Advertisement

Electron Crystallography, Charge-Density Mapping and Nanodiffraction

  • John Spence
Chapter

Chapter Preview

This chapter does contain rather a lot of physics but don’t let that put you off. You can look up Dirac–Fock calculations, the Mott formula , and what the Debye–Waller factor is later if you want to. Ditto for the Simplex algorithm , the bootstrap method , Poisson statistics and the Fienup algorithm, but if you don’t immediately do so, you should have no problem in following the discussion. We’ve left the word electron in the title of the chapter to emphasize that this is not X-ray crystallography . The electron version has many features to recommend it – the interactions are stronger and most researchers now have access to a TEM with a field-emission gun. With the FEG you can examine a very small volume. One feature that comes up again is the perennial problem that we need thin specimens, which means we may have relaxation due to the proximity of a surface. Then we discuss using QCBED to learn about bonding. Clearly this will be an incredibly important...

Keywords

Spherical Aberration Shadow Image Noncentrosymmetric Crystal Excitation Error Aberration Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

General References

  1. Bird D, King Q (1990) Absorptive form factors for high-energy electron diffraction. Acta Cryst A46:202CrossRefGoogle Scholar
  2. Champness PE (2001) Electron diffraction in the transmission electron microscope. BIOS Scientific/ Royal Micros Society, Oxford (A very useful introduction to electron diffraction)Google Scholar
  3. Cowley JM (1992) Techniques of transmission electron diffraction. Oxford Univ. Press, New York. (Many useful chapters on electron diffraction by our teacher. This early work met with mixed success, and was often not accepted by the X-ray community)Google Scholar
  4. Cowley JM (1995) ‘Introductory’ text-book on the physics of diffraction. Diffraction Physics, 3rd edn. North-Holland, New YorkGoogle Scholar
  5. Cowley JM (1953) Structure analysis of single crystals by electron diffraction. I. techniques. Acta Cryst 6:516CrossRefGoogle Scholar
  6. Dorset D (1995) Covers the organic-crystal structure field, with emphasis on non-biological organics such as waxes, lipids and polymers. Structural Electron Crystallography. Plenum Press, New YorkGoogle Scholar
  7. Peng LM, Dudarev SL, Whelan MJ (2004) High Energy Electron diffraction and Microscopy. Oxford University PressGoogle Scholar
  8. Pennycook SJ, Nellist (eds) (2011) Scanning transmission electron microscopy: imaging and analysis. Springer Science and Business MediaGoogle Scholar
  9. Rodenburg JM (2008) Ptychography and related diffractive imaging methods. Advances in Imaging and Electron Physics 150:87–184CrossRefGoogle Scholar
  10. Spence JCH (2013) High-resolution electron microscopy, 4th edn. Oxford University PressCrossRefGoogle Scholar
  11. Weirich T, Labar J, Zou X (2004) Electron Crystallography. NATO Science Series 211Google Scholar
  12. Midgley PA, Eggeman AS (2015) Precession electron diffraction – a topical review. IUCrJ 2(1):126–136CrossRefGoogle Scholar
  13. Zuo J (2004) Measurements of electron densities in solids: a real-space view of electronic structure and bonding in inorganic crystals. Rep Prog Phys 67:2053–2103 (The basic idea of CBED refinement reviewed with many applications – the best overall review of quantitative CBED)CrossRefGoogle Scholar
  14. The book on electron crystallography edited by Weirich et al. (2004) contains many useful case studies, and the books by Cowley (1992), Dorset (1995), Peng et al. (2004), and Spence and Zuo (1992) (see new 2016 edition) are essential reading for students interested primarily in electron diffraction rather than imaging.Google Scholar

