Skip to main content

Electron Nanodiffraction

  • Chapter
  • First Online:
Springer Handbook of Microscopy

Part of the book series: Springer Handbooks ((SHB))

Abstract

This chapter introduces the practice and theory of electron nanodiffraction. After a brief introduction, the chapter provides a comprehensive description of electron diffraction techniques and their use for nanodiffraction. This is followed by discussions on electron probe properties, electron energy filtering and electron diffraction data analysis. Throughout the chapter, we emphasize different electron nanoprobes that can be formed inside an electron microscope, from a focused beam to parallel illumination, and how these probes can be used to extract structural information from different materials. For this purpose, we outline the electron diffraction theories based on both kinematic approximation and dynamic diffraction, which serve as the basis for the interpretation of electron nanodiffraction patterns. The principles and applications of scanning electron nanodiffraction and coherent diffraction imaging are covered in detail with applications for orientation mapping, imaging strain, 3-D nanostructure determination, and study of defects.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 279.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 359.00
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • G. Möllenstedt: My early work on convergent-beam electron-diffraction, Phys. Status Solidi (a) 116, 13–22 (1989)

    Google Scholar 

  • C.H. MacGillavry: Examination of the dynamic theory of electron diffraction on lattice, Physica 7, 329–343 (1940)

    CAS  Google Scholar 

  • J.M. Cowley: Electron nanodiffraction, Microsc. Res. Tech. 46, 75–97 (1999)

    CAS  Google Scholar 

  • J.M. Cowley: Applications of electron nanodiffraction, Micron 35, 345 (2004)

    CAS  Google Scholar 

  • J.C.H. Spence, J.M. Zuo: Large dynamic-range, parallel detection system for electron-diffraction and imaging, Rev. Sci. Instrum. 59, 2102–2105 (1988)

    CAS  Google Scholar 

  • J.M. Zuo: Electron detection characteristics of a slow-scan CCD camera, imaging plates and film, and electron image restoration, Microsc. Res. Tech. 49, 245–268 (2000)

    CAS  Google Scholar 

  • L. Reimer (Ed.): Energy-Filtering Transmission Electron Microscopy (Springer, New York 1995)

    Google Scholar 

  • J.C.H. Spence, J.M. Zuo: Electron Microdiffraction (Plenum, New York 1992)

    Google Scholar 

  • H.E. Elsayed-Ali, P.M. Weber: Time-resolved surface electron diffraction. In: Time-Resolved Diffraction, ed. by J.R. Helliwell, P.M. Rentzepis (Oxford Univ. Press, New York 1997) pp. 284–322

    Google Scholar 

  • W.E. King, G.H. Campbell, A. Frank, B. Reed, J.F. Schmerge, B.J. Siwick, B.C. Stuart, P.M. Weber: Ultrafast electron microscopy in materials science, biology, and chemistry, J. Appl. Phys. 97, 111101 (2005)

    Google Scholar 

  • B.J. Siwick, J.R. Dwyer, R.E. Jordan, R.J.D. Miller: An atomic-level view of melting using femtosecond electron diffraction, Science 302, 1382–1385 (2003)

    CAS  Google Scholar 

  • J.M. Zuo, M. Gao, J. Tao, B.Q. Li, R. Twesten, I. Petrov: Coherent nano-area electron diffraction, Microsc. Res. Tech. 64, 347–355 (2004)

    CAS  Google Scholar 

  • G. Deptuch, A. Besson, P. Rehak, M. Szelezniak, J. Wall, M. Winter, Y. Zhu: Direct electron imaging in electron microscopy with monolithic active pixel sensors, Ultramicroscopy 107, 674–684 (2007)

    CAS  Google Scholar 

  • D. Contarato, P. Denes, D. Doering, J. Joseph, B. Krieger: Direct detection in transmission electron microscopy with a 5 μm pitch CMOS pixel sensor, Nucl. Instrum. Methods Phys. Res. A 635, 69–73 (2011)

    CAS  Google Scholar 

  • J.M. Cowley (Ed.): Electron Diffraction Techniques, Vol. I, II (Oxford Univ. Press, Oxford 1992)

    Google Scholar 

  • L.M. Peng, S.L. Dudarev, M.J. Whelan: High-Energy Electron Diffraction and Microscopy (Oxford Univ. Press, Oxford 2004)

    Google Scholar 

  • J.P. Morniroli: Large-Angle Convergent Beam Electron Diffraction (Society of French Microscopists, Paris 2002), English Version

    Google Scholar 

  • J.M. Zuo, J.C.H. Spence: Advanced Transmission Electron Microscopy, Imaging and Diffraction in Nanoscience (Springer, New York 2017)

    Google Scholar 

  • S. Morishita, J. Yamasaki, K. Nakamura, T. Kato, N. Tanaka: Diffractive imaging of the dumbbell structure in silicon by spherical-aberration-corrected electron diffraction, Appl. Phys. Lett. 93, 183103 (2008)

    Google Scholar 

  • K.D. Van der Mast, C.J. Rakels, J.B. Le Poole: A high quality multipurpose objective lens. In: Proc. Eur. Congr. Electron Microsc. (1980) pp. 72–73

