Abstract

An optical crystal (a multilayer diffraction plate) which optically simulates electron diffraction by thin crystals has been developed. The lattice was constructed with appropriate lattice constants to allow a direct optical simulation of electron diffraction by mica. The resulting optical-diffraction patterns agree with theory and vividly illustrate Laue zones. Optical-diffraction patterns for different crystal orientations are directly compared to electron-diffraction patterns for the same orientations of a thin mica crystal. The breadths of Laue zones diminish as a crystal becomes thicker, reducing the diffraction pattern to the Laue spots described by Bragg’s law.

© 1974 Optical Society of America

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References

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  1. R. R. Bergsten, Am. J. Phys. 42, 91 (1974).
    [Crossref]
  2. S. Kikuchi, Jpn. J. Phys. 5, 83 (1928).
  3. D. deFontaine, K. A. Jackson, and C. E. Miller, Am. J. Phys. 37, 789 (1969).
    [Crossref]
  4. D. G. Ast, Am. J. Physics 39, 1164 (1971).
    [Crossref]
  5. J. R. Meyer-Arendt and J. K. Wood, Am. J. Phys. 29, 341 (1961).
    [Crossref]
  6. R. B. Hoover, Am. J. Phys. 37, 871 (1969).
    [Crossref]
  7. D. G. Fedak, T. E. Fischer, and W. D. Robertson, J. Appl. Phys. 39, 5658 (1968).
    [Crossref]
  8. W. Linnik, Nature 123, 604 (1929).
    [Crossref]
  9. W.L. Bragg and F. Kirchner, Nature 127, 738 (1931).
    [Crossref]
  10. W. L. Bragg, Nature 124, 125 (1929).
    [Crossref]
  11. P. B. Hirsch, A. Howie, R. B. Nicholson, and D. W. Pashley, Electron Microscopy of Thin Crystals (Butterworth, London, 1965), Ch. 17, p. 421.
  12. K. W. Andrews, D. J. Dyson, and S. R. Keown, Interpretation of Electron Diffraction Patterns (Plenum, New York, 1971), Chs. 3 and 4.

1974 (1)

R. R. Bergsten, Am. J. Phys. 42, 91 (1974).
[Crossref]

1971 (1)

D. G. Ast, Am. J. Physics 39, 1164 (1971).
[Crossref]

1969 (2)

R. B. Hoover, Am. J. Phys. 37, 871 (1969).
[Crossref]

D. deFontaine, K. A. Jackson, and C. E. Miller, Am. J. Phys. 37, 789 (1969).
[Crossref]

1968 (1)

D. G. Fedak, T. E. Fischer, and W. D. Robertson, J. Appl. Phys. 39, 5658 (1968).
[Crossref]

1961 (1)

J. R. Meyer-Arendt and J. K. Wood, Am. J. Phys. 29, 341 (1961).
[Crossref]

1931 (1)

W.L. Bragg and F. Kirchner, Nature 127, 738 (1931).
[Crossref]

1929 (2)

W. L. Bragg, Nature 124, 125 (1929).
[Crossref]

W. Linnik, Nature 123, 604 (1929).
[Crossref]

1928 (1)

S. Kikuchi, Jpn. J. Phys. 5, 83 (1928).

Andrews, K. W.

K. W. Andrews, D. J. Dyson, and S. R. Keown, Interpretation of Electron Diffraction Patterns (Plenum, New York, 1971), Chs. 3 and 4.

Ast, D. G.

D. G. Ast, Am. J. Physics 39, 1164 (1971).
[Crossref]

Bergsten, R. R.

R. R. Bergsten, Am. J. Phys. 42, 91 (1974).
[Crossref]

Bragg, W. L.

W. L. Bragg, Nature 124, 125 (1929).
[Crossref]

Bragg, W.L.

W.L. Bragg and F. Kirchner, Nature 127, 738 (1931).
[Crossref]

deFontaine, D.

D. deFontaine, K. A. Jackson, and C. E. Miller, Am. J. Phys. 37, 789 (1969).
[Crossref]

Dyson, D. J.

K. W. Andrews, D. J. Dyson, and S. R. Keown, Interpretation of Electron Diffraction Patterns (Plenum, New York, 1971), Chs. 3 and 4.

Fedak, D. G.

D. G. Fedak, T. E. Fischer, and W. D. Robertson, J. Appl. Phys. 39, 5658 (1968).
[Crossref]

Fischer, T. E.

D. G. Fedak, T. E. Fischer, and W. D. Robertson, J. Appl. Phys. 39, 5658 (1968).
[Crossref]

Hirsch, P. B.

P. B. Hirsch, A. Howie, R. B. Nicholson, and D. W. Pashley, Electron Microscopy of Thin Crystals (Butterworth, London, 1965), Ch. 17, p. 421.

Hoover, R. B.

R. B. Hoover, Am. J. Phys. 37, 871 (1969).
[Crossref]

Howie, A.

P. B. Hirsch, A. Howie, R. B. Nicholson, and D. W. Pashley, Electron Microscopy of Thin Crystals (Butterworth, London, 1965), Ch. 17, p. 421.

