Dark-field X-ray microscopy explained

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. 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

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. 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.^[7] 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

p' and q' (as in the figure) correspondingly. The diffraction angle 2 \theta is typically 10–30°.^{[8] [9]}

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.^[10]

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

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, G , several 2D projections of the grain are obtained from various angles.^[11] A 3D map is then obtained by combining these projections using reconstruction algorithms^[12] 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 \alpha and \beta .

The current implementation of DFXM at ID06,, uses a compound refractive lens (CRL) as the objective, giving spatial resolution of 100 nm and angular resolution of 0.001°.^{[13] [14]}

Applications, limitations and alternatives

Current and potential applications

DFXM has been used for the non-destructive investigation of polycrystalline materials and composites, revealing the 3D microstructure,^[15] phases,^[16] orientation of individual grains,^{[17] [18]} and local strains.^{[19] [20]} It has also been used for in situ studies of materials recrystallisation,^[21] dislocations^{[22] [23]} and other defects, and the deformation^[19] and fracture mechanisms in materials, such as metals and composites.^[24] DFXM can provide insights into the 3D microstructure and deformation of geological materials such as minerals and rocks, and irradiated materials.^[25]

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.^{[26] [27]}

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.^[28]

Limitations

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

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.

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. 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.

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.^[29] 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.^[30]
• 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.^{[31] [32] [33]}
• 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.^{[34] [35] [36]}
• 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.^{[37] [38]}
• 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.^[39]
• 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^[40] at the submicron scale. It works by detecting the diffraction pattern of backscattered electrons, which provides information about the crystal structure of the material.^[41] 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,^[42] and can be combined with Digital image correlation, i.e., EBSD-DIC.^[43]
• 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.^[44]
• 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.^[45]
• 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.^[46]
• 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.

