Valence bond interpretation of elastic anisotropy in B.C.C. transition metals

Abstract

Abstract Valence bond theory provides a practical microscopic phenomeno-iogical context for interpretation of many properties of transition metals. In b.c.c. transition metals, the partition of the total bonding hybrids into nearest-neighbour (sd3, d4) and next-nearest-neighbour (d3) hybrids has been used previously to interpret their structure and is used here to explain the elastic properties. Constants for bond angle distortion as well as bond extension are required to describe the distortion of the localized electron orbitals. As a consequence of the partial nearest and next-nearest-neighbour electron characteristics, the shear deformation of C and C′ modes depends only on the bond angle changes. Three microscopic constants, two referring to the nearest-neighbour and the next-nearest-neighbour bond angle changes, respectively, and the third referring to the lattice dilatation are calculated from the microscopic elastic constants. Whereas strength of bonding in these metals is determined by the s and d electron densities, the nature of anisotropy in elements of groups VA and VIA depends upon the relative strengths of nearest and next-nearest-neighbour bonding, an indication of which is provided by the ratio of microscopic bond angle constants.