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X‐ray third‐order nonlinear asymmetrical diffraction has three independent parameters: the asymmetry angle, the incident wave intensity and the deviation from the exact Bragg orientation. In contrast to the linear case, in the nonlinear case the total reflection region does not exist for all intensity values and asymmetry angles. Theoretical consideration leads to analytical conditions of the total reflection region, and the analysis can be carried out by a graphical method. An exact solution in the total reflection region is found. The numerical solutions of the third‐order nonlinear diffraction allow one to find the reflection curves for a fixed asymmetry angle or for a fixed intensity. For very large or very small asymmetry factors the third‐order nonlinear effects can be observed for beams with very low intensities. [ABSTRACT FROM AUTHOR]

An algorithm is developed based on the dynamical theory of X-ray diffraction for calculating the profiles of the diffracted beam, i.e. the diagrams of the intensity distribution versus 2θ when a crystal is fixed at an angle of its maximum diffracted intensity. Similar to Fraunhofer (far-field) diffraction for a single-slit case, in the proposed algorithm the diffracted beam from one atomic layer excited by X-rays is described by the composition of ( N + 1) coherent point oscillators in the crystal. The amplitude and the initial phase of the electric field for each oscillator can be calculated based on the dynamical theory with given boundary conditions. This algorithm not only gives diffraction profiles but also provides the contribution of the excitation of modes when extremely asymmetric diffraction is involved in the diffraction process. Examples such as extremely asymmetric two-beam surface diffraction and three-beam surface diffraction are presented and discussed in detail. [ABSTRACT FROM AUTHOR]