First-principles determination of the crystallography of the low-temperature phase for NbRu and TaRu shape memory alloys

The crystallography of the low-temperature phases (beta '') for shape memory alloys (NbRu and TaRu) has been debated for decades. Though a P2/m monoclinic structure has been proposed for the beta '' phase, the proposed structure is not able to completely represent the measured diffraction data. In this work, the crystallography of the beta '' phase was investigated by first-principles calculations. We showed that the previously reported P2/m monoclinic structure was lattice unstable due to the presence of the soft phonon mode. A P2(1)/m monoclinic structure was derived from the P2/m monoclinic structure by displacing its atoms according to the eigenvector of the soft phonon mode at the Gamma point. The P2(1)/m and the P2/m monoclinic structures are structurally similar, but the former one is energetically and structurally more favorable than the latter one. We concluded that the beta '' phase preferred to crystallize in the P2(1)/m monoclinic structure rather than the previously reported P2/m monoclinic structure. Our results offer guidance for the experimental determination of the crystallography of the beta '' phase for NbRu and TaRu.