International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 5.1, pp. 534-551   | 1 | 2 |
doi: 10.1107/97809553602060000569

Chapter 5.1. Dynamical theory of X-ray diffraction

A. Authiera*

aLaboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France
Correspondence e-mail: authier@lmcp.jussieu.fr

References

Authier, A. (1970). Ewald waves in theory and experiment. Adv. Struct. Res. Diffr. Methods, 3, 1–51.
Authier, A. (1986). Angular dependence of the absorption induced nodal plane shifts of X-ray stationary waves. Acta Cryst. A42, 414–426.
Authier, A. (1989). X-ray standing waves. J. Phys. (Paris), 50, C7–215, C7–224.
Authier, A. (2001). Dynamical theory of X-ray diffraction. IUCr Monographs on Crystallography. Oxford University Press.
Authier, A. & Balibar, F. (1970). Création de nouveaux champs d'onde généralisés dus à la présence d'un objet diffractant. II. Cas d'un défaut isolé. Acta Cryst. A26, 647–654.
Authier, A. & Malgrange, C. (1998). Diffraction physics. Acta Cryst. A54, 806–819.
Batterman, B. W. (1964). Effect of dynamical diffraction in X-ray fluorescence scattering. Phys. Rev. A, 133, 759–764.
Batterman, B. W. (1969). Detection of foreign atom sites by their X-ray fluorescence scattering. Phys. Rev. Lett. 22, 703–705.
Batterman, B. W. & Bilderback, D. H. (1991). X-ray monochromators and mirrors. In Handbook on synchrotron radiation, Vol. 3, edited by G. Brown & D. E. Moncton, pp. 105–153. Amsterdam: Elsevier Science Publishers BV.
Batterman, B. W. & Cole, H. (1964). Dynamical diffraction of X-rays by perfect crystals. Rev. Mod. Phys. 36, 681–717.
Batterman, B. W. & Hildebrandt, G. (1967). Observation of X-ray Pendellösung fringes in Darwin reflection. Phys. Status Solidi, 23, K147–K149.
Batterman, B. W. & Hildebrandt, G. (1968). X-ray Pendellösung fringes in Darwin reflection. Acta Cryst. A24, 150–157.
Bedzyk, M. J. (1988). New trends in X-ray standing waves. Nucl. Instrum. Methods A, 266, 679–683.
Bonse, U. & Teworte, R. (1980). Measurement of X-ray scattering factors of Si from the fine structure of Laue case rocking curves. J. Appl. Cryst. 13, 410–416.
Born, M. & Wolf, E. (1983). Principles of optics, 6th ed. Oxford: Pergamon Press.
Borrmann, G. (1950). Die Absorption von Röntgenstrahlen in Fall der Interferenz. Z. Phys. 127, 297–323.
Borrmann, G. (1954). Der kleinste Absorption Koeffizient interfierender Röntgenstrahlung. Z. Kristallogr. 106, 109–121.
Borrmann, G. (1959). Röntgenwellenfelder. Beit. Phys. Chem. 20 Jahrhunderts, pp. 262–282. Braunschweig: Vieweg und Sohn.
Bragg, W. L. (1913). The diffraction of short electromagnetic waves by a crystal. Proc. Cambridge Philos. Soc. 17, 43–57.
Bragg, W. L., Darwin, C. G. & James, R. W. (1926). The intensity of reflection of X-rays by crystals. Philos. Mag. 1, 897–922.
Brümmer, O. & Stephanik, H. (1976). Dynamische Interferenztheorie. Leipzig: Akademische Verlagsgesellshaft.
Chang, S.-L. (1987). Solution to the X-ray phase problem using multiple diffraction – a review. Crystallogr. Rev. 1, 87–189.
Cowan, P. L., Brennan, S., Jach, T., Bedzyk, M. J. & Materlik, G. (1986). Observations of the diffraction of evanescent X-rays at a crystal surface. Phys. Rev. Lett. 57, 2399–2402.
Darwin, C. G. (1914a). The theory of X-ray reflection. Philos. Mag. 27, 315–333.
Darwin, C. G. (1914b). The theory of X-ray reflection. Part II. Philos. Mag. 27, 675–690.
