Dark-field X-ray microscopy

Dark-field X-ray microscopy (DFXM[1] or DFXRM[2]) is an imaging technique used for multiscale structural characterisation. It is capable of mapping deeply embedded structural elements with nm-resolution using synchrotron X-ray diffraction-based imaging. The technique works by using scattered X-rays to create a high degree of contrast, and by measuring the intensity and spatial distribution of the diffracted beams, it is possible to obtain a three-dimensional map of the sample's structure, orientation, and local strain.

History

The first experimental demonstration of dark-field X-ray microscopy was reported in 2006 by a group at the European Synchrotron Radiation Facility in Grenoble, France. Since then, the technique has been rapidly evolving and has shown great promise in multiscale structural characterization.[1] Its development is largely due to advances in synchrotron X-ray sources, which provide highly collimated and intense beams of X-rays. The development of dark-field X-ray microscopy has been driven by the need for non-destructive imaging of bulk crystalline samples at high resolution, and it continues to be an active area of research today. However, dark-field microscopy,[3][4] dark-field scanning transmission X-ray microscopy,[5] and soft dark-field X-ray microscopy[6] has long been used to map deeply embedded structural elements.

Principles and instrumentation

A monochromatic beam from a synchrotron source illuminates the sample. Objective is the objective lens and Detector is the 2D area detector[1][7]

In this technique, a synchrotron light source is used to generate an intense and coherent X-ray beam, which is then focused onto the sample using a specialized objective lens. The objective lens acts as a collimator to select and focus the scattered light, which is then detected by the 2D detector to create a diffraction pattern.[1] The specialized objective lens in DFXM, referred to as an X-ray objective lens, is a crucial component of the instrumentation required for the technique. It can be made from different materials such as beryllium, silicon, and diamond, depending on the specific requirements of the experiment.[8] The objective enables one to enlarge or reduce the spatial resolution and field of view within the sample by varying the number of individual lenses and adjusting ${\displaystyle p'}$ and ${\displaystyle q'}$ (as in the figure) correspondingly. The diffraction angle ${\displaystyle 2\theta }$ is typically 10–30°.[9][10]

The sample is positioned at an angle such that the direct beam is blocked by a beam stop or aperture, and the diffracted beams from the sample are allowed to pass through a detector.[11]

An embedded crystalline element (for example, a grain or domain) of choice (green) is aligned such that the detector is positioned at a Bragg angle that corresponds to a particular diffraction peak of interest, which is determined by the crystal structure of the sample. The objective magnifies the diffracted beam by a factor ${\displaystyle M=q'/p'}$ and generates an inverted 2D projection of the grain. Through repeated exposures during a 360° rotation of the element around an axis parallel to the diffraction vector, ${\displaystyle G}$, several 2D projections of the grain are obtained from various angles.[12] A 3D map is then obtained by combining these projections using reconstruction algorithms[13] similar to those developed for CT scanning. If the lattice of the crystalline element exhibits an internal orientation spread, this procedure is repeated for a number of sample tilts, indicated by the angles ${\displaystyle \alpha }$ and ${\displaystyle \beta }$.[1]

The current implementation of DFXM at ID06, ESRF, uses a compound refractive lens (CRL) as the objective, giving spatial resolution of 100 nm and angular resolution of 0.001°.[14][15]

Applications, limitations and alternatives

Current and potential applications

Multiscale mapping of 10% tensile deformed aluminium. (a) Part of the X-ray mapping of all grains in the specimen. (b) Zooming in on one embedded grain and mapping the intrinsic variation in orientation. A vertical section through the grain is shown for ease of inspection of the spatial heterogeneity. (c) Condensing the incoming beam vertically defines a sub-micron layer within the grain. Below: The corresponding keys for the orientation maps[1]

DFXM has been used for the non-destructive investigation of polycrystalline materials and composites, revealing the 3D microstructure,[16] phases,[17] orientation of individual grains,[18][19] and local strains.[20][21] It has also been used for in situ studies of materials recrystallisation,[22] dislocations[23][24] and other defects, and the deformation[20] and fracture mechanisms in materials, such as metals[11] and composites.[25] DFXM can provide insights into the 3D microstructure and deformation of geological materials such as minerals and rocks,[1] and irradiated materials.[26]

