Electron backscatter diffraction: Difference between revisions

Revision as of 12:34, 15 January 2024

Revision as of 23:29, 15 January 2024

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=== Setup geometry and pattern formation ===

{{Further information|Electron diffraction|Kikuchi lines (physics)}}

[[File:EBSD setup graphic.png|thumb|279x279px|EBSD typical hardware configuration inside a [[field emission gun scanning electron microscope]].<ref>{{Cite journal |last1=Vespucci |first1=S. |last2=Winkelmann |first2=A. |last3=Naresh-Kumar |first3=G. |last4=Mingard |first4=K. P. |last5=Maneuski |first5=D. |last6=Edwards |first6=P. R. |last7=Day |first7=A. P. |last8=O'Shea |first8=V. |last9=Trager-Cowan |first9=C. |date=2015 |title=Digital direct electron imaging of energy-filtered electron backscatter diffraction patterns |journal=Physical Review B |volume=92 |issue=20 |pages=205301 |doi=10.1103/PhysRevB.92.205301|bibcode=2015PhRvB..92t5301V |doi-access=free }}</ref>|alt=Pictorial diagram showing the major components of a field emission gun scanning electron microscope. The electron gun is at the top. Below the gun is a disk of diffraction cones in which the specimen is embedded at an oblique angle. To the left of the sample is a CCD camera assembly, including lenses and a phosphor screen. The electron beam emerges from the gun, impinging on the side of the sample facing the camera.]]

For electron backscattering diffraction microscopy, a flat polished crystalline specimen is usually placed inside the microscope chamber. The sample is tilted at ~70° from [[Scanning electron microscope]] (SEM) flat specimen positioning and 110° to the electron backscatter diffraction (EBSD) detector.<ref name=":18">{{Cite journal |last=Randle |first=Valerie |date=September 2009 |title=Electron backscatter diffraction: Strategies for reliable data acquisition and processing |journal=Materials Characterization |volume=60 |issue=9 |pages=913–922 |doi=10.1016/j.matchar.2009.05.011}}</ref> Tilting the sample elongates the interaction volume perpendicular to the tilt axis, allowing more electrons to leave the sample providing better signal.<ref>{{Citation |last1=Goldstein |first1=Joseph I. |title=Backscattered Electrons |date=2018 |work=Scanning Electron Microscopy and X-Ray Microanalysis |pages=15–28 |place=New York, New York |publisher=Springer New York |doi=10.1007/978-1-4939-6676-9_2 |isbn=978-1-4939-6674-5 |last2=Newbury |first2=Dale E. |last3=Michael |first3=Joseph R. |last4=Ritchie |first4=Nicholas W. M. |last5=Scott |first5=John Henry J. |last6=Joy |first6=David C. }}</ref><ref>{{Cite journal |last1=Winkelmann |first1=Aimo |last2=Nolze |first2=Gert |date= 2010 |title=Analysis of Kikuchi band contrast reversal in electron backscatter diffraction patterns of silicon|journal=Ultramicroscopy |volume=110 |issue=3 |pages=190–194 |doi=10.1016/j.ultramic.2009.11.008 |pmid=20005045 }}</ref> A high-energy electron beam (typically 20 kV) is focused on a small volume and scatters with a spatial resolution of ~20&nbsp;nm at the specimen surface.<ref name=":0">{{Citation |last1=Schwarzer |first1=Robert A. |title=Present State of Electron Backscatter Diffraction and Prospective Developments |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=1–20 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |publisher=Springer US |doi=10.1007/978-0-387-88136-2_1 |isbn=978-0-387-88136-2 |last2=Field |first2=David P. |last3=Adams |first3=Brent L. |last4=Kumar |first4=Mukul |last5=Schwartz |first5=Adam J. |osti=964094 |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P. }}</ref> The spatial resolution varies with the beam energy,<ref name=":0" /> angular width,<ref>{{Cite journal |last1=Venables |first1=J. A. |last2=Harland |first2=C. J. |date=1973 |title=Electron back-scattering patterns—A new technique for obtaining crystallographic information in the scanning electron microscope |journal=The Philosophical Magazine |volume=27 |issue=5 |pages=1193–1200 |doi=10.1080/14786437308225827 |bibcode=1973PMag...27.1193V }}</ref> interaction volume,<ref>{{Cite journal |last1=Chen |first1=Delphic |last2=Kuo |first2=Jui-Chao |last3=Wu |first3=Wen-Tuan |date=2011 |title=Effect of microscopic parameters on EBSD spatial resolution |journal=Ultramicroscopy |volume=111 |issue=9 |pages=1488–1494 |doi=10.1016/j.ultramic.2011.06.007 |pmid=21930021 }}</ref> nature of the material under study,<ref name=":0" /> and, in transmission Kikuchi diffraction (TKD), with the specimen thickness;<ref>{{Cite journal |year=2005 |title=Improving the Spatial Resolution of EBSD |journal=Microscopy and Microanalysis |doi=10.1017/s1431927605506445 |last1=Field |first1=D. P. |volume=11 |s2cid=138097039 |doi-access=free }}</ref> thus, increasing the beam energy increases the interaction volume and decreases the spatial resolution.<ref>{{Cite journal |last1=Deal |first1=Andrew |last2=Tao |first2=Xiaodong |last3=Eades |first3=Alwyn |date=2005 |title=EBSD geometry in the SEM: simulation and representation|journal=Surface and Interface Analysis |volume=37 |issue=11 |pages=1017–1020 |doi=10.1002/sia.2115 |s2cid=122757345 |doi-access=free }}</ref>

