The problem of N bound electrons interacting under the Coulomb attraction of a single nucleus is the basis of the extensive field of atomic-spectroscopy. For many years experimental information about the bound eigenstates of an atom or ion was obtained mainly from the photons emitted after random excitations by collisions in a gas. Energy-level differences are measured very accurately. We also have experimental data for the transition rates (oscillator strengths) of the photons from many transitions. Photon spectroscopy has the advantage that the photon interacts relatively weakly with the atom so that the emission mechanism is described very accurately by first-order perturbation theory. One disadvantage is that the accessibility of states to observation is restricted by the dipole selection rule.

Photon spectroscopy associates two numbers with the pair of states involved in a transition, the energy-level difference and the transition rate. The correlated emission directions of photons in successive transitions are determined trivially by the dipole selection rule. In most cases it is impossible to solve the many-body problem accurately enough to reproduce spectroscopic data within experimental error and we are left wondering how good our theoretical methods really are.

Because our description of differential cross sections for momentum transfer in a reaction initiated by an electron beam depends on our ability to describe both the structure and the reaction mechanism, scattering provides much more information about bound states. This is even more true of ionisation. The information is less accurate than from photon spectroscopy and is obtained only after a thorough understanding of reactions, the subject of this book, is achieved. The understanding of structure and reactions is of course achieved iteratively.

Quantitative studies of the scattering of electrons by atoms began in 1921 with Ramsauer's measurements of total collision cross sections. Ramsauer (1921) with his single-collision beam technique showed that electron–atom collision cross sections for noble gas targets pass through maxima and minima as the electron energy is varied, and can have very low minima at low electron energies. The marked transparency of rare gases over a small energy range to low energy (~1 eV) electrons was also noted by Townsend and Bailey (1922) in swarm experiments. This result was in total disagreement with the classical theory of scattering, which predicts a monotonic increase in the total collision cross section with decreasing energy. The Ramsauer–Townsend effect provided a powerful impetus to the development of quantum collision theory.

Although the history of electron impact cross-section measurements is quite long, the instrumentation and the experimental techniques used have continued to evolve, and have improved significantly in recent years. Part of the motivation for this progress has been the need for electron collision data in such fields as laser physics and development, astrophysics, plasma devices, upper atmospheric processes and radiation physics. The development of electron–atom collision studies has also been strongly motivated by the need of data for testing and developing suitable theories of the scattering and collision processes, and for providing a tool for obtaining detailed information on the structure of the target atoms and molecules and final collision products.

The advancement of knowledge of electron–atom collisions depends on an iterative interaction of experiment and theory. Experimentalists need an understanding of theory at the level that will enable them to design experiments that contribute to the overall understanding of the subject. They must also be able to distinguish critically between approximations. Theorists need to know what is likely to be experimentally possible and how to assess the accuracy of experimental techniques and the assumptions behind them. We have aimed to give this understanding to students who have completed a program of undergraduate laboratory, mechanics, electromagnetic theory and quantum mechanics courses.

Furthermore we have attempted to give experimentalists sufficient detail to enable them to set up a significant experiment. With the development of position-sensitive detectors, high-resolution analysers and monochromators, fast-pulse techniques, tuneable high-resolution lasers, and sources of polarised electrons and atoms, experimental techniques have made enormous advances in recent years. They have become sophisticated and flexible allowing complete measurements to be made. Therefore particular emphasis is given to experiments in which the kinematics is completely determined. When more than one particle is emitted in the collision process, such measurements involve coincidence techniques. These are discussed in detail for electron–electron and electron–photon detection in the final state. The production of polarised beams of electrons and atoms is also discussed, since such beams are needed for studying spin-dependent scattering parameters. Overall our aim is to give a sufficient understanding of these techniques to enable the motivated reader to design and set up suitable experiments.

The detailed study of the motion of electrons in the field of a nucleus has been made possible by quite recent developments in experimental and calculational techniques. Historically it is one of the newest of sciences. Yet conceptually and logically it is very close to the earliest beginnings of physics. Its fascination lies in the fact that it is possible to probe deeper into the dynamics of this system than of any other because there are no serious difficulties in the observation of sufficiently-resolved quantum states or in the understanding of the elementary two-body interaction.

