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 samples, information on the orientation of the investigated local structure with respect to a nanostructure (e.g., membranes, proteins, layered compounds, and polymers) or a textured macroscopic structure (e.g., a rough surface) may become accessible in case the considered molecular system is partially ordered. For systems with a preferential orientation of one axis of the molecular coordinate system ( M, e.g., the membrane normal) with respect to a vector in the macroscopic sample system ( S, typically the normal to the macroscopic sample surface), an equation is derived which describes the dependence of the EXAFS on (i) θ E, the angle between the X-ray electric field vector and S, (ii) a single order parameter, (iii) θ R, the angle between the absorber-backscatterer vector and M . A data-evaluation method is proposed which involves a joint-fit of EXAFS spectra measured for, at least, two excitation angles, θ E . Our approach accounts correctly for partial disorder; and it allows an exact single-scattering, curved-wave treatment 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.