Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T11:17:13.308Z Has data issue: false hasContentIssue false

Automated Reconstruction of Spherical Kikuchi Maps

Published online by Cambridge University Press:  31 May 2019

Chaoyi Zhu
Affiliation:
Materials Science and Engineering Program, University of CA San Diego, La Jolla, CA 92093, USA
Kevin Kaufmann
Affiliation:
Department of NanoEngineering, University of California San Diego, La Jolla, CA 92093, USA
Kenneth Vecchio*
Affiliation:
Materials Science and Engineering Program, University of CA San Diego, La Jolla, CA 92093, USA Department of NanoEngineering, University of California San Diego, La Jolla, CA 92093, USA
*
*Author for correspondence: Kenneth Vecchio, E-mail: [email protected]
Get access

Abstract

An automated approach to fully reconstruct spherical Kikuchi maps from experimentally collected electron backscatter diffraction patterns and overlay each pattern onto its corresponding position on a simulated Kikuchi sphere is presented in this study. This work demonstrates the feasibility of warping any Kikuchi pattern onto its corresponding location of a simulated Kikuchi sphere and reconstructing a spherical Kikuchi map of a known phase based on any set of experimental patterns. This method consists of the following steps after pattern collection: (1) pattern selection based on multiple threshold values; (2) extraction of multiple scan parameters and phase information; (3) generation of a kinematically simulated Kikuchi sphere as the “skeleton” of the spherical Kikuchi map; and (4) overlaying the inverse gnomonic projection of multiple selected patterns after appropriate pattern center calibration and refinement. The proposed method is the first automated approach to reconstructing spherical Kikuchi maps from experimental Kikuchi patterns. It potentially enables more accurate orientation calculation, new pattern center refinement methods, improved dictionary-based pattern matching, and phase identification in the future.

Type
Software and Instrumentation
Copyright
Copyright © Microscopy Society of America 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, BL, Wright, SI & Kunze, K (1993). Orientation imaging: The emergence of a new microscopy. Metall Trans A 24, 819831.Google Scholar
Alam, MN, Blackman, M & Pashley, DW (1954). High-angle Kikuchi patterns. Proc R Soc London Ser A Math Phys Sci 221, 224242.Google Scholar
Allen, AJ, Hutchings, MT, Windsor, CG & Andreani, C (1985). Neutron diffraction methods for the study of residual stress fields. Adv Phys 34, 445473.Google Scholar
Ayer, R (1989). Determination of unit cell. J Electron Microsc Technol 13, 1626.Google Scholar
Basinger, J, Fullwood, D, Kacher, J & Adams, B (2011). Pattern center determination in electron backscatter diffraction microscopy. Microsc Microanal 17, 330340.Google Scholar
Bragg, W & Bragg, WL (1913). The reflection of X-rays by crystals. Proc R Soc London Ser A 88, 428438.Google Scholar
Britton, TB, Jiang, J, Guo, Y, Vilalta-Clemente, A, Wallis, D, Hansen, LN, Winkelmann, A & Wilkinson, AJ (2016). Tutorial: Crystal orientations and EBSD—Or which way is up? Mater Charact 117, 113126.Google Scholar
Britton, TB, Maurice, C, Fortunier, R, Driver, JH, Day, AP, Meaden, G, Dingley, DJ, Mingard, K & Wilkinson, AJ (2010). Factors affecting the accuracy of high resolution electron backscatter diffraction when using simulated patterns. Ultramicroscopy 110, 14431453.Google Scholar
Brough, I, Bate, PS & Humphreys, FJ (2006). Optimising the angular resolution of EBSD. Mater Sci Technol 22, 12791286.Google Scholar
Callahan, PG & De Graef, M (2013). Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations. Microsc Microanal 19, 12551265.Google Scholar
Carpenter, DA, Pugh, JL, Richardson, GD & Mooney, LR (2007). Determination of pattern centre in EBSD using the moving-screen technique. J Microsc 227, 246247.Google Scholar
Chen, D, Kuo, JC & Wu, WT (2011). Effect of microscopic parameters on EBSD spatial resolution. Ultramicroscopy 111, 14881494.Google Scholar
