Introduction

The high-temperature superconductor $\rm {Bi_2Sr_2CaCu_2O_{8+\delta}}$ is a member of the series $\rm {Bi_2Sr_2Ca_{n-1}Cu_nO_{2n+4+\delta}}$ (n=1,2 or 3), and it is a representative example of the structurally similar compounds which feature perovskite copper oxide planes separated by a double layered charge reservoir of either BiO, TlO, PbO, or HgO. The Bi-2212 system is most widely studied due to the relative ease with which single crystals can be grown and for its conveniently high transition temperature of around 90K. Common to all compounds in this class the charge reservoir layers display a large degree of inherent disorder, and this has left the task of solving the precise crystallographic structure by traditional techniques of x-ray and neutron refinement a most difficult challenge. The difficulty is compounded by the problems of reliably growing large, high quality single crystals, with both the composition and structural inhomogeneities being extremely sensitive to the thermodynamic conditions of their preparation. In the past many studies by a variety of techniques have resulted in offering conflicting views. It is the purpose of this chapter to clarify the current state of knowledge relating to the modulated structure of Bi-2212.

The presence of incommensurate satellite reflections in the diffraction patterns of the $\rm {Bi_2Sr_2Ca_{n-1}Cu_nO_{2n+4+\delta}}$ phases were reported by the very earliest of studies [35,36,37]. At that stage in the general development of high-T$_c$, in early 1988, little progress had been made in characterising the structural complexities of the cuprates beyond their ideal structures. The surprise at finding such strong, easily observable distortions in this, and later the other related systems, was responsible for an intense initial effort into the study of the bismuth-based systems. A brief historical review of the main points raised by these early studies is given as the start to the next section. A detailed description of the Bi-2212 structure will then be presented, highlighting the points of consensus which have developed within this substantial body of literature. However, the difficult incommensurate nature of the modulated structure has led to various competing models being proposed to account for it. These are assessed, and the common areas of uncertainty, and some contradictions, amongst the published results will be made apparent.

The experiments presented within the remainder of this chapter set out to explore the remaining points of contention which surround the structure of Bi-2212. Within the confines of each specific cuprate structure type (be it Tl-2212, Hg-1212, etc.), there exists a wide range of composition over which the structure may be stable, and within which both physical and structural properties will vary. The accreditation of characteristics observed in the study of particular samples to the position of universal properties of a specific structure type has frequently proved the cause of experimental inconsistencies in the high-T$_c$ field. The failing of such generalisations are typically a sign that further latent variables have still to be considered. The experiments in this chapter attempt to overcome this by repeating measurements on a number of single crystals, each of the crystals having been grown by one of four different research groups, and using a variety of growth techniques. The results have made it possible to identify the features which are closely associated with sample dependent effects, and those which are genuinely associated with fundamental aspects of the structure.