Theory of Electron Diffraction

  • Ludwig Reimer
Part of the Springer Series in Optical Sciences book series (SSOS, volume 36)

Abstract

The theoretical treatment of electron diffraction at crystals needs the concepts of lattice planes and the reciprocal lattice, as in x-ray diffraction. Kinematical theory leads to the Bragg condition and to a description of the influence of the structure of a unit cell and of the external size of a crystal on the diffracted amplitude in terms of structure and lattice amplitudes, respectively. The observed diffraction pattern is equivalent to the points of intersection of the Ewald sphere of radius 1/λ with the reciprocal-lattice nodes.

Keywords

Hexagonal Chlorine GaAs Convolution Lution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 7.1
    C.G. Darwin: The theory of x-ray diffraction. Philos. Mag. 27, 315 and 675 (1914)Google Scholar
  2. 7.2
    Z.G. Pinsker: Dynamical Scattering of X-rays in Crystals, Springer Ser. Solid-State Sci., Vol. 3 ( Springer, Berlin, Heidelberg 1978 )Google Scholar
  3. 7.3
    A. Howie, M.J. Whelan: Diffraction contrast of electron microscopic images of lattice defects. Proc. Roy. Soc. A 263, 217 (1961);ADSCrossRefGoogle Scholar
  4. A. Howie, M.J. Whelan: Diffraction contrast of electron microscopic images of lattice defects. Proc. Roy. Soc. 267, 206 (1962)ADSCrossRefGoogle Scholar
  5. 7.4
    H. Bethe: Theorie der Beugung von Elektronen an Kristallen. Ann. Phys. 87, 55 (1928)CrossRefGoogle Scholar
  6. 7.5
    G. Thomas, E. Levine: Increase of extinction distance with temperature in Si. Phys. Stat. Solidi 11, 81 (1965)ADSCrossRefGoogle Scholar
  7. 7.6
    A. Howie, U. Valdrè: Temperature dependence of the extinction distance in electron diffraction. Philos. Mag. 15, 777 (1967)ADSCrossRefGoogle Scholar
  8. 7.7
    L. Sturkey: The use of electron-diffraction intensities in structure determination. Acta Cryst. 10, 858 (1957)Google Scholar
  9. 7.8
    H. Niehrs: Die Formulierung der Elektronenbeugung mittels einer Streumatrix und ihre praktische Verwendbarkeit. Z. Naturforsch. A 14, 504 (1959)ADSGoogle Scholar
  10. 7.9
    F. Fujimoto: Dynamical theory of electron diffraction in Laue-case. J. Phys. Soc. Jpn. 14, 1558 (1959);ADSCrossRefGoogle Scholar
  11. F. Fujimoto: Dynamical theory of electron diffraction in Laue-case. J. Phys. Soc. Jpn.. 15, 859 (1960)ADSCrossRefGoogle Scholar
  12. F. Fujimoto: Dynamical theory of electron diffraction in Laue-case. J. Phys. Soc. Jpn.. 15, 1022 (1960)ADSCrossRefGoogle Scholar
  13. 7.10
    C.J. Humphreys, R.M. Fisher: Bloch wave notation in many-beam electron diffraction theory. Acta Cryst. A 27, 42 (1971)Google Scholar
  14. 7.11
    J.P. Spencer, C.J. Humphreys: Electron diffraction from tilted specimens and its application to SEM, in [Ref.1.78, p.310]Google Scholar
  15. 7.12
    L.E. Thomas, C.G. Shirley, J.S. Lally, R.M. Fisher: The critical voltage effect and its applications, in High Voltage Electron Microscopy ( Academic, London 1974 ) p. 38Google Scholar
  16. 7.13
    P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, M.J. Whelan: Electron Microscopy of Thin Crystals ( Butterworths, London 1965 )Google Scholar
  17. 7.14
