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Transmission Electron Microscopy pp 266–320Cite as

Kinematical and Dynamical Theory of Electron Diffraction

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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.

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References

  1. B.K. Vainshtein: Modern Crystallography I, Springer Ser. Solid-State Sci., Vol.15 (Springer, Berlin, Heidelberg, 1981)

    Google Scholar 

  2. C.G. Darwin: The theory of X-ray reflexion. Philos. Mag. 27, 315 and 675 (1914)

    Google Scholar 

  3. A. Howie, M.J. Whelan: Diffraction contrast of electron microscopic images of crystal lattice defects. Proc. Roy. Soc A 263, 217 (1961);

    Article  ADS  Google Scholar 

  4. A. Howie, M.J. Whelan: Diffraction contrast of electron microscopic images of crystal lattice defects. Proc. Roy. Soc A 267, 206 (1962)

    Article  ADS  Google Scholar 

  5. Z.G. Pinsker: Dynamical Scattering of X-Rays in Crystals, Springer Ser. Solid-State Sci., Vol.3 (Springer, Berlin, Heidelberg, 1978)

    Book  Google Scholar 

  6. A.W.S. Johnson: The analog computation of dynamic electron diffraction intensities. Acta Cryst. A 24, 534 (1968)

    Article  Google Scholar 

  7. J.M. Cowley, A.F. Moodie: The scattering of electrons by atoms and crystals. I. A new theoretical approach. Acta Cryst. 10, 698 (1957)

    MathSciNet  Google Scholar 

  8. D.F. Lynch: Out-of-zone effects in dynamical electron diffraction intensities from Au. Acta Cryst. A 27, 399 (1971)

    Article  Google Scholar 

  9. P. Goodman, A.F. Moodie: Numerical evaluation of n-beam wave functions in electron scattering by the multi-slice method. Acta Cryst. A 30, 280 (1974)

    Article  Google Scholar 

  10. H. Bethe: Theorie der Beugung von Elektronen an Kristallen. Ann. Phys. 87, 55 (1928)

    Article  Google Scholar 

  11. G. Thomas, E. Levine: Increase of extinction distance with temperature in Si. Phys. Status Solidi 11, 81 (1965)

    Article  Google Scholar 

  12. A. Howie, U. Valdrè: Temperature dependence of the extinction distance in electron diffraction. Philos. Mag. 15, 777 (1967)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  14. H. Niehrs: Die Formulierung der Elektronenbeugung mittels einer Streumatrix und ihre praktische Verwendbarkeit. Z. Naturforsch. A 14, 504 (1959)

    ADS  Google Scholar 

  15. F. Fujimoto: Dynamical theory of electron diffraction in Laue-case. J. Phys. Soc. Jpn. 14, 1558 (1959); 15, 859 and 1022 (1960)

    Article  ADS  Google Scholar 

  16. C.J. Humphreys, R.M. Fisher: Bloch wave notation in many-beam electron diffraction theory. Acta Cryst. A 27, 42 (1971)

    Article  Google Scholar 

  17. J.P. Spencer, C.J. Humphreys: Electron diffraction from tilted specimens and its application to SEM, in Electron Microscopy and Analysis, ed. by W.C. Nixon (The Institute of Physics, London 1971) p.310

    Google Scholar 

  18. 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.38

    Google Scholar 

  19. P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, M.J. Whelan: Electron Microscopy of Thin Crystals (Butterworths, London 1965)

    Google Scholar 

  20. G. Radi: Complex lattice potentials in electron diffraction calculated for a number of crystals. Acta Cryst. A 26, 41 (1970)

    Article  Google Scholar 

  21. P.A. Doyle: Absorption coefficients for Al 111 systematics: theory and comparison with experiment. Acta Cryst. A 26, 133 (1970)

    Article  Google Scholar 

  22. H. Hashimoto: Energy dependence of extinction distance and transmission power for electron waves in crystals. J. Appl. Phys. 35, 277 (1964)

    Article  ADS  Google Scholar 

  23. L. Reimer, M. Wächter. Complex Fourier coefficients of the crystal lattice potential, in Electron Microscopy1980, Vol. 3, ed by P. Brederoo, G. Boom (Seventh European Congr. Electron Microscopy Foundation, Leiden 1980) p.192

    Google Scholar 

  24. G. Meyer-Ehmsen: Untersuchungen zur normalen und anomalen Absorption von Elektronen in Si- und Ge-Einkristallen bei verschiedenen Temperaturen. Z. Phys. 218, 352 (1969)

    Article  ADS  Google Scholar 

  25. M.J. Goringe: Temperature dependence of the absorption of fast electrons in Cu. Philos. Mag. 14, 93 (1966)

    Article  ADS  Google Scholar 

  26. M.J. Goringe, M.J. Whelan: The absorption of fast electrons in crystals, in Electron Microscopy1966, Vol.1, ed. by R. Uyeda (Maruzen, Tokyo 1966) p.49

