A geodesic octonion metric for grain boundaries
A geodesic octonion metric for grain boundaries
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DOI：
10.1016/j.actamat.2018.12.034
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发表时间：
2019-03-01
期刊：
影响因子：
9.4
通讯作者：
De Graef, Marc
中科院分区：
文献类型：
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作者：
Francis, Toby;Chesser, Ian;De Graef, Marc
我们提出了一个表示的晶界上的单位八元数7球。这种表示法带有代数和计算工具，用于在晶界之间进行比较和插值。我们推导出一个测地线度量单位八元数之间的内积的基础上，这本身包括对四元数描述的晶粒取向的参考框架中的晶界平面。我们展示了如何度量的行为下的应用程序的一些对称性：晶粒交换对称性; U（1）对称性周围的晶界法线;无边界条件;和晶体对称性。我们表明，这个度量再现的麦肯齐分布在没有边界的情况下，并正确地确定了一个共同的正常或取向差的晶界之间的角距离。我们提供了一个图形表示的映射到八元数单位球的四元数对，并描述了一些实际的计算，在补充材料随本文。(C)2018 Acta Materialia Inc.由爱思唯尔有限公司出版。保留所有权利。
We propose a representation of grain boundaries on the unit octonion 7-sphere. This representation comes with algebraic and computational tools for comparing and interpolating between grain boundaries. We derive a geodesic metric based on the inner product between unit octonions, which themselves consist of pairs of quaternions describing the grain orientations in the reference frame of the grain boundary plane. We show how the metric behaves under the application of a number of symmetries: grain exchange symmetry; U(1) symmetry around the grain boundary normal; the no-boundary condition; and crystal symmetry. We show that this metric reproduces the Mackenzie distribution in the no boundary case, and correctly determines the angular distances between grain boundaries with a common normal or misorientation. We provide a graphical representation of the mapping of quaternion pairs onto the octonion unit sphere, and describe a number of practical computations in the Supplementary Material accompanying this paper. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.