:Electron backscatter diffraction

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

File:EBSD setup graphic.png{{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 }}|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.{{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}} Tilting the sample elongates the interaction volume perpendicular to the tilt axis, allowing more electrons to leave the sample providing better signal.{{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. }}{{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 }} A high-energy electron beam (typically 20 kV) is focused on a small volume and scatters with a spatial resolution of ~20 nm at the specimen surface.{{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. }} The spatial resolution varies with the beam energy, angular width,{{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 }} interaction volume,{{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 }} nature of the material under study, and, in transmission Kikuchi diffraction (TKD), with the specimen thickness;{{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 }} thus, increasing the beam energy increases the interaction volume and decreases the spatial resolution.{{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 }}

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. The screen is coupled to lens which focuses the image from the phosphor screen onto a charge-coupled device (CCD) or complementary metal–oxide–semiconductor (CMOS) camera.{{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 }}

In this configuration, as the backscattered electrons leave the sample, they interact with the Coulomb potential and also lose energy due to inelastic scattering leading to a range of scattering angles (θ_hkl).{{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. }}{{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. }} The backscattered electrons form 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 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_hkl between lattice planes with Miller indexes h, k, and l.{{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 }}{{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 }} These Kikuchi lines and patterns were named after Seishi Kikuchi, who, together with Shoji Nishikawa, was the first to notice this diffraction pattern in 1928 using transmission electron microscopy (TEM){{Cite journal |last1=Nishikawa |first1=S. |last2=Kikuchi |first2=S. |date=June 1928 |title=Diffraction of Cathode Rays by Mica |url=http://dx.doi.org/10.1038/1211019a0 |journal=Nature |volume=121 |issue=3061 |pages=1019–1020 |doi=10.1038/1211019a0 |bibcode=1928Natur.121.1019N |issn=0028-0836}} which is similar in geometry to X-ray Kossel pattern.{{Cite journal |last1=Tixier |first1=R. |last2=Waché |first2=C. |date=1970 |title=Kossel patterns |journal=Journal of Applied Crystallography |volume=3 |issue=6 |pages=466–485 |doi=10.1107/S0021889870006726 |bibcode=1970JApCr...3..466T }}{{Citation |last1=Maitland |first1=Tim |title=Backscattering Detector and EBSD in Nanomaterials Characterization |date=2007 |work=Scanning Microscopy for Nanotechnology: Techniques and Applications |pages=41–75 |editor-last=Zhou |editor-first=Weilie |place=New York, New York |publisher=Springer |doi=10.1007/978-0-387-39620-0_2 |isbn=978-0-387-39620-0 |last2=Sitzman |first2=Scott |editor2-last=Wang |editor2-first=Zhong Lin}}

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.{{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 }} These bands and their intersections form what is known as Kikuchi patterns or electron backscatter patterns (EBSPs). To improve contrast, the patterns' background is corrected by removing anisotropic/inelastic scattering using static background correction or dynamic background correction.{{Cite journal |last1=Dingley |first1=D J |last2=Wright |first2=S I |last3=Nowell |first3=M M |date=August 2005 |title=Dynamic Background Correction of Electron Backscatter Diffraction Patterns |journal=Microscopy and Microanalysis |volume=11 |issue=S02 |doi=10.1017/S1431927605506676 |s2cid=137658758 |doi-access=free }}

{{wide image|Single crystal 4H SiC EBSP.png|550px|Single-crystal 4H-SiC, 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 is conducted using an SEM equipped with an EBSD detector containing at least a phosphor screen, compact lens and low-light Charge-coupled device (CCD) or Complementary metal–oxide–semiconductor (CMOS) camera. {{As of|2023|09}}, commercially available EBSD systems typically come with one of two different CCD cameras: for fast measurements, the CCD chip has a native resolution of 640×480 pixels; for slower, and more sensitive measurements, the CCD chip resolution can go up to 1600×1200 pixels.

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 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.{{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 }}

File:EBSP degradation.tif|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 vacuum stable. It is typically mounted using a conductive compound (e.g. an 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 SiC papers from 240 down to 4000 grit, and polished using diamond paste (from 9 to 1 μm) then in 50 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 beam polishing, for final surface preparation.{{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 }}{{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}}{{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 }}

Inside the SEM, the size of the measurement area determines local resolution and measurement time.{{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}} 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.{{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 }}{{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 }}{{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 }}{{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 }} The EBSD phosphor screen is set at an 18 mm working distance and a map's step size of less than 0.5 μm for strain and dislocations density analysis.

Decomposition of gaseous hydrocarbons and also hydrocarbons on the surface of samples by the electron beam inside the microscope results in carbon deposition,{{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 }} 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.{{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 }}{{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}}

{{Further information|Electron scattering}}

File:Electron Interaction with Matter.svg

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,{{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 }}{{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 }} or defined by pattern quality, or can be as ambiguous as "where useful information is obtained".{{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 }} 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.{{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 }} 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.{{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 }} In contrast, Isabell and David{{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 }} concluded that depth resolution in homogeneous crystals could also extend up to 1 μm due to inelastic scattering (including tangential smearing and channelling effect).

A recent comparison between reports on EBSD depth resolution, Koko et al 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. These are critical parameters for determining or simulating the depth resolution. 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.{{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}}{{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 }}

Monte Carlo simulations provide an alternative approach to quantifying the depth resolution for EBSPs formation, which can be estimated using the Bloch wave theory, where backscattered primary electrons – after interacting with the crystal lattice – exit the surface, carrying information about the crystallinity of the volume interacting with the electrons.{{Cite journal |last1=Ren |first1=S. X. |last2=Kenik |first2=E. A. |last3=Alexander |first3=K. B. |date=1997 |title=Monte Carlo Simulation of Spatial Resolution for Electron Backscattered Diffraction (EBSD) with Application to Two-Phase Materials |journal=Microscopy and Microanalysis |volume=3 |issue=S2 |pages=575–576 |doi=10.1017/S1431927600009764 |bibcode=1997MiMic...3S.575R |s2cid=137029133 |url=https://digital.library.unt.edu/ark:/67531/metadc694234/ |access-date=20 March 2023 |archive-date=25 March 2023 |archive-url=https://web.archive.org/web/20230325200544/https://digital.library.unt.edu/ark:/67531/metadc694234/ |url-status=live }} The backscattered electrons (BSE) energy distribution depends on the material's characteristics and the beam conditions.{{Cite journal |last1=Brodusch |first1=Nicolas |last2=Demers |first2=Hendrix |last3=Gauvin |first3=Raynald |date=2018 |title=Imaging with a Commercial Electron Backscatter Diffraction (EBSD) Camera in a Scanning Electron Microscope: A Review |journal=Journal of Imaging |volume=4 |issue=7 |pages=88 |doi=10.3390/jimaging4070088|doi-access=free}} This BSE wave field is also affected by the thermal diffuse scattering process that causes incoherent and inelastic (energy loss) scattering – after the elastic diffraction events – which does not, yet, have a complete physical description that can be related to mechanisms that constitute EBSP depth resolution.{{Cite book|last=Michiyoshi|first=Tanaka|title=Convergent beam electron diffraction|date=1988|publisher=Jeol|oclc=312738225|url=http://www2.tagen.tohoku.ac.jp/lab/terauchi/html/activity/Tanaka_CBED-I_.pdf|access-date=20 March 2023|archive-date=20 March 2023|archive-url=https://web.archive.org/web/20230320093510/http://www2.tagen.tohoku.ac.jp/lab/terauchi/html/activity/Tanaka_CBED-I_.pdf|url-status=live}}{{Citation |last=Winkelmann |first=Aimo |title=Dynamical Simulation of Electron Backscatter Diffraction Patterns |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=21–33 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |publisher=Springer US |doi=10.1007/978-0-387-88136-2_2 |isbn=978-0-387-88136-2 |s2cid=122806598 |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P.}}

