An Analysis of Secondary Enhancement Effects in Quantitative XRFA

An Analysis of Secondary Enhancement Effects in Quantitative XRFA Michael Mantler Institut fur Angewandte und Technische Physik Vienna University of Technology, Vienna, Austria Secondary enhancement effects are well understood and accounted for in quantitative analysis of homogeneous bulk specimens and thin films in the conventional energy range. The conventional energy range is closely related to the spectral distribution of the primary radiation (generally from an x-ray tube), which extends with useful intensities roughly from a few kev to about 30-60keV depending on tube design and operating conditions. It is characterized by the fact that primary excitation of fluorescent radiation at these energies by far exceeds secondary excitation. In the case of very light elements (Be, B, C) with absorption edge energies of loo300ev direct excitation by tube photons is rather inefficient and the relative contribution of secondary effects to the observed fluorescent counts may become quite high and even exceed primary fluorescence. This paper gives an outline of the possible secondary excitation mechanisms and focuses on those which are particularly important in light element analysis, such as cascade effects and excitation by photo-electrons and Augerelectrons. An attempt is made to apply some of the mathematical models to inhomogeneous specimens and specifically to the analysis of carbon in cast irons Copyrigl

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G,; A,,,,Y ; *;< ; :,,::,, ;$E@$ttqg,, _,, l o, c$ by _;.:.:.,&ij:,.: AMPz 0.028 Secondary Secondary A@% 0.040 Secondary &SW 0.078 Secondary W-y1 0.137 Secondary WN 0.380 Secondary AaKa, 0.710 Table 1: Some possible transitions ending in K- and L-shells Table 2: Contribution of conventional secon dary excitation and cascade effects to AgLal (pure Ag, Rb-target, 40kV). Not corrected fo Coster-Kronig transitions. The contribution Casc+Sec is initiated by KtLLL after K- ionization. The emitted AgLrl has sufficient energy to ionize AgLLLL (in an other atom). Conventional secondary excitation. When an atom of element i is ionized by primary tube photons, giving rise to the emission of fluorescent photons hv, these photons may in turn excite atoms j in an energy level Ej < hvi and thereby initiate the emission of secondary fluorescent photons hvj. Tertiary excitation occurs when a third atom, k, can be ionized by hvj and hv, is observed. In general, i, j, and k are atoms of different elements such as the most often cited set Ni, Fe, and Cr, but this is not necessarily always the case: For example, AgK-radiation in pure silver specimens can excite AgL-photons in a second atom, which in turn can excite Ag-M in a third atom, etc. Table 2 shows actual values for the contribution of several lines to secondary AgLa,-excitation as well as the influence of the cascade effect (discussed in the following paragraph) which by far outweighs conventional secondary excitation in this case. Cascade effects. Let us assume that the analyte line for silver is AgLa, and that the tube spectrum excites also AgK-lines. After a primary ionization of the AgK-shell the excited state relaxes most probably by the transition KtL, which is associated with the emission of an AgKo, photon (Table 1). The new vacancy in Lm can be filled by a variety of transition, most likely by LmtMv (La,-emission). Absolute intensities are subject to accounting for Auger-effects and Coster-Kronig transitions but most of these correction factors cancel by building relative intensities. Note that the magnitude of the effect depends on the tube spectrum and matrix elements. If ionization of the L-shell is weak compared to K-ionization this effect may be even dominating (e.g. for iron, where practically no tube photons are available to effrciently excite L, at 71OeV, but abound for K-ionization; see Figure 1). Consequently, in the presence of carbon secondary excitation of CKa by these FeLa-photons may become a very important contribution to the observed carbon photons. The equations by Shiraiwa and Funjino for conventional secondary excitation have to be slightly modified in order to describe the cascade effect (i excites i):

PjK P,L., Secondary excitation by photo-electrons and Auger-electrons. The basic idea is that during each ionization event a photo-electron is emitted from the excited atom, which carries a kinetic energy E,,=hv-E,,,,. If E,, exceeds the ionization energy of another atom the electron may ionize this atom. This is a rather rare event in the conventional energy range, where primary tube photons just above the absorption edges of the analyte elements abound. l.e l.e 1.0 Excitation Energy Fey to.0 100.0 Excitation Energy fk@vj Figure 2: Left: Contribution of photo-electrons and Augerelectrons to CKa (monochromatic excitation) in absolute numbers (emitted fluorescence photons per 1000 primary photons). Right: Relative numbers (reference = pure carbon without secondary enhancement ). Assumed sample: Fe3C. However, the situation is different for light elements, because current commercial tubes emit practically no photons near the absorption edges of beryllium (11 lev), boron (188eV) or carbon (283 ev). In this case primary excitation is poor and secondary enhancement effects gain relative importance, particularly those which translate K-shell absorption (at high energies) to efficient low energy excitation. F&target end-window tubes are often employed for light element analysis because of their strong La-lines. If for example RhLa, (2.7 kev) is absorbed by carbon, a photoelectron with E,,-2.7-0.3=2.4 kev is emitted and is capable of ionizing (theoretically) up to 8 additional atoms, and more than 70 atoms could be ionized by the kinetic energy of an electron emitted by RhKa-absorption (22.7keV). Competing electron interactions reduce these numbers quite drastically, but they nevertheless build up a very strong factor, as will be shown below.

