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{{Use dmy dates|date=March 2023}}
{{Use British English|date=March 2023}}
[[File:EBSD (001) Si.png|thumb|An electron backscatter diffraction pattern of [[monocrystalline silicon]], taken at 20 kV with a [[Field electron emission|field-emission]] electron source|alt=An electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source. The Kikuchi bands intersect at the centre of the image |300x300px]]
'''Electron backscatter diffraction''' ('''EBSD''') is a [[scanning electron microscopy]] (SEM) technique used to study the [[Crystallography|crystallographic]] structure of materials. EBSD is carried out in a scanning electron microscope equipped with an EBSD detector comprising at least a [[Phosphorescence|phosphorescent]] screen, a compact lens and a low-light [[Charge-coupled device|camera]]. In the microscope an incident beam of electrons hits a tilted sample. As backscattered electrons leave the sample, they interact with the atoms and are both elastically [[Electron diffraction|diffracted]] and lose energy, leaving the sample at various scattering angles before reaching the phosphor screen forming [[Kikuchi lines (physics)|Kikuchi patterns]] (EBSPs). The EBSD spatial resolution depends on many factors, including the nature of the material under study and the sample preparation. They can be indexed to provide information about the material's grain [[Crystal structure|structure]], grain [[Electron crystallography|orientation]], and [[Phase (matter)|phase]] at the micro-scale. EBSD is used for impurities and [[Crystallographic defect|defect studies]], [[Plasticity (physics)|plastic deformation]], and statistical analysis for average [[misorientation]], [[Grain boundary|grain]] size, and crystallographic texture. EBSD can also be combined with [[energy-dispersive X-ray spectroscopy]] (EDS), [[cathodoluminescence]] (CL), and [[wavelength dispersive X-ray spectroscopy|wavelength-dispersive X-ray spectroscopy]] (WDS) for advanced [[Phase-change material|phase identification]] and materials discovery.
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The EBSD detector is located within the specimen chamber of the SEM at an angle of approximately 90° to the pole piece. The EBSD detector is typically a phosphor screen that is excited by the backscattered electrons.<ref name=":45" /> The screen is coupled to lens which focuses the image from the phosphor screen onto a [[charge-coupled device]] (CCD) or c[[CMOS|omplementary metal–oxide–semiconductor]] (CMOS) camera.<ref>{{Cite journal |last1=Goulden |first1=J. |last2=Trimby |first2=P. |last3=Bewick |first3=A. |date=2018-08-01 |title=The Benefits and Applications of a CMOS-based EBSD Detector |journal=Microscopy and Microanalysis |volume=24 |issue=S1 |pages=1128–1129 |doi=10.1017/s1431927618006128 |bibcode=2018MiMic..24S1128G |s2cid=139967518 |doi-access=free }}</ref>
In this configuration, as the backscattered electrons leave the sample, they interact with the [[Electric potential|Coulomb potential]] and also lose energy due to [[inelastic scattering]] leading to a range of scattering angles (θ<sub>hkl</sub>).<ref name=":45">{{Citation |last=Randle |first=Valerie |title=Theoretical Framework for Electron Backscatter Diffraction |date=2000 |work=Electron Backscatter Diffraction in Materials Science |pages=19–30 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |publisher=Springer US |doi=10.1007/978-1-4757-3205-4_2 |isbn=978-1-4757-3205-4 |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. }}</ref><ref name=":19">{{Citation |last1=Eades |first1=Alwyn |title=Energy Filtering in EBSD |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=53–63 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |doi=10.1007/978-0-387-88136-2_4 |isbn=978-0-387-88136-2 |last2=Deal |first2=Andrew |last3=Bhattacharyya |first3=Abhishek |last4=Hooghan |first4=Tejpal |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P. }}</ref> The backscattered electrons form [[Kikuchi lines (physics)|Kikuchi lines]] – having different intensities – on an electron-sensitive flat film/screen (commonly phosphor), gathered to form a Kikuchi band. These Kikuchi lines are the trace of a hyperbola formed by the intersection of [[Walther Kossel|Kossel]] cones with the plane of the phosphor screen. The width of a Kikuchi band is related to the scattering angles and, thus, to the distance d<sub>hkl</sub> between lattice planes with Miller indexes h, k, and l.<ref name=":20">{{Cite journal |last1=Wilkinson |first1=Angus J. |last2=Britton |first2=T. Ben. |date=2012 |title=Strains, planes, and EBSD in materials science |journal=Materials Today |volume=15 |issue=9 |pages=366–376 |doi=10.1016/S1369-7021(12)70163-3 |doi-access=free }}</ref><ref>{{Cite journal |last1=Sawatzki |first1=Simon |last2=Woodcock |first2=Thomas G. |last3=Güth |first3=Konrad |last4=Müller |first4=Karl-Hartmut |last5=Gutfleisch |first5=Oliver |date=2015 |title=Calculation of remanence and degree of texture from EBSD orientation histograms and XRD rocking curves in Nd–Fe–B sintered magnets |journal=Journal of Magnetism and Magnetic Materials |volume=382 |pages=219–224 |doi=10.1016/j.jmmm.2015.01.046 |bibcode=2015JMMM..382..219S }}</ref> These Kikuchi lines and patterns were named after [[Seishi Kikuchi]], who, together with
The systematically arranged Kikuchi bands, which have a range of intensity along their width, intersect around the centre of the regions of interest (ROI), describing the probed volume crystallography.<ref>{{Cite journal |date=1954|title=High-angle Kikuchi patterns |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |volume=221 |issue=1145 |pages=224–242 |doi=10.1098/rspa.1954.0017 |bibcode=1954RSPSA.221..224A |last1=Alam |first1=M. N. |last2=Blackman |first2=M. |last3=Pashley |first3=D. W. |s2cid=97131764 }}</ref> These bands and their intersections form what is known as Kikuchi patterns or electron backscatter patterns (EBSPs). To improve contrast, the
{{wide image|Single crystal 4H SiC EBSP.png|550px|Single-crystal [[Polymorphs of silicon carbide|4H-SiC]], [[Gnomonic projection|gnomically]] projected EBSP collected using (left) conventional, (centre) dynamic, and (right) combined background correction|alt=Single-crystal Polymorphs of 4H-SiC EBSP patterns presented from collected raw image on the left, EBSP background, and the pattern after background removal}}
=== EBSD detectors ===
EBSD is conducted using an SEM equipped with an EBSD detector containing at least a phosphor screen, compact lens and low-light [[
The biggest advantage of the high-resolution detectors is their higher sensitivity, and therefore the information within each diffraction pattern can be analysed in more detail. For texture and orientation measurements, the diffraction patterns are [[Pixel binning|binned]] to reduce their size and computational times. Modern CCD-based EBSD systems can index patterns at a speed of up to 1800 patterns/second. This enables rapid and rich microstructural maps to be generated.<ref name=":20" /><ref name=":15">{{Cite journal |last1=Britton |first1=T. B. |last2=Jiang |first2=J. |last3=Guo |first3=Y. |last4=Vilalta-Clemente |first4=A. |last5=Wallis |first5=D. |last6=Hansen |first6=L. N. |last7=Winkelmann |first7=A. |last8=Wilkinson |first8=A. J. |date=2016 |title=Tutorial: Crystal orientations and EBSD — Or which way is up? |journal=Materials Characterization |volume=117 |pages=113–126 |doi=10.1016/j.matchar.2016.04.008 |s2cid=138070296|doi-access=free |hdl=10044/1/31250 |hdl-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