DFXM has the potential to revolutionise the field of nanotechnology by providing non-destructive, high-resolution 3D imaging of nanostructures and nanomaterials. It has been used to investigate the 3D morphology of nanowires and to detect structural defects in nanotubes.[27][28]

DFXM has shown potential for imaging biological tissues and organs with high contrast and resolution. It has been used to visualize the 3D microstructure of cartilage and bone, as well as to detect early-stage breast cancer in mouse model.[1][29]

Limitations

The intense X-ray beams used in DFXM can damage delicate samples, particularly biological specimens.[1] DFXM can suffer from imaging artefacts such as ring artefacts, which can affect image quality and limit interpretation.[11]

The instrumentation required for DFXM is expensive and typically only available at synchrotron facilities, making it inaccessible to many researchers. Although DFXM can achieve high spatial resolution, it is still not as high as the resolution achieved by other imaging techniques such as transmission electron microscopy (TEM) or X-ray crystallography.[11]

Preparation of samples for DFXM imaging can be challenging, especially for samples that are not crystalline. There are also limitations on the sample size that can be imaged as the technique works best with thin samples, typically less than 100 microns thick, due to the attenuation of the X-ray beam by thicker samples.[1] DFXM still suffers from long integration times, which can limit its practical applications. This is due to the low flux density of X-rays emitted by synchrotron sources and the high sensitivity required to detect scattered X-rays.[11]

Alternatives

There are several alternative techniques to DFXM, depending on the application, some of which are:

• Differential-aperture X-ray structural microscopy (DAXM): DAXM is a synchrotron X-ray method capable of delivering precise information about the local structure and crystallographic orientation in three dimensions at a spatial resolution of less than one micron.[30] It also provides angular precision and local elastic strain with high accuracy a wide range of materials, including single crystals, polycrystals, composites, and materials with varying properties.[31]
• Bragg Coherent diffraction imaging (BCDI): BCDI is an advanced microscopy technique introduced in 2006 to study crystalline nanomaterials' 3D structure. BCDI has applications in diverse areas, including in situ studies of corrosion, probing dissolution processes, and simulating diffraction patterns to understand atomic displacement.[32][33][34]
• Ptychography is a computational imaging method used in microscopy to generate images by processing multiple coherent interference patterns. It provides advantages such as high-resolution imaging, phase retrieval, and lensless imaging capabilities.[35][36][37]
• Diffraction Contrast Tomography (DCT): DCT is a method that uses coherent X-rays to generate three-dimensional grain maps of polycrystalline materials. DCT enables visualization of crystallographic information within samples, aiding in the analysis of materials' structural properties, defects, and grain orientations.[38][39]
• Three-dimensional X-ray diffraction (3DXRD): 3DXRD is a synchrotron-based technique that provides information about the crystallographic orientation of individual grains in polycrystalline materials. It can be used to study the evolution of microstructure during deformation and recrystallization processes and provides submicron resolution.[40]
• Electron backscatter diffraction (EBSD): EBSD is a scanning electron microscopy (SEM) technique that can be used to map - the sample surface - crystallographic orientation and strain[41] at the submicron scale. It works by detecting the diffraction pattern of backscattered electrons, which provides information about the crystal structure of the material.[42] EBSD can be used on a variety of materials, including metals, ceramics, and semiconductors, and can be extended to the third dimension, i.e., 3D EBSD,[43] and can be combined with Digital image correlation, i.e., EBSD-DIC.[44]
• Digital image correlation (DIC): DIC is a non-contact optical method used to measure the displacement and deformation of a material by analysing the digital images captured before and after the application of load. This technique can measure strain with sub-pixel accuracy and is widely used in materials science and engineering.[45]
• Transmission electron microscopy (TEM): TEM is a high-resolution imaging technique that provides information about the microstructure and crystallographic orientation of materials. It can be used to study the evolution of microstructure during deformation and recrystallization processes and provides submicron resolution.[46]
• Micro-Raman spectroscopy: Micro-Raman spectroscopy is a non-destructive technique that can be used to measure the strain of a material at the submicron scale. It works by illuminating a sample with a laser beam and analysing the scattered light. The frequency shift of the scattered light provides information about the crystal deformation, and thus the strain of the material.[47]
• Neutron diffraction: Neutron diffraction is a technique that uses a beam of neutrons to study the structure of materials. It is particularly useful for studying the crystal structure and magnetic properties of materials. Neutron diffraction can provide sub-micron resolution.[48]

