High-resolution electron microscopy of dislocation geometries

Conventional strong-beam imaging techniques have been widely applied in the study of crystal defects, the main advantage being the high intensity of the images which reduces photographic exposure times to a few seconds at most, thus avoiding problems of drift and contamination. However, such images have the disadvantage of not being related in any simple way to the defect geometry, and they are relatively insensitive to small changes in the strain field. The width of a peak from a dislocation can be ~100 Å for 100keV electrons, and so the study of dislocations separated by the much smaller distances that are found in dissociated dislocations or faulted dipoles in pure metals is very difficult, even with careful computed image matching techniques. The weak-beam technique of electron microscopy (Cockayne, Ray and Whelan 1969) overcomes this problem by tilting the specimen so that only the highly-strained regions near dislocation cores contribute to the final image; narrow (~15 Å) , relatively intense peaks which lie close to the defects are obtained by this approach, and such images are ideal for investigating closely-spaced dislocations.
This thesis describes the study of various dislocation geometries by the weak-beam technique and the calculation of equivalent images. Chapter 1 reviews the theories of electron diffraction which are needed both to understand the properties of weak-beam images and also to compute the images required for comparison with experimental micrographs. Such calculations require a knowledge of the displacement field of a dislocation, and in most cases if any useful information is to be derived from weak-beam observations of dislocation networks (e.g. the stacking-fault energy) the stress fields are also required. Chapter 2. discusses the anisotropic theory of infinite straight dislocations as given by Stroh (1958); the only defects considered here are those for which this infinite straight approximation is reasonable, e.g. the partial dislocations in a faulted dipole, or the dissociated straight edge of a very large loop.
Chapter 3 applies the weak-beam technique to the study of faulted dipoles in copper and it is shown that such images define the dipole geometry with a greater accuracy than hitherto possible using conventional techniques. Previous strong-beam studies of faulted dipoles are also discussed. An upper limit for the stacking-fault energy of copper of γmax = 47 ± 8 erg cm-2 is obtained. It is concluded that similar studies are potentially very useful for estimating the stacking-fault energy of materials for which γ and the elastic constants are such that the dissociation of single dislocations cannot be resolved.
The rest of the thesis considers the effect that a finite divergence in the illuminating beam of electrons has on weak-beam images. The oscillatory effects dependent on depth and thickness which are often observed in weak-beam image computations when assuming a parallel beam can be damped or removed altogether when calculations are performed which make allowance for a finite divergence. Chapter 4 considers divergent illumination from a theoretical point of view and it is shown that effective damping of the depth and thickness oscillations should occur if the defect is greater than a distance d = 1⁄2Δs from either surface, where Δs = gΔθ is the spread in the deviation parameter s introduced by a finite divergence Δθ in the incident beam.
Chapter 5 calculates the images of single undissociated and dissociated dislocations in copper including the effect of a finite beam divergence. The predictions of Chapter 4 concerning the damping of the oscillations and the above formula for d are shown to be valid in these cases. The effect of anisotropy on the symmetry of images of dissociated dislocations is considered and the results of the image calculations are also used to analyse the author's experimental observations of dissociated dislocations in copper. The result obtained for the stacking-fault energy is γ = 44 erg cm-2. This result is dependent on the assumption that the partial dislocation cores are singular. The effect of a finite core extension on this value is discussed, and it is argued that the good agreement between this figure and that deduced from the studies of faulted dipoles in Chapter 3 is evidence supporting the view that core extension effects are negligible in faulted dipoles and dissociated edge dislocations in this material.
Chapter 6 considers the dissociation of the Frank partial dislocation into a stair-rod and a Shockley partial. Such a dissociation is thought to occur in small Frank loops in heavy-ion irradiated copper, but previous weak-beam investigations have not resolved the partials due to the presence of stacking-fault contrast. In theory {113} reflections at the (110) pole should image both partials but not the stacking faults. To simplify the computer simulation of experimental micrographs when investigating these new diffraction conditions, very large faulted Frank loops in copper and copper-aluminium alloys were grown by electron irradiation at elevated temperatures in a high-voltage electron microscope. The partials in any one dissociated side can then be simply represented by two infinite straight dislocations and the effect of the rest of the loop is ignored. The weak-beam images in general show two peaks corresponding to the two partials; as the dissociation always produces an obtuse fault bend, the ribbon of fault between the partials is intrinsic in nature, which suggests that the intrinsic stacking-fault energy is less than the extrinsic in these materials. The images calculated assuming a parallel incident beam of electrons do not agree with the experimental images since two, three or four peaks which are very sensitive to small changes in defect depth and foil thickness are predicted; these effects are not observed in practice. However, with a finite value of beam divergence the images become more uniform and only two peaks are predicted which exhibit inside-outside contrast effects on reversing g. Therefore the assumption of a finite beam divergence has proved essential in understanding the images of a dissociated Frank partial, and suitable diffraction conditions have been developed for studying such dissociations which may be applicable to small loops.
Chapter 7 contains general conclusions and suggestions for further work.