Calculation of {112} twin and stacking fault energies in b.c.c. transition metals

Abstract

The {112} twin energies in b.c.c. transition metals are calculated by using a tight-binding description of the d band with a moment expansion of the density of states. The core-core repulsion is treated by a Born-Mayer potential. The calculations take into account (1) the variation of distances between first- and second-nearest neighbours through the pair interaction and the hopping integrals change and (2) the anisotropy of the d orbitals. The latter contribution is shown to be quite important and strongly dependent on the d filling. The twin energy can be obtained simply by adding to it the influence of distance variation on both the attractive and repulsive terms. Results are explicitly given for ferromagnetic Fe and paramagnetic V, Cr, Mo and W. For Fe, agreement with experimental data is satisfactory. Energies of stacking faults and sheared twins are also discussed.