X-ray absorption fine structure spectroscopy

The experimental setup for the laboratory XAFS spectroscopy is based on the Highly Annealed Pyrolytic Graphite (HAPG) von Hámos spectrometer with the use of a cylindrically shaped crystal for combining high spectral resolving power with a high solid angle of detection [4,50].

As detector unit the pixelated X-ray hybrid-CMOS detector Dectris EIGER2 R 500k was used. The area of detection is 77.3 mm x 38.6 mm with a pixel size of 75 µm x 75 µm. The X-ray source was a water-cooled micro focus X-ray tube with molybdenum as anode material, a power of 30 Watt optimized at 15 kV and a spot size of 70 µm.

For the setup specifics and more details on the used components, we refer to the mentioned publications [4,50].

Two common solid sample preparation techniques were considered and used in this study. In case of the pure reference substances iron(III) oxide (α-Fe₂O₃) and iron(II, III) oxide (Fe₃O₄) as well as the Mexican iron ore samples were applied on adhesive tape. To do so, the sample was applied via horsehair brush in between two tape layers. Afterwards the tape was sliced and pre-analyzed via X-ray fluorescence (XRF) to estimate the mass deposition Q of iron on each slice and also to ensure the mandatory homogeneity. The latter aspect is particularly crucial for quantitative evaluation of lab-XAFS spectra (the analyzed sample area is wide due to the large beam of the applied X-ray sources, thus, X-ray tubes in lab-based spectrometers). An adequate sample thickness for the absorption measurement is then achieved by stacking the required amount of sample slices to reach an edge jump of about µQ = 1. That can result in stacking up to 20–40 slices, depending on the properties of the powder material. In contrast, the α-Fe₂O₃/Fe₃O₄ model mixtures were prepared both via the adhesive tape and the wax pellet method. For the pellet preparation sample powder was mixed with a binder (in this case Hoechst Wax C©). The ratio of sample material and wax for pure iron oxide powder is about 1:6. The ratio was optimized to achieve a stable pellet and to avoid unnecessary absorption by the binder. Therefore, the ratio varies for different elements, different analyte concentration in the sample and for materials with different particle/preparation properties. The wax and sample materials were mixed in a plastic bottle in a vortex shaker with the addition of two inert glass (SiO₂) balls of 5 mm diameter. The obtained sample-wax mixtures were then pressed into pellets by use of a hydraulic press. Finally, these pellets were embedded between adhesive tape stripes. The main reason for preparing the samples as wax pellets in addition to applying the material on adhesive tape was that the two phases of the mixtures might have different properties on adhesive tape and would, therefore, result in different fraction after preparation. When adding and mixing with wax in a vortex mixer and pressing the material in a pellet this application properties should have no effect. For the Mexican iron ore, although it was also a phase mixture, the deposition behavior should not differ between the two phases. The raw material was grinded with a ball mill (see below) and, thus, the Fe-oxide phases should have very similar particle sizes, the mixture should be very homogeneous and the described preparation via the adhesive tape method was assumed as suitable.

The absorption spectrum was acquired by measuring with and without the sample and an in-house data processing of the 2D-images [4]. The measurements were performed at room temperature with a measurement time of 10 h for each sample/reference prepared on adhesive tape and 2.5 h for each sample/reference prepared as wax pellet in order to achieve best possible signal-to noise ratio. The energy axis of the spectra was calibrated by comparing an α-Fe foil or powder reference measurement (performed before every sample measurement) with an α-Fe foil synchrotron radiation measurement. Deviation in the energy axis could still exist but an absolute energy axis is not required in this work since the deviation will be the same for sample and reference spectra. Spectra normalization was performed using ATHENA of the Demeter software package [51] and, in case of the iron ore sample, additionally the software package Larch [52]. The linear combination fitting (LCF) for the quantitative evaluations was performed in form of different approaches using ATHENA [51], the software package Larch [52] or an in-house algorithm [4]. These packages were used based on the fact that ATHENA, due to its user-friendly graphical interface, is frequently used for XAFS analysis. However, it is no longer supported. In contrast, Larch is continuously developed and can also be used as a Python package. The in-house algorithm first applied in [4] was utilized due to its superior transparency and flexibility compared to the other two open-source software options. In all cases, the results obtained by LCF, which relate to the ratio r_i of the bound iron in each species, were converted to weight percentages of the species for comparability with the other two methods by formula (S1) (see S1 File). The details of the normalization and LCF procedures are presented as part of the results section.

