# Variation in Mechanical Properties of Ti-13 Nb-13 Zr Depending on Annealing Temperature
## 3 Results and Discussion
The annealing at the lower temperatures (i.e., 573-773 K) showed the absence of \((110)\beta\) peak. This does not indicate the absence of \(\beta\) phases but rather the low fraction insufficient for being measured through the XRD analysis. Indeed, [PERSON] et al. [18] reported an appearance of \((110)\beta\) peak even after the annealing at 773 K for sufficient periods. In their work, the peak was not confirmed after the annealing up to 1 h, as is consistent with the present study, but emerged after 3 h. Furthermore, the peak intensity was significantly increased when the annealing time was increased to 6 h, suggestive of the increasing \(\beta\) fraction with increasing annealing periods. The separation of \(\alpha\) and \(\alpha^{\prime}\) phases is difficult through XRD measurement, because both phases have the same hcp structure. Nevertheless, it is rational in terms of thermodynamics that the \(\alpha\) fraction increases with increasing annealing temperature and/or time. It is noted that \(\alpha\) phase is harder than \(\alpha^{\prime}\) martensite [19]. In other words, the decomposition of \(\alpha^{\prime}\) into \((\alpha+\beta)\) increases YS, UTS, hardness, and Young's modulus simultaneously. It well explains the tendency for mechanical properties to increase after the annealing at 573-773 K (i.e., the positive correlation with the annealing temperature), as presented in Figure 2.  
It is interesting to note that the annealing temperature for the highest strength and hardness (i.e., 773 K in Figure 2a,b) was different from that for the highest Young's modulus (873 K in Figure 2c). Figure 4 compares the microstructures after the annealing at each temperature to elucidate the mechanisms under such a disparity. SEM observation showed a shorter length of laths in the 873 K  
Figure 3: X-ray diffraction (XRD) line profile of Ti-13 Nb-13 Zr alloys depending on the annealing temperature. specimen as compared to that of the 773 K specimen. EBSD observation presented a higher \(\beta\) fraction of the former (3.0%) than the latter (1.4%). Static spheroidization (often called \"globularization\") of titanium alloys consists of two discrete steps of (i) boundary splitting and (ii) termination migration [20]. The boundary-splitting step occurs by the initiation of grooves at subgrain boundaries and their propagation in the early stage of spheroidization. The termination-migration step did not occur for the investigated alloys due to the relatively short annealing period adopted in this work (i.e., 1 h). For example, [PERSON] et al. [21] proposed that a static spheroidalization of Ti-6 Al-2 Sn-4 Zr-2 Mo-0.1 Si alloy at 1228 K required 1.4 h of boundary splitting and then 23.5 h of termination migration. Such time requirements may increase for the present case considering the significantly lower annealing temperatures. Therefore, the different characteristics between 773 K and 873 K specimens were determined by the boundary splitting. The time for boundary splitting is proportional to grain size and temperature, whereas it decreases with an increase in solute concentration, surface energy of phase interface, \(\alpha\) fraction, and solute diffusivity [22]. Increasing temperature from 773 K to 873 K changed the \(\alpha\) fraction, solute diffusivity, and the temperature itself towards the accelerated boundary splitting. This is experimentally confirmed as well [21]; a small decrease in annealing temperature (25 K) increased the time for boundary splitting from 0.5 to 2 h. Thus, the higher annealing temperature considerably accelerated the boundary splitting that mostly accounted for the static spheroidization for the present annealing conditions. Meanwhile, Young's modulus is not affected by grain boundaries but by phase compositions. For example, [PERSON] et al.