References

1. Simons . H. . King . A. . Ludwig . W. . Detlefs . C. . Pantleon . W. . Schmidt . S. . Stöhr . F. . Snigireva . I. . Snigirev . A. . Poulsen . H. F. . 2015-01-14 . Dark-field X-ray microscopy for multiscale structural characterization . Nature Communications . en . 6 . 1 . 6098 . 10.1038/ncomms7098 . 25586429 . 4354092 . 2015NatCo...6.6098S . 2041-1723.
2. Simons . Hugh . Ahl . Sonja Rosenlund . Jakobsen . Anders Clemen . Yildirim . Can . Cook . Phil K. . Detlefs . Carsten . Poulsen . Henning Friis . 2018-08-01 . Multi-Scale 3D Imaging of Strain and Structure with Dark-Field X-Ray Microscopy . Microscopy and Microanalysis . 24 . S2 . 72–75 . 10.1017/s1431927618012758 . 2018MiMic..24S..72S . 139864737 . 1431-9276. free .
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 . 10.1017/S1431927696210530. 138065437 .
4. Vogt . S. . Chapman . H. N. . Jacobsen . C. . Medenwaldt . R. . 2001-03-01 . Dark field X-ray microscopy: the effects of condenser/detector aperture . Ultramicroscopy . en . 87 . 1 . 25–44 . 10.1016/S0304-3991(00)00065-6 . 11310539 . 0304-3991.
5. Chapman . Henry N. . Williams . Shawn . Jacobsen . Chris . 1994-12-01 . Bailey . G.W. . Garratt-Reed . A.J. . 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. 10.1017/S0424820100167998 .
6. Pfauntsch . S. J . Michette . A. G . Buckley . C. J . 1996-02-15 . Toroidal condenser optics for dark-field X-ray microscopy . Optics Communications . en . 124 . 1 . 141–149 . 10.1016/0030-4018(95)00672-9 . 1996OptCo.124..141P . 0030-4018.
7. 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 . 10.1016/j.ejmp.2020.11.034 . 1724-191X . 33342666. 229343273 . free .
8. Vaughan . G. B. M. . Wright . J. P. . Bytchkov . A. . Rossat . M. . Gleyzolle . H. . Snigireva . I. . Snigirev . A. . 2011-03-01 . X-ray transfocators: focusing devices based on compound refractive lenses . Journal of Synchrotron Radiation . en . 18 . 2 . 125–133 . 10.1107/S0909049510044365 . 0909-0495 . 3267637 . 21335897. 2011JSynR..18..125V .
9. Snigirev . A. . Kohn . V. . Snigireva . I. . Lengeler . B. . November 1996 . A compound refractive lens for focusing high-energy X-rays . Nature . en . 384 . 6604 . 49–51 . 10.1038/384049a0 . 1996Natur.384...49S . 4229340 . 1476-4687.
10. 2210.08366 . Leora E. . Dresselhaus-Marais . Bernard . Kozioziemski . Simultaneous bright- and dark-field X-ray microscopy at X-ray free electron lasers . 2023 . 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. Scientific Reports . 13 . 1 . 17573 . 10.1038/s41598-023-35526-5 . 37845245 . 10579415 . 2023NatSR..1317573D .
11. Ludwig . W. . Cloetens . P. . Härtwig . J. . Baruchel . J. . Hamelin . B. . Bastie . P. . 2001-10-01 . Three-dimensional imaging of crystal defects by 'topo-tomography' . Journal of Applied Crystallography . en . 34 . 5 . 602–607 . 10.1107/S002188980101086X . 2001JApCr..34..602L . 0021-8898.
12. Ferrer . Júlia Garriga . Rodríguez-Lamas . Raquel . Payno . Henri . De Nolf . Wout . Cook . Phil . Jover . Vicente Armando Solé . Favre-Nicolin . Vincent . Yıldırım . Can . Detlefs . Carsten . 2022-05-11 . darfix: Data analysis for dark-field X-ray microscopy . Journal of Synchrotron Radiation . 30 . 3 . 527–537 . 10.1107/S1600577523001674 . 37000183 . 10161887 . 2205.05494 . 2023JSynR..30..527G .
13. 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 . 2019-08-01 . The ESRF dark-field x-ray microscope at ID06 . IOP Conference Series: Materials Science and Engineering . 580 . 1 . 012007 . 10.1088/1757-899x/580/1/012007 . 2019MS&E..580a2007K . 1757-8981 . 208267226. free .
14. Web site: ID06 - Hard X-ray Microscope . 2023-04-20 . www.esrf.fr . en . 2023-04-20 . https://web.archive.org/web/20230420102644/https://www.esrf.fr/home/UsersAndScience/Experiments/StructMaterials/id06---hard-x-ray-microscope.html . dead .
15. Bucsek . Ashley . Seiner . Hanuš . Simons . Hugh . Yildirim . Can . Cook . Phil . Chumlyakov . Yuriy . Detlefs . Carsten . Stebner . Aaron P. . 2019-10-15 . Sub-surface measurements of the austenite microstructure in response to martensitic phase transformation . Acta Materialia . en . 179 . 273–286 . 10.1016/j.actamat.2019.08.036 . 2019AcMat.179..273B . 1359-6454. free .
16. Book: Carlsen, Mads Allerup . Phase Resolved Dark-Field X-ray Microscopy . 2022 . Department of Physics, Technical University of Denmark.