X-ray diffraction

For the X-ray diffraction measurements of the α-Fe₂O₃/Fe₃O₄ model mixtures (as well as measurements of the pure reference substances α-Fe₂O₃ and Fe₃O₄) a Panalytical X’Pert PRO diffractometer with a Bragg-Brentano setup was used. The diffractometer operates with a Cu anode and without a monochromator (Cu Kα radiation) at 40 kV and 30 mA. At room temperature the diffraction data were obtained over a measurement range of 10–120° 2θ. For all three model mixtures the measurement time was 92 min (for the measurements of the pure reference substances 30 min). Samples were applied flat on a cut-off Si wafer attached to the sample holder. The quantitative XRD evaluation was performed using the standardless method of Rietveld refinement [53], since it is one of the most frequently XRD quantification techniques [25]. The Rietveld refinement was done with Fullprof [53,54].

For the examinations of the Mexican iron ore a different X-ray diffractometer was used. It is well known from the literature that the application of standard configurated diffractometers, hence, the application of copper radiation (Cu Kα), in the analyses of iron containing samples yield to limited diffractogram quality. The reasons for this are a reduced diffracted beam intensity (X-ray absorption, respectively inelastic scattering) as well as an increased background (X-ray fluorescence) [55]. This can impede and distort the phase identification, differentiation and quantification especially in cases of iron oxides/ hydroxides with very similar crystal structures (Fe₃O₄, γ-Fe₂O₃) or, in general, more complex multi-phase mixtures of iron oxides/ hydroxides as it can occur for example in geological samples. To overcome these issues the use of monochromators (e.g., a graphite monochromator as it was used in the pre-characterizations of the sample system in this study, see below and SI) or, ideally, a better suitable radiation source is required [55]. Especially cobalt radiation (Co Kα) is an ideal and common choice for examinations of such iron containing samples [55]. Therefore, to get optimal results the X-ray diffraction measurement of the Mexican iron ore sample has been performed with the Benchtop XRD diffractometer Bruker D2Phaser with a Cobalt X-ray source and a SSD160 detector (active length = 12 mm). The measurements were performed at room temperature in the measurement range 10°- 90° 2θ with 0.014° step size and 4.8 s/step, resulting in a total measurement time of 8 h. During the measurement the sample was rotated with 10 rpm. The sample was filled in PMMA-holders (Ø 2.5 mm) using the top-loading technique. The analysis was carried out using a 1-mm fixed divergence slit, a 2.5° primary and a 4° secondary soller collimator, a fixed knife edge (3 mm above the sample surface), and an Fe K_β filter (2.5). Qualitative phase analysis was conducted using DIFFRAC.EVA V5.2 (Bruker) and the Crystallography Open Database [56]. Quantitative estimations via Rietveld refinement [53] were carried out using two different evaluation programs. The reason for this was to consider both, a common commercial as well as a common non-commercial software, and to compare the results. Therefore, the Bruker software Topas V6 as well as the open-source and platform-independent software Profex 4.2.4/BGMN were applied [57–59].

