Introduction

Availability of pure, well-characterized solid samples is crucial to all solid state studies. A knowledge of the various experimental methods available for the preparation of solids therefore becomes an important and integral part of solid state chemistry (Corbett, 1987; Hagenmuller, 1972; Honig & Rao, 1981; Rao, 1994). A brief reflection on the development of solid state science reveals that, in many cases, it is the synthesis of a novel compound that has triggered off a new line of research. Tables 3.1 and 3.2 provide a few examples to illustrate the point. To many solid state scientists, preparation of solids may mean preparation of single crystals of elements or simple compounds (e.g. Si, Ge, III-V semiconductors, alkali halides, etc.) for a study of a specific property or for technical applications. Preparation of solids is, however, a much more general activity, particularly amenable to chemists. A variety of strategies are adopted to prepare solids and to grow crystals. Technological advances have enabled solid state chemists to employ a broad range of conditions for preparative purposes. Ultra-rapid quenching of materials from very high temperatures, irradiation heating by intense laser beams, melting of solids by electron-beam heating or by the skull method and use of high pressures have become common procedures. Thus, by employing high-power CO2 lasers (> 1200 W) several entropy-stabilized metastable (e.g. α-CaCr2O4, BaNi2In8O15) and mixed-valent oxides (e.g. Sr7Nb2IVNb4VO21 and Ba2TiIII12TiIVO22) have been synthesized (Möhr & Müller-Büschbaum, 1995).

Introduction

Solid state chemistry deals with a variety of solids, inorganic as well as organic; the solids can be crystalline or noncrystalline. A sound knowledge of the structure of solids as well as of the nature of bonding is essential for an appreciation of solid state chemistry since properties of solids are, by and large, determined by the structure. Crystal chemistry of inorganic solids has been reviewed widely in the literature (see, for example, Adams, 1974; Rao, 1974; Wells, 1984), but there has been effort of late to explore new ways of looking at inorganic structures and to understand their stabilities. In this chapter, we shall briefly review the highlights of inorganic crystal chemistry after summarizing some of the basic information related to crystals and the different types of bonding found in them. We shall also discuss polytypism, organic crystal structures and related topics before finally presenting the models employed to understand the structures of noncrystalline or amorphous solids.

Description of crystals

A regular crystal consists of an infinite array of constituent units in three dimensions. Since the nature of the constituent unit does not affect translational periodicity, the periodicity is generally represented by replacing the repeating unit by a point, the resulting array of such points in space being called a lattice. In a space lattice, the translation vectors a, b and c in the three crystallographic directions define a parallelepiped called a primitive cell.

The first edition of this book published in 1986 was well received by the chemistry and materials science communities and this resulted in the paperback edition published in 1989. We are most gratified by this warm reception to the book which has been found useful by students and teachers as well as practising solid state chemists and materials scientists. Since we first wrote the book, there have been many new developments in the various aspects of solid state chemistry covering synthesis, structure elucidation, properties, phenomena and reactivity. The discovery of high-temperature superconductivity in the cuprates created a great sensation and gave a boost to the study of solid state chemistry. Many new types of materials such as the fullerenes and carbon nanotubes have been discovered. We have now revised the book taking into account the new developments so that it reflects the present status of the subject adequately and points to new directions. In this edition, we have incorporated new material in all the chapters and updated references to the literature. New sections dealing with porous solids, fullerenes and related materials, metal nitrides, metal tellurides, molecular magnets and other organic materials have been added. Under preparative strategies, we have included new types of synthesis reported in the literature, specially those based on soft chemistry routes. We have a new section covering typical results from empirical theory and electron spectroscopy.

Introduction

We discussed several interesting and useful properties of solids in the previous chapter. Tailor-making materials of desired properties is an integral part of modern solid state chemistry and an account of the subject would be incomplete without reference to it. To do justice to any one class of materials or to any one type of application, we would have to deal extensively with materials design, devices and other technological details. Since this would be beyond the scope of this monograph, we shall briefly present a few of the selected materials applications.

An area of great technological relevance today is high-performance ceramics (Bowen, 1980; Katz, 1980; Sanders, 1984). The term ‘ceramic’ itself refers to an inorganic, nonmetallic material processed or consolidated at high temperatures. Some ceramic materials (e.g. cubic BN, SiC, Si3N4) are hard, oxidation-resistant and light. They can often be made from abundantly available raw materials and are less expensive than metals. The shortcomings of ceramics are that they are generally brittle and difficult to make in large complex shapes. Uniform submicron powders required for making high-technology ceramics are made by the sol-gel process or from the vapour phase. Fibres made of Si3N4, SiC or carbon are toughened by depositing metals or silicon around them; lithium aluminium silicate glass ceramics are reinforced with SiC fibre. Ceramic materials are used in heat engines (e.g. Si3N4), as materials of fabrication, as thermistors, as substrates for electronics (e.g. barium silicate) and in magnetic and other applications.