Darwin, C. G. (1922). The reflection of X-rays from imperfect crystals. Philos. Mag. 43, 800–829.
Ewald, P. P. (1917). Zur Begründung der Kristalloptik. III. Röntgenstrahlen. Ann. Phys. (Leipzig), 54, 519–597.
Ewald, P. P. (1958). Group velocity and phase velocity in X-ray crystal optics. Acta Cryst. 11, 888–891.
Fewster, P. F. (1993). X-ray diffraction from low-dimensional structures. Semicond. Sci. Technol. 8, 1915–1934.
Fingerland, A. (1971). Some properties of the single crystal rocking curve in the Bragg case. Acta Cryst. A27, 280–284.
Golovchenko, J. A., Patel, J. R., Kaplan, D. R., Cowan, P. L. & Bedzyk, M. J. (1982). Solution to the surface registration problem using X-ray standing waves. Phys. Rev. Lett. 49, 560–563.
Hart, M. (1981). Bragg angle measurement and mapping. J. Crystal Growth, 55, 409–427.
Hirsch, P. B. & Ramachandran, G. N. (1950). Intensity of X-ray reflection from perfect and mosaic absorbing crystals. Acta Cryst. 3, 187–194.
Hümmer, K. & Weckert, E. (1995). Enantiomorphism and three-beam X-ray diffraction: determination of the absolute structure. Acta Cryst. A51, 431–438.
International Tables for Crystallography (2004). Vol. C. Mathematical, physical and chemical tables, edited by E. Prince. Dordrecht: Kluwer Academic Publishers.
James, R. W. (1950). The optical principles of the diffraction of X-rays. London: G. Bell and Sons Ltd.
James, R. W. (1963). The dynamical theory of X-ray diffraction. Solid State Phys. 15, 53.
Kato, N. (1955). Integrated intensities of the diffracted and transmitted X-rays due to ideally perfect crystal. J. Phys. Soc. Jpn, 10, 46–55.
Kato, N. (1958). The flow of X-rays and material waves in an ideally perfect single crystal. Acta Cryst. 11, 885–887.
Kato, N. (1960). The energy flow of X-rays in an ideally perfect crystal: comparison between theory and experiments. Acta Cryst. 13, 349–356.
Kato, N. (1961a). A theoretical study of Pendellösung fringes. Part I. General considerations. Acta Cryst. 14, 526–532.
Kato, N. (1961b). A theoretical study of Pendellösung fringes. Part 2. Detailed discussion based upon a spherical wave theory. Acta Cryst. 14, 627–636.
Kato, N. (1963). Pendellösung fringes in distorted crystals. I. Fermat's principle for Bloch waves. J. Phys. Soc. Jpn, 18, 1785–1791.
Kato, N. (1964a). Pendellösung fringes in distorted crystals. II. Application to two-beam cases. J. Phys. Soc. Jpn, 19, 67–77.
Kato, N. (1964b). Pendellösung fringes in distorted crystals. III. Application to homogeneously bent crystals. J. Phys. Soc. Jpn, 19, 971–985.
Kato, N. (1968a). Spherical-wave theory of dynamical X-ray diffraction for absorbing perfect crystals. I. The crystal wave fields. J. Appl. Phys. 39, 2225–2230.
Kato, N. (1968b). Spherical-wave theory of dynamical X-ray diffraction for absorbing perfect crystals. II. Integrated reflection power. J. Appl. Phys. 39, 2231–2237.
Kato, N. (1974). X-ray diffraction. In X-ray diffraction, edited by L. V. Azaroff, R. Kaplow, N. Kato, R. J. Weiss, A. J. C. Wilson & R. A. Young, pp. 176–438. New York: McGraw-Hill.
Kato, N. & Lang, A. R. (1959). A study of Pendellösung fringes in X-ray diffraction. Acta Cryst. 12, 787–794.
Kikuta, S. (1971). Determination of structure factors of X-rays using half-widths of the Bragg diffraction curves from perfect single crystals. Phys. Status Solidi B, 45, 333–341.
