Curve fitting methods for quantitative analysis in electron energy loss spectroscopy

A novel approach to the determination of elemental concentrations in solids by Electron Energy Loss Spectroscopy (EELS) is presented. The method uses calculated values of the inner-shell excitation cross-sections and standard assumptions about the form of the background, to model the spectrum before and after an excitation edge. Strong features just above the threshold (white lines) can be modelled by Lorentz oscillators. A least-squares fitting routine adjusts the weights of the various components of the model until the best fit with the experimental data is found. Multiple scattering can be taken into account by using the low-loss spectrum in a deconvolution with the experimental data, or in a convolution with the calculated spectrum. When two elemental edges are treated in this fashion, a value for their relative concentrations can be obtained. The method is compared with the conventional technique of background subtraction by pre-edge extrapolation, for the cases of some iron and chromium oxides. Both methods are found to give satisfactory results for the iron compounds if the effects of multiple scattering are included. However, for the oxides of chromium, the proximity of the two edges used (O-K and Cr-L) makes the use of the background subtraction method practicallyi mpossible, but the new approach gives results close to those expected from the chemical formulae. The method should prove applicable to a wide range of other problems in which overlapping edges are a problem.