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=== Sample preparation ===

[[File:EBSP degradation.tif|thumb|Pattern degradation due to carbon deposition in a highly magnified ___location after 3-hour EBSPs acquisition around a deformation twin in the ferrite phase of [[duplex stainless steel]].<ref name=":31" />|alt=Electron backscatter diffraction's pattern degradation due to carbon deposition in a highly magnified ___location after 3-hour EBSPs acquisition around a deformation twin in the ferrite phase of duplex stainless steel.]]

The sample should be [[Outgassing|vacuum stable.]] It is typically mounted using a conductive compound (e.g. an [[Thermosetting polymer|epoxy thermoset]] filled with Cu), which minimises image drift and sample charging under electron beam irradiation. EBSP quality is sensitive to surface preparation. Typically the sample is ground using [[Sandpaper|SiC papers]] from 240 down to 4000 grit, and polished using diamond paste (from 9 to 1&nbsp;µm) then in 50&nbsp;nm [[colloidal silica]]. Afterwards, it is cleaned in [[ethanol]], rinsed with [[deionised water]], and dried with a hot air blower. This may be followed by [[Ion milling machine|ion beam polishing]], for final surface preparation.<ref>{{Cite journal |last1=Nowell |first1=Matthew M |last2=Witt |first2=Ronald A |last3=True |first3=Brian W |date=2005 |title=EBSD Sample Preparation: Techniques, Tips, and Tricks |journal=Microscopy Today |volume=13 |issue=4 |pages=44–49 |doi=10.1017/s1551929500053669 |s2cid=139585885 |doi-access=free }}</ref><ref name=":32">{{Cite journal |last1=Koko |first1=Abdalrhaman |last2=Elmukashfi |first2=Elsiddig |last3=Becker |first3=Thorsten H. |last4=Karamched |first4=Phani S. |last5=Wilkinson |first5=Angus J. |last6=Marrow |first6=T. James |date=2022 |title=In situ characterisation of the strain fields of intragranular slip bands in ferrite by high-resolution electron backscatter diffraction|journal=Acta Materialia |volume=239 |pages=118284 |doi=10.1016/j.actamat.2022.118284 |bibcode=2022AcMat.23918284K |s2cid=251783802 |doi-access=free }}{{Creative Commons text attribution notice|cc=by4|from this source=yes}}</ref><ref>{{Cite web |date=2013-11-15 |title=Sample Preparation Techniques for EBSD Analysis (Electron Backscatter Diffraction) |url=https://www.azonano.com/article.aspx?ArticleID=3702 |website=AZoNano.com |archive-date=2023-03-02 |archive-url=https://web.archive.org/web/20230302142456/https://www.azonano.com/article.aspx?ArticleID=3702 |url-status=live }}</ref>

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=== Depth resolution ===

{{Further information|Electron scattering}}

[[File:Electron Interaction with Matter.svg|thumb|Electron-matter interaction volume and various types of signal generated|alt=Pictorial diagram showing signals generated when an electron beam interacts with a sample of matter. At the top, the primary electron beam impinges on the sample. Various types of emissions are shown in order of increasing penetration depth of the beam. Near the top are Auger Electrons, followed by Secondary Electrons, then Backscattered Electrons, all emerging in the general direction towards the impinging beam. Next are four types of radiation (shown with wavy arrows): Characteristic X-rays, Continuum X-rays, Cathodo-luminescence, and FlourescentFluorescent X-rays. The later two are shown as being emitted from the same depth. Finally, shown having passed through the body of the sample are, in increasing order of angular displacement from the beam axis, Transmitted Electrons, Diffracted Electrons, and Scattered Elections.]]

