Symmetrical tilt grain boundaries in body-centred cubic transition metals:: an ab initio local-density-functional study

Atomic structures and macroscopic translation states for Sigma 5(310)[001] symmetrical tilt grain boundaries in the body-centred cubic transition metals Nb, Ta, Mo, and W have been calculated in the local-density-functional theory by means of total-energy and force calculations with an ab initio mixed-basis pseudopotential method. For Mo and W translation states of the optimized grain-boundary structures are found with the neighbouring grains being displaced parallel to the [001] tilt axis, yielding grain boundaries without mirror symmetry. For Nb a mirror-symmetry broken translation state is found as well, which however has a smaller grain displacement and is energetically almost degenerate with a mirror-symmetry conserved translation state. An experimental distinction of this mirror-symmetry broken translation state from a mirror-symmetric one in a Nb bicrystal, e.g. by high-resolution transmission electron microscopy, is difficult if not impossible. For Ta the translation state of the optimized grain-boundary structure is determined to be mirror symmetric. The ab initio results for both Nb and Mo are in close agreement with corresponding experimental observations of Nb and Mo bicrystals by means of high-resolution transmission electron microscopy, showing a conserved and a broken mirror symmetry for Nb and Mo, respectively, Consequently, the nb initio results provide a reliable comparative data base for judgement and improvement of empirical interatomic interaction models suitable for large scale atomistic simulations of defects in the body-centred cubic transition metals.