Inside the SEM, the size of the measurement area determines local resolution and measurement time.<ref>{{Cite book |last=Williams |first=B. David |title=Transmission electron microscopy: a textbook for materials science. |date=2009 |publisher=Plenum Press |isbn=978-0-387-76501-3 |pages=11 |oclc=633626308}}</ref> Usual settings for high-quality EBSPs are 15 nA current, 20 kV beam energy, 18 mm working distance, long exposure time, and minimal CCD pixel binning.<ref>{{Cite journal |last1=Britton |first1=T.B. |last2=Jiang |first2=J. |last3=Clough |first3=R. |last4=Tarleton |first4=E. |last5=Kirkland |first5=A.I. |last6=Wilkinson |first6=A.J. |date=2013 |title=Assessing the precision of strain measurements using electron backscatter diffraction – Part 2: Experimental demonstration |journal=Ultramicroscopy |volume=135 |pages=136–141 |doi=10.1016/j.ultramic.2013.08.006 |pmid=24034981 }}</ref><ref>{{Cite journal |last1=Jiang |first1=J. |last2=Britton |first2=T.B. |last3=Wilkinson |first3=A.J. |date=2013 |title=Evolution of dislocation density distributions in copper during tensile deformation |journal=Acta Materialia |volume=61 |issue=19 |pages=7227–7239 |doi=10.1016/j.actamat.2013.08.027 |bibcode=2013AcMat..61.7227J|doi-access=free }}</ref><ref>{{Cite journal |last1=Abdolvand |first1=Hamidreza |last2=Wilkinson |first2=Angus J. |date=2016|title=On the effects of reorientation and shear transfer during twin formation: Comparison between high-resolution electron backscatter diffraction experiments and a crystal plasticity finite element model |journal=International Journal of Plasticity |volume=84 |pages=160–182 |doi=10.1016/j.ijplas.2016.05.006 |s2cid=139049848|doi-access=free }}</ref><ref name=":29">{{Cite journal |last1=Koko |first1=Abdalrhaman |last2=Becker |first2=Thorsten H. |last3=Elmukashfi |first3=Elsiddig |last4=Pugno |first4=Nicola M. |last5=Wilkinson |first5=Angus J. |last6=Marrow |first6=T. James |date=2023 |title=HR-EBSD analysis of in situ stable crack growth at the micron scale |journal=Journal of the Mechanics and Physics of Solids |volume=172 |pages=105173 |arxiv=2206.10243 |bibcode=2023JMPSo.17205173K |doi=10.1016/j.jmps.2022.105173 |s2cid=249889649 }}</ref> The EBSD phosphor screen is set at an 18 mm working distance and a map's step size of less than 0.5
Decomposition of gaseous hydrocarbons and also hydrocarbons on the surface of samples by the electron beam inside the microscope results in carbon deposition,<ref>{{Cite journal |last1=Griffiths |first1=A J V |last2=Walther |first2=T |date=2010 |title=Quantification of carbon contamination under electron beam irradiation in a scanning transmission electron microscope and its suppression by plasma cleaning |journal=Journal of Physics: Conference Series |volume=241 |issue=1 |pages=012017 |bibcode=2010JPhCS.241a2017G |doi=10.1088/1742-6596/241/1/012017 |s2cid=250689401|doi-access=free }}</ref> which degrades the quality of EBSPs inside the probed area compared to the EBSPs outside the acquisition window. The gradient of pattern degradation increases moving inside the probed zone with an apparent accumulation of deposited carbon. The black spots from the beam instant-induced carbon deposition also highlight the immediate deposition even if agglomeration did not happen.<ref name=":4">{{Cite journal |last1=Koko |first1=Abdalrhaman |last2=Elmukashfi |first2=Elsiddig |last3=Dragnevski |first3=Kalin |last4=Wilkinson |first4=Angus J. |last5=Marrow |first5=Thomas James |date=2021 |title=J-integral analysis of the elastic strain fields of ferrite deformation twins using electron backscatter diffraction |journal=Acta Materialia |volume=218 |pages=117203 |bibcode=2021AcMat.21817203K |doi=10.1016/j.actamat.2021.117203 |url=https://ora.ox.ac.uk/objects/uuid:4071edea-3bfc-4d2b-8d32-c3b05bd73372 |access-date=20 March 2023 |archive-date=5 July 2022 |archive-url=https://web.archive.org/web/20220705095819/https://ora.ox.ac.uk/objects/uuid:4071edea-3bfc-4d2b-8d32-c3b05bd73372 |url-status=live }}</ref><ref name=":12">{{Cite journal |last1=Bachmann |first1=F. |last2=Hielscher |first2=Ralf |last3=Schaeben |first3=Helmut |date=2010 |title=Texture Analysis with MTEX – Free and Open Source Software Toolbox |journal=Solid State Phenomena |volume=160 |pages=63–68 |doi=10.4028/www.scientific.net/SSP.160.63 |s2cid=136017346}}</ref>
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{{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 Fluorescent 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
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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=== Pattern indexing ===
[[File:EBSP Indexing and formation.tif|thumb|Formation of Kossel cone which
If the setup geometry is well described, it is possible to relate the bands present in the diffraction pattern to the underlying crystal and [[Orientation (geometry)|crystallographic orientation]] of the material within the electron interaction volume. Each band can be indexed individually by the [[Miller index|Miller indices]] of the diffracting plane which formed it. In most materials, only three bands/planes intersect and are required to describe a unique solution to the crystal orientation (based on their interplanar angles). Most commercial systems use look-up tables with international crystal databases to index. This crystal orientation relates the orientation of each sampled point to a reference crystal orientation.<ref name=":18" /><ref name=":21">{{Citation |last1=El-Dasher |first1=Bassem |title=Application of Electron Backscatter Diffraction to Phase Identification |date=2009 |url=https://digital.library.unt.edu/ark:/67531/metadc1012145/ |work=Electron Backscatter Diffraction in Materials Science |pages=81–95 |editor-last=Schwartz |editor-first=Adam J. |access-date=20 March 2023 |archive-url=https://web.archive.org/web/20230325200543/https://digital.library.unt.edu/ark:/67531/metadc1012145/ |url-status=live |place=Boston, MA |publisher=Springer US |doi=10.1007/978-0-387-88136-2_6 |isbn=978-0-387-88136-2 |archive-date=25 March 2023 |last2=Deal |first2=Andrew |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P.|url-access=subscription }}</ref>
