Introduction

As outlined in the historical introduction (chapter 1), a slight but puzzling discrepancy between the early experimental results on the de Haas–van Alphen oscillations in Bi (Shoenberg 1939) and Landau's theoretical formula was that the observed field and temperature dependences of the amplitude could not be consistently reconciled with the formula. To a fair approximation it was as if the temperature needed to fit the formula was higher than the actual temperature. An explanation of the discrepancy was suggested by Dingle (1952b) who showed (as discussed in §2.3.7.2) that if electron scattering is taken into account, the Landau levels are broadened and this leads to a reduction of amplitude very nearly the same as would be caused by a rise of temperature from the true temperature T to T + x. This extra temperature, x, which is needed to reconcile theory and experiment, has come to be known as the Dingle temperature and we shall refer to the amplitude reduction factor exp(- 2π2kx/βH) as the Dingle factor. Dingle's suggestion also explained an earlier puzzling observation, which was that addition of any impurity to Bi always reduced the oscillation amplitude (Shoenberg and Uddin 1936); this would be expected in view of the increased probability of electron scattering.

For a good many years Dingle temperatures were recorded somewhat casually in studies devoted mainly to FS determinations from frequency measurements, but no systematic studies were attempted and there was little attempt to interpret such results as there were.

Introduction

During the last 25 years de Haas–van Alphen studies have led to a spectacular advance in our knowledge of the Fermi surface of metals and (to a lesser extent) of the differential properties of the surfaces of constant energy in the vicinity of the FS. This progress has been made possible partly by parallel developments in the theoretical understanding of band structures, but perhaps more significantly by advances in technology. These advances, in the production of high magnetic fields and low temperatures, in electronic techniques and data processing and in the growing of purer and more perfect single crystals, are still continuing and hopefully will continue to be exploited to extend our knowledge still further.

By far the greatest effort has gone into measurements of dHvA frequencies F with a view to the determination of the FS of metals through the Onsager relation and by now the FS of nearly all the metallic elements and of many intermetallic compounds have in fact been determined. The level of determination achieved however, varies both in the degree of certainty with which the qualitative nature of the surface has been established and in the precision of the quantitative specification of the surface. At best, the qualitative nature of the surface (i.e. the number and shapes of the separate sheets) is reliably known and the dimensions of the various sheets determined with a precision of order 1 in 10.

It is just over 50 years ago that an oscillatory magnetic field dependence was first observed in the electrical resistance of bismuth by Shubnikov and de Haas and in the magnetization by de Haas and van Alphen. It was not long before Peierls showed how these effects could be understood in principle and, indeed, Landau had implicitly predicted oscillatory behaviour even before the experimental discovery, but the effects remained somewhat of a scientific curiosity for upward of 20 years. It was only in the 1950s with the observation of magnetic oscillations in many metals other than bismuth and the advent of improved theoretical understanding that it began to be realized that the effect was not only an aesthetically pleasing curiosity but potentially a powerful tool for understanding the electronic structure of metals.

During the following 20 years, exploitation of this possibility became somewhat of a ‘band wagon’ and with ever improving experimental and theoretical techniques, an immense amount of detailed information about the ‘Fermiology’ of individual metals has emerged. More recently the pace has slackened, though there are still many loose ends and unsolved problems, and during a sabbatical half year at the University of Waterloo in 1977, I felt the time was ripe for a new comprehensive review and somewhat light-heartedly embarked on it little thinking it would be five years before it was ready for the Press.

INTRODUCTION

Before direct observations could be made on dislocations there were four main classes of experimental evidence pointing to the existence of a class of crystal imperfections which we now analyse in terms of the dislocation concept. The earliest body of evidence was that from X-ray diffraction: within a year or two of the discovery of this phenomenon by Friedrich, Knipping, and von Laue in 1912, it became evident that the diffraction intensities from most real crystals were very different from those one would calculate on the assumption of ideal crystal structures. A rather ill-defined concept of mosaic structure was employed for a generation to account in general terms for these discrepancies. We have ultimately learnt that their cause is sometimes well described by the term ‘mosaicstructure’, sometimes not, but in either case we are able to describe the inferred departure from the ideal structure in some detail in terms of dislocations. The next body of evidence was concerned with the mechanical properties of solids, which, to put it briefly, are a thousand times weaker than ideal crystals. The fact became increasingly evident as people acquired confidence in the Born type of model for the ideal crystal, which accounts very well for the elastic or thermal properties, but indicates plastic strengths vastly in excess of those of technical materials. It was to explain these discrepancies that Taylor and Orowan independently put forward the concept of crystal dislocations in 1934.

INTRODUCTION

It is now just over ten years ‡ since the first observations of dislocations in metal foils by transmission electron microscopy were reported by Hirsch, Home and Whelan (1956) and independently by Bollmann (1956). Since that time the technique has been applied to such a variety of problems in crystal and metal physics and the literature on the subject is now so voluminous that it is impossible in a chapter of this length to give an exhaustive review. Instead the author intends to concentrate first on an exposition of the principles of the technique (sections 3.2 and 3.3) both from the practical point of view and from the point of view of theories of interpretation of image contrast. Some applications to various problems in metal physics will then be described (sections 3.4 and 3.5), which will mainly be illustrative of work done in the Cavendish Laboratory. For this the author makes no apologies in view of the above remark, believing that this work is fairly typical of current applications of the technique.

EXPERIMENTAL TECHNIQUES

Preparation of thin specimens for transmission electron microscopy

Metallic specimens suitable for examination by transmission of electrons in the electron microscope must be of the order of a few (about two) thousand Ångstrom units in thickness or less depending on atomic number. Several methods exist for preparing thin specimens:

1. Chemical deposition and electrodeposition from solution.

2. Vacuum evaporation onto a suitable substrate followed by stripping.

3. […]