*3.3. Crystal Structures*

After applying Rietveld refinement to TOF neutron diffraction patterns, the crystal structures of Al2O<sup>3</sup> and AT in the stress-free reference powders and A–AT composites were obtained. Table 3 summarizes the average values of refined lattice parameters of α-Al2O<sup>3</sup> (*a*, *c*) and orthorhombic AT (*a*, *b*, and *c*) at different scanning points in each sample (standard deviations are shown in brackets). Based on these standard deviations, no remarkable variance was found in the lattice parameters of both Al2O<sup>3</sup> and AT in the in-plane and normal directions as well as at different scanning points in the same bulk sample. This indicates the existence of phases and microstructure distributions that are virtually homogeneous in the above materials.

**Table 3.** Average lattice parameters (A◦ ) of Al2O<sup>3</sup> and Al2TiO<sup>5</sup> phases obtained by Rietveld refinement of initial powders and A–AT composite samples.


The lattice parameters (*a* and *c*) of Al2O<sup>3</sup> in all the studied A–AT ceramics were found to be slightly lower than those of the initial Al2O<sup>3</sup> powders. Thus, compressive strain was anticipated in the Al2O<sup>3</sup> phase of A–AT ceramics. With increasing AT content, changes in the lattice parameters of Al2O<sup>3</sup> were not remarkable, and the *c* value only slightly decreased. Compared with the initial AT powders, the *a* value of orthorhombic AT in all the studied A–AT ceramics decreased, whereas the *b* and *c* values increased. As the AT content increased from 10 to 40 vol.%, the *a* value of AT increased, whereas the *b* and *c* values distinctly decreased.

In comparing the A–AT samples with the same composition but fabricated at different sintering temperatures, no remarkable difference was observed among the lattice parameters of the Al2O<sup>3</sup> and AT crystallites, except for AT in the A-40AT samples. In the A-40AT composites, the materials sintered at a higher temperature value (1550 ◦C) exhibited an increase in the *a* values of the AT phase; however, the *b* and *c* values reduced compared with the materials sintered at 1450 ◦C.

These behaviors can be understood by considering the thermal expansion mismatch between the Al2O<sup>3</sup> and AT phases, the thermal expansion anisotropy of each phase, and the microstructure characteristics of composites. According to the microstructure described

above, the A-10AT composites (Figure 3a,b) were dense, and fine AT grains were surrounded by Al2O<sup>3</sup> matrix grains. The average crystallographic thermal expansion (CTE) coefficient of the Al2O<sup>3</sup> matrix (*αA*,25−<sup>1000</sup> ◦<sup>C</sup> = 8.6 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ◦<sup>C</sup> −1 ) is smaller than that of the AT inclusions (*αAT*,25−<sup>1000</sup> ◦<sup>C</sup> = 10.1 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ◦<sup>C</sup> −1 ) [24] when subjected to cooling from the maximum sintering temperature to room temperature in the fabrication procedure. Consequently, Al2O<sup>3</sup> matrix grains were compressed, and lattice parameters *a* and *c* decreased.

In contrast, for AT particles, most of the contact and restraints emanated from the Al2O<sup>3</sup> matrix in the A-10AT composites. Owing to the CTE mismatch between Al2O<sup>3</sup> and AT, the AT grains were presumed to be in tension, and the lattice parameters increased. However, according to the lattice parameters obtained by neutron diffraction, the *b* and *c* values of orthorhombic AT in A-10AT ceramics increased as the *a* value decreased. The strong CTE anisotropy exhibited by AT (*αa*,*AT*25−<sup>1000</sup> ◦<sup>C</sup> <sup>=</sup> <sup>−</sup>2.4 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ◦<sup>C</sup> −1 , *<sup>α</sup>b*,*AT*25−<sup>1000</sup> ◦<sup>C</sup> = 11.9 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ◦<sup>C</sup> <sup>−</sup><sup>1</sup> and *<sup>α</sup>c*,*AT*25−<sup>1000</sup> ◦C= 20.8 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ◦<sup>C</sup> −1 ) [13] indicates that this anisotropy is the predominant effect rather than the CTE mismatch with Al2O3, although only a small quantity of AT was included in the A–AT ceramics. By increasing the AT content, the contact among AT grains was enhanced. Most restraints were from the closed AT grains, and the effect of CTE anisotropy on the AT phase became more distinct. A decrease in the *a* value and further increases in *b* and *c* values were anticipated in AT. However, the derived lattice parameter results compared with those in the A-10AT ceramics showed that the *a* value of AT increased in the A-40AT ceramics, whereas the *b* and *c* values decreased. Such phenomena can be explained by the microstructure of the A–AT composites. As presented in Figure 3, spontaneous microcracking occurred in the AT of the A-40AT composites. Thus, restraints among grains were evidently released, and changes in the lattice parameters of AT weakened. This also explains the difference in AT lattice parameters between the A-40AT(1450) and A-40AT(1550) ceramics. At higher sintering temperatures, more microcracks were observed in A-40AT(1550) than in A-40AT(1450). Thus, changes in the lattice parameters of AT in the A-40AT(1550) ceramics compared with the A-40AT(1450) materials weakened, leading to an increase in *a* values of the AT phase but reductions in the *b* and *c* values.

In addition, the lattice parameters could reflect the thermal stability of Al2TiO5. Skala et al. [13] reported that the thermal stability of Al2TiO<sup>5</sup> is closely related to its lattice constant *c*. Its increase will lead to a reduction of the distortion of the octahedra in the crystal structure of Al2TiO5, so that the stability of Al2TiO<sup>5</sup> is improved. In our study, in A–AT ceramics with the same AT addition, as the sintering temperature increased from 1450 ◦C to 1550 ◦C, the lattice parameter *c* of AT reduced, indicating less thermal stability of the AT phase. This explains why the decomposition of AT occurred in the 1550 ◦C sintered A–AT samples.
