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Introduction

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Part of the book series: Springer Series in Solid-State Sciences ((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].

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References

  1. E. Wagner: Phys. Z. 21, 94 (1923)

    Google Scholar 

  2. O. Berg: Wiss. Veröff. (Siemen’s conference) 5, 89 (1926)

    Google Scholar 

  3. G. Mayer: Z. Kristallogr. 66, 585 (1928)

    Google Scholar 

  4. M. Renninger: Z. Kristallogr. 106, 141 (1937); Naturwissenschaften 25, 43 (1937)

    Google Scholar 

  5. A. Pabst: Am. Mineral. 24, 566 (1939)

    Google Scholar 

  6. C.J. Davisson, F.E. Haworth: Phys. Rev. 66, 351 (1944)

    ADS  Google Scholar 

  7. W.N. Lipscomb: Acta Crystallogr. 2, 193 (1949)

    Google Scholar 

  8. G. Borrmann, W. Hartwig: Z. Kristallogr. 121, 401 (1965)

    Google Scholar 

  9. G. Borrmann: Phys. Z. 42, 157 (1941); Z. Phys. 127, 297 (1950)

    Google Scholar 

  10. H. Bethe: Ann. Phys. (Leipzig) 87, 55 (1928)

    ADS  Google Scholar 

  11. H. Raether: Z. Phys. 78, 527 (1932)

    ADS  Google Scholar 

  12. J.A. Darbyshire, E.R. Cooper: Proc. Roy. Soc. A152, 104 (1935)

    ADS  Google Scholar 

  13. S. Miyake, K. Kambe: Acta Crystallogr. 7, 216 (1954)

    Google Scholar 

  14. K. Kambe, S. Miyake: Acta Crystallogr. 7, 218 (1954)

    Google Scholar 

  15. K. Kambe: J. Phys. Soc. Jpn. 12. 13, 25 (1957)

    ADS  Google Scholar 

  16. J.C. Slater: Rev. Mod. Phys. 30, 197 (1958)

    MATH  ADS  MathSciNet  Google Scholar 

  17. R.W. James: Solid State Phys. 15, 53 (1962)

    Google Scholar 

  18. P.P. Ewald: J. Phys. Soc. J.n. Suppl. B-II 17, 48 (1962); Rev. Mod. Phys. 37, 48 (1965)

    Google Scholar 

  19. B.W. Battermann, H. Cole: Rev. Mod. Phys. 36, 681 (1964)

    ADS  Google Scholar 

  20. G. Borrmann: Z. Kristallogr. 120, 143 (1964)

    Google Scholar 

  21. A. Authier: In Advances in Structure Research by Diffraction Methods, ed. by. R. Brill, R. Mason ( Pergamon, Oxford 1970 )

    Google Scholar 

  22. N. Kato: In X-Ray Diffraction, ed. by L.V. Azaroff ( McGraw-Hill, New York 1974 )

    Google Scholar 

  23. W.H. Zachariasen: Theory of X-Ray Diffraction in Crystals ( Wiley, New York 1945 )

    Google Scholar 

  24. R.W. James: The Optical Principle of the Diffraction of X-Rays (Bell, London 1950 )

    Google Scholar 

  25. M. von Laue: Röntgenstrahl-Interferenzen ( Akademische, Frankfurt 1960 )

    Google Scholar 

  26. L.H. Schwartz, J.B. Cohen: Diffraction from Materials ( Academic, New York 1977 )

    Google Scholar 

  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. M. von Laue, W. Friedrich, P. Knipping: Ann. Phys. (Leipzig) 41, 971 (1913)

    Google Scholar 

  29. C.G. Darwin: Philos. Mag. 27, 315, 675 (1914)

    Google Scholar 

  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. M. von Laue: Ergebn. Exakten Naturwiss. 10, 133 (1931)

    Google Scholar 

  32. N. Kato, R.A. Lang: Acta Crystallogr. 12, 787 (1959)

    Google Scholar 

  33. N. Kato: Z. Naturforsch. 15a, 369 (1960); Acta Crystallogr. 14, 526, 627 (1961); J. Appl. Phys. 39, 2225, 2231 (1968)

    ADS  Google Scholar 

  34. P. Penning, D. Polder: Acta Crystallogr. 17, 950 (1964)

    Google Scholar 

  35. S. Takagi: Acta Crystallogr. 15, 1311 (1962); J. Phys. Soc. Jpn. 27, 1239 (1969)

    Google Scholar 

  36. D. Taupin: Bull. Soc. Fr. Mineral. Cristallogr. 87, 469 (1964)

    Google Scholar 

  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. K. Kambe: Z. Naturforsch. 20a, 770 (1965)

