# Variation in Mechanical Properties of Ti-13 Nb-13 Zr Depending on Annealing Temperature
## 3 Results and Discussion  
Figure 1 shows the microstructure of ST alloy (i.e., the initial microstructure) composed of fine laths with a submicron thickness. These laths are known to \(\alpha^{\prime}\) martensite with the hexagonal close-packed (hcp) structure. ST Ti-13 Nb-13 Zr is transformed into the full-\(\beta\) structure in the first step of the ST process (i.e., the heat treatment in the \(\beta\) domain), which is converted into the full \(\alpha^{\prime}\)-martensitic structure in the second step (i.e., the rapid cooling) due to the martensite-starting temperature of 823 K and the martensite-finishing temperature of 758 K, respectively [15]. Figure 2 demonstrates the variation in mechanical properties of the investigated Ti-13 Nb-13 Zr alloys including yield strength (YS), ultimate tensile strength (UTS), Vickers hardness, Young's modulus, and mechanical compatibility. ST Ti-13 Nb-13 Zr exhibited YS of \(478\pm 22\) MPa, UTS of \(666\pm 15\) MPa, hardness of \(219\pm 6\) HV, Young's modulus of 63 GPa, and mechanical compatibility of \(7.5\times 10^{-3}\). These results are highly consistent with values in the literature [16], ensuring the data reliability of this study. All mechanical properties of the annealed alloys increased with increasing temperature up to an intermediate temperature, above which they showed a negative correlation with the temperatures. Specifically, an increasing temperature of annealing from 573 K to 773 K gave rise  
to an increment in YS (\(507\pm 29\) MPa for \(573\) K, \(623\pm 11\) MPa for \(673\) K, and \(672\pm 7\) MPa for \(773\) K, respectively), UTS (\(674\pm 19\) MPa, \(746\pm 9\) MPa, and \(762\pm 8\) MPa), and hardness (\(220\pm 4\) HV, \(258\pm 4\) HV, and \(277\pm 5\) HV). However, the annealing at the higher temperatures resulted in decreasing mechanical properties with increasing temperature. YS values were measured to be \(560\pm 1\) MPa for \(873\) K and \(366\pm 47\) MPa for \(973\) K. UTS also decreased with increasing temperature as \(718\pm 11\) MPa for \(  
and hardness were obtained after the annealing at 773 K for 1 h, whereas that of elastic modulus was confirmed at 873 K for 1 h. Such a disparity is discussed below in more detail. Mechanical compatibilities were determined as \(8.0\times 10^{-3}\) for 573 K, \(9.4\times 10^{-3}\) for 673 K, \(9.5\times 10^{-3}\) for 773 K, \(6.7\times 10^{-3}\) for 873 K, and \(5.5\times 10^{-3}\) for 973 K. Their correlation with the annealing temperature is similar to those found in strength and hardness. This is understood by the definition of mechanical compatibility, which is a ratio of YS to Young's modulus. In other words, the highest Young's modulus of the 873 K specimen decreased its mechanical compatibility. Figure 3 shows the XRD line profile of the investigated Ti-13 Nb-13 Zr alloys. The annealed alloys presented three XRD peaks at \(2\theta\approx 35^{\circ}\), \(38^{\circ}\), and \(40^{\circ}\). These peaks correspond to \((100)\alpha/\alpha^{\prime}\), \((002)\alpha/\alpha^{\prime}\), and \((101)\alpha/\alpha^{\prime}\), respectively [12]. In addition, the annealing at 873 K and 973 K gave rise to the formation of an additional XRD peak at \(2\theta\approx 38.5^{\circ}\), as marked by the arrows in Figure 3. This peak indicates the precipitation of \((110)\beta\) in these samples [12]. [PERSON] et al. [17] and [PERSON] et al. [18] reported five types of phase transformations during an annealing of Ti-13 Nb-13 Zr alloy. Two of them are stable phases: hcp \(\alpha\) and body-centered cubic \(\beta\). The other three are unstable phases: hcp \(\alpha^{\prime}\), orthorhombic \(\alpha^{\prime\prime}\), and hcp \(\omega\). \(\alpha^{\prime}\) and \(\alpha^{\prime\prime}\) are also called a martensite. The full \(\alpha^{\prime}\)-martensitic structure of ST Ti-13 Nb-13 Zr tends to be decomposed into the dual phase of \(\alpha\) and \(\beta\) during the tempering due to the thermal equilibrium. The \((110)\beta\) peak shown in the alloys annealed at 873 K and 973 K provided clear evidence for such a decomposition.