Both the EBSD experiment and simulations typically make two assumptions: that the surface is pristine and has a homogeneous depth resolution; however, neither of them is valid for a deformed sample.

File:EBSP Indexing and formation.tif|alt=Formation of Kossel cone which intersect with CCD screen to form EBSP which can be Bravais-Miller indexed]]

If the setup geometry is well described, it is possible to relate the bands present in the diffraction pattern to the underlying crystal and crystallographic orientation of the material within the electron interaction volume. Each band can be indexed individually by the 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.{{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.}}

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.{{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 }}{{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}} 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.

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;{{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}}{{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 }} minimising the 'fit' between the experimental pattern and a computationally determined orientation,{{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 }}{{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}} and or/and neighbour pattern averaging and re-indexing, NPAR{{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 }}). Indexing then give a unique solution to the single crystal orientation that is related to the other crystal orientations within the field-of-view.{{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}}{{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}}

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 (four choose three, i.e. $C(4,3)$) 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.{{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 }}{{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 }}{{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. }} 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.

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.

While this geometric description related to the kinematic solution using the Bragg condition is very powerful and useful for orientation and texture analysis, it only describes the geometry of the crystalline lattice. It ignores many physical processes involved within the diffracting material. To adequately describe finer features within the electron beam scattering pattern (EBSP), one must use a many-beam dynamical model (e.g. the variation in band intensities in an experimental pattern does not fit the kinematic solution related to the structure factor).

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).{{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 }}

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.

The recent development of AstroEBSD{{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 }} and PCGlobal,{{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 }} open-source MATLAB codes, increased the precision of determining the pattern centre (PC) and – consequently – elastic strains{{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 }} by using a pattern matching approach{{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 }} which simulates the pattern using EMSoft.{{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}}

File:EBSD orientation map of ferrous lath martensite.jpg 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.{{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 }}{{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 }} 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.{{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}}{{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 }} The orientation data can be visualised using a variety of techniques, including colour-coding, contour lines, and pole figures.{{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}}

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.{{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}} 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.

Full-field displacement, elastic strain, and the GND density provide quantifiable information about the material's elastic and plastic behaviour at the microscale. Measuring strain at the microscale requires careful consideration of other key details besides the change in length/shape (e.g., local texture, individual grain orientations). These micro-scale features can be measured using different techniques, e.g., hole drilling, monochromatic or polychromatic energy-dispersive X-ray diffraction or neutron diffraction (ND). EBSD has a high spatial resolution and is relatively sensitive and easy to use compared to other techniques.{{Cite journal |last1=Adams |first1=Brent L. |last2=Wright |first2=Stuart I. |last3=Kunze |first3=Karsten |date=1993 |title=Orientation imaging: The emergence of a new microscopy |journal=Metallurgical Transactions A |volume=24 |issue=4 |pages=819–831 |doi=10.1007/BF02656503 |bibcode=1993MTA....24..819A |s2cid=137379846 }}{{Cite journal |last=Humphreys |first=F. J. |date=2001 |title=Review Grain and subgrain characterisation by electron backscatter diffraction |journal=Journal of Materials Science |volume=36 |issue=16 |pages=3833–3854 |doi=10.1023/A:1017973432592 |s2cid=135659350 }}{{Cite journal |last1=Wilkinson |first1=Angus J. |last2=Hirsch |first2=Peter B. |date=1997 |title=Electron diffraction based techniques in scanning electron microscopy of bulk materials |journal=Micron |volume=28 |issue=4 |pages=279–308 |doi=10.1016/S0968-4328(97)00032-2 |arxiv=1904.05550 |s2cid=118944816 }} Strain measurements using EBSD can be performed at a high spatial resolution, allowing researchers to study the local variation in strain within a material. This information can be used to study the deformation and mechanical behaviour of materials,{{Cite journal |last1=Shi |first1=Qiwei |last2=Roux |first2=Stéphane |last3=Latourte |first3=Félix |last4=Hild |first4=François |date=2019 |title=Estimation of elastic strain by integrated image correlation on electron diffraction patterns |journal=Ultramicroscopy |volume=199 |pages=16–33 |doi=10.1016/j.ultramic.2019.02.001 |pmid=30738984 |s2cid=73418370 |doi-access=free }} to develop models of material behaviour under different loading conditions, and to optimise the processing and performance of materials. Overall, strain measurement using EBSD is a powerful tool for studying the deformation and mechanical behaviour of materials, and is widely used in materials science and engineering research and development.

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),{{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 }} where IQ is calculated from the sum of the peaks detected when using the conventional Hough transform. Wilkinson{{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}} first used the changes in high-order Kikuchi line positions to determine the elastic strains, albeit with low 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.}} (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.{{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 }} In the early 1990s, Troost et al.{{Cite journal |last1=Troost |first1=K. Z. |last2=van der Sluis |first2=P. |last3=Gravesteijn |first3=D. J. |date=1993 |title=Microscale elastic-strain determination by backscatter Kikuchi diffraction in the scanning electron microscope |journal=Applied Physics Letters |volume=62 |issue=10 |pages=1110–1112 |doi=10.1063/1.108758 |bibcode=1993ApPhL..62.1110T }} and Wilkinson et al.{{Cite journal |last1=Wilkinson |first1=A. J. |last2=Dingley |first2=D. J. |date=1991 |title=Quantitative deformation studies using electron back scatter patterns |journal=Acta Metallurgica et Materialia |volume=39 |issue=12 |pages=3047–3055 |doi=10.1016/0956-7151(91)90037-2 }}{{Cite journal |last=Wilkinson |first=Angus J. |date=1996 |title=Measurement of elastic strains and small lattice rotations using electron back scatter diffraction |journal=Ultramicroscopy |volume=62 |issue=4 |pages=237–247 |doi=10.1016/0304-3991(95)00152-2 |pmid=22666906 }} used pattern degradation and change in the zone axis position to measure the residual elastic strains and small lattice rotations with a 0.02% precision.

