Introduction

The response of the incommensurate modulation to elevated temperature can provide important information about its properties and origin. The modulation is believed to be closely associated with the presence of excess oxygen atoms in the Bi$_2$O$_2$ layers (this was discussed in detail in Chapter 3). However, direct proof of this is difficult to obtain, and whether the oxygen plays a fundamental role in the formation of the modulation is not known. An obvious indirect test is to study the response of the modulation to high temperatures, as it is well established that under suitable high temperature vacuum conditions oxygen will diffuse out of the structure. The behaviour of the intensity of satellite reflections relative to that of the fundamental reflections is sensitive to changes in the modulation amplitude, and hence an x-ray scattering study of the annealing process in situ is an ideal method to study the relationship between oxygen stoichiometry and the incommensurability.

Of further motivation to this work is the potential for structural change due to the variation in layer mismatch which must accompany any change in temperature. Amongst the misfit layer structures, such as the examples discussed in Chapter 2, the variation with temperature of a structure's modulation wavevector is a commonly observed property, and amongst perovskite-related structures generally a wide range of structural phase transitions are commonplace. The mismatch stress is dependent upon temperature due to the different expansivities of the intralayer bonds (in this case, the difference being between the Cu-O and Bi-O bonds). Determination of this function is of interest in itself, and its precise nature may also shed additional light upon the origins of the modulation.

The Chapter begins with an assessment of the limited number of experiments to date, which have previously investigated the structure at high temperature. It has been observed for instance that the structure undergoes transitions at $\approx$290$^o$C and $\approx$490$^o$C, due perhaps to ordering of oxygen vacancies [106]. The diffuse streaks have been observed to disappear upon heating above 450$^o$C [92]. Yet in spite of these studies it has still to be definitively established how any of these changes come to be actualised in the real atomic structure positions. And most importantly, none have been able to measure any change in the periodicity of the modulation with oxygen content.

In situ x-ray scattering is a powerful technique for investigating all of these features and the bulk of this chapter presents the results of a detailed study made between room temperature and 450$^o$C under vacuum. The results reveal the complete temperature behaviour of the incommensurate modulation over this range and demonstrate the fundamental control exerted by oxygen content over the structure. This latter feature is a theme which will be further developed in Chapter 5, where the effects of oxygen variation beyond those of a purely structural nature are explored.