On the magnitude of error in the determination of rotation axes

IF 5.2 3区 材料科学 Q2 CHEMISTRY, MULTIDISCIPLINARY
Adam Morawiec
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引用次数: 0

Abstract

Rotation axes (together with rotation angles) are often used to describe crystal orientations and misorientations, and they are also needed to characterize some properties of crystalline materials. Since experimental orientation data are subject to errors, the directions of the axes obtained from such data are also inaccurate. A natural question arises: given the resolution of input rotations, what is the average error of the rotation axes? Assuming that rotation data characterized by a rotation angle ω deviate from the actual data by error rotations with fixed angle δ but which are otherwise random, the average error of the rotation axes of the data is expressed analytically as a function of ω and δ. A scheme for using this formula in practical cases when rotation errors δ follow the von Mises–Fisher distribution is also described. Finally, the impact of crystal symmetry on the determination of the average errors of the axis directions is discussed. The presented results are important for assessing the reliability of rotation axes in studies where the directions of crystal rotations play a role, e.g. in identifying deformation slip mechanisms.

Abstract Image

关于旋转轴测定中的误差大小
旋转轴(连同旋转角度)通常用于描述晶体的取向和错误取向,也需要它们来表征晶体材料的某些特性。由于实验取向数据存在误差,因此从这些数据中获得的轴线方向也不准确。这自然会产生一个问题:在输入旋转分辨率的情况下,旋转轴的平均误差是多少?假设以旋转角度 ω 为特征的旋转数据通过固定角度 δ 的误差旋转偏离实际数据,但在其他方面是随机的,那么数据旋转轴的平均误差可以用 ω 和 δ 的函数来分析表示。此外,还介绍了在旋转误差 δ 遵循 von Mises-Fisher 分布的实际情况中使用该公式的方案。最后,讨论了晶体对称性对确定轴方向平均误差的影响。在晶体旋转方向起作用的研究中,例如在确定变形滑移机制时,所提出的结果对于评估旋转轴的可靠性非常重要。
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来源期刊
Journal of Applied Crystallography
Journal of Applied Crystallography CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY
CiteScore
7.80
自引率
3.30%
发文量
178
期刊介绍: Many research topics in condensed matter research, materials science and the life sciences make use of crystallographic methods to study crystalline and non-crystalline matter with neutrons, X-rays and electrons. Articles published in the Journal of Applied Crystallography focus on these methods and their use in identifying structural and diffusion-controlled phase transformations, structure-property relationships, structural changes of defects, interfaces and surfaces, etc. Developments of instrumentation and crystallographic apparatus, theory and interpretation, numerical analysis and other related subjects are also covered. The journal is the primary place where crystallographic computer program information is published.
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