The Lattice Parameters

The b and c lattice parameters were regularly determined throughout the experiment. The measurements involved a least-squares refinement of five fundamental positions. The complete results are presented in Figures 4.11and 4.12. The values were measured both during heating cycles to determine temperature behaviour, and also at regular intervals during periods of fixed temperature as a potential additional indicator of oxygen loss.

**Figure 4.11:** The b lattice parameter measured during each of the experiment's three heating cycles labeled chronologically A, B, and C.
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**Figure 4.12:** The c lattice parameter measured during each of the experiment's three heating cycles labeled chronologically A, B, and C.
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The three heating cycles are labeled in order: A, B, and C. Both the b and c lattice parameters show essentially linear behaviour up to approximately 400

C. The irreversible effects observed due to the first annealing cycle in Section 4.3.2 are made manifest here in the permanent changes seen in both b and c. Comparing the values at 20

C at the start of the A cycle to the the starting values of the subsequent B cycle, the b value has extended by 0.019 ${\rm\AA}$ and c by 0.12 ${\rm\AA}$ , changes of roughly 0.4 $\%$ . An extension of a similar magnitude again is observed in b between cycle B and cycle C, resulting from the additional effects described in Section 4.3.3. A lessening in the expansivity of the b axis also follows from its extension, which is seen as a decrease of slope from A to B to C. The expansion of the b axis above 400

C is strongly exponential, and by 450

C all three cycles have reached similar values of around 5.455 ${\rm\AA}$ .

**Figure 4.13:** The interplay between the b and c lattice parameters plotted against the number of hours of annealing at 450C.
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The c lattice parameter shows an altogether different form of behaviour in the change between cycle B and cycle C as shown in Figure 4.12. The start of cycle C, for instance, shows it to have returned roughly to its original value before annealing, reversing the expansion of the previous cycle, and in complete contrast to the b axis behaviour. The vertical line of points in Figure 4.12 corresponds to the extended annealing at 450

C and show it to be responsible for this contraction of the c axis. The values of both b and c are plotted together against time in Figure 4.13 for the duration of the annealing at 450

C. A clear interplay between the two axes exists, the collapse of the c axis being compensated for by an expansion of the b axis. The leveling out of the values above 400 hours suggests the transition in the structure to be completed after this time, and is presumably the consequence of the oxygen diffusion ultimately abating. The reaching of an equilibrium after a similar time was also indicated by the profile measurements. Since during subsequent reheating in cycle C, the c axis shows lower expansivity and is restored only as far as the end equilibrium value of the annealing cycle, the transition can be considered to be permanent.