Indexing is often the first step in the EBSD process after pattern collection. This allows for the identification of the crystal orientation at the single volume of the sample from where the pattern was collected.<ref>{{Cite web |title=New technique provides detailed views of metals' crystal structure |url=https://news.mit.edu/2016/metals-crystal-structure-0706 |url-status=live |archive-url=https://web.archive.org/web/20230302142459/https://news.mit.edu/2016/metals-crystal-structure-0706 |archive-date=2023-03-02 |website=MIT News {{!}} Massachusetts Institute of Technology|date=6 July 2016 }}</ref><ref name="EBSDSpringer2009">{{cite book |url=https://archive.org/details/electronbackscat00ajsc |title=Electron backscatter diffraction in materials science |date=2009 |publisher=Springer Science+Business Media |isbn=978-0-387-88135-5 |edition=2nd |page=[https://archive.org/details/electronbackscat00ajsc/page/n21 1] |url-access=limited}}</ref> With EBSD software, pattern bands are typically detected via a mathematical routine using a modified [[Hough transform]], in which every pixel in Hough space denotes a unique line/band in the EBSP. The Hough transform enables band detection, which is difficult to locate by computer in the original EBSP. Once the band locations have been detected, it is possible to relate these locations to the underlying crystal orientation, as angles between bands represent angles between lattice planes. Thus, an orientation solution can be determined when the position/angles between three bands are known. In highly symmetric materials, more than three bands are typically used to obtain and verify the orientation measurement.<ref name="EBSDSpringer2009" />
The diffraction pattern is pre-processed to remove noise, correct for detector distortions, and normalise the intensity. Then, the pre-processed diffraction pattern is compared to a library of reference patterns for the material being studied. The reference patterns are generated based on the material's known crystal structure and the crystal lattice's orientation. The orientation of the crystal lattice that would generate the best match to the measured pattern is determined using a variety of algorithms. There are three leading methods of indexing that are performed by most commercial EBSD software: triplet voting;<ref>{{Cite journal |last1=Wright |first1=Stuart I. |last2=Zhao |first2=Jun-Wu |last3=Adams |first3=Brent L. |date=1991 |title=Automated Determination of Lattice Orientation From Electron Backscattered Kikuchi Diffraction Patterns |journal=Texture, Stress, and Microstructure |volume=13 |issue=2–3 |pages=123–131 |doi=10.1155/TSM.13.123 |doi-access=free}}</ref><ref>{{Cite journal |last1=Wright |first1=Stuart I. |last2=Adams |first2=Brent L. |last3=Kunze |first3=Karsten |date=1993|title=Application of a new automatic lattice orientation measurement technique to polycrystalline aluminum |journal=Materials Science and Engineering: A |volume=160 |issue=2 |pages=229–240 |doi=10.1016/0921-5093(93)90452-K }}</ref> minimising the 'fit' between the experimental pattern and a computationally determined orientation,<ref>{{Cite journal |last=Lassen |first=Niels Chr. Krieger |date=1992 |title=Automatic crystal orientation determination from EBSPs |journal=Micron and Microscopica Acta |volume=23 |issue=1 |pages=191–192 |doi=10.1016/0739-6260(92)90133-X }}</ref><ref>{{Cite journal |last1=Krieger Lassen |first1=N.C. |last2=Juul Jensen |first2=Dorte |last3=Condradsen |first3=K. |date=1994 |title=Automatic Recognition of Deformed and Recrystallized Regions in Partly Recrystallized Samples Using Electron Back Scattering Patterns |journal=Materials Science Forum |volume=157–162 |pages=149–158 |doi=10.4028/www.scientific.net/msf.157-162.149 |s2cid=137129038}}</ref> and or/and neighbour pattern averaging and re-indexing, NPAR<ref>{{Cite journal |last1=Wright |first1=Stuart I. |last2=Nowell |first2=Matthew M. |last3=Lindeman |first3=Scott P. |last4=Camus |first4=Patrick P. |last5=De Graef |first5=Marc |last6=Jackson |first6=Michael A. |date=2015|title=Introduction and comparison of new EBSD post-processing methodologies |journal=Ultramicroscopy |volume=159 |pages=81–94 |doi=10.1016/j.ultramic.2015.08.001 |pmid=26342553 |doi-access=free }}</ref>). Indexing then give a unique solution to the [[single crystal]] orientation that is related to the other crystal orientations within the field-of-view.<ref>{{cite journal |last1=Randle |first1=Valerie |date= 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><ref name=":14">{{Cite thesis |last=Lassen |first=Niels Christian Krieger |title=Automated Determination of Crystal Orientations from Electron Backscattering Patterns |date=1994 |degree=PhD |publisher=The Technical University of Denmark |url=http://www.ebsd.info/pdf/PhD_KriegerLassen.pdf |archive-date=2022-03-08 |archive-url=https://web.archive.org/web/20220308024650/http://www.ebsd.info/pdf/PhD_KriegerLassen.pdf |url-status=live}}</ref>
Triplet voting involves identifying multiple 'triplets' associated with different solutions to the crystal orientation; each crystal orientation determined from each triplet receives one vote. Should four bands identify the same crystal orientation, then four ([[Combination|four choose three]], i.e. <math>C(4,3)</math>) votes will be cast for that particular solution. Thus the candidate orientation with the highest number of votes will be the most likely solution to the underlying crystal orientation present. The number of votes for the solution chosen compared to the total number of votes describes the confidence in the underlying solution. Care must be taken in interpreting this 'confidence index' as some pseudo-symmetric orientations may result in low confidence for one candidate solution vs another.<ref>{{Cite journal |journal=Microscopy and Microanalysis |doi=10.1017/s143192761501096x |title=Addressing Pseudo-Symmetric Misindexing in EBSD Analysis of γ-TiAl with High Accuracy Band Detection |year=2015 |last1=Sitzman |first1=Scott |last2=Schmidt |first2=Niels-Henrik |last3=Palomares-Garcia |first3=Alberto |last4=Munoz-Moreno |first4=Rocio |last5=Goulden |first5=Jenny |volume=21 |issue=S3 |pages=2037–2038 |bibcode=2015MiMic..21S2037S |s2cid=51964340 |doi-access=free }}</ref><ref>{{Cite journal |last1=Lenthe |first1=W. |last2=Singh |first2=S. |last3=De Graef |first3=M. |date=2019 |title=Prediction of potential pseudo-symmetry issues in the indexing of electron backscatter diffraction patterns |url=https://journals.iucr.org/j/issues/2019/05/00/po5152/ |journal=Journal of Applied Crystallography |volume=52 |issue=5 |pages=1157–1168 |doi=10.1107/S1600576719011233 |bibcode=2019JApCr..52.1157L |osti=1575873 |s2cid=204108200 }}</ref><ref>{{Citation |last1=Dingley |first1=David J. |title=Phase Identification Through Symmetry Determination in EBSD Patterns |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=97–107 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |publisher=Springer US |doi=10.1007/978-0-387-88136-2_7 |isbn=978-0-387-88136-2 |last2=Wright |first2=S.I. |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P. }}</ref> Minimising the fit involves starting with all possible orientations for a triplet. More bands are included, which reduces the number of candidate orientations. As the number of bands increases, the number of possible orientations converges ultimately to one solution. The 'fit' between the measured orientation and the captured pattern can be determined.<ref name=":14" />
