Theory and applications of x-ray standing waves in real crystals

Abstract

Theoretical aspects of x-ray standing wave method for investigation of the real structure of crystals are considered in this review paper. Starting from the general approach of the secondary radiation yield from deformed crystals this theory is applied to different concreate cases. Various models of deformed crystals like: bicrystal model, multilayer model, crystals with extended deformation field are considered in detailes. Peculiarities of x-ray standing wave behavior in different scattering geometries (Bragg, Laue) are analysed in detailes. New possibilities to solve the phase problem with x-ray standing wave method are discussed in the review. General theoretical approaches are illustrated with a big number of experimental results. * present address:

Making use of x-ray optical effects in photoelectron-, Auger electron-, and x-ray emission spectroscopies: Total reflection, standing-wave excitation, and resonant effects

“…13 Beyond these total reflection studies, x-ray optical effects have not been rigorously accounted for in the analysis of most photoemission or x-ray emission data, with the assumption being made that the x-rays penetrate much more deeply, and essentially without attenuation or modulation, into the sample, as compared to the depths from which the photoelectrons or fluorescent x-rays are emitted. Yet x-ray optical effects can play a particularly significant role for measurements done at grazing incidence angles, 9-13 near absorption-edge resonances, 14 in Bragg-like reflection from single-crystal planes [15][16][17] and synthetic multilayers, 8,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and with variable polarization so as to produce magnetic and other dichroic effects. 19,21,30 In beginning this discussion, it is worthwhile to discuss in more detail the specific types of x-ray optical effects that need to be considered: first are optical interference effects that modify the total electric field intensity vs. depth into the sample.…”

Optical properties of X-rays – dynamical diffraction

“…The technique has given rise to quite a new field for the study of impurities and adsorbed atoms at crystal surfaces, as well as for the determination of reconstructed crystal surfaces. For reviews, see, for instance, Zegenhagen (1993), Vartanyants & Koval'chuk (2001) or Authier (2001).…”

Holographic analysis of diffraction structure factors

“…Besides the fine structure of the KL or XSW produced when the crystal orientation satisfies a Bragg or Laue condition, tails are formed far from the Bragg angle. These coarse features, also formed by poorer-quality mosaic crystals provide information on the real and imaginary part of the structure factor [10,11].Unlike standard imaging methods, holography offers the possibility of extracting both intensity and phase information. X-ray fluorescence holography (XFH) is thus a very promising new method for obtaining a direct image in real space of the local environments of different atomic species in reasonably well-ordered crystals or molecular ensembles.…”

“…The fine structure of these lines has been explained by the dynamical theory of x-ray diffraction via the reciprocity theorem used in optics [4]. A proper analysis of the KL fine structure allows the determination of the phases of reflections [5,6,8,10,11]. In parallel to this work on KL, the x-ray standing wave (XSW) method has been developed [5,6,7,10].…”

“…A proper analysis of the KL fine structure allows the determination of the phases of reflections [5,6,8,10,11]. In parallel to this work on KL, the x-ray standing wave (XSW) method has been developed [5,6,7,10]. In this case, the source and the detector are interchanged as compared to the KL method: the atoms are subject to the changing wave-field in the crystal as the incident beam goes through a Bragg reflection, and fluorescent radiation proportional to the field at the atom is generated.…”