Convergent beam electron diffraction

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Convergent beam electron diffraction (CBED) is an electron diffraction technique where a convergent or divergent beam (conical electron beam) of electrons is used to study materials.

Contents

CBED scheme, adapted from W. Kossel and G. Mollenstedt, Elektroneninterferenzen im konvergenten Bundel, Annalen der Physik 36, 113 (1939). CBED scheme.png
CBED scheme, adapted from W. Kossel and G. Möllenstedt, Elektroneninterferenzen im konvergenten Bündel, Annalen der Physik 36, 113 (1939).

History

CBED was first introduced in 1939 by Kossel and Möllenstedt. [1] The development of the Field Emission Gun (FEG) in the 1970s, [2] the Scanning Transmission Electron Microscopy (STEM), energy filtering devices and so on, made possible smaller probe diameters and larger convergence angles, and all this made CBED more popular. In the seventies, CBED was being used for the determination of the point group and space group symmetries by Goodman and Lehmpfuh, [3] and Buxton, [4] and starting in 1985, CBED was used by Tanaka et al. for studying crystals structure. [5] [6] [7] [8] [9]

Applications

By using CBED, the following information can be obtained:

Parameters

where is the distance between the crystallographic planes , is the Bragg angle, is an integer, and is the wavelength of the probing electrons.

Advantages and disadvantages of CBED

Since the diameter of the probing convergent beam is smaller than in the case of a parallel beam, most of the information in the CBED pattern is obtained from very small regions, which other methods cannot reach. For example, in Selected Area Electron Diffraction (SAED), where a parallel beam illumination is used, the smallest area that can be selected is 0.5 μm at 100 kV, whereas in CBED, it is possible to go to areas smaller than 100 nm. [41] Also, the amount of information that is obtained from a CBED pattern is larger than that from a SAED pattern. Nonetheless, CBED also has its disadvantages. The focused probe may generate contamination, which can cause localized stresses. But this was more of a problem in the past, and now, with the high vacuum conditions, one should be able to probe a clean region of the specimen in minutes to hours. Another disadvantage is that the convergent beam may heat or damage the chosen region of the specimen. [42] Since 1939, CBED has been mainly used to study thicker materials.

CBED on 2D crystals

Recently, CBED was applied to study graphene [43] and other 2D monolayer crystals and van der Waals structures. For 2D crystals, the analysis of CBED patterns is simplified, because the intensity distribution in a CBED disk is directly related to the atomic arrangement in the crystal. The deformations at a nanometer resolution have been retrieved, the interlayer distance of a bilayer crystal has been reconstructed, and so on, by using CBED. [44]

