Introduction

  • Shih-Lin Chang
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 50)

Abstract

Multiple diffraction, in contrast to a simple Bragg—the so-called two-beam (incident and reflected) ∔ reflection, occurs when several sets of atomic planes in a crystal are simultaneously brought into position to diffract an incident x-ray beam. The interaction among the diffracted beams within the crystal gives rise to an increase or a decrease in the intensity of a given two- beam reflection. The decrease in intensity, which brightens the two-beam diffraction images on an x-ray film (a negative), is called ‘Aufhellung’. This phenomenon was first discovered by Wagner in 1923 [1.1] and extensively investigated by Berg [1.2].

Keywords

Coherence Refraction Gallium Germanium Kato 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.1
    E. Wagner: Phys. Z. 21, 94 (1923)Google Scholar
  2. 1.2
    O. Berg: Wiss. Veröff. (Siemen’s conference) 5, 89 (1926)Google Scholar
  3. 1.3
    G. Mayer: Z. Kristallogr. 66, 585 (1928)Google Scholar
  4. 1.4
    M. Renninger: Z. Kristallogr. 106, 141 (1937); Naturwissenschaften 25, 43 (1937)Google Scholar
  5. 1.5
    A. Pabst: Am. Mineral. 24, 566 (1939)Google Scholar
  6. 1.6
    C.J. Davisson, F.E. Haworth: Phys. Rev. 66, 351 (1944)ADSGoogle Scholar
  7. 1.7
    W.N. Lipscomb: Acta Crystallogr. 2, 193 (1949)Google Scholar
  8. 1.8
    G. Borrmann, W. Hartwig: Z. Kristallogr. 121, 401 (1965)Google Scholar
  9. 1.9
    G. Borrmann: Phys. Z. 42, 157 (1941); Z. Phys. 127, 297 (1950)Google Scholar
  10. 1.10
    H. Bethe: Ann. Phys. (Leipzig) 87, 55 (1928)ADSGoogle Scholar
  11. 1.11
    H. Raether: Z. Phys. 78, 527 (1932)ADSGoogle Scholar
  12. 1.12
    J.A. Darbyshire, E.R. Cooper: Proc. Roy. Soc. A152, 104 (1935)ADSGoogle Scholar
  13. 1.13
    S. Miyake, K. Kambe: Acta Crystallogr. 7, 216 (1954)Google Scholar
  14. 1.14
    K. Kambe, S. Miyake: Acta Crystallogr. 7, 218 (1954)Google Scholar
  15. 1.15
    K. Kambe: J. Phys. Soc. Jpn. 12. 13, 25 (1957)ADSGoogle Scholar
  16. 1.16
    J.C. Slater: Rev. Mod. Phys. 30, 197 (1958)MATHADSMathSciNetGoogle Scholar
  17. 1.17
    R.W. James: Solid State Phys. 15, 53 (1962)Google Scholar
  18. 1.18
    P.P. Ewald: J. Phys. Soc. J.n. Suppl. B-II 17, 48 (1962); Rev. Mod. Phys. 37, 48 (1965)Google Scholar
  19. 1.19
    B.W. Battermann, H. Cole: Rev. Mod. Phys. 36, 681 (1964)ADSGoogle Scholar
  20. 1.20
    G. Borrmann: Z. Kristallogr. 120, 143 (1964)Google Scholar
  21. 1.21
    A. Authier: In Advances in Structure Research by Diffraction Methods, ed. by. R. Brill, R. Mason ( Pergamon, Oxford 1970 )Google Scholar
  22. 1.22
    N. Kato: In X-Ray Diffraction, ed. by L.V. Azaroff ( McGraw-Hill, New York 1974 )Google Scholar
  23. 1.23
    W.H. Zachariasen: Theory of X-Ray Diffraction in Crystals ( Wiley, New York 1945 )Google Scholar
  24. 1.24
    R.W. James: The Optical Principle of the Diffraction of X-Rays (Bell, London 1950 )Google Scholar
  25. 1.25
