Dispersion equation for X-ray scattering by elastically bent single crystals

For the elastically bent single crystal, when distortion tensor parallel to w(i,j)parallel to much less than 1, from integral dispersion equation, the transcendental equation is obtained, that is fit for computer calculations. The solutions of dispersion equation are found for the weak and strong bend. In the case of the strong bend, we conclude that the crystal can scatter X-ray similarly to the mosaic crystal having the size of blocks significantly less then the extinction length. It follows from this conclusion that intensity of the diffracted wave has the kinematical limit. The cause of this phenomenon consists in appearance of the quasi-symmetric and anti-phase oscillations for the phase function, that is the phase multiplier in the expression for structure factor. The phase multiplier describes the deviation of the lattice from perfection. As a result, the diffracted wave will be effectively formed in crystal regions (blocks), which are determined by asymmetry of the phase function. Meanwhile, extinguishing of X-ray will be effectively realized in symmetric parts of anti-phase crystal regions. When deformation is increased, the angles of orientation of blocks from each other are increased too, but the size of blocks is decreased. Finally, the <<quasi-mosaic>> structure is formed under deformation corresponding to the kinematical limit. In addition, the anomalous splitting of waves corresponding to the different branches of the dispersion surface happens, when transition from dynamical regime of diffraction to kinematical regime takes place.