Structure and Its Influence on Superionic Conduction: EXAFS Studies

Abstract

With 17 Figures Superionic conductors are a class of materials which achieve ionic conductivities comparable with those of molten salts while still in the solid phase. As discussed in Chap.7, the transition from insulating to conducting behavior may take place sharply at a specific temperature, as in the case of AgI, or gradually over a large temperature range, as in the case of PbF 2 [2.1]. In either case, it involves a disordering of one of the ion sublattices of the material. At low temperature, all the ions are situated on well-defined lattice sites and have a very low mobility. As the temperature is increased, the mobile ions begin populating interstitial sites. In the superionic phase, these ions are distributed over a large number of available sites [2.2]. It follows that this superionic phase is quite naturally characterized structurally in terms of the mobile and immobile sublattices [2.3]. The immobile ions form a complex structure through which the mobile ions move. This structure is not rigid since these ions execute large vibrations about their lattice sites; nonetheless, they do not leave those sites and so do not contribute to the ionic conductivity. The positions of the immobile ions define characteristic voids which are populated to varying degrees by the mobile ions and through which these ions move. In AgI, for example, the iodine forms a bcc lattice, while the Ag ions are located in and move among the tetrahedral voids, with negligible occupation of the octahedral locations [2.4,5]. Since many of the fundamental questions about superionic conductors are structural in nature, the structural probes have been essential in understanding these materials. The transition to the superionic state involves the disordering of the arrangement of the mobile ions, and so must be characterized structurally. In the superionic phase itself, elementary considerations of mass and temperature suggest that the mobile ions spend a significant fraction of time in flight from one location to another [2.4,6,7]. Therefore, structural studies yield substantial information not only on the sites that are occupied, but also on the flight path from one site to another. These measurements can thus yield insight into the conduction process as well as the order-disorder transformation. In this chapter, we discuss the structural information probed through the extended X-ray absorption fine structure (EXAFS), and the relationship between this information and the high ionic conductivity of these materials. The EXAFS consists M. B. Salamon (ed.), Physics of Superionic Conductors © Springer-Verlag Berlin Heidelberg 1979 6 of the oscillations, as a function of photon energy, in the absorption cross section for the photoexcitation of an electron from a deep core state to a continuum state. These oscillations are a final state electron effect, arising from the interference between the outgoing wavefunction and that small fraction of itself which is scattered back from the near-neighbor atoms. This interference reflects directly the net phase shift of the backscattered electron, which is predominantly proportional to the product of the momentum of the electron, k, and the distance traveled. The atomic identity of both the excited and backscattering atoms has a more subtle but nonetheless significant effect on the interference. As a consequence, analysis of the EXAFS can yield not only the distance but also the type and number of the nearest neighbors of the excited atoms. Since EXAFS arises from scattering by the near neighbors of the excited atom species only, a given measurement involves a subset of those pair correlation functions which are probed in a single diffraction measurement. This is a sUbstantial simplification. In X-ray and neutron diffraction studies of superionic conductors, the complicated diffraction pattern contains both Bragg peaks (or Debye lines) from long-range order and a liquid-like diffuse scattering pattern from short-range correlations [2.8,9]. These two contributions are often dominated by the stationary lattice and the mobile-ion/mobile-ion correlations, respectively. EXAFS, on the other hand, measures primarily the pair correlation function of the mobile species with respect to the immobile ions. Thus, the EXAFS technique is especially well suited to determining the path taken by the conducting ions. In Sect.2.1 we discuss the EXAFS technique and compare it with x-ray and neutron scattering. In Sect.2.2 various structural models for superionic conductors are discussed. In Sects.2.3,4 the experimental results on AgI and the cuprous halides, respectively, are presented and analyzed in terms of these structural models. We show that an excluded volume model not only explains the measured pair distribution function well, but can also yield important insight into the conduction process. 2.1 Technique of EXAFS 2.1.1 Theory The microscopic orlgln of the EXAFS is very well understood, having been discussed at length in the literature [2.10-14]. Of particular importance is the demonstration by LEE and PENDRY [2.12] that, except in unusual circumstances, electrons which have been scattered by more than one neighboring atom make a negligible contribution to the measured EXAFS. This leads to an enormous simplification in the interpretation of the EXAFS, and is used in the following treatment. From general considerations [2.13,14], the absorption cross section for the photoexcitation of an elec-7 tron from the K shell of atom species a by an X-ray photon of energy E can be expressed as a (E) = aO(E)[l + ~ (k)] a a a (2.1) where the EXAFS for randomly oriented local environments or for powders is given by (2.2) and Aas(k,r) ~ (-2iTI 2)t;(-k,k) exp[-2v(k)r + 2io a (k)] (2.3) Here, k 2 /2 = E 1s + E is the final state electron energy with E 1s the binding energy of the K-shell electron. The aO(E) factor in (2.1) contributes a broad, atomlike background to aa(E), essentially featureless except for the K edge. The term which