References

1. Simons, H.; King, A.; Ludwig, W.; Detlefs, C.; Pantleon, W.; Schmidt, S.; Stöhr, F.; Snigireva, I.; Snigirev, A.; Poulsen, H. F. (14 January 2015). "Dark-field X-ray microscopy for multiscale structural characterization". Nature Communications. 6 (1): 6098. Bibcode:2015NatCo...6.6098S. doi:10.1038/ncomms7098. ISSN 2041-1723. PMC 4354092. PMID 25586429. This article incorporates text from this source, which is available under the CC BY 4.0 license.
2. Simons, Hugh; Ahl, Sonja Rosenlund; Jakobsen, Anders Clemen; Yildirim, Can; Cook, Phil K.; Detlefs, Carsten; Poulsen, Henning Friis (1 August 2018). "Multi-Scale 3D Imaging of Strain and Structure with Dark-Field X-Ray Microscopy". Microscopy and Microanalysis. 24 (S2): 72–75. Bibcode:2018MiMic..24S..72S. doi:10.1017/s1431927618012758. ISSN 1431-9276. S2CID 139864737.
3. Chapman, Henry N; Fu, Jenny; Jacobsen, Chris; Williams, Shawn (31 July 2003). "Dark-Field X-Ray Microscopy of Immunogold-Labeled Cells". Microscopy and Microanalysis. 2 (2): 53–62. doi:10.1017/S1431927696210530. S2CID 138065437.
4. Vogt, S.; Chapman, H. N.; Jacobsen, C.; Medenwaldt, R. (1 March 2001). "Dark field X-ray microscopy: the effects of condenser/detector aperture". Ultramicroscopy. 87 (1): 25–44. doi:10.1016/S0304-3991(00)00065-6. ISSN 0304-3991. PMID 11310539.
5. Chapman, Henry N.; Williams, Shawn; Jacobsen, Chris (1 December 1994). Bailey, G.W.; Garratt-Reed, A.J. (eds.). "Imaging of 30 nm gold spheres by dark-field scanning transmission x-ray microscopy: Proceedings of the 52nd Annual Meeting of the Microscopy Society of America". Proceedings - Annual Meeting, Microscopy Society of America: 52–53. doi:10.1017/S0424820100167998.
6. Pfauntsch, S. J; Michette, A. G; Buckley, C. J (15 February 1996). "Toroidal condenser optics for dark-field X-ray microscopy". Optics Communications. 124 (1): 141–149. Bibcode:1996OptCo.124..141P. doi:10.1016/0030-4018(95)00672-9. ISSN 0030-4018.
7. Simons, Hugh; Jakobsen, Anders Clemen; Ahl, Sonja Rosenlund; Detlefs, Carsten; Poulsen, Henning Friis (1 June 2016). "Multiscale 3D characterization with dark-field x-ray microscopy". MRS Bulletin. 41 (6): 454–459. Bibcode:2016MRSBu..41..454S. doi:10.1557/mrs.2016.114. ISSN 1938-1425. S2CID 263278153.
8. Ando, Masami; Gupta, Rajiv; Iwakoshi, Akari; Kim, Jong-Ki; Shimao, Daisuke; Sugiyama, Hiroshi; Sunaguchi, Naoki; Yuasa, Tetsuya; Ichihara, Shu (November 2020). "X-ray dark-field phase-contrast imaging: Origins of the concept to practical implementation and applications". Physica Medica. 79: 188–208. doi:10.1016/j.ejmp.2020.11.034. ISSN 1724-191X. PMID 33342666. S2CID 229343273.
9. Vaughan, G. B. M.; Wright, J. P.; Bytchkov, A.; Rossat, M.; Gleyzolle, H.; Snigireva, I.; Snigirev, A. (1 March 2011). "X-ray transfocators: focusing devices based on compound refractive lenses". Journal of Synchrotron Radiation. 18 (2): 125–133. Bibcode:2011JSynR..18..125V. doi:10.1107/S0909049510044365. ISSN 0909-0495. PMC 3267637. PMID 21335897.
10. Snigirev, A.; Kohn, V.; Snigireva, I.; Lengeler, B. (November 1996). "A compound refractive lens for focusing high-energy X-rays". Nature. 384 (6604): 49–51. Bibcode:1996Natur.384...49S. doi:10.1038/384049a0. ISSN 1476-4687. S2CID 4229340.
