Ultramicroscopy 9 (1982) 283-288 283 North-Holland Publishing Company CROSS-SECTIONS FOR ENERGY LOSS SPECTROMETRY Peter REZ Department of Materials Science and Minerals Engineering, University of California, Berkeley, California 94720, USA Received 14 June 1982 (presented at Workshop January 1982) The various methods for calculating partial cross-sections for energy loss spectrometry are reviewed. Comparison is made between Hartree-Slater calculations, the efficiency factor method, and the hydrogenic model. A scheme for parameterisation to be used in fast calculations of partial cross-sections is also proposed. It has been recognised for some time that relia- ble cross-sections integrated over relevant collec- tion angles and energy windows are necessary for quantitative energy loss analysis. Originally these partial cross-sections were derived from the total ionisation cross-section by multiplying by two ef- ficiency factors [ 1]. The energy integration after a core edge was taken into account by an energy efficiency factor. This was calculated assuming the spectrum after the edge followed the well known power law AE -r, E being the energy loss and A and r fitted parameters. An angular efficiency factor took account of the finite collection angle accepted by the spectrometer. One obvious prob- lem with such an approach is the variation of the exponent in the power law with collection angle. It is hard to see whether an exponent relevant for small collection angles or an exponent appropriate to the collection angle of interest should be used. These exponents can vary between about 2.5 and 4.5, and as the energy efficiency term is very sensitive to this factor it can lead to serious errors in quantitative analysis. Another method of performing quantitative analysis is to measure the relevant partial cross- section from a standard [2]. If only atomic ratios are needed this is not too difficult, but absolute measurements of partial cross-sections require ac- curate thickness measurements. The difficulties of preparing specimens for every edge of interest and the storage requirements for a range of collection angles for each edge make this method unattrac- tive for general use. The other alternative is to use cross-sections calculated from atomic wave functions. Either the hydrogenic model [3] can be used or the wave functions can be calculated from a Hartree-Slater model [4]. The hydrogenic model does not involve much computation and can be implemented on the mini-computers which are part of the analytical system. The hydrogenic model should be quite accurate for K shells, but there is no reason to expect that hydrogenic wave functions are good descriptions of L, M or N shells. The Hartree- Slater calculations give reasonable agreement with experiment but, as with spectra from standards, large amounts of data have to be stored. In a previous paper comparisons were made between the hydrogenic and Hartree-Slater cross- sections for K shell ionisations [5]. It was found that there was no more than 5% difference for carbon K ionisation. The spectrum generated from the Hartree-Slater cross-section showed a slight peak at threshold, in agreement with experiment (see figs. 1 and 2). This is presumably, because the potential seen by the continuum electron just above threshold is deeper for the hydrogenic model, and the overlap integral between initial and final sate wave functions is therefore lower. If it is assumed that the Hartree-Slater cross- sections are correct it is possible to gauge the accuracy of a correction procedure by dividing the 0304-3991/82/0000-0000/$02.75 © 1982 North-Holland