but that where it appears not to be followed it is useful to try first removing certain obvious processes, like , the direct-current (d.c.) conductivity, ; any low-frequency dispersion (LFD) [3, 4], which follows the same laws, Equation 1 and 2, but with a very small value of n; and also any dipolar processes that may be present. At the end of this analysis it is often possible to obtain good self-consis- tent fractional power-law trends underlying the be- haviour and this leads to a better analysis of the physical processes involved. 2. Experimental procedure Of the samples referred to in this paper, NFT2 is the parent sample, the others having Na extracted by chemical means, with the following parameters NFT2 has x"0.875, "0, giving x!"0.875 for Na content NFT3 has x"0.875, "0.2 giving x!"0.675 NFT4 has x"0.875, "0.3 giving x!"0.375 NFT5 has x"0.875, "0.03 giving x!"0.845 These samples were prepared from finely ground pow- ders by cold pressing into the form of pellets 5 mm in diameter and 0.3 mm in thickness, with silver painted contacts. These materials are ‘‘fast ionic conductors’’ in that their structure contains unidirectional double chan- nels along which Na ions move relatively freely [1] and obvious limitations to free transport arise from structural imperfections and the finite size of the grains in the ceramic. 3. Results We begin this presentation with two of the results of the removal of secondary processes for the parent sample NFT2, which correspond to extreme forms of response. Fig. 1 gives the result for 250 °C, where a Debye process is at 410 Hz. The two dotted lines have exponents 1!n"0.67, which correspond to relatively dispersive regimes. The corresponding data for the lower temperatures of 82 and 135 °C are 0022—2461 1998 Kluwer Academic Publishers 4485