11. Dresselhaus-Marais, Leora E.; Kozioziemski, Bernard; Holstad, Theodor S.; Ræder, Trygve Magnus; Seaberg, Matthew; Nam, Daewoong; Kim, Sangsoo; Breckling, Sean; Chollet, Matthieu; Cook, Philip K.; Folsom, Eric; Galtier, Eric; Gavilan, Lisseth; Gonzalez, Arnulfo; Gorhover, Tais (2023). "Simultaneous bright- and dark-field X-ray microscopy at X-ray free electron lasers". Scientific Reports. 13 (1): 17573. arXiv:2210.08366. Bibcode:2023NatSR..1317573D. doi:10.1038/s41598-023-35526-5. PMC 10579415. PMID 37845245.
12. Ludwig, W.; Cloetens, P.; Härtwig, J.; Baruchel, J.; Hamelin, B.; Bastie, P. (1 October 2001). "Three-dimensional imaging of crystal defects by 'topo-tomography'". Journal of Applied Crystallography. 34 (5): 602–607. Bibcode:2001JApCr..34..602L. doi:10.1107/S002188980101086X. ISSN 0021-8898.
13. Ferrer, Júlia Garriga; Rodríguez-Lamas, Raquel; Payno, Henri; De Nolf, Wout; Cook, Phil; Jover, Vicente Armando Solé; Favre-Nicolin, Vincent; Yıldırım, Can; Detlefs, Carsten (11 May 2022). "darfix: Data analysis for dark-field X-ray microscopy". Journal of Synchrotron Radiation. 30 (3): 527–537. arXiv:2205.05494. Bibcode:2023JSynR..30..527G. doi:10.1107/S1600577523001674. PMC 10161887. PMID 37000183.
14. Kutsal, M; Bernard, P; Berruyer, G; Cook, P K; Hino, R; Jakobsen, A C; Ludwig, W; Ormstrup, J; Roth, T; Simons, H; Smets, K; Sierra, J X; Wade, J; Wattecamps, P; Yildirim, C (1 August 2019). "The ESRF dark-field x-ray microscope at ID06". IOP Conference Series: Materials Science and Engineering. 580 (1): 012007. arXiv:2410.13391. Bibcode:2019MS&E..580a2007K. doi:10.1088/1757-899x/580/1/012007. ISSN 1757-8981. S2CID 208267226.
15. "ID06 - Hard X-ray Microscope". www.esrf.fr. Archived from the original on 20 April 2023. Retrieved 20 April 2023.
16. Bucsek, Ashley; Seiner, Hanuš; Simons, Hugh; Yildirim, Can; Cook, Phil; Chumlyakov, Yuriy; Detlefs, Carsten; Stebner, Aaron P. (15 October 2019). "Sub-surface measurements of the austenite microstructure in response to martensitic phase transformation". Acta Materialia. 179: 273–286. Bibcode:2019AcMat.179..273B. doi:10.1016/j.actamat.2019.08.036. ISSN 1359-6454.
17. Carlsen, Mads Allerup (2022). Phase Resolved Dark-Field X-ray Microscopy. Department of Physics, Technical University of Denmark.
18. Yildirim, C.; Jessop, C.; Ahlström, J.; Detlefs, C.; Zhang, Y. (1 May 2021). "3D mapping of orientation variation and local residual stress within individual grains of pearlitic steel using synchrotron dark field X-ray microscopy". Scripta Materialia. 197: 113783. doi:10.1016/j.scriptamat.2021.113783. ISSN 1359-6462. S2CID 233536615.
19. Chen, Y.; Tang, Y. T.; Collins, D. M.; Clark, S. J.; Ludwig, W.; Rodriguez-Lamas, R.; Detlefs, C.; Reed, R. C.; Lee, P. D.; Withers, P. J.; Yildirim, C. (1 September 2023). "High-resolution 3D strain and orientation mapping within a grain of a directed energy deposition laser additively manufactured superalloy". Scripta Materialia. 234: 115579. arXiv:2303.04764. doi:10.1016/j.scriptamat.2023.115579. ISSN 1359-6462. S2CID 257405123.
