X-ray Measurements

The x-ray measurements described in this, and subsequent chapters were all performed upon the same triple-crystal diffractometer, using a GEC Avionics GX21 rotating anode x-ray source. The rotating anode operates at 3kW on a copper target producing CuK$\alpha$ radiation. A schematic picture of the triple-crystal arrangement is shown in Figure 3.6, illustrating the scattering geometry of monochromator, sample, and analyser crystals. The CuK$\alpha_1$ wavelength, $\rm {\lambda=1.5405\AA}$ is selected by the appropriate adjustment of monochromator and source-slit. A further adjustable pre-sample slit is used to reduce both vertical and horizontal beam size to the appropriate dimensions of the sample. The detector is a proportional counter.

The use of an analyser crystal ensures a resolution which is limited only by the mosaic spread of the set of crystals chosen for monochromator and analyser. This has the advantage of discriminating against scattering from any slightly misaligned secondary crystallites, and also provides for a well-defined resolution in two dimensions in the scattering plane making possible the mapping out of the intensity distribution of the scattered x-rays in an area of reciprocal space. The set of monochromator and analyser crystals is selected so as to meet the resolution needs of a particular experiment but the trade-off in intensity paid for using higher resolution also has an important bearing on this choice. There are three sets of crystals from which to choose, the properties and shape of the resulting resolution function in reciprocal space have been described for each in detail by Lucas [105]:
(1) Low resolution, using pyrolitic graphite crystals which have a mosaic spread of $\approx$0.4$^o$; these provide a maximum of intensity and are ideally suited to measuring weak and very diffuse features. They have been utilised in the bulk of measurements described in this thesis.
(2) Medium resolution, using the 111 reflection from germanium crystals with a mosaic spread of 4.3x10$^{-3}$ degrees, the intensity is reduced by a factor of $\approx$100 compared to graphite but provides a resolution which is more than sufficient for measuring the intrinsic widths of high-T$_c$ crystals.
(3) High resolution, which uses the (111) reflection of perfect silicon crystals, limits the available intensity still further and therefore ideally requires a scattering volume greater than the largest of high-T$_c$ single crystals which can be currently grown. They have not consequently been used in this work.

Figure 3.6: A schematic diagram of the triple-crystal X-ray diffractometer.

The sample crystal was fixed to a suitable holder which was then screwed onto the goniometer head. The goniometer has two axes of tilt and two of translation to allow alignment of the sample in the beam. A sample was aligned on the diffractometer in Bragg reflection geometry with its reciprocal ${\bf b}^*-{\bf c}^*$ axes in the horizontal scattering plane. Because the incident beam is reduced to a size less than that of the sample's face, it allows the elimination of secondary crystallites by the translation of the sample across the beam.