| TaRu and NbRu alloys are considered to be attractive candidates for SMAs used at high-temperatures and have great potential in industrial applications. However, the space group, atomic positions and more detailed structural parameters of TaRu and NbRu are unknown and vibrational properties of each phase have not been investigated. In this paper we investigate structural stability, elastic constants, electronic structure and report the complete results of the phonon dispersion relations of the β, β’ and β" phases for the first time by first-principle method.For TaRu alloys, we theoretically confirmed that the β phase has a cubic CsCl structure (Pm-3m) and the β’ phase has a P4/mmm space group, both with atomic positions:Ta (0,0,0), Ru (0.5,0.5,0.5). The optimal c/a for the β’ phase is1.12, which is very close to the experimental value1.09. The shear modulus C’=((C11-C12)/2) of β phase is-128and is related to the instability of the cubic β phase with respect to tetragonal distortions. There are lattice instabilities throughout the entire Brillouin zone for β’ phase, with the dominant instability at R (01/21/2). According to the soft-mode theory of structural transitions, the soft mode at R reducing the tetragonal symmetry to the orthorhombic β" phase. The β" phase is determined to be a Cmmm space group with Wyckoff Site:Ru (4j):(0.00.730.5), Ta (4g):(0.2400.00.0) for the first time from ab initio calculations. The calculated lattice constants deviate below1.26%from the measured ones. The total ground-state energies of these phases were computed, β" phase is lower in energy than the β and β’ phases by0.071eV/atom,0.113eV/atom respsctively. All phonon branches exhibit real frequencies in the entire Brillouin zone and the lowest value of the density of states at EF confirms that the β" phase is the ground state equilibrium phase of TaRu at low temperatures. The total ground-state energies of these phases were computed, corresponding to the determined lattice parameters in Table1. It can be seen that β’ phase is lower in energy than the β phase by0.071eV/atom. So β’ phase is energetically more stable than the parent β phase. The calculations also indicate that the observed orthorhombic β" phase is the lowest in energy (Eβ"-Eβ=-0.113 eV/atom).This suggests that the β" phase may be considered the ground state structure of TaRu.According to our research, we found that many properties of NbRu alloys are similar to which of TaRu. β and β’ phases of NbRu are also cubic and tetragonal structure, respectively and their calculated lattice parameters are in close agreement with the experimental data. There are lattice instabilities of phonon dispersion at M [110] and along F-R for β phase, which confirms the experiment result that the acoustic branches decrease along [110] and become to be unstable with the decrease of temperature. In addition, we found that the phonon dispersion of NbRu β’phase has the largest negative eigenvalue at R point. According to the soft mode theory, the orthorhombic β" phase of NbRu is obtained, the lattice constants are a=2.853A, b=3.056A and c=3.420A, which are in good agreement with the experiment results. By comparing the phonon dispersion relations and DOS of β, β’and β", we found that the orthorhombic β" phase of NbRu is more stable than β and β’ phases. |
PDF Full Text Request