20. Yildirim, Can; Cook, Phil; Detlefs, Carsten; Simons, Hugh; Poulsen, Henning Friis (1 April 2020). "Probing nanoscale structure and strain by dark-field x-ray microscopy". MRS Bulletin. 45 (4): 277–282. Bibcode:2020MRSBu..45..277Y. doi:10.1557/mrs.2020.89. ISSN 0883-7694. S2CID 216535051.
21. Simons, Hugh; Haugen, Astri Bjørnetun; Jakobsen, Anders Clemen; Schmidt, Søren; Stöhr, Frederik; Majkut, Marta; Detlefs, Carsten; Daniels, John E.; Damjanovic, Dragan; Poulsen, Henning Friis (1 September 2018). "Long-range symmetry breaking in embedded ferroelectrics". Nature Materials. 17 (9): 814–819. Bibcode:2018NatMa..17..814S. doi:10.1038/s41563-018-0116-3. ISSN 1476-4660. PMID 29941920. S2CID 49413867.
22. Ahl, S R; Simons, H; Jakobsen, A C; Zhang, Y B; Stöhr, F; Jensen, D Juul; Poulsen, H F (7 August 2015). "Dark field X-ray microscopy for studies of recrystallization". IOP Conference Series: Materials Science and Engineering. 89 (1): 012016. Bibcode:2015MS&E...89a2016A. doi:10.1088/1757-899X/89/1/012016. ISSN 1757-8981. S2CID 23480120.
23. Jakobsen, A. C.; Simons, H.; Ludwig, W.; Yildirim, C.; Leemreize, H.; Porz, L.; Detlefs, C.; Poulsen, H. F. (1 February 2019). "Mapping of individual dislocations with dark-field X-ray microscopy". Journal of Applied Crystallography. 52 (1): 122–132. Bibcode:2019JApCr..52..122J. doi:10.1107/S1600576718017302. ISSN 1600-5767.
24. Huang, Pin-Hua; Coffee, Ryan; Dresselhaus-Marais, Leora (28 February 2023). "Automatic Determination of the Weak-Beam Condition in Dark Field X-ray Microscopy". Integrating Materials and Manufacturing Innovation. 12 (2): 83–91. arXiv:2211.05247. doi:10.1007/s40192-023-00295-6. S2CID 258287377.
25. Hlushko, K.; Keckes, J.; Ressel, G.; Pörnbacher, J.; Ecker, W.; Kutsal, M.; Cook, P. K.; Detlefs, C.; Yildirim, C. (1 October 2020). "Dark-field X-ray microscopy reveals mosaicity and strain gradients across sub-surface TiC and TiN particles in steel matrix composites". Scripta Materialia. 187: 402–406. doi:10.1016/j.scriptamat.2020.06.053. ISSN 1359-6462. S2CID 224903821.
26. Yildirim, C.; Vitoux, H.; Dresselhaus-Marais, L. E.; Steinmann, R.; Watier, Y.; Cook, P. K.; Kutsal, M.; Detlefs, C. (12 June 2020). "Radiation furnace for synchrotron dark-field x-ray microscopy experiments". Review of Scientific Instruments. 91 (65109): 065109. arXiv:1912.01255. Bibcode:2020RScI...91f5109Y. doi:10.1063/1.5141139. PMID 32611059. S2CID 208548585.
27. Ormstrup, Jeppe; Østergaard, Emil V.; Detlefs, Carsten; Mathiesen, Ragnvald H.; Yildirim, Can; Kutsal, Mustafacan; Cook, Philip K.; Watier, Yves; Cosculluela, Carlos; Simons, Hugh (3 June 2020). "Imaging microstructural dynamics and strain fields in electro-active materials in situ with dark field x-ray microscopy". Review of Scientific Instruments. 91 (65103): 065103. Bibcode:2020RScI...91f5103O. doi:10.1063/1.5142319. PMID 32611058. S2CID 220307399.
28. Plumb, Jayden; Poudyal, Ishwor; Dally, Rebecca L.; Daly, Samantha; Wilson, Stephen D.; Islam, Zahir (2023). "Dark field X-ray microscopy below liquid-helium temperature: The case of NaMnO2". Materials Characterization. 204. arXiv:2211.09247. doi:10.1016/j.matchar.2023.113174.
