Speciation of iron sulfide compounds by means of X-ray Emission Spectroscopy using a compact full-cylinder von Hamos spectrometer

Abstract

We present experimental and theoretical X-ray emission spectroscopy (XES) data of the Fe Kβ line for Iron(II)sulfide (FeS) and Iron(II)disulfide (FeS₂). In comparison to X-ray absorption spectroscopy (XAS), XES offers different discrimination capabilities for chemical speciation, depending on the valence states of the compounds probed and, more importantly in view of a a broader, laboratory-based use, a larger flexibility with respect to the excitation source used. The experimental Fe Kβ XES data was measured using polychromatic X-ray radiation and a compact full-cylinder von Hamos spectrometer while the calculations were realized using the OCEAN code. The von Hamos spectrometer used is characterized by an energy window of up to 700 eV and a spectral resolving power of E/ΔE = 800. The large energy window at a single position of the spectrometer components is made profit of to circumvent the instrumental sensitivity of wavelength-dispersive spectrometers to sample positioning. This results in a robust energy scale which is used to compare experimental data with ab initio valence-to-core calculations, which are carried out using the ocean package. To validate the reliability of the ocean package for the two sample systems, near edge X-ray absorption fine structure measurements of the Fe K absorption edge are compared to theory using the same input parameters as in the case of the X-ray emission calculations. Based on the example of iron sulfide compounds, the combination of XES experiments and ocean calculations allows unravelling the electronic structure of different transition metal sulfides and qualifying XES investigations for the speciation of different compounds.

1. Introduction

The study of Kβ X-ray emission spectra of 3d transition metal compounds by means of high-resolution XES is a suitable and established experimental tool in a broad range of research fields that aim to gain information on the valence electronic structure^1–3. The energies of these chemically sensitive Kβ emission lines are in the range from 4.0 keV to 9.5 keV, ensuring large penetration depths and flexibility with respect to the sample environment, i.e. favourable conditions for in situ and operando experiments, as opposed to the L-edge spectroscopy which, however, provides a direct access to the partially filled 3d states via dipole transitions.

In XES the radiative relaxation (fluorescence emission) of a core hole is analyzed⁴. The K fluorescence emission, which results from relaxation processes following an ionization of the atom in the K shell, is composed of two main regimes caused by transitions of electrons of principle quantum number n = 2 (Kα) and principle quantum numbers n = 3,4 (Kβ). Due to spin and angular momentum the transitions are further subdivided into Kα₁ and Kα₂, as well as Kβ_1,3 and Kβ_2,5, respectively. The Kβ emission lines exhibit a more distinct sensitivity to the electronic structure of the partially filled 3d electron shell and other occupied valence states that are involved in chemical bonding². While the modification of the Kβ_1,3 main line is dominated by spin state contributions⁵,⁶, the spectral region around the Kβ_2,5 line is more sensitive to changes in the valence state energies^7–9. The spectroscopy of this spectral region is referred to as valence-to-core XES (vtc-XES)¹⁰.

As the features associated with vtc-XES exhibit low transition probabilities as well as small energy differences on the order of a few eV or less, measurements require instrumentation capable of efficiently resolving these features. There are many spectrometer types that meet this requirement, ranging from transition edge sensors (E/ΔE = 1300)⁶ to multi-crystal wavelength-dispersive spectrometers (WDS, E/ΔE = 5000 to 10000) with spatial dimensions exceeding several meters¹¹,¹². There are generally three characteristics that classify these spectrometers: energetic resolving power, detection efficiency, and energy window defining the accessible spectral energy range at a preselected, fixed spectrometer setting¹³. While the resolving power is usually the most interesting parameter as it is the significant number for revealing details in the experimental data, efficiency and energy window are more of practical nature. Higher efficiency enables shorter measurement times, lower detection limits and possibly circumvents radiation damage to the sample. A large energy window allows covering a broad spectral region enabling the analysis of widely distributed spectroscopic features with only one spectrometer setting, e.g., simultaneous detection of 3d metal Kα and Kβ emission lines without moving any spectrometer component during which one of the key parameters of a spectrometer could be modified.