    Google Scholar 

  27. 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)

    Article  ADS  Google Scholar 

  28. H.G. Badde, L. Reimen. Measurement of complex structure potentials in Au and PbTe by convergent electron diffraction, in Electron Microscopy 1972, (The Institute of Physics, London 1972) p.440

    Google Scholar 

  29. P. Goodman, G. Lehmpfuhl: Electron diffraction study of MgO h00-system-atic interactions. Acta Cryst. 22, 14 (1967)

    Article  Google Scholar 

  30. K.G. Gaukler, K. Graff: Struktur- und Absorptionspotentiale von KCl and NaCl aus Beugungsaufnahmen in konvergentem Elektronenbündel. Z. Phys. 232, 190 (1970)

    Article  ADS  Google Scholar 

  31. A. Howie: Inelastic scattering of electrons by crystals. Proc. Roy. Soc. A 271, 268 (1963)

    Article  ADS  MATH  Google Scholar 

  32. H. Yoshioka: Effect of inelastic waves on electron diffraction. J. Phys. Soc. Jpn. 12, 618 (1957)

    Article  MathSciNet  ADS  Google Scholar 

  33. E.N. Economou: Green’s Functions in Quantum Physics, 2nd ed., Springer Ser. Solid-State Sci., Vol.7 (Springer, Berlin, Heidelberg, 1983)

    Book  Google Scholar 

  34. G. Radi: Unelastische Streuung in der dynamischen Theorie der Elektronenbeugung. Z. Phys. 212, 146 (1968)

    Article  ADS  Google Scholar 

  35. R. Serneels, D. Haentjens, R. Gevers: Extension of the Yoshioka theory of inelastic electron scattering in crystals. Philos. Mag. A 42, 1 (1980)

    Article  ADS  Google Scholar 

  36. C.J. Humphreys, M.J. Whelan: Inelastic scatting of fast electrons by crystals. Philos Mag. 20, 165 (1969)

    Article  ADS  Google Scholar 

  37. 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)

    Article  ADS  Google Scholar 

  38. 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)

    Article  ADS  Google Scholar 

  39. Y. Kainuma: The theory of Kikuchi patterns. Acta Cryst. 8, 247 (1955)

    Article  Google Scholar 

  40. 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)

    Article  ADS  Google Scholar 

  41. J.W. Steeds: Many-beam diffraction effects in gold and measurements of absorption parameters by fitting computer graphs. Phys. Status Solidi 38, 203 (1970)

    Article  Google Scholar 

  42. 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 

  43. G. Dupouy, F. Perrier, R. Uyeda, R. Ayroles, A. Mazel: Mesure du coefficient d’absorption des électrons accélérés sons des tensions comprises entre 100 et 1200 kV. J. Microscopie 4, 429 (1965)

    Google Scholar 

  44. H. Hashimoto, A. Howie, M.J. Whelan: Anomalous electron absorption effects in metal foils. Proc. Roy. Soc. A 269, 80 (1962)

    Article  ADS  Google Scholar 

  45. P. Hagemann, L. Reimer: An experimental proof of the dependent Bloch wave model by large angle electron scattering from thin crystals. Philos. Mag. 40, 367 (1979)

    Article  ADS  Google Scholar 

  46. M.V. Berry: Diffraction in crystals at high energies. J. Phys. C 4, 697 (1971)

    Article  ADS  Google Scholar 

  47. M.V. Berry, K.E. Mount: Semiclassical approximations in wave mechanics. Rep. Prog. Phys. 35, 315 (1972)

    Article  ADS  Google Scholar 

  48. K. Kambe, G. Lehmpfuhl, F. Fujimoto: Interpretation of electron channelling by the dynamical theory of electron diffraction. Z. Naturforsch. A 29, 1034 (1974)

    ADS  Google Scholar 

  49. F. Nagata, A. Fukuhara: 222 electron reflection from Al and systematic intera-tion. Jpn. J. Appl. Phys. 6, 1233 (1967)

    Article  ADS  Google Scholar 

  50. R. Uyeda: Dynamical effects in high voltage electron diffraction. Acta Cryst. A 24, 175 (1968)

    Article  Google Scholar 

  51. 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)

    Article  ADS  Google Scholar 

  52. L.E. Thomas: Kikuchi patterns in HVEM. Philos. Mag. A 26, 1447 (1972)

    Article  ADS  Google Scholar 

  53. A.F. Moodie, J.R. Sellar, D. Imeson, C.J. Humphreys: Convergent beam diffraction in the high voltage electron microscope, in High Voltage Electron Microscopy 1977, ed. by T. Imura, H. Hashimoto (Japanese Soc. Electron Microscopy, Kyoto 1977) p. 191