Overall, indexing diffraction patterns in EBSD involves a complex set of algorithms and calculations, but is essential for determining the crystallographic structure and orientation of materials at a high spatial resolution. The indexing process is continually evolving, with new algorithms and techniques being developed to improve the accuracy and speed of the process. Afterwards, a confidence index is calculated to determine the quality of the indexing result. The confidence index is based on the match quality between the measured and reference patterns. In addition, it considers factors such as noise level, detector resolution, and sample quality.<ref name="EBSDSpringer2009" />
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=== Pattern centre ===
To relate the orientation of a crystal, much like in [[X-ray diffraction]] (XRD), the geometry of the system must be known. In particular, the pattern centre describes the distance of the interaction volume to the detector and the ___location of the nearest point between the phosphor and the sample, on the phosphor screen. Early work used a single crystal of known orientation being inserted into the SEM chamber, and a particular feature of the EBSP was known to correspond to the pattern centre. Later developments involved exploiting various geometric relationships between the generation of an EBSP and the chamber geometry (shadow casting and phosphor movement).<ref name=":1">{{Cite journal |last1=Britton |first1=T. B. |last2=Tong |first2=V. S. |last3=Hickey |first3=J. |last4=Foden |first4=A. |last5=Wilkinson |first5=A. J. |date=2018 |title=AstroEBSD: exploring new space in pattern indexing with methods launched from an astronomical approach |url=https://journals.iucr.org/j/issues/2018/06/00/nb5225/ |journal=Journal of Applied Crystallography |volume=51 |issue=6 |pages=1525–1534 |doi=10.1107/S1600576718010373 |arxiv=1804.02602 |bibcode=2018JApCr..51.1525B |s2cid=51687153 }}</ref><ref name=":14" />
Unfortunately, each of these methods is cumbersome and can be prone to some systematic errors for a general operator. Typically they cannot be easily used in modern SEMs with multiple designated uses. Thus, most commercial EBSD systems use the indexing algorithm combined with an iterative movement of crystal orientation and suggested pattern centre ___location. Minimising the fit between bands located within experimental patterns and those in look-up tables tends to converge on the pattern centre ___location to an accuracy of ~0.5–1% of the pattern width.<ref name=":15" /><ref name=":0" />
The recent development of AstroEBSD<ref>{{Cite journal |last1=Britton |first1=Thomas Benjamin |last2=Tong |first2=Vivian S. |last3=Hickey |first3=Jim |last4=Foden |first4=Alex |last5=Wilkinson |first5=Angus J. |date=2018 |title=AstroEBSD : exploring new space in pattern indexing with methods launched from an astronomical approach|journal=Journal of Applied Crystallography |volume=51 |issue=6 |pages=1525–1534 |doi=10.1107/S1600576718010373 |arxiv=1804.02602 |bibcode=2018JApCr..51.1525B |s2cid=51687153 }}</ref> and PCGlobal,<ref>{{Cite journal |last1=Pang |first1=Edward L. |last2=Larsen |first2=Peter M. |last3=Schuh |first3=Christopher A. |date=2020 |title=Global optimization for accurate determination of EBSD pattern centers |journal=Ultramicroscopy |volume=209 |pages=112876 |doi=10.1016/j.ultramic.2019.112876 |pmid=31707232 |s2cid=201651309|arxiv=1908.10692 }}</ref> open-source [[MATLAB]] codes, increased the precision of determining the pattern centre (PC) and – consequently – elastic strains<ref>{{Cite journal |last1=Tanaka |first1=Tomohito |last2=Wilkinson |first2=Angus J. |date=2019-07-01 |title=Pattern matching analysis of electron backscatter diffraction patterns for pattern centre, crystal orientation and absolute elastic strain determination – accuracy and precision assessment |journal=Ultramicroscopy|volume=202 |pages=87–99 |doi=10.1016/j.ultramic.2019.04.006 |pmid=31005023 |arxiv=1904.06891 |s2cid=119294636 }}</ref> by using a [[pattern matching]] approach<ref>{{Cite journal |last1=Foden |first1=A. |last2=Collins |first2=D.M. |last3=Wilkinson |first3=A.J. |last4=Britton |first4=T.B. |date=2019 |title=Indexing electron backscatter diffraction patterns with a refined template matching approach |journal=Ultramicroscopy |volume=207 |pages=112845 |doi=10.1016/j.ultramic.2019.112845 |pmid=31586829 |arxiv=1807.11313 |s2cid=203307560 }}</ref> which simulates the pattern using EMSoft.<ref>{{Cite journal |last1=Jackson |first1=M. A. |last2=Pascal |first2=E. |last3=De Graef |first3=M. |date=2019 |title=Dictionary Indexing of Electron Back-Scatter Diffraction Patterns: a Hands-On Tutorial |journal=Integrating Materials and Manufacturing Innovation |volume=8 |issue=2 |pages=226–246 |doi=10.1007/s40192-019-00137-4 |s2cid=182073071}}</ref>
=== 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 |bibcode=2019JApCr..52..984H |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>
Microscope misalignment, image shift, scan distortion that increases with decreasing magnification, roughness and contamination of the specimen surface, boundary indexing failure and detector quality can lead to uncertainties in determining the crystal orientation.<ref name=":2">{{Cite journal |last=Prior |date= 1999 |title=Problems in determining the misorientation axes, for small angular misorientations, using electron backscatter diffraction in the SEM |journal=Journal of Microscopy |volume=195 |issue=3 |pages=217–225 |doi=10.1046/j.1365-2818.1999.00572.x |pmid=10460687 |s2cid=10144078}}</ref> The EBSD [[signal-to-noise ratio]] depends on the material and decreases at excessive acquisition speed and beam current, thereby affecting the angular resolution of the measurement.<ref name=":2" />
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=== Earlier trials ===
The change and degradation in electron backscatter patterns (EBSPs) provide information about the diffracting volume. Pattern degradation (i.e., diffuse quality) can be used to assess the level of plasticity through the pattern/image quality (IQ),<ref>{{Cite journal |last1=Lassen |first1=N. C. Krieger |last2=Jensen |first2=Dorte Juul |last3=Condradsen |first3=K. |date=1994 |title=Automatic Recognition of Deformed and Recrystallized Regions in Partly Recrystallized Samples Using Electron Back Scattering Patterns |url=https://www.scientific.net/MSF.157-162.149 |journal=Materials Science Forum |volume=157–162 |pages=149–158 |doi=10.4028/www.scientific.net/MSF.157-162.149 |s2cid=137129038 |access-date=2 March 2023 |archive-date=2 March 2023 |archive-url=https://web.archive.org/web/20230302135533/https://www.scientific.net/MSF.157-162.149 |url-status=live |url-access=subscription }}</ref> where IQ is calculated from the sum of the peaks detected when using the conventional Hough transform. [[Angus Wilkinson|Wilkinson]]<ref>{{Cite journal |last=Wilkinson |first=A. J. |date=1997-01-01 |title=Methods for determining elastic strains from electron backscatter diffraction and electron channelling patterns |journal=Materials Science and Technology |volume=13 |issue=1 |pages=79–84 |doi=10.1179/mst.1997.13.1.79 |bibcode=1997MatST..13...79W}}</ref> first used the changes in high-order Kikuchi line positions to determine the elastic strains, albeit with low [[Accuracy and precision|precision]]{{NoteTag|Throughout this page, the terms ‘error’, and ‘precision’ are used as defined in the [[International Bureau of Weights and Measures]] (BIPM) [https://www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf/cb0ef43f-baa5-11cf-3f85-4dcd86f77bd6 guide to measurement uncertainty]. In practice, ‘error’, ‘accuracy’ and ‘uncertainty’, as well as ‘true value’ and ‘best guess’, are synonymous. Precision is the variance (or standard deviation) between all estimated quantities. Bias is the difference between the average of measured values and an independently measured ‘best guess’. Accuracy is then the combination of bias and precision.