File:HR-EBSD schematic.tif

Cross-correlation-based, high angular resolution electron backscatter diffraction (HR-EBSD) – introduced by Wilkinson et al.{{Cite journal |last1=Wilkinson |first1=A. J. |last2=Meaden |first2=G. |last3=Dingley |first3=D. J. |date=2006-11-01 |title=High resolution mapping of strains and rotations using electron backscatter diffraction |journal=Materials Science and Technology |volume=22 |issue=11 |pages=1271–1278 |doi=10.1179/174328406X130966 |bibcode=2006MatST..22.1271W |s2cid=135875163 |url=https://ora.ox.ac.uk/objects/uuid:d9bf9a52-8ec7-45b5-a099-a89e9dc83d18 |access-date=20 March 2023 |archive-date=25 March 2023 |archive-url=https://web.archive.org/web/20230325200554/https://ora.ox.ac.uk/objects/uuid:d9bf9a52-8ec7-45b5-a099-a89e9dc83d18 |url-status=live }}{{Cite journal |last1=Wilkinson |first1=Angus J. |last2=Meaden |first2=Graham |last3=Dingley |first3=David J. |date=2006 |title=High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity |journal=Ultramicroscopy |volume=106 |issue=4 |pages=307–313 |doi=10.1016/j.ultramic.2005.10.001 |pmid=16324788 }} – is an SEM-based technique to map relative elastic strains and rotations, and estimate the geometrically necessary dislocation (GND) density in crystalline materials. HR-EBSD method uses image cross-correlation to measure pattern shifts between regions of interest (ROI) in different electron backscatter diffraction patterns (EBSPs) with sub-pixel precision. As a result, the relative lattice distortion between two points in a crystal can be calculated using pattern shifts from at least four non-collinear ROI. In practice, pattern shifts are measured in more than 20 ROI per EBSP to find a best-fit solution to the deformation gradient tensor, representing the relative lattice distortion.{{NoteTag|Strain, distortion, and deformation can refer to several quantities in different fields. Here they are used as follows. A mechanically loaded object changes shape in response to applied load; when measured in a mechanical test frame, it is called (total) engineering strain. Plastic strain is the shape change that persists after removing the macroscopic load. On the microscale, plastic deformation in most crystalline materials is accommodated by dislocation glide and deformation twinning. However, dislocations are also generated in a material as plastic deformation progresses, and dislocations with similar crystallographic character and sign that end up near each other in a material (e.g., lined up at a slip band) can be characterised as GNDs. Increasing plastic strain in a polycrystal also elastically distorts the crystal lattice to accommodate crystal defects (e.g., dislocation cores), groups of defects (e.g., dislocation cell walls), and maintains compatibility at polycrystal grain boundaries. This lattice distortion can be expressed as a deformation gradient tensor, which can be decomposed into elastic strain (symmetric) and lattice rotation (antisymmetric) components.{{Cite book |last1=Barabash |first1=Rozaliya |last2=Ice |first2=Gene |date=2013|title=Strain and Dislocation Gradients from Diffraction |doi=10.1142/p897 |isbn=978-1-908979-62-9 }} In this article 'lattice distortion' refers to elastic distortion components derived from the deformation gradient, elastic strain, and lattice rotation tensors.}}{{Cite journal |last1=Britton |first1=T. B. |last2=Wilkinson |first2=A. J. |date=2012 |title=High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations |journal=Ultramicroscopy |volume=114 |pages=82–95 |doi=10.1016/j.ultramic.2012.01.004 |pmid=22366635 }}

The displacement gradient tensor ($\backslash beta$) (or local lattice distortion) relates the measured geometrical shifts in the pattern between the collected point ($\backslash widehat\{p\}$) and associate (non-coplanar) vector ($\backslash widehat\{r\}$), and reference point ($p$) pattern and associate vector ($r$). Thus, the (pattern shift) vector ($q$) can be written as in the equations below, where $x\_\{i\}$ and $u\_\{i\}$ are the direction and displacement in $i$th direction, respectively.

$q=\backslash beta\; r-(\backslash beta\; r.\backslash widehat\{r\})\backslash widehat\{r\}$

The shifts are measured in the phosphor (detector) plane ($\backslash beta\_3\; r\_3=0$), and the relationship is simplified; thus, eight out of the nine displacement gradient tensor components can be calculated by measuring the shift at four distinct, widely spaced regions on the EBSP.{{Citation |last1=Wilkinson |first1=Angus J. |title=Strain Mapping Using Electron Backscatter Diffraction |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=231–249 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |publisher=Springer US |doi=10.1007/978-0-387-88136-2_17 |isbn=978-0-387-88136-2 |last2=Dingley |first2=David J. |last3=Meaden |first3=Graham |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P. }} This shift is then corrected to the sample frame (flipped around Y-axis) because EBSP is recorded on the phosphor screen and is inverted as in a mirror. They are then corrected around the X-axis by 24° (i.e., 20° sample tilt plus ≈4° camera tilt and assuming no angular effect from the beam movement). Using infinitesimal strain theory, the deformation gradient is then split into elastic strain (symmetric part, where $ij=ji$), $e\_\{ij\}$and lattice rotations (asymmetric part, where $ii=jj=0$), $\backslash omega\_\{ij\}$.

$e\_\{ij\}=\{1\backslash over\{2\}\}(\backslash beta\_\{ij\}+\backslash beta^\{r\}\_\{ij\}),\; \backslash qquad\; \backslash omega\_\{ij\}=\{1\backslash over\{2\}\}(\backslash beta\_\{ij\}-\backslash beta^\{r\}\_\{ij\})$

These measurements do not provide information about the volumetric/hydrostatic strain tensors. By imposing a boundary condition that the stress normal to the surface ($\backslash sigma\_\{33\}$) is zero (i.e., traction-free surface{{Cite journal |last1=Hardin |first1=T.J. |last2=Ruggles |first2=T.J. |last3=Koch |first3=D.P. |last4=Niezgoda |first4=S.R. |last5=Fullwood |first5=D.T. |last6=Homer |first6=E.R. |date= 2015 |title=Analysis of traction-free assumption in high-resolution EBSD measurements: HR-EBSD TRACTION-FREE ASSUMPTION |journal=Journal of Microscopy |volume=260 |issue=1 |pages=73–85 |doi=10.1111/jmi.12268 |pmid=26138919 |s2cid=25692536 }}), and using Hooke's law with anisotropic elastic stiffness constants, the missing ninth degree of freedom can be estimated in this constrained minimisation problem by using a nonlinear solver.

$\backslash sigma\_\{33\}=C\_\{33kl\}e\_\{kl\}=0$

Where $C$ is the crystal anisotropic stiffness tensor. These two equations are solved to re-calculate the refined elastic deviatoric strain ($\backslash varepsilon\_\{kl\}$), including the missing ninth (spherical) strain tensor. An alternative approach that considers the full $\backslash beta$ can be found in.

