Properties of low dislocation density metal crystals

This thesis describes the growth, X-ray diffraction assessment and tensile deformation properties of dislocation-free copper single crystals. As such it has been possible to conveniently section the work carried out into these three main areas within this thesis. Consequently, each chapter may be read almost independently of the others with references and further work suggestions being incorporated at the end of each chapter. This format, it is felt, does not disjoint the work: rather, it enables the central theme (i.e. the title of this thesis) to be developed in a much more continuously clear way than is normally apparent in a thesis where conclusions, further work suggestions and references are not drawn together until the end of the volume. Chapter I opens with a brief outline of the crystal growth methods which could have been used to produce low dislocation density (andlt;106 cm/cm3) crystals by utilising the three fundamental phase transitions, i.e. solid to solid, vapour to solid and liquid to solid. The Czochralski method is then discussed in detail since it was used by the author to produce dislocation-free copper single crystals. The technological problems in obtaining such crystals are extensively enumerated and solutions presented. For instance, melt surface vibrations were eliminated by using a continuous flow of cooling water, by standing the complete crystal puller on a bed of foam, and by rigidly clamping the R.F. coil. It is emphasised that these technological problems must be solved before the scientific aspects of the growth of dislocation-free crystals can be studied. It is further shown that the author's modified crystal growing technique can be reliably used to grow dislocation-free crystals of copper each time, providing adequate care is taken over growth rates (andasymp;1.2 cm/hr); specimen shape (a long thin "double-neck" must precede the required crystal to eliminate dislocations propagating from the seed and to act as a heat flow resistance); and crystal cooling rates (a long "tail" allowed the crystal to reach the ambient temperature slowly thereby minimising dislocation by thermal stresses and/or vacancy condensation). In the future, it is suggested, an automated crystal pulling system would be advantageous and a study of crystal growth in a synchrotron X-ray beam could be potentially definitive experiment on crystal growth. Chapter II looks at the theoretical aspects of Czochralski crystal growth with the aid of a new model which has been analysed on the Oxford University Computer. The model assumes a crystal-neck-seed configuration to be "sitting" on a liquid and examines the influence of geometric changes of the seed-neck-crystal and of radiation changes on the temperature gradients, primarily at the growth front. Four elements were chosen for study in this way: Si, Ge, Ag, Cu, i.e. four elements which have been grown dislocation-free. It was found that the seed size and shape played a small part in determining the interfacial temperature gradients, DTc(0), of all the elements. The neck, however, could have a marked influence on DTc(0) values in metals but not so much in semiconductor crystals. By geometric control alone it was found that the best way to reduce DTc(0) values was to grow a large diameter crystal. The influence of radiation losses was found to be marked for semiconductor crystals but not for metal crystals. Finally, it is concluded that to minimise DTc(0) values then the seed and neck must be long and thin and the crystal fat. These results fit in well with experimental knowledge. Further work to be carried out could consider the influence of a varying ambient temperature and convective heat losses on the interfacial temperature gradients. Chapter III is concerned with the interaction of X-rays with perfect crystals. The Lang-Borrmann X-ray topography technique is examined, and the experimental methods used to obtain X-ray topographs taken throughout this work are discussed. The major part of the chapter takes up the discussion of the theoretical interaction of X-rays with a perfect crystal set to diffract such X-rays. It is demonstrated that for a plane-wave incident on a cylindrical crystal, for the boundary condition to be satisfied the dispersion surface tie-points are displaced as the crystal traverses the incident X-ray beam. Thus the crystal wave-vectors no longer exactly satisfy the Bragg condition. This effect, was never unambiguously monitored experimentally because of the incident beam divergence. It is suggested that a future study could consider this problem in more detail. The Takagi-Taupin-Uragami generalised X-ray diffraction theory is reviewed and then used to calculate the intensity in the diffracted beam of a traverse topograph from a perfect cylindrical copper crystal. This computer simulation is also compared to an experimental condition. In both cases it is found that the Bragg surface of the crystal produces a very intense reflection whilst the remainder of the crystal gives a much reduced diffracted intensity in comparison. This asymmetric profile is interpreted in terms of absorption mechanisms which are strong at the centre of the crystal but not at the surface. The general agreement between theory and experiment is considered to be good although a few discrepancies arose, e.g. the lateral extent of the Bragg surface peak was found to be larger for the experiment than for the theory. Continued research in this area must explore further these small discrepancies; and it is suggested that a possible line of future study would be to examine theoretically and experimentally the X-ray diffraction from dislocation-free cylindrical crystals which possess low absorption coefficients (e.g. aluminium, silicon) for harder radiations (e.g. MoKandprop;1, AgKandprop;1). It should then be possible to produce interference fringes and then it should be possible to examine the effects of a strain gradient on fringe spacing and visibility. Chapter IV sets out to discuss the tensile deformation behaviour of [1and#773;2and#773;3] growth axis, dislocation-free, chromium plated copper single crystals. This is done using the results from two sets of coupled experiments: an Instron deformation study and a synchrotron deformation investigation. It is first shown that chromium plating can destroy the perfection of the crystal unless care is exercised over plating temperatures and times. It was finally found that after plating for 10 seconds at 55C (andasymp;1 andmu;m of Cr deposited) that there was no indication of lattice dislocation. The stress-strain curve of a chromium plated dislocation-free copper crystal (Cr thickness and#8815;1 andmu;m) is shown to exhibit a yield point commensurate with that for a non-plated, dislocation-free copper crystal, i.e. andasymp;90 g/mm2. The work hardening curve is shown to be comprised of three distinct regions: an initial rapid work hardening rate; a transitionary work hardening rate; and a stabilised work hardening rate up to a shear strain of 6%. In straining the crystal through these regions the work hardening rate progressively decreased. For a plated crystal which is dislocation-free initially it is shown that serrations in the flow curve occur, whilst for all other crystals these are shown to be absent. Such serrations are argued to occur by a source suppression and new source operation mechanism during the early deformation stages (andasymp;1% shear strain), and then by a crack formation mechanism at the copper-chromium interface during the later stages of deformation. The initial work hardening rates (andasymp;18 kg/mm2) were found to be independent of coating thickness (0.5 andmu;m and 1 andmu;m) but in the latter two regions the thicker coating imparted a higher work hardening rate to the crystal than the thinner layer, e.g. for a 0.5 andmu;m chromium layer the work hardening rate was andasymp;1.65 kg/mm2 in region iii and for a 1 andmu;m chromium layer it was 2.97 kg/mm2 in region iii. It is tentatively suggested that the chromium layer affected mobile dislocation motion rather than dislocation generation. The synchrotron work produced no evidence to support the argument that dislocation motion up the elastic line took place. Yielding was found to occur at a stress level similar to that measured in the Instron work. The complex stress system imposed by the deformation jig and the lack of resolution rendered it impossible to decide where the dislocation sources were located. Further increases in the load on the crystal produced double slip and this was argued to prematurely occur because of the combination of torsion, bending and tension which the crystal experienced. Certain interfacial dislocation activity was registered but this was not readily analysed in terms of surface sources. The yielding behaviour was inhomogeneous and appeared to be remote from the few slip bands induced by specimen transport. After yielding evidence was found for dislocation pile-up at the centre of the crystal. It is pointed out that future studies should use a better design of deformation jig so as to apply only a tensile stress to the crystal. Plating thickness and specimen size could be further explored.