Introduction

That compounds have definite compositions is taken as a matter of faith and yet there are several inorganic solids which exhibit a wide range of compositions or show no simple correspondence between the composition and the detailed structure (or chemical identity). It has been known since the 1920s that stoichiometric FeO1.00 does not fall in the stability range of iron (II) oxide (FeO1.05–FeO1.15). Point defects in crystals such as vacancies and interstitials first described by Schottky, Frenkel and Wagner account for the transport properties of ionic solids, but there are serious difficulties in applying the point-defect formalism to solids possessing a wide stoichiometric range or to those solids exhibiting ordering of defects or extended defects (such as crystallographic shear planes). Although there is no clear-cut transition between the point-defect regime and the regime of highly ordered structural imperfections in nonstoichiometric solids, we can certainly say that the point-defect model is really valid only when the defect concentration (or the deviation from stoichiometry) is extremely small. Only in such dilute point-defect systems can one satisfactorily relate the electronic properties and the nonstoichiometry to the concentration of point defects.

A few general comments related to disorder and nonstoichiometry in crystals would be in order. Solids rarely attain a state of perfect order even when they are cooled close to absolute zero of temperature. At ordinary temperatures, crystalline solids generally depart from perfect order and contain several types of imperfections, which are, indeed, responsible for many important solid state phenomena such as diffusion, electrical conduction, plasticity and so on.

Although oxides have been the subject of active research for many years, they have attracted an increasing interest in the last decade. One reason for this interest is the discovery of superconductivity in copper oxide based materials, in 1986, with critical temperatures higher than the temperature of liquid nitrogen. Simple oxides have also been more thoroughly studied and a detailed analysis of their surface properties has been undertaken, thanks to several technological advances made during this period. The success in compensating charging effects, for example, has allowed spectroscopic measurements to be performed. Photoemission, x-ray absorption, Auger spectroscopy and low-energy electron diffraction now yield quantitative information, as they do for semi-conductors and metals. Topographic images of insulating surfaces can be recorded with an atomic force microscope. On the theoretical side, advanced numerical codes have been developed, which solve the electronic structure, optimize the geometry, and start accounting for dynamical effects in an ab initio way. The results presently available allow a first synthesis of the field.

The interest and the richness of the field of oxide surfaces lies in its inter-disciplinary nature and in the diversity of questions it raises, both on a fundamental and on an applied level. For example, geophysicists and geologists consider in detail the surface properties and porosity of the rocks of our earth, made of complex oxides whose properties are, to a large extent, controlled by the grain boundaries and internal surfaces.

In the surface layers, the breaking of anion–cation bonds and the modifications of inter-atomic distances, induced by relaxation, rumpling or reconstruction effects, perturb the electrostatic potentials and the orbital hybridization. The surface electronic structure is thus modified and presents specific features compared to the bulk characteristics. In this chapter, we will discuss various aspects of these changes, relevant for planar semi-infinite systems, thin films and defected surfaces. We will restrict ourselves to the results obtained on single crystals, prepared under controlled conditions and studied in ultra-high vacuum (Henrich, 1983; 1985; Henrich and Cox, 1994). Instead of focusing on specific properties of this or that oxide, we will try to extract the general trends concerning the density of states, the gap width, the charge densities, etc., and, whenever this is possible, we will point out the physical origin of the differences found between the bulk and the surface electronic structure.

Experimental and theoretical studies

The study of the surface electronic structure requires specific tools. For example, in spectroscopic experiments, in order to enhance the surface signal with respect to the bulk one, to obtain information on the outer layers, one has to send or detect particles with small mean free paths, which mainly sample the few outer layers. Similarly, special care has to be taken in the numerical approaches. We will quickly review some aspects of this question, both from the experimental and the theoretical sides.

Introduction

The research field of metal–oxide interfaces is very active, partly because of their important technological applications. For example, in heterogeneous catalysis, oxide powders or porous compounds, such as zeolites, are used as supports for transition metal clusters, because they provide a large – external or internal – specific area of contact with the metal. In many cases, it is also recognized that they modify the cluster reactivity (Dufour and Perdereau, 1988). Oxide surfaces, such as those of MgO or SrTiO3, whose quality and planarity are well controlled, have been used as substrates for the deposition of thin superconductor films. This has been particularly important since the discovery that some copper oxide based compounds remain superconductors above liquid nitrogen temperature. Thin metallic films are also deposited on various oxides in the fabrication of optical devices, or on glass in the fabrication of mirrors.

Oxides are often chosen as insulation materials, for example as sheaths for resistive heaters, due to their low electrical and thermal conductivity. In MOS transitors (MOS = Metal–Oxide–Semi-conductor), a thin SiO2 layer is deposited between a doped silicon substrate and the metallic gate to control the channel conductivity. In more complicated electronic devices, with several integration levels, SiO2 is also used to make insulating dielectric layers.

