The effects of non-central forces were investigated in atomistic studies of grain boundaries in transition metals with a half-filled d-band. Two different types of potential were used. These were the central-force Finnis-Sinclair potential, which included the scalar second moment, and potentials which had been constructed by Carlsson and which included the fourth and matrix second moments. The energy terms which were associated with these 2 moments represented non-central interactions and ensured that the energy difference between body-centered cubic and face-centered cubic structures was reproduced accurately. In the case of the 3 boundaries which were studied, the non-central forces were found to be very important in determining the lowest-energy structures. In particular, the energy differences between multiple structures depended upon the specific orientations and geometries of the atomic clusters at, and near to, the interface. On the other hand, central-force potentials favored structures with atomic separations that were close to those found in the bulk; regardless of bond orientation. Consequently, the lowest-energy structures which were predicted by the 2 potential schemes differed with regard to the details of local atomic relaxation and the magnitude of the rigid-body displacements of the grains, even though many general features of the boundary structures remained the same; regardless of the potentials used. The calculations also showed that it was not possible to deduce the major non-central contribution from the fourth moment alone. It was concluded that inclusion of the matrix second moment and the fourth moment energy contributions was essential for a correct description of non-central atomic interactions.

A.G.Marinopoulos, V.Vitek, A.E.Carlsson: Philosophical Magazine A, 1995, 72[5], 1311-30