Temperature Response up to 400$^o$C

The profile shapes and peak intensities of the fundamental reflections displayed no observable changes up to 300$^o$C, illustrated in Figure 4.1 by the (0 0 20) and (0 0 30) reflections. In contrast, the satellite reflections underwent steady, well behaved decreases in peak intensity, examples of which are shown in Figure 4.2. Despite the changes in intensity, no change in the location of the satellites was observed. Although a slight shift in the shape of the profiles in Figure 4.2 is apparent, this is asymmetric about the (0 0 l) axis and, as becomes apparent in the higher temperature profiles of Figure 4.1, is linked rather to a growing asymmetry of the fundamental reflections. The ${\bf c}^*$ positions of the satellites were also monitored, scans along the (0 -0.21 l) position of two satellites are shown in Figure 4.3(a), displaying their well behaved intensity decreases in combination with constant FWHM values. The ${\bf c}^*$ positions of the satellites can be seen to remain unperturbed from their starting values. The constancy of both the ${\bf b}^*$ and ${\bf c}^*$ coordinates of the satellites means the incommensurate wavevector can be considered to be constant over this temperature range.

A diffuse streak is also present in Figure 4.3(a) at the l=26 position, stretching out from the tail of one of the satellites; it is shown expanded in Figure 4.3(b). No change in nature or discernible difference in behaviour from that of the satellites was apparent in the diffuse streaks up to 400$^o$C. The only noticeable feature is a steady decrease in intensity with increasing temperature.

The relative values of fundamental and satellite peak intensities up to 400$^o$C are plotted in Figure 4.4. The theoretical logarithmic response of the Debye-Waller requires decreasing intensity for increasing temperature. The response of the fundamental reflections up to 300$^o$C is, however, in the opposite sense to that expected. This suggests that the strong loss in intensity of the satellites over the same interval goes at least in part towards reinforcing the fundamental reflections, compensating for the loss which would otherwise be brought about by their Debye-Waller component. The overall behaviour is consistent with a decrease in the amplitude of the modulated atomic displacements with an accompanying gain in order of the average structure.

Figure 4.1: Profiles of fundamental reflections, (a) the (0 0 20), and (b) the (0 0 30), at a succession of temperatures during heating from 26$^o$C to 400$^o$C.

Figure 4.2: Profiles (at three temperatures), of two first order satellites, the (0 -0.21 19) and (0 0.21 19), and of the second order satellite (0 -0.42 20). Each shows the decreasing intensity, and the asymmetry commencing at 300$^o$C but no change in the incommensurate position.

Figure 4.3: (a) Scans along the [0 0 1] direction through two first order satellites, the (0 -0.21 25) and (0 -0.21 27). (b) An expanded view of the diffuse streak which lies between the two satellites at (0 -0.21 26).

Figure 4.4: The peak intensity values plotted logarithmically as a function of temperature for five reflections. The difference in behaviour between fundamental and satellite reflections is made most apparent in this plot by the onset of the strong decrease in intensity of the two fundamental reflections above 300$^o$C.

A change in the nature of the observed behaviour in Figure 4.4 is apparent at temperatures above 300$^o$C. The onset of strong reductions in the peak intensities are observed for the fundamental reflections and a continued but re-doubled decrease for the satellites. The change in response is also accompanied by a strong broadening of all reflections in the [0 1 0] direction. The profiles in Figure 4.5 were measured at 400$^o$C over a period of time and show how the developing asymmetry and broadening becomes more and more evident. By the time of the final profile after 110 hours at this temperature a drastic change in the line shape due to multiple splitting has occurred which makes the quantitative comparison with intensity values below 400$^o$C inappropriate.

A careful realignment of the sample was undertaken at 340$^o$C, at the first appearance of this change, to ensure it was not the result of any growing misalignment, caused potentially by thermal expansion of the sample holder. This was found not to be the case. The evolution of the broadening over an extended time period and the consistency of the changes in reflections across reciprocal space make it certain that a real physical process is being witnessed. Although the splitting of the profiles along ${\bf b}^*$ is suggestive of a twinning process, this possibility was eliminated by measurement of off-axis fundamental reflections, the (0 2 20) and (0 -2 20). In these reflections the splitting was identical but at an angle to the [0 1 0] direction, indicating that the splitting of the reflections is restricted solely to the mosaic direction, and is therefore of a more crude origin.

Figure 4.5: The (0 0 20) reflection measured at the start of the heating cycle at 20$^o$C. Then at 400$^o$C at various times over the continuous 110 hour period at this temperature. The evolution of the broadening and splitting of the reflection in the mosaic direction seen here was witnessed similarly in all other reflections.

The observed broadening and eventual splitting in the mosaic direction is consistent with the separation of the previously homogeneous single crystal into domains with varying angles of tilt between their c axis. The time evolutionary nature of these changes strongly suggests that they are linked to the diffusion of oxygen out of the crystal. The threshold for their commencement between 300 and 340$^o$C is in good agreement with the results of oxygen diffusion studies [111,112], and is also in accordance with the results of electron diffraction studies which reveal the formation of a-b plane oxygen vacancy superstructures, commencing at 300$^o$C [106]. Also, the development of a-b twinning which is believed to be due to oxygen loss around 340$^o$C [110]. The related superstructure reflections observed in electron diffraction experiments are confined to the ${\bf a}^*-{\bf b}^*$ plane and are therefore not observable in the experiments here. However, the broadening observed here at these temperatures is almost certainly a secondary effect of phase separation within the sample into domains of varying oxygen stoichiometries and ordering due to oxygen diffusing out of the sample.

After annealing for 110 hours at 400$^o$C the sample was returned to room temperature. The profiles remained broadened, with essentially the same shape but slightly narrowed to those in Figure 4.5, and had significantly changed from the original state before annealing. A behaviour which is again consistent with oxygen loss being the cause.