Jackson, K. A.

D. deFontaine, K. A. Jackson, and C. E. Miller, Am. J. Phys. 37, 789 (1969).
[Crossref]

Keown, S. R.

K. W. Andrews, D. J. Dyson, and S. R. Keown, Interpretation of Electron Diffraction Patterns (Plenum, New York, 1971), Chs. 3 and 4.

Kikuchi, S.

S. Kikuchi, Jpn. J. Phys. 5, 83 (1928).

Kirchner, F.

W.L. Bragg and F. Kirchner, Nature 127, 738 (1931).
[Crossref]

Linnik, W.

W. Linnik, Nature 123, 604 (1929).
[Crossref]

Meyer-Arendt, J. R.

J. R. Meyer-Arendt and J. K. Wood, Am. J. Phys. 29, 341 (1961).
[Crossref]

Miller, C. E.

D. deFontaine, K. A. Jackson, and C. E. Miller, Am. J. Phys. 37, 789 (1969).
[Crossref]

Nicholson, R. B.

P. B. Hirsch, A. Howie, R. B. Nicholson, and D. W. Pashley, Electron Microscopy of Thin Crystals (Butterworth, London, 1965), Ch. 17, p. 421.

Pashley, D. W.

P. B. Hirsch, A. Howie, R. B. Nicholson, and D. W. Pashley, Electron Microscopy of Thin Crystals (Butterworth, London, 1965), Ch. 17, p. 421.

Robertson, W. D.

D. G. Fedak, T. E. Fischer, and W. D. Robertson, J. Appl. Phys. 39, 5658 (1968).
[Crossref]

Wood, J. K.

J. R. Meyer-Arendt and J. K. Wood, Am. J. Phys. 29, 341 (1961).
[Crossref]

Am. J. Phys. (4)

J. R. Meyer-Arendt and J. K. Wood, Am. J. Phys. 29, 341 (1961).
[Crossref]

R. B. Hoover, Am. J. Phys. 37, 871 (1969).
[Crossref]

R. R. Bergsten, Am. J. Phys. 42, 91 (1974).
[Crossref]

D. deFontaine, K. A. Jackson, and C. E. Miller, Am. J. Phys. 37, 789 (1969).
[Crossref]

Am. J. Physics (1)

D. G. Ast, Am. J. Physics 39, 1164 (1971).
[Crossref]

J. Appl. Phys. (1)

D. G. Fedak, T. E. Fischer, and W. D. Robertson, J. Appl. Phys. 39, 5658 (1968).
[Crossref]

Jpn. J. Phys. (1)

S. Kikuchi, Jpn. J. Phys. 5, 83 (1928).

Nature (3)

W. Linnik, Nature 123, 604 (1929).
[Crossref]

W.L. Bragg and F. Kirchner, Nature 127, 738 (1931).
[Crossref]

W. L. Bragg, Nature 124, 125 (1929).
[Crossref]

Other (2)

P. B. Hirsch, A. Howie, R. B. Nicholson, and D. W. Pashley, Electron Microscopy of Thin Crystals (Butterworth, London, 1965), Ch. 17, p. 421.

K. W. Andrews, D. J. Dyson, and S. R. Keown, Interpretation of Electron Diffraction Patterns (Plenum, New York, 1971), Chs. 3 and 4.

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Figures (6)

Fig. 1
Fig. 1

Sketch of the diffraction pattern produced by one layer of a monoclinic crystal. The vertical rows correspond to the orders associated with the lattice constant a, which is horizontal.

Fig. 2
Fig. 2

White regions of the drawing correspond to the coincidence of two sets of elliptical Laue zones. When the spots of Fig. 1 are restricted to these zones, the resulting pattern resembles those shown in Figs. 5 and 6.

Fig. 3
Fig. 3

Diffraction pattern formed by He–Ne laser beam incident parallel to the lattice constant c of the optical crystals. Note the circular Laue zones. The pattern was recorded by photographing the pattern that was displayed on a screen.

Fig. 4
Fig. 4

Diffraction pattern formed by 4.12 × 10−2 Å wavelength electrons incident parallel to the lattice constant c of a thin mica crystal. Note the similarity to the optical pattern shown in Fig. 3. The pattern was obtained by use of an electron microscope.

Fig. 5
Fig. 5

Diffraction pattern formed by light obliquely incident on the optical crystal. Note the existence of the coincident Laue zones shown in Fig. 2. The pattern was recorded by photographing the pattern that was displayed on a screen.

Fig. 6
Fig. 6

Diffraction pattern formed by electrons obliquely incident on a thin mica crystal. Note the similarity to the pattern shown in Fig. 5. The pattern was obtained by use of an electron microscope.

Tables (1)

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Table I Description of the crystals.

Equations (4)

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d ( cos θ - cos ϕ ) = k λ ,
d ( cos θ - cos ϕ ) = ( k n ± 1 n ) λ ,
θ = tan - 1 ( a 2 c )
( c / a ) tan [ 1 2 ( θ + ϕ ) ] = m / k ,