In the manufacturing process of hard metals and ceramics used as tooling materials, there is strong interest to determine the phases formed within the sintered bulk material or the thin coating of this sintered substrate. A compositional analysis of these, frequently sub-stoichiometric, phases based on electron energy-loss spectroscopy (EELS) is challenging and requires – besides the knowledge of other parameters – accurate ionization cross-sections. Most commonly, EELS ionization cross-sections are derived from analytical models (hydrogenic approximation) or from Hartree Slater oszillator strengths, and hence lack EELS fine-structure details (ELNES). Since fine-structures, however, can be indicative of chemical phases, a proper calculation of cross-sections around the ELNES regime can be beneficial for a more reliable analysis.

For this, an alternative route was followed, trying to obtain detailed differential cross-sections from ab initio multiple scattering calculations, as implemented in the FEFF9 code [1]. With this tool one can calculate EEL spectra (and energy differential cross-sections) based on Green’s functions theory when fed with crystal structure data.

One point of interest first of all is how integrated cross-sections for K-shell ionization edges between the hydrogenic model, calculated with the SIGMAK3 program [2] and FEFF9 [1] simulations compare with each other (Conditions for calculations were: E₀= 200 eV; β= 5 mrad, integration window (Δ)= 200 eV starting at the edge’s threshold) (Fig.1). This is also interesting in the light of the fact that, over the past decades, hydrogenic calculations have been adjusted to better match experimental data for instance by adjusting the inner-shell screening constant (s) for non hydrogen-like atoms [e.g. 3, 4] (Fig.1).

Secondly, structural data, needed as input for FEFF, for known phases can be taken from data bases (e.g. FIZ Karlsruhe). Alternate, for materials with unknown structure or undefined phases the atomic positions can be determined by electron diffraction tomography experiments directly from single nano crystalline domains, as shown by Kolb et al. [e.g. 5,6].

In certain cases selected area electron diffraction (SAED) along with diffraction pattern (DP) simulations can help for phase determination of potential EELS reference samples as the example of Ti_xSiC_1-x shows (Fig. 2): three different structures of Ti_xSiC_1-x are described in literature [7]. The different stoichiometries can be distinguished by the length of the c-axis as there are a different numbers of Ti-layers between the Si-layers (Fig. 2.a). SAED does not only reveal epitactic growth of the carbide coating on the corundum substrate (Fig. 2(b, d, e)) but also, when compared to a diffraction simulation (JEMS) the stoichiometry of the coating can be clearly determined as Ti₃SiC₂ as the distances and intensities of the reflexions match the simulation (Fig. 2(c, f)).

The paper will discuss new possibilities in quantification and findings with this approach.

Acknowledgments

This work was carried out with the financial support by Sandvik Coromant and Sandvik Mining.

References:

[1] J.J. Rehr et al., Phys. Chem. Chem. Phys., 12, pp. 5503-5513 (2010).

[2] R.F. Egerton, EELS in the Electron Microscope, 3rd edition, Springer (2011).

[3] E. Clementi and D.L. Raimondi, J. Chem. Phys., 38, pp. 2686-2689 (1963).

[4] R.F. Egerton, Ultramicroscopy, 63, pp. 11-13 (1996).

[5] U. Kolb et al., Ultramicroscopy 107: 507-513 (2007).

[6] U. Kolb et al., Ultramicroscopy 108: 763-772 (2008).

[7] H. Högberg et al., Surf. Coat. Technol. 193: 6.10 (2005).

Figures:

Figure 1. Comparison of integrated cross-sections for K-edges calculated with SIGMAK3 [2] and FEFF9 [1]. Within the graph the used screening constants (s) are indicated. Beneath the graph, the deviations of the SIGMAK3 values from the FEFF9 simulations are noted and Egerton’s recommended s values [4] are compared to values calculated by Clementi and Raimondi [3].

Figure 2. (a) Different structures of TixSiC1-x. (b) TixSiC1-x coating in between the Al2O3 substrate and the Pt protection layer. (c) Diffraction simulation of Ti3SiC2 (JEMS). (d) Diffraction pattern of the Al2O3 substrate. (e, f) Diffraction pattern of the TixSiC1-x coating.

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