Specific References

  1. Allpress JG, Sanders JV, Wadsley AD (1969) Multiple phase formation in the binary system Nb 2 O 5 -WO 3 . VI. Electron microscopic observation and evaluation of non-periodic shear structures. Acta Cryst B25:1156–1164 (The first useful observations of atomic structure by electron microscopy)CrossRefGoogle Scholar
  2. Armigliato A, Balboni R, Frabboni S (2005) Improving spatial resolution of convergent beam electron diffraction strain mapping in silicon microstructures. Appl Phys Lett 86 (063508-1-3. The ASAC software package)Google Scholar
  3. Blackman M (1939) On the intensities of electron diffraction rings. Proc Roy Soc A173:68–82 (The beginning of the precession technique)CrossRefGoogle Scholar
  4. Doyle P, Turner P (1968) Relativistic Hartree-Fock X-ray and electron scattering factors. Acta Cryst A24:390–397 (For the electron atomic scattering factors – with over 2,600 citations)CrossRefGoogle Scholar
  5. Fienup J (1982) Phase retrieval algorithms – a comparison. Appl Optics 21:2758–2769 (Signal processing field algorithm – with over 1,800 citations)CrossRefGoogle Scholar
  6. Humphreys CJ (1979) The scattering of fast electrons by crystals. Rep Prog Phys 42:1825–1887 (How CBED software works)CrossRefGoogle Scholar
  7. Humphry MJ, Kraus B, Hurst AC, Maiden AM, Rodenburg JM (2012) Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging. Nature Commun 3:730CrossRefGoogle Scholar
  8. Nellist P, McCallum B, Rodenburg J (1995) Resolution beyond the ‘information limit’ in transmission electron microscopy. Nature 374:630–632 (Ptychography, as a method of super-resolution in STEM)CrossRefGoogle Scholar
  9. O’Keeffe M, Spence JCH (1994) On the average coulomb potential (Φ 0 ) and constraints on the electron-density in crystals. Acta Cryst A50:33–44 (On the surface dipole layers of a thin slab)CrossRefGoogle Scholar
  10. Press W, Flannery B, Teukolsky S, Vetterling W (1986) Numerical Recipes. Cambridge University Press, New York (For the simplex algorithm)Google Scholar
  11. Spence J, Zuo JM (1992) Electron Microdiffraction. Plenum, New York (Gives a Fortran source-code to calculate CBED intensity distributions Ig(Kt) with full documentation. Also plot out the kinematic positions of HOLZ lines. Includes discussion of the ‘Tanaka’ method of large-angle CBED. This book has been extensively revised and extended for publication in 2016 as “Electron diffraction and Imaging”. Zuo JM, Spence JCH, Springer (2016).)CrossRefGoogle Scholar
  12. Spence JCH, Cowley JM (1978) Lattice imaging in STEM. Optik 50:129–142 (The probe spans many unit cells. A full analysis of the case where orders do overlap)Google Scholar
  13. Tsuda K, Tanaka M (1995) Refinement of crystal structure parameters using convergent-beam electron diffraction: the low-temperature phase of SrTiO 3. Acta Cryst A51:7–19 (Rotation of Oxygen octahedra with temperature in SrTiO3 by QCBED)CrossRefGoogle Scholar
  14. Zuo J (1992) Automated lattice-parameter measurement from HOLZ lines and their use for the measurement of oxygen-content in YBa 2 Cu 3 O 7-δ from nanometer-sized region. Ultramicroscopy 41:211–223 (More on how CBED software works)CrossRefGoogle Scholar
  15. Zuo J, O’Keeffe M, Rez P, Spence JCH (1997) Charge Density of MgO: Implications of Precise New Measurements for Theory. Phys Rev Lett 78:4777–4780 (How ionic is MgO? Full dynamical refinement)CrossRefGoogle Scholar
  16. Zuo J, Kim M, O’Keeffe M, Spence JCH (1999) Direct observation of d-orbital holes and Cu-Cu bonding in Cu 2 O. Nature 401:49–52 (The example of Cu2O)CrossRefGoogle Scholar
  17. Zuo J, Hoier R, Spence JCH (1989) 3-beam and many-beam theory in electron-diffraction and its use for structure-factor phase determination in non-centrosymmetric crystal-structures. Acta Cryst A45:839–851 (For references to the work of Kambe, Gjonnes, Moodie, etc)CrossRefGoogle Scholar
  18. http://emaps.mrl.uiuc.edu/ – Go there for a free web-based program for these simulations. Input data is entered on the web and results returned as a pdf email attachment. The job runs on computers at the University of Illinois. Chapter 16 describes use of the JEMS program for similar purposes.