Mössbauer spectroscopy

Mössbauer spectroscopy was performed at a MIMOS II type spectrometer set-up with a ⁵⁷Co source (in rhodium matrix) and Si-PIN detector [39,60]. In contrast to the backscattering-operated MIMOS II applied for the Martian surface analyses, the set-up used in this study can be operated either in backscattering or transmission mode. For the analyses the ⁵⁷Fe-γ-line E = 14.4 keV was used and α-iron (α-Fe foil) was applied for the velocity/ energy calibration before the samples were analyzed. The samples were prepared in Mössbauer plastic powder sample holders consisting of an outer and an inner part which fit smoothly but tightly into each other. Thus, small amounts of the sample powders were placed in the outer parts in that way that a thin and even powder layer was obtained. Afterwards, to cap and to fixate the sample, the inner part was placed into the sample containing outer part. This was performed by gently rotating the inner part during the insertion into the outer part. This combination of careful pushing and rotating yielded to relatively thin, even and fixed sample layers. After a visual check for the mandatory absence of holes or gaps in the powder layers, the finished processed sample holders were sealed with Parafilm around the edges to ensure the tight fit of the sample holder parts, the fixation of the sample layers as well as a further reduction of air contact of the samples. The prepared samples were measured in transmission mode at room temperature. For all samples the measured velocity range was v = –10 mm/s - 10 mm/s (acceleration, synchronized with a 512 velocity channels multichannel analyzer, by Mössbauer drive in triangle-mode). The measurement time varied between 10 h and 120 h depending on the sample. In detail the measurement times were: α-Fe₂O₃ reference 24 h, Fe₃O₄ reference 72 h, α-Fe₂O₃-Fe₃O₄ model mixture 30/70 24 h, α-Fe₂O₃-Fe₃O₄ model mixture 50/50 120 h, α-Fe₂O₃-Fe₃O₄ model mixture 70/30 72 h and Mexican iron ore 10 h. The obtained spectra were mainly evaluated in two steps. In a first step the raw spectra were folded (software: Fold it!, Johannes Gutenberg Universität Mainz, Germany). Usually, this folding process is basically a “mirroring” of a raw 1024 channel spectrum (which consists of two mirror-imaged spectra of 512 channels each) relative to a center line. Thus, the transmitted gamma radiation intensities recorded in the channels that are symmetrical to this line are simply added or interpolated to get the “folded” 512 channel raw spectrum [61]. However, as it is typical for MIMOS II type spectrometers [61], the spectrometer applied in this study just had 512 velocity channels available. Therefore, 512 channel mirror-imaged raw spectra were transferred into “folded” 256 channel raw spectra. In the second step the fits were done in the form of Lorentzian site analyses (Software: Recoil, Department of Physics, Ottawa, Canada). The Lorentzian multiplet analysis is one of the most common least-squares based (reduced chi-squared ) fitting approaches in Mössbauer spectroscopy to perform a full spectrum analysis and to consider several line shapes (singlets, doublets and also sextets). Basic principles of this approach are the assumption that a measured spectrum consists of accumulated different subspectra as well as the approximations of all line shapes observed in the spectrum in form of Lorentzian lines/ distributions (Cauchy distribution) [62,63]. For the subsequently quantitative evaluations a common approximating approach, described in [32], was used. In this approach the ratio N(A)/N(B) of the amount of iron atoms of two different types A and B is in a simple association only with the observed Mössbauer signal areas A(A) and A(B) as well as the Mössbauer fractions f(A) and f(B). This correlation is described by the formula (S4) (see S1 File). The obtained atom amount ratios were transferred into weight percentages, respectively mass ratios of the species. The details on the quantitative evaluations are presented as part of the results section.

Sample system

As reference substances pure iron(III) oxide (α-Fe₂O₃) from Honeywell and iron(II, III) oxide (Fe₃O₄) from Sigma Aldrich were obtained [64,65]. Both were described as micro particle powders (α-Fe₂O₃: d < 5 µm, Fe₃O₄: d < 5 µm) with a purity of ≥ 99% in case of iron(III) oxide and 95% in case of the iron(II, III) oxide. The reference substance samples analyzed in scope of this study were collected with plastic spatulas from freshly opened containers and were stored in snap-on cap bottles sealed with Parafilm beforehand and in between the examinations. The primarily analyzed sample of this study was an oxidic iron ore from Mexico and was purchased from Mineraliengrosshandel Hausen GmbH (Telfs, Austria). It must be emphasized that this iron ore has been available and obtained under the inaccurate name “Mexican magnetite” and, thus, has been expected to be a (relatively) pure mineral. However, the examinations performed in this study (pre-characterizations as well as the measurements in focus, quantitative XAFS, XRD and Mössbauer spectroscopy) clearly showed that the sample was not a (pure) mineral, but rather a rock because it consisted of more than just magnetite. Hence, in the following, the sample will be referred to by the more accurate name “Mexican iron ore”. The sample was delivered as grey massive polycrystalline pieces, which had sizes of a few centimeters (see SI Fig S1 in S1 File). Hence, some of the sample pieces were crushed with a hammer (wrapped with Parafilm to minimize contaminations) and then milled for 5 min at 650 rpm by the use of a ball mill Pulverisette 6 (Fritsch, Idar-Oberstein, Germany) with zirconium dioxide (zirconium(IV) oxide, ZrO₂) grinding tools. The resulting grey-red powder was utilized in all described further analyses and experiments. The observed powder color was a first indication that the sample was actually a mixture of magnetite and hematite (see microscopic examination, Fig S2c in S1 File). Beforehand and in between the numerous measurements of this study the sample powder was stored in HDPE containers or snap-on cap bottles which were sealed with Parafilm and additionally packed in sample bags to minimize the chance of speciation changes, e.g., by further oxidation due to profound air contact.

