Electron backscatter diffraction: Difference between revisions

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{{Use British English|date=March 2023}}

[[File:EBSD Si.png|thumb|An electron backscatter diffraction pattern of [[monocrystalline silicon]], taken at 20 kV with a [[Field electron emission|field-emission]] electron source|alt=An electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source. The Kikuchi bands intersect at the centre of the image ]]

'''Electron backscatter diffraction''' ('''EBSD''') is a [[scanning electron microscopy]] (SEM) technique used to study the [[Crystallography|crystallographic]] structure of materials. EBSD is carried out in a scanning electron microscope equipped with an EBSD detector comprising at least a [[Phosphorescence|phosphorescent]] screen, a compact lens and a low-light [[Charge-coupled device|camera]]. In this configuration, the SEMmicroscope an incident beam of electrons hits thea tilted sample. As backscattered electrons leave the sample, they interact with the crystal's periodic atomic lattice planesatoms and diffractare accordingboth toelastically [[Bragg'sElectron lawdiffraction|diffracted]] and lose energy, leaving the sample at various scattering angles before reaching the phosphor screen forming [[Kikuchi lines (physics)|Kikuchi patterns]] (EBSPs). The EBSD spatial resolution depends on many factors, including the nature of the material under study and the sample preparation. Thus, EBSPsThey can be indexed to provide information about the material's grain [[Crystal structure|structure]], grain [[Electron crystallography|orientation]], and [[Phase (matter)|phase]] at the micro-scale. EBSD is appliedused for impurities and [[Crystallographic defect|defect studies]], [[Plasticity (physics)|plastic deformation]], and statistical analysis for average [[misorientation]], [[Grain boundary|grain]] size, and crystallographic texture. EBSD can also be combined with [[energy-dispersive X-ray spectroscopy]] (EDS), [[cathodoluminescence]] (CL), and [[wavelength dispersive X-ray spectroscopy|wavelength-dispersive X-ray spectroscopy]] (WDS) for advanced [[Phase-change material|phase identification]] and materials discovery.

The change and degradationsharpness inof the electron backscatter patterns (EBSPs) provide information about [[Deformation (physics)|lattice distortion]] in the diffracting volume. Pattern degradation (i.e., diffuse quality)sharpness can be used to assess the level of plasticity. Changes in the EBSP zone axis position can be used to measure the [[residual stress]] and small lattice rotations. EBSD can also provide information about the density of [[geometrically necessary dislocations]] (GNDs). However, the lattice distortion is measured relative to a reference pattern (EBSP₀). The choice of reference pattern affects the measurement precision; e.g., a reference pattern deformed in tension will directly reduce the tensile strain magnitude derived from a high-resolution map while indirectly influencing the magnitude of other components and the spatial distribution of strain. Furthermore, the choice of EBSP₀ slightly affects the GND density distribution and magnitude.<ref name=":10" />

==Pattern formation and collection==

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

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

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

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 made of a phosphor screen that is excited by the backscattered electrons.<ref name=":45" /> The screen is coupled to lens which focuses the image from the phosphor screen onto thea [[Chargecharge-coupled device]] (CCD) or c[[CMOS|Complementaryomplementary metal–oxide–semiconductor]] (CMOS) camera.<ref>{{Cite journal |last1=Goulden |first1=J. |last2=Trimby |first2=P. |last3=Bewick |first3=A. |date=2018-08-01 |title=The Benefits and Applications of a CMOS-based EBSD Detector |journal=Microscopy and Microanalysis |volume=24 |issue=S1 |pages=1128–1129 |doi=10.1017/s1431927618006128 |bibcode=2018MiMic..24S1128G |s2cid=139967518 |doi-access=free }}</ref>