<ref name=":10" />}} (0.3% to 1%); however, this approach cannot be used for characterising residual elastic strain in metals as the elastic strain at the yield point is usually around 0.2%. Measuring strain by tracking the change in the higher-order Kikuchi lines is practical when the strain is small, as the band position is sensitive to changes in lattice parameters.<ref name=":24">{{Cite journal |last1=Zhu |first1=Chaoyi |last2=De Graef |first2=Marc |date=2020 |title=EBSD pattern simulations for an interaction volume containing lattice defects |journal=Ultramicroscopy |volume=218 |pages=113088 |doi=10.1016/j.ultramic.2020.113088 |pmid=32784084 |s2cid=221123906 |doi-access=free }}</ref> In the early 1990s, Troost ''et al.''<ref>{{Cite journal |last1=Troost |first1=K. Z. |last2=van der Sluis |first2=P. |last3=Gravesteijn |first3=D. J. |date=1993 |title=Microscale
=== High-resolution electron backscatter diffraction (HR-EBSD)===
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Where <math>C</math> is the crystal anisotropic stiffness tensor. These two equations are solved to re-calculate the refined elastic deviatoric strain (<math>\varepsilon_{kl}</math>), including the missing ninth (spherical) strain tensor. An alternative approach that considers the full <math>\beta</math> can be found in.<ref name=":17" />
<math>e_{ij}=\begin{pmatrix} {e_{11}} \\{e_{22}} \\{e_{33}}\\{
<math>\varepsilon_{33}={k_1C_{1133}+k_2C{2233}+k_3\over C_{1133}+C_{2233}+C_{3333}},\qquad \therefore\varepsilon_{kl}=\begin{pmatrix} {k_1+\varepsilon_{33}} \\{k_2+\varepsilon_{33}} \\{\varepsilon_{33}}\\{2e_{12}}\\{2e_{13}}\\{2e_{23}} \\\end{pmatrix}</math>
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=== Precision and development ===
The HR-EBSD method can achieve a precision of ±10<sup>−4</sup> in components of the displacement gradient tensors (i.e., variations in lattice strain and lattice rotation in radians) by measuring the shifts of zone axes within the pattern image with a resolution of ±0.05 pixels.<ref name=":6" /><ref name=":7">{{Cite journal |last1=Plancher |first1=E. |last2=Petit |first2=J. |last3=Maurice |first3=C. |last4=Favier |first4=V. |last5=Saintoyant |first5=L. |last6=Loisnard |first6=D. |last7=Rupin |first7=N. |last8=Marijon |first8=J.-B. |last9=Ulrich |first9=O. |last10=Bornert |first10=M. |last11=Micha |first11=J.-S. |last12=Robach |first12=O. |last13=Castelnau |first13=O. |date=2016-03-01 |title=On the Accuracy of Elastic Strain Field Measurements by Laue Microdiffraction and High-Resolution EBSD: a Cross-Validation Experiment |journal=Experimental Mechanics |volume=56 |issue=3 |pages=483–492 |doi=10.1007/s11340-015-0114-1 |s2cid=255157494 |url=https://hal.archives-ouvertes.fr/hal-02141119/file/PIMM%20-%20EM%20-%20PLANCHER%20-%202016.pdf |access-date=20 March 2023 |archive-date=13 March 2020 |archive-url=https://web.archive.org/web/20200313042805/https://hal.archives-ouvertes.fr/hal-02141119/file/PIMM%20-%20EM%20-%20PLANCHER%20-%202016.pdf |url-status=live }}</ref> It was limited to small strains and rotations (>1.5°) until [[Ben Britton|Britton]] and Wilkinson<ref name=":5" /> and Maurice et al.<ref>{{Cite journal |last1=Maurice |first1=Claire |last2=Driver |first2=Julian H. |last3=Fortunier |first3=Roland |date=2012 |title=On solving the orientation gradient dependency of high angular resolution EBSD |journal=Ultramicroscopy |volume=113 |pages=171–181 |doi=10.1016/j.ultramic.2011.10.013}}</ref> raised the rotation limit to ~11° by using a re-mapping technique that recalculated the strain after transforming the patterns with a [[rotation matrix]] (<math>R</math>) calculated from the first cross-correlation iteration.<ref name=":10" />
<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 EBSP<sub>0</sub> is highlighted with a star in <math>\sigma_{yz}</math>. The step size is 250 nm<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<sup>−5</sup> 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>
{| class="wikitable plainrowheaders"
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|0.006° (1×10<sup>−4</sup> rad)
|-
!GND @ 1
In lines/m<sup>2</sup> (b = 0.3 nm)
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=== The reference pattern problem ===
In HR-EBSD analysis, the lattice distortion field is calculated relative to a reference pattern or point (EBSP<sub>0</sub>) per grain in the map, and is dependent on the lattice distortion at the point. The lattice distortion field in each grain is measured with respect to this point; therefore, the absolute lattice distortion at the reference point (relative to the unstrained crystal) is excluded from the HR-EBSD elastic strain and rotation maps.<ref name=":8">{{Cite journal |last1=Maurice |first1=Claire |last2=Fortunier |first2=Roland |last3=Driver |first3=Julian |last4=Day |first4=Austin |last5=Mingard |first5=Ken |last6=Meaden |first6=Graham |date=2010 |title=Comments on the paper "Bragg's law diffraction simulations for electron backscatter diffraction analysis" by Josh Kacher, Colin Landon, Brent L. Adams & David Fullwood |journal=Ultramicroscopy |volume=110 |issue=7 |pages=758–759 |doi=10.1016/j.ultramic.2010.02.003 |pmid=20223590 }}</ref><ref name=":9">{{Cite journal |last1=Mikami |first1=Yoshiki |last2=Oda |first2=Kazuo |last3=Kamaya |first3=Masayuki |last4=Mochizuki |first4=Masahito |date=2015 |title=Effect of reference point selection on microscopic stress measurement using EBSD |journal=Materials Science and Engineering: A |volume=647 |pages=256–264 |doi=10.1016/j.msea.2015.09.004}}</ref> This
The local lattice distortion at the EBSP<sub>0</sub> influences the resultant HR-EBSD map, e.g., a reference pattern deformed in tension will directly reduce the HR-EBSD map tensile strain magnitude while indirectly influencing the other component magnitude and the strain's spatial distribution. Furthermore, the choice of EBSP<sub>0</sub> slightly affects the GND density distribution and magnitude, and choosing a reference pattern with a higher GND density reduces the cross-correlation quality, changes the spatial distribution and induces more errors than choosing a reference pattern with high lattice distortion. Additionally, there is no apparent connection between EBSP<sub>0</sub>