    ADS  Google Scholar 

  39. M. Wilkins: Phys. Status Solidi 13, 529 (1966)

    Google Scholar 

  40. F. Balibar, A. Authier: Phys. Status Solidi 21, 413 (1967)

    Google Scholar 

  41. F.N. Chukhovskii, A. A. Shtolberg: Phys. Status Solidi 41, 815 (1970)

    Google Scholar 

  42. A.M. Afanas’ev, V.G. Kohn: Acta Crystallogr. A27, 421 (1971)

    Google Scholar 

  43. A. Howie, M.J. Whelan: Proc. Roy. Soc. A263, 217 (1961)

    ADS  Google Scholar 

  44. U. Bonse: Z. Phys. 177, 385 (1964)

    ADS  Google Scholar 

  45. N. Kato: Acta Crystallogr. A32, 453, 458 (1976); A35, 9 (1979); A36, 171 (1980)

    Google Scholar 

  46. N. Kato: Acta Crystallogr. A36, 763, 770 (1980)

    Google Scholar 

  47. G. Molière: Ann. Phys. (Leipzig) 35, 272, 297 (1939); 36, 265 (1939)

    MATH  Google Scholar 

  48. H. Wagenfeld: Phys. Rev. 144, 216 (1966)

    ADS  Google Scholar 

  49. Y.H. Ohtsuki: J. Phys. Soc. Jpn. 19, 2285 (1964); 20, 374 (1965)

    MATH  ADS  Google Scholar 

  50. M. Ashkin, M. Kuriyama: J. Phys. Soc. Jpn. 21, 1549 (1966)

    ADS  Google Scholar 

  51. Y.H. Ohtsuki, S. Yanagawa: J. Phys. Soc. Jpn. 21, 326, 502 (1966)

    ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  53. J.P. Hannon, G.T. Trammell: Phys. Rev. 169, 315 (1968); Phys. Rev. 186, 306 (1969)

    ADS  Google Scholar 

  54. A.M. Afanas’ev, Y. Kagan: Acta Crystallogr. A24, 163 (1968)

    Google Scholar 

  55. P.H. Dederichs: Phys. Kondens. Mater. 5, 347 (1966); Phys. Status Solidi 23, 377 (1967)

    ADS  Google Scholar 

  56. H. Sano, K. Ohtaka, Y.H. Ohtsuki: J. Phys. Soc. Jpn. 27, 1254 (1969)

    ADS  Google Scholar 

  57. P.P. Ewald: Z. Kristallogr. A97, 1 (1937)

    Google Scholar 

  58. E. Lamla: Ann. Phys. (Leipzig) 36, 194 (1939)

    MATH  ADS  Google Scholar 

  59. N. Kato: Acta Crystallogr. 11, 885 (1958)

    Google Scholar 

  60. E.J. Saccocio, A. Zajac: Acta Crystallogr. 18, 478 (1965); Phys. Rev. A139, 255 (1965)

    Google Scholar 

  61. G. Hildebrandt: Phys. Status Solidi 24, 245 (1967); Acta Crystallogr. A25, 209 (1969); Phys. Status Solidi (a)15, K83 (1973)

    Google Scholar 

  62. T. Joko, A. Fukuhara: J. Phys. Soc. Jpn. 22, 597 (1967)

    ADS  Google Scholar 

  63. P.P. Ewald, Y. Heno: Acta Crystallogr. A24, 5 (1968)

    Google Scholar 

  64. Y. Heno, P.P. Ewald: Acta Crystallogr. A24, 16 (1968)

    Google Scholar 

  65. A.M. Afanas’ev, V.G. Kohn: Acta Crystallogr. A32, 2, 308 (1976)

    Google Scholar 

  66. A. Dalisa, A. Zajac, C.H. Ng: Phys. Rev. 168, 859 (1968)

    ADS  Google Scholar 

  67. W. Uebach, G. Hildebrandt: Z. Kristallogr. 129, 1 (1969)

    Google Scholar 

  68. P. Penning, D. Polder: Philips Res. Rep. 23, 1 (1968)

    Google Scholar 

  69. P. Penning: Advan. X-Ray Anal. 10, 67 (1967); Philips Res. Rep. 23, 12 (1968)

    Google Scholar 

  70. Yu S. Terminasov, L.V. Tuzov: Usp. Fiz. Nauk. 83, 223 (1964) [English transl.: Sov. Phys.- Usp. 7, 734 (1964)]

    Google Scholar 

  71. S. Balter, R. Feldman, B. Post: Phys. Rev. Lett. 27, 307 (1971)

    ADS  Google Scholar 

  72. R. Feldman, B. Post: Phys. Status Solidi (a)12, 273 (1972)

    ADS  Google Scholar 

  73. T.C. Huang, B. Post: Acta Crystallogr. A29, 35 (1973)

    Google Scholar 

  74. T.C. Huang, M.H. Tillinger, B. Post: Z. Naturforsch. 28a, 600 (1973)

    ADS  Google Scholar 

  75. M. Umeno: Phys. Status Solidi (a)2, K203 (1970)

    ADS  Google Scholar 

  76. M. Umeno, G. Hildebrandt: Phys. Status Solidi (a)31, 583 (1975)

    ADS  Google Scholar 

  77. M. Umeno: Phys. Status Solidi (a)37, 561 (1976); (a)38, 701 (1976)

    ADS  Google Scholar 

  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. S.A. Kshevetsky, I.P. Mikhailyuk: Sov. Kristallogr. 21, 381 (1976) [English transl.: Sov. Phys.-Crystallogr. 21, 209 (1976)]