In this configuration, as thesethe backscattered electrons leave the sample, they interact with the crystal's[[Electric periodicpotential|Coulomb atomicpotential]] latticeand planesalso andlose diffractenergy accordingdue to [[Bragg'sinelastic lawscattering]] atleading to a range of scattering angles (θ_hkl).<ref name=":45">{{Citation |last=Randle |first=Valerie |title=Theoretical Framework for Electron Backscatter Diffraction |date=2000 |work=Electron Backscatter Diffraction in Materials Science |pages=19–30 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |publisher=Springer US |doi=10.1007/978-1-4757-3205-4_2 |isbn=978-1-4757-3205-4 |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. }}</ref><ref name=":19">{{Citation |last1=Eades |first1=Alwyn |title=Energy Filtering in EBSD |date=2009 |work=Electron Backscatter Diffraction in Materials Science |pages=53–63 |editor-last=Schwartz |editor-first=Adam J. |place=Boston, MA |doi=10.1007/978-0-387-88136-2_4 |isbn=978-0-387-88136-2 |last2=Deal |first2=Andrew |last3=Bhattacharyya |first3=Abhishek |last4=Hooghan |first4=Tejpal |editor2-last=Kumar |editor2-first=Mukul |editor3-last=Adams |editor3-first=Brent L. |editor4-last=Field |editor4-first=David P. }}</ref> The backscattered electrons form [[Kikuchi lines (physics)|Kikuchi lines]] – having different intensities – on an electron-sensitive flat film/screen (commonly phosphor), gathered to form a Kikuchi band. These Kikuchi lines are the trace of a hyperbola formed by the intersection of [[Walther Kossel|Kossel]] cones with the plane of the phosphor screen. The width of a Kikuchi band is related to the scattering angles and, thus, to the distance d_hkl between lattice planes with Miller indexes h, k, and l.<ref name=":20">{{Cite journal |last1=Wilkinson |first1=Angus J. |last2=Britton |first2=T. Ben. |date=2012 |title=Strains, planes, and EBSD in materials science |journal=Materials Today |volume=15 |issue=9 |pages=366–376 |doi=10.1016/S1369-7021(12)70163-3 |doi-access=free }}</ref><ref>{{Cite journal |last1=Sawatzki |first1=Simon |last2=Woodcock |first2=Thomas G. |last3=Güth |first3=Konrad |last4=Müller |first4=Karl-Hartmut |last5=Gutfleisch |first5=Oliver |date=2015 |title=Calculation of remanence and degree of texture from EBSD orientation histograms and XRD rocking curves in Nd–Fe–B sintered magnets |journal=Journal of Magnetism and Magnetic Materials |volume=382 |pages=219–224 |doi=10.1016/j.jmmm.2015.01.046 |bibcode=2015JMMM..382..219S }}</ref> These Kikuchi lines and patterns were named after [[Seishi Kikuchi]], who, together with {{interlanguage link|Shoji Nishikawa|ja|西川正治}}, was the first to notice this diffraction pattern in 1928 using [[transmission electron microscopy]] (TEM)<ref>{{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}}</ref> which is similar in geometry to X-ray Kossel pattern.<ref>{{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 }}</ref><ref>{{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}}</ref>

The systematically arranged Kikuchi bands, which have a range of intensity along their width, intersect around the centre of the regions of interest (ROI), describing the probed volume crystallography.<ref>{{Cite journal |date=1954|title=High-angle Kikuchi patterns |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |volume=221 |issue=1145 |pages=224–242 |doi=10.1098/rspa.1954.0017 |bibcode=1954RSPSA.221..224A |last1=Alam |first1=M. N. |last2=Blackman |first2=M. |last3=Pashley |first3=D. W. |s2cid=97131764 }}</ref> These bands and their intersections form what is known as Kikuchi patterns or electron backscatter patterns (EBSPs). To improve contrast, the patterns’ background is corrected by removing anisotropic/inelastic scattering using static background correction or dynamic background correction.<ref>{{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 }}</ref>