This first chapter summarizes the main bulk characteristics of insulating oxides, as a prerequisite to the study of surfaces. The foundations of the classical models of cohesion are first recapitulated, and the distinction between charge-transfer oxides and correlated oxides is subsequently established. Restricting ourselves to the first family, which is the subject of this book, we analyse the mixed iono–covalent character of the anion–cation bonding and the peculiarities of the bulk electronic structure. This presentation will allow us to introduce various theoretical and experimental methods – for example, the most common techniques of band structure calculation – as well as some models – the partial charge model, the alternating lattice model – which will be used in the following chapters.

Classical models of cohesion

Ionic solids are made up of positively and negatively charged ions – the cations and the anions, respectively. The classical models postulate that the outer electronic shells of these ions are either completely filled or empty, so that the charges have integer values: e.g. O–– (2p6 configuration) or Mg++ (3s0 configuration). The strongest cohesion is obtained when anions and cations are piled up in an alternating way – the anions surrounded by cations and vice versa –, a stacking which minimizes the repulsion between charges of the same sign.

The hard-sphere model

In the first models, due to Born and Madelung, the ions are described as hard spheres, put together in the most compact way (Kittel, 1990).

When a crystal is cut along some orientation, the atoms located in the few outer layers experience non-zero forces which are induced by the breaking of oxygen–cation bonds. Generally, they do not remain at the positions fixed by the three-dimensional lattice. Point or extended defects may result, as well as lattice distortions. This chapter analyses the structural features of oxide surfaces, which is also a useful step, before starting the discussion of the surface electronic properties. Yet, conceptually, this presentation is not fully satisfactory, because the structural and electronic degrees of freedom are coupled and both determine the ground state configuration. Despite a rich literature, the structural properties of oxide surfaces are not fully elucidated. It is often difficult to prepare stoichiometric and defect-free surfaces, and the characterization is hindered by charging effects and by an uncertainty about the actual crystal termination.

Preliminary remarks

We will make some preliminary remarks concerning the designation of the surfaces, their polar or non-polar character and their structural distortions – relaxation, rumpling and reconstruction.

Notations

A plane in a crystal, is identified by three integers (h, k, l), called the Miller indices, which are in the same ratio as (1/x, 1/y, 1/z), the inverses of the coordinates of the intersections of this plane with the crystallographic axes (van Meerssche and Feneau-Dupont, 1977). Notations with four indexes (h, k, –(h + k), l) are used in hexagonal structures, such as α-quartz, corundum α-alumina, or the wurtzite ZnO structure.

A semi-infinite crystal supports specific excitations which are not present in the bulk material. In oxides, these new modes result from the breaking of anion–cation bonds at the surface, whose effects on the electronic and atomic structure have been the subject of the two previous chapters. Here, we will describe the excitations associated with the atomic and electronic degrees of freedom. The phonons, which are the quantized modes of vibrations of the atoms, have small characteristic energies, of the order of a few tens of milli-electron volts (meV). The electron–hole pairs and plasmons, which are characteristic of the electronic degrees of freedom, have much higher energies, of the order of a few electron-volts. Due to the different time scales involved, a decoupling between these two types of excitations takes place (Born–Oppenheimer decoupling). The electrons are able to follow ‘instantly’ the atomic displacements, while the atoms have no time to move at the time scale of the electron delocalization and excitations.

Surface phonons

We have seen in Chapter 2 that bond-breaking on a surface greatly modifies the atomic energy levels. The same is true for the atomic vibrations around the equilibrium positions. In this section, we will review the main experimental and theoretical results concerning surface phonons on oxide surfaces.

Experimental and theoretical approaches

High-resolution electron energy loss (HREELS = high-resolution electron energy loss spectroscopy) experiments and inelastic scattering of helium atoms allow a determination of the surface vibration modes and of the phonon dispersion curves.

Condensed matter physics by its very nature deals with systems with a large number of degrees of freedom, i.e. systems for which a statistical description is essential. In this chapter, we will present a rather comprehensive review of the fundamentals of thermodynamics and statistical mechanics. Much of this chapter, especially the parts dealing with homogeneous fluids (ideal and interacting gases and liquids), should be familiar to everyone. They are included here mostly to establish a basis for discussing more complicated ordered systems. As we saw in the preceding chapter, a great deal of useful and experimentally accessible information is contained in correlation functions such as the density-density correlation function Cnn(x,x′). This chapter will define these functions in a statistical mechanical context and develop a method of calculating them using functional differentiation with respect to spatially varying external fields. Functional differentiation will allow us to calculate position-dependent correlation and response functions by a simple generalization of the familiar technique used to calculate the magnetic susceptibility by differentiating the free energy with respect to the magnetic field. This is a very powerful tool that will be used throughout this book. It is presented here first in a familiar context that should make it easy to grasp.

After reviewing the properties of homogeneous fluids, we will introduce order parameters in Sec. 3.5 and show how they modify both thermodynamics and statistical mechanics.