X-ray Scattering Measurements

A comparison of the x-ray measurements made prior to the annealing of the two samples revealed only one clear difference. Overlaid in Figure 5.4 are $c^*$ profiles along the (0 -0.21 l) position for both crystals, they encompass two first order satellites and a diffuse streak lying between them. To allow comparison of the relative intensities, the values have been normalised to that of the neighbouring fundamental reflection, in this instance the (0 0 26); this method of normalisation will be used for all subsequent data presented in this Chapter. It can be seen that while the shape and the peak intensities of the satellites are very similar in both cases, the shape of the diffuse streak is much less well defined for the crystal denoted as B1. This is made quite explicit by the expanded picture of the streaks shown in Figure 5.5. As well as being more diffuse and flattened in nature, it has an intensity at the peak almost half that of the diffuse streak for the A1 crystal. The data for the Oxford crystal has also been included in Figure 5.4. It has a broader width to the incommensurate satellites compared to those of A1 and B1 due to the splitting discussed in Chapter 3, however, it too has an intensity for the diffuse streak almost double that of B1. The same differences in shape and relative intensity were consistently observed for the three crystals in the diffuse streaks at the other reciprocal space positions investigated, (0 $\pm$0.21 20) and (0 $\pm$0.21 26).

Figure 5.4: Scans along the (0 -0.21 l) position comparing measurements of the A1 and B1 crystals before annealing. Intensity values are normalised to the (0 0 26) fundamental reflection.

Figure 5.5: An expanded view of the of the diffuse streak at (0 -0.21 26), comparing measurements of the A1, B1, and Oxford crystals. Intensity values are normalised to the (0 0 26) Fundamental reflection.

The values of the lattice parameters, b and c, and of the incommensurate wavevector $\beta$ were determined from the x-ray measurements. They are summarised in Table 5.2, for the samples both as-grown and post annealed. The most significant observation which can be made from Table 5.2 is the constancy of $\beta$ for both B1 and A1 despite the annealing treatments, and despite their differences in oxygen content in the as-grown state. Yet a slight difference is discernible between the Oxford and A1 crystals which have similar T$_c$ values and oxygen contents. This is a further demonstration that the value of the incommensurate wavevector cannot, in any way, be considered a continuous function of oxygen content. In addition, the lattice parameters for B1 showed a clear change after the annealing. The c axis expanded by 0.08${\rm\AA}$, a change which is commonly reported to correlate with an increase in T$_c$, as is the case here. Anomalously, no decrease in the c axis of the A1 crystal was observed (within the errors at least) which might have been expected considering the decrease in T$_c$ for this sample.

Table 5.2: Lattice parameters of as-grown and annealed crystals.

	b$_o$ (${\rm\AA}$)	c$_o$ (${\rm\AA}$)	$\beta{\bf b}^*$ (r.l.u.)
Oxford	5.40(1)	30.910(5)	0.207(2)
A1 (as-grown)	5.40(1)	30.864(5)	0.212(2)
A1 (O$_2$ anneal)	5.40(1)	30.854(5)	0.212(2)
B1 (as-grown)	5.37(1)	30.686(5)	0.210(2)
B1 (N$_2$ anneal)	5.40(1)	30.770(5)	0.212(2)

The x-ray measurements of crystal A1, made after it had undergone oxygen annealing, are illustrated in Figure 5.6. It can be seen that there is remarkably little difference from the picture before annealing. A very slight increase in the intensity of the satellites is observed, relative to that of the fundamental reflection. The peak intensity of the diffuse streak is unchanged but it has possibly narrowed slightly in width. Measurements made of the same reflections for the crystal B1 after it had undergone nitrogen annealing are shown in Figure 5.7. The change in intensity of the satellites is this time in the opposite sense to the A1 crystal, with a quite strong decrease. But the most pronounced change is in the shape of the diffuse streak, where previously it was flattened in the as-grown crystal, it has now transformed into a well defined peak. This change is further illustrated in Figure 5.8 for the streak at (0 -0.21 20) which shows an even more pronounced re-shaping. The increased prominence of the streak is also accompanied by a decreasing FWHM value, and so cannot be the result of increased disorder or defects being introduced by the annealing process. The observed changes are rather indicative of a disorder-order related change having taken place. No changes in the widths in the ${\bf b}^*$ direction could be observed due to the limiting graphite resolution in this direction. So, it cannot be ruled out that an improved FWHM may also have resulted in the [0 1 0] direction as well.