17. Yildirim . C. . Jessop . C. . Ahlström . J. . Detlefs . C. . Zhang . Y. . 2021-05-01 . 3D mapping of orientation variation and local residual stress within individual grains of pearlitic steel using synchrotron dark field X-ray microscopy . Scripta Materialia . en . 197 . 113783 . 10.1016/j.scriptamat.2021.113783 . 233536615 . 1359-6462. free .
18. 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. . 2023-09-01 . High-resolution 3D strain and orientation mapping within a grain of a directed energy deposition laser additively manufactured superalloy . Scripta Materialia . en . 234 . 115579 . 2303.04764 . 10.1016/j.scriptamat.2023.115579 . 1359-6462 . 257405123.
19. Yildirim . Can . Cook . Phil . Detlefs . Carsten . Simons . Hugh . Poulsen . Henning Friis . 2020-04-01 . Probing nanoscale structure and strain by dark-field x-ray microscopy . MRS Bulletin . en . 45 . 4 . 277–282 . 10.1557/mrs.2020.89 . 2020MRSBu..45..277Y . 216535051 . 0883-7694.
20. Simons . Hugh . Haugen . Astri Bjørnetun . Jakobsen . Anders Clemen . Schmidt . Søren . Stöhr . Frederik . Majkut . Marta . Detlefs . Carsten . Daniels . John E. . Damjanovic . Dragan . Poulsen . Henning Friis . 2018-09-01 . Long-range symmetry breaking in embedded ferroelectrics . Nature Materials . en . 17 . 9 . 814–819 . 10.1038/s41563-018-0116-3 . 29941920 . 2018NatMa..17..814S . 49413867 . 1476-4660.
21. Ahl . S R . Simons . H . Jakobsen . A C . Zhang . Y B . Stöhr . F . Jensen . D Juul . Poulsen . H F . 2015-08-07 . Dark field X-ray microscopy for studies of recrystallization . IOP Conference Series: Materials Science and Engineering . 89 . 1 . 012016 . 10.1088/1757-899X/89/1/012016 . 2015MS&E...89a2016A . 23480120 . 1757-8981. free .
22. Jakobsen . A. C. . Simons . H. . Ludwig . W. . Yildirim . C. . Leemreize . H. . Porz . L. . Detlefs . C. . Poulsen . H. F. . 2019-02-01 . Mapping of individual dislocations with dark-field X-ray microscopy . Journal of Applied Crystallography . en . 52 . 1 . 122–132 . 10.1107/S1600576718017302 . 2019JApCr..52..122J . 1600-5767.
23. Huang . Pin-Hua . Coffee . Ryan . Dresselhaus-Marais . Leora . 2023-02-28 . Automatic Determination of the Weak-Beam Condition in Dark Field X-ray Microscopy . Integrating Materials and Manufacturing Innovation . 12 . 2 . 83–91 . 10.1007/s40192-023-00295-6 . 2211.05247 . 258287377 .
24. Hlushko . K. . Keckes . J. . Ressel . G. . Pörnbacher . J. . Ecker . W. . Kutsal . M. . Cook . P. K. . Detlefs . C. . Yildirim . C. . 2020-10-01 . Dark-field X-ray microscopy reveals mosaicity and strain gradients across sub-surface TiC and TiN particles in steel matrix composites . Scripta Materialia . en . 187 . 402–406 . 10.1016/j.scriptamat.2020.06.053 . 224903821 . 1359-6462.
25. C. . Yildirim . H. . Vitoux . L. E. . Dresselhaus-Marais . R. . Steinmann . Y. . Watier . P. K. . Cook . M. . Kutsal . C. . Detlefs . 2020-06-12 . Radiation furnace for synchrotron dark-field x-ray microscopy experiments . Review of Scientific Instruments . 91 . 65109 . 065109 . 10.1063/1.5141139. 32611059 . 208548585 . 1912.01255 . 2020RScI...91f5109Y .
26. Jeppe . Ormstrup . Emil V. . Østergaard . Carsten . Detlefs . Ragnvald H. . Mathiesen . Can . Yildirim . Mustafacan . Kutsal . Philip K. . Cook . Yves . Watier . Carlos . Cosculluela . Hugh . Simons . 2020-06-03 . 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 . 10.1063/1.5142319. 32611058 . 2020RScI...91f5103O . 220307399 . free .
27. Plumb . Jayden . Poudyal . Ishwor . Dally . Rebecca L. . Daly . Samantha. Samantha Daly . Wilson . Stephen D. . Islam . Zahir . 2022-11-16 . Dark Field X-ray Microscopy Below Liquid-Helium Temperature: The Case of NaMnO2 . cond-mat.mtrl-sci . 2211.09247 .
28. Cook . Phil K . Simons . Hugh . Jakobsen . Anders C . Yildirim . Can . Poulsen . Henning F . Detlefs . Carsten . Insights into the Exceptional Crystallographic Order of Biominerals Using Dark-Field X-ray Microscopy . Microscopy and Microanalysis . 2018 . 24 . S2 . 88–89 . 10.1017/S1431927618012837. 2018MiMic..24S..90C . free .
29. Yang . Wenge . Larson . B. C . Tischler . J. Z . Ice . G. E . Budai . J. D . Liu . W . 2004-08-01 . 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 . en . 35 . 6 . 431–439 . 10.1016/j.micron.2004.02.004 . 15120127 . 0968-4328.
30. 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 . en . 415 . 6874 . 887–890 . 10.1038/415887a . 11859363 . 2002Natur.415..887L . 4415765 . 1476-4687.
