Advertisement

Crystal Structure Analysis by Diffraction

  • Ludwig Reimer
Chapter
  • 547 Downloads
Part of the Springer Series in Optical Sciences book series (SSOS, volume 45)

Abstract

Electrons are Bragg diffracted at lattice planes. The geometry of a diffraction pattern can be described by the kinematical theory. For the discussion of intensities it is necessary to use the dynamical theory of electron diffraction and the Bloch-wave model. Because a Bloch-wave field has nodes and antinodes at the nuclei and the probability density at the nuclei depends sensitively on the tilt relative to the Bragg position, the backscattering coefficient shows an anisotropy. When rocking an electron probe, this anisotropy of the backscattering results in the electron channelling pattern (ECP). For a stationary electron probe, the angular distribution of backscattered electrons is modulated by excess and defect Kikuchi bands, leading to an electron backscattering pattern (EBSP) which can be observed on a fluorescent screen or recorded on a photographic emulsion. At oblique incidence of the electron beam, the reflection high-energy electron diffraction (RHEED) pattern may contain Bragg diffraction spots and Kikuchi lines. ECP and EBSP are related by the theorem of reciprocity. These patterns contain information about the crystal structure, orientation and distortion.

Keywords

Crystal Structure Analysis Bloch Wave Bragg Condition Kikuchi Line Ewald Sphere 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 8.1
    P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, M.J. Whelan: Electron Microscopy of Thin Crystals ( Butterworths, London 1965 )Google Scholar
  2. 8.2
    S. Amelinckx, R. Gevers, G. Remaut, J. Van Landuyt: Modern Diffraction and Imaging Techniques in Material Science ( North-Holland, Amsterdam 1970 )Google Scholar
  3. 8.3
    L. Reimer: Transmission Electron Microscopy. Physics of Image Formation and Microanalysis. Springer Ser. Opt. Sci., Vol. 36 ( Springer, Berlin, Heidelberg 1984 )Google Scholar
  4. 8.4
    B.K. Vainshtein: Modern Crystazzography I. Springer Ser. Solid-State Sci., Vol. 15 ( Springer, Berlin, Heidelberg 1981 )Google Scholar
  5. 8.5
    B.K. Vainshtein, V.M. Fridkin, V.L. Indenbom: Modern Crystazzography II, Springer Ser. Solid-State Sci., Vol. 21 ( Springer, Berlin, Heidelberg 1982 )Google Scholar
  6. 8.6
    C.T. Young, J.L. Lytton: Computer generation and identification of Kikuchi projections. J.Appl.Phys. 43, 1408 (1972)ADSCrossRefGoogle Scholar
  7. 8.7
    J.P. Spencer, C.J. Humphreys: Electron diffraction from tilted specimens and its application in SEM. In Electron Microscopy and Analysis, ed. by W.C. Nixon (Inst. of Physics, London 1971) p.310 P. Pirouz, L.M. Boswarva: Pseudo-Kikuchi pattern contrast from tilted specimens. In Scanning Electron Microscopy: systems and applications.(Inst. of Physics, London 1973 ) p. 238Google Scholar
  8. 8.8
    P. Hagemann, L. Reimer: An experimental proof of the dependent Bloch wave model by large-angle electron scattering from thin crystals. Phil.Mag. A 40, 367 (1979)Google Scholar
  9. 8.9
    G.R. Booker, A.M.B. Shaw, M.J. Whelan, P.B. Hirsch: Some comments on the interpretation of the Kikuchi-like reflection patterns observed by SEM. Phil.Mag. 16, 1185 (1967)ADSCrossRefGoogle Scholar
  10. 8.10
