电子背散衍射花样的数学特征

摘要/Abstract

摘要： 电子背散衍射(EBSD)花样揭示了材料的物相成分、晶体结构、晶粒取向、晶粒大小和晶界的信息。EBSD花样非常复杂,通常需要借助专门的计算软件才能解析。本文系统地研究了EBSD花样的数学特征,建立了任意晶体取向与EBSD花样之间的数理关系,推导了面心立方、体心立方和六方晶体的基本晶带轴的理论EBSD花样的数学特征,以及面心立方晶体的(001)<110>取向和(001)<100>取向的理论菊池(Kikuchi)花样特征。在实测EBSD花样的分析中与各晶系各点阵的基本晶带轴的理论EBSD花样特征比较,即通过图像特征对比,就可以直接确定实测EBSD花样所属的晶系、点阵和Kikuchi线交点对应的晶带轴[uvw],再由基本晶带轴的坐标计算出晶体取向,还能提供基本晶面信息,如原子密排晶面在样品中的空间分布,这有利于晶体的变形或生长机理研究。EBSD为单晶芯片质量检验提供了新方法。

关键词: 电子背散衍射, 晶体结构, 晶体取向, 晶粒大小, 结构表征, 数学特征, 菊池花样, 晶带轴

Abstract: Electron backscattering diffraction (EBSD) patterns reveal information about the phase component, crystal structure, grain orientation, grain size and grain boundaries of the material. EBSD patterns are very complex and usually require special computing software to analyze. A systematic study of the mathematical characteristics of EBSD patterns is carried out in this paper. A mathematical relationship between arbitrary crystal orientation and EBSD pattern is established, mathematical characteristics of EBSD patterns at pattern center of the basal zone axes of face-centered cubic, body-centered cubic, and close-packed hexagonal crystals are derived, as well as the theoretical Kikuchi patterns of (001)<110> orientation and (001)<100> orientation of face-centered cubic crystals. The theoretical EBSD pattern characteristics of the basic crystal zone axes of each lattice are compared in the analysis of the measured EBSD patterns, that is, by comparing the image features, the crystal system, lattice and the crystal zone axes [uvw] corresponding to the intersection points of some Kikuchi lines of the measured patterns can be directly determined. The crystal orientation or texture can be calculated from the coordinates of the basic crystal zone axes, and the spatial distribution of the basic crystal plane can also be provided, such as atomic close-packed plane in the sample, which is beneficial to the study on the deformation or growth mechanism of the crystal. EBSD provides new methods for single-crystal chip quality inspection.

Key words: electron backscattering diffraction, crystal structure, crystal orientation, grain size, structural characterization, mathematical characteristic, Kikuchi pattern, zone axis

中图分类号:

O722

杨成超, 陈亮维, 骆婉君, 梁琦, 宋宏远, 刘斌, 虞澜. 电子背散衍射花样的数学特征[J]. 人工晶体学报, 2022, 51(8): 1437-1444.

YANG Chengchao, CHEN Liangwei, LUO Wanjun, LIANG Qi, SONG Hongyuan, LIU Bin, YU Lan. Mathematical Characterization of Electron Backscattering Diffraction Patterns[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2022, 51(8): 1437-1444.