The von Hamos spectrometer used in the present work is based on a full cylinder geometry with a small radius of curvature. This concept grants on the one hand in conjunction with the use of mosaic crystals an optimized detection efficiency and on the other hand permits covering a larger energy window at a given crystal width and a fixed position of the spectrometer components. The compromise made by selecting the small radius of curvature is a reduced resolving power of the spectrometer. We demonstrate that the resolving power achieved by the spectrometer used is sufficient to realize chemical speciation of a 3d transition metal by means of Kβ spectroscopy including vtc-XES. Additionally, the spectrometer’s energy window of over 700 eV allows for referencing the chemical sensitive Kβ line energies to the Kα doublet. This alleviates the challenge of correcting the energy scale to account for possible changes in the sample position when using different reference lines. The sensitivity of WDS to sample position commonly requires employing entrances slits, resulting in a potential loss of detection efficiency¹⁴.

The presented XES data is complemented with ab initio calculations using the ocean package^15,16. As such the discrimination capability of theoretical and experimental methods for chemical speciation will be demonstrated. In order to validate the calculations and demonstrate the performance of the ocean package, we compare near-edge X-ray absorption fine structure spectra (NEXAFS) of the two compounds with calculations using the same input parameters as for XES. A recent publication has already demonstrated the potential in non-resonant XES by validating vtc-XES of titanium oxides⁹. Finally, using the combination of experiment and theory we are able to provide benchmark results for the Fe K XES and NEXAFS.

2. Materials

We investigate the iron sulfur compounds Iron(II)sulfide (troilite, FeS) and Iron(II)disulfide (pyrite, FeS₂) using X-ray emission spectroscopy (XES) in the hard X-ray range by means of a wavelength-dispersive spectrometer based on a modified von Hamos geometry. Both compounds were purchased in the form of powder which were pressed to pellets prior to investigation. Iron sulfide species and the discrimination between them are of importance in chemical reactions and processes^17–19. More specifically, pyrite (FeS₂) has been demonstrated to be of use in batteries²⁰ and remains a compound of interest for improving the cycling performance of Li/S batteries. Indeed, with renewable energies on the rise and the ongoing change from combustion based transportation to electric transportation there is a growing demand for electric energy storage devices. In this respect metal sulfides are cheap, abundant, and environmental friendly materials for energy storage applications^21–23 and chemistry^24–28.

3. Calculation

Calculations of XES and XAFS were carried out using the ocean package^15,16. Electron orbitals were calculated using density-functional theory as implemented in the Quantum ESPRESSO code²⁹, using the generalized gradient approximation³⁰. Pseudopotentials were taken from the PseudoDojo collection^31,32. An energy cut-off of 120 Ry was used for both materials. Within ocean, absorption spectra are calculated using the Bethe-Salpeter equation, requiring electron orbitals for both the final states and for a calculation of the core hole screening. For FeS₂ the electron orbitals were calculated on an 8³ shifted k-point mesh with 212 conduction band states for the final states, while the screening was carried out using a 2³ k-point mesh and 412 conduction bands. The parameters for FeS were scaled by the differences between the two unit cell sizes with a 6 × 6 × 4 k-point mesh and 484 conduction bands for the final states and a 2 × 2 × 1 k-point mesh and 940 conduction bands for the screening. Experimental lattice constants were used for both FeS₂³³ and FeS³⁴. Both dipole and quadrupole terms are included in the transition operator for absorption and emission. In addition to 0.6 eV broadening to simulate the Fe 1s core-hole lifetime, Gaussian broadening has been applied to the calculated XAS spectra and Lorentzian broadening has been applied to the calculated vtc-XES spectra to match experiment. Note that the calculation of XES spectra is focused on the vtc-XES region of the Kβ_2,5 line because there are some challenges in describing the 3p-3d splitting which results in the occurrence of the Kβ′ satellite line⁸. The energy of the core level is missing in ocean calculations. A single offset parameter is required to shift the calculated spectra to match experiment³⁵. The same parameter is used for both the Fe K absorption and emission and shared between FeS₂ and FeS.

