Phasing of resonant anomalous X-ray reflectivity spectra and direct Fourier synthesis of element-specific partial structures at buried interfaces

A formalism for model-independent determination of element-specific partial structures at buried interfaces using the phase-dependent behavior of resonant anomalous X-ray reflectivity (RAXR) data is described. Each RAXR spectrum (i.e. reflectivity versus energy at a fixed momentum transfer near the absorption edge of interest) is uniquely constrained by the amplitude and phase of the resonant partial structure factor with pre-determined non-resonant total structure factor and anomalous dispersion corrections of the resonant species. The element-specific partial density distribution is then imaged by discrete Fourier synthesis with the partial structure factor. The utility of this approach is demonstrated in the comparison of Rb⁺ and Sr²⁺ distributions at muscovite (001)-aqueous solution interfaces derived by model-independent and model-dependent approaches. This imaging method is useful for rapid determination of complex buried interfacial structures where element-specific atomic distributions are poorly constrained by conventional X-ray reflectivity analysis.