What Remains to Be Done to Allow Quantitative X-Ray Microanalysis Performed with EDS to Become a True Characterization Technique?

Abstract

This article reviews different methods used to perform quantitative X-ray microanalysis in the electron microscope and also demonstrates the urgency of measuring the fundamental parameters of X-ray generation for the development of accurate standardless quantitative methods. Using ratios of characteristic lines acquired on the same X-ray spectrum, it is shown that the Cliff and Lorimer K A-B factor can be used in a general correction method that is appropriate for all types of specimens and electron microscopes, providing that appropriate corrections are made for X-ray absorption, fluorescence, and indirect generation. Since the fundamental parameters appear in the K A-B factor, only the ratio of the ionization cross sections needs to be known, not their absolute values. In this regard, the measurement of ratios of the K A-B factor (or intensities at different beam energies of the same material with no change of beam spreading in the material) permits the validation for the best models to compute the ratio of ionization cross sections. It is shown, using this method, that the nonrelativistic Bethe equation, to compute ionization cross section, is very close to the equation of E. Casnati et al. (J Phys B 15, 155-167, 1982) and also to the equations proposed by D. Bote and F. Salvat (Phys Rev A 77, 042701, 2008) for the computation of the ratio of ionization cross sections. The method is extended to show that it could be used to determine the values of the Coster-Kronig transitions factors, an important fundamental parameter for the generation of L and M lines that is mostly known with poor accuracy. The detector efficiency can be measured with specimens where their intensities were measured with an energy dispersive spectrometer detector, the efficiency of which has been measured in an X-ray synchrotron (M. Alvisi et al., Microsc Microanal 12, 406-415, 2006). The spatial resolution should always be computed when performing quantitative X-ray microanalysis and the equations of R. Gauvin (Microsc Microanal 13(5), 354-357, 2007) for bulk materials and the one presented in this article for thin films should be used. The effects of X-rays generated by fast secondary electrons and by Auger electrons are reviewed, and their effect can be detrimental for the spatial resolution of materials involving low-energy X-ray lines, in certain specific conditions. Finally, quantitative X-ray microanalysis of heterogeneous materials is briefly reviewed.

Electron Probe Microanalysis of Ni Silicides Using Ni-L X-Ray Lines

“…Nonradiative Coster–Kronig transitions may also be affected by chemical bonding effects, and as a result, the Coster–Kronig correction factor (1+ T CK ) may no longer cancel out in equation (3). For the L-subshells of Ni, the factor T CK can be written as (Gauvin, 2012): where f 13 , f 12 , and f 13 are yields for Coster–Kronig transitions L i →L j between the L-subshells indicated by the subscripts, and σ L i is the cross-section for the ionization of the L i subshell. Kurmaev et al (2005 a ) showed that the L 2 L 3 M 4,5 Coster–Kronig transition rate is much higher in Fe metal than in the corresponding Fe oxides (see also Sorensen et al, 1991; Kurmaev et al, 2005 b ).…”

“…Subsequently, an electron from an outer shell may make a radiative transition thus filling the vacancy, with the emission of characteristic X-rays. For each element i that makes up the sample, the intensity of the X-ray line of energy E ph originated by the transition of an electron from shell k to shell j can be written as where c i is the weight fraction of element i , E 0 the incident electron beam energy, ω jk the partial fluorescence yield, (1+ T CK ) a factor that takes into account the increase of X-rays due to nonradiative Coster–Kronig transitions from vacancies produced in other subshells (see e.g., Gauvin, 2012), ϕ j ( ρz ) dρz gives the number of vacancies created in shell j between ρz and ρz + dρz , μ / ρ ( E ph ) is the mass-attenuation coefficient (MAC) for photons of energy E ph in the material, and ψ is the X-ray take-off angle. For compound materials, the MAC is usually calculated by means of a weighted sum, i.e.…”

High-resolution imaging with SEM/T-SEM, EDX and SAM as a combined methodical approach for morphological and elemental analyses of single engineered nanoparticles

“…Systematic efforts must be spent in order to develop new and suitable quantitative concepts. 40 Another empirical quantication approach would be to directly compare the elemental intensity ratios of the reference materials of similar concentration and size distribution as the particles to be investigated. The main drawback here is constituted by the lack of silica nanoparticle reference materials with valid elemental compositions.…”

The qualitative f‐ratio method applied to electron channelling‐induced x‐ray imaging with an annular silicon drift detector in a scanning electron microscope in the transmission mode

“…The f‐ratio for element i , f i , is given by the following equation: where I i is the net intensity for element i and n the number of elements. Originally based on the thin film Cliff‐Lorimer method (Cliff & Lorimer, ), the method's main goal was to circumvent the lack of beam current stability in CFE‐SEMs and to improve the applicability of quantification when the concentration of the denominator of a single element's ratio tends to zero, inevitably making the Cliff‐Lorimer factor to diverge significantly (Gauvin, ) because of the statistical noise in the signal.…”

“…where I i is the net intensity for element i and n the number of elements. Originally based on the thin film Cliff-Lorimer method (Cliff & Lorimer, 1975), the method's main goal was to circumvent the lack of beam current stability in CFE-SEMs and to improve the applicability of quantification when the concentration of the denominator of a single element's ratio tends to zero, inevitably making the Cliff-Lorimer factor to diverge significantly (Gauvin, 2012) because of the statistical noise in the signal. In this work, the f-ratio method was applied qualitatively to the x-ray images obtained under high channelling conditions to subtract the diffraction contrast from the net intensity images.…”