How multiple scattering simulations help for
EELS
compositional analysis of hard metals and ceramics
Authors: Konrad Lukas , Lattemann Martina , Rehr John , Kolb Ute , Haishuang Zhao , Kothleitner Gerald 
Published: December 2016

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: E
0
= 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
x
SiC
1‐x
shows (Fig. 2): three different structures of Ti
x
SiC
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 Ti
3
SiC
2
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.