There is no agreement about the definition of depth resolution. For example, it can be defined as the depth where ~92% of the signal is generated,<ref>{{Cite journal |last1=Powell |first1=C. J. |last2=Jablonski |first2=A. |date=2011 |title=Surface Sensitivity of Auger-Electron Spectroscopy and X-ray Photoelectron Spectroscopy |journal=Journal of Surface Analysis |volume=17 |issue=3 |pages=170–176 |doi=10.1384/jsa.17.170|doi-access=free }}</ref><ref>{{Cite journal |last1=Piňos |first1=J. |last2=Mikmeková |first2=Š. |last3=Frank |first3=L. |date=2017 |title=About the information depth of backscattered electron imaging |journal=Journal of Microscopy |volume=266 |issue=3 |pages=335–342 |doi=10.1111/jmi.12542|pmid=28248420 |s2cid=35266526 }}</ref> or defined by pattern quality,<ref name=":27" /> or can be as ambiguous as "''where useful information is obtained''".<ref>{{Cite journal |last=Seah |first=M. P. |date=2001 |title=Summary of ISO/TC 201 Standard: VIII, ISO 18115:2001—Surface chemical analysis—Vocabulary|journal=Surface and Interface Analysis |volume=31 |issue=11 |pages=1048–1049 |doi=10.1002/sia.1139 |s2cid=97982609 }}</ref> Even for a given definition, depth resolution increases with electron energy and decreases with the average atomic mass of the elements making up the studied material: for example, it was estimated as 40 nm for Si and 10 nm for Ni at 20 kV energy.<ref>{{Cite journal |last=Dingley |first=D. |date=2004 |title=Progressive steps in the development of electron backscatter diffraction and orientation imaging microscopy: EBSD AND OIM |journal=Journal of Microscopy |volume=213 |issue=3 |pages=214–224 |doi=10.1111/j.0022-2720.2004.01321.x |pmid=15009688 |s2cid=41385346 }}</ref> Unusually small values were reported for materials whose structure and composition vary along the thickness. For example, coating monocrystalline silicon with a few nm of amorphous chromium reduces the depth resolution to a few nm at 15 kV energy.<ref name=":27">{{Cite journal |last=Zaefferer |first=S. |date=2007|title=On the formation mechanisms, spatial resolution and intensity of backscatter Kikuchi patterns |journal=Ultramicroscopy |volume=107 |issue=2 |pages=254–266 |doi=10.1016/j.ultramic.2006.08.007 |pmid=17055170 }}</ref> In contrast, Isabell and David<ref name=":28">{{Cite journal |last1=Isabell |first1=Thomas C. |last2=Dravid |first2=Vinayak P. |date=1997-06-01 |title=Resolution and sensitivity of electron backscattered diffraction in a cold field emission gun SEM |journal=Ultramicroscopy |series=Frontiers in Electron Microscopy in Materials Science |volume=67 |issue=1 |pages=59–68 |doi=10.1016/S0304-3991(97)00003-X }}</ref> concluded that depth resolution in homogeneous crystals could also extend up to 1&nbsp;µm due to [[inelastic scattering]] (including tangential smearing and channelling effect).<ref name=":32" />

A recent comparison between reports on EBSD depth resolution, Koko et al<ref name=":32" /> indicated that most publications do not present a rationale for the definition of depth resolution, while not including information on the beam size, tilt angle, beam-to-sample and sample-to-detector distances.<ref name=":32" /> These are critical parameters for determining or simulating the depth resolution.<ref name=":28" /> The beam current is generally not considered to affect the depth resolution in experiments or simulations. However, it affects the beam spot size and [[signal-to-noise ratio]], and hence, indirectly, the details of the pattern and its depth information.<ref>{{Cite journal |last=Humphreys |first=F. J |date=2004 |title=Characterisation of fine-scale microstructures by electron backscatter diffraction (EBSD) |journal=Scripta Materialia |series=Viewpoint set no. 35. Metals and alloys with a structural scale from the micrometer to the atomic dimensions |volume=51 |issue=8 |pages=771–776 |doi=10.1016/j.scriptamat.2004.05.016}}</ref><ref>{{Citation |last1=Goldstein |first1=Joseph I. |title=The Visibility of Features in SEM Images |date=2018 |work=Scanning Electron Microscopy and X-Ray Microanalysis |pages=123–131 |editor-last=Goldstein |editor-first=Joseph I. |place=New York, New York |publisher=Springer |doi=10.1007/978-1-4939-6676-9_8 |isbn=978-1-4939-6676-9 |last2=Newbury |first2=Dale E. |last3=Michael |first3=Joseph R. |last4=Ritchie |first4=Nicholas W. M. |last5=Scott |first5=John Henry J. |last6=Joy |first6=David C. |editor2-last=Newbury |editor2-first=Dale E. |editor3-last=Michael |editor3-first=Joseph R. |editor4-last=Ritchie |editor4-first=Nicholas W.M. |doi-access=free }}</ref><ref name=":24" />