    E. Vicario, M. Pitaval, G. Fontaine: Etude des pseudo-lignes de Kikuchi observeés en microscopie electronique à balayage. Acta Cryst. A 27, 1 (1971)Google Scholar
  11. 8.11
    L. Reimer, H.G. Badde, H. Seidel: Orientierungsanisotropie des Rückstreukoeffizienten and der Sekundärelektronenausbeute von 10–100 keV Elektronen. Z.angew.Phys. 31, 145 (1971)Google Scholar
  12. 8.12
    H.G. Badde, H. Drescher, E.R. Krefting, L. Reimer, H. Seidel, W. Bühring: Use of Mott scattering cross sections for calculating backscattering of 10–100 keV electrons. In Proc. 25th Anniv.Ì0eetinq EMAG (Inst. of Physics, London 1971 ) p. 74Google Scholar
  13. 8.13
    H. Drescher, E.R. Krefting, L. Reimer, H. Seidel: The orientation dependence of the electron backscattering coefficient of gold single crystal films. Z.Naturforschg. 29a, 833 (1974)ADSGoogle Scholar
  14. 8.14
    J.P. Spencer, C.J. Humphreys, P.B. Hirsch: A dynamical theory for the contrast of perfect and imperfect crystals in the SEM using backscattered electrons. Phil.Mag. 26, 193 (1972)ADSCrossRefGoogle Scholar
  15. 8.15
    R. Sandström, J.P. Spencer, C.J. Humphreys: A theoretical model for the energy dependence of electron channelling patterns in the SEM. J.Phys. D 7, 1030 (1974)Google Scholar
  16. 8.16
    E.M. Schulson: Interpretation of the width of SEM electron channelling lines. Phys.stat.sol. (b) 46, 95 (1971)CrossRefGoogle Scholar
  17. 8.17
    H. Seiler, G. Kuhnle: Zur Anisotropie der Elektronenausbeute in Abhängigkeit von der Energie der auslösenden Primärelektronen von 5–50 keV. Z.angew.Phys. 29, 254 (1970)Google Scholar
  18. 8.18
    H. Niedrig: Electron backscattering from thin films. J.Appl.Phys. 53, R15 (1982)ADSCrossRefGoogle Scholar
  19. 8.19
    M. von Laue: Materiewellen and ihre Interferenzen (Akad. Verlagsges. Leipzig 1948Google Scholar
  20. 8.20
    Y. Kainuma: The theory of Kikuchi pattern. Acta Cryst. 8, 247 (1955) 8.21 R. E. De Wames, W.F. Hall, G.W. Lehman: Mass dependence on the angular distribution of charged particle emission from crystals: transition to the classical limit. Phys.Rev. 174, 392 (1968)Google Scholar
  21. 8.22
    D.S. Gemmell: Channelling and related effects in the motion of charged particles through crystals. Rev.Mod.Phys. 46, 129 (1974)ADSCrossRefGoogle Scholar
  22. 8.23
    H. Boersch: Ober Bänder bei Elektronenbeugung. Phys. 38, 1000 (1937)Google Scholar
  23. 8.24
    C.R. Hall: On the thickness dependence of Kikuchi band contrast. Phil.Mag. 22, 63 (1970)ADSCrossRefGoogle Scholar
  24. 8.25
    M. Komura, S. Kojima, T. Ichinokawa: Contrast reversals of Kikuchi bands in transmission electron diffraction. J.Phys.Soc.Japan 33, 1415 (1972)ADSCrossRefGoogle Scholar
  25. 8.26
    L. Reimer, W. Pöpper, B. Volbert: Contrast reversals in the Kikuchi bands of backscattered and transmitted electron diffraction patterns. In Developments in Electron Microscopy and Analysis, ed. By D.L. Misell ( Inst. of Physics, London 1977 ) p. 259Google Scholar
  26. 8.27
    M.N. Alam, M. Blackman, D.W. Pashley: High-angle Kikuchi patterns Proc.Roy.Soc. A 221, 224 (1954)Google Scholar
  27. 8.28
    J.A. Venables, C.J. Harland: Electron backscattering patterns - a new technique for obtaining crystallographic information in the SEM. Phil.Mag. 27, 1193 (1973)ADSCrossRefGoogle Scholar
  28. 8.29
    D.G. Coates: Kikuchi-like reflection patterns obtained with the SEM Phil.Mag. 16, 1179 (1967)Google Scholar
  29. 8.
