## 4 Summary and Conclusions  
U-6 Nb is a _metastable_ alloy that is most often produced with a microstructure that forms _martensitially_ during rapid cooling from the high-temperature phase, \(\gamma\) (BCC). This alloy is primarily \(\alpha^{\prime\prime}\) (monoclinic), but it can also contain \(\gamma^{0}\) (tetragonal) in high Nb regions of the microstructure [16; 29]. [PERSON] et al. [29] investigated the microstructure-property behaviors of two U-6 Nb alloys with different impurity levels that were fabricated while using laser powder bed-based additive manufacturing (AM). Two powder alloys have been investigated, which differ in composition, such that one alloy (referred to as the high impurity alloy, HI) contains a significantly higher amount of Ti than the other (referred to as the low impurity alloy, LI) [29]. Both HI and LI alloys contain 13.6-13.9 at.% (5.9-6.0 wt.%) Nb; however, the HI alloy contains 2.37 at.% (0.49 wt.%) of Ti and LI alloy contains almost no Ti \(-\) 0.0022 at.% (0.0004 wt.%). Neutron diffraction measurements of the LI alloy indicated a mixed phase in the as-built condition, resembling 42% \(\gamma^{0}\) and 58% \(\alpha^{\prime\prime}\)[29]. After homogenization and water quenching from high to room temperatures (WQ), the LI alloy had approximately 100% \(\alpha^{\prime\prime}\) structure and this structure was not affected by aging at 200 \({}^{\circ}\)C for 2 h [29]. The HI alloy possessed approximately 50% \(\gamma^{0}\) and 50% \(\alpha^{\prime\prime}\) in the as-built condition; however, after homogenization and WQ, the HI alloy had 100% \(\gamma_{0}\) structure and aging also did not affect this structure [29]. The mechanical properties of these two alloys were affected by their different microstructures: after homogenization/WQ/aging, the HI alloy with 100% \(\gamma^{0}\)-structure showed a yield strength increase of 550 MPa, over 2\(\times\) that of the LI alloy, which contained 100% \(\alpha^{\prime\prime}\)-structure. This increase in yield strength was accompanied by super-elastic strains up to 4.5% [29]. In addition to the significant amount of Ti in the HI alloy, LI and HI alloys both contain a very small amount of Mo, Zr, V, Ta, W, Fe, Al, Ni, Cu, Mn, and O. We assumed that the LI alloy had no impurities at all and is represented as the U\({}_{86.23}\)Nb\({}_{13.77}\) alloy with 7.80 wt.% Nb in order to simplify our modeling conditions. We also assumed that the HI alloy had no impurities, except 2.60 at.% of Ti, and it is represented as the U\({}_{83.56}\)Nb\({}_{13.84}\)Ti\({}_{2.60}\) alloy with 6.04 wt.% Nb. Figure 10: DFT-FPLMTO energies for the U\({}_{3}\)Nb compound in the \(\gamma\) (BCC) and \(\gamma^{\rm s}\) structures relative to the orthorhombic \(\alpha\) phase. Our calculations show that the addition of 2.60 at.% of Ti at the expense of U to the U-6 Nb alloy promotes the formation of the \(\gamma^{0}\)-tetragonal phase at the expense of the \(\alpha^{\prime\prime}\) monoclinic phase, which is in perfect accord with the experimental results [29]. We explain this phenomenon by comparing the Nb equivalent for the U\({}_{86.23}\)Nb\({}_{13.77}\) alloy (Nb\({}_{\text{eq}}\) (at.%) = 13.77 at.%) with one for the U\({}_{83.56}\)Nb\({}_{13.84}\)Ti\({}_{2.60}\) alloy (Nb\({}_{\text{eq}}\) (at.%) = 16.44 at.%). At intermediate Nb content (9-15 at.% Nb), the metastable \(\alpha^{\prime\prime}\)-monoclinic structure is formed and at the higher Nb content (16-20 at.% Nb) the metastable \(\gamma^{0}\)-tetragonal structure is formed. We argue that the U\({}_{86.23}\)Nb\({}_{13.77}\) alloy has a Nb\({}_{\text{eq}}\) (at.%) = 13.77 at.%, which corresponds to the stability region of the \(\alpha^{\prime\prime}\)-monoclinic structure, but the U\({}_{83.56}\)Nb\({}_{13.84}\)Ti\({}_{2.60}\) alloy has a Nb\({}_{\text{eq}}\) (at.%) = 16.44 at.%, which corresponds to the stability region of the \(\gamma^{0}\)-tetragonal structure.