Background References

  1. Allen LJ, Faulkner HML, Leeb H (2000) Inversion or dynamical electron diffraction data including absorption. Acta Cryst A56:119–126 (Ptychography giving a charge-density map of the sample crystal structure showing all the atom types and their positions. (See also Spence 1998.))CrossRefGoogle Scholar
  2. Bader R (1990) Atoms in molecules: A Quantum Theory. Oxford University Press, New York (Partitioning problem and the multipole expansion)Google Scholar
  3. Coppens P (1997) X-ray charge densities and chemical bonding. Partitioning problem and the multipole expansion. Oxford Univ. Press, New YorkGoogle Scholar
  4. Liu Y, Eades J, Mazumder J (1994) Solving the crystal-structure of a submicrometer phase in TEM. Ultramicroscopy 56:253–268CrossRefGoogle Scholar
  5. Eades JA (1988) Microbeam Analysis 75. San Francisco Press, San FranciscoGoogle Scholar
  6. Ecob RC (1986) Comments on the measurement of foil thickness by convergent beam electron-diffraction. Scripta Metall 20(7):1001–1006CrossRefGoogle Scholar
  7. Godden TM, Suman R, Humphry MJ, Rodenburg JM, Maiden AM (2014) Ptychographic microscope for three-dimensional imaging. Opt Express 22(10):12513–12523CrossRefGoogle Scholar
  8. Gramm F, Baerlocher C, McCusker LB, Warrender SJ, Wright PA, Han B, Hong SB, Liu Z, Ohsuna T, Terasaki O (2006) Solving a complex zeolite by a combining powder diffraction and electron microscopy. Nature 444(7115):79–81CrossRefGoogle Scholar
  9. Hoier R, Kim M, Zuo J, Spence J, Shindo D (1995) Sample thickness and beam divergence, using an image plate detector and elastic imaging filter. Proc MSA. Springer, New YorkGoogle Scholar
  10. Holmestad R, Zuo JM, Spence JCH, Hoier R, Horita Z (1995) Effect of Mn doping on charge-density in gamma-TiAl by quantitative convergent-beam electron-diffraction. Philos Mag 72:579–601CrossRefGoogle Scholar
  11. Honjo G, Kodera S, Kitamura N (1964) Diffuse streak diffraction patterns from single crystals .i. General discussion + aspects of electron diffraction diffuse streak patterns. J Phys Soc 19:351 (Japan. Plot outlines and sheets of this thermal diffuse scattering)CrossRefGoogle Scholar
  12. Hoppe W (1969) First proposed Ptychography for electron microscopy. Acta Cryst A25:495CrossRefGoogle Scholar
  13. Humphreys CJ, Maher DM, Fraser HL, Eaglesham DJ (1988) Convergent-beam imaging – a transmission electron-microscopy technique for investigating small localized distortions in crystals. Philos Mag A58:787–798CrossRefGoogle Scholar
  14. Kim M, Zuo JM, Park GS (2004) High-resolution strain measurement in shallow trench isolation structures using dynamic electron diffraction. Appl Phys Lett 84:2181–2183CrossRefGoogle Scholar
  15. Kirk MA, Davidson R, Jenkins M, Twesten R (2005) Measurement of diffuse electron scattering by single nanometre-sized defects in gold. Philos Mag 85:497–507 (See Kirk et al. (2005))CrossRefGoogle Scholar
  16. Lin JA, Cowley JM (1986) Reconstruction from in-line electron holograms by digital processing. Ultramicroscopy 19(31):179–190 (Development of the Ronchigram as an aberration figure to give values of the aberration constants. Electron holograms using an STEM)CrossRefGoogle Scholar
  17. Lin YP, Bird DM, Vincent R (1989) Errors and correction term for holz line simulations. Ultramicroscopy 27:233–240 (Complications when measuring strain)CrossRefGoogle Scholar
  18. Liu Z, Ohsuna T, Terasaki O, Camblor M, Diaz-Cabanas M, Hiraga K (2001) The first zeolite with three-dimensional intersecting straight-channel system of 12-membered rings. J Am Chem Soc 123:5370–5371 (Solving the structure of a zeolite)CrossRefGoogle Scholar
  19. Loretto M (1984) Electron beam analysis of materials. Chapman and Hall, LondonCrossRefGoogle Scholar
  20. Lynch DF, Moodie AF, O’Keefe MA (1975) N-beam lattice images. V. The use of the charge-density approximation in the interpretation of lattice images. Acta Cryst A31:300–307 (Detailed calculations, showing the maximum thickness we can use for oxides – see other papers in the series too)CrossRefGoogle Scholar