Figure 5.6: Scans along the (0 -0.21 l) position measured for the A1 crystal before and after annealing in oxygen; an expanded view of the diffuse streak at (0 -0.21 26) is shown in (b). Intensity values are normalised to the (0 0 26) fundamental reflection.

Figure 5.7: Scans along the (0 -0.21 l) position measured for the B1 crystal before and after annealing in nitrogen; an expanded view of the diffuse streak at (0 -0.21 26) is shown in (b). Intensity values are normalised to the (0 0 26) fundamental reflection.

Figure 5.8: Further scans for the B1 crystal before and after annealing in nitrogen, here showing the changes in the (0 -0.21 20 ) streak. Intensity values are normalised to the (0 0 20) fundamental reflection.

The changes in the relative values of the normalised intensity which are observed in the scans, and the variations which also existed between the different crystals in their as-grown states, in Figure 5.4, are difficult to quantify reliably. The measurements have to be first normalised in some way before quantitative comparisons can be made; for instance, the intensity measurements presented here have all been normalised to the intensity of a nearby fundamental reflection. However, there exist differences in the intensity ratios of fundamental reflections between crystals, and this makes the interpretation of absolute differences between crystals far from clear cut. The intensity of the satellites do, however, relate potentially important and relevant information regarding the amplitude of the modulated atomic displacements. So, although precise quantitative statements about the intensity changes cannot be made from this data, it is appropriate here to at least attempt a qualitative assessment of the manner of the change caused by the annealing of the crystals.

Measurements were therefore made of the intensity changes from scans through peak positions in the [0 1 0] direction, shown for example in Figure 5.9; these are preferable to the [0 0 1] scans because they allow for the subtraction of the background contribution. The tail of the fundamental reflection which overlaps with the positions of the diffuse streaks is responsible for the high sloping background seen in Figure 5.9 for example. The data presented in Table 5.3 for the crystal A1, and Table 5.4 for B1, summarise the differences in normalised intensity for both satellites and streaks measured in this way. It should be noted that no change in either position or shape was observed in the [0 1 0] scans for either crystal, confirming the invariance of $\beta{\bf b}^*$.

Figure 5.9: Scans along the [0 l 0] direction through the (0 0.21 20) streak of the B1 crystal, showing the strong increase in intensity upon annealing.

The intensity changes measured for crystal B1 show large and quite certain decreases in the satellites, in addition to the very definite increase in the diffuse streak already discussed. The measurements for the A1 crystal, on the other hand, appear to show changes which are on the whole of an opposite nature to those for B1, all be they of a much smaller magnitude. The overall qualitative trend suggested by the data presented for both crystals in Tables 5.3 and 5.4, is that the sense of the change in satellite intensity, and hence in the modulation's amplitude, is opposite to that of the change in T$_c$. That is, where the T$_c$ has decreased in A1, and perhaps more importantly the oxygen content has increased, it has been accompanied by an increase in the amplitude of the distorting modulation. While the increase in T$_c$ in B1 has been accompanied by a decrease of the amplitude. A variation in the amplitude of the atomic displacement function is certainly a physically reasonable structural adjustment to associate with changes in the oxygen content or configuration. However, with the results here of only two crystals to consider, it is somewhat too speculative to suggest that this variation in amplitude can be directly associated with the changes in $T_c$ observed.

Table 5.4: Normalised peak intensities for the B1 crystal, measured before and after annealing in nitrogen.

$(h k l)$	A1 (as-grown)	A1 (annealed)	$\%$ change
(0 -0.21 27)	0.112	0.115	+3%
(0 -0.21 25)	0.461	0.451	-2%
(0 -0.21 26)	0.022	0.020	-9%
diffuse streak

Table 5.3: Normalised peak intensities for the A1 crystal, measured before and after annealing in oxygen.

$(h k l)$	B1 (as-grown)	B1 (annealed)	$\%$ change
(0 -0.21 27)	0.159	0.139	-12%
(0 -0.21 25)	0.555	0.460	-17%
(0 -0.21 26)	0.009	0.024	+170%
diffuse streak