THEORY OF THE LINEAR DICHROISM IN THE EXTENDED X-RAY-ABSORPTION FINE-STRUCTURE (EXAFS) OF PARTIALLY VECTORIALLY ORDERED SYSTEMS

Using linearly polarized X-rays for investigations on noncrystalline s amples, information on the orientation of the investigated local struc ture with respect to a nanostructure (e.g., membranes, proteins. layer ed compounds, and polymers) or a textured macroscopic structure (e.g., a rough surface) may become accessible in case the considered molecul ar system is partially ordered. For systems with a preferential orient ation of ons axis of the molecular coordinate system (M, e.g., the mem brane normal) with respect to a vector in the macroscopic sample syste m (S, typically the normal to the macroscopic sample surface), an equa tion is derived which describes the dependence of the EXAFS on (i) the ta(E), the angle between the X-ray electric field vector and S, (ii) a single order parameter, (iii) theta(R), the angle between the absorbe r-backscatterer vector and M. A data-evaluation method is proposed whi ch involves a joint-fit of EXAFS spectra measured for, at least, two e xcitation angles, theta(E). Our approach accounts correctly for partia l disorder; and it allows an exact single-scattering, curved-wave trea tment of the EXAFS originating from an absorber-backscatterer pair of unknown orientation. An approximative and the curved-wave approach for evaluation of EXAFS dichroism data are compared.