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Inside the SEM, the size of the measurement area determines local resolution and measurement time.<ref>{{Cite book |last=Williams |first=B. David |title=Transmission electron microscopy: a textbook for materials science. |date=2009 |publisher=Plenum Press |isbn=978-0-387-76501-3 |pages=11 |oclc=633626308}}</ref> Usual settings for high-quality EBSPs are 15 nA current, 20 kV beam energy, 18 mm working distance, long exposure time, and minimal CCD pixel binning.<ref>{{Cite journal |last1=Britton |first1=T.B. |last2=Jiang |first2=J. |last3=Clough |first3=R. |last4=Tarleton |first4=E. |last5=Kirkland |first5=A.I. |last6=Wilkinson |first6=A.J. |date=2013 |title=Assessing the precision of strain measurements using electron backscatter diffraction – Part 2: Experimental demonstration |journal=Ultramicroscopy |volume=135 |pages=136–141 |doi=10.1016/j.ultramic.2013.08.006 |pmid=24034981 }}</ref><ref>{{Cite journal |last1=Jiang |first1=J. |last2=Britton |first2=T.B. |last3=Wilkinson |first3=A.J. |date=2013 |title=Evolution of dislocation density distributions in copper during tensile deformation |journal=Acta Materialia |volume=61 |issue=19 |pages=7227–7239 |doi=10.1016/j.actamat.2013.08.027 |bibcode=2013AcMat..61.7227J|doi-access=free }}</ref><ref>{{Cite journal |last1=Abdolvand |first1=Hamidreza |last2=Wilkinson |first2=Angus J. |date=2016|title=On the effects of reorientation and shear transfer during twin formation: Comparison between high-resolution electron backscatter diffraction experiments and a crystal plasticity finite element model |journal=International Journal of Plasticity |volume=84 |pages=160–182 |doi=10.1016/j.ijplas.2016.05.006 |s2cid=139049848|doi-access=free }}</ref><ref name=":29">{{Cite journal |last1=Koko |first1=Abdalrhaman |last2=Becker |first2=Thorsten H. |last3=Elmukashfi |first3=Elsiddig |last4=Pugno |first4=Nicola M. |last5=Wilkinson |first5=Angus J. |last6=Marrow |first6=T. James |date=2023 |title=HR-EBSD analysis of in situ stable crack growth at the micron scale |journal=Journal of the Mechanics and Physics of Solids |volume=172 |pages=105173 |arxiv=2206.10243 |bibcode=2023JMPSo.17205173K |doi=10.1016/j.jmps.2022.105173 |s2cid=249889649 }}</ref> The EBSD phosphor screen is set at an 18&nbsp;mm working distance and a map's step size of less than 0.5&nbsp;µm for [[Infinitesimal strain theory|strain]] and [[Geometrically necessary dislocations|dislocations density]] analysis.<ref name=":30" /><ref name=":31" />

Decomposition of gaseous hydrocarbons and also hydrocarbons on the surface of samples by the electron beam inside the microscope results in carbon deposition,<ref>{{Cite journal |last1=Griffiths |first1=A J V |last2=Walther |first2=T |date=2010 |title=Quantification of carbon contamination under electron beam irradiation in a scanning transmission electron microscope and its suppression by plasma cleaning |journal=Journal of Physics: Conference Series |volume=241 |issue=1 |pages=012017 |bibcode=2010JPhCS.241a2017G |doi=10.1088/1742-6596/241/1/012017 |s2cid=250689401|doi-access=free }}</ref> which degrades the quality of EBSPs inside the probed area compared to the EBSPs outside the acquisition window. The gradient of pattern degradation increases moving inside the probed zone with an apparent accumulation of deposited carbon. The black spots from the beam instant-induced carbon deposition also highlight the immediate deposition even if agglomeration did not happen.<ref name=":4">{{Cite journal |last1=Koko |first1=Abdalrhaman |last2=Elmukashfi |first2=Elsiddig |last3=Dragnevski |first3=Kalin |last4=Wilkinson |first4=Angus J. |last5=Marrow |first5=Thomas James |date=2021 |title=J-integral analysis of the elastic strain fields of ferrite deformation twins using electron backscatter diffraction |journal=Acta Materialia |volume=218 |pages=117203 |bibcode=2021AcMat.21817203K |doi=10.1016/j.actamat.2021.117203 |url=https://ora.ox.ac.uk/objects/uuid:4071edea-3bfc-4d2b-8d32-c3b05bd73372 |access-date=20 March 2023 |archive-date=5 July 2022 |archive-url=https://web.archive.org/web/20220705095819/https://ora.ox.ac.uk/objects/uuid:4071edea-3bfc-4d2b-8d32-c3b05bd73372 |url-status=live }}</ref><ref name=":12">{{Cite journal |last1=Bachmann |first1=F. |last2=Hielscher |first2=Ralf |last3=Schaeben |first3=Helmut |date=2010 |title=Texture Analysis with MTEX – Free and Open Source Software Toolbox |journal=Solid State Phenomena |volume=160 |pages=63–68 |doi=10.4028/www.scientific.net/SSP.160.63 |s2cid=136017346}}</ref>