    A. Howie: Inelastic scattering of electrons by crystals. Proc. Roy. Soc. A 271, 268 (1963)ADSMATHCrossRefGoogle Scholar
  18. 7.15
    H. Yoshioka: Effect of inelastic waves on electron diffraction. J. Phys. Soc. Jpn. 12, 618 (1957)ADSCrossRefMathSciNetGoogle Scholar
  19. 7.16
    G. Radi: Unelastische Streuung in der dynamischen Theorie der Elektronenbeugung. Z. Phys. 212, 146 (1968)ADSCrossRefGoogle Scholar
  20. 7.17
    R. Serneels, D. Haentjens, R. Gevers: Extension of the Yoshioka theory of inelastic electron scattering in crystals. Philos. Mag. A 42, 1 (1980)ADSCrossRefGoogle Scholar
  21. 7.18
    C.J. Humphreys, M.J. Whelan: Inelastic scattering of fast electrons by crystals. Philos. Mag. 20, 165 (1969)ADSCrossRefGoogle Scholar
  22. 7.19
    C.R. Hall, P.B. Hirsch: Effect of thermal diffuse scattering on propagation of high energy electrons through crystals. Proc. Roy. Soc. A 286, 158 (1965)ADSCrossRefGoogle Scholar
  23. 7.20
    P. Rez, C.J. Humphreys, M.J. Whelan: The distribution of intensity in electron diffraction patterns due to phonon scattering. Philos. Mag. 35, 81 (1977)ADSCrossRefGoogle Scholar
  24. 7.21
    Y. Kainuma: The theory of Kikuchi pattern. Acta Cryst. 8, 247 (1955)CrossRefGoogle Scholar
  25. 7.22
    R.G. Blake, A. Jostsons, P.M. Kelly, J.G. Napier: The determination of extinction distances and anomalous absorption coefficients by STEM. Philos. Mag. A 37, 1 (1978)ADSCrossRefGoogle Scholar
  26. 7.23
    J.W. Steeds: Many-beam diffraction effects in gold and measurements of absorption parameters by fitting computer graphs. Phys. Status Solidi 38, 203 (1970)CrossRefGoogle Scholar
  27. 7.24
    D.M. Bird, Q.A. King: Aborptive factors for high-energy electron diffraction. Acta Cryst. A 46, 202 (1990)CrossRefGoogle Scholar
  28. 7.25
    C.J. Allen, C.J. Rossouw: Absorptive potentials due to ionization and thermal diffuse scattering by fast electrons in crystals. Phys. Rev. B 42, 11644 (1990)ADSCrossRefGoogle Scholar
  29. 7.26
    W. Coene, D. Van Dyck: Inelastic scattering of high-energy electrons in real space. Ultramicroscopy 33, 261 (1990)CrossRefGoogle Scholar
  30. 7.27
    H. Hashimoto: Energy dependence of extinction distance and transmission power for electron waves in crystals. J. Appl. Phys. 35, 277 (1964)ADSCrossRefGoogle Scholar
  31. 7.28
    A. Mazel: R. Ayroles: Étude de la distance d’extinction et du coefficient d’absorption des electrons dans des échantillons d’aluminium pour des tensions comprises 50 et 1200 kilovolts. J. Microscopie 7, 793 (1968)Google Scholar
  32. 7.29
    G. Dupouy, F. Perrier, R. Uyeda, R. Ayroles, A. Mazel: Mesure de coefficient d’absorption des électrons accélérés sons des tensions comprises 100 et 1200 kV. J. Microscopie 4, 429 (1965)Google Scholar
  33. 7.30
    G. Radi: Complex lattice potentials in electron diffraction calculated for a number of crystals. Acta Cryst. A 26, 41 (1970)CrossRefGoogle Scholar
  34. 7.31
    P.A. Doyle: Absorption coefficients for Al 111 systematics: Theory and comparison with experiment. Acta Cryst. A 26, 133 (1970)CrossRefGoogle Scholar
  35. 7.32
    L. Reimer, M. Wächter: Complex Fourier coefficients of the crystal lattice potential, in Electron Microscopy 1980, Vol. 3, ed. by P. Brederoo, G. Boom (7th Europ. Congr. Electron Microscopy Foundation, Leiden 1980 ) p. 192Google Scholar