$e\_\{ij\}=\backslash begin\{pmatrix\}\; \{e\_\{11\}\}\; \backslash \backslash \{e\_\{22\}\}\; \backslash \backslash \{e\_\{33\}\}\backslash \backslash \{e\_\{12\}+e\_\{21\}\}\backslash \backslash \{e\_\{13\}+e\_\{31\}\}\backslash \backslash \{e\_\{23\}+e\_\{32\}\}\; \backslash \backslash \backslash end\{pmatrix\},\; \backslash qquad\; \backslash begin\{pmatrix\}\; \{k\_\{1\}\}\; \backslash \backslash \{k\_\{2\}\}\; \backslash \backslash \{k\_\{3\}\}\; \backslash \backslash \backslash end\{pmatrix\}=\backslash begin\{pmatrix\}\; \{e\_\{11\}-e\_\{33\}\}\; \backslash \backslash \{e\_\{22\}-e\_\{33\}\}\; \backslash \backslash \{e\_\{12\}C\_\{3312\}+e\_\{13\}C\_\{3313\}+e\_\{23\}C\_\{3323\}\}\; \backslash \backslash \backslash end\{pmatrix\}$

$\backslash varepsilon\_\{33\}=\{k\_1C\_\{1133\}+k\_2C\{2233\}+k\_3\backslash over\; C\_\{1133\}+C\_\{2233\}+C\_\{3333\}\},\backslash qquad\; \backslash therefore\backslash varepsilon\_\{kl\}=\backslash begin\{pmatrix\}\; \{k\_1+\backslash varepsilon\_\{33\}\}\; \backslash \backslash \{k\_2+\backslash varepsilon\_\{33\}\}\; \backslash \backslash \{\backslash varepsilon\_\{33\}\}\backslash \backslash \{2e\_\{12\}\}\backslash \backslash \{2e\_\{13\}\}\backslash \backslash \{2e\_\{23\}\}\; \backslash \backslash \backslash end\{pmatrix\}$

Finally, the stress and strain tensors are linked using the crystal anisotropic stiffness tensor ($C\_\{klij\}$), and by using the Einstein summation convention with symmetry of stress tensors ($\backslash sigma\_\{ij\}=\backslash sigma\_\{ji\}$).

$\backslash sigma\_\{ij\}=C\_\{ijkl\}\backslash varepsilon\_\{kl\}$

The quality of the produced data can be assessed by taking the geometric mean of all the ROI's correlation intensity/peaks. A value lower than 0.25 should indicate problems with the EBSPs' quality. Furthermore, the geometrically necessary dislocation (GND) density can be estimated from the HR-EBSD measured lattice rotations by relating the rotation axis and angle between neighbour map points to the dislocation types and densities in a material using Nye's tensor.{{Cite journal |last1=Wilkinson |first1=Angus J. |last2=Randman |first2=David |date=2010 |title=Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction |journal=Philosophical Magazine |volume=90 |issue=9 |pages=1159–1177 |bibcode=2010PMag...90.1159W |doi=10.1080/14786430903304145 |s2cid=121903030 |url=https://hal.science/hal-00581027/file/PEER_stage2_10.1080%252F14786430903304145.pdf |access-date=20 March 2023 |archive-date=3 March 2023 |archive-url=https://web.archive.org/web/20230303205320/https://hal.science/hal-00581027/file/PEER_stage2_10.1080%252F14786430903304145.pdf |url-status=live }}{{Cite journal |last=Pantleon |first=W. |date=2008-06-01 |title=Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction |journal=Scripta Materialia |volume=58 |issue=11 |pages=994–997 |doi=10.1016/j.scriptamat.2008.01.050 }}{{Citation |last1=Brewer |first1=Luke N. |title=Mapping and Assessing Plastic Deformation Using EBSD |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=251–262 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |publisher=Springer US |doi=10.1007/978-0-387-88136-2_18 |isbn=978-0-387-88136-2 |last2=Field |first2=David P. |last3=Merriman |first3=Colin C. |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P. }}

The HR-EBSD method can achieve a precision of ±10⁻⁴ 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.{{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 }} It was limited to small strains and rotations (>1.5°) until Britton and Wilkinson and Maurice et al.{{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}} raised the rotation limit to ~11° by using a re-mapping technique that recalculated the strain after transforming the patterns with a rotation matrix ($R$) calculated from the first cross-correlation iteration.

{{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 ($\backslash rho\_\{GND\}$). The location of EBSP₀ is highlighted with a star in $\backslash sigma\_\{yz\}$. The step size is 250 nm{{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}}||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.{{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}} 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{{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 }} also established a method that achieves a precision of ±10⁻⁵ in the displacement gradient components using a full-field integrated 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°.{{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 }}{{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 }}

These measurements do not provide information about the hydrostatic or volumetric strains, because there is no change in the orientations of lattice planes (crystallographic directions), but only changes in the position and width of the Kikuchi bands.{{Cite journal |journal=Microscopy and Microanalysis |doi=10.1017/s1431927606060090 |title=EBSD Image Quality Mapping |year=2006 |last1=Wright |first1=Stuart I. |last2=Nowell |first2=Matthew M. |volume=12 |issue=1 |pages=72–84 |pmid=17481343 |bibcode=2006MiMic..12...72W |s2cid=35055001 |doi-access=free }}{{Cite journal |last1=Jiang |first1=Jun |last2=Zhang |first2=Tiantian |last3=Dunne |first3=Fionn P. E. |last4=Britton |first4=T. Ben |date= 2016 |title=Deformation compatibility in a single crystalline Ni superalloy |journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |volume=472 |issue=2185 |pages=20150690 |doi=10.1098/rspa.2015.0690 |pmc=4786046 |pmid=26997901|bibcode=2016RSPSA.47250690J }}

