*4.1. HPT-Induced Formation of* ω*-Ti(Fe) in Samples Containing* α*-Ti As a Dominant Phase*

The ω-Ti(Fe) phase can be produced in different ways in a HPT process. In previous studies, in which Ti-rich Ti–Fe samples were heat treated at temperatures above the eutectoid reaction [25–28], ω-Ti(Fe) was formed either from a single β-(Ti,Fe) phase or from a mixture of α -Ti(Fe) martensite and β-(Ti,Fe). In Reference [26], it was shown that the iron concentration and the phase composition prior to the HPT process influence strongly the amount of the HPT-induced ω-Ti(Fe). For 4 wt.% of Fe, the transformation β-(Ti,Fe) → ω-Ti(Fe) already occurred at low pressures and it was almost completed after few HPT rotations, because the coincidence of the lattice parameters of pseudo-cubic ω-Ti(Fe) with the lattice parameter of β-(Ti,Fe) facilitates the diffusionless phase transition at this particular Fe concentration. For 2 wt.% Fe, still approximately 80% of the sample was transformed to ω-Ti(Fe) [26]. In the current study, the fractions of the ω-Ti(Fe) phase in samples Ti-2Fe and Ti-4Fe (~50%, c.f., Table 2) were significantly lower than the amount of ω-Ti(Fe) in samples with the same Fe content that were annealed at high temperatures [26]. The phase fractions of ω-Ti(Fe) produced in samples with 10 wt.% Fe are very similar for different annealing temperatures and, therefore, for different phase compositions prior to the HPT process.

The microstructure characterization using XRD and SEM confirmed that all of the samples under study (Ti-2Fe, Ti-4Fe, and Ti-10Fe) contained α-Ti and TiFe after annealing at 470 ◦C for 4000 h. The HPT induced the formation of the high-pressure ω-Ti(Fe) phase, which also remained stable at ambient conditions. The ω-Ti(Fe) phase was mainly produced from severely plastically deformed α-Ti, which absorbed the majority of the deformation energy. The TiFe grains were only slightly affected by

the HPT process. Still, the TiFe precipitates, which were ordered in chains along the grain boundaries of the α-Ti phase in the annealed samples, were more randomly distributed after the HPT treatment, and the amount of crystalline TiFe was slightly reduced (c.f., Tables 1 and 2). After the long-term annealing, i.e., under thermodynamically equilibrium conditions, α-Ti can accommodate approximately 9.4 × 10−<sup>3</sup> wt.% Fe. This means that α-Ti is practically free of iron in the samples that were annealed at 470 ◦C and that the ω-Ti(Fe) formation in these samples should be inhibited by the lack of iron in the parent phase. On the other hand, the shift of the diffraction line 0002α-Ti(Fe) towards lower diffraction angles, which is visible in Figure 5, indicates that the iron content in back-transformed α-Ti(Fe) varies upon heating and, consequently, ω-Ti(Fe) did not originate from pure α-Ti, but from supersaturated α-Ti(Fe) like in the samples from Reference [27].

Two approaches were used in order to estimate the iron content in ω-Ti(Fe). In the first one, the iron content in ω-Ti(Fe) was determined from the phase fractions before and after the HPT process. This approach is based on the assumptions that the application of pressure does not significantly change the homogeneity range of TiFe and that the residual hexagonal α-Ti(Fe), which is still present after HPT, contains the same amount of iron, like the high-pressure ω-Ti(Fe) phase. In the second approach, the iron content was estimated from the measured lattice parameter of ω-Ti(Fe) and from the Vegard dependence of *a*ω-Ti(Fe) known from literature.

