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Mitch Ames (talk | contribs) m Remove space before ref, footnote, per MOS:REFSPACE |
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<math>R=\begin{pmatrix} \cos \omega_{12} & \sin \omega_{12} & 0 \\ -\sin \omega_{12} & \cos \omega_{12} & 0\\ 0 & 0& 1 \end{pmatrix} \begin{pmatrix} 1&0&0\\0&\cos \omega_{23} & \sin \omega_{23} \\ 0&-\sin \omega_{23} & \cos \omega_{23} \end{pmatrix} \begin{pmatrix} \cos \omega_{31} &0& -\sin \omega_{31} \\ 0 & 1& 0 \\ \sin \omega_{31}&0 & \cos \omega_{31} \end{pmatrix}</math>
{{Wide image|Indent Si.tif|800|(a) Secondary electron (SE) image for the indentation on the (001) mono crystal. (b) HR-EBSD stress and rotation components, and geometrical necessary dislocations density (<math>\rho_{GND}</math>). The ___location of EBSP<sub>0</sub> is highlighted with a star in <math>\sigma_{yz}</math>. The step size is 250 nm
However, further lattice rotation, typically caused by severe plastic deformations, produced errors in the elastic strain calculations. To address this problem, Ruggles ''et al.''<ref>{{Cite journal |last1=Ruggles |first1=T. J. |last2=Bomarito |first2=G. F. |last3=Qiu |first3=R. L. |last4=Hochhalter |first4=J. D. |date=2018-12-01 |title=New levels of high angular resolution EBSD performance via inverse compositional Gauss–Newton based digital image correlation |journal=Ultramicroscopy |volume=195 |pages=85–92 |doi=10.1016/j.ultramic.2018.08.020 |pmc=7780544 |pmid=30216795}}</ref> improved the HR-EBSD precision, even at 12° of lattice rotation, using the inverse compositional Gauss–Newton-based (ICGN) method instead of cross-correlation. For simulated patterns, Vermeij and Hoefnagels<ref>{{Cite journal |last1=Vermeij |first1=T. |last2=Hoefnagels |first2=J. P. M. |date=2018 |title=A consistent full-field integrated DIC framework for HR-EBSD |journal=Ultramicroscopy |volume=191 |pages=44–50 |doi=10.1016/j.ultramic.2018.05.001 |pmid=29772417 |s2cid=21685690 |url=https://pure.tue.nl/ws/files/101858753/Manuscript_HR_EBSD_Vermeij_Hoefnagels.pdf |access-date=20 March 2023 |archive-date=16 July 2021 |archive-url=https://web.archive.org/web/20210716043300/https://pure.tue.nl/ws/files/101858753/Manuscript_HR_EBSD_Vermeij_Hoefnagels.pdf |url-status=live }}</ref> also established a method that achieves a precision of ±10<sup>−5</sup> in the displacement gradient components using a full-field integrated [[Digital image correlation and tracking|digital image correlation]] (IDIC) framework instead of dividing the EBSPs into small ROIs. Patterns in IDIC are distortion-corrected to negate the need for re-mapping up to ~14°.<ref>{{Cite journal |last1=Ernould |first1=Clément |last2=Beausir |first2=Benoît |last3=Fundenberger |first3=Jean-Jacques |last4=Taupin |first4=Vincent |last5=Bouzy |first5=Emmanuel |date=2021 |title=Integrated correction of optical distortions for global HR-EBSD techniques |journal=Ultramicroscopy |volume=221 |pages=113158 |doi=10.1016/j.ultramic.2020.113158 |pmid=33338818 |s2cid=228997006 |doi-access=free }}</ref><ref>{{Cite journal |last1=Shi |first1=Qiwei |last2=Loisnard |first2=Dominique |last3=Dan |first3=Chengyi |last4=Zhang |first4=Fengguo |last5=Zhong |first5=Hongru |last6=Li |first6=Han |last7=Li |first7=Yuda |last8=Chen |first8=Zhe |last9=Wang |first9=Haowei |last10=Roux |first10=Stéphane |date=2021 |title=Calibration of crystal orientation and pattern center of EBSD using integrated digital image correlation |journal=Materials Characterization |volume=178 |pages=111206 |doi=10.1016/j.matchar.2021.111206 |s2cid=236241507 |url=https://hal.archives-ouvertes.fr/hal-03652308/file/calibrationMC_final.pdf |access-date=20 March 2023 |archive-date=25 March 2023 |archive-url=https://web.archive.org/web/20230325200435/https://hal.science/hal-03652308/file/calibrationMC_final.pdf |url-status=live }}</ref>
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