Structure of tilt grain boundaries in b.c.c. metals

Structures and energies have been calculated for periodic, symmetrical [001] and [110] tilt boundaries in b.c.c. metals using a variety of central-force potentials. The structures were found to be independent of the potential used and in general more than one relaxed structure was found for each type of grain boundary studied. The boundary structures are analysed in terms of polyhedral groups, called compact polyhedra, with edge lengths which vary between the first- and second-nearest-neighbour separations. A smooth transition occurs between the low-angle and high-angle regimes. Relative to corresponding f.c.c. boundaries, local relaxations were found to be at least as important as rigid translations and atoms were often found to occupy coincidence sites in minimum energy b.c.c. boundaries. The symmetries of relaxed b.c.c. bicrystals were consequently found to be different, usually higher, from those for corresponding boundaries in f.c.c. bicrystals.