Chen, YH, Park, SU, Wei, D, Newstadt, G, Jackson, MA, Simmons, JP, De Graef, M & Hero, AO (2015). A dictionary approach to electron backscatter diffraction indexing. Microsc Microanal 21, 739752.Google Scholar
Chou, CT, Thomsen, K, Goulden, J & Jiang, H (2013). A method for the correction of EBSPs distorted by lens magnetic fields. Microsc Microanal 19, 730731.Google Scholar
Day, AP (2008). Spherical EBSD. J Microsc 230, 472486.Google Scholar
Demir, E, Raabe, D, Zaafarani, N & Zaefferer, S (2009). Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography. Acta Mater 57, 559569.Google Scholar
Dingley, DJ (1984). On-line determination of crystal orientation and texture determination in an SEM. Proc R Microsc Soc 19, 7475.Google Scholar
Dingley, DJ, Longden, M, Weinbren, J & Alderman, J (1987). Online analysis of electron back scatter diffraction patterns. 1. Texture analysis of zone refined polysilicon. Scanning Microsc 1, 451456.Google Scholar
Dingley, DJ & Wright, SI (2009). Determination of crystal phase from an electron backscatter diffraction pattern. J Appl Crystallogr 42, 234241.Google Scholar
Doyle, PA & Turner, PS (1968). Relativistic Hartree–Fock X-ray and electron scattering factors. Acta Crystallogr Sect A Cryst Physics Diffr Theor Gen Crystallogr 24, 390397.Google Scholar
Engler, O & Randle, V (2014). Introduction to Texture Analysis: Macrotexture, Microtexture and Orientation Mapping. London: CRC Press.Google Scholar
Foden, A, Collins, D, Wilkinson, A & Britton, TB (2018). Indexing electron backscatter diffraction patterns with a refined template matching approach. arXiv Prepr. arXiv1807.11313.Google Scholar
Goulden, J, Trimby, P & Bewick, A (2018). The benefits and applications of a CMOS-based EBSD detector. Microsc Microanal 24, 11281129.Google Scholar
Han, M, Chen, C, Zhao, G, Li, L, Nolze, G, Yu, B, Huang, X & Zhu, Y (2018a). Blind lattice-parameter determination of cubic and tetragonal phases with high accuracy using a single EBSD pattern. Acta Crystallogr Sect A Found Adv 74, 630639.Google Scholar
Han, M, Zhao, G & Zhu, Y (2018b). Accurate determination of low-symmetry Bravais unit cells by EBSD. Ultramicroscopy 195, 136146.Google Scholar
Heinz, A & Neumann, P (1991). Representation of orientation and disorientation data for cubic, hexagonal, tetragonal and orthorhombic crystals. Acta Crystallogr Sect A 47, 780789.Google Scholar
Hielscher, R, Bartel, F & Britton, TB (2018). Gazing at crystal balls-Electron backscatter diffraction indexing and cross correlation on a sphere. arXiv Prepr. arXiv1810.03211.Google Scholar
Humphreys, FJ (1999). Quantitative metallography by electron backscattered diffraction. J Microsc 195, 170185.Google Scholar
Humphreys, FJ (2001). Grain and subgrain characterisation by electron backscatter diffraction. J Mater Sci 36, 38333854.Google Scholar
Kacher, J, Landon, C, Adams, BL & Fullwood, D (2009). Bragg's Law diffraction simulations for electron backscatter diffraction analysis. Ultramicroscopy 109, 11481156.Google Scholar
Kaufmann, K, Zhu, C, Rosengarten, AS, Maryanovsky, D, Harrington, TJ, Marin, E & Vecchio, KS (2019). Paradigm shift in electron-based crystallography via machine learning. eprint arXiv:1902.03682.Google Scholar
Krieger Lassen, NC (1992). Image processing procedures for analysis of electron backscattering patterns. Scanning Microsc 6, 115121.Google Scholar
Krieger Lassen, NC (1999). Source point calibration from an arbitrary electron backscattering pattern. J Microsc 195, 204211.Google Scholar
Li, L & Han, M (2015). Determining the Bravais lattice using a single electron backscatter diffraction pattern. J Appl Crystallogr 48, 107115.Google Scholar
Li, L, Ouyang, S, Yang, Y & Han, M (2014). EBSDL: A computer program for determining an unknown Bravais lattice using a single electron backscatter diffraction pattern. J Appl Crystallogr 47, 14661468.Google Scholar