In HR-EBSD analysis, the lattice distortion field is calculated relative to a reference pattern or point (EBSP₀) 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.{{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 }}{{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}} This 'reference pattern problem' is similar to the 'd₀ problem' in X-ray diffraction,{{Cite journal |last1=Koko |first1=A. |last2=Earp |first2=P. |last3=Wigger |first3=T. |last4=Tong |first4=J. |last5=Marrow |first5=T. J. |date=2020 |title=J-integral analysis: An EDXD and DIC comparative study for a fatigue crack |journal=International Journal of Fatigue |volume=134 |pages=105474 |doi=10.1016/j.ijfatigue.2020.105474 |s2cid=214391445 |url=https://researchportal.port.ac.uk/portal/en/publications/jintegral-analysis-an-edxd-and-dic-comparative-study-for-a-fatigue-crack(ccf37f3f-1a30-493e-86ea-d1ecab4fee2f).html |access-date=20 March 2023 |archive-date=27 January 2021 |archive-url=https://web.archive.org/web/20210127070347/https://researchportal.port.ac.uk/portal/en/publications/jintegral-analysis-an-edxd-and-dic-comparative-study-for-a-fatigue-crack(ccf37f3f-1a30-493e-86ea-d1ecab4fee2f).html |url-status=live }} and affects the nominal magnitude of HR-EBSD stress fields. However, selecting the reference pattern (EBSP₀) plays a key role, as severely deformed EBSP₀ adds phantom lattice distortions to the map values, thus, decreasing the measurement precision.File:Linear correlation coefficients between the local conditions at the EBSP0 point and the averaged conditions.svg (Fe-α) and austenite (Fe-γ) phase of age-hardened DSS, and Silicon (Si). The analysis considers the average deformation gradient tensor determinant ($A^\{0\}$), maximum in-plane principal strain ($\backslash epsilon\_\{MAX\}$), rotation magnitude ($\backslash omega\_\{T\}=\backslash sqrt(\backslash omega\_\{32\}^2+\backslash omega\_\{13\}^2+\backslash omega\_\{21\}^2)$), correlation peak height (PH), mean angular error (MAE) and GND density.|300x300px|alt=Linear correlation coefficients between the local conditions at the EBSP0 point and the averaged conditions at the grain for the ferrite (Fe-α) and austenite (Fe-γ) phase of age-hardened DSS, and Silicon (Si). The analysis considers the average deformation gradient tensor determinant, maximum in-plane principal strain, rotation magnitude, correlation peak height, mean angular error and GND density.]]

The local lattice distortion at the EBSP₀ 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 EBSP₀ 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 EBSP₀'s IQ and EBSP₀'s local lattice distortion.

The use of simulated reference patterns for absolute strain measurement is still an active area of research{{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}}{{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}}{{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}}{{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 }}{{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=Trager-Cowan |first7=Carol |date=November 2021 |title=Kikuchi pattern simulations of backscattered and transmitted electrons |journal=Journal of Microscopy |volume=284 |issue=2 |pages=157–184 |doi=10.1111/jmi.13051 |pmid=34275156 |s2cid=236091618 |url=https://strathprints.strath.ac.uk/78647/1/Winkelmann_etal_JM_2021_Kikuchi_pattern_simulations_of_backscattered_and_transmitted.pdf |access-date=20 March 2023 |archive-date=25 March 2023 |archive-url=https://web.archive.org/web/20230325200434/https://strathprints.strath.ac.uk/78647/1/Winkelmann_etal_JM_2021_Kikuchi_pattern_simulations_of_backscattered_and_transmitted.pdf |url-status=live }}{{Cite journal |last=Winkelmann |first=A. |date= 2010 |title=Principles of depth-resolved Kikuchi pattern simulation for electron backscatter diffraction: KIKUCHI PATTERN SIMULATION FOR EBSD |journal=Journal of Microscopy |volume=239 |issue=1 |pages=32–45 |doi=10.1111/j.1365-2818.2009.03353.x |pmid=20579267 |s2cid=23590722}}{{Cite journal |last1=Vermeij |first1=Tijmen |last2=De Graef |first2=Marc |last3=Hoefnagels |first3=Johan |date=2019-03-15 |title=Demonstrating the potential of accurate absolute cross-grain stress and orientation correlation using electron backscatter diffraction |journal=Scripta Materialia |volume=162 |pages=266–271 |doi=10.1016/j.scriptamat.2018.11.030 |arxiv=1807.03908 |s2cid=54575778 }}{{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 }} and scrutiny{{Cite journal |last1=Kacher |first1=Josh |last2=Basinger |first2=Jay |last3=Adams |first3=Brent L. |last4=Fullwood |first4=David T. |date=2010-06-01 |title=Reply to comment by Maurice et al. in response to "Bragg's Law Diffraction Simulations for Electron Backscatter Diffraction Analysis" |journal=Ultramicroscopy |volume=110 |issue=7 |pages=760–762 |doi=10.1016/j.ultramic.2010.02.004 |pmid=20189305 }}{{Cite journal |last1=Britton |first1=T. B. |last2=Maurice |first2=C. |last3=Fortunier |first3=R. |last4=Driver |first4=J. H. |last5=Day |first5=A. P. |last6=Meaden |first6=G. |last7=Dingley |first7=D. J. |last8=Mingard |first8=K. |last9=Wilkinson |first9=A. J. |date=2010 |title=Factors affecting the accuracy of high resolution electron backscatter diffraction when using simulated patterns |journal=Ultramicroscopy |volume=110 |issue=12 |pages=1443–1453 |doi=10.1016/j.ultramic.2010.08.001 |pmid=20888125 }}{{Cite journal |last=Alkorta |first=Jon |date=2013-08-01 |title=Limits of simulation based high resolution EBSD |journal=Ultramicroscopy |volume=131 |pages=33–38 |doi=10.1016/j.ultramic.2013.03.020 |pmid=23676453 }}{{Cite journal |last1=Jackson |first1=Brian E. |last2=Christensen |first2=Jordan J. |last3=Singh |first3=Saransh |last4=De Graef |first4=Marc |last5=Fullwood |first5=David T. |last6=Homer |first6=Eric R. |last7=Wagoner |first7=Robert H. |date=August 2016 |title=Performance of Dynamically Simulated Reference Patterns for Cross-Correlation Electron Backscatter Diffraction |journal=Microscopy and Microanalysis |volume=22 |issue=4 |pages=789–802 |doi=10.1017/S143192761601148X |pmid=27509538 |bibcode=2016MiMic..22..789J |s2cid=24482631}} as difficulties arise from the variation of inelastic electron scattering with depth which limits the accuracy of dynamical diffraction simulation models, and imprecise determination of the pattern centre which leads to phantom strain components which cancel out when using experimentally acquired reference patterns. Other methods assumed that absolute strain at EBSP₀ can be determined using crystal plasticity finite-element (CPFE) simulations, which then can be then combined with the HR-EBSD data (e.g., using linear 'top-up' method{{Cite journal |last1=Zhang |first1=Tiantian |last2=Collins |first2=David M. |last3=Dunne |first3=Fionn P. E. |last4=Shollock |first4=Barbara A.|author4-link=Barbara Shollock |date=2014|title=Crystal plasticity and high-resolution electron backscatter diffraction analysis of full-field polycrystal Ni superalloy strains and rotations under thermal loading |journal=Acta Materialia |volume=80 |pages=25–38 |doi=10.1016/j.actamat.2014.07.036 |hdl=10044/1/25979 |hdl-access=free }}{{Cite journal |last1=Guo |first1=Yi |last2=Zong |first2=Cui |last3=Britton |first3=T. B. |date=2021 |title=Development of local plasticity around voids during tensile deformation |journal=Materials Science and Engineering: A |volume=814 |pages=141227 |doi=10.1016/j.msea.2021.141227 |arxiv=2007.11890 |s2cid=234850241 }} or displacement integration) to calculate the absolute lattice distortions.