The purchased pure substances were characterized in detail before they were used as reference substances or standards in the XAFS spectrometer. To check the particle sizes light microscopy was done, micro X-ray fluorescence analysis (µ-XRF) and a microwave assisted digestion (in aqua regia) followed by inductively coupled plasma optical emission spectroscopy (ICP-OES) were used for elemental analysis and qualitative X-ray powder diffraction (XRD) for speciation. Additional to the initial classical macroscopic mineral determination methods to raw sample pieces (Table S1 in S1 File), the milled iron ore sample was also characterized in the same way as the reference substances. In this section, the characterization results are just presented in the form of a short overview (for more details see [66] and S1 File ).

The observed particle sizes (Fig S2a–c in S1 File) were in case of the iron(III) oxide and iron(II, III) oxide powders in XAFS suitable magnitudes (d < µ^–1 [45]) since, consistent with the manufacturer information, both samples consisted of particles smaller than 5 µm (see boundary µ^–1 particle size at E = 7.14756 keV based on NIST [67]: d(Fe₂O₃) ≈ 6.8 µm, d(Fe₃O₄) ≈ 6.6 µm). In contrast, the prepared iron ore powder mainly contained particles in the range of 10–20 µm. Assuming a composition of iron oxides it is evident that the particle size was slightly above the ideally XAFS suitable magnitude. Thus, slightly limiting effects on the XAFS spectra quality (e.g., suppression of white line features) could not be excluded and had to be considered.

The ICP-OES analyses were done regarding the element contents of iron, aluminum and chromium as well as cobalt and nickel. Based on µ-XRF results (Table S2 in S1 File), manganese and, in case of the iron ore sample, calcium were also considered. Additionally, the ore sample was semi-quantitatively analyzed with regard to possible contents of rare earth elements (REE), because some REEs can interfere with the Fe K-edge in XAFS [45]. The determined iron as well as iron oxide contents of the iron(III) oxide (ω_rel(Fe) = 68.16% ± 1.34%) and iron(II, III) oxide micro particles (ω_rel(Fe) = 68.25% ± 1.37%) were in good accordance to the manufacturer information (Table S3 in S1 File). It has to be pointed out that the iron(II, III) oxide micro particles also contained, inter alia (Table S4 in S1 File), relatively high contents of aluminum (ω_rel(Al) = 2515.7 mg/kg ± 68.5 mg/kg), which could somewhat limit the suitability of these as a reference substance, for instance due to matrix effects, which can have numerous effects on the analytical signal in each method [68]. Nevertheless, in general the purity of both substances was sufficient for the use as a laboratory XAFS reference substance. The measured iron content of the Mexican iron ore (ω_rel(Fe) = 63.05% ± 1.45%) was lower than literature values of pure magnetite or hematite (Table S3 in S1 File) and the contents of aluminum, calcium as well as silicon were relatively high (Table S2 and S4 in S1 File). This observation is explainable by impurities of the magnetite and hematite as well as common accompanying minerals. REEs were not detected.

