Solid State Chemistry
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Solid State Chemistry

An Introduction

Elaine A. Moore, Lesley E. Smart

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eBook - ePub

Solid State Chemistry

An Introduction

Elaine A. Moore, Lesley E. Smart

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Über dieses Buch

Solid State Chemistry: An Introduction presents a wide range of the synthetic and physical techniques used to prepare and characterize solids. Going beyond this, this largely nonmathematical introduction to solid state chemistry includes the bonding and electronic, magnetic, electrical and optical properties of solids. Solids of particular interest – porous solids, superconductors and nanostructures are included. Practical examples of applications and modern developments are given. It offers students the opportunity to apply their knowledge in real-life situations and serve them well throughout their degree course.

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CRC Press

1 An Introduction to Crystal Structures

The last few decades have seen much exciting research into solid-state chemistry. We have seen immense strides in the development of nanotechnology and solids contributing to the development of sustainable energy devices such as photovoltaic cells, fuel cells, and batteries, to mention but a few areas. It would be impossible to cover all the developments and topics in detail in an introductory text such as this, but we endeavour to give you a flavour of the excitement that some of the research has engendered and perhaps, more importantly, sufficient background with which to understand these developments and those that are yet to come.
Most substances, helium being a notable exception, if cooled sufficiently form a solid phase; the vast majority form one or more crystalline phases, where the atoms, molecules, or ions pack together to form a regular repeating array. This book is concerned mostly with the structures of metals, ionic solids, and extended covalent structures; structures that do not contain discrete molecules as such, but that comprise extended arrays of atoms or ions. We look at the structure of, and bonding in, these solids, how the properties of a solid depend on its structure, and how the properties can be modified by changes to the structure.

1.1 Introduction

To understand the solid state, we need to have some insight into the structure of simple crystals and the forces that hold them together, so it is here that we start this book. Crystal structures are usually determined by the technique of X-ray crystallography. This technique relies on the fact that the distances between the atoms in the crystals are of the same order of magnitude as the wavelength of X-rays (of the order of 1 Å or 100 pm): a crystal thus acts as a three-dimensional diffraction grating to a beam of X-rays. The resulting diffraction pattern can be interpreted to give the internal positions of the atoms in the crystal very precisely, thus defining interatomic distances and angles. (Some of the principles underlying this technique are discussed in Chapter 2, where we review the physical methods available for characterising solids.) Most of the structures discussed in this book would have been determined in this way.

1.2 Lattices and Unit Cells

Crystals are regular-shaped solid particles with flat shiny faces. In 1664, Robert Hooke first noted that the regularity of their external appearance is a reflection of a high degree of internal order. Crystals of the same substance, however, vary in shape considerably. In 1671, Nicolas Steno observed that this is not because their internal structure varies, but because some faces develop more than others. The angles between similar faces on different crystals of the same substance are always identical. The constancy of the interfacial angles reflects the internal order within the crystals. Each crystal is derived from a basic ‘building block’ that repeats over and over again, in all directions, in a perfectly regular way. This building block is known as the unit cell.
In order to talk about and compare the many thousands of crystal structures that are known, there has to be a way of defining and categorising the structures. This is achieved by defining the shape, symmetry, and also the size of each unit cell and the positions of the atoms within it.

1.2.1 Lattices

The simplest regular array is a line of evenly spaced objects such as that depicted by the commas in Figure 1.1a. There is a dot at the same place in each object: if we now remove the objects leaving the dots, we have a line of equally spaced dots of spacing a (Figure 1.1b). The line of dots is called the lattice, and by definition each lattice point (dot) has identical surroundings. This is the only example of a one-dimensional lattice and it can vary only in the spacing a. There are five possible two-dimensional lattices, and everyday examples of these can be seen all around in wallpapers and tiling.
FIGURE 1.1 (a–c) A one-dimensional lattice and the choice of unit cells.

1.2.2 One- and Two-Dimensional Unit Cells

The unit cell for the one-dimensional lattice in Figure 1.1a lies between the two vertical lines. If we took this unit cell and repeated it over and over again, we would reproduce the original array. Notice that it does not matter where in the structure we place the lattice points as long as they each have identical surroundings. In Figure 1.1c, we have moved th...