Llopart, X, Ballabriga, R, Campbell, M, Tlustos, L & Wong, W (2007). Timepix, a 65k programmable pixel readout chip for arrival time, energy and/or photon counting measurements. Nucl Instruments Methods Phys Res Sect A Accel Spectrom Detect Assoc Equip 581, 485494.Google Scholar
Llopart, X, Campbell, M, Dinapoli, R, San Segundo, D & Pernigotti, E (2002). Medipix2: A 64-k pixel readout chip with 55-/spl mu/m square elements working in single photon counting mode. IEEE Trans Nucl Sci 49, 22792283.Google Scholar
Lühr, T, Winkelmann, A, Nolze, G, Krull, D & Westphal, C (2016). Direct atom imaging by chemical-sensitive holography. Nano Lett 16, 31953201.Google Scholar
Marquardt, K, De Graef, M, Singh, S, Marquardt, H, Rosenthal, A & Koizuimi, S (2017). Quantitative electron backscatter diffraction (EBSD) data analyses using the dictionary indexing (DI) approach: Overcoming indexing difficulties on geological materials. Am Mineral 102, 18431855.Google Scholar
Maurice, C, Dzieciol, K & Fortunier, R (2011). A method for accurate localisation of EBSD pattern centres. Ultramicroscopy 111, 140148.Google Scholar
Maurice, C & Fortunier, R (2008). A 3D Hough transform for indexing EBSD and Kossel patterns. J Microsc 230, 520529.Google Scholar
Michael, JR & Eades, JA (2000). Use of reciprocal lattice layer spacing in electron backscatter diffraction pattern analysis. Ultramicroscopy 81, 6781.Google Scholar
Michael, JR & Goehner, RP (1999). Ab-initio primitive cell calculations from EBSD patterns. 2nd international conference Union microbeam analysis societies, Hawai. In Conference Series, Institute of Physics D, W. & R, S. (Eds.), 165, pp. 203–204.Google Scholar
Michael, JR & Goehner, RP (2000). Reduced unit cell determination from unindexed EBSD patterns. Microsc Microanal 6, 946947.Google Scholar
Nishikawa, S & Kikuchi, S (1928). Diffraction of cathode rays by calcite. Nature 122, 726.Google Scholar
Nolze, G (2015). Euler angles and crystal symmetry. Cryst Res Technol 50, 188201.Google Scholar
Nolze, G, Jürgens, M, Olbricht, J & Winkelmann, A (2018). Improving the precision of orientation measurements from technical materials via EBSD pattern matching. Acta Mater 159, 408415.Google Scholar
Nowell, MM & Wright, SI (2004). Phase differentiation via combined EBSD and XEDS. J Microsc 213, 296305.Google Scholar
Page, YL (1992). Ab-initio primitive cell parameters from single convergent beam electron diffraction patterns: A converse route to the identification of microcrystals with electrons. Microsc Res Technol 21, 158165.Google Scholar
Ram, F, Zaefferer, S, Jäpel, T & Raabe, D (2015). Error analysis of the crystal orientations and disorientations obtained by the classical electron backscatter diffraction technique. J Appl Crystallogr 48, 797813.Google Scholar
Ram, F, Zaefferer, S & Raabe, D (2014). Kikuchi bandlet method for the accurate deconvolution and localization of Kikuchi bands in Kikuchi diffraction patterns. J Appl Crystallogr 47, 264275.Google Scholar
Schwartz, AJ, Kumar, M, Adams, BL & Field, DP (2000). Electron Backscatter Diffraction in Materials Science. New York: Kluwer Academic.Google Scholar
Singh, S, Guo, Y, Winiarski, B, Burnett, TL, Withers, PJ & De Graef, M (2018). High resolution low kV EBSD of heavily deformed and nanocrystalline aluminium by dictionary-based indexing. Sci Rep 8, 10991.Google Scholar
Small, JA & Michael, JR (2001). Phase identification of individual crystalline particles by electron backscatter diffraction. J Microsc 201, 5969.Google Scholar
Smith, GH & Burge, RE (1962). The analytical representation of atomic scattering amplitudes for electrons. Acta Crystallogr 15, 182186.Google Scholar
Tanaka, T & Wilkinson, AJ (2018). High angular resolution electron backscatter diffraction studies of tetragonality in Fe-C martensitic steels. Microsc Microanal 24, 962963.Google Scholar
Thomsen, K, Schmidt, NH, Bewick, A, Larsen, K & Goulden, J (2013). Improving the accuracy of orientation measurements using EBSD. Microsc Microanal 19, 724725.Google Scholar
Trimby, PW (2012). Orientation mapping of nanostructured materials using transmission Kikuchi diffraction in the scanning electron microscope. Ultramicroscopy 120, 1624.Google Scholar
