There are, in general, many possible transitions of electrons in atoms. In some processes of practical interest more than one electron may undergo a transition. Such multiple electron transitions are the topic of the next and subsequent chapters. In this chapter the simpler topic of single electron transitions is considered, where the activity of a single electron in an atom is the focus of attention. Even this relatively simple case may be impossible to fully understand if the electron of interest is influenced by other electrons in the atom. So in this chapter the interdependency of electrons in the system is ignored. That is, the electrons are treated independently. Typically, such an independent electron is regarded as beginning in an initial state characterized by some effective nuclear charge ZT and a set of quantum numbers n, l, m, s, ms from which all possible properties (e.g., energy, shape, magnetic properties, etc.) may be determined. Interaction with something else, (usually a particle of charge Z and velocity, v), may cause a transition to a different final state of the atom.

The simplest transition occurs in interaction of atomic hydrogen with a structureless projectile. There are various ways to evaluate the transition probability for such a system. Exact calculations usually require use of a computer. Approximate calculations may be done more easily. Calculations for many electron systems are often done approximately using single electron transition probabilities.

Correlation

There is a significant difference between complex and merely large. This difference is related to the the notion of correlation which defines the rules of interdependency in large systems. The relevant question is: how may one make complicated things from simple ones? Biological systems are complex because the atomic and molecular subsystems are correlated. From the point of view of atomic physics correlation in condensed matter, chemistry and biology is determined at least in part by electron correlation in chemical bonds and the complex interdependent structures of electronic densities. Understanding correlation in this broad sense is a major challenge common to most of science and much of technology. This is sometimes referred to as the many body problem. In a general sense correlation is a conceptual bridge from properties of individuals to properties of groups or families.

The concept of correlation arises in many different contexts. ‘Individual’ may mean an individual electron, an individual molecule or in principle an individual person, musical note or ingredient in a recipe. In this book individual refers to electron for the most part. In this case the interaction between individuals is well known, namely l/r12. However, that does not mean that electron correlation is well understood in general. Although much has been done to investigate correlation in various areas of physics, chemistry, statistics, biology and materials science, in many cases little is well understood except in the limit of weak correlation.

In previous chapters interactions with structureless point charge projectiles have been considered. There are many interactions, however, which involve at least two atomic centers with one or more electrons on each center. In such cases the projectile is not well localized and there is a need to integrate over the non localized electron cloud density of the projectile. Evaluation of cross sections and transition rates for such processes requires a method for dealing with at least four interacting bodies. If multiple electron transitions occur on any of the atomic centers, then some form of even higher order many body theory is required. In general such a many body description is difficult.

In this chapter the probability amplitude for a transition of a target electron caused by a charged projectile carrying an electron is formulated. This probability amplitude may be used for transitions of multiple target electrons if the correlation interaction between the target electrons is neglected. Unless the projectile is simply considered as an effective point projectile with a charge Zeff, the interaction between the target and the projectile electrons may not be ignored. Since this interaction is between electrons on two different atomic centers, the effects of this interaction have been referred to as two center correlation effects (Cf. section 6.2.4).

Introduction

In this chapter interactions of photons with atoms are considered. Here the emphasis is on systems interacting with weak electromagnetic fields so that a single atomic electron interacts with a single photon. Initially interactions with a single electron are considered. In this case the photon tends to probe in a comparatively delicate way the details of the atomic wavefunction (e.g. effects of static correlation in multi-electron atoms). Later two electron transitions are considered. Because these two electron transitions are often negligible in the absence of electron correlation the two electron transitions are usually a direct probe of the dynamics of electron correlation.

In previous chapters the impact parameter (or particle) picture has been used wherever possible in order to recover the product form for the transition probability in the limit of zero correlation. However, here the likelihood of interacting with more than a single photon is quite small since the electromagnetic field of a photon, even for strong laser fields, is almost always small compared with the electric field provided by the target nucleus. Consequently, this independent electron limit is not often useful. Also, photon wavepackets are usually much larger in size than an atom. Consequently the wave picture is used where the electric and magnetic fields of the photon are considered to be plane waves. Transformation to the particle picture may be done using the usual Fourier transform from the scattering amplitude to the probability amplitude (Cf. section 3.3.3).

Introduction

The study of reactions involving solids is an important aspect of solid state chemistry from the point of view of understanding the influence of structure and imperfections on the chemical reactivity of solids. It is important to identify the factors governing solid state reactivity in order to be able to synthesize new solid materials with desired structure and properties. Solid state reactions differ from those in homogeneous fluid media in a fundamental respect; whereas reactions in the liquid or the gaseous state depend mainly on the intrinsic reactivity and concentration of the chemical species involved, solid state reactions depend to a large extent on the arrangement of the chemical constituents in crystals. The fact that the constituents are fixed in specific positions in crystals introduces a new dimension in the reactivity of solids, not present in other states of matter. In other words, chemical reactivity is determined more often by the crystal structure and defect structure of solids rather than by the intrinsic chemical reactivity of the constituents. This feature of solid state reactions is clearly brought out in topochemical and topotactic reactions. Most of the photochemical transformations of organic solids are controlled by crystal chemistry. We shall discuss organic solid state reactions in some detail and devote our attention to intercalation reactions of solids that have gained considerable importance recently. We shall briefly deal with some aspects of catalysis to point out how solid state chemistry plays a role in this crucial branch of chemical technology.