s. -1 n i,seo = c0nst.q.ai.l i PjK PjI. j Secondary excitation by photo-electrons and Auger-electrons. The basic idea is that during each ionization event a photo-electron is emitted from the excited atom, which carries a kinetic energy bin=hv-eedge. If E,, exceeds the ionization energy of another atom the electron may ionize this atom. This is a rather rare event in the conventional energy range, where primary tube photons just above the absorption edges of the analyte elements abound. Figure 2: Left: Contribution of photo-electrons and Auger-electrons to CKa (monochromatic excitation) in absolute numbers (emitted fluorescence photons per 1000 primary photons). Right: Relative numbers (reference = pure carbon without secondary enhancement ). Assumed sample: Fe3C. However, the situation is different for light elements, because current commercial tubes emit practically no photons near the absorption edges of beryllium (11 lev), boron (1SSeV) or carbon (283 ev). In this case primary excitation is poor and secondary enhancement effects gain relative importance, particularly those which translate K-shell absorption (at high energies) to efficient low energy excitation. Rh-target end-window tubes are often employed for light element analysis because of their strong La-lines. If for example RhLa, (2.7 kev) is absorbed by carbon, a photoelectron with E,,=2.7-0.3=2.4 kev is emitted and is capable of ionizing (theoretically) up to 8 additional atoms, and more than 70 atoms could be ionized by the kinetic energy of an electron emitted by RhKa-absortion (227keV). Competing electron interactions reduce these numbers quite drastically, but they nevertheless build up a very strong factor, as will be shown below. Copyright 0 JCPDS-international Centre for Diffraction Data 1997

Absorption of RhKa by carbon is of course rather unlikely (see the p//p - curves in Figure l), but in a heavy matrix it may be efficiently absorbed by a heavier element: e.g. by iron when analyzing carbon in steels; in this case the emitted photo-electron has an energy of E,,w22.7-7.1=15.6 kev. Similarly, absorption of RhLa by iron yields a somewhat lower electron energy (=2keV) than absorption by carbon (=2.4keV), but the absorption probability is again much higher. Note that the relative contribution of photo-electrons to the observed light element counts is independent of any fluorescent yields which cancel in the term NpJo\Tpti+Np,). Accounting for the contributions of Auger-electrons follows the same basic principles and yields numbers of up to the same order of magnitude as for photo-electrons, depending on element-combinations and excitation conditions. Figure 2 shows the contribution of these effects in the system Fe-C (assuming Fe&, =7wgt% C). The computations are based upon the mathematical model described in detail in a previous contribution to these Proceedings. Absolute and relative (pureelement) intensities exhibit a different dependence upon primary photon energy which reflects the higher absorption probability of iron than of carbon in the reference sample for high energy photons, and in turn yield strong cascade-effects and photo-electron contributions. Absolute intensities decrease with increasing primary photon-energy and at higher energies secondary excitation by far exceeds primary excitation. The data agree nicely with the results by Pavlinsky et a1.2,, who computed the contributions of photo-electrons and Auger-electron in binaries of lwgt% carbon with a varying second element Z (712GO) for excitation by an x-ray tube (Figure 3). In this case the numbers of monochromatic primary photons (as in Figure 2) must be appropriately weighted as a function of energy. Results of our own computations for Fe-C are included for comparison. Not all details of Pavlinsky s calculations have been reported in their paper, and the two (red) data-points reflect our uncertainty regarding their geometry of the x-ray tube and their general set-up. Additional differences may arise from the rather unreliable numerical values of some of the fundamental parameters. 100 % 80 60 40 0 10 20 30 40 Atomic Nuder of Matrix [99 wgt%] Figure 3: Curve: Contribution of Photo-electrons and Auger-electrons to the observed carbon Kcx-counts (computations by Pavlinksy etal). Red datapoints: Own computations for Fe-C for different geometrical set-ups (see text). Copyright@ JCPDS-International Centre for Diffraction Data 1997