The qualitative XRD (Fig S3a–c in S1 File) analyses also demonstrated the identity and purity of the reference substances. Especially the fact, that the XRD pattern of the Fe₃O₄ micro particles only showed the desired Fe₃O₄ reflections (Fig S3b in S1 File), confirmed that these particles were also sufficiently pure for the use as a laboratory XAFS reference substance in course of this work. The XRD of the Mexican iron ore finally verified the assumption of a mineral mixture mainly consisting of magnetite and hematite. This paragenesis is explainable by the fact that magnetite can be transferred to iron(III) species (e.g., hematite, maghemite or oxide-hydroxides like goethite and others [limonite]) due to secondary mineral formation processes based on weathering, metamorphism and especially pseudomorph formation (martitization) [69–72].

Furthermore, alpha-iron(III) oxide/ iron(II, III) oxide model mixtures with precisely determined (weigh-in) mass ratios ω_rel(α-Fe₂O₃)/ω_rel(Fe₃O₄) were prepared and also quantitatively analyzed by XAFS, XRD and Mössbauer spectroscopy, beforehand the iron ore examinations. The goal was to get more information on the general accuracy of the Lab-XAFS and the other two methods by considering this, in comparison to the natural iron ore, similar but simpler and more precisely known sample system. Thus, it was appropriate to count the actually achieved weigh-in ratios as true values and, based on ISO 5725–1 [49], the accuracy as closeness (or distance) to these. Hence, the accuracy is in relation to the deviation of the measured values and the true values. As source materials the same iron(III) oxide and iron(II, III) oxide which had already been pre-characterized and used as pure reference materials in this study (see above), were applied. The mixtures were prepared by weigh-in (precision balance Adventurer Pro, σ = 0.0001 g, Ohaus, Greifensee, Switzerland) the pure reference substance powders and mixing them in an agate mortar. In total three different α-Fe₂O₃-Fe₃O₄ mixtures with the nominal mass ratios ω_rel(α-Fe₂O₃)/ω_rel(Fe₃O₄) 30/70, 50/50 and 70/30 were produced (see Table 1 and S5 in in S1 File for the actually achieved ratios). The mixtures were stored in sealed snap-on cap bottles. To compensate possible segregations occurred during the storage and transport, the mixtures were always re-homogenized beforehand the measurement preparations.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Quantitative results for the α-Fe₂O₃/Fe₃O₄ model mixtures of the lab-based methods XAFS, XRD and Mössbauer. The results are presented as mass ratios ω_rel(α-Fe₂O₃)/ω_rel(Fe₃O₄).

https://doi.org/10.1371/journal.pone.0323678.t001

X-ray absorption fine structure spectroscopy

XAFS – Pure reference substances.

The obtained XAFS spectra of the pure substances alpha-iron(III) oxide and iron(II, III) oxide micro particles can be seen in Fig 1a. A qualitative analysis with focus on the XANES area including the pre-edge of these pure potential reference substances was performed. This was essential to verify the quality of the obtained spectra regarding, e.g., the presence of all theoretically expected essential substance specific fine structures as well as if the spectral resolution is high enough to distinguish the different species, before these spectra were used in the quantitative analysis as references. As a result, the qualitative analysis revealed the expected characteristic fine structures of α-Fe₂O₃ and Fe₃O₄ and the differences between them, as it can be seen in Fig 1a and S5 in S1 File between 7110 eV and 7150 eV and Fig 1a between 7225 eV and 7350 eV (though the spectra of both compounds also show distinct similarities in general) due to different structures. All of these aspects were in correlation with the theory of influences of the chemical and structural environment of an absorber atom on the XAFS, as it is described in literature in general [45–48] as well as with regard to iron compounds and the Fe K-edge in particular [73–76]. Thus, as observable in Fig 1a and S5 in S1 File, the edge and the pre-edge of Fe₃O₄ are shifted to slightly lower energies compared to α-Fe₂O₃. This can be explained by the fact that Fe₃O₄ is a mixed-valence compound containing both Fe(II) and Fe(III) (in case of Fe(II) somewhat lower energy for the electron excitations is required) whereas α-Fe₂O₃ just contains Fe(III). Furthermore, the pre-edge of Fe₃O₄ is more intensive than the Fe₂O₃ pre-edge (Fig 1a inlet a.1 and Fig S5 in S1 File), which is in relation to the different crystal structures (Fe₃O₄: inverse spinel-type structure, α-Fe₂O₃: corundum-type structure) [43,71,77–79] and, therefore, to different coordination polyhedra. In case of Fe₃O₄ 2/3 of the iron cations are in an octahedral coordination (Fe(II) and Fe(III)), but the remaining 1/3 of the cations are in a tetrahedral coordination (Fe(III)), whereas in case of the α-Fe₂O₃ all Fe(III) cations are in octahedral sites.[43,71,77,79] Since a tetrahedral coordination enables the more intensive E1 (electric dipole) transitions in the 1s – 3d excitations in addition to the generally less probable, but in case of octahedral coordination solely present E2 (electric quadrupole) transitions in the 1s – 3d excitation, this more intensive pre-edge of Fe₃O₄ is explainable.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. XAFS-spectra of the reference substances

