GENERALIZED LAUE DYNAMICAL THEORY FOR X-RAY REFLECTIVITY AT LOW-INCIDENCE AND HIGH-INCIDENCE ANGLES ON IDEAL CRYSTALS OF FINITE-SIZE

We present a generalized dynamical theory within the Laue formalism va lid for x-ray Bragg and Laue diffraction on ideal crystals of finite t hickness (crystal slab, film). In our model only the following two app roximations are made: to consider a two-beam case and to neglect quadr atic terms of the dielectric susceptibility. In fact, we take into acc ount: (i) the asymptotic sphericity of the dispersion surface and all the four solutions of the secular equation; (ii) the difference betwee n electric and displacement fields; (iii) the boundary conditions of c ontinuity of the tangential components of the electric and magnetic fi elds at the two crystal-vacuum interfaces. With the equation derived i t is possible to describe the interaction of the x-ray beam with the c rystal of finite thickness in a dynamical way in the whole angular ran ge from 0 to pi/2. Our improved theory can be applied for describing: (i) symmetric and asymmetric reflections both close to the Bragg angle and at the far tails of the Bragg peaks; (ii) Bragg and Laue diffract ions of x rays at very small incidence angles of the order of the crit ical angle; (iii) Bragg and Laue diffractions in which the diffracted beam travels almost parallel to the crystal surface; (iv) diffractions with Bragg angles close to pi/2.