Extended Annealing at 450$^o$C

The second heating cycle followed immediately from the first, and without interruption to the vacuum, by restoring the sample's temperature to 400$^o$C. The reflection profiles appeared identical in both shape and intensity to those observed at the same temperatures during the first cycle. The high degree of reproducibility is a further indication of the stability of the sample alignment throughout the experiment.

The temperature was next raised to 450$^o$C and was then maintained at this temperature without interruption for close to 21 days; measurements were collected continuously throughout the period. Thus eliminating changes of a wholly temperature dependent nature from the measurements, and allowing for the study of the time evolution of processes associated solely with the vacuum annealing. The potential processes of interest being oxygen diffusion out of the sample, and decomposition of the sample into separate constituent phases. The upper limit for operating the furnace was around 470$^o$C, and so 450$^o$C was chosen for the measurements as the maximum temperature which could be reliably maintained. An unfortunate loss of x-ray intensity, due to a blown filament in the rotating anode source, occurred after approximately 120 hours of annealing and is responsible for the gap in the data up to 300 hours, and also for the anneal time being extended beyond what had been first intended.

A sequence of profiles in Figure 4.6 show the evolution of the (0 0 20) fundamental reflection over the entire period of this annealing at 450$^o$C. A very strong reduction in intensity occurred, which was similarly observed in all other reflections, the (0 0 20) having halved in peak intensity by 438 hours of annealing. The full width at half maximum (FWHM), surprisingly, also decreased. This is opposed to the strong broadening which was observed at temperatures up to 400$^o$C during the first cycle of the experiment. This suggests that the previous multiplicity of crystallites caused by the annealing at 300$^o$C to 400$^o$C have now, in part, re-merged together due perhaps to the re-establishment of a more homogeneous oxygen distribution within the sample at this higher temperature. The halving in intensity is too large to be attributable to any possible change in the structure factor, and is of course, not due to any Debye-Waller effect because of the constant temperature. It is most likely caused by the decomposition of some of the sample into an amorphous state which therefore no longer contributes to the Bragg diffraction, in particular the surface decomposition is a commonly reported feature of annealed samples [113,114,115].

Figure 4.6: The (0 0 20) reflection observed at intervals over the entire period of annealing at 450$^o$C.

Figure 4.7: Contrasting profiles of the (0 0 26) reflection measured before at 120$^o$C, commencing annealing at 450$^o$C, and after having been annealed for 462 hours at 450$^o$C. The final profile is at 50$^o$C upon cooling.

Figure 4.8: The four first order satellites, as they are arranged around the (0 0 26) fundamental position, illustrating the changes induced by annealing over 400 hours at 450$^o$C. The satellites are (a) (0 -0.21 27), (b) (0 0.21 27), (c) (0 -0.21 25), and (d) (0 0.21 25).

The changes in the satellite reflections over this period are illustrated in Figure 4.8 by the four first order satellites from around the (0 0 26) fundamental position; it can be seen that the second order reflections are already extremely weak. Intensity reductions of a similar order to those for the fundamental reflections of Figure 4.6 are seen. Although still broad, the FWHM values have also reduced in accord with the reduction of the fundamental reflections. And, unlike the asymmetrical changes seen during the first cycle in Figure 4.2, a perceptible shift in the centre position of the satellites is now apparent. The measurable change in peak position is very small, and the reflection shapes make it too uncertain to determine beyond stating that the $\beta{\bf b}^*$ value has reduced to approximately 0.20. But the redistribution of intensity from the outer side of the satellites to the inner, ${\bf c}^*$ axis, side is quite distinct, and most importantly, the changes are observed symmetrically about the ${\bf c}^*$ axis.

The nature of this redistribution of scattering away from the previously unperturbed 0.21${\bf b}^*$ satellite positions becomes further evident if the scattering which lies between adjacent satellite positions across the ${\bf c}^*$ axis is examined in detail. Two such scans, taken after $\approx$440 hours of annealing, along the [0 1 0] direction are shown in Figure 4.9, one crosses the ${\bf c}^*$ axis at ( 0 0 19) and one at (0 0 21). The change is dramatic, a new and very prominent reflection line has appeared inside the -0.2${\bf b}^*$ satellites. It is, in fact, so strong as to be almost equal in intensity to the satellite of the (0 0 21) scan, whilst for the (0 0 19) it is roughly half. The new reflections correspond to a position of approximately -0.14${\bf b}^*$. These new reflections could potentially be satellite reflections with a shortened $\beta{\bf b}^*$ value, and correspondingly relate to the formation of a new longer period modulation within the structure due to the removal of excess oxygens. However, if this is indeed the case, it is to be expected that accompanying satellites should also be found at the $+\beta {\bf b}^*$ positions.

