Discussion

The results presented in this chapter have revealed new information about three important aspects of the reciprocal space patterns: (i) the forbidden (0 0 l) positions, (ii) the ${\bf c}^*$ splitting of satellites, and (iii) diffuse streaks lying between satellites. All three have been reported to varying degrees in the past, and with little consensus, but the results here do allow some definite conclusions to be drawn about the origin of each, and of the particular relevance of each to the real question in hand which is the intrinsic structural characteristics of the Bi-2212 phase.

(i) The observations have established that the features around the forbidden (0 0 l) positions are not located upon the nodes of the reciprocal lattice but in fact consist of two very diffuse areas of scattering displaced to either side of the node, in incommensurate positions. Where they are present in any one crystal, their precise position and intensities fluctuate apparently at random from one reciprocal space location to the next. They also show no consistencies between the two crystals in which they have been observed, and more significantly have been found to be entirely absent in the two higher quality crystals studied. Their character is therefore very different from that previously postulated, of being weak symmetry violating fundamental reflections, and it must be concluded that these features do not represent any fundamental aspect of the structure. The result therefore confirms the established spacegroup classification. Perhaps the most important clue to their origin is that they have only been observed to be present in the two crystals which were grown by similar methods using alumina crucibles, while they are entirely absent from both the Oxford crystal grown using a platinum crucible, and the Warwick crystal grown using the TSFZ method. Alumina has been perhaps the most widely used crucible material for crystal growth, even though it is commonly known to result in aluminium contamination of the growth at levels as high as a few percent. In contrast, in studies of other platinum grown crystals, taken from the same melt as the one used in this work, no contamination at all could be detected using electron probe microanalysis [103]. Likewise, one of the reasons for the suitability of the TSFZ growth technology is the prevention of contact with any potentially contaminating crucible material, and hence the ability to grow crystals which are free from impurities. This apparent correlation between the use of alumina crucibles and the presence of the diffuse features strongly suggests them to be caused by the inclusion of crucible contaminants, probably acting as growth centres for defect structures such as dislocations or stacking faults. The results highlight the significant effect such low levels of impurities can have upon crystal quality.

(ii) The ${\bf c}^*$ splitting of the satellites has been observed consistently in two crystals, one of which is of a very high quality. The splitting appears in low resolution to have a predominantly disordered nature, producing a strong broadening of the profile along the ${\bf c}^*$ axis. A similar observation led Kan [97] to propose that the phase of the modulation was poorly correlated from layer to layer. This would mean, in Le Page's description of the structure, that there is some variation in the 5,5,4,5... periodic sequence of blocks from layer to layer, or that in the sinusoidal description of the modulation, the modulation function loses phase from layer to layer. However, the high resolution measurements show the splitting to in fact be very well-defined, with the widths of these 'splinters' being only slightly greater than the primary satellites. This is not consistent with the disorder model proposed by Kan [97]. Instead it requires that the modulation wavevector is well defined, and that it is tilted by an irrational angle with respect to the c axis to produce the incommensurate ${\bf c}^*$ component. The wavevector is rigidly defined within a large domain volume, but there exists a range of values through which the wavevector angle may vary, and this angle distinguishes each domain; the large majority still possessing a commensurate ${\bf c}^*$ component. The doubling of the separation of the splinters at second-order is further evidence for this interpretation. The situation is very similar to that of the Bi-2201 case, though the angle is different. Why the effect should arise in one high-quality crystal while it is entirely absent from a second is not yet clear, however, and further studies using other crystals will be required to clarify the matter. The ${\bf c}^*$ component does also vary in the Bi-2201 phase but what factors influence this, and indeed why it should depart from the commensurate at all, have not yet been explained. Perhaps the most likely influence here is a compositional difference between the two crystals. The model of Kan [97] was based upon the knowledge that bonding between adjacent BiO layers is weak and so would therefore be conducive to the slipping of the phase between them, the fact that this continuous disorder is not observed but instead domains with well-defined alignment may perhaps indicate an increased interlayer bonding linked with compositional changes.

(iii) The origin of the diffuse streaks is more puzzling. They have been described previously by both Novomlinsky [99] and Bdikin [92] as satellites of the forbidden (0 0 l) reflections, a description which was dependent upon the presence of the forbidden fundamental reflections. However, such features have been shown here to be impurity-related and completely absent in crystals of a high quality while the diffuse streaks remain undiminished. The fact that the streaks are positioned with the characteristic 0.21${\bf b}^*$ value does undoubtedly relate them to the modulation, and the nature of the streaking along the ${\bf c}^*$ direction strongly suggests an origin linked to some form of interlayer disorder. However, any straightforward model of interlayer disorder, as has just been discussed in relation to the splitting, would be accompanied by the broadening of the satellites in ${\bf c}^*$, and none is observed. So as to avoid broadening the satellites, a mechanism is required then which leaves the overall coherence of the modulation undisturbed but which is itself poorly correlated along the c axis; measurement of widths along ${\bf c^*}$ suggest a coherence of no more than 2 to 3 unit cells. Located as they are between the satellites, the diffuse streaks can also be considered to correspond to a violation of the body centred symmetry of the modulated structure, something which has the effect of removing the ${\bf c}^*$ component of q. In fact, just such a modulation without a ${\bf c}^*$ component is already known to exist in Pb doped Bi-systems. Although the Pb-type modulation has a ${\bf b}^*$ component which is less than 0.21, it has been observed to co-exist with the normal undoped modulation, even within the same region of a sample. A model for the diffuse streaks based upon this would seem the most promising explanation.

In conclusion, no evidence has been found for any secondary modulation of the Bi-2212 structure, all observed anomalous reciprocal space features can be accounted for within the existing modulation models. In particular, the detailed observations of the features around the forbidden (0 0 l) positions re-affirms the accepted spacegroup, and the sample-dependent evidence intimates these features to instead be of an impurity-related origin. The results do require two specific embellishments to the single wavevector modulation, however, neither of which have been considered in the refined models. One is sample-dependent and therefore related to either composition or thermal history, and involves a variation in the direction of the modulation giving a wavevector with a slight incommensurate ${\bf c}^*$ component, a situation previously thought to be confined exclusively to the Bi-2201 phase. The second is a universal characteristic of all crystals it would seem, and is suggestive of some element in the modulation which is relatively coherent and orderly within the b - c plane, most probably within the Bi$_2$O$_2$ layers, but which is strongly disordered between layers. Given the system's strongly anisotropic nature, this is consistent with the belief that the CuO$_2$ layers are rigid and extremely effective at isolating the Bi$_2$O$_2$ layers from each other.