In addition, GND density estimation is nominally insensitive to (or negligibly dependent upon{{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 }}{{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 }}) EBSP₀ choice, as only neighbour point-to-point differences in the lattice rotation maps are used for GND density calculation.{{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 }}{{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 }} However, this assumes that the absolute lattice distortion of EBSP₀ 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 EBSP₀ choice.{{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}}

Criteria for EBSP₀ selection can be one or a mixture of:

• Selecting from points with low GND density or low Kernel average misorientation (KAM) based on the Hough measured local grain misorientations;{{Cite journal |last1=Moussa |first1=C |last2=Bernacki |first2=M |last3=Besnard |first3=R |last4=Bozzolo |first4=N |date=2015 |title=About quantitative EBSD analysis of deformation and recovery substructures in pure Tantalum |journal=IOP Conference Series: Materials Science and Engineering |volume=89 |issue=1 |pages=012038 |doi=10.1088/1757-899x/89/1/012038 |bibcode=2015MS&E...89a2038M |s2cid=53137730 |doi-access=free }}
• Selecting from points with high image quality (IQ), which may have a low defect density within its electron interaction volume, is therefore assumed to be a low-strained region of a polycrystalline material.{{cite journal |last1=Wright |first1=Stuart I. |last2=Matthew |first2=M. Nowell |last3=David |first3=P. Field. |year=2011 |title=A review of strain analysis using electron backscatter diffraction. |journal=Microscopy and Microanalysis |series=17 |volume=17 |issue=3 |pages=316–329 |bibcode=2011MiMic..17..316W |doi=10.1017/S1431927611000055 |pmid=21418731 |s2cid=26116915}} However, IQ does not carry a clear physical meaning,{{Cite journal |journal=Microscopy and Microanalysis |doi=10.1017/s1431927602106465 |title=Alternatives to Image Quality (IQ) Mapping in EBSD |year=2002 |last1=Tao |first1=Xiaodong |last2=Eades |first2=Alwyn |volume=8 |issue=S02 |pages=692–693 |bibcode=2002MiMic...8S.692T |s2cid=138999871 |doi-access=free }} and the magnitudes of the measured relative lattice distortion are insensitive to the IQ of EBSP₀;
• EBSP₀ can also be manually selected to be far from potential stress concentrations such as grain boundaries, inclusions, or cracks using subjective criteria;
• Selecting an EBSP₀ after examining the empirical relationship between the cross-correlation parameter and angular error, used in an iterative algorithm to identify the optimal reference pattern that maximises the precision of HR-EBSD.

These criteria assume these parameters can indicate the strain conditions at the reference point, which can produce an accurate measurements of up to 3.2×10⁻⁴ elastic strain. However, experimental measurements point to the inaccuracy of HR-EBSD in determining the out-of-plane shear strain components distribution and magnitude.{{Cite journal |last1=McLean |first1=Mark J. |last2=Osborn |first2=William A. |date=2018|title=In-situ elastic strain mapping during micromechanical testing using EBSD |journal=Ultramicroscopy |volume=185 |pages=21–26 |doi=10.1016/j.ultramic.2017.11.007 |pmid=29161620 }}{{Cite journal |last1=Yu |first1=Hongbing |last2=Liu |first2=Junliang |last3=Karamched |first3=Phani |last4=Wilkinson |first4=Angus J. |last5=Hofmann |first5=Felix |date=2019 |title=Mapping the full lattice strain tensor of a single dislocation by high angular resolution transmission Kikuchi diffraction (HR-TKD) |journal=Scripta Materialia |volume=164 |pages=36–41 |doi=10.1016/j.scriptamat.2018.12.039 |s2cid=119075799|doi-access=free |arxiv=1808.10055 }}

EBSD is used in a wide range of applications, including materials science and engineering, geology,{{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 }} and biological research.{{Cite journal |last1=Choi |first1=Seung |last2=Han |first2=Seokyoung |last3=Lee |first3=Yuong-Nam |date=2019 |editor-last=Rahman |editor-first=Imran |title=Electron backscatter diffraction (EBSD) analysis of maniraptoran eggshells with important implications for microstructural and taphonomic interpretations |journal=Palaeontology |volume=62 |issue=5 |pages=777–803 |doi=10.1111/pala.12427 |bibcode=2019Palgy..62..777C |s2cid=182770470 }}{{Cite journal |last1=Wolfe |first1=Kennedy |last2=Smith |first2=Abigail M. |last3=Trimby |first3=Patrick |last4=Byrne |first4=Maria |date=2013-08-01 |title=Microstructure of the paper nautilus (Argonauta nodosa) shell and the novel application of electron backscatter diffraction (EBSD) to address effects of ocean acidification |journal=Marine Biology |volume=160 |issue=8 |pages=2271–2278 |doi=10.1007/s00227-012-2032-4 |bibcode=2013MarBi.160.2271W |s2cid=253745873 }} In materials science and engineering, EBSD is used to study the microstructure of metals, ceramics, and polymers, and to develop models of material behaviour.{{Cite journal |last1=Piazolo |first1=S. |last2=Jessell |first2=M. W. |last3=Prior |first3=D. J. |last4=Bons |first4=P. D. |date=2004 |title=The integration of experimental in-situ EBSD observations and numerical simulations: a novel technique of microstructural process analysis |journal=Journal of Microscopy |volume=213 |issue=3 |pages=273–284 |doi=10.1111/j.0022-2720.2004.01304.x|pmid=15009695 |s2cid=24037204 }} In geology, EBSD is used to study the crystallographic structure of minerals and rocks. In biological research, EBSD is used to study the microstructure of biological tissues and to investigate the structure of biological materials such as bone and teeth.{{Cite journal |last1=Koblischka-Veneva |first1=Anjela |last2=Koblischka |first2=Michael R. |last3=Schmauch |first3=Jörg |last4=Hannig |first4=Matthias |date=2018 |title=Human dental enamel: A natural nanotechnology masterpiece investigated by TEM and t-EBSD |journal=Nano Research |volume=11 |issue=7 |pages=3911–3921 |doi=10.1007/s12274-018-1968-1 |s2cid=139757769 }}

{{Multiple images

| image1 = EBSD setup.jpg

| image2 = VFSD image of DSS.jpg

| total_width = 400

| caption1 = The EBSD detector has forward scattered electron diodes (FSDs) at the bottom, in the middle (MSD) and at the top of the detector.

| caption2 = Far-field image of 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 diodes (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.{{Cite journal |last1=Schwarzer |first1=Robert A |last2=Hjelen |first2=Jarle |date=2015-01-09 |title=Backscattered Electron Imaging with an EBSD Detector |journal=Microscopy Today |volume=23 |issue=1 |pages=12–17 |doi=10.1017/S1551929514001333|s2cid=138740715 |doi-access=free }} The FSE signal is also sensitive to the crystallographic orientation of the sample. By analysing the intensity and contrast of the FSE signal, researchers can determine the crystallographic orientation of each pixel in the image.{{Cite journal |last1=Tong |first1=Vivian S. |last2=Knowles |first2=Alexander J. |last3=Dye |first3=David |last4=Britton |first4=T. Ben |date=2019-01-01 |title=Rapid electron backscatter diffraction mapping: Painting by numbers |journal=Materials Characterization |volume=147 |pages=271–279 |arxiv=1809.07283 |doi=10.1016/j.matchar.2018.11.014 |s2cid=119328762}}

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.{{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 }}

Image generation has a lot of freedom when using the EBSD detector as an imaging device. An image created using a combination of diodes is called virtual or VFSD. It is possible to acquire images at a rate akin to slow scan imaging in the SEM by excessive binning of the EBSD CCD camera. It is possible to suppress or isolate the contrast of interest by creating composite images from simultaneously captured images, which offers a wide range of combinations for assessing various microstructure characteristics. Nevertheless, VFSD images do not include the quantitative information inherent to traditional EBSD maps; they simply offer representations of the microstructure.

