Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix

摘要

The logarithm ln⁡>R of rotation matrix >R is a skew symmetric tensor consisting of three independent elements of real numbers. In addition to the Euler angles and the axis/angle pair, the elements of ln⁡>R called the log angles are also the set of three parameters of >R. In this paper, we will show that the concept of the log angles is also useful to discuss changes in crystal orientations. The changes in >R as a function of the position are given by the changes in the log angles. As an example, orientation changes caused by arrays of dislocations in a plastically deformed Cu single crystal are discussed.