The use of simulated reference patterns for absolute strain measurement is still an active area of research<ref name=":22">{{Cite journal |last1=Winkelmann |first1=Aimo |last2=Trager-Cowan |first2=Carol |last3=Sweeney |first3=Francis |last4=Day |first4=Austin P. |last5=Parbrook |first5=Peter |date=2007 |title=Many-beam dynamical simulation of electron backscatter diffraction patterns |journal=Ultramicroscopy |volume=107 |issue=4 |pages=414–421 |doi=10.1016/j.ultramic.2006.10.006 |pmid=17126489}}</ref><ref>{{Cite journal |last1=Kacher |first1=Josh |last2=Landon |first2=Colin |last3=Adams |first3=Brent L. |last4=Fullwood |first4=David |date=2009-08-01 |title=Bragg's Law diffraction simulations for electron backscatter diffraction analysis |journal=Ultramicroscopy |volume=109 |issue=9 |pages=1148–1156 |doi=10.1016/j.ultramic.2009.04.007 |pmid=19520512}}</ref><ref>{{Cite journal |last1=Winkelmann |first1=A |last2=Nolze |first2=G |last3=Vos |first3=M |last4=Salvat-Pujol |first4=F |last5=Werner |first5=W S M |date=2016 |title=Physics-based simulation models for EBSD: advances and challenges |journal=IOP Conference Series: Materials Science and Engineering |volume=109 |issue=1 |pages=012018 |doi=10.1088/1757-899x/109/1/012018 |arxiv=1505.07982 |bibcode=2016MS&E..109a2018W |s2cid=38586851}}</ref><ref>{{Cite journal |last1=Alkorta |first1=Jon |last2=Marteleur |first2=Matthieu |last3=Jacques |first3=Pascal J. |date=2017 |title=Improved simulation based HR-EBSD procedure using image gradient based DIC techniques |journal=Ultramicroscopy |volume=182 |pages=17–27 |doi=10.1016/j.ultramic.2017.06.015 |pmid=28644960 |hdl=2078.1/186551 |hdl-access=free }}</ref><ref>{{Cite journal |last1=Winkelmann |first1=Aimo |last2=Nolze |first2=Gert |last3=Cios |first3=Grzegorz |last4=Tokarski |first4=Tomasz |last5=Bała |first5=Piotr |last6=Hourahine |first6=Ben |last7=
In addition, GND density estimation is nominally insensitive to (or negligibly dependent upon<ref>{{Cite journal |last1=Jiang |first1=J. |last2=Britton |first2=T. B. |last3=Wilkinson |first3=A. J. |date=2013-11-01 |title=Evolution of dislocation density distributions in copper during tensile deformation |journal=Acta Materialia |volume=61 |issue=19 |pages=7227–7239 |doi=10.1016/j.actamat.2013.08.027 |bibcode=2013AcMat..61.7227J |doi-access=free }}</ref><ref>{{Cite journal |last1=Britton |first1=T B |last2=Hickey |first2=J L R |date= 2018 |title=Understanding deformation with high angular resolution electron backscatter diffraction (HR-EBSD) |journal=IOP Conference Series: Materials Science and Engineering |volume=304 |issue=1 |pages=012003 |doi=10.1088/1757-899x/304/1/012003 |bibcode=2018MS&E..304a2003B |s2cid=54529072 |arxiv=1710.00728 }}</ref>) EBSP<sub>0</sub> choice, as only neighbour point-to-point differences in the lattice rotation maps are used for GND density calculation.<ref>{{Cite journal |last1=Kalácska |first1=Szilvia |last2=Dankházi |first2=Zoltán |last3=Zilahi |first3=Gyula |last4=Maeder |first4=Xavier |last5=Michler |first5=Johann |last6=Ispánovity |first6=Péter Dusán |last7=Groma |first7=István |date=2020 |title=Investigation of geometrically necessary dislocation structures in compressed Cu micropillars by 3-dimensional HR-EBSD |journal=Materials Science and Engineering: A |volume=770 |pages=138499 |doi=10.1016/j.msea.2019.138499 |s2cid=189928469 |url=https://bib-pubdb1.desy.de/record/426593 |access-date=20 March 2023 |archive-date=17 July 2020 |archive-url=https://web.archive.org/web/20200717095713/http://bib-pubdb1.desy.de/record/426593 |url-status=live |arxiv=1906.06980 }}</ref><ref>{{Cite journal |last1=Wallis |first1=David |last2=Hansen |first2=Lars N. |last3=Britton |first3=T. Ben |last4=Wilkinson |first4=Angus J. |date= 2017 |title=Dislocation Interactions in Olivine Revealed by HR-EBSD: Dislocation Interactions in Olivine |journal=Journal of Geophysical Research: Solid Earth |volume=122 |issue=10 |pages=7659–7678 |doi=10.1002/2017JB014513|hdl=10044/1/50615 |s2cid=134570945 |url=https://ora.ox.ac.uk/objects/uuid:54d4800c-a2c5-4434-be22-776d11aa2156 |hdl-access=free }}</ref> However, this assumes that the absolute lattice distortion of EBSP<sub>0</sub> only changes the relative lattice rotation map components by a constant value which vanishes during derivative operations, i.e., lattice distortion distribution is insensitive to EBSP<sub>0</sub> choice.<ref name=":9" /><ref name=":10">{{Cite journal |last1=Koko |first1=Abdalrhaman |last2=Tong |first2=Vivian |last3=Wilkinson |first3=Angus J. |author-link3=Angus Wilkinson |last4=Marrow |first4=T. James |author-link4=James Marrow |date=2023 |title=An iterative method for reference pattern selection in high-resolution electron backscatter diffraction (HR-EBSD) |journal=Ultramicroscopy |volume=248 |pages=113705 |arxiv=2206.10242 |doi=10.1016/j.ultramic.2023.113705 |pmid=36871367 |s2cid=249889699}}{{Creative Commons text attribution notice|cc=by4|from this source=yes}}</ref>
=== Selecting a reference pattern ===
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== Applications ==
EBSD is used in a wide range of applications, including materials science and engineering,<ref name=":20" /> geology,<ref>{{Citation |last1=Prior |first1=David J. |title=EBSD in the Earth Sciences: Applications, Common Practice, and Challenges |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=345–360 |place=Boston, MA |publisher=Springer US |isbn=978-0-387-88135-5 |last2=Mariani |first2=Elisabetta |last3=Wheeler |first3=John|doi=10.1007/978-0-387-88136-2_26 }}</ref> and biological research.<ref>{{Cite journal |last1=Choi |first1=Seung |last2=Han |first2=Seokyoung |last3=Lee |first3=
=== Scattered electron imaging ===
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| caption2 = Far-field image of [[475 °C embrittlement|475 °C embrittled duplex stainless steel]] with the virtual forward-scatter detector (VFSD) positioned at 38 mm from the sample
}}
EBSD detectors can have forward scattered electron [[diode]]s (FSD) at the bottom, in the middle (MSD) and at the top of the detector. Forward-scattered electron (FSE) imaging involves collecting electrons scattered at small angles from the surface of a sample, which provides information about the surface topography and composition.<ref name=":34" /><ref name=":46">{{Cite journal |last1=Schwarzer |first1=Robert A |last2=Hjelen |first2=Jarle |date=2015-01-09 |title=Backscattered Electron Imaging with an EBSD Detector
The FSE signal is typically collected simultaneously with the BSE signal in EBSD analysis. The BSE signal is sensitive to the average atomic number of the sample, and is used to generate an image of the surface topography and composition. The FSE signal is superimposed on the BSE image to provide information about the crystallographic orientation.<ref name=":37" /><ref name=":34">{{Cite journal |last1=Wright |first1=Stuart I. |last2=Nowell |first2=Matthew M. |last3=de Kloe |first3=René |last4=Camus |first4=Patrick |last5=Rampton |first5=Travis |date=2015 |title=Electron imaging with an EBSD detector |journal=Ultramicroscopy |volume=148 |pages=132–145 |doi=10.1016/j.ultramic.2014.10.002 |pmid=25461590|doi-access=free }}</ref>
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=== Integrated EBSD/EDS mapping ===