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=== EBSD mapping ===

[[File:EBSD orientation map of ferrous lath martensite.jpg|thumb|A map of indexed EBSD orientations for a ferrous [[martensite]] with high-angle (>10°) boundaries.|alt=A. EBSD map of ferrous martensite with high-angle (>10°) boundaries hilighted. Colour scheme follows the typic IPF for BCC crystal plotted in Z-direction]]

The indexing results are used to generate a map of the crystallographic orientation at each point on the surface being studied. Thus, scanning the electron beam in a prescribed fashion (typically in a square or hexagonal grid, correcting for the image foreshortening due to the sample tilt) results in many rich microstructural maps.<ref>{{Cite journal |last1=Dingley |first1=D. J. |last2=Randle |first2=V. |date=1992 |title=Microtexture determination by electron back-scatter diffraction |journal=Journal of Materials Science |volume=27 |issue=17 |pages=4545–4566 |doi=10.1007/BF01165988 |bibcode=1992JMatS..27.4545D |s2cid=137281137 }}</ref><ref>{{Cite journal |last=Adams |first=Brent L. |date=1997 |title=Orientation imaging microscopy: Emerging and future applications|journal=Ultramicroscopy |series=Frontiers in Electron Microscopy in Materials Science |volume=67 |issue=1 |pages=11–17 |doi=10.1016/S0304-3991(96)00103-9 }}</ref> These maps can spatially describe the crystal orientation of the material being interrogated and can be used to examine microtexture and sample morphology. Some maps describe grain orientation, boundary, and diffraction pattern (image) quality. Various statistical tools can measure the average [[misorientation]], grain size, and crystallographic texture. From this dataset, numerous maps, charts and plots can be generated.<ref>{{Cite journal |last1=Hielscher |first1=Ralf |last2=Bartel |first2=Felix |last3=Britton |first3=Thomas Benjamin |date= 2019 |title=Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross-correlation on the sphere |journal=Ultramicroscopy |volume=207 |pages=112836 |doi=10.1016/j.ultramic.2019.112836 |pmid=31539865 |arxiv=1810.03211 |s2cid=202711517}}</ref><ref>{{Cite journal |last1=Hielscher |first1=R. |last2=Silbermann |first2=C. B. |last3=Schmidl |first3=E. |last4=Ihlemann |first4=Joern |date=2019 |title=Denoising of crystal orientation maps |journal=Journal of Applied Crystallography |volume=52 |issue=5 |pages=984–996 |doi=10.1107/s1600576719009075 |s2cid=202068671 }}</ref><ref name=":3" /> The orientation data can be visualised using a variety of techniques, including colour-coding, contour lines, and pole figures.<ref name=":23">{{cite book |last1=Randle |first1=Valerie |title=Introduction to texture analysis: macrotexture, microtexture and orientation mapping |last2=Engler |first2=Olaf |date=2000 |publisher=[[CRC Press]] |isbn=978-9056992248 |edition=Digital printing 2003 |___location=Boca Raton}}</ref>

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<math>R=\begin{pmatrix} \cos \omega_{12} & \sin \omega_{12} & 0 \\ -\sin \omega_{12} & \cos \omega_{12} & 0\\ 0 & 0& 1 \end{pmatrix} \begin{pmatrix} 1&0&0\\0&\cos \omega_{23} & \sin \omega_{23} \\ 0&-\sin \omega_{23} & \cos \omega_{23} \end{pmatrix} \begin{pmatrix} \cos \omega_{31} &0& -\sin \omega_{31} \\ 0 & 1& 0 \\ \sin \omega_{31}&0 & \cos \omega_{31} \end{pmatrix}</math>

