Conclusions and Further Work

The preliminary results obtained in this chapter have shown that the simulation of diffraction patterns from the complex modulated structure of Bi-2212 is entirely possible by means of large scale calculation of scattering from computer models of the structure. Unfortunately, the computational algorithm requires further tailoring for optimising its performance to the parallel architecture of the Connection Machine. It is expected this would then allow fully two-dimensional maps of reciprocal space to be generated without excessive requirements for processor time. It should also be possible to improve the simulation further by subtracting the contribution of the average structure from the scattering, leaving only the diffuse scattering component which is the quantity of interest. Although this would lengthen the amount of processor time required for a calculation, it would be repaid for by the removal of the background features, seen as spikes at commensurate points, which are artefacts of the size of the model crystal. Unfortunately, due to the constraints placed on the time for writing a thesis, it has not yet been possible to implement any of these further developments.

The next step in this work is, of course, to introduce disorder effects, in addition to the modulation, into the model of the structure with the intention of reproducing the experimentally observed diffuse streaks. The methods used in this simulation, of generating a fully developed real space model of the structure, makes it an easy task to manipulate the atomic coordinates in any manner necessary to introduce the disorder, and as this can be done entirely separately to the intensity calculation, the computational task is in no way lengthened. In the model of the structure used here, a harmonic approximation has been used. One possible route, for instance, to simulating the diffuse streaks would be to introduce a second modulation wavevector q, using equation 7.2 but with a variation in its symmetry, or amplitude components u and v as necessary. The model suggested at the close of Chapter 5 could also be tested, by the incorporation of additional oxygen sites into the Bi$_2$O$_2$ layer and by applying different correlations to their positions along the b axis.

Considerable scope also exists for further experimental investigations of the changes which were observed to be induced in the diffuse streaks by annealing, in Chapter 5. This is a potentially important observation which could provide another key to finally understanding the inter-relationships between oxygen stoichiometry, structure, and transport properties in both normal and superconducting regimes. The x-ray study needs to be extended to a number of additional single crystals, to confirm the nature of the changes, and rule out any possibility that they could be some effect specific to that one particular crystal. Annealing schemes at temperatures different to those used in Chapter 5 should be adopted, and the effects of slow cooling instead of quenching the samples could be explored (as low temperature oxygen-ordering has proved significant in Y-123). Ideally, although always problematic, more precise efforts need to be made to measure the change in oxygen content induced by the annealing using again EPMA, or some other method, and this time measuring the same sample both before and after the annealing. A most valuable complement to this, and a more direct way of linking the structural changes with the charge transfer process is to carry out Hall measurements of the carrier density before and after annealing (should it prove that a more significant change in $n_s$ occurs than can be attributed to a small or non-existant measured value of $\Delta\delta$, then oxygen ordering would be a likely candidate). Ultimately, if the specific oxygen sites associated with the diffuse streaks, and with the two distinct oxygen diffusion mechanisms of Chapter 4 are to be unequivocably identified, then neutron diffraction studies of the structure will be required, which would unfortunately require crystals of a larger size than are presently available.

The strong dependence of a number of other properties, such as magnetic flux pinning, and c-axis and ab-plane resistivity, upon oxygen stoichiometry suggests that correlations might also be found between changes in their unusual behaviour and the effects of annealing observed in the diffuse streaks. A coordinated programme of measurements of all these variables alongside the characterisation just described, could prove the most productive route to establishing conclusive evidence for the importance of oxygen microstructure within the Bi$_2$O$_2$ layers, which has been suggested by the conclusions of Chapter 5, and potentially throw light on a number of poorly understood phenomena associated with these properties. Such results would certainly provide the most persuasive link to relating the effects observed, so far in isolation by using x-ray scattering, with the effects discussed more generally in the literature and observed by other more conventional means (the electron diffraction evidence relating to flux pinning mechanisms discussed in Chapter 4, is just one example).

Finally, the experimental work in this thesis has been limited to only a single cuprate system, Bi-2212. This was not a deliberate choice but rather an enforced one due to the unavailability of crystals of a size large enough to make feasible the kinds of laboratory based x-ray measurements which have been undertaken here. However, now that the value of x-ray scattering measurements in characterising the complexities of the cuprate structures has been thoroughly demonstrated in its application in this thesis to Bi-2212, future efforts should be encouraged to extend this work to other systems. Improvements in growth techniques have been such that single crystals of Bi-2201 of a suitable size may now be available. Where crystal sizes remain severely restricted, as is the case in the Tl-systems and Bi-2223, valuable measurements should still prove possible if use is made of the availability of the far greater x-ray intensity (combined with smaller beam size) at a synchrotron source. The extra efforts needed to undertake such work could be rewarded by revealing the subtleties of these structures, which are amongst the least well described. Also, how the the modulations in the Tl- and Bi-systems respond differently, particularly with regard to the strength of the bonding between the double rocksalt-type layers (the separation of these layers is only 2$\AA$ in Tl-2212 compared with 3.25$\AA$ in Bi-2212) may provide new insight into establishing which crystallographic parameters have the dominant influence in determining the nature of the modulations in this whole class of layered structures.