Significance of non-central forces in atomistic studies of grain boundaries in bcc transition metals

The effects of non-central forces in atomistic studies of grain boundaries in molybdenum and tungsten, the transition metals with half-filled d-band, are investigated. For this purpose we have used two different types of potential which include different number of moments of the local density of electronic states when evaluating the total energy: the central-force Finnis-Sinclair potentials which include the scalar second moment and the potentials constructed by Carlsson which include the fourth and the matrix second moments. The energy terms associated with these two moments represent non-central interactions and assure that the bcc-fcc structural energy difference is reproduced with good accuracy. For the three boundaries studied, the non-central forces have been found to be very important in determining the lowest energy structures. In particular, the energy differences between multiple structures depend on specific orientations and geometries of the atomic clusters at and near the interface. On the other hand, central-force potentials favour structures with atomic separations close to those found in the bulk with no regard to bond orientation. As a consequence the lowest-energy structures predicted by the two potential schemes differ in details in both the local atomic relaxations and the magnitude of the rigid-body displacements of the grains, although many general features of the boundary structures remain the same, independent of the potentials used. The calculations also show that it is not possible to identify the major non-central contribution with the fourth moment alone. Thus inclusion of both the matrix second moment and the fourth moment energy contributions is essential for an appropriate description of non-central atomic interactions.