多結晶材料における平均の結晶方位の定義とその応用

抄録

The present paper introduces a new statistical method of analyzing the distribution of crystal orientation in a polycrystalline material using ‘quaternion’ presentation instead of ‘matrix’ one.
At first, a crystal orientation space is metrized, and the ‘mean crystal orientation (MCO)’ is defined considering the symmetry of the cubic system. In practice, the distribution of deviations from MCO is analyzed. The deviation is defined three-dimensionally and consists of the disorientation angle (1-dim) and the rotation axis of the deviation (2-dim). It is shown that the ‘quaternion’ presentation is superior to the ‘matrix’ presentation in the separation of these components.
The distribution of disorientation angle is investigated at the first stage of analysis. The degree of randomness is evaluated secondly. When the material is textured in some degree, a further analysis can be made by the ‘stereographic projection of four-dimensional sphere to three-dimensional space’.