The subject of lattice dynamics is taught in most undergraduate courses in solid state physics, usually to a very simple level. The theory of lattice dynamics is also central to many aspects of research into the behaviour of solids. In writing this book I have tried to include among the readership both undergraduate and graduate students, and established research workers who find themselves needing to get to grips with the subject.

A large part of the book (Chapters 1–9) is based on lectures I have given to second and third year undergraduates at Cambridge, and is therefore designed to be suitable for teaching lattice dynamics as part of an undergraduate degree course in solid state physics or chemistry. Where I have attempted to make the book more useful for teaching lattice dynamics than many conventional solid state physics textbooks is in using real examples of applications of the theory to materials more complex than simple metals.

I perceive that among research workers there will be two main groups of readers. The first contains those who use lattice dynamics for what I might call modelling studies. Calculations of vibrational frequencies provide useful tests of any proposed model interatomic interaction. Given a working microscopic model, lattice dynamics calculations enable the calculation of macroscopic thermodynamic properties. The systems that are tackled are usually more complex than the simple examples used in elementary texts, yet the theoretical methods do not need the sophistication found in more advanced texts. Therefore this book aims to be a half-way house, attempting to keep the theory at a sufficiently low level, but developed in such a way that its application to complex systems is readily understood.

We begin by describing the interatomic forces that cause the atoms to move about. The main interactions that we will use later on are defined, and methods for the determination of specific interactions are discussed. The second part of the chapter is concerned with the behaviour of travelling waves in any crystal.

Indications that dynamics of atoms in a crystal are important: failure of the static lattice approximation

Crystallography is generally concerned with the static properties of crystals, describing features such as the average positions of atoms and the symmetry of a crystal. Solid state physics takes a similar line as far as elementary electronic properties are concerned. We know, however, that atoms actually move around inside the crystal structure, since it is these motions that give the concept of temperature, and the structures revealed by X-ray diffraction or electron microscopy are really averaged over all the motions. The only signature of these motions in the traditional crystallographic sense is the temperature factor (otherwise known as the Debye–Waller factor (Debye 1914; Waller 1923, 1928) or displacement amplitude), although diffuse scattering seen between reciprocal lattice vectors is also a sign of motion (Willis and Pryor 1975). The static lattice model, which is only concerned with the average positions of atoms and neglects their motions, can explain a large number of material features, such as chemical properties, material hardness, shapes of crystals, optical properties, Bragg scattering of X-ray, electron and neutron beams, electronic structure and electrical properties, etc.

Measurements of phonon dispersion curves for non-metallic crystals that have been published since 1984 and some that have been published during 1979–1983 are tabulated.

A compilation of the measured phonon dispersion curves, with references, for a number of metals is given by Willis and Pryor (1975, p 226). A similar compilation for insulators is given by Bilz and Kress (1979). The following tables update the compilation of phonon dispersion curves measured in non-metallic crystals. The references from 1984 have been extracted by searching through computer databases, but given that the searches are based on a choice of keywords it cannot be guaranteed that the list is exhaustive.

Sadly a large number of measured dispersion curves never get as far as publication! However, each neutron scattering institute publishes an annual report, which often contains such unpublished data. Alternative sources of dispersion curves are conference proceedings.

The references have been grouped under three headings: molecular crystals, silicates, and ionic crystals.

The discussion in the previous chapter on structure at the molecular level is now extended to include an examination of the more macroscopic features of polymers. This is important because most useful commercial polymers are heterogeneous with properties that depend sensitively upon the dimensional scale of the different component structures in the material. Such is the case for partially crystalline polymers, blends and composites, segregated block copolymers, filled and plasticised systems. Various processing steps can radically alter the scale of heterogeneity, notably thermal treatment. Blending component polymers to achieve desirable properties also introduces many factors which influence the degree of miscibility in the system; method of mixing, solvents, molecular weight and polydispersity, tacticity, the weight fractions of polymer components and the presence or absence of specific chemical entities which act as compatibility promoters.

Clearly, dimensional scale is all important in defining structural heterogeneity. Before discussing the specific contribution of NMR as such, a brief digression is in order to clarify the way in which different experimental and theoretical approaches relate to one another.

Experimental probes of heterogeneity: an overview

The sensitivity of different experimental probes to dimensional scale spans many orders of magnitude. Criteria such as experimental procedure and inherent detection limits of the measuring equipment can lead to differences even within a given technique.