Structure and energy of general grain boundaries in bcc metals

The zero-temperature energies and equilibrium volume expansions of point-defect-free asymmetrical grain boundaries (GBs) in bcc metals are determined using both a many-body potential fitted for Mo and a Johnson-type pair potential spline-fitted for α-Fe. The asymmetrical combinations of lattice planes considered involve one of the five densest planes of the bcc lattice on one side of the interface and a commensurate higher-index plane on the other. As in similar recent work on fcc metals, the two asymmetrical pure tilt boundaries obtained for any given combination of lattice planes give rise to pronounced energy cusps. When a twist component is added to the asymmetrical GB, thus forming a general (or ''asymmetrical twist'') boundary, the energy and planar unit-cell area increase due to the introduction of screw dislocations. A comparison with earlier work on symmetrical GBs in bcc metals suggests that, except for the densest lattice planes, asymmetrical boundaries may actually have lower energies than symmetrical ones. The underlying causes are elucidated via a comparison with recent simulations of free surfaces and with the random grain-boundary limit (in which the interactions of the atoms across the interface are assumed to be entirely random)