It was recalled that a grain boundary was defined by 5 macroscopic parameters, and a method was proposed here for representing the grain-boundary properties of polycrystalline materials as a function of these 5 parameters. Such properties could include distribution, energy, mobility, segregation and wetting conditions. The method was based upon the Wolf-Lutsko interface-plane scheme, in which a grain boundary was characterized by 2 interface-plane normals and a twist angle (n1, n2, φ). By considering the equivalent grain boundary descriptions in cubic materials, the interface-plane space, (n1, n2, φ), was reduced to a unit triangle (100-110-111) for n1, a double unit triangle (100-110-111 and 100-101-111) for n2 and φ was between 0 and 2π. All of the equivalent grain boundaries, whose 2 normals were within a given range of angles from the reference planes, were plotted as a function of the twist angle, φ.

A Representation Method for Grain-Boundary Character. M.Takashima, A.D.Rollett, P.Wynblatt: Philosophical Magazine A, 2000, 80[10], 2457-65