    M. von Laue: Röntgenstrahl-Interferenzen ( Akademische, Frankfurt 1960 )Google Scholar
  26. 1.26
    L.H. Schwartz, J.B. Cohen: Diffraction from Materials ( Academic, New York 1977 )Google Scholar
  27. 1.27
    Z.G. Pinsker: Dynamical Scattering of X-Rays in Crystals, Springer Ser. Solid-State Sci., Vol. 3 ( Springer, Berlin, Heidelberg, New York 1977 )Google Scholar
  28. 1.28
    M. von Laue, W. Friedrich, P. Knipping: Ann. Phys. (Leipzig) 41, 971 (1913)Google Scholar
  29. 1.29
    C.G. Darwin: Philos. Mag. 27, 315, 675 (1914)Google Scholar
  30. 1.30
    P.P. Ewald: Ann. Phys. (Leipzig) 49, 1, 117 (1916); Ann. Phys. (Leipzig) 54, 519 (1917); Z. Kristallogr. 97, 1 (1937)Google Scholar
  31. 1.31
    M. von Laue: Ergebn. Exakten Naturwiss. 10, 133 (1931)Google Scholar
  32. 1.32
    N. Kato, R.A. Lang: Acta Crystallogr. 12, 787 (1959)Google Scholar
  33. 1.33
    N. Kato: Z. Naturforsch. 15a, 369 (1960); Acta Crystallogr. 14, 526, 627 (1961); J. Appl. Phys. 39, 2225, 2231 (1968)ADSGoogle Scholar
  34. 1.34
    P. Penning, D. Polder: Acta Crystallogr. 17, 950 (1964)Google Scholar
  35. 1.35
    S. Takagi: Acta Crystallogr. 15, 1311 (1962); J. Phys. Soc. Jpn. 27, 1239 (1969)Google Scholar
  36. 1.36
    D. Taupin: Bull. Soc. Fr. Mineral. Cristallogr. 87, 469 (1964)Google Scholar
  37. 1.37
    N. Kato: Acta Crystallogr. 16, 276, 282 (1963); J. Phys. Soc. Jpn. 18,1785 (1963); J. Phys. Soc. Jpn. 19, 67, 971 (1964)Google Scholar
  38. 1.38
    K. Kambe: Z. Naturforsch. 20a, 770 (1965)ADSGoogle Scholar
  39. 1.39
    M. Wilkins: Phys. Status Solidi 13, 529 (1966)Google Scholar
  40. 1.40
    F. Balibar, A. Authier: Phys. Status Solidi 21, 413 (1967)Google Scholar
  41. 1.41
    F.N. Chukhovskii, A. A. Shtolberg: Phys. Status Solidi 41, 815 (1970)Google Scholar
  42. 1.42
    A.M. Afanas’ev, V.G. Kohn: Acta Crystallogr. A27, 421 (1971)Google Scholar
  43. 1.43
    A. Howie, M.J. Whelan: Proc. Roy. Soc. A263, 217 (1961)ADSGoogle Scholar
  44. 1.44
    U. Bonse: Z. Phys. 177, 385 (1964)ADSGoogle Scholar
  45. 1.45
    N. Kato: Acta Crystallogr. A32, 453, 458 (1976); A35, 9 (1979); A36, 171 (1980)Google Scholar
  46. 1.46
    N. Kato: Acta Crystallogr. A36, 763, 770 (1980)Google Scholar
  47. 1.47
    G. Molière: Ann. Phys. (Leipzig) 35, 272, 297 (1939); 36, 265 (1939)MATHGoogle Scholar
  48. 1.48
    H. Wagenfeld: Phys. Rev. 144, 216 (1966)ADSGoogle Scholar
  49. 1.49
    Y.H. Ohtsuki: J. Phys. Soc. Jpn. 19, 2285 (1964); 20, 374 (1965)MATHADSGoogle Scholar
  50. 1.50
    M. Ashkin, M. Kuriyama: J. Phys. Soc. Jpn. 21, 1549 (1966)ADSGoogle Scholar
  51. 1.51
    Y.H. Ohtsuki, S. Yanagawa: J. Phys. Soc. Jpn. 21, 326, 502 (1966)ADSGoogle Scholar
  52. 1.52
    M. Kuriyama: J. Phys. Soc. J.n. 23, 1369 (1967); Phys. Status Solidi 24, 743 (1967); J. Phys. Soc. Jpn. 25, 846 (1968); Acta Crystallogr. A25, 682 (1969); A26, 56 (1970); A27, 273 (1971); A28, 588 (1972)ADSGoogle Scholar
  53. 1.53