    Google Scholar 

  • K. Ran, X. Mi, Z.J. Shi, Q. Chen, Y.F. Shi, J.M. Zuo: Molecular packing of fullerenes inside single-walled carbon nanotubes, Carbon 50, 5450–5457 (2012)

    CAS  Google Scholar 

  • J.T. McKeown, J.C.H. Spence: The kinematic convergent-beam electron diffraction method for nanocrystal structure determination, J. Appl. Phys. 106, 074309 (2009)

    Google Scholar 

  • R. Vincent: Techniques of convergent beam electron-diffraction, J. Electron Microsc. Tech. 13, 40–50 (1989)

    CAS  Google Scholar 

  • M. Tanaka, R. Saito, K. Ueno, Y. Harada: Large-angle convergent-beam electron-diffraction, J. Electron Microsc. 29, 408–412 (1980)

    Google Scholar 

  • J.A. Eades: Zone-axis diffraction patterns by the Tanaka method, J. Electron Microsc. Tech. 1, 279–284 (1984)

    CAS  Google Scholar 

  • I.K. Jordan, C.J. Rossouw, R. Vincent: Effects of energy filtering in LACBED patterns, Ultramicroscopy 35, 237–243 (1991)

    Google Scholar 

  • K.K. Fung: Large-angle convergent-beam zone axis patterns, Ultramicroscopy 12, 243–246 (1984)

    Google Scholar 

  • M. Terauchi, M. Tanaka: Simultaneous observation of zone-axis pattern and ±G-dark-field pattern in convergent-beam electron-diffraction, J. Electron Microsc. 34, 347–356 (1985)

    CAS  Google Scholar 

  • M. Tanaka, M. Terauchi, T. Kaneyama: Convergent Beam Electron Diffraction II (JEOL, Tokyo 1988)

    Google Scholar 

  • J.P. Morniroli: CBED and LACBED analysis of stacking faults and antiphase boundaries, Mater. Chem. Phys. 81, 209–213 (2003)

    CAS  Google Scholar 

  • J.P. Morniroli, F. Gaillot: Trace analyses from LACBED patterns, Ultramicroscopy 83, 227–243 (2000)

    CAS  Google Scholar 

  • J.P. Morniroli, R.K.W. Marceau, S.P. Ringerz, L. Boulanger: LACBED characterization of dislocation loops, Philos. Mag. 86, 4883–4900 (2006)

    CAS  Google Scholar 

  • C.T. Koch: Aberration-compensated large-angle rocking-beam electron diffraction, Ultramicroscopy 111, 828–840 (2011)

    CAS  Google Scholar 

  • W. Krakow, L.A. Howland: A method for producing hollow cone illumination electronically in the conventional transmission microscope, Ultramicroscopy 2, 53–67 (1976)

    CAS  Google Scholar 

  • J.A. Eades: Zone-axis patterns formed by a new double-rocking technique, Ultramicroscopy 5, 71–74 (1980)

    CAS  Google Scholar 

  • R. Vincent, P.A. Midgley: Double conical beam-rocking system for measurement of integrated electron-diffraction intensities, Ultramicroscopy 53, 271–282 (1994)

    CAS  Google Scholar 

  • J.M. Zuo, J. Tao: Scanning electron nanodiffraction and diffraction imaging. In: Scanning Transmission Electron Microscopy, ed. by S. Pennycook, P. Nellist (Springer, New York 2011)

    Google Scholar 

  • K.H. Kim, H. Xing, J.M. Zuo, P. Zhang, H.F. Wang: TEM based high resolution and low-dose scanning electron nanodiffraction technique for nanostructure imaging and analysis, Micron 71, 39–45 (2015)

    CAS  Google Scholar 

  • K.H. Downing, R.M. Glaeser: Improvement in high-resolution image quality of radiation-sensitive specimens achieved with reduced spot size of the electron-beam, Ultramicroscopy 20, 269–278 (1986)

    CAS  Google Scholar 

  • C.S. Own, L.D. Marks, W. Sinkler: Electron precession: A guide for implementation, Rev. Sci. Instrum. 76, 033703 (2005)

    Google Scholar 

  • D. Jacob, P. Cordier, J.P. Morniroli, H.P. Schertl: Precession electron diffraction for the characterization of twinning in pseudo-symmetrical crystals: Case of coesite. In: Proc. EMC 2008 14th Eur. Microsc. Congr, ed. by M. Luysberg, K. Tillmann, T. Weirich (Springer, Berlin, Heidelberg 2008) pp. 193–194

    Google Scholar 

  • M. Blackman: On the intensities of electron diffraction rings, Proc. R. Soc. A 173, 68–82 (1939)

    CAS  Google Scholar 

  • M. Horstmann, G. Meyer: Messung der Elektronenbeugungsintensitäten polykristalliner Aluminiumschichten bei tiefer Temperatur und Vergleich mit der dynamischen Theorie, Z. Phys. 182, 380–397 (1965)

