####
J. Japan Inst. Met. Mater, Vol. 79, No. 1 (2015),

pp. 9-15

##
Log Angles: Characteristic Angles of Crystal Orientation Given by the Logarithm of Rotation Matrix

**
Kunio Hayashi**^{1}, Motoki Osada^{2}, Yuki Kurosu^{1,∗}, Yoji Miyajima^{1} and Susumu Onaka^{1}

^{1}Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama 226-8502

^{2}Department of Metallurgical Engineering, School of Engineering, Tokyo Institute of Technology, Tokyo 152-8552

#### Abstract:

A rotation matrix *R* with respect to a reference frame is used to describe certain crystal orientation. The logarithm of *R*, ln *R* is a skew symmetric tensor with three independent elements of real numbers. The goniometer-stage model in the present study shows that the three independent elements of ln *R* are the characteristic angles of *R* representing the rotation angles around coordinate axes. Different from various kinds of the Euler angles, the characteristic angles called the log angles are uniquely determined for certain *R*. [doi:10.2320/jinstmet.J2014036]

(Received 2014/8/25)

#### Keywords:

logarithm of matrix, misorientation, microstructure, Euler angles, axis/angle pair

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