    Google Scholar 

  54. 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 Microscopy1980, Vol.1, ed. by P. Brederoo, G. Boom (Seventh European Congr. Electron Microscopy Foundation, Leiden 1980) p. 120

    Google Scholar 

  55. T. Arii, R. Uyeda: Vanishing voltages of the second order reflections in electron diffraction. Jpn. J. Appl. Phys. 8, 621 (1969)

    Article  ADS  Google Scholar 

  56. 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)

    Article  Google Scholar 

  57. A. Fukuhara, A. Yanagisawa: Vanishing of 222 Kikuchi line from Ag crystal. Jpn. J. Appl. Phys. 8, 1166 (1969)

    Article  ADS  Google Scholar 

  58. 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)

    Article  ADS  Google Scholar 

  59. A. Rocher, B. Jouffrey: Contribution à l’étude des tensions critiques dans le Cu et Al. C.R. Acad. Sci. Paris B 275, 133 (1972)

    Google Scholar 

  60. D. Watanabe, R. Uyeda, A. Fukuhara: Determination of the atom form factor by high voltage electron diffraction. Acta Cryst. A 25, 138 (1969)

    Article  Google Scholar 

  61. E.A. Hewat, C.J. Humphreys: Si(111) and Ge(111) and (220) scattering factors determined from critical voltage measurements, in High Voltage Electron Microscopy, ed. by P.R. Swann, C.J. Humphreys, M.J. Goringe (Academic, London 1974) p.52

    Google Scholar 

  62. E.P. Butler: Application of the critical voltage effect to the study of compositional changes in Ni-Au alloys. Philos. Mag. 26, 33 (1972)

    Article  ADS  Google Scholar 

  63. 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 High Voltage Electron Microscopy, ed. by P.R. Swann, C.J. Humphreys, M.J. Goringe (Academic, London 1974) p.48

    Google Scholar 

  64. K. Kuroda, Y. Tomokiyo, T. Eguchi: Temperature dependence of critical voltages in Cu-based alloys, in Electron Microscopy1980, Vol.4, ed. by P. Brederoo, J. Van Landuyt (Seventh European Congr. Electron Microscopy Foundation, Leiden 1980) p. 112

    Google Scholar 

  65. C.G. Shirley, R.M. Fisher: Application of the critical voltage effect to alloy studies, in Electron Microscopy1980, Vol.4, ed. by P. Brederoo, J. Van Landuyt (Seventh European Congr. Electron Micrscopy Foundation, Leiden 1980) p.88

    Google Scholar 

  66. J. Gjønnes, R. Høier: The application of non-systematic many-beam dynamic effects to structure-factor determination. Acta Cryst. A 27, 313 (1971)

    Article  Google Scholar 

  67. J. Tafto, J. Gjønnes: The intersecting Kikuchi line technique; critical voltage at any voltage. Ultramicroscopy 17, 329 (1985)

    Article  Google Scholar 

  68. R. Leonhardt, H. Richter, W. Rossteutscher: Elektronenbeugungsuntersuchungen zur Struktur dünner nichtkristalliner Schichten. Z. Phys. 165, 121 (1961)

    Article  ADS  Google Scholar 

  69. M. Horstmann, G. Meyer: Messung der elastischen Elektronenbeugungsintensitäten polykristalliner AI-Schichten. Acta Cryst. 15, 271 (1962)

    Article  Google Scholar 

  70. M. Blackman: On the intensities of electron diffraction rings. Proc. Roy. Soc. A 173, 68 (1939)

    Article  ADS  Google Scholar 

  71. C.J. Humphreys, P.B. Hirsch: Absorption parameters in electron diffraction theory. Philos. Mag. 18, 115 (1968)

    Article  ADS  Google Scholar 

  72. C.R. Hall: The scattering of high energy electrons by the thermal vibrations of crystals. Philos. Mag. 12, 815 (1965)

    Article  ADS  Google Scholar 

  73. K. Komatsu, K. Teramoto: Diffuse streak patterns from various crystals in x-ray and electron diffraction. J. Phys. Soc. Jpn. 21, 1152 (1966)

    Article  ADS  Google Scholar 

  74. N. Kitamura: Temperature dependence of diffuse streaks in single crystals Si electron diffraction patterns. J. Appl. Phys. 37, 2187 (1966)

    Article  ADS  Google Scholar 

  75. H.P. Herbst, G. Jeschke: Diffuse streak-patterns from PbJ2- and Bi-single crystals and their temperature dependence, in Electron Microscopy1968, Vol.1, ed. by D.S. Bocciarelli (Tipografia Poliglotta Vaticana, Rome 1968) p.293