    G.R. Booker: Scanning electron microscopy: electron channeling effects, in [Ref.8.2, p.613]Google Scholar
  30. 8.31
    D.C. Joy, D.E. Newbury, D.L. Davidson: Electron channelling patterns in the SEM. J.Appl.Phys. 53, R81 (1982)ADSCrossRefGoogle Scholar
  31. 8.32
    D.C. Joy: Electron channelling patterns in the SEM. In Quantitative Electron Microscopy, ed. by D.B. Holt et al. ( Academic, London 1974 ) p. 131Google Scholar
  32. 8.33
    D.E. Newbury: The origin, detection and uses of electron channeling contrast. SEM 1974, p. 1047Google Scholar
  33. 8.34
    E.M. Schulson, C.G. van Essen: Optimum conditions for generating channelling patterns in the SEM. J.Phys. E 2, 247 (1969)Google Scholar
  34. 8.35
    E.D. Wolf, T.E. Everhart: Annular diode detector for high annular resolution pseudo-Kikuchi patterns. SEM 1969, p. 41Google Scholar
  35. 8.36
    D.G. Coates: Pseudo-Kikuchi orientation analysis in the SEM. SEM 1969, p. 27Google Scholar
  36. 8.37
    E.M. Schulson, C.G. van Essen, D.C. Joy: The generation and application of SEM electron channelling patterns. SEM 1969, p. 45Google Scholar
  37. 8.38
    J. Frosien, W. Gaebler, H. Niedrig: New display and specimen stage for large angle Kikuchi-like patterns. In Electron Microscopy 1974, VoZ.1 ed. by J.V. Sanders and D.J. Goodchild (Australian Acad. of Science, Canberra 1974 ) p. 158Google Scholar
  38. 8.39
    M. Brunner, H.J. Kohl, H. Niedrig: Großwinkel-Elektronen-Channeling-Diagramme zur Untersuchung epitaktisch hergestellter Schichten. Optik 49, 477 (1978)Google Scholar
  39. 8.40
    A.R. Dinnis: Limiting factors in direct stereo viewing. In Scanning Electron Microscopy: systems and applications (Inst. of Physics, London 1973 ) p. 76Google Scholar
  40. 8.41
    A.R. Dinnis: Stereoscopic viewing in the SEM. In Developments in Electron Microscopy and Analysis, ed. by D.L. Misell ( Inst. of Physics, London 1977 ) p. 87Google Scholar
  41. 8.42
    C.G. van Essen, E.M. Schulson: Selected area channelling patterns in the SEM. J. Mater.Sci. 4, 336 (1969)ADSCrossRefGoogle Scholar
  42. 8.43
    C.G. van Essen, E.M. Schulson, R.H. Donaghay: Electron channeling patterns from small (10 pm) selected areas in the SEM. Nature 225, 847 (1970); The generation and identification of SEM channelling patterns from 10 micron areas. J.Mater.Sci. 6, 213 (1971)Google Scholar
  43. 8.44
    G.R. Booker, R. Stickler: SEM selected area channelling patterns: dependence of area on rocking angle and working distance. J.Mater. Sci. 7, 712 (1972)Google Scholar
  44. 8.45
    C.G. van Essen: Selected area diffraction in the SEM - towards 1 micron. In Proc. 25th Anniv. Meeting of EMAG ( Inst.of Physics, London 1971 ) p. 314Google Scholar
  45. 8.46
    D.C. Joy, D.E. Newbury: SEM selected area channelling patterns from 1 micron specimen areas. J.Mater.Sci. 7, 714 (1972)ADSCrossRefGoogle Scholar
  46. 8.47
    H. Seiler: Determination of “information depth” in the SEM. SEM 1967/I, p.9Google Scholar
  47. 8.48
    E.D. Wolf, M. Braunstein, A.I. Braunstein: Pseudo-Kikuchi pattern degradation by a thin amorphous silicon film. Appl.Phys. Lett. 15, 389 (1969)Google Scholar
  48. 8.49
    S.M. Davidson, G.R. Booker: Decollimation of a parallel beam by thin surface films and its effect on SEM channelling patterns. In Microscopic Electronique 1970, Vol. 1, ed. by P. Favard ( Soc. Française Micr. Electronique, Paris 1970 ) p. 235Google Scholar
  49. 8.50
    M. Hoffmann, L. Reimer: Channelling contrast on metal surfaces after ion beam etching. Scanning 4, 91 (1981)CrossRefGoogle Scholar
  50. 8.51
    E.M. Schulson: A SEM study of the degradation of electron channelling effects in alkali halide crystals during electron irradiation. J.Mater.Sci. 6, 377 (1971)ADSCrossRefGoogle Scholar
  51. 8.52