To aid the interpretation of the multiplicity of lesser features, a matching scan is included for reference in Figure 4.9 across the (0 0 20) fundamental position. From this scan it is possible to attribute features in the satellite profiles to their features of origin, displaced by 0.2${\bf b}^*$, in the mosaic of the fundamental profile. All the features in the satellite profiles should, after all, be identifiable in this way as the satellites of secondary crystallites, except, if they exist, the q=0.14${\bf b}^*$ satellites. It can be seen, for example, that the strong reflection in the very centre of the two satellite reflections, marked $X$ in the figure, originates from a quite prominent secondary reflection in the fundamental profile. In this way, the asymmetry and splitting of the primary fundamental reflection is reflected clearly in the shape of its satellites, with large tails to the left, and several prominent steps in these tails which match up between the profiles. In contrast, the right side of the fundamental reflection is quite clean from any such features, and this means that a clean shape should also be expected to the right side of the satellites. This can be seen to be the case for the +${\bf b}^*$ satellites, but for the -${\bf b}^*$ satellites it is in just this position that the strong new reflections are observed, at -0.14${\bf b}^*$. Now, looking at the more involved left side of the reflections, an additional feature is distinguishable in the tail of the +${\bf b}^*$ satellites, which does not have any equivalent feature in either the fundamental profile or in the $-{\bf b}^*$ satellites. Although this feature is weaker than that at -0.14${\bf b}^*$, and is less distinct due to the large tail which stretches through the position, it is located close to +0.14${\bf b}^*$. It is found, therefore, that there exist no corresponding secondary crystallites in the fundamental profile to which the features at $\pm0.14{\bf b}^*$ could be attributed.

Figure 4.9: Scans in the [0 1 0] direction, after 460 hours annealing at 450$^o$C, across the (0 0 20) fundamental position, and the (0 0 19) and (0 0 21) positions showing the splitting of the satellite reflections. The intensity scale is logarithmic.

Further evidence in support of interpreting these new features as being due to longer period modulations comes from the response upon cooling. No further development in any of the observations was observed beyond 438 hours up to the end of the annealing at 504 hours, suggesting an equilibrium had already been reached before these measurements. After this, the sample was returned to room temperature. Upon cooling, all satellite reflections, both those from the primary and secondary crystallites, were observed to increase strongly and in unison. The only exception was the reflections at $\pm0.14{\bf b}^*$ which showed little or no change, and so in relative terms decreased in intensity. This further suggests that they cannot be described as satellites of a secondary crystallite.

Figure 4.10: The diffuse streak in the (0 -0.21 26) position measured in (a) the [0 1 0] direction and in (b) the [0 0 1] direction.

The behaviour of the diffuse streaks was also studied during this extended period, Figure 4.10 shows the streak at (0 -0.21 26) measured in both [0 1 0] and [0 0 1] directions. The interpretation of the behaviour is complicated by the mosaic of the fundamental reflection which extends through this position, and which varies over a greater range in intensity than the streak itself. This can be seen best in the [0 1 0] scans where the fundamental mosaic is seen as a sloping background upon which the streak is superimposed; the reduction in this mosaic which has already been discussed can be seen in the change from the profile at 120$^o$C with a very strong background to the lowest profile at the end of annealing at 450$^o$C. The effect of the mosaic is to exaggerate the height of the streak in the [0 0 1] scans. So, while a significant intensity appears still to remain at the end of annealing in Figure 4.10(a), a measurement from the [0 1 0] profile shows the intensity of the peak to be entirely accounted for by the mosaic background. Similar results from other positions suggest that the streaks have indeed disappeared by this point of the experiment. The same result has also been claimed by Bdikin [92]. Unfortunately, the quality of the data is not adequate to be able to conclude whether this is the result of a true transition or whether it is merely a consequence of the greatly reduced intensities which have effected satellite, fundamental, and streaks equally. It is however notable that the [0 1 0] scans indicate for certain that the ${\bf b}^*$ widths of the diffuse streaks are consistently increasing during a period when the widths of satellites and the fundamental reflections were both observed to sharpen. This would support the interpretation that the behaviour of the streaks is distinguished from that of the other reflections and that they undergo a order-disorder transition at temperatures above 400$^o$C.