Numerical simulation of the resonant forbidden Bragg reflection in Ge

The “forbidden” reflections are observed in the synchrotron radiation diffraction when the energy of incident radiation is close to the absorption edges in crystals. In the present paper, a new method for calculations of the thermal-motion-induced forbidden reflections intensity is proposed. It includes two steps: the simulation of the temporary atomic displacements with the help of the ab initio molecular dynamics followed by the quantum-mechanical calculations of the resonant scattering amplitude for various configurations. This technique is applied to the calculation of the 600 reflection thermal behavior in Ge and gives an adequate quantitative fitting of experimental data. The proposed simulation method of the thermal-motion-induced forbidden reflections is available for any crystal structure and promises to explain many results obtained up to now at the synchrotrons.