  36. 7.33
    G. Meyer-Ehmsen: Untersuchungen zur normalen und anomalen Absorption von Elektronen in Si-und Ge-Einkristallen bei verschiedenen Temperaturen. Z. Phys. 218, 352 (1969)ADSCrossRefGoogle Scholar
  37. 7.34
    M.J. Goringe: Temperature dependence of the absorption of fast electrons in Cu. Philos. Mag. 14, 93 (1966)ADSCrossRefGoogle Scholar
  38. 7.35
    M.J. Goringe, M.J. Whelan: The absorption of fast electrons in crystals, in [Ref.1.54, Vol. 1, p.49]Google Scholar
  39. 7.36
    D. Renard, P. Croce, M. Gandais, M. Sauvin: Etude expérimentale de l’absorption des électrons dans l’or. Phys. Status Solidi B 47, 411 (1971)ADSCrossRefGoogle Scholar
  40. 7.37
    H.G. Badde, L. Reimer: Measurement of complex structure potentials in Au and PbTe by convergent electron diffraction, in Electron Microscopy 1972 ( IoP, London 1972 ) p. 440Google Scholar
  41. 7.38
    P. Goodman, G. Lehmpfuhl: Electron diffraction study of MgO h00-systematic interactions. Acta Cryst. 22, 14 (1967)CrossRefGoogle Scholar
  42. 7.39
    K.G. Gaukler, K. Graff: Struktur-und Absorptionspotentiale von KC1 und NaCl aus Beugungsaufnahmen in konvergentem Elektronenbündel. Z. Phys. 232, 190 (1970)ADSCrossRefGoogle Scholar
  43. 7.40
    H. Hashimoto, A. Howie, M.J. Whelan: Anomalous electron absorption effects in metal foils. Proc. Roy. Soc. A 269, 80 (1962)ADSCrossRefGoogle Scholar
  44. 7.41
    P. Hagemann, L. Reimer: An experimental proof of the dependent Bloch wave model by large angle scattering from thin crystals. Philos. Mag. 40, 367 (1979)ADSCrossRefGoogle Scholar
  45. 7.42
    M.V. Berry: Diffraction in crystals at high energies. J. Phys. C 4, 697 (1971) 7.43 M.V. Berry, K.E. Mount: Semiclassical approximations in wave mechanics. Rep. Progr. Phys. 35, 315 (1972)Google Scholar
  46. 7.44
    K. Kambe, G. Lehmpfuhl, F. Fujimoto: Interpretation of electron channelling by the dynamical theory of electron diffraction. Z. Naturforsch. A 29, 1034 (1974)ADSGoogle Scholar
  47. 7.45
    F. Nagata, A. Fukuhara: 222 electron reflection from Al and systematic interaction. Jpn. J. Appl. Phys. 6, 1233 (1967)Google Scholar
  48. 7.46
    R. Uyeda: Dynamical effects in high voltage electron diffraction. Acta Cryst. A 24, 175 (1968)Google Scholar
  49. 7.47
    J.S. Lally, C.J. Humphreys, A.J.F. Metherell, R.M. Fisher: The critical voltage effect in high voltage electron microscopy. Philos. Mag. 25, 321 (1972)ADSCrossRefGoogle Scholar
  50. 7.48
    L.E. Thomas: Kikuchi patterns in HVEM. Philos. Mag. A 26, 1447 (1972)ADSCrossRefGoogle Scholar
  51. 7.49
    A.F. Moodie, J.R. Sellar, D. Imeson, C.J. Humphreys: Convergent beam diffraction in the high voltage electron microscope, in [Ref.1.80, p.191]Google Scholar
  52. 7.50
    J.R. Sellar, D. Imeson, C.J. Humphreys: Experimental and theoretical study of the convergent-beam critical voltage effect in high voltage electron diffraction, in Electron Microscopy 1980, Vol. 1, ed. by P. Brederoo, G. Boom (7th Europ. Congr. Electron Microscopy, Leiden 1980 ) p. 120Google Scholar
  53. 7.51
    T. Arii, R. Uyeda: Vanishing voltages of the second order reflections in electron diffraction. Jpn. J. Appl. Phys. 8, 621 (1969)ADSCrossRefGoogle Scholar