    E.M. Schulson: SEM electron channelling line width (broadening) and pattern degradation in alkali halide crystals. SEM 1971, p. 489Google Scholar
  52. 8.53
    A.D.G. Stewart: Recent developments in SEM. BEDO 1, 283 (1968) 8.54 A. Boyde: Practical problems and methods in 3D analysis of SEM images. SEM 1970, p. 105Google Scholar
  53. 8.55
    S. Murray, A.H. Windle: Characterisation and correction of distortions in SEM micrographs. In Scanning Electron Microscopy: systems and applications (Inst. of Physics, London 1973 ) p. 88Google Scholar
  54. 8.56
    J.D. Verhoeven, E.D. Gibson: Rotation between SEM micrograph and electron channelling patterns. J. Phys. E 8, 15 (1975)ADSCrossRefGoogle Scholar
  55. 8.57
    D.C. Joy, C.M. Maruszewski: The rotation between selected area channelling patterns and micrographs. J.Mater.Sci. 10, 178 (1975)ADSCrossRefGoogle Scholar
  56. 8.58
    D.L. Davidson: Rotation between SEM micrographs and electron channelling patterns. J.Phys. E 9, 341 (1976)Google Scholar
  57. 8.59
    D.E. Newbury, D.C. Joy: A computer technique for the analysis of electron channelling patterns. In Proc. 25th Anniv. Meeting EMAG (Inst. of Physics, London 1971 ) p. 306Google Scholar
  58. 8.60
    D.C. Joy, G.R. Booker, E.O. Fearon, M. Bevis: Quantitative crystallographic orientation determination of microcrystals present on solid specimens using the SEM. SEM 1971, p. 497Google Scholar
  59. 8.61
    G.R. Booker: Electron channelling effects using the SEM. SEM 1970, p. 489Google Scholar
  60. 8.62
    J.D. Ayers, D.C. Joy: A crystallographic study of massive precipitates in Cu-Zn and Ag-Zn alloys utilizing selected area electron channelling. Acta Met. 20, 1371 (1972)CrossRefGoogle Scholar
  61. 8.63
    D.E. Newbury, D.C. Joy: SEM dynamical studies of the deformation of Pb-Sn superplastic alloys. In Proc. 25th Anniv. Meeting EMAG ( Inst.of Physics, London 1971 ) p. 216Google Scholar
  62. 8.64
    D.C. Joy, E.M. Schulson, J.P. Jacubovics, C.G. van Essen: Electron channelling patterns from ferromagnetic crystals in the SEM. Phil.Mag. 20, 843 (1969)ADSCrossRefGoogle Scholar
  63. 8.65
    H. Solovsky, J.R. Beaman: The measurement of electron wavelength. Rev.Sci.Instr. 43, 1100 (1972)CrossRefGoogle Scholar
  64. 8.66
    K.-J. Hanszen, G. Ade, W. Lucas, H. Sieoert, P. Becker: Berichte über Arbeiten am Röntgenverschiebeinterferometer Teil III: Erste Bestimmung des Netzebenabstandes (220) von Silizium. PTB-APh-14 ( Physikal.Techn.Bundesanstalt, Braunschweig 1981 )Google Scholar
  65. 8.67
    L. Reimer, H. Seidel, R. Blaschke: Energieabhänoiokeit der Feinstruktur eines Channelling-Diagrammes am Beispiel des 111-Poles von Silizium. BEDO 4/2, 289 (1971)Google Scholar
  66. 8.68
    R. Stickler, C.W. Hughes, G.R. Booker: Application of the SA-ECP method to deformation studies. SEM 1971, p. 473Google Scholar
  67. 8.69
    J.P. Spencer, G.R. Booker, D.C. Joy, C.J. Humphreys: Electron channelling patterns from deformed crystals. SEM 1974, p. 919Google Scholar
  68. 8.70
    D.L. Davidson: A method for quantifying electron channeling pattern degradation due to material deformation. SEM 1974, p. 927Google Scholar
  69. 8.71
    R.C. Farrow, D.C. Joy: Measurements of electron channelling pattern linewidths in silicon. Scanning 2, 249 (1979)CrossRefGoogle Scholar
  70. 8.72
    C.W. Grigson: Improved scanning electron diffraction system. Rev. Sci.Instr. 36, 1587 (1965)ADSCrossRefGoogle Scholar
  71. 8.73
    M.F. Tompsett: Scanning high-energy electron diffraction in materials science. J.Mater.Sci. 7, 1069 (1972)ADSCrossRefGoogle Scholar
  72. 8.74
    L. Reimer: Electron diffraction methods in TEM, STEM and SEM. Scanning 2, 3 (1979)CrossRefGoogle Scholar
  73. 8.75
    J.A. Venables, R. bin-Jaya: Accurate microcrystallography using electron backscattering patterns. Phil.Mag. 35, 1317 (1977)ADSCrossRefGoogle Scholar
  74. 8.