参考文献

[1] KIKUCHI S. The diffraction of cathode rays by mica. (part Ⅳ.)[J]. Proceedings of the Imperial Academy, 1928, 4(8): 471-474.
[2] HUMPHREYS F J. The determination of crystallographic textures from selected areas of a specimen by electron diffraction[J]. Textures and Microstructures, 1983, 6: 103983.
[3] DINGLEY D, LONGDEN M, WEINBREN J. On-line analysis of electron back scatter diffraction patterns. I. texture analysis of zone refined polysilicon[J]. Scanning Microsc,1987,1(2): 451-456.
[4] DINGLEY D, LONGDEN M. Online analysis of electron back scatter diffraction patterns[J].Scan Elect Micros,1984,2:569
[5] BABA-KISHI K Z, DINGLEY D J. Backscatter Kikuchi diffraction in the SEM for identification of crystallographic point groups[J]. Scanning, 1989, 11(6): 305-312.
[6] GOEHNER R P, MICHAEL J R. Phase identification in a scanning electron microscope using backscattered electron Kikuchi patterns[J]. Journal of Research of the National Institute of Standards and Technology, 1996, 101(3): 301-308.
[7] RUSS J, BRIGHT D, RUSS J, et al. Application of the Hough transform to electron diffraction patterns[J]. Journal of Computer Assisted Microscopy, 1989,1(1):3-37.
[8] WRIGHT S I, ZHAO J W, ADAMS B L. Automated determination of lattice orientation from electron backscattered Kikuchi diffraction patterns[J]. Textures and Microstructures, 1991, 13(2/3): 123-131.
[9] ADAMS B L. Automatic analysis of electron backscatter diffraction patterns[J]. Metallurgical Transactions A, 1992, 23(3): 759-767.
[10] SCHWARTZ A J, KUMAR M, ADAMS B L. Electron backscatter diffraction in materials science[M]. Boston, MA: Springer US, 2000.
[11] BALIC-ZUNIC T, PIAZOLO S, KATERINOPOULOU A, et al. Full analysis of feldspar texture and crystal structure by combining X-ray and electron techniques[J]. American Mineralogist, 2013, 98(1): 41-52.
[12] HSU W C, CHANG L W, SUN P L, et al. Correlation between recrystallization texture and heterogeneities in deformed structure of an electrical steel by electron back-scatter diffraction[J]. ISIJ International, 2015, 55(10): 2212-2216.
[13] JAGTAP P, CHAKRABORTY A, EISENLOHR P, et al. Identification of whisker grain in Sn coatings by analyzing crystallographic micro-texture using electron back-scatter diffraction[J]. Acta Materialia, 2017, 134: 346-359.
[14] 陈亮维,刘状,虞澜,等.工业纯钛金属织构标准极图的计算及分析[J].材料科学与工艺,2020,28(1):17-23.
CHEN L W, LIU Z, YU L, et al. Calculation and analysis of standard pole figure for metal texture in industrial pure titanium[J]. Materials Science and Technology, 2020, 28(1): 17-23(in Chinese).
[15] 陈亮维,霍广鹏,虞澜,等.金属锆织构的标准极图计算及分析[J].昆明理工大学学报(自然科学版),2019,44(2):19-25.
CHEN L W, HUO G P, YU L, et al. Standard pole figure calculation and analysis of zirconium metal texture[J]. Journal of Kunming University of Science and Technology (Natural Science), 2019, 44(2): 19-25(in Chinese).
[16] 胡一丁,王孟金,陈亮维,等.锌金属织构的标准极图计算[J].物理测试,2021,39(1):26-30.
HU Y D, WANG M J, CHEN L W, et al. Standard pole figure calculation of zinc metal texture[J]. Physics Examination and Testing, 2021, 39(1): 26-30(in Chinese).
[17] 陈亮维,史庆南,王剑华,等.一种晶体织构极图分析方法: CN102542163A[P].2012-07-04.
CHEN L W, SHI Q N, WANG J H, et al. A method for crystal texture pole diagram analysis:CN102542163A[P].2012-07-04(in Chinese).
[18] LIANGWEI C, YUYU H, LAN Y, et al. Rethinking about the formulae of the relationship between Euler angles and texture[J]. Journal of Harbin Institute of Technology (New Series), 2021(5): 70-77.
[19] 陈亮维,王孟金,霍广鹏,等.单晶衍射花样与晶体结构之间的数理关系及绘制方法[J].昆明理工大学学报(自然科学版),2020,45(5):17-20.
CHEN L W, WANG M J, HUO G P, et al. Mathematical relationship between a single crystal's diffraction pattern and structure and its drawing method[J]. Journal of Kunming University of Science and Technology (Natural Science), 2020, 45(5): 17-20(in Chinese).
[20] 霍广鹏,陈亮维,胡一丁,等.正交晶系单晶标准透射电子衍射斑点图及绘制原理[J].人工晶体学报,2020,49(7):1281-1285+1293.
HUO G P, CHEN L W, HU Y D, et al. Single crystal standard transmission electron diffraction spot patterns of orthonormal system and its drawing principle[J]. Journal of Synthetic Crystals, 2020, 49(7): 1281-1285+1293(in Chinese).