Electron backscatter diffraction: Difference between revisions

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=== Precision and development ===

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.<ref name=":6" /><ref name=":7">{{Cite journal |last1=Plancher |first1=E. |last2=Petit |first2=J. |last3=Maurice |first3=C. |last4=Favier |first4=V. |last5=Saintoyant |first5=L. |last6=Loisnard |first6=D. |last7=Rupin |first7=N. |last8=Marijon |first8=J.-B. |last9=Ulrich |first9=O. |last10=Bornert |first10=M. |last11=Micha |first11=J.-S. |last12=Robach |first12=O. |last13=Castelnau |first13=O. |date=2016-03-01 |title=On the Accuracy of Elastic Strain Field Measurements by Laue Microdiffraction and High-Resolution EBSD: a Cross-Validation Experiment |journal=Experimental Mechanics |volume=56 |issue=3 |pages=483–492 |doi=10.1007/s11340-015-0114-1 |s2cid=255157494 |url=https://hal.archives-ouvertes.fr/hal-02141119/file/PIMM%20-%20EM%20-%20PLANCHER%20-%202016.pdf |access-date=20 March 2023 |archive-date=13 March 2020 |archive-url=https://web.archive.org/web/20200313042805/https://hal.archives-ouvertes.fr/hal-02141119/file/PIMM%20-%20EM%20-%20PLANCHER%20-%202016.pdf |url-status=live }}</ref> It was limited to small strains and rotations (>1.5°) until [[Ben Britton|Britton]] and Wilkinson<ref name=":5" /> & Maurice et al. raised the rotation limit to ~11° by using a re-mapping technique<ref>{{Cite journal |last1=Maurice |first1=Claire |last2=Driver |first2=Julian H. |last3=Fortunier |first3=Roland |date=2012 |title=On solving the orientation gradient dependency of high angular resolution EBSD |journal=Ultramicroscopy |volume=113 |pages=171–181 |doi=10.1016/j.ultramic.2011.10.013 }}</ref> raised the rotation limit to ~11° by using a re-mapping technique that recalculated the strain after transforming the patterns with a rotation matrix (<math>R</math>) calculated from the first cross-correlation iteration.<ref name=":10" />

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