  54. 7.52
    T. Arii, R. Uyeda, O. Terasaki, D. Watanabe: Accurate determination of atomic scattering factors of fcc and hcp metals by high voltage electron diffraction. Acta Cryst. A 29, 295 (1973)CrossRefGoogle Scholar
  55. 7.53
    A. Fukuhara, A. Yanagisawa: Vanishing of 222 Kikuchi line from Ag crystal. Jpn. J. Appl. Phys. 8, 1166 (1969)ADSCrossRefGoogle Scholar
  56. 7.54
    M. Fujimoto, O. Terasaki, D. Watanabe: Determination of atomic scattering factors of V and Cr by means of vanishing Kikuchi line method. Phys. Lett. A 41, 159 (1972)ADSCrossRefGoogle Scholar
  57. 7.55
    A. Rocher, B. Jouffrey: Contribution a l’étude des tensions critiques dans le Cu et Al. C.R. Acad. Sci. Paris B 275, 133 (1972)Google Scholar
  58. 7.56
    D. Watanabe, R. Uyeda, A. Fukuhara: Determination of the atom form factor by high voltage electron diffraction. Acta Cryst. A 25, 138 (1969)CrossRefGoogle Scholar
  59. 7.57
    E.A. Hewet, C.J. Humphreys: Si(111) and Ge(111) and (200) scattering factors determined from critical voltage measurements, in [Ref.1.78, p.52]Google Scholar
  60. 7.58
    E.P. Butler: Application of the critical voltage effect to the study of compositional changes in Ni-Au alloys. Philos. Mag. 26, 33 (1972)ADSCrossRefGoogle Scholar
  61. 7.59
    I.P. Jones, E.G. Tapetado: The dependence of electron distribution and atom vibration in hcp metals on the c/a ratio: An investigation using the critical voltage technique, in [Ref.1.78, p.48]Google Scholar
  62. 7.60
    K. Kuroda, Y. Tomokiyo, T. Eguchi: Temperature dependence of critical voltages in Cu-based alloys, in Electron Microscopy 1980, Vol. 4, ed. by P. Brederoo, J. Van Landuyt (7th Europ. Congr. Electron Microscopy Foundation, Leiden 1980 ) p. 112Google Scholar
  63. 7.61
    C.G. Shirley, R.M. Fisher: Application of the critical voltage effect to alloy studies, in Electron Microscopy 1980, Vol. 4, ed. by P. Brederoo, J. Van Landuyt (7th Europ. Congr. Electron Microscopy Foundation, Leiden 1980 ) p. 88Google Scholar
  64. 7.62
    J. Gjonnes, R. Hoier: The application on non-systematic many-beam dynamic effects to structure-factor determination. Acta Cryst. A 27, 313 (1971)CrossRefGoogle Scholar
  65. 7.63
    J. Tafto, J. Gjonnes: The intersecting Kikuchi line technique: critical voltage at any voltage. Ultramicroscopy 17, 329 (1985)CrossRefGoogle Scholar
  66. 7.64
    R. Leonhardt, H. Richter, W. Rossteutscher: Elektronenbeugungsuntersuchungen zur Struktur dünner nichtkristalliner Schichten. Z. Phys. 165, 121 (1961)ADSCrossRefGoogle Scholar
  67. 7.65
    D.J.H. Cockayne, D.R. McKenzie: Electron diffraction analysis of polycrystalline and amorphous thin films Acta Cryst. A 44, 870 (1988)CrossRefGoogle Scholar
  68. 7.66
    D. Cockayne, D. McKenzie: Structural studies of amorphous and polycrystalline materials using energy filtered RDF analysis, in Electron Microscopy 1992, Vold, ed. by A. Rios et al. ( Secr. Publ. Univ. de Granada, Spain 1992 ) p. 179Google Scholar
  69. 7.67
    M. Horstmann, G. Meyer: Messung der elastischen Elektronenbeugungsintensitäten polykristalliner Al-Schichten. Acta Cryst. 15, 271 (1962)CrossRefGoogle Scholar
