Mathematical Analysis of the Energy and Relaxation of Grain Boundaries in Metals

Systematical analytical description of the atomic density and energy on high-angle grain boundaries (GBs) is performed by the methods of molecular statics in reciprocal space. The multilayer oscillatory relaxation profile in the core region of tilt symmetric twin boundaries was found. It was found that the non-monotonic relaxation near the core of the GB is accompanied by the excess internal energy with the distance from the Σ3 {111} incoherent tilt twin boundary. The displacements normal to the GB in the {211} and {110} general type boundaries correspond to the vast majority of the grain- boundary expansion taken up right at the boundary plane. In the case of the {211} GB there are oscillations in the normal displacements that decay exponentially away from the GB. At the {110} general boundary most of the dilatation is again taken up at the GB, but there are no oscillations in the normal displacements.