{{Wide image|Indent Si.tif|800|(a) Secondary electron (SE) image for the indentation on the (001) mono crystal. (b) HR-EBSD stress and rotation components, and geometrical necessary dislocations density (<math>\rho_{GND}</math>). The ___location of EBSP₀ is highlighted with a star in <math>\sigma_{yz}</math>.<ref name=":33">{{Cite arXiv |last1=Koko |first1=Abdalrhaman |last2=Marrow |first2=James |last3=Elmukashfi |first3=Elsiddig |date=2022-06-12 |title=A Computational Method for the Determination of the Elastic Displacement Field using Measured Elastic Deformation Field |class=cond-mat.mtrl-sci |eprint=2107.10330}}{{Creative Commons text attribution notice|cc=by4|from this source=yes}}</ref>||center|alt=(a) Secondary electron (SE) image for the indentation on the (001) mono crystal at the centre of the image. (b) shows HR-EBSD calculated stress and rotation components, and geometrical necessary dislocations density. The ___location of EBSP0 is highlighted with a star in in-plane [[shear stress]]}}

However, further lattice rotation, typically caused by severe plastic deformations, produced errors in the elastic strain calculations. To address this problem, Ruggles ''et al.''<ref>{{Cite journal |last1=Ruggles |first1=T. J. |last2=Bomarito |first2=G. F. |last3=Qiu |first3=R. L. |last4=Hochhalter |first4=J. D. |date=2018-12-01 |title=New levels of high angular resolution EBSD performance via inverse compositional Gauss–Newton based digital image correlation |journal=Ultramicroscopy |volume=195 |pages=85–92 |doi=10.1016/j.ultramic.2018.08.020 |pmc=7780544 |pmid=30216795}}</ref> improved the HR-EBSD precision, even at 12° of lattice rotation, using the inverse compositional Gauss–Newton-based (ICGN) method instead of cross-correlation. For simulated patterns, Vermeij and Hoefnagels<ref>{{Cite journal |last1=Vermeij |first1=T. |last2=Hoefnagels |first2=J. P. M. |date=2018 |title=A consistent full-field integrated DIC framework for HR-EBSD |journal=Ultramicroscopy |volume=191 |pages=44–50 |doi=10.1016/j.ultramic.2018.05.001 |pmid=29772417 |s2cid=21685690 |url=https://pure.tue.nl/ws/files/101858753/Manuscript_HR_EBSD_Vermeij_Hoefnagels.pdf |access-date=20 March 2023 |archive-date=16 July 2021 |archive-url=https://web.archive.org/web/20210716043300/https://pure.tue.nl/ws/files/101858753/Manuscript_HR_EBSD_Vermeij_Hoefnagels.pdf |url-status=live }}</ref> also established a method that achieves a precision of ±10⁻⁵ in the displacement gradient components using a full-field integrated [[Digital image correlation and tracking|digital image correlation]] (IDIC) framework instead of dividing the EBSPs into small ROIs. Patterns in IDIC are distortion-corrected to negate the need for re-mapping up to ~14°.<ref>{{Cite journal |last1=Ernould |first1=Clément |last2=Beausir |first2=Benoît |last3=Fundenberger |first3=Jean-Jacques |last4=Taupin |first4=Vincent |last5=Bouzy |first5=Emmanuel |date=2021 |title=Integrated correction of optical distortions for global HR-EBSD techniques |journal=Ultramicroscopy |volume=221 |pages=113158 |doi=10.1016/j.ultramic.2020.113158 |pmid=33338818 |s2cid=228997006 |doi-access=free }}</ref><ref>{{Cite journal |last1=Shi |first1=Qiwei |last2=Loisnard |first2=Dominique |last3=Dan |first3=Chengyi |last4=Zhang |first4=Fengguo |last5=Zhong |first5=Hongru |last6=Li |first6=Han |last7=Li |first7=Yuda |last8=Chen |first8=Zhe |last9=Wang |first9=Haowei |last10=Roux |first10=Stéphane |date=2021 |title=Calibration of crystal orientation and pattern center of EBSD using integrated digital image correlation |journal=Materials Characterization |volume=178 |pages=111206 |doi=10.1016/j.matchar.2021.111206 |s2cid=236241507 |url=https://hal.archives-ouvertes.fr/hal-03652308/file/calibrationMC_final.pdf |access-date=20 March 2023 |archive-date=25 March 2023 |archive-url=https://web.archive.org/web/20230325200435/https://hal.science/hal-03652308/file/calibrationMC_final.pdf |url-status=live }}</ref>

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