    Google Scholar 

  76. E.M. Hörl: Thermisch-diffuse Elektronenstreuung in As-, Sb- und Bi-Kri-stallen. Optik 27, 99 (1968)

    Google Scholar 

  77. M. Horstmann: Einfluß der Kristalltemperatur auf die Intensitäten dynamischer Elektroneninterferenzen. Z. Phys. 183, 375 (1965)

    Article  ADS  Google Scholar 

  78. M. Horstmann, G. Meyer: Messung der Elektronenbeugungs-Intensitäten polykristalliner AI-Schichten bei tiefer Temperatur und Vergleich mit der dynamischen Theorie. Z. Phys. 182, 380 (1965)

    Article  ADS  Google Scholar 

  79. M. Horstmann: Messung der thermisch diffusen Elektronenstreuung in polykristallinen AI-Schichten. Z. Phys. 188, 412 (1965)

    Article  ADS  Google Scholar 

  80. W. Zechnall: Temperaturabhängigkeit des Streuuntergrundes im Elektronenin-terferenzdiagramm polykristalliner Ag-Schichten. Z. Phys. 229, 62 (1969)

    Article  ADS  Google Scholar 

  81. J. Hansen-Schmidt, M. Horstmann: Temperaturabhängigkeit der Streuabsorption schneller Elektronen in polykristallinen Au-Schichten. Z. Naturforsch. A 20, 1239 (1965)

    ADS  Google Scholar 

  82. H. Boersch, O. Bostanjoglo, H. Niedrig: Temperaturabhängigkeit der Transparenz dünner Schichten für schnelle Elektronen. Z. Phys. 180, 407 (1964)

    Article  ADS  Google Scholar 

  83. W. Glaeser, H. Niedrig: Temperature dependence of dynamical electron diffraction intensities of polycrystalline foils. J. Appl. Phys. 37, 4303 (1966)

    Article  ADS  Google Scholar 

  84. W.W. Albrecht, H. Niedrig: Temperature dependence of dynamical electron diffraction intensities of polycrystalline foils. J. Appl. Phys. 39, 3166 (1968)

    Article  ADS  Google Scholar 

  85. G. Jeschke, D. Willasch: Temperaturabhängigkeit der anomalen Elektronenabsorption von Bi-Einkristallen. Z. Phys. 238, 421 (1970)

    Article  ADS  Google Scholar 

  86. C.R. Hall: On the thickness dependence of Kikuchi band contrast. Philos. Mag. 22, 63 (1970)

    Article  ADS  Google Scholar 

  87. H. Boersch: Über Bänder bei Elektronenbeugung. Phys. Z. 38, 1000 (1937)

    Google Scholar 

  88. H. Pfisten. Elektroneninterferenzen an Bleijodid bei Durchstrahlung im konvergenten Bündel. Ann. Phys. 11, 239 (1953)

    Article  Google Scholar 

  89. M. Komura, S. Kojima, T. Ichinokawa: Contrast reversal of Kikuchi bands in transmission electron diffraction. J. Phys. Soc. Jpn. 33, 1415 (1972)

    Article  ADS  Google Scholar 

  90. S. Takagi: On the temperature diffuse scattering of electrons. J. Phys. Soc. Jpn. 13, 287 (1958)

    Article  ADS  Google Scholar 

  91. J. Gjønnes: The influence of Bragg scattering on inelastic and other forms of diffuse scattering of electrons. Acta Cryst. 20, 240 (1966)

    Article  Google Scholar 

  92. K. Ishida: Inelastic scattering of fast electrons by crystals. J. Phys. Soc. Jpn. 28, 450 (1970); 30, 1439 (1971)

    Article  ADS  Google Scholar 

  93. K. Okamato, T. Ichinokawa, Y.H. Ohtsuki: Kikuchi patterns and inelastic scattering. J. Phys. Soc. Jpn. 30, 1690 (1971)

    Article  ADS  Google Scholar 

  94. R. Høier: Multiple scattering and dynamical effects in diffuse electron scattering. Acta Cryst. A 29, 663 (1973)

    Article  Google Scholar 

  95. R. Serneels, C. van Roost, G. Knuyt Kikuchi patterns in transmission electron diffraction. Phil. Mag. A 45, 677 (1982)

    Article  ADS  Google Scholar 

  96. L. Reimer, U. Heilers, G. Saligen Kikuchi band contrast in diffraction patterns recorded by transmitted and backscattered electrons. Scanning 8, 101 (1986)

    Article  Google Scholar 

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  1. Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 10, D-4400, Münster, Fed. Rep. of Germany

    Prof. Dr. Ludwig Reimer

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Reimer, L. (1989). Kinematical and Dynamical Theory of Electron Diffraction. In: Transmission Electron Microscopy. Springer Series in Optical Sciences, vol 36. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21579-1_7

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  • DOI: https://doi.org/10.1007/978-3-662-21579-1_7

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