    CAS  Google Scholar 

  • K. Gjonnes: On the integration of electron diffraction intensities in the Vincent-Midgley precession technique, Ultramicroscopy 69, 1–11 (1997)

    CAS  Google Scholar 

  • J. Hwang, J.Y. Zhang, J. Son, S. Stemmer: Nanoscale quantification of octahedral tilts in perovskite films, Appl. Phys. Lett. 100, 191909 (2012)

    Google Scholar 

  • J.C.H. Spence, J.M. Cowley: Lattice imaging in STEM, Optik 50, 129–142 (1978)

    CAS  Google Scholar 

  • J.C.H. Spence, J. Lynch: STEM microanalysis by transmission electron-energy loss spectroscopy in crystals, Ultramicroscopy 9, 267–276 (1982)

    CAS  Google Scholar 

  • J. Zhu, J.M. Cowley: Micro-diffraction from stacking-faults and twin boundaries in fcc crystals, J. Appl. Crystallogr. 16, 171–175 (1983)

    CAS  Google Scholar 

  • J.M. Cowley, J.C.H. Spence: Convergent beam electron microdiffraction from small crystals, Ultramicroscopy 6, 359–366 (1981)

    CAS  Google Scholar 

  • J.M. LeBeau, S.D. Findlay, L.J. Allen, S. Stemmer: Position averaged convergent beam electron diffraction: Theory and applications, Ultramicroscopy 110, 118–125 (2010)

    CAS  Google Scholar 

  • C. Mory, C. Colliex, J.M. Cowley: Optimum defocus for STEM imaging and microanalysis, Ultramicroscopy 21, 171–177 (1987)

    Google Scholar 

  • S.D. Berger, I.G. Salisbury, R.H. Milne, D. Imeson, C.J. Humphreys: Electron energy-loss spectroscopy studies of nanometer-scale structures in alumina produced by intense electron-beam irradiation, Philos. Mag. B 55, 341–358 (1987)

    CAS  Google Scholar 

  • J.M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L.A. Nagahara: Atomic resolution imaging of a carbon nanotube from diffraction intensities, Science 300, 1419–1421 (2003)

    CAS  Google Scholar 

  • A. Beche, J.L. Rouviere, L. Clement, J.M. Hartmann: Improved precision in strain measurement using nanobeam electron diffraction, Appl. Phys. Lett. 95, 123114 (2009)

    Google Scholar 

  • G. Botton: Analytical Electron Microscopy. In: Science of Microscopy, Vol. I, ed. by P. Hawkes, J.C.H. Spence (Springer, New York 2007)

    Google Scholar 

  • H. Lichte, M. Lehmann: Electron holography—Basics and applications, Rep. Prog. Phys. 71, 016102 (2008)

    Google Scholar 

  • R.F. Egerton: Electron Energy-Loss Spectroscopy in the Electron Microscope, 2nd edn. (Springer, New York 2011)

    Google Scholar 

  • P. Duval, N. Hoan, J. Brian, L. Henry: Réalisation d'un dispositif de filtrage en énergie des images de microdiffraction électronique, Nouv. Rev. Opt. Appl. 1, 221–228 (1970)

    CAS  Google Scholar 

  • M.M.J. Treacy, J.M. Gibson: The effects of elastic relaxation on transmission electron-microscopy studies of thinned composition-modulated materials, J. Vac. Sci. Technol. B 4, 1458–1466 (1986)

    CAS  Google Scholar 

  • P. Hirsch, A. Howie, R.B. Nicolson, D.W. Pashley, M.J. Whelan: Electron Microscopy of Thin Crystals (Krieger, Malabar 1977)

    Google Scholar 

  • J.M. Zuo, A.L. Weickenmeier: On the beam selection and convergence in the Bloch-wave method, Ultramicroscopy 57, 375–383 (1995)

    CAS  Google Scholar 

  • I.A. Sheremetyev, A.V. Turbal, Y.M. Litvinov, M.A. Mikhailov: Computer deciphering of Laue patterns: Application to white synchrotron x-ray topography, Nucl. Instrum. Methods Phys. Res. A 308, 451–455 (1991)

    Google Scholar 

  • H.R. Wenk, F. Heidelbach, D. Chateigner, F. Zontone: Laue orientation imaging, J. Synchrotron Radiat. 4, 95–101 (1997)

    CAS  Google Scholar 

  • S. Zaefferer: New developments of computer-aided crystallographic analysis in transmission electron microscopy, J. Appl. Crystallogr. 33, 10–25 (2000)

    CAS  Google Scholar 

  • E.F. Rauch, L. Dupuy: Rapid spot diffraction patterns identification through template matching, Arch. Metall. Mater. 50, 87–99 (2005)

    CAS  Google Scholar 

  • E.F. Rauch, A. Duft: Orientation maps derived from TEM diffraction patterns collected with an external CCD camera, Mater. Sci. Forum 495–497, 197–202 (2005)

    Google Scholar 

  • E.F. Rauch, M. Veron: Coupled microstructural observations and local texture measurements with an automated crystallographic orientation mapping tool attached to a TEM, Materialwiss. Werkstofftech. 36, 552–556 (2005)