4. Experimental

All measurements were realized in the Physikalisch-Technische Bundesanstalt laboratory at the electron storage ring BESSY II³⁶. The XAFS spectra were measured at the four-crystal-monochromator (FCM) beamline^37,38 in transmission mode using a photodiode as detector and tuning the incident photon energy over the Fe K absorption edge, referred to as near-edge X-ray absorption fine structure (NEXAFS). For each incident photon energy the detected photocurrent was averaged over a five time readout of the photodiode. Note that NEXAFS experiments in the fluorescence mode require incident radiation with a tunable photon energy as offered commonly at synchrotron radiation beamlines while XES experiments can be realized also with radiation sources having a broad energy bandwidth, e.g. non-monochromatized synchrotron radiation (white light) or Bremsstrahlung from an X-ray tube (laboratory instrumentation). In this view, the XES measurements were performed at the dipole-white light beamline³⁹ in the same laboratory delivering a polychromatic excitation spectrum corresponding to bending magnet radiation with a critical energy of 2.5 keV originating from a 1.3 Tesla dipole magnet. A beamline filter of 2 μm aluminum is used to attenuate the polychromatic excitation spectrum below the Fe K-edge and, thus, to drastically reduce unwanted background radiation caused by scattering. Furthermore, a pinhole was used for collimation of the incident radiation.

The von Hamos spectrometer was built in-house and can be operated in a single or double Bragg crystal configuration⁴⁰. The spectrometer is attached to an ultra-high vacuum chamber that contains a sample manipulator and a photo diode for transmission measurements similar to the chamber presented by Lubeck at al.⁴¹. A position sensitive back-illuminated in-vacuum X-ray charge-coupled device (CCD) with 2048 pixels × 2048 pixels and 13.5 μm × 13.5 μm pixel size is used as the detector unit. The diffractive element consists of a 40-μm-thick highly-annealed pyrolytic graphite (HAPG) mosaic crystal^42,43 mounted on the inner surface of a Zerodur cylinder with a radius of only 50 mm. This makes this device very compact such that it can readily be used at different synchrotron radiation beamlines or with laboratory X-ray sources. HAPG exhibits high reflectivity⁴⁴, and it can be mounted to almost any shape suitable for X-ray optics. In the double crystal configuration, the spectrometer was already successfully applied to vtc-XES of binary titanium compounds, achieving a resolving power of E/ΔE = 2700⁹. The resolving power of a von Hamos spectrometer generally depends on the radius of curvature. Previous publications of Anklamm et al.⁴⁵ and Malzer et al.⁴⁶ report on full-cylinder HAPG based von Hamos spectrometers with respective radius of curvature of 150 mm (E/ΔE = 2000) and 300 mm (E/ΔE = 4000), scaling the entire setup to multiple meters and, hence, dedicating these devices to stationary use only. For the present spectrometer with 50 mm radius of curvature, the resolving power for the Kβ_1,3 line of FeS₂ was determined by fitting the lineshape and taking the natural line width of 3.53 eV⁴⁷ into account. The achieved resolving power of the used setup was found to be in the order of E/ΔE = 800 which corresponds to roughly 9 eV full width at half maximum (FWHM). Furthermore, the ratio of cylinder height to cylinder radius defines the energy window of a von Hamos spectrometer. In order to maintain the same energy window per crystal position, increasing the radius results in a quadratic increase of the overall needed crystal surface and therewith material. Thus, the advantage of a small radius of curvature in this regard becomes obvious. The employed cylinder has a width of 20 mm along the cylinder axis such that it enables covering a very large energy window of up to 700 eV. As the spectral resolving power depends on the source size, the excitation beam is focused by means of a polycapillary X-ray lens achieving a source size of around 60 μm.