Venables, JA & Bin-Jaya, R (1977). Accurate microcrystallography using electron back-scattering patterns. Philos Mag 35, 13171332.Google Scholar
Venables, JA & Harland, CJ (1973). Electron back-scattering patterns—a new technique for obtaining crystallographic information in the scanning electron microscope. Philos Mag 27, 11931200.Google Scholar
Vermeij, T, De Graef, M & Hoefnagels, J (2019). Demonstrating the potential of accurate absolute cross-grain stress and orientation correlation using electron backscatter diffraction. Scr Mater 162, 266271.Google Scholar
Vespucci, S, Winkelmann, A, Naresh-Kumar, G, Mingard, KP, Maneuski, D, Edwards, PR, Day, AP, O'Shea, V & Trager-Cowan, C (2015). Digital direct electron imaging of energy-filtered electron backscatter diffraction patterns. Phys Rev B: Condens Matter Mater Phys 92, 205301.Google Scholar
Villert, S, Maurice, C, Wyon, C & Fortunier, R (2009). Accuracy assessment of elastic strain measurement by EBSD. J Microsc 233, 290301.Google Scholar
Vystavěl, T, Stejskal, P, Unčovský, M & Stephens, C (2018). Tilt-free EBSD. Microsc Microanal 24, 11261127.Google Scholar
Wilkinson, AJ, Collins, DM, Zayachuk, Y, Korla, R & Vilalta-Clemente, A (2018). Applications of multivariate statistical methods and simulation libraries to analysis of electron backscatter diffraction and transmission Kikuchi diffraction datasets. Ultramicroscopy 196, 8898.Google Scholar
Wilkinson, AJ, Meaden, G & Dingley, DJ (2006). High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity. Ultramicroscopy 106, 307313.Google Scholar
Wilkinson, AJ, Moldovan, G, Britton, TB, Bewick, A, Clough, R & Kirkland, AI (2013). Direct detection of electron backscatter diffraction patterns. Phys Rev Lett 111, 065506.Google Scholar
Williams, DB & Carter, CB (2009). Transmission Electron Microscopy: A Textbook for Materials Science. Boston: Springer.Google Scholar
Winkelmann, A (2008). Dynamical effects of anisotropic inelastic scattering in electron backscatter diffraction. Ultramicroscopy 108, 15461550.Google Scholar
Winkelmann, A (2010). Principles of depth-resolved Kikuchi pattern simulation for electron backscatter diffraction. J Microsc 239, 3245.Google Scholar
Winkelmann, A, Nolze, G, Vos, M, Salvat-Pujol, F & Werner, WSM (2016). Physics-based simulation models for EBSD: Advances and challenges. IOP Conf Ser Mater Sci Eng 239, 3245.Google Scholar
Wright, SI & Adams, BL (1992). Automatic analysis of electron backscatter diffraction patterns. Metall Trans A 23, 759767.Google Scholar
Wright, SI, Nowell, MM & Basinger, J (2011a). Precision of EBSD based orientation measurements. Microsc Microanal 17, 406407.Google Scholar
Wright, SI, Nowell, MM, De Kloe, R, Camus, P & Rampton, T (2015). Electron imaging with an EBSD detector. Ultramicroscopy 148, 132145.Google Scholar
Wright, SI, Nowell, MM & Field, DP (2011b). A review of strain analysis using electron backscatter diffraction. Microsc Microanal 17, 316329.Google Scholar
Zaafarani, N, Raabe, D, Singh, RN, Roters, F & Zaefferer, S (2006). Three-dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations. Acta Mater 54, 18631876.Google Scholar
Zaefferer, S & Elhami, NN (2014). Theory and application of electron channelling contrast imaging under controlled diffraction conditions. Acta Mater 75, 2050.Google Scholar
Zhu, C, Harrington, T, Gray, GT & Vecchio, KS (2018). Dislocation-type evolution in quasi-statically compressed polycrystalline nickel. Acta Mater 155, 104116.Google Scholar
Zhu, C, Harrington, T, Livescu, V, Gray, GT & Vecchio, KS (2016). Determination of geometrically necessary dislocations in large shear strain localization in aluminum. Acta Mater 118, 389394.Google Scholar
Zhu, C, Livescu, V, Harrington, T, Dippo, O, Gray, GT & Vecchio, KS (2017). Investigation of the shear response and geometrically necessary dislocation densities in shear localization in high-purity titanium. Int J Plast.Google Scholar