29. Cook, Phil K; Simons, Hugh; Jakobsen, Anders C; Yildirim, Can; Poulsen, Henning F; Detlefs, Carsten (2018). "Insights into the Exceptional Crystallographic Order of Biominerals Using Dark-Field X-ray Microscopy". Microscopy and Microanalysis. 24 (S2): 88–89. Bibcode:2018MiMic..24S..90C. doi:10.1017/S1431927618012837.
30. Yang, Wenge; Larson, B. C; Tischler, J. Z; Ice, G. E; Budai, J. D; Liu, W (1 August 2004). "Differential-aperture X-ray structural microscopy: a submicron-resolution three-dimensional probe of local microstructure and strain". Micron. International Wuhan Symposium on Advanced Electron Microscopy. 35 (6): 431–439. doi:10.1016/j.micron.2004.02.004. ISSN 0968-4328. PMID 15120127.
31. Larson, B. C.; Yang, Wenge; Ice, G. E.; Budai, J. D.; Tischler, J. Z. (February 2002). "Three-dimensional X-ray structural microscopy with submicrometre resolution". Nature. 415 (6874): 887–890. Bibcode:2002Natur.415..887L. doi:10.1038/415887a. ISSN 1476-4687. PMID 11859363. S2CID 4415765.
32. Hofmann, Felix; Phillips, Nicholas W.; Das, Suchandrima; Karamched, Phani; Hughes, Gareth M.; Douglas, James O.; Cha, Wonsuk; Liu, Wenjun (14 January 2020). "Nanoscale imaging of the full strain tensor of specific dislocations extracted from a bulk sample". Physical Review Materials. 4 (1): 013801. arXiv:1903.04079. Bibcode:2020PhRvM...4a3801H. doi:10.1103/PhysRevMaterials.4.013801. S2CID 195798830.
33. Vicente, Rafael A.; Neckel, Itamar T.; Sankaranarayanan, Subramanian K. R. S.; Solla-Gullon, José; Fernández, Pablo S. (27 April 2021). "Bragg Coherent Diffraction Imaging for In Situ Studies in Electrocatalysis". ACS Nano. 15 (4): 6129–6146. doi:10.1021/acsnano.1c01080. ISSN 1936-0851. PMC 8155327. PMID 33793205.
34. Yang, David; Lapington, Mark T.; He, Guanze; Song, Kay; Zhang, Minyi; Barker, Clara; Harder, Ross J.; Cha, Wonsuk; Liu, Wenjun; Phillips, Nicholas W.; Hofmann, Felix (1 October 2022). "Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation". Journal of Applied Crystallography. 55 (5): 1184–1195. Bibcode:2022JApCr..55.1184Y. doi:10.1107/S1600576722007646. ISSN 1600-5767. PMC 9533756. PMID 36249491.
35. Li, Peng; Hofmann, Felix; Leake, Steven; Allain, Marc; Chamard, Virginie (10 March 2019). Multi-angle Bragg projection ptychography with probe retrieval. The Minerals, Metals & Materials Society Annual Meeting (TMS2019). San Antonio, TX, United States.
36. "Ptychography - - Diamond Light Source". www.diamond.ac.uk. Retrieved 17 August 2023.
37. Zheng, Guoan; Shen, Cheng; Jiang, Shaowei; Song, Pengming; Yang, Changhuei (March 2021). "Concept, implementations and applications of Fourier ptychography". Nature Reviews Physics. 3 (3): 207–223. Bibcode:2021NatRP...3..207Z. doi:10.1038/s42254-021-00280-y. ISSN 2522-5820. S2CID 257114076.
38. "Diffraction Contrast Tomography (DCT)". www.esrf.fr. Retrieved 17 August 2023.
39. Reischig, Péter; King, Andrew; Nervo, Laura; Viganò, Nicola; Guilhem, Yoann; Palenstijn, Willem Jan; Batenburg, K. Joost; Preuss, Michael; Ludwig, Wolfgang (2013). "Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials". Journal of Applied Crystallography. 46 (2): 297. Bibcode:2013JApCr..46..297R. doi:10.1107/S0021889813002604.
