*3.4. Thermodynamic Calculations*

A pressure-dependent thermodynamic description of the binary Ti–Fe system was generated with the aid of the CalPhaD (Calculation of Phase Diagrams) approach for a better understanding of the experimental observations and especially for validation of the phase stabilities and reverse transformation of ω-Ti(Fe) to α-Ti [49]. The details of the thermodynamic calculations will be described elsewhere [50]. Exemplarily, the temperature-pressure (*t*–*p*) phase diagram is shown for alloy Ti-4Fe (see Figure 8a). Figure 8b illustrates the effect of the chemical composition for the hydrostatic pressure of 10 GPa. In contrast to unary *t*–*p* phase diagrams, which solely contain single-phase regions, two-phase regions can be present in those binary *t*–*p* phase diagrams (calculated for a given binary composition). The black lines represent either solvus lines or three-phase equilibria, with varying pressure and temperature. The presence of two-phase regions become obvious if a binary *t*–*p* phase diagram (Figure 8a) is compared with a *t*–*w*(*Fe*) phase diagram (Figure 8b). In Figure 8a, the vertical dashed line marks the pressure value of 10 GPa in Figure 8b the alloy composition of Ti-4Fe.

For an ambient temperature, the thermodynamic calculations revealed that the α-Ti + TiFe two-phase mixture, which is stable at ambient pressure, transforms at the pressure of ~0.8 GPa into a two-phase mixture of ω-Ti(Fe) and TiFe. Thus, the applied pressure during the HPT (7 GPa) should be sufficient for initiating the phase transformation of α-Ti + TiFe to ω-Ti(Fe) + TiFe. The high-pressure phase persists, even after the HPT process, being stabilized by the interaction with other phases that are present in the HPT samples.

In alloys that were annealed at high temperatures (800 ◦C) and subsequently quenched [26], the high-temperature phase assemblage was retained for the iron contents ≥4 wt.%. In that case, the transformation pathway was found to proceed from β-(Ti,Fe) or from an α-Ti + β-(Ti,Fe) mixture to a β-(Ti,Fe) + ω-Ti(Fe) mixture [26,28,29]. However, it was also reported that minor amounts of α-Ti are preserved after the HPT process. The initiation of the ω-Ti(Fe) transformation was found to be very easy, which means that the phase transformation should already occur at low pressures [26]. The metastable extension of the β-(Ti,Fe) + ω-Ti(Fe) region was thermodynamically calculated in order to predict this behavior (see black dashed line in Figure 8a) by suspending the formation of the TiFe phase. Thermodynamic calculations revealed that the phase transformation into the high-pressure phase assemblage should occur at room temperature already at the atmospheric pressure. This indicates that the transformation to the high-pressure ω-Ti(Fe) phase should already occur at very low pressures using HPT, which was also experimentally observed [26]. It is worth noting that the CalPhaD calculations reflect the equilibrium state in the samples under hydrostatic pressures, which is far away from the sample state that is generated in the HPT process. The main features of the HPT process are (i) the large portion of torsional stain, which mainly induces shear stresses and (ii) the short process times at ambient temperatures. However, the predicted transformations pathways are comparable with those experimentally observed—the trends are correct.

**Figure 8.** (**a**) Temperature-pressure phase diagram calculated for the composition Ti-4Fe (wt.%) and (**b**) temperature–composition phase diagram calculated for the pressure of 10 GPa. The vertical dashed lines mark the pressure value of 10 GPa (in (**a**)) and the alloy composition of Ti-4Fe (in (**b**)). The black dashed line in the bottom left corner of panel (**a**) indicates the metastable extension of the β-(Ti,Fe) + ω-Ti(Fe) region.