    J.P. Hannon, G.T. Trammell: Phys. Rev. 169, 315 (1968); Phys. Rev. 186, 306 (1969)ADSGoogle Scholar
  54. 1.54
    A.M. Afanas’ev, Y. Kagan: Acta Crystallogr. A24, 163 (1968)Google Scholar
  55. 1.55
    P.H. Dederichs: Phys. Kondens. Mater. 5, 347 (1966); Phys. Status Solidi 23, 377 (1967)ADSGoogle Scholar
  56. 1.56
    H. Sano, K. Ohtaka, Y.H. Ohtsuki: J. Phys. Soc. Jpn. 27, 1254 (1969)ADSGoogle Scholar
  57. 1.57
    P.P. Ewald: Z. Kristallogr. A97, 1 (1937)Google Scholar
  58. 1.58
    E. Lamla: Ann. Phys. (Leipzig) 36, 194 (1939)MATHADSGoogle Scholar
  59. 1.59
    N. Kato: Acta Crystallogr. 11, 885 (1958)Google Scholar
  60. 1.60
    E.J. Saccocio, A. Zajac: Acta Crystallogr. 18, 478 (1965); Phys. Rev. A139, 255 (1965)Google Scholar
  61. 1.61
    G. Hildebrandt: Phys. Status Solidi 24, 245 (1967); Acta Crystallogr. A25, 209 (1969); Phys. Status Solidi (a)15, K83 (1973)Google Scholar
  62. 1.62
    T. Joko, A. Fukuhara: J. Phys. Soc. Jpn. 22, 597 (1967)ADSGoogle Scholar
  63. 1.63
    P.P. Ewald, Y. Heno: Acta Crystallogr. A24, 5 (1968)Google Scholar
  64. 1.64
    Y. Heno, P.P. Ewald: Acta Crystallogr. A24, 16 (1968)Google Scholar
  65. 1.65
    A.M. Afanas’ev, V.G. Kohn: Acta Crystallogr. A32, 2, 308 (1976)Google Scholar
  66. 1.66
    A. Dalisa, A. Zajac, C.H. Ng: Phys. Rev. 168, 859 (1968)ADSGoogle Scholar
  67. 1.67
    W. Uebach, G. Hildebrandt: Z. Kristallogr. 129, 1 (1969)Google Scholar
  68. 1.68
    P. Penning, D. Polder: Philips Res. Rep. 23, 1 (1968)Google Scholar
  69. 1.69
    P. Penning: Advan. X-Ray Anal. 10, 67 (1967); Philips Res. Rep. 23, 12 (1968)Google Scholar
  70. 1.70
    Yu S. Terminasov, L.V. Tuzov: Usp. Fiz. Nauk. 83, 223 (1964) [English transl.: Sov. Phys.- Usp. 7, 734 (1964)]Google Scholar
  71. 1.71
    S. Balter, R. Feldman, B. Post: Phys. Rev. Lett. 27, 307 (1971)ADSGoogle Scholar
  72. 1.72
    R. Feldman, B. Post: Phys. Status Solidi (a)12, 273 (1972)ADSGoogle Scholar
  73. 1.73
    T.C. Huang, B. Post: Acta Crystallogr. A29, 35 (1973)Google Scholar
  74. 1.74
    T.C. Huang, M.H. Tillinger, B. Post: Z. Naturforsch. 28a, 600 (1973)ADSGoogle Scholar
  75. 1.75
    M. Umeno: Phys. Status Solidi (a)2, K203 (1970)ADSGoogle Scholar
  76. 1.76
    M. Umeno, G. Hildebrandt: Phys. Status Solidi (a)31, 583 (1975)ADSGoogle Scholar
  77. 1.77
    M. Umeno: Phys. Status Solidi (a)37, 561 (1976); (a)38, 701 (1976)ADSGoogle Scholar
  78. 1.78
    T.I. Borodina, V.I. Iveronova, A.A. Katznelson, T.K. Runova: Sov. Kristallogr. 20, 490 (1975) [English transl.: Sov. Phys.-Crystallogr. 20, 300 (1975)]Google Scholar
  79. 1.79
    S.A. Kshevetsky, I.P. Mikhailyuk: Sov. Kristallogr. 21, 381 (1976) [English transl.: Sov. Phys.-Crystallogr. 21, 209 (1976)]Google Scholar
  80. 1.80
    A.M. Afanas’ev, V.G. Kohn: Phys. Status Solidi (a)28, 61 (1975); Acta Crystallogr. A33, 178 (1977)ADSGoogle Scholar
  81. 1.81
    V.D. Kos’mik, S.A. Kshevetsky, M.L. Kshevetskaya, I.P. Mikhailyuk, M.V. Ostapovich: Sov. Kristallogr. 21, 899 (1976) [English transl.: Sov. Phys.-Crystallogr. 21, 514 (1976)]Google Scholar