  21. Matsumura S, Tomokiyo Y, Oki K (1989) Study of temperature factors in cubic-crystals by high-voltage electron-diffraction. J Electron Microsc Techn 12(3):262–271CrossRefGoogle Scholar
  22. Moodie AF, Etheridge J, Humphreys CJ (1996) The symmetry of three-beam scattering equations: Inversion of three-beam diffraction patterns from centrosymmetric crystals. Acta Cryst A52:596–605CrossRefGoogle Scholar
  23. Morniroli JP Large-angle convergent-beam electron diffraction Application to crystal defects. (in english). Monograph of the French Society of Microscopies. ISBN 2-901483-05-4. Gives method of determining Burgers vectors for dislocations from CBED patterns.Google Scholar
  24. Ohsuna T, Liu Z, Terasaki O (2002) Framework determination of a polytype of zeolite beta by using electron crystallography. J Phys Chem B106:5673–5678 (Practical details of the method of combining images and diffraction patterns to solve the sensitive zeolite structures)CrossRefGoogle Scholar
  25. Own CS, Marks LD, Sinkler W (2005) Electron precession: A guide for implementation. Rev Sci Instr 76(3) (article # 033703. Practical details of one system for the precession method)Google Scholar
  26. Pike WT, Brown LM, Kubiak RAA, Newstead SM, Powell AR, Parker EHC, Whall TE (1991) The determination of strain in Si-Ge superlattices by electron-diffraction in a scanning-transmission electron-microscope. J Cryst Growth 111(1–4):925–930 (Strain measurements in Si/Si-Ge layers)CrossRefGoogle Scholar
  27. Plamann T, Rodenburg J (1998) Electron ptychography. II. Theory of three-dimensional propagation effects. Acta Cryst A54:61–73 (The idea ptychography elaborated extensively, a systematic method is given which involves recording these patterns as a function of probe position)CrossRefGoogle Scholar
  28. Spence J (1978) Phase determination by STEM. SEM 1978. Ed. Johari, O. IITRI, ChicagoGoogle Scholar
  29. Spence JCH, Taftø J (1983) ALCHEMI: a new technique for locating atoms in small crystals. J Microsc 130:147–154CrossRefGoogle Scholar
  30. Spence JCH, Zuo JM, O’Keeffe M, Marthinsen K, Hoier R (1994) On the minimum number of beams needed to distinguish enantiomorphs in x-ray and electron-diffraction. Acta Cryst A50:647–650CrossRefGoogle Scholar
  31. Spence JCH (2006) Diffractive (lensless) imaging. Science of Microscopy. In: Hawkes P, Spence JCH (eds) Aberration-free images using radiations for which no lenses exist. Springer, New YorkGoogle Scholar
  32. Spence JCH (1998) Direct inversion of dynamical electron diffraction patterns to structure factors. Acta Cryst A54:7–18CrossRefGoogle Scholar
  33. Tanaka M, Terauchi M, Tsuda K (2003) Convergent-beam electron diffraction III. JEOL, TokyoGoogle Scholar
  34. Terasaki O (2000) The structure of MCM-48 determined by electron crystallography. J Electron Microsc 48:795–798 (see also Nature 408, 449 Applications of electron crystallography to block-copolymers and liquid crystals)Google Scholar
  35. Treacy M, Gibson J, Howie A (1985) On elastic relaxation and long wavelength microstructures in spinodally decomposed In x Ga 1-x As y P 1-y epitaxial layers. Philos Mag A51:389–417 (Finite-element modeling of the thin-film elastic relaxation)CrossRefGoogle Scholar
  36. Vainshtein B (1964) Structure analysis by electron diffraction. Pergamon, New York (The early days of electron diffraction in Russia)Google Scholar
  37. Vincent R, Midgley P (1994) Precession method of electron diffraction. Ultramicroscopy 53(3):271–282 (Precession method of electron diffraction)CrossRefGoogle Scholar
  38. Weirich TE, Portillo J, Cox G, Hibst H, Nicolopoulos S (2006) Ab initio determination of the framework structure of the heavy-metal oxide CsxNb2.54W2.46O14 from 100 kV precession electron diffraction data. Ultramicroscopy 106(3):164–175 (Electron crystallography applied to transition metal oxides and to the mesoporous framework silicates; asymmetric unit of a (Cs,Nb,W)5O14 oxide framework)CrossRefGoogle Scholar