Kikuta, S. & Kohra, K. (1970). X-ray collimators using successive asymmetric diffractions and their applications to measurements of diffraction curves. I. General considerations on collimators. J. Phys. Soc. Jpn, 29, 1322–1328.
Kovalchuk, M. V. & Kohn, V. G. (1986). X-ray standing waves – a new method of studying the structure of crystals. Sov. Phys. Usp. 29, 426–446.
Laue, M. von (1931). Die dynamische Theorie der Röntgenstrahl interferenzen in neuer Form. Ergeb. Exakten Naturwiss. 10, 133–158.
Laue, M. von (1952). Die Energie Strömung bei Röntgenstrahl interferenzen Kristallen. Acta Cryst. 5, 619–625.
Laue, M. von (1960). Röntgenstrahl-Interferenzen. Frankfurt am Main: Akademische Verlagsgesellschaft.
Lefeld-Sosnowska, M. & Malgrange, C. (1968). Observation of oscillations in rocking curves of the Laue reflected and refracted beams from thin Si single crystals. Phys. Status Solidi, 30, K23–K25.
Lefeld-Sosnowska, M. & Malgrange, C. (1969). Experimental evidence of plane-wave rocking curve oscillations. Phys. Status Solidi, 34, 635–647.
Ludewig, J. (1969). Debye–Waller factor and anomalous absorption (Ge; 293–5 K). Acta Cryst. A25, 116–118.
Materlik, G. & Zegenhagen, J. (1984). X-ray standing wave analysis with synchrotron radiation applied for surface and bulk systems. Phys. Lett. A, 104, 47–50.
Ohtsuki, Y. H. (1964). Temperature dependence of X-ray absorption by crystals. I. Photo-electric absorption. J. Phys. Soc. Jpn, 19, 2285–2292.
Ohtsuki, Y. H. (1965). Temperature dependence of X-ray absorption by crystals. II. Direct phonon absorption. J. Phys. Soc. Jpn, 20, 374–380.
Penning, P. & Polder, D. (1961). Anomalous transmission of X-rays in elastically deformed crystals. Philips Res. Rep. 16, 419–440.
Pinsker, Z. G. (1978). Dynamical scattering of X-rays in crystals. Springer series in solid-state sciences. Berlin: Springer-Verlag.
Prins, J. A. (1930). Die Reflexion von Röntgenstrahlen an absorbierenden idealen Kristallen. Z. Phys. 63, 477–493.
Renninger, M. (1955). Messungen zur Röntgenstrahl-Optik des Idealkristalls. I. Bestätigung der Darwin–Ewald–Prins–Kohler-Kurve. Acta Cryst. 8, 597–606.
Saka, T., Katagawa, T. & Kato, N. (1973). The theory of X-ray crystal diffraction for finite polyhedral crystals. III. The Bragg–(Bragg)m cases. Acta Cryst. A29, 192–200.
Takagi, S. (1962). Dynamical theory of diffraction applicable to crystals with any kind of small distortion. Acta Cryst. 15, 1311–1312.
Takagi, S. (1969). A dynamical theory of diffraction for a distorted crystal. J. Phys. Soc. Jpn, 26, 1239–1253.
Tanner, B. K. (1976). X-ray diffraction topography. Oxford: Pergamon Press.
Tanner, B. K. (1990). High resolution X-ray diffraction and topography for crystal characterization. J. Cryst. Growth, 99, 1315–1323.
Tanner, B. K. & Bowen, D. K. (1992). Synchrotron X-radiation topography. Mater. Sci. Rep. 8, 369–407.
Uragami, T. (1969). Pendellösung fringes of X-rays in Bragg case. J. Phys. Soc. Jpn, 27, 147–154.
Uragami, T. (1970). Pendellösung fringes in a crystal of finite thickness. J. Phys. Soc. Jpn, 28, 1508–1527.
Wagner, E. H. (1959). Group velocity and energy (or particle) flow density of waves in a periodic medium. Acta Cryst. 12, 345–346.
Zachariasen, W. H. (1945). Theory of X-ray diffraction in crystals. New York: John Wiley.
Zegenhagen, J. (1993). Surface structure determination with X-ray standing waves. Surf. Sci. Rep. 18, 199–271.