    D.J. Dingley: Diffraction from sub-micron areas using electron backscattering in a SEM. SEM 1984/II, p.569Google Scholar
  75. 8.77
    J.A. Venables, C.J. Harland, R. bin-Jaya: Crystallographic orientation determination in the SEM using electron backscattering patterns and channel plates. In Developments in Electron Microscopy and Analysis, ed. by J.A. Venables ( Academic, London 1976 ) p. 101Google Scholar
  76. 8.78
    C.J. Harland, P. Akhter, J.A. Venables: Accurate microcrystallography at high spatial resolution using electron backscattering patterns in a field emission gun SEM. J.Phys. E 14, 175 (1981)Google Scholar
  77. 8.79
    T. Ichinokawa, M. Nishimura, H. Wada: Contrast reversals of pseudo-Kikuchi bands and lines due to detector oosition in SEM. J.Phys.Soc. Jap. 36, 221 (1974)Google Scholar
  78. 8.
    M. Pitaval, P. Morin, J. Baudry, E. Vicario, G. Fontaine: Advances in crystalline contrast from defects. SEM 1977/I, p. 439Google Scholar
  79. 8.81
    W. Kossel, H. Voges: Röntgeninterferenzen an der Einkristallanti- kathode. Ann.Phys. 23, 677 (1935)CrossRefGoogle Scholar
  80. 8.82
    W. Kossel: Zur Systematik der Röntgenreflexe eines Raumgitters. Ann. Phys. 25, 512 (1936); Messungen am vollständigen Reflexsystem eines Kristallgitters. Ann.Phys. 26, 533 (1936)Google Scholar
  81. 8.83
    H. Yakowitz: The divergent beam x-ray technique. In Electron Probe Microanalysis, Suppl.IV, Adv.Electr.Electron Phys. ( Academic, New York 1969 ) p. 361Google Scholar
  82. 8.84
    R. Tixier, C. Wade: Kossel patterns. J.Appl.Cryst. 3, 466 (1970)CrossRefGoogle Scholar
  83. 8.85
    H. Yakowitz: Role of divergent beam (Kossel) x-ray technique in SEM. In Quantitative Scanning Electron Microscopy, ed. by D.B. Holt et al. ( Academic, London 1974 ) p. 451Google Scholar
  84. 8.86
    D.J. Dingley, J.W. Steeds: Application of the Kossel x-ray back reflection technique in the SEM. In Quantitative Scanning Electron Microscopy, ed. by D.B. Holt et al. ( Academic, London 1974 ) p. 487Google Scholar
  85. 8.87
    D.J. Dingley: Theory and application of Kossel x-ray diffraction in the SEM. Scanning 1, 79 (1978)CrossRefGoogle Scholar
  86. 8.88
    N. Swindells, J.C. Ruckman: A new Kossel camera design concept for the SEM. In Scanning Electron Microscopy: systems and applications (Inst. of Physics, London 1973 ) p. 302Google Scholar
  87. 8.89
    S. Biggin, D.J. Dingley: A general method for locating the x-ray source point in Kossel diffraction. J.Appl.Cryst. 10, 376 (1977)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Ludwig Reimer
    • 1
  1. 1.Physikalisches InstitutWestfätlische Wilhelms-Univeraität MünsterMünsterFed. Rep. of Germany

Personalised recommendations