A representation method for grain-boundary character

As is well known, a grain boundary (GB) is defined by five macroscopic parameters. We propose a method that is useful for representing the GB properties of polycrystalline materials as a function of these five parameters. The properties might include distribution, energy, mobility, segregation and wetting conditions. This method is based on the 'interface-plane scheme', proposed by Wolf and Lutsko. where a GB is characterized by two interface-plane normals and a twist angle (n(1),n(2),phi). Considering the equivalent GB descriptions in cubic materials, the 'interface-plane scheme' space (n(1),n(2),phi) is reduced to a unit triangle (100-110-111) for n(1), a double unit triangle (100-110-111 and 100-101-111) for n(2) and 0 less than or equal to phi < 2 pi. All equivalent GBs whose two GB normals are within a given tolerance angle from reference planes are plotted as a function of the twist angle phi. This representation method is applied to the GB distributions of an Fe-Mn-Cu polycrystalline alloy. As a result, significantly high frequencies of the GB distribution were observed at (111)(111), Sigma = 3, and small-angle boundaries.