An algorithm for calculating diffraction profiles of 2θ scans for multiple diffraction from crystals and thin films

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 2 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.