When simultaneous EDS/EBSD collection can be achieved, the capabilities of both techniques can be enhanced.<ref>{{Cite news |date=2015 |title=Discriminating Phases with Similar Crystal Structures Using Electron Backscatter Diffraction (EBSD) and Energy Dispersive X-Ray Spectrometry (EDS) |url=https://www.azonano.com/article.aspx?ArticleID=3955 |url-status=live |archive-url=https://web.archive.org/web/20230302142457/https://www.azonano.com/article.aspx?ArticleID=3955 |archive-date=2023-03-02 |website=AZoNano.com }}</ref> There are applications where sample chemistry or phase cannot be differentiated via EDS alone because of similar composition, and structure cannot be solved with EBSD alone because of ambiguous structure solutions.<ref>{{Cite journal |last1=Nolze |first1=G. |last2=Geist |first2=V. |last3=Neumann |first3=R. Saliwan |last4=Buchheim |first4=M. |date=2005|title=Investigation of orientation relationships by EBSD and EDS on the example of the Watson iron meteorite |journal=Crystal Research and Technology |volume=40 |issue=8 |pages=791–804 |doi=10.1002/crat.200410434|s2cid=96785527|doi-access=free |bibcode=2005CryRT..40..791N }}</ref><ref>{{Cite web |date=2022-11-29 |title=Uncovering the tiny defects that make materials fail |url=https://physicsworld.com/uncovering-the-tiny-defects-that-make-materials-fail/ |url-status=live |archive-url=https://web.archive.org/web/20230303225536/https://physicsworld.com/a/uncovering-the-tiny-defects-that-make-materials-fail/ |archive-date=2023-03-03 |website=Physics World}}</ref> To accomplish integrated mapping, the analysis area is scanned, and at each point, Hough peaks and EDS region-of-interest counts are stored. Positions of phases are determined in [[X-ray crystallography|X-ray]] maps, and each element's measured EDS intensities are given in charts. The chemical intensity ranges are set for each phase to select the grains.<ref>{{Cite journal |last1=Kell |first1=J. |last2=Tyrer |first2=J. R. |last3=Higginson |first3=R. L. |last4=Thomson |first4=R. C. |date=2005 |title=Microstructural characterization of autogenous laser welds on 316L stainless steel using EBSD and EDS |journal=Journal of Microscopy |volume=217 |issue=2 |pages=167–173 |doi=10.1111/j.1365-2818.2005.01447.x|pmid=15683414 |s2cid=12285114}}</ref> All patterns are then re-indexed off-line. The recorded chemistry determines which phase/crystal-structure file is used to index each point. Each pattern is indexed by only one phase, and maps displaying distinguished phases are generated. The interaction volumes for EDS and EBSD are significantly different (on the order of [[micrometre]]s compared to tens of [[nanometres]]), and the shape of these volumes using a highly tilted sample may have implications on algorithms for phase discrimination.<ref name=":21" /><ref>{{Cite journal |last1=West |first1=G.D. |last2=Thomson |first2=R.C. |date=2009 |title=Combined EBSD/EDS tomography in a dual-beam FIB/FEG-SEM |journal=Journal of Microscopy |volume=233 |issue=3 |pages=442–450 |doi=10.1111/j.1365-2818.2009.03138.x |pmid=19250465 |s2cid=42955621}}</ref>
EBSD, when used together with other in-SEM techniques such as [[cathodoluminescence]] (CL),<ref>{{Cite journal |last1=Moser |first1=D. E. |last2=Cupelli |first2=C. L. |last3=Barker |first3=I. R. |last4=Flowers |first4=R. M. |last5=Bowman |first5=J. R. |last6=Wooden |first6=J. |last7=Hart |first7=J.R. |date=2011 |editor-last=Davis |editor-first=William J. |title=New zircon shock phenomena and their use for dating and reconstruction of large impact structures revealed by electron nanobeam (EBSD, CL, EDS) and isotopic U–Pb and (U–Th)/He analysis of the Vredefort domeThis article is one of a series of papers published in this Special Issue on the theme of Geochronology in honour of Tom Krogh|journal=Canadian Journal of Earth Sciences |volume=48 |issue=2 |pages=117–139 |bibcode=2011CaJES..48..117D |doi=10.1139/E11-011 }}</ref> [[wavelength dispersive X-ray spectroscopy]] (WDS)<ref>{{Cite journal |last1=Laigo |first1=J. |last2=Christien |first2=F. |last3=Le Gall |first3=R. |last4=Tancret |first4=F. |last5=Furtado |first5=J. |date=2008 |title=SEM, EDS, EPMA-WDS and EBSD characterization of carbides in HP type heat resistant alloys |journal=Materials Characterization |volume=59 |issue=11 |pages=1580–1586 |doi=10.1016/j.matchar.2008.02.001 }}</ref> and/or EDS can provide a deeper insight into the specimen's properties and enhance phase identification.<ref>{{Cite web |date=2023-01-18 |title=Microscale Analysis of Lithium-Containing Compounds and Alloys |url=https://www.azom.com/article.aspx?ArticleID=22349 |url-status=live |archive-url=https://web.archive.org/web/20230217121105/https://www.azom.com/article.aspx?ArticleID=22349 |archive-date=2023-02-17 |website=AZoM.com }}</ref><ref>{{Cite journal |last1=Wisniewski |first1=Wolfgang |last2=Švančárek |first2=Peter |last3=Prnová |first3=Anna |last4=Parchovianský |first4=Milan |last5=Galusek |first5=Dušan |date=2020|title=Y<sub>2</sub>O<sub>3</sub>–Al<sub>2</sub>O<sub>3</sub> microsphere crystallization analyzed by electron backscatter diffraction (EBSD) |journal=Scientific Reports |volume=10 |issue=1 |pages=11122 |bibcode=2020NatSR..1011122W |doi=10.1038/s41598-020-67816-7 |pmc=7338460 |pmid=32632218}}</ref> For example, the minerals [[calcite]] ([[limestone]]) and [[aragonite]] ([[
=== Integrated EBSD/DIC mapping ===
EBSD and [[digital image correlation]] (DIC) can be used together to analyse the microstructure and deformation behaviour of materials. DIC is a method that uses digital image processing techniques to measure deformation and strain fields in materials.<ref>{{Cite journal |last1=Stinville |first1=J. C. |last2=Callahan |first2=P. G. |last3=Charpagne |first3=M. A. |last4=Echlin |first4=M. P. |last5=Valle |first5=V. |last6=Pollock |first6=T. M. |date=2020 |title=Direct measurements of slip irreversibility in a nickel-based superalloy using high-resolution digital image correlation |journal=Acta Materialia |volume=186 |pages=172–189 |doi=10.1016/j.actamat.2019.12.009 |bibcode=2020AcMat.186..172S |osti=1803462 |s2cid=213631580 |doi-access=free }}</ref> By combining EBSD and DIC, researchers can obtain both crystallographic and mechanical information about a material simultaneously.<ref>{{Cite journal |last1=Charpagne |first1=Marie-Agathe |last2=Strub |first2=Florian |last3=Pollock |first3=Tresa M. |date=2019|title=Accurate reconstruction of EBSD datasets by a multimodal data approach using an evolutionary algorithm |journal=Materials Characterization |volume=150 |pages=184–198 |doi=10.1016/j.matchar.2019.01.033 |arxiv=1903.02988 |s2cid=71144677 }}</ref> This allows for a more comprehensive understanding of the relationship between microstructure and mechanical behaviour, which is particularly useful in fields such as materials science and engineering.<ref>{{Cite journal |last1=Zhao |first1=Chong |last2=Stewart |first2=David |last3=Jiang |first3=Jun |last4=Dunne |first4=Fionn P. E. |date=2018 |title=A comparative assessment of iron and cobalt-based hard-facing alloy deformation using HR-EBSD and HR-DIC |journal=Acta Materialia |volume=159 |pages=173–186 |doi=10.1016/j.actamat.2018.08.021 |bibcode=2018AcMat.159..173Z |hdl=10044/1/68967 |s2cid=139436094 |hdl-access=free }}</ref>
