Electronic Selection Rules Controlling Dislocation Glide in bcc Metals

The validity of the structure-property relationships governing the low-temperature deformation behavior of many bcc metals was brought into question with recent ab initio density functional studies of isolated screw dislocations in Mo and Ta. These relationships were semiclassical in nature, having grown from atomistic investigations of the deformation properties of the group V and VI transition metals. We find that the correct form for these structure-property relationships is fully quantum mechanical, involving the coupling of electronic states with the strain field at the core of long $a/2⟨111⟩$ screw dislocations.

Figure 1

A projection onto the $(111)$ plane of stress free Mo (A) and Ta (B) cores. Solid spheres give atom positions and open spheres are the locations of bond critical points. Bond paths are shown with connecting lines. The core regions are shaded with triangles. Bonds paths are present across the Mo core, but absent in Ta. Outside the core region the topologies of the two metals are identical. The insert (top) shows the fractional displacement of the atoms in the $z$ direction (in and out of the page) for the atoms immediately adjacent to the core. Any full circuit around the dislocation results in a translation along $z$ equal to one Burgers vector.

Figure 2

Structure around Mo (A) and Ta (B) core atoms corresponding to those labeled $1/6$, $3/6$, and $5/6$ in Fig. 1. For Mo, the symmetry of the charge density about the central atom is nearly $D_{2d}$—a rotation by 90° about the $z$ axis followed by a reflection in the $xy$ plane will carry the bond critical points above the plane into those below the plane. Under this symmetry, the $d_{xz}$ orbitals, which participate in the bonding above the $xy$ plane, are nearly degenerate with the $d_{yz}$ atomic orbitals, which form the two bonds below the plane. In Ta, the absence of bond critical points above the plane reduces the symmetry of the charge density to $C_{2v}$, lifting the degeneracy between the $d_{xz}$ and $d_{yz}$ atomic orbitals.