Electron energy loss quantitative analysis has been extensively applied to determining the relative concentration of light elements. There are circumstances in which it would be desirable to quantify the concentration of a light element with respect to a heavy element. A particular example is the study of the composition of rare-earth oxides in which polytypes of submicron dimensions can coexist with different stoechiometry. In electron energy loss spectra of rare-earths there are two edges that are detectable. The N45 edge due to 4d transitions to f-states are between 100 and 190 eV and the M45 edges from 3d transitions are between 830 and 1550 eV. The analysis of N45 edges is complicated by multiple scattering, multiplet effects and interactions between bound and continuum final states resulting in a Fano resonance. The M45 edges are more suitable for quantitative analysis and are made up from two parts. In the threshold region there are two strong peaks (M5 and M4 white lines) due to transitions to unfilled bound f-states. They are separated by the spin-orbit splitting which varies between 16 and 45 eV. In addition to these peaks are the edges due to transitions to continuum f-states (see fig 1). The aim of this work is to investigate the accuracy of quantitative energy loss using rare earth M45 edges and to explore the variation of the white lines intensity ratio and compare it with multiplet theory. The spectra were all recorded on a field emission gun VG HB 501 STEM with a Gatan 607 spectrometer operated at 100 kV. The illumination angle was typically 15 mrad and the collection angle 25 mrad which gave an effective collection angle of 22.6 mrad. Hartree Slater calculations of M45 edges only include transitions to continuum states and it is therefore necessary to subtract the white lines from the intensity in the edge. The traditional approach is to fit an inverse power law AE−r to the region before the edge where E is the energy loss and A and r are constants. This is then extrapolated under the edge and subtracted. The white lines contribution is removed by assuming that the M4 line is added to the M5 continuum. An alternative approach is to fit the background, the continuum part of the edge and the white lines all simultaneously. The inverse power law can still be used for the background, the continuum can be modelled using the Hartree Slater results and the white lines modelled by lorentzians. This method was used to extract data on white line intensity and peak separation as shown in fig 1. Cross section data can be analysed in terms of ratio of the lanthanide M45 cross section to the oxygen K shell cross section for a given energy window (in our case 100 eV), which is an effective k-ratio. An alternative is to calculate a lanthanide M45 cross section by using the oxygen cross section of (2.31 ± 0.12) × 10-21 cm2 calculated by the Hartree Slater method. This value is in good agrement with the hydrogenic calculation of Egerton. For comparison purposes we have taken the k-ratios published by Hofer et al.(5) taken under different experimental conditions (primary energy 120 kV, effective collection angle 5.9 mrad) and scaled them to our data. It is also useful to work with an oscillator strength assuming a dipole selection rule when comparing results recorded under different conditions. Our experimental results agree with the Hartree Slater cross sections to within 10% for the elements Sm to Lu as shown in Fig 2. This is less than the discrepancy between our data and that of Hofer. There are more serious discrepancies for La, Ce and Pr where the difference is of order 20%. For Ce and Pr the theory gives values lower than experiment whereas for La the theory overestimates the cross section. In these three cases, there is reasonable agreement between our results and the scaled results of Hofer. We think that it is possible that this is related to the different charge states of Ce and Pr. In conclusion we have shown that it is possible to quantify rare-earth compounds using the M45 edges to the same accuracy as quantification using L and K edges.