The phase amount of α-Ti(Fe) is significantly reduced due to the formation of ω-Ti(Fe) (compare Tables 1 and 2). However, the HPT process also reduced the amount of TiFe. Even though the decrease of the phase fraction of TiFe after HPT is small, their variation falls outside the estimated error limit. Using the law of the mass conservation, the initiation of the phase transitions due to HPT can be expressed, as follows:

$$m\_{\rm lin}^a \times w\_{\rm lin}^a + m\_{\rm lin}^{\rm TiFe} \times w\_{\rm lin}^{\rm TiFe} = m\_{\rm HPT}^a \times w\_{\rm HPT}^a + m\_{\rm HPT}^{\rm TiFe} \times w\_{\rm HPT}^{\rm TiFe} + m\_{\rm HPT}^{a\nu} \times w\_{\rm HPT}^{a\nu} \tag{3}$$

In Equation (3), *m*<sup>ϕ</sup> *<sup>i</sup>* (in wt.%) and *<sup>w</sup>*<sup>ϕ</sup> *<sup>i</sup>* (in wt.% of Fe) are the fractions of the involved phases (α, TiFe and ω) and their chemical compositions in the sample state (initial, after HPT), respectively. While assuming a constant chemical composition of TiFe before and after HPT (*wTiFe Ini*/*HPT* <sup>=</sup> *<sup>w</sup>TiFe Ini* <sup>=</sup> *wTiFe HPT*), and the same chemical composition of α-Ti(Fe) and ω-Ti(Fe) in HPT processed samples (*w*<sup>α</sup> *HPT* <sup>=</sup> *<sup>w</sup>*<sup>ω</sup> *HPT*), Equation (3) can be written as:

$$w\_{\rm HPT}^{\alpha} = \frac{m\_{\rm Ini}^{\alpha} \cdot w\_{\rm Ini}^{\alpha} + \left(m\_{\rm Ini}^{\rm TiFe} - m\_{\rm HPT}^{\rm TiFe}\right) \cdot w\_{\rm Ini/HPT}^{\rm TiFe}}{m\_{\rm HPT}^{\alpha} + m\_{\rm HPT}^{\alpha}} \tag{4}$$

For *w*<sup>α</sup> *Ini* <sup>=</sup> 9.4 <sup>×</sup> <sup>10</sup>−<sup>3</sup> wt.% Fe, *<sup>w</sup>TiFe Ini*/*HPT* = 53.6 wt.% Fe, and for the phase compositions, according to Tables 1 and 2, the Fe content in ω-Ti(Fe) was determined to be *w*<sup>ω</sup> *HPT* -1 wt.%.

The comparison of the lattice parameters was used as a complementary approach for the estimation of the iron content in ω-Ti(Fe). In commercially pure HPT-deformed Ti samples, the lattice parameters of ω-Ti were *a*ω-Ti = 0.4627 nm and *c*ω-Ti = 0.2830 nm [25]. The lattice parameters of ω-Ti(Fe) measured for the iron-containing alloys in this study were *a*ω-Ti(Fe) = 0.4620(1) nm and *c*ω-Ti(Fe) = 0.2829(1) nm. This confirms that iron atoms that are dissolved in the ω-Ti(Fe) phase lead to a reduction of the elementary cell volume, as already stated in References [25,26]. Moreover, the change of *a*ω-Ti(Fe) is larger than the change of *c*ω-Ti(Fe). At the iron contents of 4 wt.%, the pseudo-cubic lattice parameter of ω-Ti(Fe) coincides with the lattice parameter of β-(Ti,Fe) [26]. The whole dependence of the lattice parameter of β-(Ti,Fe) on the iron content was described in References [14,26,29]. The lattice parameters *a*ω-Ti(Fe) = 0.4603(6) nm and *c*ω-Ti(Fe) = 0.2819(1) nm containing 4 wt.% Fe were calculated using Equation (2) from the lattice parameter of β-(Ti,Fe) with the same amount of Fe (*a*bcc = 0.3255(2) nm) [29]. Assuming a linear dependence of the lattice parameter *a*ω-Ti(Fe) on the Fe concentration between Fe-free ω-Ti and ω-Ti(Fe) containing 4 wt.% Fe, the iron content in the sample under study was estimated to be approximately 1.2 wt.%. This value is in good agreement with the iron concentration of ~1 wt.% that was concluded from the difference in the phase fractions before and after the HPT

deformation. The lattice parameter *a*ω-Ti(Fe) was used for the estimation of the Fe concentration in ω-Ti(Fe), because it is more sensitive to the iron concentration than *c*ω-Ti(Fe).