DIC can identify regions of strain localisation in a material, while EBSD can provide information about the microstructure in these regions. By combining these techniques, researchers can gain insights into the mechanisms responsible for the observed strain localisation.<ref>{{Cite journal |last1=Orozco-Caballero |first1=Alberto |last2=Jackson |first2=Thomas |last3=da Fonseca |first3=João Quinta |date=2021 |title=High-resolution digital image correlation study of the strain localization during loading of a shot-peened RR1000 nickel-based superalloy |journal=Acta Materialia |volume=220 |pages=117306 |doi=10.1016/j.actamat.2021.117306 |bibcode=2021AcMat.22017306O |s2cid=240539022 |url=https://pure.manchester.ac.uk/ws/files/198822339/210828_ShotP_Manuscript_w_Figures_clean.pdf |access-date=20 March 2023 |archive-date=25 March 2023 |archive-url=https://web.archive.org/web/20230325200439/https://pure.manchester.ac.uk/ws/files/198822339/210828_ShotP_Manuscript_w_Figures_clean.pdf |url-status=live }}</ref> For example, EBSD can be used to determine the grain orientations and boundary misorientations before and after deformation. In contrast, DIC can be used to measure the strain fields in the material during deformation.<ref>{{Cite journal |last1=Ye |first1=Zhenhua |last2=Li |first2=Chuanwei |last3=Zheng |first3=Mengyao |last4=Zhang |first4=Xinyu |last5=Yang |first5=Xudong |last6=Gu |first6=Jianfeng |date=2022 |title=In situ EBSD/DIC-based investigation of deformation and fracture mechanism in FCC- and L12-structured FeCoNiV high-entropy alloys |journal=International Journal of Plasticity |volume=152 |pages=103247 |doi=10.1016/j.ijplas.2022.103247 |s2cid=246553822 }}</ref><ref name=":40">{{Cite journal |last1=Hestroffer |first1=Jonathan M. |last2=Stinville |first2=Jean-Charles |last3=Charpagne |first3=Marie-Agathe |last4=Miller |first4=Matthew P. |last5=Pollock |first5=Tresa M. |last6=Beyerlein |first6=Irene J. |date=2023 |title=Slip localization behavior at triple junctions in nickel-base superalloys |journal=Acta Materialia |volume=249 |pages=118801 |doi=10.1016/j.actamat.2023.118801 |bibcode=2023AcMat.24918801H |osti=2420863 |s2cid=257216017 }}</ref> Or EBSD can be used to identify the activation of different slip systems during deformation, while DIC can be used to measure the associated strain fields.<ref>{{Cite journal |last1=Sperry |first1=Ryan |last2=Han |first2=Songyang |last3=Chen |first3=Zhe |last4=Daly |first4=Samantha H.|author4-link= Samantha Daly |last5=Crimp |first5=Martin A. |last6=Fullwood |first6=David T. |date=2021 |title=Comparison of EBSD, DIC, AFM, and ECCI for active slip system identification in deformed Ti-7Al |journal=Materials Characterization |volume=173 |pages=110941 |doi=10.1016/j.matchar.2021.110941 |s2cid=233839426 |doi-access=free }}</ref> By correlating these data, researchers can better understand the role of different deformation mechanisms in the material's mechanical behaviour.<ref>{{Cite journal |last1=Gao |first1=Wenjie |last2=Lu |first2=Junxia |last3=Zhou |first3=Jianli |last4=Liu |first4=Ling'en |last5=Wang |first5=Jin |last6=Zhang |first6=Yuefei |last7=Zhang |first7=Ze |date=2022|title=Effect of grain size on deformation and fracture of Inconel718: An in-situ SEM-EBSD-DIC investigation |journal=Materials Science and Engineering: A |volume=861 |pages=144361 |doi=10.1016/j.msea.2022.144361 |s2cid=253797056 }}</ref>
Overall, the combination of EBSD and DIC provides a powerful tool for investigating materials' microstructure and deformation behaviour. This approach can be applied to a wide range of materials and deformation conditions and has the potential to yield insights into the fundamental mechanisms underlying mechanical behaviour.<ref name=":40" /><ref>{{Cite journal |last1=Di Gioacchino |first1=Fabio |last2=Quinta da Fonseca |first2=João |date=2015 |title=An experimental study of the polycrystalline plasticity of austenitic stainless steel |journal=International Journal of Plasticity |volume=74 |pages=92–109 |doi=10.1016/j.ijplas.2015.05.012 |doi-access=free }}</ref>
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* {{Cite journal |last1=Britton |first1=T. Ben |author-link=Ben Britton |last2=Jiang |first2=Jun |last3=Guo |first3=Y. |last4=Vilalta-Clemente |first4=A. |last5=Wallis |first5=D. |last6=Hansen |first6=L.N. |last7=Winkelmann |first7=A. |last8=Wilkinson |first8=A.J. |author-link8=Angus Wilkinson |date=July 2016 |title=Tutorial: Crystal orientations and EBSD — Or which way is up? |journal=Materials Characterization |volume=117 |pages=113–126 |doi=10.1016/j.matchar.2016.04.008 |s2cid=138070296|ref=none|doi-access=free |hdl=10044/1/31250 |hdl-access=free }}
* {{Cite journal |last1=Charpagne |first1=Marie-Agathe |last2=Strub |first2=Florian |last3=Pollock |first3=Tresa M. |author-link3=Tresa Pollock |date=April 2019 |title=Accurate reconstruction of EBSD datasets by a multimodal data approach using an evolutionary algorithm |journal=Materials Characterization |volume=150 |pages=184–198 |doi=10.1016/j.matchar.2019.01.033|arxiv=1903.02988 |s2cid=71144677 |ref=none}}
* {{Cite journal |last1=Jackson |first1=M. A. |last2=Pascal |first2=E. |last3=De Graef |first3=M. |date=2019 |title=Dictionary Indexing of Electron Back-Scatter Diffraction Patterns: a Hands-On Tutorial |url=https://link.springer.com/article/10.1007/s40192-019-00137-4 |journal=Integrating Materials and Manufacturing Innovation |volume=8 |issue=2 |pages=226–246 |doi=10.1007/s40192-019-00137-4|s2cid=182073071 |ref=none|url-access=subscription }}
* {{Cite journal |last=Randle |first=Valerie |author-link=Valerie Randle |date=September 2009 |title=Electron backscatter diffraction: Strategies for reliable data acquisition and processing |journal=Materials Characterization |volume=60 |issue=90 |pages=913–922 |doi=10.1016/j.matchar.2009.05.011|ref=none}}
* {{Cite book |title=Electron Backscatter Diffraction in Materials Science |editor-first1=Adam J. |editor-first2=Mukul |editor-first3=Brent L. |editor-first4=David P. |editor-last1=Schwartz |editor-last2=Kumar |editor-last3=Adams |editor-last4=Field |year=2009 |publisher=Springer New York, New York |isbn=978-0-387-88135-5 |edition=2nd |___location=New York, New York |publication-date=12 August 2009 |doi=10.1007/978-0-387-88136-2|ref=none}}
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=== Codes ===
* {{Cite web |last=De Graef |first=M. |date=July 2017 |title=EMsoft (simulate EBSP) |url=https://github.com/EMsoft-org/EMsoft |website=GitHub|ref=none}}
* {{Cite web |last=Anes |first=Hakon |date=2020 |title=kikuchipy (process, simulate, analyze EBSD patterns with python) |url=https://kikuchipy.org |website=kikuchipy|ref=none}}
* {{Cite web |last=Hielscher |first=Schaeben |date=2008 |title=MTEX (EBSD analysis) |url=https://mtex-toolbox.github.io/ |website=MTEX|ref=none}}
* {{Cite web |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=OpenXY (HR-EBSD) |url=https://github.com/BYU-MicrostructureOfMaterials/OpenXY |website=GitHub |ref=none}}
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[[Category:Scientific techniques]]
[[Category:Spectroscopy]]
[[Category:Scattering]]
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