α-Fe₂O₃ and Fe₃O₄, the α-Fe₂O₃/Fe₃O₄ model mixtures and the Mexican iron ore. a unnormalized XAFS-spectra of the sample and the references, with insets of the normalized edge region (a.2) and the pre-peak area (a.1). The complete normalized spectra can be seen in Fig S4a,b (SI). b LCF results performed by the ATHENA software [51] on the normalized spectra with the flatten algorithm of the Mexican iron ore. Fit and data show only minor deviations, indicated by the residual. The LCF results with the Larch software [52] and the in-house algorithm on the unflattened and flattened normalized spectra can be seen in Fig S8 (S1 File ). The LCF results are displayed in Table S7 (S1 File ). c LCF results of the 50/50 α-Fe₂O₃/Fe₃O₄ model mixture (adhesive tape preparation). For each sample/reference the measurements were performed at room temperature with a measurement time of 10 h.

https://doi.org/10.1371/journal.pone.0323678.g001

XAFS – iron ore.

The obtained Mexican iron ore spectrum is shown in comparison to the reference substance spectra in Fig 1a. In accordance to the pre-characterization results, the qualitative analysis of the ore sample revealed a composition of both iron oxides, as the spectrum clearly contained fine structures of both iron compounds and, e.g., edge and pre-edge positions between the two (see Fig 1a and S5 in S1 File).

For further analysis and quantification evaluation by linear combination fitting (LCF) the spectra where normalized using ATHENA of the Demeter software package [51] (see Fig S4a in S1 File) and the software package Larch [52] (see Fig S4b in S1 File). The differences in the normalized spectra result from the flatten algorithm in ATHENA which is set to default. While ATHENA can perform LCF on the flattened and unflattend normalized spectra, Larch can only perform LCF on unflattened XAFS-spectra. In general, normalization is carried out in the following steps: First, the pre-edge region is interpolated using a linear fit (pre-edge line), while the normalization range beyond the edge is interpolated using a polynomial fit (post-edge line). These fits can be manually adjusted by modifying the pre-edge and normalization ranges. The criteria for defining a suitable pre- and post-edge line are subjective. In case of the iron ore sample (and also the model mixtures) examined in this study, the post-edge line was chosen to pass through the middle of the data. A detailed documentation of this process is available in the ATHENA online manual [80]. The next step involves determining the normalization constant µ₀(E₀), analogous to the edge step, by extrapolating the pre- and post-edge lines to E₀ − their intersection point − which defines the edge step parameter. In conventional normalization (without the flattening algorithm), the extrapolated pre-edge line is subtracted from the spectrum, which is then divided by the edge step parameter. In contrast, when using the flattening algorithm, the difference in slope and curvature between the pre- and post-edge lines is subtracted from the data, aligning all oscillations to µQ or y = 1. This approach facilitates data comparison, as conventional normalization can cause spectra to diverge at higher energies.

The normalization procedure is a crucial part for the linear combination fitting. Different normalized spectra can lead to different results. A broad energy range enables a better normalization with a more reliable result. But even if a single person took great care to perform a consistent normalization of sample and reference standards the results could be off relative to each other by 10% [81]. Due to the meridional limitation of the HAPG-crystal of 5 cm the recorded energy range extends only from about 50 eV before the edge to 400 eV behind the edge. This impedes consistent normalization even further, hence, as described above, the points for the post edge line need to be manually adjusted until the line passes through the middle of the oscillations.

