## 3 Results
The _metastable_\(\gamma^{0}\) phase of the U\({}_{83.56}\)Nb\({}_{13.84}\)Ti\({}_{2.60}\) alloy exhibits a lower energy than another _metastable_\(\alpha^{\prime\prime}\) phase indicating the stability of the \(\gamma^{0}\) phase over \(\alpha^{\prime\prime}\) phase observed in this alloy, as can be seen from Figure 8b [29]. Hence, the effect of Ti is to favor \(\gamma^{0}\) over \(\alpha^{\prime\prime}\). The authors of the experimental results, as presented in Ref. [29], tried to keep the amount of Nb constant: 13.77 at.% (7.80 wt.% in the U-Nb alloy and 13.84 at.% (6.04 wt.%) in the U-Nb-Ti alloy. The addition of some amount (2.60 at.%) of titanium metal to the U-Nb alloy was only possible by decreasing the amount of uranium metal in that alloy from 86.23 at.% (U-Nb) to 83.56 at.% (U-Nb-Ti), in order to fulfill this condition. As a result of alloying the U-Nb alloy with Ti, the so-called \"Nb equivalent\" (Nb\({}_{\rm eq}\) (at.%) = Nb (at.%) + \(\Sigma_{\rm impurities}\) (at.%)) increases from 13.77 at.% (U-Nb alloy) to 13.84 + 2.60 = 16.44 at.%. As has been mentioned in the Introduction, depending on the Nb concentration, the U-Nb alloys exhibit the following room-temperature structures on quenching from the \(\gamma\) phase: \(\alpha^{\prime}\) orthorhombic (0 to 9 at.%); \(\alpha^{\prime\prime}\) monoclinic (9 to 15 at.%); and, \(\gamma^{0}\) tetragonal (16 to 20 at.%). By keeping the amount of niobium metal almost the same as was in the original U-Nb alloy and adding 2.60 at.% of titanium, the authors [29] increased the Nb equivalent, Nb\({}_{\rm eq}\), from 13.77 at.% (U-Nb) to 16.44 at.% (U-Nb-Ti). Nb\({}_{\rm eq}\) (at.%) = 13.77 at.% corresponds to the stability region of the metastable \(\alpha^{\prime\prime}\)-monoclinic structure, but Nb\({}_{\rm eq}\) (at.%) = 16.44 at.% corresponds to the stability region of the \(\gamma^{0}\)-tetragonal structure, as has been mentioned above. These arguments explain why the addition of some small amount of titanium metal to the U-6 Nb alloy promotes the stabilization of the \(\gamma^{0}\)-tetragonal phase at the expense of the \(\alpha^{\prime\prime}\)-monoclinic phase, resulting in better mechanical properties of U-6 Nb alloys [28]. According to numerous investigations summarized in Ref. [16] and presented in Figure 3, the reaction path for _diffusion-less_ transitions in U-Nb alloys progressively proceeds as (see the expression (2)): \(\gamma\rightarrow\gamma^{0}\rightarrow\alpha^{\prime\prime}\rightarrow\alpha ^{\prime}\). However, the additional metastable phase, \(\gamma^{s}\), could be quenched in the U-22.2 at.% Nb alloy, according to the experiments of [PERSON] and [PERSON] [34] and recent modeling of [PERSON] et al. [35]. [PERSON] et al. [35] suggested that the _diffusion-less_ transitions in the U-Nb system can follow the scheme (see the expression (3)): \(\gamma\to\gamma^{s}\to\gamma^{0}\to\alpha^{\prime\prime}\to\alpha^{\prime}\). In Figure 3, we schematically show the metastable phases for the U-Nb phase diagram [16; 29]. Because of the sluggish solid-state diffusion in the U1-xNbx alloys, the metastable phase variants of the stable \(\alpha\) and \(\gamma_{2}\) phases, \(\alpha^{\prime}\), \(\alpha^{\prime\prime}\), and \(\gamma^{0}\), form depending on the niobium content. According to Figure 3, increasing Nb content leads to a sequence of the metastable phases: \(\alpha^{\prime}\to\alpha^{\prime\prime}\to\gamma^{0}\)[16; 29]. This progression is consistent with the results shown in Figure 5 where the _stable_\(\alpha\) phase of uranium metal has the lowest energy followed by the _metastable_\(\alpha\)\" and \(\gamma^{0}\) phases, and finally the _stable_\(\gamma\) uranium phase. As was experimentally established in Ref. [34], another metastable phase, \(\gamma^{s}\), in a U-22.2 at.% Nb alloy could be quenched from the \(\gamma\) phase region. Of course, it makes sense that a relatively large amount of the BCC metal Nb (\(>\)20 at.%) can \"stabilize\" this _metastable_\(\gamma\) phase.