Evaluation of crystal orientations in materials using characteristic angles given by the logarithm of rotation matrix

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K06703
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Physical properties of metals/Metal-base materials
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Onaka Susumu 東京工業大学, 物質理工学院, 教授 (40194576)
• Co-Investigator(Kenkyū-buntansha): 宮嶋 陽司 東京工業大学, 物質理工学院, 助教 (80506254)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 結晶方位 / 材料組織 / 回転行列 / 対数角 / 塑性変形 / 転位組織

Outline of Final Research Achievements

Crystal orientations and their changes are important factors when we consider microstructures of materials. A rotation matrix R with respect to a reference frame is used to describe a certain crystal orientation. The logarithm of R, lnR is a skew symmetric tensor with three independent elements of real numbers. We have shown that the three independent elements called log angles are the characteristic angles of R and can be interpreted as components of rotation angles around coordinate axes. The log angles are useful values to discuss changes in crystal orientations. For example, we can discuss the position dependence of crystal orientations by the position dependence of the log angles. As an application, dislocation arrangement in metals caused by plastic deformation is discussed by the log-angle analysis on experimental results of changes in crystal orientations.

Free Research Field

材料科学，結晶学

Academic Significance and Societal Importance of the Research Achievements

方位変化を解析する際，従来はミスオリエンテーション角（MA）やオイラー角(EA)が使われてきた．しかし，MAは回転軸を無視して回転角のみに注目しており，方位変化を再現することはできない．一方，EAは方位変化が再現可能な基準軸周りの三つの角度の組であるが，回転の結果は基準軸での回転の順番に依存するので，回転角の成分として扱うことはできない．これらとは異なり，合理的に回転の成分とみなせるという特徴が対数角にはあり，このような特性角を導いた点に本研究の学術的な意義がある．また，回転という現象には普遍性があり，このような普遍的な現象に対数角という新規な概念を与えた点に本研究の社会的な意義がある．