  70. 7.68
    M. Blackman: On the intensities of electron diffraction rings. Proc. Roy. Soc. A 173, 68 (1939)ADSCrossRefGoogle Scholar
  71. 7.69
    M. Horstmann, G. Meyer: Eine Gegenfeldanordung zur Messung von Energie-und Winkelverteilungen gestreuter Elektronen. Z. Physik 159, 563 (1960)ADSCrossRefGoogle Scholar
  72. 7.70
    P.H. Denbigh, C.W.B. Grigson: Scanning electron diffraction with energy analysers. J. Sci. Instr. 42, 395 (1965)ADSCrossRefGoogle Scholar
  73. 7.71
    M.F. Tompsett: Review: Scanning high-energy electron diffraction in materials science. J. Mat. Sci. 7, 1069 (1972)ADSCrossRefGoogle Scholar
  74. 7.72
    L. Reimer, I. Fromm, I. Naundorf: Electron spectroscopic diffraction. Ultra-microscopy 32, 80 (1990)Google Scholar
  75. 7.73
    J. Mayer, C. Deininger, L. Reimer: Electron spectroscopic diffraction, in Energy-Filtering Transmission Electron Microscopy, Springer Ser. Opt. Sci., Vol. 71, ed. by L. Reimer ( Springer, Berlin, Heidelberg 1995 ) p. 291Google Scholar
  76. 7.74
    C.J. Humphreys, P.B. Hirsch: Absorption parameters in electron diffraction. Philos. Mag. 18, 115 (1968)ADSCrossRefGoogle Scholar
  77. 7.75
    C.R. Hall: The scattering of high energy electrons by the thermal vibrations of crystals. Philos. Mag. 12, 815 (1965)ADSCrossRefGoogle Scholar
  78. 7.76
    G. Honjo, S. Kodera, N. Kitamura: Diffuse streak diffraction patterns from single crystals. J. Phys. Soc. Jpn. 19, 351 (1964)ADSCrossRefGoogle Scholar
  79. 7.77
    K. Komatsu, K. Teramoto: Diffuse streak patterns from various crystals in x-ray and electron diffraction. J. Phys. Soc. Jpn. 21, 1152 (1966)ADSCrossRefGoogle Scholar
  80. 7.78
    N. Kitamura: Temperature dependence of diffuse streaks in single crystal Si electron diffraction patterns. J. Appl. Phys. 37, 2187 (1966)ADSCrossRefGoogle Scholar
  81. 7.79
    H.P. Herbst, G. Jeschke: Diffuse streak-patterns from PbJ2- and Bi-single crystals and their temperature dependence, in Electron Microscopy 1968, Vol. 1, ed. by D.S. Bocciarelli ( Tipografia Poliglotta Vaticana, Rome 1968 ) p. 293Google Scholar
  82. 7.80
    E.M. Hörl: Thermisch-diffuse Elektronenstreuung in As-, Sb-und Bi-Kristallen. Optik 27, 99 (1968)Google Scholar
  83. 7.81
    Z.L. Wang: Dynamics of thermal diffuse scattering in high-energy electron diffraction and imaging: theory and experiments. Philos. Mag. B 65, 559 (1992)CrossRefGoogle Scholar
  84. 7.82
    M. Horstmann: Einflu der Kristalltemperatur auf die Intensitäten dynamischer Elektroneninterferenzen. Z. Phys. 183, 375 (1965)ADSCrossRefGoogle Scholar
  85. 7.83
    M. Horstmann, G. Meyer: Messung der Elektronenbeugungs-Intensitäten polykristalliner Al-Schichten bei tiefer Temperatur und Vergleich mit der dynamischen Theorie. Z. Phys. 182, 380 (1965)ADSCrossRefGoogle Scholar
  86. 7.84
    M. Horstmann: Messung der thermisch diffusen Elektronenstreuung in polykristallinen Al-Schichten. Z. Phys. 188, 412 (1965)ADSCrossRefGoogle Scholar
  87. 7.85
    W. Zechnall: Temperaturabhängigkeit des Streuuntergrundes im Elektroneninterferenzdiagramm polykristalliner Ag-Schichten. Z. Phys. 229, 62 (1969)ADSCrossRefGoogle Scholar
  88. 7.86