    Google Scholar 

  80. A.M. Afanas’ev, V.G. Kohn: Phys. Status Solidi (a)28, 61 (1975); Acta Crystallogr. A33, 178 (1977)

    ADS  Google Scholar 

  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. B. Post, S.L. Chang, T.C. Huang: Acta Crystallogr. A33, 90 (1977)

    Google Scholar 

  83. S.L. Chang: Z. Naturforsch. 37a, 501 (1982)

    ADS  Google Scholar 

  84. B. Post, P.W. Wang, T. Horn: Z. Naturforsch. 37a, 528 (1982)

    ADS  Google Scholar 

  85. O. Pacherová, R. Bubáková: Z. Naturforsch. 37a, 617 (1982)

    ADS  Google Scholar 

  86. R.M. Moon, C.G. Shull: Acta Crystallogr. 17, 805 (1964)

    Google Scholar 

  87. W.H. Zachariasen: Acta Crystallogr. 18, 705 (1965)

    Google Scholar 

  88. W.H. Zachariasen: Acta Crystallogr. 16, 1139 (1965)

    Google Scholar 

  89. S. Caticha-Ellis: Acta Crystallogr. A25, 666 (1969)

    Google Scholar 

  90. S.L. Chang: Acta Crystallogr. A38, 41 (1982)

    Google Scholar 

  91. R. Colella: Acta Crystallogr. A30, 413 (1974)

    Google Scholar 

  92. V.G. Kohn: Phys. Status Solidi (a)54, 375 (1979)

    ADS  Google Scholar 

  93. S.L. Chang: Acta Crystallogr. A35, 543 (1979); A38, 516 (1982)

    ADS  Google Scholar 

  94. K. Lonsdale: Philos. Trans. A240, 219 (1947)

    ADS  Google Scholar 

  95. B.J. Isherwood, C.A. Wallace: Nature 212, 173 (1966)

    ADS  Google Scholar 

  96. F.J. Spooner, C.G. Wilson: J. Appl. Crystallogr. 6, 132 (1973)

    Google Scholar 

  97. B. Post: J. Appl. Crystallogr. 8, 452 (1975)

    Google Scholar 

  98. T. Horn, W. Kiszenik, B. Post: J. Appl. Crystallogr. 8, 457 (1975)

    Google Scholar 

  99. B.R. Brown, M.A.G. Halliwell, B.J. Isherwood: J. Microscopy 118, 375 (1980)

    Google Scholar 

  100. B.J. Isherwood, B.R. Brown, M.A.G. Halliwell: J. Cryst. Growth 54, 449 (1981)

    ADS  Google Scholar 

  101. S.L. Chang: Appl. Phys. Lett. 34, 239 (1979); 37, 819 (1980); Acta Crystallogr. A37, 876 (1981)

    ADS  Google Scholar 

  102. M. Hart, A.R. Lang: Phys. Rev. Lett. 7, 120 (1961)

    ADS  Google Scholar 

  103. B. Post: Phys. Rev. Lett. 39, 760 (1977); Acta Crystallogr. A35, 17 (1979)

    ADS  Google Scholar 

  104. L.D. Chapman, D.R. Yoder, R. Colella: Phys. Rev. Lett. 46, 1578 (1981)

    ADS  Google Scholar 

  105. S.L. Chang: Appl. Phys. A26, 221 (1981); Phys. Rev. Lett. 48, 163 (1982)

    ADS  Google Scholar 

  106. H.J. Juretschke: Phys. Rev. Lett. 48, 1487 (1982); Phys. Lett. 92A, 183 (1982)

    ADS  Google Scholar 

  107. M.F.C. Ladd, R.A. Palmer (eds.): Theory and Practice cf Direct Methods in Crystallography ( Plenum, New York 1980 )

    Google Scholar 

  108. S.L. Chang, F.S. Han: Acta Crystallogr. A38, 414 (1982)

    Google Scholar 

  109. F.S. Han, S.L. Chang: Acta Crystallogr. A39, 98 (1983)

    Google Scholar 

  110. S.L. Chang: Phys. Bl. 39, 46 (1983)

    Google Scholar 

  111. P. Mikula, J. Kulda, M. Vrána, R.T. Michalec, J. Vávra: Nucl. Instrum. Meth. 197, 563 (1982)

    Google Scholar 

  112. S.L. Chang: Appl. Phys. Lett. 40 (9), 793 (1982)

    ADS  Google Scholar 

