The first results of the theory of the behaviour of standing waves in curved crystals are presented. The proposed theory is based on the Taupin theory of dynamical X-ray diffraction in curved crystals and the theory of the secondary radiation yield in deformed crystals. This theory is applied for calculation of the angular dependence of the secondary emission yield in a cylindrically bent Si(400) monocrystal, Cu Kalpha radiation. Processes with different depth of secondary emission yield, i.e. photoemission (Lyi=0.1 mu m) and fluorescence (Lyi=70 mu m) are considered. The behaviour of the reflection coefficient and standing waves in the bulk of the curved crystal is investigated. The standing wave intensities in the depth of the curved crystal show much more sensitivity to the phaseshift than in the perfect one. This fact can be used for the investigation of thin layers of impurity atoms embedded in the crystal matrix.

The X-ray standing wave and Rutherford backscattering spectroscopy in channelling geometry were applied for the investigation of the structure of silicon single crystals implanted with 80 keV Fe ions. Both methods were used for the determination of crystal damage and lattice location of implanted metal atoms before and alter thermal annealing. Both methods gave consistent results regarding the amorphization of Si due to the Fe-ion implantation. Moreover, using both methods some Fe substitution fraction was determined. The depth profiles of implanted atoms were compared to the results of computer simulations. Complementary use of X-ray standing wave and Rutherford backscattering spectroscopy channelling techniques for studies of radiation damage and lattice location of implanted atoms is discussed.

The results of theoretical investigation of X-ray Standing Waves (XSW) on the surface of the crystal with the Uniform Strain Gradient (USG) are presented. Bent crystals are the typical examples of the crystals with the USG. The proposed theory is based on the Takagi-Taupin theory of X-ray propagation in a weakly deformed crystal. This theory is applied for calculation of the angular dependencies of reflection coefficient and XSW on the surface of the crystal with USG for the specific case of Si(400) thick crystal, CuKa radiation. The behaviour of the XSW with the different position of adsorbed atoms (different values of the phase shift) are analyzed

The applications of the external photoeffect excited by an X-ray standing wave to structure studies of crystal subsurface layers are discussed. In experiments conducted with an epitaxial Si film doped with B and Ge, with Ge concentrations ranging from 3.7 x 1019 to 1.5 x 1070 atoms cm -3, a change of phase of the scattering amplitude on the photoemission curve is found. This change is caused by the total surface displacement due to a change in the interplanar spacing in the disturbed layer. The experimental results are compared with accurate theoretical calculations in a bicrystal model. Values for the phase q~ (0) and degree of amorphization exp [ W(0)] on the surface are obtained by least-squares fitting. Universal analytical formulae for the computation of functions describing electron transport and the escape depth of electrons in a crystal are suggested. The potentialities of the depth-selective analysis of X-ray standing waves are analysed. The theoretical foundations of the secondary-radiation yield under the conditions of multiple diffraction are developed. A direct observation of an enhanced Borrmann effect in Laue multi-wave diffraction is predicted.

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