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References

  1. ↑ Kossel, W.; Möllenstedt, G. (1939). "Elektroneninterferenzen im konvergenten Bündel". Annalen der Physik. 428 (2): 113–140. Bibcode:1939AnP...428..113K. doi:10.1002/andp.19394280204.
  2. ↑ Crewe, A. V.; Isaacson, M.; Johnson, D. (February 1969). "A Simple Scanning Electron Microscope". Review of Scientific Instruments. 40 (2): 241–246. Bibcode:1969RScI...40..241C. doi:10.1063/1.1683910.
  3. ↑ Goodman, P.; Lehmpfuhl, G. (1 May 1968). "Observation of the breakdown of Friedel's law in electron diffraction and symmetry determination from zero-layer interactions". Acta Crystallographica Section A. 24 (3): 339–347. Bibcode:1968AcCrA..24..339G. doi:10.1107/S0567739468000677.
  4. ↑ Buxton, B. F.; Eades, J. A.; Steeds, John Wickham; Rackham, G. M.; Frank, Frederick Charles (11 March 1976). "The symmetry of electron diffraction zone axis patterns". Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 281 (1301): 171–194. Bibcode:1976RSPTA.281..171B. doi:10.1098/rsta.1976.0024. S2CID   122890943.
  5. ↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I. JEOL Ltd.
  6. ↑ Tanaka, Michiyoshi; Terauchi, Masami (1988). Convergent beam electron diffraction II. JEOL Ltd.
  7. ↑ Tanaka, Michiyoshi; Terauchi, Masami; Tsuda, Kenji (1994). Convergent beam electron diffraction III. JEOL Ltd.
  8. ↑ Tanaka, Michiyoshi (1994). "Convergent-beam electron diffraction". Acta Crystallographica Section A. 50 (3): 261–286. Bibcode:1994AcCrA..50..261T. doi:10.1107/S0108767393010426.
  9. ↑ Tanaka, Michiyoshi; Terauchi, Masami; Tsuda, Kenji; Saitoh, Koh (2002). Convergent beam electron diffraction IV.
  10. ↑ Jones, P. M.; Rakham, G. M.; Steeds, John Wick (30 May 1977). "Higher order Laue zone effects in electron diffraction and their use in lattice parameter determination". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 354 (1677): 197–222. Bibcode:1977RSPSA.354..197J. doi:10.1098/rspa.1977.0064. S2CID   98158162.
  11. ↑ Kelly, P. M.; Jostsons, A.; Blake, R. G.; Napier, J. G. (16 October 1975). "The determination of foil thickness by scanning transmission electron microscopy". Physica Status Solidi A. 31 (2): 771–780. Bibcode:1975PSSAR..31..771K. doi:10.1002/pssa.2210310251.
  12. ↑ Clément, L.; Pantel, R.; Kwakman, L. F. Tz.; Rouvière, J. L. (26 July 2004). "Strain measurements by convergent-beam electron diffraction: The importance of stress relaxation in lamella preparations". Applied Physics Letters. 85 (4): 651–653. Bibcode:2004ApPhL..85..651C. doi:10.1063/1.1774275.
  13. ↑ Morniroli, J. P. (September 2006). "CBED and LACBED characterization of crystal defects". Journal of Microscopy. 223 (3): 240–245. doi:10.1111/j.1365-2818.2006.01630.x. PMID   17059540. S2CID   21117117.
  14. ↑ Carpenter, R. W.; Spence, J. C. H. (1 January 1982). "Three-dimensional strain-field information in convergent-beam electron diffraction patterns". Acta Crystallographica Section A. 38 (1): 55–61. Bibcode:1982AcCrA..38...55C. doi:10.1107/S0567739482000102.
  15. ↑ Wu, Lijun; Zhu, Yimei; Tafto, J.; Welch, D. O.; Suenaga, M. (19 September 2002). "Quantitative analysis of twist boundaries and stacking faults in Bi-based superconductors by parallel recording of dark-field images with a coherent electron source". Physical Review B. 66 (10): 104517. Bibcode:2002PhRvB..66j4517W. doi:10.1103/PhysRevB.66.104517.
  16. ↑ Wu, Lijun; Zhu, Yimei; Tafto, J. (11 December 2000). "Picometer Accuracy in Measuring Lattice Displacements Across Planar Faults by Interferometry in Coherent Electron Diffraction". Physical Review Letters. 85 (24): 5126–5129. Bibcode:2000PhRvL..85.5126W. doi:10.1103/PhysRevLett.85.5126. PMID   11102202.
  17. ↑ Tanaka, M.; Saito, R.; Sekii, H. (1 May 1983). "Point-group determination by convergent-beam electron diffraction". Acta Crystallographica Section A. 39 (3): 357–368. Bibcode:1983AcCrA..39..357T. doi:10.1107/S010876738300080X.
  18. ↑ Goodman, P. (1 November 1975). "A practical method of three-dimensional space-group analysis using convergent-beam electron diffraction". Acta Crystallographica Section A. 31 (6): 804–810. Bibcode:1975AcCrA..31..804G. doi: 10.1107/S0567739475001738 . S2CID   98081846.
  19. ↑ Tanaka, M.; Sekii, H.; Nagasawa, T. (1 November 1983). "Space-group determination by dynamic extinction in convergent-beam electron diffraction". Acta Crystallographica Section A. 39 (6): 825–837. Bibcode:1983AcCrA..39..825T. doi:10.1107/S0108767383001695.
  20. ↑ Schnitzer, N.; Sung, S.H.; Hovden, R.H. (2019). "Introduction to the Ronchigram and its Calculation with Ronchigram". Microscopy Today. 3 (3): 12–15. doi: 10.1017/S1551929519000427 . S2CID   155224415.
  21. ↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I.
  22. ↑ Morniroli, J. P. (2006). "CBED and LACBED characterization of crystal defects". Journal of Microscopy. 223 (3): 240–245. doi:10.1111/j.1365-2818.2006.01630.x. ISSN   1365-2818. PMID   17059540. S2CID   21117117.
  23. ↑ Cowley, J. M. (1987). Advances in electronics and electron physics.