The results of the LCF can be seen in Fig 1b and S8 in S1 File. It shows the fit and the data as well as the residual of the Mexican iron ore for four different LCF. LCF has been performed with ATHENA (flattened),[51] Larch (unflattened) [52], and with the in house algorithm [4] on the flattened and unflattened normalized spectra. The four different LCF were performed in the energy range between 7095 eV to 7475 eV. The LCF results and thus the resulting determined compositions are listed in detail in the SI (Table S7 in S1 File). It is clearly visible, that all LCF approximate the data well and have only minor oscillations in the residual, especially in the white line. Table 2 shows the averaged result of the four differently performed LCF. Thus, an overall averaged sample mass ratio composition of about 72% ± 3% hematite (α-Fe₂O₃) and 28% ± 3% magnetite (Fe₃O₄) was determined.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Quantitative results for the Mexican iron ore of the lab-based methods XAFS, XRD and Mössbauer.

https://doi.org/10.1371/journal.pone.0323678.t002

To compare the actual quality of the LCF of the different fitting approaches by open-source and in-house software and reduced have been calculated by the equation (S2 in S1 File) in the SI. By considering the value of the of all fits (Table S7 in S1 File) both in-house LCFs for flattened and unflattened normalized spectra achieved the best fit to approximate the data, even though all applied LCFs overall showed good results.

X-ray diffraction

XRD – iron ore.

The obtained XRD pattern of the Mexican iron ore with the results of the Rietveld refinement by Profex 4.2.4/BGMN for the quantitative determination of the iron species can be seen in Fig 2 (for the refinement with Topas V6 see Fig S14 in S1 File). The quantitative results obtained with both software packages (Topas V6 and Profex 4.2.4) are listed in Table S10 (in S1 File). Applying both programs, the identified crystalline phases were magnetite (Fe₃O₄), hematite (α-Fe₂O₃), (low) quartz (α-SiO₂) and monoclinic zirconium(IV) oxide (ZrO₂). While the α-SiO₂ is of natural origin the ZrO₂ was introduced into the sample through the grinding/milling process using a ZrO₂ grinding tool (see above).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. XRD pattern of the Mexican iron ore with quantitative evaluation by Rietveld refinement with Profex 4.2.4/BGMN.

The results of the Rietveld refinement with Topas V6 (Bruker) can be seen in SI, Fig S14a in S1 File. The quantitative results are listed in Table S10 (in S1 File). The measurement time was 8 h. The measurements were performed at room temperature.

https://doi.org/10.1371/journal.pone.0323678.g002

The statistical parameters R_wp, R_exp and GOF (Goodness of fit also known as χ) for the Rietveld refinement are listed for both software in the Table S10 (in S1 File). The GOF is 2.53 for the Profex software and 2.73 for Topas, suggesting that the used model is reasonable, even though it is no guarantee that the model is correct.[82] Since there is no rule-of-thumb to tell if the model/fit can describe the sample accurate other aspects like the chemical model or the graphical results of data and fit should be considered [82]. The uncertainty of the mineral composition in Table S10 in S1 File is given by 3x e.s.d. according to ASTM E117-13 [83]. It has to be pointed out that this is only a mathematical estimation of the uncertainty. The calculated and the observed pattern have minor deviation, which means that missing a species in the used model cannot be excluded. However, all observed peaks can be explained by the chosen species. If there are any additional phases present, these must be very similar (very similar/ identical peak quantities, positions, and intensities) to those phases which have already been found (e.g., similarity γ-Fe₂O₃ and Fe₃O₄). Additionally, the purities of the identified iron phases must also be taken into account. Since noticeable amounts of aluminum, which could be accommodated in the two iron oxides (isomorphic substitution: Al(III) can Fe(III), see details Mössbauer results) of the iron ore sample, have been detected in scope of the sample pre-characterizations, slight effects on diffraction peak intensities and positions can also contribute to the deviation. However, in total, the XRD results suggest that the used chemical model should be sufficient for the purpose of this work.