Two different CCD and HAPG crystal positions were used to measure the full Fe K emission spectrum and the Fe Kβ emission lines only. The Kβ XES spectra are obtained by summing up 220 CCD images of 40 seconds exposure time each, resulting in a total measurement time of 2h 26 min per spectrum. The spectrum showing Fe Kα and Fe Kβ emission to reference the chemically sensitive energy of the Kβ lines is derived from only one CCD image of 40 seconds exposure time because the transition probabilities of these main lines are rather high. Both samples were prepared from high-purity powders as powder spread on adhesive Kapton tape. The samples were set to an incident and emission angle of 45°.

5. Results and Discussion

5.1. X-ray emission spectroscopy

The energy scale of the Kβ XES spectra is referenced to the Fe Kα₁ and Kα₂ assuming a negligible chemically induced energy shift of the doublet. The works of Glatzel et al.⁴⁸ and Joe et al.⁶ report on a chemical sensitivity of the Kα emission with regard to the line width and relative transition probability of the Kα₁ and Kα₂ emission lines. However, only small energetic shifts on the order of less than 1 eV of the respective centroid are expected. Hence, by referencing the Kβ emission lines to the Kα emission lines we omit the sensitivity of the spectrometer energy scale to the sample positioning. Figure 1 displays the complete Fe K emission of FeS and illustrates the large energy window covered by the spectrometer in the single crystal configuration. The photon energies and uncertainties of Kα_1,2 emission lines are taken from Holzer et al.⁴⁷. Radius channel and photon energy are geometrically related by the Bragg equation as explained in Anklamm et al.⁴⁵. Note that the resolving power of the spectrometer depends on the radii of the detected circles⁴⁹.

Figure 1.

Fe Kα and Kβ emission lines of FeS demonstrating the large energy window covered by the spectrometer. The displayed spectrum is fitted with four Pseudo-Voigt function⁵⁰: one for the Kα₁ and one for the Kα₂ line, and two for Kβ_1,3. Assuming a negligible chemical shift of Kα₁, 6404.01(1) eV⁴⁷, and Kα₂, 6391.03(1) eV⁴⁷, the Kβ_1,3 line energy is determined to be 7059.4(10) eV. The experimental uncertainty consists of the uncertainty caused by the polar integration of the CCD images (0.5 eV) and the non-linear least square fitting procedure (0.5 eV). The two contributions are summed up leading to a more conservative uncertainty estimation as compared to the square root of the quadratic sum as explained in detail in Ref.⁴⁹ for the used von Hamos spectrometer setup. Relative line intensities of Kα and Kβ are influenced by the experimental setting and are not corrected in the displayed spectrum. Indeed, the resolving power varies throughout the covered energy range as a function of the Bragg angle and the distance between the CCD position and the respective focus position for each emission energy⁴⁹. The exposure time was 40 seconds.

The Fe Kβ emission spectra of FeS and FeS₂ are displayed in Figure 2 (a). The spectra are normalized to their respective area and fitted with an asymmetric Pseudo-Voigt function⁵⁰. A shift of the Kβ_1,3 line to higher photon energies (1.7(5) eV) and a Kβ′ satellite on the low-energy side (E_Kβ1,3 – $\left(E_{K{\beta }_{1,3}}-E_{K\beta \text{'}}=12\left(1\right)eV\right)$ for FeS as compared to FeS₂ is recorded. The respective uncertainties of the energy shifts are estimated as described in Wansleben et al⁴⁹. The Kβ′ satellite is caused by the final state exchange interaction between the 3p hole and 3d valence states allowing for conclusions on the spin state (e.g. number of unpaired electrons)⁵¹: A pronounced Kβ′ satellite yields a high-spin state (HS), a less pronounced satellite, as in the case of FeS₂, yields a low-spin state (LS) in the valence band^6,52,53. This observation has already been made and discussed in detail by Rueff et al.⁵⁴ with the focus on pressure induced spin sensitivity of the Kβ′ satellite in FeS. They report on a splitting between Kβ′ and Kβ_1,3 of 12.5 eV which confirms our result of 12(1) eV.