  39. Woolfson M, Fan HF (1995) Physical and non-physical methods of solving crystal structures. Cambridge University Press (A good introduction to the numerical methods used to solve the phase problem)CrossRefGoogle Scholar
  40. Wu J, Spence J (2003) Low-dose, low-temperature convergent-beam electron diffraction and multiwavelength analysis of hydrocarbon films by electron diffraction. Microsc Microanal 9:428–441 (Blank Disks. Compare four different kinematic approximations with experimental TED data from the known structure tetracontane)CrossRefGoogle Scholar
  41. Yagi K, Cowley JM (1978) Electron microscopy study of ordering of potassium ions in cubic KSbO 3. Acta Cryst A34:625–634 (Gives a superb example of using electron crystallography applied to the family of zeolite structures, which students should read, in which atomic defects seen in the high-resolution are related to the diffuse scattering)CrossRefGoogle Scholar
  42. Zhang P, Istratov A, Weber E, Kisielowski C, He H, Nelson C, Spence JCH (2006) Direct strain measurement in a 65 nm node strained silicon transistor by convergent-beam electron diffraction. Appl Phys Lett 89 (161907-1-3. Strains are mapped in FET with SiGe source and drain)Google Scholar
  43. Zhu J, Cowley JM (1983) Microdiffraction from stacking faults and twin boundaries in F.c.c. crystals. J Appl Cryst 16:171–175 (Fault vector of planar faults in CuAu alloys are determined by applying a kind of ‘g.b’ analysis in microdiffraction patterns)CrossRefGoogle Scholar
  44. Zuo JM, McCartney MR, Spence JCH (1996) Performance of imaging plates for electron recording. Ultramicroscopy 66:35–47CrossRefGoogle Scholar
  45. Zuo JM, Spence JCH (1993) Coherent electron nanodiffraction from perfect and imperfect crystals. Philos Mag A68(5):1055–1078CrossRefGoogle Scholar
  46. Zuo JM (1994) New method of Bravais lattice determination. Ultramicroscopy 52:459–464CrossRefGoogle Scholar
  47. Zuo J, Pacuad J, Hoier R, Spence J (2000) Diffuse electron scattering measurements have been correlated with bulk resistivity measurements against temperature. Micron 31:527–532CrossRefGoogle Scholar
  48. Zuo JM, Spence JCH, Hoier R (1989) Accurate structure-factor phase determination by electron-diffraction in noncentrosymmetric crystals. Phys Rev Lett 62:547–550CrossRefGoogle Scholar
  49. Tafto J, Gjonnes J (1985) The intersecting kikuchi line technique – critical voltage at any voltage. Ultramicroscopy 17:329–334CrossRefGoogle Scholar
  50. Zuo JM, Spence JCH, Downs J, Mayer J (1993) Measurement of individual structure-factor phases with tenth-degree accuracy: the 00.2 reflection in BeO studied by electron and X-ray diffraction. Acta Cryst A49:422–429CrossRefGoogle Scholar
  51. Zuo JM, O’Keeffe M, Rez P, Spence JCH (1997) Charge density of MgO: Implications of precise new measurements for theory. Phys Rev Lett 78:4777–4780CrossRefGoogle Scholar
  52. Zuo JM (1993) Automated structure-factor refinement from convergent-beam electron diffraction patterns. Acta Cryst A49:429–435CrossRefGoogle Scholar
  53. Zuo JM (2000) Electron detection characteristics of a slow-scan CCD camera, imaging plates and film, and electron image restoration. Microsc Res Techniq 49:245–268CrossRefGoogle Scholar
  54. Zuo JM (1996) Electron detection characteristics of slow-scan CCD camera. Ultramicroscopy 66:21–33 (Comparison of film, CCD, Image Plate detectors and in-column filter. See also later papers by this author)CrossRefGoogle Scholar
  55. Zuo JM, Vartanyants I, Gao M, Zhang R, Nagahara LA (2003) Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 300:1419–1421 (Demonstrates reconstruction of the image of a double-walled carbon nanotube at atomic resolution (stretched across a hole) from an electron microdiffraction pattern. True “Lensless imaging.”)CrossRefGoogle Scholar
  56. Zvyagin B (1967) Electron diffraction analysis of clay minerals. Plenum, New York (More on the early days of electron diffraction in Russia)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of PhysicsArizona State UniversityPhoenixUSA

Personalised recommendations