When simultaneous EDS/EBSD collection can be achieved, the capabilities of both techniques can be enhanced.{{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 }} 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.{{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 }}{{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}} 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 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.{{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}} 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 micrometres compared to tens of nanometres), and the shape of these volumes using a highly tilted sample may have implications on algorithms for phase discrimination.{{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}}

EBSD, when used together with other in-SEM techniques such as cathodoluminescence (CL),{{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 }} wavelength dispersive X-ray spectroscopy (WDS){{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 }} and/or EDS can provide a deeper insight into the specimen's properties and enhance phase identification.{{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 }}{{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=Y₂O₃–Al₂O₃ 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}} For example, the minerals calcite (limestone) and aragonite (shell) have the same chemical composition – calcium carbonate (CaCO₃) therefore EDS/WDS cannot tell them apart, but they have different microcrystalline structures so EBSD can differentiate between them.{{Cite journal |last1=Ohfuji |first1=Hiroaki |last2=Yamamoto |first2=Masashi |date=2015 |title=EDS quantification of light elements using osmium surface coating |journal=Journal of Mineralogical and Petrological Sciences |volume=110 |issue=4 |pages=189–195 |bibcode=2015JMPeS.110..189O |doi=10.2465/jmps.141126 |s2cid=93672390|doi-access=free }}{{Citation |last=Frahm |first=Ellery |title=Scanning Electron Microscopy (SEM): Applications in Archaeology |date=2014 |encyclopedia=Encyclopedia of Global Archaeology |pages=6487–6495 |place=New York, New York |publisher=Springer New York |doi=10.1007/978-1-4419-0465-2_341 |isbn=978-1-4419-0426-3 }}

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.{{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 }} By combining EBSD and DIC, researchers can obtain both crystallographic and mechanical information about a material simultaneously.{{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 }} 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.{{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 }}

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.{{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 }} 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.{{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 }}{{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 }} 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.{{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 }} By correlating these data, researchers can better understand the role of different deformation mechanisms in the material's mechanical behaviour.{{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 }}

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.{{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 }}

File:3D EBSD.jpg-6%Co with 62 slices of 10×10×3 mm size and 50 nm resolution in x, y and z directions{{Cite journal |last1=Mingard |first1=K. P. |last2=Roebuck |first2=B. |last3=Jones |first3=H. G. |last4=Stewart |first4=M. |last5=Cox |first5=D. |last6=Gee |first6=M. G. |date=2018 |title=Visualisation and measurement of hardmetal microstructures in 3D |journal=International Journal of Refractory Metals and Hard Materials |volume=71 |pages=285–291 |doi=10.1016/j.ijrmhm.2017.11.023 }}|alt=3D EBSD map for WC-6%Co compiled from 62 slices after sectioning 10×10×3 mm size and 50 nm resolution in x, y and z directions]]

3D EBSD combines EBSD with serial sectioning methods to create a three-dimensional map of a material's crystallographic structure.{{Cite journal |last1=Lin |first1=F. X. |last2=Godfrey |first2=A. |last3=Jensen |first3=D. Juul |last4=Winther |first4=G. |date=2010 |title=3D EBSD characterization of deformation structures in commercial purity aluminum |journal=Materials Characterization |volume=61 |issue=11 |pages=1203–1210 |doi=10.1016/j.matchar.2010.07.013 }} The technique involves serially sectioning a sample into thin slices, and then using EBSD to map the crystallographic orientation of each slice.{{Cite journal |last1=Khorashadizadeh |first1=A. |last2=Raabe |first2=D. |last3=Zaefferer |first3=S. |last4=Rohrer |first4=G. S. |last5=Rollett |first5=A. D. |last6=Winning |first6=M. |date=2011 |title=Five-Parameter Grain Boundary Analysis by 3D EBSD of an Ultra Fine Grained CuZr Alloy Processed by Equal Channel Angular Pressing |journal=Advanced Engineering Materials |volume=13 |issue=4 |pages=237–244 |doi=10.1002/adem.201000259|s2cid=18389821 }} The resulting orientation maps are then combined to generate a 3D map of the crystallographic structure of the material. The serial sectioning can be performed using a variety of methods, including mechanical polishing,{{Cite journal |last1=Tsai |first1=Shao-Pu |last2=Konijnenberg |first2=Peter J. |last3=Gonzalez |first3=Ivan |last4=Hartke |first4=Samuel |last5=Griffiths |first5=Thomas A. |last6=Herbig |first6=Michael |last7=Kawano-Miyata |first7=Kaori |last8=Taniyama |first8=Akira |last9=Sano |first9=Naoyuki |last10=Zaefferer |first10=Stefan |date=2022 |title=Development of a new, fully automated system for electron backscatter diffraction (EBSD)-based large volume three-dimensional microstructure mapping using serial sectioning by mechanical polishing, and its application to the analysis of special boundaries in 316L stainless steel |journal=Review of Scientific Instruments |volume=93 |issue=9 |pages=093707 |doi=10.1063/5.0087945 |pmid=36182491 |bibcode=2022RScI...93i3707T |s2cid=252628156 |doi-access=free }} focused ion beam (FIB) milling,{{Cite journal |last1=Zaafarani |first1=N. |last2=Raabe |first2=D. |last3=Singh |first3=R. N. |last4=Roters |first4=F. |last5=Zaefferer |first5=S. |date=2006 |title=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 |journal=Acta Materialia |volume=54 |issue=7 |pages=1863–1876 |doi=10.1016/j.actamat.2005.12.014 |bibcode=2006AcMat..54.1863Z |hdl=11858/00-001M-0000-0019-5A14-4 |hdl-access=free }} or ultramicrotomy.{{Cite journal |last1=Hashimoto |first1=Teruo |last2=Thompson |first2=George E. |last3=Zhou |first3=Xiaorong |last4=Withers |first4=Philip J. |date=2016 |title=3D imaging by serial block face scanning electron microscopy for materials science using ultramicrotomy |journal=Ultramicroscopy |volume=163 |pages=6–18 |doi=10.1016/j.ultramic.2016.01.005 |pmid=26855205 |doi-access=free }} The choice of sectioning method depends on the size and shape of the sample, on its chemical composition, reactivity and mechanical properties, as well as the desired resolution and accuracy of the 3D map.{{Cite journal |last1=DeMott |first1=Ryan |last2=Haghdadi |first2=Nima |last3=Kong |first3=Charlie |last4=Gandomkar |first4=Ziba |last5=Kenney |first5=Matthew |last6=Collins |first6=Peter |last7=Primig |first7=Sophie |date=2021 |title=3D electron backscatter diffraction characterization of fine α titanium microstructures: collection, reconstruction, and analysis methods |journal=Ultramicroscopy |volume=230 |pages=113394 |doi=10.1016/j.ultramic.2021.113394 |pmid=34614440 |s2cid=238422160 |doi-access=free }}