  82. 1.82
    B. Post, S.L. Chang, T.C. Huang: Acta Crystallogr. A33, 90 (1977)Google Scholar
  83. 1.83
    S.L. Chang: Z. Naturforsch. 37a, 501 (1982)ADSGoogle Scholar
  84. 1.84
    B. Post, P.W. Wang, T. Horn: Z. Naturforsch. 37a, 528 (1982)ADSGoogle Scholar
  85. 1.85
    O. Pacherová, R. Bubáková: Z. Naturforsch. 37a, 617 (1982)ADSGoogle Scholar
  86. 1.86
    R.M. Moon, C.G. Shull: Acta Crystallogr. 17, 805 (1964)Google Scholar
  87. 1.87
    W.H. Zachariasen: Acta Crystallogr. 18, 705 (1965)Google Scholar
  88. 1.88
    W.H. Zachariasen: Acta Crystallogr. 16, 1139 (1965)Google Scholar
  89. 1.89
    S. Caticha-Ellis: Acta Crystallogr. A25, 666 (1969)Google Scholar
  90. 1.90
    S.L. Chang: Acta Crystallogr. A38, 41 (1982)Google Scholar
  91. 1.91
    R. Colella: Acta Crystallogr. A30, 413 (1974)Google Scholar
  92. 1.92
    V.G. Kohn: Phys. Status Solidi (a)54, 375 (1979)ADSGoogle Scholar
  93. 1.93
    S.L. Chang: Acta Crystallogr. A35, 543 (1979); A38, 516 (1982)ADSGoogle Scholar
  94. 1.94
    K. Lonsdale: Philos. Trans. A240, 219 (1947)ADSGoogle Scholar
  95. 1.95
    B.J. Isherwood, C.A. Wallace: Nature 212, 173 (1966)ADSGoogle Scholar
  96. 1.96
    F.J. Spooner, C.G. Wilson: J. Appl. Crystallogr. 6, 132 (1973)Google Scholar
  97. 1.97
    B. Post: J. Appl. Crystallogr. 8, 452 (1975)Google Scholar
  98. 1.98
    T. Horn, W. Kiszenik, B. Post: J. Appl. Crystallogr. 8, 457 (1975)Google Scholar
  99. 1.99
    B.R. Brown, M.A.G. Halliwell, B.J. Isherwood: J. Microscopy 118, 375 (1980)Google Scholar
  100. 1.100
    B.J. Isherwood, B.R. Brown, M.A.G. Halliwell: J. Cryst. Growth 54, 449 (1981)ADSGoogle Scholar
  101. 1.101
    S.L. Chang: Appl. Phys. Lett. 34, 239 (1979); 37, 819 (1980); Acta Crystallogr. A37, 876 (1981)ADSGoogle Scholar
  102. 1.102
    M. Hart, A.R. Lang: Phys. Rev. Lett. 7, 120 (1961)ADSGoogle Scholar
  103. 1.103
    B. Post: Phys. Rev. Lett. 39, 760 (1977); Acta Crystallogr. A35, 17 (1979)ADSGoogle Scholar
  104. 1.104
    L.D. Chapman, D.R. Yoder, R. Colella: Phys. Rev. Lett. 46, 1578 (1981)ADSGoogle Scholar
  105. 1.105
    S.L. Chang: Appl. Phys. A26, 221 (1981); Phys. Rev. Lett. 48, 163 (1982)ADSGoogle Scholar
  106. 1.106
    H.J. Juretschke: Phys. Rev. Lett. 48, 1487 (1982); Phys. Lett. 92A, 183 (1982)ADSGoogle Scholar
  107. 1.107
    M.F.C. Ladd, R.A. Palmer (eds.): Theory and Practice cf Direct Methods in Crystallography ( Plenum, New York 1980 )Google Scholar
  108. 1.108
    S.L. Chang, F.S. Han: Acta Crystallogr. A38, 414 (1982)Google Scholar
  109. 1.109
    F.S. Han, S.L. Chang: Acta Crystallogr. A39, 98 (1983)Google Scholar
  110. 1.110
    S.L. Chang: Phys. Bl. 39, 46 (1983)Google Scholar
  111. 1.111
    P. Mikula, J. Kulda, M. Vrána, R.T. Michalec, J. Vávra: Nucl. Instrum. Meth. 197, 563 (1982)Google Scholar
  112. 1.112
    S.L. Chang: Appl. Phys. Lett. 40 (9), 793 (1982)ADSGoogle Scholar
  113. 1.113
