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.

Since its inception, nuclear magnetic resonance (NMR) has been used with remarkable success to investigate polymeric materials. However, application to solid polymers was for many years largely the province of physicists and physical chemists because of the need for specialised spectrometers to gain access to the broad spectra (usually H) typical of solids, and because interpretation of these spectra and associated relaxation times required theoretical models of a strongly physical nature. The chemist, meanwhile, was more than satisfied to exploit the enormous potential provided by the increasing power of liquid-state NMR spectroscopy which had benefited considerably from the introduction of Fourier transform (FT) methods, the availability of higher fields generated by superconducting magnets with concomitant enhanced sensitivity, formidable on-line computing capabilities, and the added flexibility of multidimensional NMR. The rich site-specific information in high-resolution liquid-state NMR remained undetected in early solid-state spectra because of the dominant dipolar contribution. Sustained efforts to achieve comparable results for solids led to procedures to suppress dipolar contributions using high-power decoupling techniques, sample spinning and the application of ingenious pulse sequences. Today the full power of high-resolution one-, two- and three-dimensional NMR is available for solid materials, albeit requiring more sophisticated experimentation and analysis. Specifically, multidimensional NMR permits different spin interactions to be correlated or separated, exchange between different states of a resonant nucleus to be monitored over selected timeframes and the intricacies of complex molecular motions to be elucidated.