{"title":"关于旋转轴测定中的误差大小","authors":"Adam Morawiec","doi":"10.1107/S1600576724004692","DOIUrl":null,"url":null,"abstract":"<p>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, <i>e.g.</i> in identifying deformation slip mechanisms.</p>","PeriodicalId":48737,"journal":{"name":"Journal of Applied Crystallography","volume":"57 4","pages":"1059-1066"},"PeriodicalIF":5.2000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the magnitude of error in the determination of rotation axes\",\"authors\":\"Adam Morawiec\",\"doi\":\"10.1107/S1600576724004692\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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, <i>e.g.</i> in identifying deformation slip mechanisms.</p>\",\"PeriodicalId\":48737,\"journal\":{\"name\":\"Journal of Applied Crystallography\",\"volume\":\"57 4\",\"pages\":\"1059-1066\"},\"PeriodicalIF\":5.2000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Crystallography\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1107/S1600576724004692\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Crystallography","FirstCategoryId":"88","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1107/S1600576724004692","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
On the magnitude of error in the determination of rotation axes
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.
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.