Multiple scattering and disorder in extended x-ray-absorption fine-structure analysis

Analysis of extended x-ray-absorption fine-structure (EXAFS) spectra for non-nearest-neighbor distances must explicitly consider large variations in multiple-scattering effects over the range of thermal motion or static disorder of the positions of the atoms involved. This is illustrated with temperature-dependent data for two $\mu$-oxo-bridged iron compounds with different bridging geometries. Two extreme curve-fitting models assuming different correlations of Fe-Fe distance with bond angle were applied to the data. The model assuming flexible bond angles was better than the model fixing the bond angle. The disparity between the models was greatest for the more linear arrangements of atoms where multiple scattering is sensitive to small displacements. The accuracy of the Fe-Fe distance relative to the x-ray crystallographic result was never better than 0.024 Å. Because the EXAFS amplitude was dominated by the contribution of collinear bridges, the precision was small (+0.02, -0.08 Å) when the briding angle was within 15° of linearity. The possibility of asymmetry of the Fe-Fe distance distribution was explored in temperature-dependent studies. A negative third central moment of the distribution gave a marginally better fit and a more accurate distance. The origins of this negative moment are discussed.