A systematic analytical description of rigid grain-boundary relaxation in metals was achieved by using a Morse potential. Expressions were derived which described (in reciprocal space) the dependence of the energy, of interatomic interaction in bicrystals, upon the microscopic and macroscopic parameters of the grain-boundary structure. The energy of intergranular adhesion, and the grain-boundary dilatation at incommensurate grain boundaries, were shown to depend appreciably upon the distance between atomic planes parallel to the boundary. This model made it possible to describe satisfactorily the so-called translational state of symmetrical special boundaries.

Analytical Model of Rigid Relaxation of Grain Boundaries in Metals. V.I.Gerasimenko, T.I.Mazilova, I.M.Mikhailovskii: Physics of Metals and Metallography, 2001, 91[4], 335-9