The utility of the study is twofold. First the understanding of the collisions of electrons with single-nucleus electronic systems is essential to the understanding of many astrophysical and terrestrial systems, among the latter being the upper atmosphere, lasers and plasmas. Perhaps more important is its use for developing and sharpening experimental and calculational techniques which do not require much further development for the study of the electronic properties of multinucleus systems in the fields of molecular chemistry and biology and of condensed-matter physics.

For many years after Galileo's discovery of the basic kinematic law of conservation of momentum, and his understanding of the interconversion of kinetic and potential energy in some simple terrestrial systems, there was only one system in which the dynamical details were understood. This was the gravitational two-body system, whose understanding depended on Newton's discovery of the 1/r law governing the potential energy. By understanding the dynamics we mean keeping track of all the relevant energy and momentum changes in the system and being able to predict them accurately.

A brief history of solid state electrochemistry

Solid state electrochemistry may be divided into two broad topics.

1. (a) Solid electrolytes, which conduct electricity by the motion of ions, and exhibit negligible electronic transport. Included in this group are crystalline and amorphous inorganic solids as well as ionically conducting polymers.

2. (b) Intercalation electrodes, which conduct both ions and electrons. Again there are numerous examples based mainly on inorganic solids and polymers.

The field of solid state electrochemistry is not new. It has its origins, as does so much of electrochemistry, with Michael Faraday who discovered that PbF2 and Ag2S were good conductors. He therefore established both the first solid electrolyte and the first intercalation electrode (Faraday, 1838).

In this chapter we shall discuss both the theoretical and experimental aspects of the following types of interfaces:

1. (a) metal/polymer electrolyte, e.g. Li/PEO–LiCF3SO3 or Pt/PEO–LiCF3SO3;

2. (b) metal/crystalline ionically conducting solid, e.g. Ag/Ag4RbI5 or C/Ag4RbI5;

3. (c) aqueous salt solution/polymer electrolyte, e.g. AsPh4Cl-H2O/ AsPh4BPh4–PVC or KCl–H2O/AsPh4BPh4–PVC;

4. (d) polymer electrolyte/electronically and ionically conducting solid, e.g. PEO-LiCF3SO3/LixV6O13;

5. (e) solid electrolyte/solid electrolyte, e.g. Ag4RbI5/Ag-β-Al2O3.

We shall not attempt to review exhaustively the literature on interfacial electrochemistry in solid state systems. Instead we shall indicate the appropriate theoretical models for different situations. Most of the models and the related equations were developed some time ago in relation to the electrochemistry of aqueous systems. However, we will not assume a knowledge of these models on the part of the reader. It is important to realise that a direct transposition of models from one situation to another is fraught with difficulty, particularly since in aqueous electrochemistry a supporting electrolyte is generally present.

It is convenient for the purposes of this chapter initially to make a number of simplifying assumptions about the nature of the electrolytes under discussion. For example, Ag4RbI5 will be assumed to be an ionic conductor with negligible electronic conductivity and with only the silver ion mobile. Likewise Na-β-Al2O3 will be assumed to be a substance in which the only mobile charge is Na+.

Introduction

The discovery that certain classes of polymers may acquire high electronic conductivity following chemical or electrochemical treatment has opened a new and exciting area of research and development.

The concept of electric transport in polymers due to the availability of polymeric materials with characteristics similar to those of metals is certainly fascinating and, indeed, many studies have been directed towards the preparation and the characterisation of these new electroactive conductors. The final goal is their use as new components for the realisation of electronic and electrochemical devices with exotic designs and diverse applications.

The idea of exploiting these new conducting polymers for the development of flexible diodes and junction transistors, as well as for selective field effect transistor sensors, has been proposed and experimentally confirmed, and thus we may, perhaps optimistically, look forward to a time when popular electronic devices can be based on low cost, flexible and modular polymer components.

Even more interesting than all this is the fact that conducting polymers allow the fabrication of not only polymer-like electronic devices but also the battery which is necessary to power them. Indeed, such polymers are capable of acquiring high conductivity by reversible electrochemical processes, and thus they may be regarded as new electrode materials which can operate in the same way as the conventional battery electrodes, while still maintaining their unique mechanical characteristics.