  113. W. Graeff, U. Bonse: Z. Phys. B27, 19 (1977)

    Google Scholar 

  114. S.L. Chang: J. Appl. Phys. 53 (4), 2988 (1982)

    ADS  Google Scholar 

  115. B.W. Battermann: Appl. Phys. Lett. 1, 68 (1962); Phys. Rev. 133, A759 (1964)

    ADS  Google Scholar 

  116. J.A. Golovchenko, J.R. Patel, D.R. Kaplan, P.L. Cowan, M.J. Bedzyk: Phys. Rev. Lett. 49, 560 (1982)

    ADS  Google Scholar 

  117. B.S. Fraenkel: Appl. Phys. Lett. 41 (3), 234 (1982)

    ADS  Google Scholar 

  118. W. Kossel: Nachr. Akad. Wiss. Göttingen, Math. Phys. 1, 229 (1935)

    Google Scholar 

  119. W. Kossel: Ann. Phys. (Leipzig) 25, 512 (1935)

    Google Scholar 

  120. W. Kossel: Ann. Phys. (Leipzig) 26, 533 (1936)

    ADS  Google Scholar 

  121. W. Kossel: Ergebn. Exakten Naturwiss. 16, 295 (1937)

    Google Scholar 

  122. W. Kossel, H. Voges: Ann. Phys. (Leipzig) 23, 677 (1935)

    ADS  Google Scholar 

  123. R. Kohler, W. Mohling, H. Peibst: Phys. Status Solidi 41, 75 (1970); 61 (b), 173 (1974)

    Google Scholar 

  124. S. Kishino, K. Kohra: Jpn. J. Appl. Phys. 10, 551 (1971)

    ADS  Google Scholar 

  125. T. Bedynska: Phys. Status Solidi (a)19, 365 (1973)

    ADS  Google Scholar 

  126. S. Kishino: J. Phys. Soc. Jpn. 31, 1168 (1971)

    ADS  Google Scholar 

  127. S. Kishino, A. Noda, K. Kohra: J. Phys. Soc. Jpn. 33, 158 (1972)

    ADS  Google Scholar 

  128. T. Bedynska: Phys. Status Solidi (a)25, 405 (1974)

    ADS  Google Scholar 

  129. D.A. O’Connor: Proc. Phys. Soc. 91, 917 (1967)

    ADS  Google Scholar 

  130. H.W. Schurmann: Z. Phys. 194, 425 (1966)

    ADS  Google Scholar 

  131. K. Haruta: J. Appl. Phys. 38, 3312 (1967)

    ADS  Google Scholar 

  132. M. Kuriyama, T. Miyakawa: J. Appl. Phys. 40, 1967 (1969)

    Google Scholar 

  133. A.R. Hutson, J.H. McFee, D.L. White: Phys. Rev. Lett. 7, 235 (1961)

    ADS  Google Scholar 

  134. D.L. White: J. Appl. Phys. 33, 2547 (1962)

    MATH  ADS  Google Scholar 

  135. D.G. Carlson, A. Segmüller, E. Mosekilde, H. Cole, J.A. Armstrong: Appl. Phys. Lett. 18, 330 (1971)

    ADS  Google Scholar 

  136. D.G. Carlson, A. Segmüller: Phys. Rev. Lett. 28, 175 (1972)

    ADS  Google Scholar 

  137. Ishibashi, M. Kitamura, A. Odajima: Phys. Lett. 44A, 371 (1973)

    Google Scholar 

  138. S.D. LeRoux, R. Colella, R. Bray: Phys. Rev. Lett. 35, 230 (1975); 37, 1056 (1976)

    ADS  Google Scholar 

  139. G. Hildebrandt: J. Phys. E15, 1140 (1982)

    ADS  Google Scholar 

  140. H. Fricke, V. Gerold: J. Appl. Phys. 30, 661 (1959)

    ADS  Google Scholar 

  141. K. Thomas, A. Franks: J. Appl. Phys. 30, 649 (1959)

    ADS  Google Scholar 

  142. V.I. Betekhtin, A.I. Slutsker: Sov. Phys. - Solid State 4, 94 (1962)

    Google Scholar 

  143. U. Bonse, M. Hart: Appl. Phys. Lett. 7, 238 (1965)

    ADS  Google Scholar 

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Chang, SL. (1984). Introduction. In: Multiple Diffraction of X-Rays in Crystals. Springer Series in Solid-State Sciences, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82166-0_1

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