New configuration for generation of the parametric X-ray radiation (PXR) by an ultrarelativisticelectron beam is considered. The beam propagates along the external surface of periodical multilayer structure(superlattice) while the photons are emitted under the condition of grazing incidence diffraction. PXR spectralintensity is calculated for this case. It is shown that this specific configuration of the electron beam andtarget radiator can be used for the PXR generation in a storage ring. It can allow one to obtain themonochromatic X-ray beams with the smoothly tuned frequency and the spectral intensity exceeding intensity of thesynchrotron radiation in the narrow spectral ranges.

The modified expression for Debye-Waller factor is derived for the scattering of X-rays from rough surfaces and interfaces. For the large values of scattering vector, the non-Gaussian behaviour of this factor is predicted. This effect can be essential for interpretation of X-ray reflectivity from very rough surfaces and high-order X-ray diffraction data. The experimental X-ray reflectivity measurements are interpreted using the derived expression.

Simple formula for microscopical estimation of the Debye temperature for polyatomic crystals is reported. It is based on the calculation of the force constants for arbitrary pair of interacting atoms by means of the phenomenological spectroscopy data for oscillation frequencies of homonuclear molecules. For that purporse a special combinative rule is suggested. The table of necessary parameters for calculation of Debye temperatures of arbitrary crystals and solid solutions is included.