=== Depth resolution ===

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

[[Monte Carlo method|Monte Carlo]] simulations provide an alternative approach to quantifying the depth resolution for EBSPs formation, which can be estimated using the [[Bloch's theorem|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.<ref>{{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 }}</ref> The backscattered electrons (BSE) energy distribution depends on the material's characteristics and the beam conditions.<ref>{{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}}</ref> This BSE wave field is also affected by the thermal diffuse scattering process that causes incoherent and inelastic (energy loss) scattering – after the Braggelastic diffraction events – which does not, yet, have a complete physical description that can be related to mechanisms that constitute EBSP depth resolution.<ref>{{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}}</ref><ref name=":26">{{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.}}</ref>

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.<ref name=":27" />

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These measurements do not provide information about the hydrostatic or [[volumetric strain]]s,<ref name=":5" /><ref name=":6" /> 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.<ref name="EBSD Image Quality Mapping">{{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 }}</ref><ref>{{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 }}</ref>

=== The reference pattern problem ===

Nonetheless, inIn HR-EBSD analysis, the lattice distortion field is still 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.<ref name=":8">{{Cite journal |last1=Maurice |first1=Claire |last2=Fortunier |first2=Roland |last3=Driver |first3=Julian |last4=Day |first4=Austin |last5=Mingard |first5=Ken |last6=Meaden |first6=Graham |date=2010 |title=Comments on the paper "Bragg's law diffraction simulations for electron backscatter diffraction analysis" by Josh Kacher, Colin Landon, Brent L. Adams & David Fullwood |journal=Ultramicroscopy |volume=110 |issue=7 |pages=758–759 |doi=10.1016/j.ultramic.2010.02.003 |pmid=20223590 }}</ref><ref name=":9">{{Cite journal |last1=Mikami |first1=Yoshiki |last2=Oda |first2=Kazuo |last3=Kamaya |first3=Masayuki |last4=Mochizuki |first4=Masahito |date=2015 |title=Effect of reference point selection on microscopic stress measurement using EBSD |journal=Materials Science and Engineering: A |volume=647 |pages=256–264 |doi=10.1016/j.msea.2015.09.004}}</ref> This ‘reference pattern problem’ is similar to the ‘d₀ problem’ in X-ray diffraction,<ref name=":20" /><ref>{{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 }}</ref> 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.<ref name=":8" />[[File:Linear correlation coefficients between the local conditions at the EBSP0 point and the averaged conditions.svg|thumb|Linear correlation coefficients between the local conditions at the EBSP0 point and the averaged conditions at the grain for the [[Ferrite (magnet)|ferrite]] (Fe-α) and [[austenite]] (Fe-γ) phase of [[age-hardened DSS]], and [[Silicon]] (Si). The analysis considers the average deformation gradient tensor determinant (<math>A^{0}</math>), maximum in-plane principal strain (<math>\epsilon_{MAX}</math>), rotation magnitude (<math>\omega_{T}=\sqrt(\omega_{32}^2+\omega_{13}^2+\omega_{21}^2)</math>), correlation peak height (PH), mean angular error (MAE) and GND density.<ref name=":10" />|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.<ref name=":10" />