40. Poulsen, H. F.; Nielsen, S. F.; Lauridsen, E. M.; Schmidt, S.; Suter, R. M.; Lienert, U.; Margulies, L.; Lorentzen, T.; Juul Jensen, D. (2001). "Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders". Journal of Applied Crystallography. 34 (6): 751–756. Bibcode:2001JApCr..34..751P. doi:10.1107/s0021889801014273.
41. Koko, Abdalrhaman; Tong, Vivian; Wilkinson, Angus J.; Marrow, T. James (1 June 2023). "An iterative method for reference pattern selection in high-resolution electron backscatter diffraction (HR-EBSD)". Ultramicroscopy. 248: 113705. arXiv:2206.10242. doi:10.1016/j.ultramic.2023.113705. ISSN 0304-3991. PMID 36871367. S2CID 249889699.
42. Schwartz, Adam J.; Kumar, Mukul; Adams, Brent L.; Field, David P., eds. (2009). Electron Backscatter Diffraction in Materials Science. doi:10.1007/978-0-387-88136-2. ISBN 978-0-387-88135-5.
43. Lin, F. X.; Godfrey, A.; Jensen, D. Juul; Winther, G. (1 November 2010). "3D EBSD characterization of deformation structures in commercial purity aluminum". Materials Characterization. 61 (11): 1203–1210. doi:10.1016/j.matchar.2010.07.013. ISSN 1044-5803.
44. Stinville, J. C.; Callahan, P. G.; Charpagne, M. A.; Echlin, M. P.; Valle, V.; Pollock, T. M. (1 March 2020). "Direct measurements of slip irreversibility in a nickel-based superalloy using high resolution digital image correlation". Acta Materialia. 186: 172–189. Bibcode:2020AcMat.186..172S. doi:10.1016/j.actamat.2019.12.009. ISSN 1359-6454. S2CID 213631580.
45. Zhao, Zhipeng; Zhu, Guoming; Kang, Yonglin; Peng, Lin (13 January 2020). "Analysis of the formation of sub-grain boundaries in commercially pure titanium compressed at elevated temperature". Materials Science and Engineering: A. 771: 138680. doi:10.1016/j.msea.2019.138680. ISSN 0921-5093. S2CID 210240660.
46. Kirkland, E (1998). Advanced computing in Electron Microscopy. Springer. ISBN 978-0-306-45936-8.
47. Li, Qiu; Wang, Yong; Li, Tiantian; Li, Wei; Wang, Feifan; Janotti, Anderson; Law, Stephanie; Gu, Tingyi (14 April 2020). "Localized Strain Measurement in Molecular Beam Epitaxially Grown Chalcogenide Thin Films by Micro-Raman Spectroscopy". ACS Omega. 5 (14): 8090–8096. doi:10.1021/acsomega.0c00224. ISSN 2470-1343. PMC 7161023. PMID 32309718.
48. Liang, Xingzhong; Rivera-Díaz-del-Castillo, Pedro E. J. (1 January 2022), "Neutron Diffraction", in Caballero, Francisca G. (ed.), Encyclopedia of Materials: Metals and Alloys, Oxford: Elsevier, pp. 695–702, ISBN 978-0-12-819733-2, retrieved 20 April 2023

Further reading

• Carlsen, Mads Allerup (30 August 2022). Phase Resolved Dark-Field X-ray Microscopy (PhD thesis). Technical University of Denmark.
• Poulsen, H. F.; Dresselhaus-Marais, L. E.; Carlsen, M. A.; Detlefs, C.; Winther, G. (1 December 2021). "Geometrical-optics formalism to model contrast in dark-field X-ray microscopy". Journal of Applied Crystallography. 54 (6): 1555–1571. arXiv:2007.09475. Bibcode:2021JApCr..54.1555P. doi:10.1107/S1600576721007287. ISSN 1600-5767. S2CID 220647543.