    CAS  Google Scholar 

  • G. Wu, S. Zaefferer: Advances in TEM orientation microscopy by combination of dark-field conical scanning and improved image matching, Ultramicroscopy 109, 1317–1325 (2009)

    CAS  Google Scholar 

  • E.F. Rauch, J. Portillo, S. Nicolopoulos, D. Bultreys, S. Rouvimov, P. Moeck: Automated nanocrystal orientation and phase mapping in the transmission electron microscope on the basis of precession electron diffraction, Z. Kristallogr. 225, 103–109 (2010)

    CAS  Google Scholar 

  • Y. Meng, J.-M. Zuo: Improvements in electron diffraction pattern automatic indexing algorithms, Eur. Phys. J. Appl. Phys. 80, 10701 (2017)

    Google Scholar 

  • J.P. Lewis: Fast template matching, Vis. Interface 95, 120–123 (1995)

    Google Scholar 

  • D. Dingley: Progressive steps in the development of electron backscatter diffraction and orientation imaging microscopy, J. Microsc. 213, 214–224 (2004)

    CAS  Google Scholar 

  • R. van Bremen, D. Ribas Gomes, L.T.H. de Jeer, V. Ocelík, J.T.M. De Hosson: On the optimum resolution of transmission-electron backscattered diffraction (t-EBSD), Ultramicroscopy 160, 256–264 (2016)

    Google Scholar 

  • K.J. Ganesh, A.D. Darbal, S. Rajasekhara, G.S. Rohrer, K. Barmak, P.J. Ferreira: Effect of downscaling nano-copper interconnects on the microstructure revealed by high resolution TEM-orientation-mapping, Nanotechnology 23, 135702 (2012)

    CAS  Google Scholar 

  • E.F. Rauch, M. Véron: Automated crystal orientation and phase mapping in TEM, Mater. Charact. 98, 1–9 (2014)

    CAS  Google Scholar 

  • A.D. Darbal, K.J. Ganesh, X. Liu, S.B. Lee, J. Ledonne, T. Sun, B. Yao, A.P. Warren, G.S. Rohrer, A.D. Rollett, P.J. Ferreira, K.R. Coffey, K. Barmak: Grain boundary character distribution of nanocrystalline Cu thin films using stereological analysis of transmission electron microscope orientation maps, Microsc. Microanal. 19, 111–119 (2013)

    CAS  Google Scholar 

  • Y. Hu, J.H. Huang, J.M. Zuo: In situ characterization of fracture toughness and dynamics of nanocrystalline titanium nitride films, J. Mater. Res. 31, 370–379 (2016)

    CAS  Google Scholar 

  • J.L. Rouviere, A. Beche, Y. Martin, T. Denneulin, D. Cooper: Improved strain precision with high spatial resolution using nanobeam precession electron diffraction, Appl. Phys. Lett. 103, 241913 (2013)

    Google Scholar 

  • H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.R. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, D. Shapiro: High-resolution ab initio three-dimensional x-ray diffraction microscopy, J. Opt. Soc. Am. A 23, 1179–1200 (2006)

    Google Scholar 

  • H. Poulsen: An introduction to three-dimensional x-ray diffraction microscopy, J. Appl. Crystallogr. 45, 1084–1097 (2012)

    CAS  Google Scholar 

  • B.C. Larson, W. Yang, G.E. Ice, J.D. Budai, J.Z. Tischler: Three-dimensional x-ray structural microscopy with submicrometre resolution, Nature 415, 887–890 (2002)

    CAS  Google Scholar 

  • W. Ludwig, S. Schmidt, E.M. Lauridsen, H.F. Poulsen: X-ray diffraction contrast tomography: A novel technique for three-dimensional grain mapping of polycrystals. I. Direct beam case, J. Appl. Crystallogr. 41, 302–309 (2008)

    CAS  Google Scholar 

  • A.D. Rollett, S.B. Lee, R. Campman, G.S. Rohrer: Three-dimensional characterization of microstructure by electron back-scatter diffraction, Annu. Rev. Mater. Res. 37, 627–658 (2007)

    CAS  Google Scholar 

  • H.H. Liu, S. Schmidt, H.F. Poulsen, A. Godfrey, Z.Q. Liu, J.A. Sharon, X. Huang: Three-dimensional orientation mapping in the transmission electron microscope, Science 332, 833–834 (2011)

    CAS  Google Scholar 

  • A.S. Eggeman, R. Krakow, P.A. Midgley: Scanning precession electron tomography for three-dimensional nanoscale orientation imaging and crystallographic analysis, Nat. Commun. 6, 7267 (2015)

    CAS  Google Scholar 

  • P.A. Midgley, R.E. Dunin-Borkowski: Electron tomography and holography in materials science, Nat. Mater. 8, 271–280 (2009)

    CAS  Google Scholar 

  • Y. Meng, J.-M. Zuo: Three-dimensional nanostructure determination from a large diffraction data set recorded using scanning electron nanodiffraction, IUCrJ 3, 300–308 (2016)