31. Hofmann . Felix . Phillips . Nicholas W. . Das . Suchandrima . Karamched . Phani . Hughes . Gareth M. . Douglas . James O. . Cha . Wonsuk . Liu . Wenjun . 2020-01-14 . Nanoscale imaging of the full strain tensor of specific dislocations extracted from a bulk sample . Physical Review Materials . 4 . 1 . 013801 . 10.1103/PhysRevMaterials.4.013801. 1903.04079 . 2020PhRvM...4a3801H . 195798830 .
32. Vicente . Rafael A. . Neckel . Itamar T. . Sankaranarayanan . Subramanian K. R. S. . Solla-Gullon . José . Fernández . Pablo S. . 2021-04-27 . Bragg Coherent Diffraction Imaging for In Situ Studies in Electrocatalysis . ACS Nano . en . 15 . 4 . 6129–6146 . 10.1021/acsnano.1c01080 . 1936-0851 . 8155327 . 33793205.
33. 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 . 2022-10-01 . Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation . Journal of Applied Crystallography . 55 . 5 . 1184–1195 . 10.1107/S1600576722007646 . 1600-5767 . 9533756 . 36249491. 2022JApCr..55.1184Y .
34. Li . Peng . Hofmann . Felix . Leake . Steven . Allain . Marc . Chamard . Virginie . 2019-03-10 . Multi-angle Bragg projection ptychography with probe retrieval . The Minerals, Metals & Materials Society Annual Meeting (TMS2019) . San Antonio, TX, United States . en.
35. Web site: Ptychography - - Diamond Light Source . 2023-08-17 . www.diamond.ac.uk.
36. Zheng . Guoan . Shen . Cheng . Jiang . Shaowei . Song . Pengming . Yang . Changhuei . March 2021 . Concept, implementations and applications of Fourier ptychography . Nature Reviews Physics . en . 3 . 3 . 207–223 . 10.1038/s42254-021-00280-y . 2021NatRP...3..207Z . 257114076 . 2522-5820.
37. Web site: Diffraction Contrast Tomography (DCT) . 2023-08-17 . www.esrf.fr . en.
38. 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 . en . 46 . 2 . 297 . 10.1107/S0021889813002604. 2013JApCr..46..297R .
39. 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 . 10.1107/s0021889801014273 . 2001JApCr..34..751P . free.
40. Koko . Abdalrhaman . Tong . Vivian . Wilkinson . Angus J. . Marrow . T. James . 2023-06-01 . An iterative method for reference pattern selection in high-resolution electron backscatter diffraction (HR-EBSD) . Ultramicroscopy . en . 248 . 113705 . 10.1016/j.ultramic.2023.113705 . 36871367 . 2206.10242 . 249889699 . 0304-3991.
41. Book: Electron Backscatter Diffraction in Materials Science . 2009 . en . 10.1007/978-0-387-88136-2 . 978-0-387-88135-5 . Schwartz . Kumar . Adams . Field . Adam J. . Mukul . Brent L. . David P. .
42. Lin . F. X. . Godfrey . A. . Jensen . D. Juul . Winther . G. . 2010-11-01 . 3D EBSD characterization of deformation structures in commercial purity aluminum . Materials Characterization . en . 61 . 11 . 1203–1210 . 10.1016/j.matchar.2010.07.013 . 1044-5803.
43. Stinville . J. C. . Callahan . P. G. . Charpagne . M. A. . Echlin . M. P. . Valle . V. . Pollock . T. M. . 2020-03-01 . Direct measurements of slip irreversibility in a nickel-based superalloy using high resolution digital image correlation . Acta Materialia . en . 186 . 172–189 . 10.1016/j.actamat.2019.12.009 . 2020AcMat.186..172S . 213631580 . 1359-6454. free .
44. Zhao . Zhipeng . Zhu . Guoming . Kang . Yonglin . Peng . Lin . 2020-01-13 . Analysis of the formation of sub-grain boundaries in commercially pure titanium compressed at elevated temperature . Materials Science and Engineering: A . en . 771 . 138680 . 10.1016/j.msea.2019.138680 . 210240660 . 0921-5093.
45. Book: Kirkland, E . Advanced computing in Electron Microscopy . Springer . 1998 . 978-0-306-45936-8.
46. Li . Qiu . Wang . Yong . Li . Tiantian . Li . Wei . Wang . Feifan . Janotti . Anderson . Law . Stephanie . Gu . Tingyi . 2020-04-14 . Localized Strain Measurement in Molecular Beam Epitaxially Grown Chalcogenide Thin Films by Micro-Raman Spectroscopy . ACS Omega . en . 5 . 14 . 8090–8096 . 10.1021/acsomega.0c00224 . 2470-1343 . 7161023 . 32309718.

Further reading

• Carlsen . Mads Allerup . Phase Resolved Dark-Field X-ray Microscopy . 2022-08-30 . PhD . .
• Poulsen . H. F. . Dresselhaus-Marais . L. E. . Carlsen . M. A. . Detlefs . C. . Winther . G. . 2021-12-01 . Geometrical-optics formalism to model contrast in dark-field X-ray microscopy . Journal of Applied Crystallography . en . 54 . 6 . 1555–1571 . 2007.09475 . 10.1107/S1600576721007287 . 2021JApCr..54.1555P . 1600-5767 . 220647543.