    J. Hansen-Schmidt, M. Horstmann: Temperaturabhängigkeit der Streuabsorption schneller Elektronen in polykristallinen Au-Schichten. Z. Naturforsch. A 20, 1239 (1965)ADSGoogle Scholar
  89. 7.87
    H. Boersch, O. Bostanjoglo, H. Niedrig: Temperaturabhängigkeit der Transparenz dünner Schichten für schnelle Elektronen. Z. Phys. 180, 407 (1964)ADSCrossRefGoogle Scholar
  90. 7.88
    W. Glaeser, H. Niedrig: Temperature dependence of dynamical electron diffraction intensities of polycrystalline foils. J. Appl. Phys. 37, 4303 (1966)ADSCrossRefGoogle Scholar
  91. 7.89
    W.W. Albrecht, H. Niedrig: Temperature dependence of dynamical electron diffraction intensities of polycrstalline foils. J. Appl. Phys. 39, 3166 (1968)ADSCrossRefGoogle Scholar
  92. 7.90
    G. Jeschke, D. Willasch: Temperaturabhängigkeit der anomalen Elektronenabsorption von Bi-Einkristallen. Z. Phys. 238, 421 (1970)ADSCrossRefGoogle Scholar
  93. 7.91
    C.R. Hall: On the thickness dependence of Kikuchi band contrast. Philos. Mag. 22, 63 (1970)ADSCrossRefGoogle Scholar
  94. 7.92
    H. Boersch: Über Bänder bei Elektronenbeugung. Phys. Z. 38, 1000 (1937) 7.93 H. Pfister: Elektroneninterferenzen an Bleijodid bei Durchstrahlung im konvergenten Bündel: Ann. Phys. 11, 239 (1953)Google Scholar
  95. 7.94
    M. Komura, S. Kojima, T. Ichinokawa: Contrast reversal of Kikuchi bands in transmission electron diffraction. J. Phys. Soc. Jpn. 33, 1415 (1972)ADSCrossRefGoogle Scholar
  96. 7.95
    S. Takagi: On the temperature diffuse scattering of electrons. J. Phys. Soc. Jpn. 13, 287 (1958)ADSCrossRefGoogle Scholar
  97. 7.96
    J. Gjonnes: The influence of Bragg scattering on inelastic and other forms of diffuse scattering of electrons. Acta Cryst. 20, 240 (1966)CrossRefGoogle Scholar
  98. 7.97
    K. Ishida: Inelastic scattering of fast electrons by crystals. J. Phys. Soc. Jpn. 28, 450 (1970)ADSCrossRefGoogle Scholar
  99. K. Ishida: Inelastic scattering of fast electrons by crystals. J. Phys. Soc. Jpn.. 30, 1439 (1971)ADSCrossRefGoogle Scholar
  100. 7.98
    K. Okamoto, T. Ichinokawa, Y.H. Ohtsuki: Kikuchi patterns and inelastic scattering. J. Phys. Soc. Jpn. 30, 1690 (1971)ADSCrossRefGoogle Scholar
  101. 7.99
    R. Hoier: Multiple scattering and dynamical effects in diffuse electron scattering. Acta Cryst. A 29, 663 (1973)CrossRefGoogle Scholar
  102. 7.100
    R. Serneels, C. van Roost, G. Knuyt: Kikuchi patterns in transmission electron diffraction. Philos. Mag. A 45, 677 (1982)ADSCrossRefGoogle Scholar
  103. 7.101
    L. Reimer, U. Heilers, G. Saliger: Kikuchi band contrast in diffraction patterns recorded by transmitted and backscattered electrons. Scanning 8, 101 (1986)CrossRefGoogle Scholar
  104. 7.102
    J.G. Philip, M.J. Whelan, R.F. Egerton: The contribution of inelastically scattered electrons to the diffraction pattern and images of a crystalline specimen. In [Ref.1.56, Vol. 1, p.276]Google Scholar
  105. 7.103
    L. Reimer, I. Fromm, Ch. Hülk, R. Rennekamp: Energy-filtering transmission electron microscopy in materials science. Microsc. Microanal. Microstruct. 3, 141 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ludwig Reimer
    • 1
  1. 1.Physikalisches InstitutWestfälische Wilhelms-Universität MünsterMünsterGermany

Personalised recommendations