    CAS  Google Scholar 

  • J.M. Zuo, A.B. Shah, H. Kim, Y.F. Meng, W.P. Gao, J.L. Rouviere: Lattice and strain analysis of atomic resolution Z-contrast images based on template matching, Ultramicroscopy 136, 50–60 (2014)

    CAS  Google Scholar 

  • S. Zaefferer: A critical review of orientation microscopy in SEM and TEM, Cryst. Res. Technol. 46, 607–628 (2011)

    CAS  Google Scholar 

  • G.T. Herman: Fundamentals of Computerized Tomography: Image Reconstruction from Projections, Advances in Pattern Recognition (Springer, London 2009)

    Google Scholar 

  • J. Amanatides, A. Woo: A fast voxel traversal algorithm for ray tracing, Eurographics 87, 3–10 (1987)

    Google Scholar 

  • S. Kaczmarz: Angenäherte Auflösung von Systemen linearer Gleichungen, Bull. Intern. Acad. Pol. Sci. Lett., Cl. Sci. Math. Nat. A 35, 335–357 (1937)

    Google Scholar 

  • F.L. Markley: Attitude determination using vector observations and the singular value decomposition, J. Astronaut. Sci. 38, 245–258 (1988)

    Google Scholar 

  • S.V. Fortuna, Y.P. Sharkeev, A.J. Perry, J.N. Matossian, I.A. Shulepov: Microstructural features of wear-resistant titanium nitride coatings deposited by different methods, Thin Solid Films 377/378, 512–517 (2000)

    Google Scholar 

  • W.-L. Pan, G.-P. Yu, J.-H. Huang: Mechanical properties of ion-plated tin films on AISI D-2 steel, Surf. Coat. Technol. 110, 111–119 (1998)

    CAS  Google Scholar 

  • A.-N. Wang, G.P. Yu, J.-H. Huang: Fracture toughness measurement on tin hard coatings using internal energy induced cracking, Surf. Coat. Technol. 239, 20–27 (2014)

    CAS  Google Scholar 

  • C.H. Ma, J.-H. Huang, H. Chen: Nanohardness of nanocrystalline tin thin films, Surf. Coat. Technol. 200, 3868–3875 (2006)

    CAS  Google Scholar 

  • P.H. Mayrhofer, C. Mitterer, J. Musil: Structure–property relationships in single- and dual-phase nanocrystalline hard coatings, Surf. Coat. Technol. 174/175, 725–731 (2003)

    Google Scholar 

  • P.H. Mayrhofer, F. Kunc, J. Musil, C. Mitterer: A Comparative study on reactive and non-reactive unbalanced magnetron sputter deposition of tin coatings, Thin Solid Films 415, 151–159 (2002)

    CAS  Google Scholar 

  • L.M. Peng, S.L. Dudarev, M.J. Whelan: High Energy Electron Diffraction and Microscopy (Oxford Univ. Press, Oxford 2004)

    Google Scholar 

  • D.M. Bird, Q.A. King: Absorptive form-factors for high-energy electron-diffraction, Acta Crystallogr. A 46, 202–208 (1990)

    Google Scholar 

  • A. Weickenmeier, H. Kohl: Computation of absorptive form-factors for high-energy electron-diffraction, Acta Crystallogr. A 47, 590–597 (1991)

    Google Scholar 

  • L.M. Peng: Anisotropic thermal vibrations and dynamical electron diffraction by crystals, Acta Crystallogr. A 53, 663–672 (1997)

    Google Scholar 

  • L. Sturkey: The use of electron-diffraction intensities in structure determination, Acta Crystallogr. 10, 858 (1957)

    Google Scholar 

  • D. Jacob, J.M. Zuo, A. Lefebvre, Y. Cordier: Composition analysis of semiconductor quantum wells by energy filtered convergent-beam electron diffraction, Ultramicroscopy 108, 358–366 (2008)

    CAS  Google Scholar 

  • C.J. Rossouw, M. Alkhafaji, D. Cherns, J.W. Steeds, R. Touaitia: A treatment of dynamic diffraction for multiply layered structures, Ultramicroscopy 35, 229–236 (1991)

    Google Scholar 

  • J.M. Cowley, A.F. Moodie: The scattering of electrons by atoms and crystals. I. A new theoretical approach, Acta Crystallographica 10(10), 609–619 (1957)

    CAS  Google Scholar 

  • K. Ishizuka: Multislice formula for inclined illumination, Acta Crystallogr. A 38, 773–779 (1982)

    Google Scholar 

  • B.F. Buxton, J.A. Eades, J.W. Steeds, G.M. Rackham: Symmetry of electron-diffraction zone axis patterns, Philos. Trans. R. Soc. A 281, 171 (1976)

    CAS  Google Scholar 

  • M. Tanaka, R. Saito, H. Sekii: Point-group determination by convergent-beam electron-diffraction, Acta Crystallogr. A 39, 357–368 (1983)