  24. ↑ Tanaka, Michiyoshi (1986). "Conventional Transmission-Electron-Microscopy Techniques in Convergent-Beam Electron Diffraction". Journal of Electron Microscopy. doi:10.1093/oxfordjournals.jmicro.a050584.
  25. ↑ Tanaka, Michiyoshi; Saito, Ryuichi; Ueno, Katsuyoshi; Harada, Yoshiyasu (1980). "Large-Angle Convergent-Beam Electron Diffraction". Journal of Electron Microscopy. doi:10.1093/oxfordjournals.jmicro.a050262.
  26. ↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I.
  27. ↑ O'Leary, C. M.; Allen, C. S.; Huang, C.; Kim, J. S.; Liberti, E.; Nellist, P. D.; Kirkland, A. I. (23 March 2020). "Phase reconstruction using fast binary 4D STEM data". Applied Physics Letters. 116 (12): 124101. Bibcode:2020ApPhL.116l4101O. doi:10.1063/1.5143213. S2CID   216342216.
  28. ↑ Tsuda, Kenji; Yasuhara, Akira; Tanaka, Michiyoshi (19 August 2013). "Two-dimensional mapping of polarizations of rhombohedral nanostructures in the tetragonal phase of BaTiO 3 by the combined use of the scanning transmission electron microscopy and convergent-beam electron diffraction methods". Applied Physics Letters. 103 (8): 082908. Bibcode:2013ApPhL.103h2908T. doi:10.1063/1.4819221.
  29. ↑ van Oostrum, K. J.; Leenhouts, A.; Jore, A. (September 1973). "A new scanning microdiffraction technique". Applied Physics Letters. 23 (5): 283–284. Bibcode:1973ApPhL..23..283V. doi:10.1063/1.1654890.
  30. ↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I.
  31. ↑ Tanaka, Michiyoshi; Saito, Ryuichi; Ueno, Katsuyoshi; Harada, Yoshiyasu (1 January 1980). "Large-Angle Convergent-Beam Electron Diffraction". Journal of Electron Microscopy. 29 (4): 408–412. doi:10.1093/oxfordjournals.jmicro.a050262. ISSN   0022-0744.
  32. ↑ Tanaka, Michiyoshi; Ueno, Katsuyoshi; Hirata, Yoshihiro (April 1980). "Signal Processing of Convergent-Beam Electron Diffraction Patterns Obtained by the Beam-Rocking Method". Japanese Journal of Applied Physics. 19 (4): L201–L204. Bibcode:1980JaJAP..19L.201T. doi:10.1143/JJAP.19.L201. S2CID   122484061.
  33. ↑ Spence, J.C.H.; Poon, H.C.; Saldin, D.K. (February 2004). "Convergent-Beam Low Energy Electron Diffraction (CBLEED) and the Measurement of Surface Dipole Layers". Microscopy and Microanalysis. 10 (1): 128–133. Bibcode:2004MiMic..10..128S. doi:10.1017/S1431927604040346. PMID   15306076. S2CID   46584545.
  34. ↑ Ruben, G.; Jesson, D.E.; Paganin, D.M.; Smith, A.E. (May 2009). "Kinematic simulation of convergent beam low-energy electron diffraction patterns". Optik. 120 (9): 401–408. Bibcode:2009Optik.120..401R. doi:10.1016/j.ijleo.2007.10.006.
  35. ↑ Constantinou, Procopios C.; Jesson, David E. (September 2019). "On the sensitivity of convergent beam low energy electron diffraction patterns to small atomic displacements". Applied Surface Science. 489: 504–509. Bibcode:2019ApSS..489..504C. doi: 10.1016/j.apsusc.2019.05.274 . S2CID   182169602.
  36. ↑ Jiang, Yi; Chen, Zhen; Han, Yimo; Deb, Pratiti; Gao, Hui; Xie, Saien; Purohit, Prafull; Tate, Mark W.; Park, Jiwoong; Gruner, Sol M.; Elser, Veit; Muller, David A. (July 2018). "Electron ptychography of 2D materials to deep sub-ångström resolution". Nature. 559 (7714): 343–349. arXiv: 1801.04630 . Bibcode:2018Natur.559..343J. doi:10.1038/s41586-018-0298-5. PMID   30022131. S2CID   119359004.
  37. ↑ "Highest resolution microscope". Guinness World Records.
  38. ↑ Carpenter, R. W.; Spence, J. C. H. (November 1984). "Applications of modern microdiffraction to materials science". Journal of Microscopy. 136 (2): 165–178. doi:10.1111/j.1365-2818.1984.tb00526.x. S2CID   136906069.
  39. ↑ Williams, David B. (2009). Transmission electron microscopy: a textbook for materials science (2nd ed.). New York: Springer. ISBN   978-0-387-76501-3.
  40. ↑ Steeds, John Wickham; Hren, J. J.; Goldstein, J. I.; Joy, D. C. (1979). Introduction to Analytical Electron Microscopy. Plenum Press. p. 387.
  41. ↑ Champness, P. E. (March 1987). "Convergent beam electron diffraction". Mineralogical Magazine. 51 (359): 33–48. Bibcode:1987MinM...51...33C. doi:10.1180/minmag.1987.051.359.04. S2CID   30145465.
  42. ↑ Williams, David B. (2009). Transmission electron microscopy : a textbook for materials science (2nd ed.). New York: Springer. ISBN   978-0-387-76501-3.
  43. ↑ Meyer, Jannik; Geim, Andre K.; Katsnelson, M. I.; Novoselov, K. S.; Obergfell, D.; Roth, S.; Girit, C.; Zettl, A. (2007). "On the roughness of single- and bi-layer graphene membranes". Solid State Communications. 143 (1–2): 101–109. arXiv: cond-mat/0703033 . Bibcode:2007SSCom.143..101M. doi:10.1016/j.ssc.2007.02.047.
  44. ↑ Latychevskaia, Tatiana; Woods, Colin Robert; Wang, Yi Bo; Holwill, Matthew; Prestat, Eric; Haigh, Sarah J.; Novoselov, Kostya S. (17 July 2018). "Convergent beam electron holography for analysis of van der Waals heterostructures". Proceedings of the National Academy of Sciences. 115 (29): 7473–7478. arXiv: 1807.01927 . Bibcode:2018PNAS..115.7473L. doi: 10.1073/pnas.1722523115 . PMC   6055151 . PMID   29970422.
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