Introduction

Relating properties of substances to their structures has been a major objective of modern chemistry and this also happens to be a prime concern of solid state chemists. Some of the aspects of importance in solid state chemistry are electronic, magnetic, superconducting, dielectric and optical properties. We shall briefly discuss these properties and present highlights in the solid state chemistry of some interesting classes of materials. An important class of materials is that of ferroics, which possess several orientation states that can be switched from one to another by the application of an appropriate force; ferroelectric materials form a subgroup of this class of materials. Other classes of materials discussed are amorphous solids, mixed-valence compounds, low-dimensional solids and liquid crystals which are of considerable importance. We have also devoted attention to different types of metal-nonmetal transitions and have briefly examined the question, ‘what makes a metal?’. While a detailed discussion of the theory of electronic structure would be outside the scope of the book, we have presented the necessary background material at an elementary level and discussed some of the typical results obtained from empirical theory as well as electron spectroscopy.

Electrons in solids

In order to correlate the structure and physical properties of solids, it is essential to have a description of valence electrons that bind the atoms in the solid state. Two limiting descriptions of atomic outer electrons in solids are available: the band theory and the localized-electron theory or the ligand-field theory.

Introduction

Characterization is an essential part of all investigations in solid state chemistry and materials science. The various aspects of characterization are: (i) chemical composition and compositional homogeneity of the specimen, (ii) impurities that may affect the properties, (iii) structure, revealing the crystallinity or otherwise of the specimen, crystal system, unit cell and where possible (or necessary) atomic coordinates, bonding and ultrastructure and (iv) the nature and concentration of imperfections (defects) influencing properties. While it may not be possible to achieve complete characterization of a given solid by a single investigator or at any given time, yet without a minimum level of characterization no investigation can be initiated or completed. The scope of ‘characterization’ is so vast that nearly all aspects of solid state chemistry can be included under its domain. According to the US Materials Advisory Board Committee, ‘characterization describes those features of the composition and structure (including defects) of a material that are significant for a particular preparation, study of properties or use, and suffice for reproduction of the material’. The subject of characterization has been reviewed sufficiently in the literature (Cheetham & Day, 1987; Meinke, 1973; Newnham & Roy, 1973; Honig & Rao, 1981; West, 1985) and we shall therefore recount the main essentials and highlight some of the recent developments. The advances made in the last few years in characterization techniques, especially in structure elucidation, have been truly remarkable and have opened new vistas in solid state chemistry.

Introduction

Many solids undergo transformations from one crystal structure to another as the temperature or pressure is varied and this phenomenon is popularly referred to as polymorphism. Whereas polymorphism normally refers to phase transitions involving changes in the atomic configurations in crystals, there are also transitions where the electronic or spin configuration undergoes changes. The subject of phase transitions is not only of great academic interest but also of technological importance. Phase transitions are exhibited by a wide variety of systems (Table 4.1) from simple metals and alloys to complex inorganic and organic materials. The subject has grown enormously in the last two decades with new types of transitions as well as new approaches to explain the phenomena. Traditionally, the subject has been of vital concern to metallurgists (Porter & Easterling, 1981) but there are many aspects of great importance to solid state chemistry (Rao, 1984). Varied aspects of phase transitions such as critical phenomena, soft modes, mechanisms and changes in properties at phase transitions have been treated in a unified manner by Rao & Rao (1978). We shall deal with some highlights of the subject and examine some classes of transitions in this chapter.

Thermodynamics

During a phase transition at the equilibrium temperature, the free energy of the solid remains continuous, but thermodynamic quantities like entropy, volume and heat capacity undergo discontinuous changes. Depending on which derivative of the Gibbs free energy shows a discontinuous change at the transition, phase transitions have been classified as first-order, second-order and so on.

Although solid state science is an area of intense research activity pursued by physicists and materials scientists, the contributions of chemists to this area have a distinct identity. The great skill of chemists in developing novel methods for the synthesis of complex materials, and their understanding of the intricacies of structure and bonding, make their contributions to solid state science unique. At the present time, solid state chemistry is mainly concerned with the development of new methods of synthesis, new ways of identifying and characterizing materials and of describing their structure and above all, with new strategies for tailor-making materials with desired and controllable properties be they electronic, magnetic, dielectric, optical, adsorptive or catalytic. It is heartening that solid state chemistry is increasingly coming to be recognized as an emerging area of chemical science.

In this monograph, we have attempted to present the highlights of modern solid state chemistry and indicate the new directions in a concise manner. In doing so, we have not described the varied principles, properties and techniques that embody this subject at length, but have concerned ourselves with the more important task of bringing out the flavour of the subject to show how it works. We believe that the material covered is up to date, taking the reader to the very frontiers of the subject. We have been careful to include some introductory material for each aspect in order to enable students and beginners to benefit from the book.