    Google Scholar 

  • M. Tanaka, H. Sekii, T. Nagasawa: Space-group determination by dynamic extinction in convergent-beam electron-diffraction, Acta Crystallogr. A 39, 825–837 (1983)

    Google Scholar 

  • G.B. Hu, L.M. Peng, Q.F. Yu, H.Q. Lu: Automated identification of symmetry in CBED patterns: A genetic approach, Ultramicroscopy 84, 47–56 (2000)

    CAS  Google Scholar 

  • R. Vincent, T.D. Walsh: Quantitative assessment of symmetry in CBED patterns, Ultramicroscopy 70, 83–94 (1997)

    CAS  Google Scholar 

  • J.F. Mansfield: Error bars in CBED symmetry?, Ultramicroscopy 18, 91–96 (1985)

    CAS  Google Scholar 

  • K.H. Kim, J.M. Zuo: Symmetry quantification and mapping using convergent beam electron diffraction, Ultramicroscopy 124, 71–76 (2013)

    CAS  Google Scholar 

  • J.M. Kiat, Y. Uesu, B. Dkhil, M. Matsuda, C. Malibert, G. Calvarin: Monoclinic structure of unpoled morphotropic high piezoelectric PMN-PT and PZN-PT compounds, Phys. Rev. B 65, 064106 (2002)

    Google Scholar 

  • Y.-T. Shao, J.-M. Zuo: Fundamental symmetry of barium titanate single crystal determined using energy-filtered scanning convergent beam electron diffraction, Microsc. Microanal. 22, 516–517 (2016)

    Google Scholar 

  • J.M. Zuo, J.C.H. Spence: Automated structure factor refinement from convergent-beam patterns, Ultramicroscopy 35, 185–196 (1991)

    CAS  Google Scholar 

  • J.M. Zuo: Accurate structure refinement and measurement of crystal charge distribution using convergent beam electron diffraction, Microsc. Res. Tech. 46, 220–233 (1999)

    CAS  Google Scholar 

  • Y. Ogata, K. Tsuda, M. Tanaka: Determination of the electrostatic potential and electron density of silicon using convergent-beam electron diffraction, Acta Crystallogr. A 64, 587–597 (2008)

    CAS  Google Scholar 

  • P.N.H. Nakashima, B.C. Muddle: Differential convergent beam electron diffraction: Experiment and theory, Phys. Rev. B 81, 115135 (2010)

    Google Scholar 

  • J.M. Zuo: Quantitative convergent beam electron diffraction, Mater. Trans. JIM 39, 938–946 (1998)

    CAS  Google Scholar 

  • J. Friis, B. Jiang, J.C.H. Spence, R. Holmestad: Quantitative convergent beam electron diffraction measurements of low-order structure factors in copper, Microsc. Microanal. 9, 379–389 (2003)

    CAS  Google Scholar 

  • P.N.H. Nakashima: Improved quantitative CBED structure-factor measurement by refinement of nonlinear geometric distortion corrections, J. Appl. Crystallogr. 38, 374–376 (2005)

    CAS  Google Scholar 

  • K. Tsuda, M. Tanaka: Refinement of crystal structural parameters using two-dimensional energy-filtered CBED patterns, Acta Crystallogr. A 55, 939–954 (1999)

    CAS  Google Scholar 

  • B. Jiang, J.M. Zuo, J. Friis, J.C.H. Spence: On the consistency of QCBED structure factor measurements for TiO2 (Rutile), Microsc. Microanal. 9, 457–467 (2003)

    CAS  Google Scholar 

  • M. Saunders, D.M. Bird, N.J. Zaluzec, W.G. Burgess, A.R. Preston, C.J. Humphreys: Measurement of low-order structure factors for silicon from zone-axis CBED patterns, Ultramicroscopy 60, 311–323 (1995)

    CAS  Google Scholar 

  • B.T.M. Willis, A.W. Pryor: Thermal Vibrations in Crystallography (Cambridge Univ. Press, Cambridge 1975)

    Google Scholar 

  • G. Ren, J.M. Zuo, L.M. Peng: Accurate measurements of crystal structure factors using a FEG electron microscope, Micron 28, 459–467 (1997)

    Google Scholar 

  • J.M. Zuo: Measurements of electron densities in solids: A real-space view of electronic structure and bonding in inorganic crystals, Rep. Prog. Phys. 67, 2053–2103 (2004)

    CAS  Google Scholar 

  • J.M. Rodenburg: Ptychography and related diffractive imaging methods, Adv. Imaging Electron Phys. 150, 87–184 (2008)

    Google Scholar 

  • W. Hoppe: Trace structure-analysis, ptychography, phase tomography, Ultramicroscopy 10, 187–198 (1982)

    Google Scholar 

  • J.C.H. Spence, U. Weierstall, M. Howells: Phase recovery and lensless imaging by iterative methods in optical, x-ray and electron diffraction, Philos. Trans. R. Soc. A 360, 875–895 (2002)

    CAS  Google Scholar 

  • H. Lichte: Electron holography approaching atomic resolution, Ultramicroscopy 20, 293–304 (1986)

