arXiv subjects
Publications and source records attributed to Luis H. Avanci.
This work reports the incompatibility of the Stokes relation for time reversibility of wave's propagation and the usage of complex atomic form-factor in diffraction theories. The implications behind a diffraction theory that obeys the Stokes relation is discussed.
By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained. Diffraction phenomena in crystals are reproducible after assigning probability amplitudes to every classical outcome. When applied to X-ray diffraction in reflection geometry, this procedure has provided simple recursive equations to calculated the X-ray reflectivity of crystals with thickness varying since a few atomic layers to infinity. The results are in agreement with the dynamical theory of X-ray diffraction, even when absorption is considered.
Phase invariants are important pieces of information about the atomic structures of crystals. There are several mathematical methods in X-ray crystallography to estimate phase invariants. The multi-wave diffraction phenomenon offers a unique opportunity of physically measuring phase invariants. In this work, the underneath principals for developing an automatic procedure to extract accurate phase-invariant values are described. A general systematic procedure is demonstrated, in practice, by analyzing intensity data from a KDP crystal.
Solutions in the form of series expansion, as the Born approximation, are very useful for describing time-independent scattering of quantum particles. In this work, it is mathematically demonstred that such solutions, when applied to multiple beam scattering phenomena, can lead to energy violation where the number of incident and scattered particles is not preserved. General basic conditions for developing consistent solutions of time-dependent multiple beam scattering problems are outlined.