Electronic structure and chemical bonding effects upon the bcc toΩphase transition:Ab initiostudy of Y, Zr, Nb, and Mo

The bcc $\to \Omega$ phase transition is diffusionless: two-thirds of the atoms in the $\mathrm{}\left(111\right)\mathrm{}$ planes of the bcc phase collapse into double layers, whereas the third remains a single layer. This transformation is observed in the group-IV elements Ti, Zr, and Hf at high pressure, but it may be induced at zero pressure by quenching the samples at room temperature in alloys of these elements with other transition metals (TM’s). This paper presents a systematic theoretical study of the bc$\overrightarrow{\mathrm{c}}$Ω transformation in Y, Zr, Nb, and Mo using the full-potential linearized-augmented-plane-wave method. Equilibrium volumes, total-energy differences, density of electron states, and the band structure of Y, Zr, Nb, and Mo in the stable and metastable bcc and $\Omega$ structures are presented. In addition, the bc$\overrightarrow{\mathrm{c}}$Ω energy difference is studied as a function of the specific lattice distortion as well as of pressure. These results are related to a picture that involves the softening of the $(\frac{2}{3},\frac{2}{3},\frac{2}{3})$ longitudinal phonon mode. Charge-density calculations are performed for both the bcc and $\Omega$ phases, and the electronic contributions that stiffen the bcc lattice against the $\Omega$ distortion are identified. The physical picture of the electronic and chemical bonding effects emerging from the present work should be useful in understanding the observed trends in the relative stability of the $\Omega$ phase in the TM’s and their alloys.