    CAS  Google Scholar 

  • A. Orchowski, W.D. Rau, H. Lichte: Electron holography surmounts resolution limit of electron-microscopy, Phys. Rev. Lett. 74, 399–402 (1995)

    CAS  Google Scholar 

  • S.G. Podorov, K.M. Pavlov, D.M. Paganin: A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging, Opt. Express 15, 9954–9962 (2007)

    CAS  Google Scholar 

  • I.L. Karle, J. Karle: The crystal and molecular structure of the alkaloid jamine from Ormosia jamaicensis, Acta Crystallogr. 17, 1356 (1964)

    CAS  Google Scholar 

  • J. Karle, I.L. Karle: The symbolic addition procedure for phase determination for centrosymmetric and noncentrosymmetric crystals, Acta Crystallogr. 21, 849 (1966)

    CAS  Google Scholar 

  • D. Gabor: A new microscopic principle, Nature 161, 777–778 (1948)

    CAS  Google Scholar 

  • J.C.H. Spence: Stem and shadow-imaging of biomolecules at 6 eV beam energy, Micron 28, 101–116 (1997)

    CAS  Google Scholar 

  • J.C.H. Spence, T. Vecchione, U. Weierstall: A coherent photofield electron source for fast diffractive and point-projection imaging, Philos. Mag. 90, 4691–4702 (2010)

    CAS  Google Scholar 

  • H. Nyquist: Certain topics in telegraph transmission theory, Trans. Am. Inst. Electr. Eng. 47, 617 (1928)

    Google Scholar 

  • C.E. Shannon: Communication in the presence of noise, Inst. Radio Eng. 37, 10 (1949)

    Google Scholar 

  • D. Sayre, H.N. Chapman, J. Miao: On the extendibility of x-ray crystallography to noncrystals, Acta Crystallogr. A 54, 232–239 (1998)

    Google Scholar 

  • J.C.H. Spence, U. Weierstall, M. Howells: Coherence and sampling requirements for diffraction imaging, Ultramicroscopy 101, 149–152 (2004)

    CAS  Google Scholar 

  • W.J. Huang, B. Jiang, R.S. Sun, J.M. Zuo: Towards sub-Å atomic resolution electron diffraction imaging of metallic nanoclusters: A simulation study of experimental parameters and reconstruction algorithms, Ultramicroscopy 107, 1159–1170 (2007)

    CAS  Google Scholar 

  • V. Elser: Phase retrieval by iterated projections, J. Opt. Soc. Am. A 20, 40 (2003)

    Google Scholar 

  • J.R. Fienup: Phase retrieval algorithms—A comparison, Appl. Opt. 21, 2758–2769 (1982)

    CAS  Google Scholar 

  • J.R. Fienup: Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint, J. Opt. Soc. Am. 6, 118 (1987)

    Google Scholar 

  • R.W. Gerchberg, W.O. Saxton: Practical algorithm for determination of phase from image and diffraction plane pictures, Optik 35, 237 (1972)

    Google Scholar 

  • G. Oszlanyi, A. Suto: Ab initio structure solution by charge flipping, Acta Crystallogr. A 60, 134–141 (2004)

    Google Scholar 

  • J.S. Wu, J.C.H. Spence: Reconstruction of complex single-particle images using charge-flipping algorithm, Acta Crystallogr. A 61, 194–200 (2005)

    CAS  Google Scholar 

  • J.M. Zuo, J. Zhang, W.J. Huang, K. Ran, B. Jiang: Combining real and reciprocal space information for aberration free coherent electron diffractive imaging, Ultramicroscopy 111, 817–823 (2011)

    CAS  Google Scholar 

  • R.P. Millane, W.J. Stroud: Reconstructing symmetric images from their undersampled Fourier intensities, J. Opt. Soc. Am. A 14, 568–579 (1997)

    CAS  Google Scholar 

  • C.C. Chen, J. Miao, C.W. Wang, T.K. Lee: Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method, Phys. Rev. B 76, 064113 (2007)

    Google Scholar 

  • R. Dronyak, K.S. Liang, Y.P. Stetsko, T.K. Lee, C.K. Feng, J.S. Tsai, F.R. Chen: Electron diffractive imaging of nano-objects using a guided method with a dynamic support, Appl. Phys. Lett. 95, 111908 (2009)

    Google Scholar 

  • H.D. Jiang, C.Y. Song, C.C. Chen, R. Xu, K.S. Raines, B.P. Fahimian, C.H. Lu, T.K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, J.W. Miao: Quantitative 3-D imaging of whole, unstained cells by using x-ray diffraction microscopy, Proc. Natl. Acad. Sci. U.S.A. 107, 11234–11239 (2010)

    CAS  Google Scholar 

  • J. Gulden, O.M. Yefanov, A.P. Mancuso, V.V. Abramova, J. Hilhorst, D. Byelov, I. Snigireva, A. Snigirev, A.V. Petukhov, I.A. Vartanyants: Coherent x-ray imaging of defects in colloidal crystals, Phys. Rev. B 81, 224105 (2010)

