An Hermite expansion method for EXAFS data treatment and its application to Fe K-edge spectra

A new Hermite expansion method has been developed for EXAFS data treatment. This transformation technique involves an expansion into a series of odd Hermite functions, which are eigenfunctions of the sine Fourier transform. In this communication, we report mainly the use of the method to filter iron K-edge X-ray absorption data. Unlike the other numerical Fourier techniques, the new method takes into consideration additional physical information on the experimental data, i.e. both the length of the interval of the measurements and an estimation of the length of the interval of significant structure changes in real space are parameters of the method. The method was validated with iron K-edge fluorescence spectra of magnetite and applied to iron exchanged ZSM-5 zeolite with low iron loadings (0.75 wt.%). We are able to show that, compared to the same data unfiltered or spectra Fourier filtered with a large Gaussian window, the noise level is strongly reduced and artefacts at higher distances disappear. The validity of the method was proved by applying it to magnetite (Fe3O4), where it is possible to fit the two Fe–O distances (octahedral and tetrahedral sites) known from X-ray diffraction. With the new method, these shells are statistically significant and are observed as individual contributions in the Fourier transforms. We also show that the new method, unlike conventional Fourier techniques, retains the statistical independence of the data.