IMPROVED DYNAMICAL THEORY FOR X-RAY REFLECTIVITY OF IDEAL CRYSTALS OFFINITE-SIZE AT LOW AND HIGH-INCIDENCE ANGLES

In this work we present an improved dynamical theory within the Laue f ormalism for the two-beam case, which is valid for X-ray Bragg and Lan e diffraction on ideal crystals of finite thickness. In our calculatio ns no approximations, which are generally used in the conventional dyn amical theory, are made. We limit ourselves to the two-beam case and n eglect only the quadratic terms of the dielectric susceptibility. We t ake into account: i) the asymptotic sphericity of the dispersion surfa ce and all the four solutions of the secular equation; ii) the differe nce between electric and displacement fields; iii) the boundary condit ions of continuity of the tangential components of the electric and ma gnetic fields at the two crystal-vacuum interfaces. With the equations derived it is possible to describe the interaction of the X-ray beam with the crystal in a dynamical way in the whole angular range from 0 to x/2. Our improved theory can be applied for describing: i) symmetri c and asymmetric reflections both near the Bragg condition and at the far tails of the Bragg peaks; ii) Bragg diffraction of X-rays at very small glancing angles of the order of the critical angle; iii) Bragg a nd Laue diffractions in which the diffracted beam travels almost paral lel to the crystal surface.