lnhomogenoeous specimens. Many kinds of specimens, such as steels and cast irons, appear to be homogeneous from the view point of higher energies but are highly inhomogeneous for the fluorescent radiation of light elements. For example when carbon is analyzed in cast irons, conventional secondary excitation takes place within Fe&grains, but carbon in graphite precipitations is excited by the heavy matrix elements surrounding the graphite particles Self absorption for the emitted carbon photons is then very low within the grain and high count rates are observed from graphite particles at the specimen s surface. Obvi- Figure 4: carbon spherolites ously the measured count rates are strongly dependent (black) embedded in other phases of cast iron3 ratio. Micrometer II 1-_-_-L. I.....I rial as a function of specimen thickness. Top curve: CKa from Fe3C. middle: CKa from graphite. bottom: FeKa from Fe3C. Figure 6: Model for computations of carbon count rates from graphite spherolites (near the surface of the specimen) in iron matrix. Black: carbon, white and gray: other phases. - Figure 5 can be used to determine the information depths for FeK-, FeL-, and CKradiation in Fe,C and in the respective pure elements (data are not corrected for secondary excitation by electrons, which is not yet possible for thin film specimens with our software). 99% of CKa-bulk intensity is reached with roughly lt.rrn Fe,C and 1Opm pure graphite (note that this is also the size of many microstructural grains). Assuming for simplicity spherolytic carbon precipitation in cast iron, the surface of such specimens will exhibit a random-like distribution of spherical carbon segments (Figure 6). CKa-radiation from these areas of pure carbon is least affected by matrix absorption (only by some shadowing effects) and most enhanced by electrons emitted from the surrounding heavy matrix elements. On the other hand, carbon radiation from Fe& is strongly absorbed by the matrix, so that the same amount of carbon in a specimen delivers quite different photon counts depending on its physical/chemical state (including the graphite/cementite ratio, eventual other carbides, as well as precipitation shapes and sizes) in the specimen.

Figure 7: Computed and experimental CKa count rates Preliminary computations based upon this simple model deliver the working curves for the system Fe-C shown in Figure 7. The graphite model assumes all carbon to be in (large, lourn) graphite precipitations, while the Fe+C -model is based on a homogeneous solution of carbon in iron (which gives practically the same results as the Fe,C-Fe with appropriate scaling). No excitation by electrons is included in the computations (this is not yet possible for inhomogeneous specimens), and from the discussion of these effects in the previous chapter it has to be assumed that both curves should have in fact a much higher slope, particularly that of the graphite-model. A number of measurements have been made from cast iron specimens and their relative (to pure carbon) CKa-intensities are included in Figure 7. The fact that these values are not all within the limits of the theoretical curves is obviously due to the lack of proper accounting for excitation by electrons, as discussed above. The second striking fact is that the experimental data scatter considerably and a reliable working curve cannot be derived. An attempt has been made therefore to correlate the deviation from the lower (Fe+C-model) curve with the microstructure of the specimens. The images of the specimen surfaces obtained by optical microscopy are shown in Figure 8, sorted to follow decreasing blackness (i.e. sum of dark pixels representing carbon precipitations, obtained by imaging software after proper discrimination of noise). The deviations of the experimental CKa-counts from the Fe+C-model data were computed and the results are shown on an arbitrary scale in Figure 9, again in the sequence of decreasing blackness or visible carbon. The qualitative correlation is obvious: specimens with large and many carbon precipitations show much larger intensity values than indicated by the working curve compared to those with few and small precipitations.

9 5 6 8 Figure 8: Microscopic images from cast iron samples. Black dots are graphite precipitations. The numbers below each image are specimen ID s and correspond to those in figures 7 and 9. Figure 9: Deviation of experimental data-points from a theoretical working curve (Fe-C model in Figure 7). The numbers are specimen ID s and the same as in Figures 7 and 8. Scaling and offset of the ordinate are arbitrary.

Literature 1. M.Mantler, Advances in X-ray Analysis 36,27 (1993) 2. C.G.Pavlinsky, A.Yu.Dukhanin: XRS 23,221 (1994) 3. H.Ebel, F.Landler, H.Dirschmidt, Z.Naturforschung A, 25, 927 (1971) 4. E. Hornbogen, H.Warlmont, Metallkunde, Springer (1991) Acknowledgements This work has been supported by the Jubiliiumsstiftung der Oesterreichischen Nationalbank (project 5587) and Hochschuljubilaumsstiftung der Stadt Wien (project H235/96).