    W. Graeff, U. Bonse: Z. Phys. B27, 19 (1977)Google Scholar
  114. 1.114
    S.L. Chang: J. Appl. Phys. 53 (4), 2988 (1982)ADSGoogle Scholar
  115. 1.115
    B.W. Battermann: Appl. Phys. Lett. 1, 68 (1962); Phys. Rev. 133, A759 (1964)ADSGoogle Scholar
  116. 1.116
    J.A. Golovchenko, J.R. Patel, D.R. Kaplan, P.L. Cowan, M.J. Bedzyk: Phys. Rev. Lett. 49, 560 (1982)ADSGoogle Scholar
  117. 1.117
    B.S. Fraenkel: Appl. Phys. Lett. 41 (3), 234 (1982)ADSGoogle Scholar
  118. 1.118
    W. Kossel: Nachr. Akad. Wiss. Göttingen, Math. Phys. 1, 229 (1935)Google Scholar
  119. 1.119
    W. Kossel: Ann. Phys. (Leipzig) 25, 512 (1935)Google Scholar
  120. 1.120
    W. Kossel: Ann. Phys. (Leipzig) 26, 533 (1936)ADSGoogle Scholar
  121. 1.121
    W. Kossel: Ergebn. Exakten Naturwiss. 16, 295 (1937)Google Scholar
  122. 1.122
    W. Kossel, H. Voges: Ann. Phys. (Leipzig) 23, 677 (1935)ADSGoogle Scholar
  123. 1.123
    R. Kohler, W. Mohling, H. Peibst: Phys. Status Solidi 41, 75 (1970); 61 (b), 173 (1974)Google Scholar
  124. 1.124
    S. Kishino, K. Kohra: Jpn. J. Appl. Phys. 10, 551 (1971)ADSGoogle Scholar
  125. 1.125
    T. Bedynska: Phys. Status Solidi (a)19, 365 (1973)ADSGoogle Scholar
  126. 1.126
    S. Kishino: J. Phys. Soc. Jpn. 31, 1168 (1971)ADSGoogle Scholar
  127. 1.127
    S. Kishino, A. Noda, K. Kohra: J. Phys. Soc. Jpn. 33, 158 (1972)ADSGoogle Scholar
  128. 1.128
    T. Bedynska: Phys. Status Solidi (a)25, 405 (1974)ADSGoogle Scholar
  129. 1.129
    D.A. O’Connor: Proc. Phys. Soc. 91, 917 (1967)ADSGoogle Scholar
  130. 1.130
    H.W. Schurmann: Z. Phys. 194, 425 (1966)ADSGoogle Scholar
  131. 1.131
    K. Haruta: J. Appl. Phys. 38, 3312 (1967)ADSGoogle Scholar
  132. 1.132
    M. Kuriyama, T. Miyakawa: J. Appl. Phys. 40, 1967 (1969)Google Scholar
  133. 1.133
    A.R. Hutson, J.H. McFee, D.L. White: Phys. Rev. Lett. 7, 235 (1961)ADSGoogle Scholar
  134. 1.134
    D.L. White: J. Appl. Phys. 33, 2547 (1962)MATHADSGoogle Scholar
  135. 1.135
    D.G. Carlson, A. Segmüller, E. Mosekilde, H. Cole, J.A. Armstrong: Appl. Phys. Lett. 18, 330 (1971)ADSGoogle Scholar
  136. 1.136
    D.G. Carlson, A. Segmüller: Phys. Rev. Lett. 28, 175 (1972)ADSGoogle Scholar
  137. 1.137
    Ishibashi, M. Kitamura, A. Odajima: Phys. Lett. 44A, 371 (1973)Google Scholar
  138. 1.138
    S.D. LeRoux, R. Colella, R. Bray: Phys. Rev. Lett. 35, 230 (1975); 37, 1056 (1976)ADSGoogle Scholar
  139. 1.139
    G. Hildebrandt: J. Phys. E15, 1140 (1982)ADSGoogle Scholar
  140. 1.140
    H. Fricke, V. Gerold: J. Appl. Phys. 30, 661 (1959)ADSGoogle Scholar
  141. 1.141
    K. Thomas, A. Franks: J. Appl. Phys. 30, 649 (1959)ADSGoogle Scholar
  142. 1.142
    V.I. Betekhtin, A.I. Slutsker: Sov. Phys. - Solid State 4, 94 (1962)Google Scholar
  143. 1.143
    U. Bonse, M. Hart: Appl. Phys. Lett. 7, 238 (1965)ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Shih-Lin Chang
    • 1
  1. 1.Instituto de FísicaUniversidade Estadual de CampinasCampinasBrazil

Personalised recommendations