Introduction

High ionic conductivity in crystalline solids is a widely recognised, although still relatively rare, phenomenon. Most ionic solids are electrical insulators unless they exhibit electronic conductivity. They begin to show significant levels of ionic conductivity only at high temperatures, as the melting point is approached. Materials in the family of crystalline solid electrolytes (also called superionic conductors, fast ion conductors or optimised ionic conductors), however, exhibit high conductivity in one of their ionic sublattices – the mobile ion sublattice – at temperatures well below melting and often as low as room temperature.

The first half of this chapter concentrates on the mechanisms of ion conduction. A basic model of ion transport is presented which contains the essential features necessary to describe conduction in the different classes of solid electrolyte. The model is based on the isolated hopping of the mobile ions; in addition, brief mention is made of the influence of ion interactions between both the mobile ions and the immobile ions of the solid lattice (ion hopping) and between different mobile ions. The latter leads to either ion ordering or the formation of a more dynamic structure, the ion atmosphere. It is likely that in solid electrolytes, such ion interactions and cooperative ion movements are important and must be taken into account if a quantitative description of ionic conductivity is to be attempted.

Introduction

Within the field of electrochemistry the topic of electrolytes, that is the study of salts dissolved in solvents, is regarded by some as a mature discipline. It is viewed as less exciting than its sister topic of electrodics, which is concerned with the interface between electrolytes and electrodes; however, this is far from true for solid polymer electrolytes. These materials consist of salts dissolved in a solid, coordinating, polymeric solvent. They were first investigated by Fenton, Parker and Wright (1973) and have been intensively studied since Armand (1978) recognised their unique potential as electrolytes with a ‘solid-solvent’. In recent years many such electrolytes have been prepared. An introduction to polymer electrolytes including a discussion of the different systems is presented in the preceding chapter by Shriver and Bruce. A sufficient body of knowledge has now accumulated on polymer electrolytes to permit the establishment of the fundamental physical principles on which such materials are based. It is with the physical aspects of solid polymer electrolytes that this chapter deals and in this sense it differs from the previous chapter.

Our fundamental understanding of polymer electrolytes is derived from both the general examination of a wide range of distinct electrolytes and from some very detailed studies of a few model systems.

Introduction

In the early part of this century, many types of solid electrolyte had already been reported. High conductivity was found in a number of metal halides. One of the first applications of solid electrolytes was to measure the thermodynamic properties of solid compounds at high temperatures. Katayama (1908) and Kiukkola and Wagner (1957) made extensive measurements of free enthalpy changes of chemical reactions at higher temperatures. Similar potentiometric measurements of solid electrolyte cells are still made in the context of electrochemical sensors which are one of the most important technical applications for solid electrolytes.

Another application of solid electrolytes is to be found in the field of power sources. Baur and Preis (1937) proposed a fuel cell system with an oxide ion conductive solid. The solid oxide fuel cells (SOFC) are attractive electric power generation systems, and over the last decade research devoted to their development has become intense. In 1967, Yao and Kummer found that β-alumina exhibited high sodium ion conductivity, and Weber and Kummer (1967) proposed a sodium-sulphur battery with β-alumina. This type of battery may be attractive as a power source for electric vehicles and for electric energy storage as part of a load-levelling system in consumer power distribution. Solid electrolyte cells, which operate at room temperature, have been developed over the past two decades.

Important aspects of ionic and electronic structure

Intercalation or insertion compounds are solids made of host atoms and guest atoms (or molecules). The host atoms provide a lattice or framework; the guest atoms occupy sites within this framework. Two properties distinguish intercalation compounds from other solids: the guests are mobile, moving between sites in the host lattice; and the guests can be added to the host or removed from it, so the concentration of guests can change. These two properties are exploited when intercalation compounds are used as electrodes in electrochemical cells.

There are many kinds of guests, ranging from protons through to divalent cations (Bruce, Krok, Nowinski, Gibson and Tavakkolik, 1991) and on to large organic molecules. I shall limit this chapter to alkali metal guests, and almost exclusively to lithium. There are also many kinds of hosts, and I shall focus on transition metal oxides or chalcogenides (sulphides, selenides, and tellurides). I shall also mention graphite intercalation compounds, but only briefly, for there are detailed review articles (Solin, 1982; Dresselhaus and Dresselhaus, 1981). Even within these limitations, I can only discuss a small fraction of the known compounds. The examples chosen illustrate the fundamental chemistry and physics of intercalation, which is the primary aim of this chapter.