2.3.1. Rietveld Refinement

Rietveld refinement is a well-known structure refinement method of the entire profile based on least-squares fitting. It is powerful for determining the complete crystal structure (e.g., lattice parameters, atomic coordinates, and occupancy) of a multiphase material [28,29]. The peak position, intensity, and width of each phase were independently derived. Quantitative phase analysis was also performed using Rietveld analysis.

The ENGIN-X instrument diffraction profile was modeled using a convolution of a pseudo-Voigt function, *pV*(*t*), with two back-to-back exponentials, *E*(*t*) [22]. Instrumentdependent diffractometer constants and profile parameters were calibrated by the refinement of data from the CeO<sup>2</sup> standard powder (cubic phase, space group *Fm*3*m*, and *a* = 5.4114 Å). The derived parameters were then used to refine the studied bulk samples and stress-free reference powders.

The refinements of A–AT composites were undertaken with a two-phase model consisting of a hexagonal α-Al2O<sup>3</sup> phase and an orthorhombic AT phase. Parameters, such as lattice parameters, atomic coordinates, isotropic thermal parameters, scale factors, and polynomial background parameters, were improved by Rietveld refinement. All refinements were implemented step-by-step to avoid correlation effects among parameters. The space groups and initial atomic structure information used in the refinements are listed in Table 1. The overall fitting quality was assessed in terms of *R* values [30] obtained from the refinements.


**Table 1.** Initial crystal structure parameters of Al2O<sup>3</sup> and Al2TiO<sup>5</sup> phase used in refinement.