Figure 2.

(a) Fe Kβ_1,3 and Kβ′ lines and (b) the magnified vtc-XES of FeS₂ (black) and FeS (red). The spectra in (a) are each fitted with two Pseudo-Voigt functions⁵⁰. The intensity of the residual in the energy range of the maximum of the spectra is in the order of 2% with respect to the data. The extracted data in (b) is shifted for better visibility. The exposure time was 2h 26min.

The fit of the Kβ_1,3 lines allows to extract the vtc-XES around the Kβ_2,5 line from the Kβ_1,3 high-energy tail as described for example by Gallo et al.¹⁰. The result is depicted in figure 2 (b). Two structures labeled as Kβ_2,5 and Kβ″ are revealed. The Kβ_2,5 feature is generally not assigned to one specific transition from one state to the core hole but a mixture of valence states. It also involves the quadrupole 3d-1s transition⁵⁵. More recent calculations regarding binary zinc compounds indicate that a major contribution to the Kβ_2,5 line originates from 4p metal states⁸. The energy shift of the Kβ_2,5 line has been proven to shift with oxidation state due to screening mechanisms that depend on the valence electron density on the metal ion, i.e., the smaller the oxidation state the more the Kβ_2,5 is shifted to lower energies⁴. In the present two sample systems Fe is in the same oxidation state. Although the position of the Kβ_1,3 line in the case of FeS shifts roughly by 1.7(5) eV due to exchange interaction, the Kβ_2,5 line has the same emission energy (7108(1) eV) for both FeS and FeS₂. The Kβ″ feature is associated with cross-over transitions from ligand orbitals and, thus, is only observed with a ligand atom present^8,9. In the case of sulfur these ligand orbitals correspond to 3s and 3p orbitals.

Figure 3 (a) displays the extracted experimental and calculated ocean vtc-XES spectra of FeS and FeS₂. Differences are mainly seen in the amplitude of the Kβ_2,5. The Kβ″ peak is also more pronounced in the case of FeS₂. The experimental data suggests in general an asymmetric structure towards the low-energy side which is not satisfactorily resolved. The asymmetry, however, indicates an ensemble of peaks. Below the experimental data, the theoretical spectra are plotted. They are both equally shifted in energy (energy offset of 7097 eV) and scaled in intensity to align with the experiment. In order to compare experiment and theory figures 3 (b) and (c) display the respective spectra for FeS and FeS₂ and a convolution of the calculated spectra with the experimental resolution achieving good agreement. The respective contributions of quadrupole transitions are included in the plots and are found to be minor. In the case of FeS₂ the results confirm calculations by Antonov et al.⁵⁶. The minor contribution of the quadrupole transitions leads to the conclusion that the observed vtc-XES features originate mostly from dipole-allowed transitions between valence states with p character and the 1s vacancy.

Figure 3.

Experimental and calculated ocean Fe valence-to-core spectra of FeS₂ and FeS. The experimental data is normalized to the total intensity of the Kβ emission. The theoretical results (solid line) are shifted in energy, scaled in intensity to align with the experiment and include dipole (dip.) and quadrupole (quad.) transitions. For better comparison the theoretical results in (b) and (c) are additionally convolved with the expected spectrometer response (dashed line) which is estimated with a Lorentzian of 9 eV FWHM.