    Google Scholar 

  • P.E. Batson, N. Dellby, O.L. Krivanek: Sub-Angstrom resolution using aberration corrected electron optics, Nature 418, 617–620 (2002)

    CAS  Google Scholar 

  • P.D. Nellist, M.F. Chisholm, N. Dellby, O.L. Krivanek, M.F. Murfitt, Z.S. Szilagyi, A.R. Lupini, A. Borisevich, W.H. Sides, S.J. Pennycook: Direct sub-angstrom imaging of a crystal lattice, Science 305, 1741–1741 (2004)

    CAS  Google Scholar 

  • R. Erni, M.D. Rossell, C. Kisielowski, U. Dahmen: Atomic-resolution imaging with a sub-50-pm electron probe, Phys. Rev. Lett. 102, 096101 (2009)

    Google Scholar 

  • H. Sawada, Y. Tanishiro, N. Ohashi, T. Tomita, F. Hosokawa, T. Kaneyama, Y. Kondo, K. Takayanagi: STEM imaging of 47-pm-separated atomic columns by a spherical aberration-corrected electron microscope with a 300-kV cold field emission gun, J. Electron Microsc. 58, 357–361 (2009)

    CAS  Google Scholar 

  • S. Van Aert, K.J. Batenburg, M.D. Rossell, R. Erni, G. Van Tendeloo: Three-dimensional atomic imaging of crystalline nanoparticles, Nature 470, 374–377 (2011)

    Google Scholar 

  • A.Y. Borisevich, A.R. Lupini, S.J. Pennycook: Depth sectioning with the aberration-corrected scanning transmission electron microscope, Proc. Natl. Acad. Sci. U.S.A. 103, 3044–3048 (2006)

    CAS  Google Scholar 

  • A.Y. Borisevich, A.R. Lupini, S. Travaglini, S.J. Pennycook: Depth sectioning of aligned crystals with the aberration-corrected scanning transmission electron microscope, J. Electron Microsc. 55, 7–12 (2006)

    CAS  Google Scholar 

  • H.L. Xin, D.A. Muller: Aberration-corrected ADF-STEM depth sectioning and prospects for reliable 3-D imaging in S/TEM, J. Electron Microsc. 58, 157–165 (2009)

    CAS  Google Scholar 

  • R. Ishikawa, A.R. Lupini, S.D. Findlay, S.J. Pennycook: Quantitative annular dark field electron microscopy using single electron signals, Microsc. Microanal. 20, 99–110 (2014)

    CAS  Google Scholar 

  • E.C. Cosgriff, P.D. Nellist: A Bloch wave analysis of optical sectioning in aberration-corrected STEM, Ultramicroscopy 107, 626–634 (2007)

    CAS  Google Scholar 

  • M.C. Scott, C.-C. Chen, M. Mecklenburg, C. Zhu, R. Xu, P. Ercius, U. Dahmen, B.C. Regan, J. Miao: Electron tomography at 2.4-ångström resolution, Nature 483, 444–491 (2012)

    CAS  Google Scholar 

  • C.-C. Chen, C. Zhu, E.R. White, C.-Y. Chiu, M.C. Scott, B.C. Regan, L.D. Marks, Y. Huang, J. Miao: Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution, Nature 496, 74 (2013)

    CAS  Google Scholar 

  • X.W. Lu, W.P. Gao, J.M. Zuo, J.B. Yuan: Atomic resolution tomography reconstruction of tilt series based on a GPU accelerated hybrid input-output algorithm using polar fourier transform, Ultramicroscopy 149, 64–73 (2015)

    CAS  Google Scholar 

  • J. Miao, T. Ohsuna, O. Terasaki, K.O. Hodgson, M.A. O'Keefe: Atomic resolution three-dimensional electron diffraction microscopy, Phys. Rev. Lett. 89, 155502 (2002)

    Google Scholar 

  • J. Keiner, S. Kunis, D. Potts: Using NFFT 3---A software library for various nonequispaced fast Fourier transforms, ACM Trans. Math. Softw. 36, 19 (2009)

    Google Scholar 

  • M. Fenn, S. Kunis, D. Potts: On the computation of the polar FFT, Appl. Comput. Harmon. Anal. 22, 257–263 (2007)

    Google Scholar 

  • S. Kunis, S. Kunis: The nonequispaced FFT on graphics processing units, Proc. Appl. Math. Mech. 12, 7–10 (2012)

    Google Scholar 

Download references

Acknowledgements

The writing of this chapter was made possible with the support by US Department of Energy, Grant DEFG02-01ER45923 and NSF DMR 1410596. The work described here would not have been possible without the outstanding efforts of students and postdoc students, especially work by Weijie Huang, Yifei Meng, Yu-Tsun Shao, Kyouhyun Kim, Xiangwen Lu, Wenpei Gao, and Piyush Vivek Deshpande has contributed directly to the writing of this chapter.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian-Min Zuo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zuo, JM. (2019). Electron Nanodiffraction. In: Hawkes, P.W., Spence, J.C.H. (eds) Springer Handbook of Microscopy. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-00069-1_18

Download citation

Publish with us

Policies and ethics