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Misorientation is the difference in crystallographic orientation between two crystallites in a polycrystalline material. In crystalline materials, the orientation of a crystallite is defined by a transformation from a sample reference frame (i.e. defined by the direction of a rolling or extrusion process and two orthogonal directions) to the local reference frame of the crystalline lattice, as defined by the basis of the unit cell. In the same way, misorientation is the transformation necessary to move from one local crystal frame to some other crystal frame. That is, it is the distance in orientation space between two distinct orientations. If the orientations are specified in terms of matrices of direction cosines gA and gB, then the misorientation operator ∆gAB going from A to B can be defined as follows: : : where the term gA−1 is the reverse operation of gA, that is, transformation from crystal frame A back to the sample frame. This provides an alternate description of misorientation as the successive operation of transforming from the first crystal frame (A) back to the sample frame and subsequently to the new crystal frame (B). Various methods can be used to represent this transformation operation, such as: Euler angles, Rodrigues vectors, axis/angle (where the axis is specified as a crystallographic direction), or unit quaternions. == Symmetry and Misorientation == The effect of crystal symmetry on misorientations is to reduce the fraction of the full orientation space necessary to uniquely represent all possible misorientation relationships. For example, cubic crystals (i.e. FCC) have 24 symmetrically related orientations. Each of these orientations is physically indistinguishable, though mathematically distinct. Therefore, the size of orientation space is reduced by a factor of 24. This defines the fundamental zone (FZ) for cubic symmetries. For the misorientation between two cubic crystallites, each possesses its 24 inherent symmetries. In addition, there exists a switching symmetry, defined by: : which recognizes the invariance of misorientation to direction; A→B or B→A. The fraction of the total orientation space in the cubic-cubic fundamental zone for misorientation is then given by: : or 1/48th the volume of the cubic fundamental zone. This also has the effect of limiting the maximum unique misorientation angle to 62.8° Disorientation describes the misorientation with the smallest possible rotation angle out of all symmetrically equivalent misorientations that falls within the FZ (usually specified as having an axis in the standard stereographic triangle for cubics). Calculation of these variants involves application of crystal symmetry operators to each of the orientations during the calculation of misorientation. where Ocrys denotes one of the symmetry operators for the material. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Misorientation」の詳細全文を読む スポンサード リンク
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