Stability of the $\ddot{I}‰$ structure of transition elements

Abstract

Properties of the $\ddot{I}‰$ structure are investigated for 27 transition elements from the viewpoints of thermodynamical and mechanical stability based on first-principles calculations. The thermodynamical stability of the $\ddot{I}‰$ structure is compared with those for the body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures. Similarly to the case of those popular crystal structures, the occupation number for $d$ orbitals is found to roughly determine relative energy and volume of the nonmagnetic (NM) $\ddot{I}‰$ structure. For the group 4 elements (Ti, Zr, and Hf), the $\ddot{I}‰$ structure is almost the lowest in energy among the investigated crystal structures and is also mechanically stable. The $\ddot{I}‰$ structure of the group 7 elements (Mn, Tc, and Re) is also mechanically stable. The $\ddot{I}‰$ Fe is found to exhibit a complicated magnetic state that is different from the ferromagnetic (FM) and NM ones. This magnetic state is the most favorable among the investigated magnetic states. The $\ddot{I}‰$ Fe in this magnetic state is also mechanically stable. Energies of binary alloys composed of the elements in the group 4 and those in the groups 5 and 6 are estimated by linear interpolation, and most of the alloys show concentration ranges where the $\ddot{I}‰$ structure is the lowest in energy among the investigated crystal structures.