Medium Resolution

The low-resolution results have indicated that two of the crystals are of a very high quality, and established the general nature of diffuse features which can be observed in the scattering patterns. However, in order to resolve the intrinsic width of the crystals and make a more quantitative comparison, the high-quality Oxford and Warwick crystals have been studied further using higher resolution germanium optics.

The Figures 3.15 and 3.16 illustrates the difference between measurements obtained using the two resolution modes. The profiles in Figure 3.15 are of the Warwick (0 0 20) reflection, showing how much narrower the intrinsic widths are, in both ${\bf c}^*$ and ${\bf b}^*$ directions, compared to those presented in the previous section which were limited by the graphite resolution. The limit of the germanium resolution function has also indicated in the Figure, indicating that the true intrinsic widths of the sample are now being measured. In Figure 3.16 the same results are presented for the Oxford crystal, and finally Figure 3.17 compares the ${\bf b}^*$ profiles of the two crystals. The Oxford crystal is revealed here to have a superior mosaic width.

Figure 3.15: Profiles of the Warwick (0 0 20) reflection in (a) ${\bf b}^*$ and (b) ${\bf c}^*$ directions, measured using both graphite and germanium optics.

Figure 3.16: The profile of the (0 0 20) reflection from the Oxford crystal, measured in both low- and medium-resolution, to contrast the difference between the two modes.

Figure 3.17: The (0 0 20) reflection using germanium resolution for both the Oxford and Warwick crystals.

The widths and positions of the satellites have also been measured for the two crystals, and values determined for the FWHM and the modulation wavevector ${\bf q}$. The overall results are presented in Table 3.2, with the values averaged from measurements of a number of reflections. Figure 3.18(a) shows an example of a satellite profile for the Oxford crystal compared to that measured under low-resolution. Despite the substantially lower intensity using germanium it was still possible to determine widths for the diffuse streaks, and Figure 3.18(b) shows one example set against a first-order satellite for comparison. Even with the much longer count times, statistics are still poor however. The values presented in the table for the Oxford crystal show the FWHM of the satellites to be $\approx$1.5 times greater than that of the fundamental reflections, while the diffuse streaks are a further 2.5 times greater than the satellites. The FWHM values of the Warwick crystal are greater all round, but are in similar proportions to each other.

Table 3.2: The characteristic values measured using medium resolution compared for the Warwick and Oxford crystals. All values are in rlu.

	Warwick	Oxford
Fundamental FWHM	0.010(1)	0.003(1)
Satellite FWHM	0.014(2)	0.005(1)
incommensurate $\beta{\bf b}^*$	0.209(1)	0.209(1)
Diffuse streaks FWHM	0.017(2)	0.015(2)

Figure 3.18: A ${\bf b}^*$ profile of the (0 -0.21 19) satellite of the Oxford crystal measured in medium-resolution is compared in (a) to the same reflection measured using low-resolution, and in (b) to the (0 -0.21 20) diffuse streak also using medium-resolution.

It was noted from the low-resolution measurements that an asymmetry existed in the ${\bf c}^*$ profiles of the satellite reflections of the Oxford and Beijing crystals, while this was absent from the Birmingham and Warwick crystals. The absence of such features in the Warwick crystal is confirmed, to a degree, by the medium-resolution profile presented in Figure 3.19. Although the Warwick profile shape is not completely free from all asymmetry, it certainly is free of any distinct splitting. And when compared to the same profiles made under medium resolution for the Oxford crystal, the difference between the crystals becomes very clear. Two examples are shown in Figure 3.20. What in low-resolution was an ill defined profile shape which appeared to consist of several overlapping peaks, has now been resolved by the higher resolution into two quite distinct reflections. The strongest reflection is precisely located upon the commensurate l position in both figures, as is to be expected. The second, weaker satellite is well separated from the first and positioned with an incommensurate value of l, implying a modulation wavevector with a ${\bf c}^*$ component $\gamma < 1$. Both the value of l and the intensity are different in the two figures, however.

Similar observations of the splitting could be made around all the satellites studied, with no observable systematic pattern to the variations. The behaviour is characteristic of a domain structure with a range of $\gamma$ values, which are selectively sampled as the angle of incidence to the crystal is varied. The range of $\gamma$ values can be seen to extend out as a tail from the primary satellite as far as a cut-off point, which is the same in all cases, at $(1-\gamma) \approx$ 0.15. Whether there exists a discrete set of values, or whether the range is continuous, is not possible to establish from these results. In Figure 3.20(a) two definite values are measurable, $(1-\gamma)$=0.14, and a very much weaker reflection at the intermediate value of $(1-\gamma)$=0.07. The dominant value in Figure 3.20(b) corresponds to $(1-\gamma)$=0.11. These observations of multiple values for the splitting, when convoluted with the resolution function of the graphite, would account for the very complicated satellite profiles which were observed in low-resolution.

Figure 3.19: A ${\bf c}^*$ profile measurement of the (0 -0.21 25) satellite position for the Warwick crystal. In both low- and medium-resolution the profile is free of any signs of splitting.

Figure 3.20: ${\bf c}^*$ profiles measured from the Oxford crystal of (a) the (0 -0.21 19) satellite position, and (b) the (0 0.21 21) satellite position. In both the apparent splitting of the satellite observed in low-resolution has been separated into two distinct reflections by the higher resolution.