3D EBSD has several advantages over traditional 2D EBSD. First, it provides a complete picture of a material's crystallographic structure, allowing for a more accurate and detailed analysis of the microstructure.{{Cite journal |last1=Konrad |first1=J. |last2=Zaefferer |first2=S. |last3=Raabe |first3=D. |date=2006 |title=Investigation of orientation gradients around a hard Laves particle in a warm-rolled Fe₃Al-based alloy using a 3D EBSD-FIB technique |journal=Acta Materialia |volume=54 |issue=5 |pages=1369–1380 |doi=10.1016/j.actamat.2005.11.015 |bibcode=2006AcMat..54.1369K |doi-access=free }} Second, it can be used to study complex microstructures, such as those found in composite materials or multi-phase alloys. Third, it can be used to study the evolution of microstructure over time, such as during deformation{{Cite journal |last1=Calcagnotto |first1=Marion |last2=Ponge |first2=Dirk |last3=Demir |first3=Eralp |last4=Raabe |first4=Dierk |date=2010 |title=Orientation gradients and geometrically necessary dislocations in ultrafine-grained dual-phase steels studied by 2D and 3D EBSD |journal=Materials Science and Engineering: A |volume=527 |issue=10 |pages=2738–2746 |doi=10.1016/j.msea.2010.01.004 }} or heat treatment.{{Cite journal |last1=Gholinia |first1=A. |last2=Brough |first2=I. |last3=Humphreys |first3=J. |last4=McDonald |first4=D. |last5=Bate |first5=P. |date=2010 |title=An investigation of dynamic recrystallisation on Cu–Sn bronze using 3D EBSD |journal=Materials Science and Technology |volume=26 |issue=6 |pages=685–690 |doi=10.1179/026708309X12547309760966 |bibcode=2010MatST..26..685G |s2cid=137530768}}

However, 3D EBSD also has some limitations. It requires extensive data acquisition and processing, proper alignment between slices, and can be time-consuming and computationally intensive.{{Cite journal |last=Pirgazi |first=Hadi |date=2019 |title=On the alignment of 3D EBSD data collected by serial sectioning technique |journal=Materials Characterization |volume=152 |pages=223–229 |doi=10.1016/j.matchar.2019.04.026 |s2cid=149835216 }} In addition, the quality of the 3D map depends on the quality of the individual EBSD maps, which can be affected by factors such as sample preparation, data acquisition parameters, and analysis methods.{{Cite journal |last1=Winiarski |first1=B. |last2=Gholinia |first2=A. |last3=Mingard |first3=K. |last4=Gee |first4=M. |last5=Thompson |first5=G. |last6=Withers |first6=P. J. |date=2021 |title=Correction of artefacts associated with large area EBSD |journal=Ultramicroscopy |volume=226 |pages=113315 |doi=10.1016/j.ultramic.2021.113315 |pmid=34049196 |s2cid=235241941 |doi-access=free }} Overall, 3D EBSD is a powerful technique for studying the crystallographic structure of materials in three dimensions, and is widely used in materials science and engineering research and development.{{Cite journal |last1=Konijnenberg |first1=P. J. |last2=Zaefferer |first2=S. |last3=Raabe |first3=D. |date=2015 |title=Assessment of geometrically necessary dislocation levels derived by 3D EBSD |journal=Acta Materialia |volume=99 |pages=402–414 |doi=10.1016/j.actamat.2015.06.051 |bibcode=2015AcMat..99..402K }}

{{reflist|group=note}}

{{Reflist}}

• {{Cite web |last= |title=Electron Backscatter Diffraction (EBSD) |url=https://www.doitpoms.ac.uk/tlplib/crystallographic_texture/ebsd.php |website=DoITPoMS|ref=none}}
• {{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}}
• {{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}}
• {{Cite web |last1=Zaefferer |first1=S. |last2=Raabe |first2=D. |author-link2=Dierk Raabe |last3=A. |first3=Khorashadizadeh |title=Tomographic orientation microscopy (3D EBSD) on steels using a joint FIB SEM technique |url=https://www.mpie.de/2991103/Tomographic_orientation_microscopy_3D_EBSD_on_steels |website=Max Planck Institute for Iron Research|ref=none}}

{{Commons}}

• {{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}}
• {{Cite journal |last1=Tong |first1=Vivian |first2=Ben |last2=Britton |date=July 2017 |title=TrueEBSD: correcting spatial distortions in electron backscatter diffraction maps |url=https://zenodo.org/record/4282885 |journal=Ultramicroscopy|volume=221 |page=113130 |author-link2=Ben Britton|doi=10.1016/j.ultramic.2020.113130|pmid=33290982 |arxiv=1909.00347 |s2cid=202538027 |ref=none}}

• {{Cite AV media |url=https://www.youtube.com/watch?v=BTx16E7YUbs |title=Introduction to EBSD: Section 1 - What can EBSD tell you? |date=2021-01-11 |last=Britton |first=Ben |publisher=YouTube|ref=none}}
• {{Cite AV media |url=https://www.youtube.com/watch?v=uHDvIwvqzDc |title=Learn How I Prepare Samples for EBSD Analysis |date=2022-02-22 |last=Nowell |first=Matt |publisher=EDAX (YouTube) |ref=none}}
• {{Cite AV media |url=https://www.youtube.com/watch?v=-0k4cnyQh-g |title=EBSD Analysis of Deformed Microstructures |date=2022-01-31 |last=Wright |first=Stuart |publisher=EDAX (YouTube)|ref=none}}
• {{Cite AV media |url=https://www.youtube.com/watch?v=TOGRtACDw7M&ab_channel=BrukerNanoAnalytics |title=Electron Backscatter Diffraction Explained: QUANTAX EBSD |date=2020-09-01 |publisher=Bruker Nano Analytics (YouTube)|ref=none}}

{{Electron microscopy}}

{{DEFAULTSORT:Electron backscatter diffraction}}

Category:Diffraction

Category:Scientific techniques

Category:Spectroscopy

Category:Scattering