*3.2. Characterization of the Deformed Samples after HPT Process*

Microstructural changes in the HPT-deformed alloys were characterized while using SEM (Figure 3a–c). Apparently, the TiFe phase (white grains) is only slightly affected by the HPT process, because the α-Ti matrix mainly absorbed the deformation energy. After HPT, the grains of the α-Ti matrix are strongly refined. This behavior is expected, because the intermetallic compound TiFe is much harder (481 ± 44 HV0.025 [44]) than the soft α-Ti matrix (~180 HV0.5 [45]). Still, the chains of the TiFe precipitates, which were initially ordered in the annealed samples, were destroyed (compare the micrographs in Figures 1 and 3). The oxygen content within the deformed samples measured while using CGHE was very low, namely 0.0049(3) wt.%, 0.0055(3) wt.%, and 0.0024(3) wt.% for the alloys Ti-2Fe, Ti-4Fe, and Ti-10Fe, respectively.

**Figure 3.** Microstructures of the high-pressure torsion (HPT) samples Ti-2Fe (**a**), Ti-4Fe (**b**), and Ti-10Fe (**c**) as seen by SEM/BSE. Prior to the HPT process, the samples were annealed at 470 ◦C for 4000 h. The white grains are TiFe, the gray areas correspond to the α-Ti and ω-Ti(Fe) phases.

ė The phase analysis using XRD confirmed that the HPT process produced ω-Ti(Fe). The comparison of the phase fractions in the annealed (Table 1) and HPT-treated samples (Table 2) shows that the amount of TiFe only decreased slightly, while the amount of α-Ti was drastically reduced during the HPT process. Thus, the ω-Ti(Fe) phase predominantly developed from α-Ti. In the alloys Ti-2Fe and Ti-4Fe, approximately 50 wt.% of α-Ti, was transformed into ω-Ti(Fe). Higher Fe contents and, consequently, a higher amount of the TiFe phase present in the respective alloys impede the HPT-induced phase transition, as can be seen on the lower relative amount of ω-Ti(Fe) in alloy Ti-10Fe (Table 2). As the lattice parameters of α-Ti in the annealed samples does not depend on the chemical composition of the alloy (see Section 3.1) the HPT-induced phase transformation α-Ti + TiFe → ω-Ti(Fe) + TiFe must be impeded by a higher amount of TiFe because the concentration of Fe in α-Ti is the same.


**Table 2.** Phase fractions (wt.%) in HPT-deformed samples, as determined using XRD. nα→<sup>ω</sup> = ω/(α + ω) is the fraction of α-Ti, which transformed to ω-Ti(Fe). The errors of the XRD phase analysis (1% to 3%) were estimated based on the goodness of fit.

After the HPT treatment, the line positions of the α-Ti(Fe) and TiFe phases were found to be shifted towards lower diffraction angles in all alloys. Such an increase of the unit cell volume of the phases after the deformation by HPT was already detected in earlier observations [24–26]. A large amount of defects and lattice distortions are generated during the severe plastic deformation in the HPT process [9,46], which lead to an increase of the lattice parameter of α-Ti and TiFe were *a*α-Ti = 0.2956(1) nm, *c*α-Ti = 0.4694(1) nm, and *a*TiFe = 0.2982(1) nm, respectively. The refined lattice parameters of ω-Ti(Fe), *a*ω-Ti(Fe) = 0.4620(1) nm and *c*ω-Ti(Fe) = 0.2829(1) nm, obey the relationship

$$c\_{\omega}/a\_{\omega} = \sqrt{3}/\left(2\sqrt{2}\right) \tag{1}$$

which indicates that the crystal structure of ω-Ti(Fe) is pseudo-cubic. Consequently, the XRD lines 1011 and 1120 from ω-Ti(Fe) are located at the same position. Because of the orientation relationship {111}*bcc* (0001)<sup>ω</sup> and <sup>110</sup>*bcc* <sup>1120</sup><sup>ω</sup> between the hexagonal <sup>ω</sup> phase and the cubic bcc lattice [18,22,47,48], the lattice parameters of ω-Ti(Fe) can be expressed in terms of a cubic bcc lattice parameter

$$a\_{\omega} = \sqrt{2}a\_{bcc} \text{ and } c\_{\omega} = \left(\sqrt{3}/2\right)a\_{bcc} \tag{2}$$

with *a*bcc = 0.3267(1) nm. After HPT deformation, a satisfying agreement between the measured and refined XRD data was achieved, even for Ti-10Fe, when the preferred orientation was implemented into the Rietveld refinement using TOPAS [32], as described above. It was found that the α-Ti phase possesses a {0001} texture, which is, however, almost negligible for Ti-2Fe.