5.2. X-ray absorption spectroscopy

In order to validate the capabilities of the ocean package, we extended the comparison of experiment and theory to the Fe K NEXAFS of the two samples. NEXAFS complements XES, probing the unoccupied electronic states. The results are displayed in Figure 4 where the normalized absorption coefficient is plotted as a function of incident photon energy. Experimental NEXAFS studies that explain the spectra in more detail can be found elsewhere^57–59. Distinct differences between the two compounds are observed in the three spectral regions labeled A, B, and C. While the pre-edge feature A of FeS is more pronounced and slightly shifted to lower energy, FeS₂ shows an additional features C at an incident photon energy of about 7.14 keV. The FeS spectrum appears to have more broadening than the FeS₂, as evidenced by the shallower slope from A up to B. The calculated absorption spectra are also plotted in Figure 4, displaced vertically above the measured data. The measured spectra inherently reflect the effects of several sources of broadening that are not included in the ab inito calculations. The core-hole lifetime and the finite energy resolution of the incident X-ray radiation provide energy-independent broadening, while the photo-electron lifetime and vibrational disorder contribute an energy-dependent broadening. Therefore, the theoretical results have been artificially broadened to better match the experimental data. A Gaussian broadening was applied with a width dependent on the incident photon energy. Starting at threshold the broadening was gradually increased from 0.5 eV FWHM up to a maximum of 8.0 eV FWHM, a choice which was empirically guided to best match the experimental data.

Figure 4.

Experimental (bottom) and calculated ocean (top) Fe K NEXAFS of FeS₂ and FeS. The integration time for each photon energy was 5 seconds. The experimental data is fitted using a sum of a step function and four Gaussians which allowed reproducing the experimental data quite well as highlighted by the respective residuals. The theoretical spectra are convolved with an energy-dependent Gaussian broadening (see text) and shifted vertically for clarity. Note that the used energy offset is the same as was used for the XES calculations.

The calculated spectra adequately capture the qualitative differences in the NEXAFS features between the FeS and FeS₂. The positions of the vtc-XES and NEXAFS features are captured well using only a single energy offset common to both materials. This demonstrates that ocean calculations give reliable excitation energies across compounds given a single calibration spectrum. Peak B, arising from 1s → 4p transitions, shows a more pronounced structure in the calculated spectra of both compounds. The pre-edge feature A is a combination of quadrupole 1s → 3d transitions as well as dipole-allowed transitions into Fe 3d orbitals hybridized with the neighboring sulfur 3p orbitals. For FeS₂, peak A appears stronger in the measured spectrum. Some of this apparent relative strength may be due to the width of peak B. For K edges, both the strength and broadening of the pre-edge and main-edge features are sensitive to disorder from thermal and zero-point vibrations^60,61. Better quantitative agreement with experiment would likely require calculations that better incorporate the effects of disorder.

6. Conclusion

In summary, we have studied the Fe K X-ray emission and absorption spectra of FeS and FeS₂. Despite the moderate resolving power (E/ΔE = 800) of the full-cylinder von Hamos spectrometer we demonstrate that the analysis of the chemically sensitive Fe Kβ emission spectrum is still feasible. The large spectrometer band width of over 700 eV of the spectrometer enables to derive an energy scale insensitive to sample positioning by referencing the chemically less sensitive Fe Kα emission to literature values.

The occurrence of a strong Kβ′ satellite line in the case of FeS reveals a high valence spin state and agrees well with previously published results. The vtc-XES are extracted from the Kβ_1,3 high-energy tail and are found to be in good agreement with ab initio calculations using the ocean software package. To validate the calculations, we used the same set of input parameters and energy offset to calculate Fe K NEXAFS spectra of the two samples and compared the results to experiment. Here, the onset of the pre-edge peak and respective resonances in the absorption coefficient match satisfactorily in energy. However, an artificial broadening had to be added to the calculated spectra. In future work, this ad hoc broadening might be replaced with explicit calculations. In conclusion, this manuscript showed that the ocean software package is well suited for calculating XES and XAS for first row 3d transition metals. Thus, it can be used to support and validate experimental results achieved with only moderate resolving power. Using the same approach as we demonstrated for iron sulphides, the combination of XES experiments and OCEAN calculations allows investigating the electronic structure of different transition metal sulphides for speciation purposes with sufficiently high discrimination capabilities.

7. Appendix

Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.