Focusing on the XRD quantification of the Fe-phases, a sample composition of 73% ± 1% hematite (α-Fe₂O₃) and 27% ± 1% magnetite (Fe₃O₄) for Topas and 74% ± 1% hematite and 27% ± 1% magnetite for Profex respectively was determined. Because the deviation between the two obtained results is small and both applied fits are of sufficient quality, it is appropriate to use the averaged result of about 74% ± 1% hematite and 27% ± 1% magnetite (Table 2) in addition to the individual Topas- and Profex-based values for the further comparison. Percentages may not sum up to exactly 100% due to rounding.

Mössbauer spectroscopy

Mössbauer spectroscopy – pure reference substances.

Fig 3a,b show the resulting spectra of the reference substances alpha-iron(III) oxide and iron(II, III) oxide micro particles. The determined hyperfine parameters are listed in detail in Table S11 and S12 (S1 File) in comparison to literature.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Mössbauer spectra of the reference substances, the model mixtures and the Mexican iron ore sample.

a α-Fe₂O₃ micro particles (), b Fe₃O₄ micro particles (sextet site 1: A-site, sextet site 2: B-site) (), c Mexican iron ore (). d 50/50 α-Fe₂O₃/Fe₃O₄ model mixture () (see SI Fig. S15 in S1 File for 30/70 and 70/30 ratio). The total spectra fits are marked in red and the individual sextets in blue, green and orange. The measurement time was 24 h for α-Fe₂O₃, 72 h for Fe₃O₄, 10 h for the Mexican iron ore and 120 h for the 50/50 model mixture. The measurements were performed at room temperature.

https://doi.org/10.1371/journal.pone.0323678.g003

The obtained spectra and hyperfine parameters of the two reference iron oxides were in quite good accordance to the chosen representative literature values considering the actual possible ranges in each hyperfine parameter. These ranges are caused by the dependency of the exact values on several sample parameters (e.g., crystallinity, particle sizes, purity) as it is described widely, for example in [31,32,84–87]. In case of the iron(III) oxide micro particle powder (Fig 3a) a single sextet was found which had hyperfine parameters in the typical range of octahedral coordinated Fe(III) in high-spin state [31,32]. In the iron(II, III) oxide micro particle´s case (Fig 3b) the two different sextets expected for the inverse spinel-type structure (Fe₃O₄: Fe(III)[T]Fe(II)[O]Fe(III)[O] O₄, Fe(III)AFe(II, III)₂B O₄, resp.) were observed. The one for the tetrahedral high-spin Fe(III) (A-site) [32,88] and the second with a slightly broadened linewidth for high-spin Fe(II) and Fe(III) in the octahedral sites (B-site) (at room temperature Fe(II) and Fe(III) in these sites cannot be easily distinguished by Mössbauer spectroscopy because of a fast electron transfer between these iron cations) [32,43,88]. However, the expected ideal sextet area ratio A(B-site)/A(A-site) of 2:1 or, more practical (considering the A- and B-site´s different Mössbauer-Lamb factors/ Mössbauer fractions f), 1.8:1 [32,43] was not obtained. This is clearly visible at the obtained reversed absorption maxima ratios of the outer A-site sextet and the inner B-site sextet (Fig 3b, Table S11 in S1 File). In detail an area ratio of about 1:1 (≠ 1.8:1) was determined from the results (SI, Table S11 in S1 File). But as it is described in [32] this area ratio often differs in practical measurements from the ideal amount due to sample deviations from an ideal Fe₃O₄, or in case of mineral or rock samples deviations from an ideal magnetite. In general, these divergences can be caused by two effects.

Mainly, the sample deviations can be caused by partial Fe(II) oxidation (simplified a partial transition into γ-Fe₂O₃, in detail the formation of an oxidized, non-stoichiometric magnetite phase Fe_3–xO₄) [32]. Therefore, the absorption of the B-site decreases and a third sextet, which is very close to and in some cases difficult to distinguish from the pure Fe₃O₄ A-site sextet, appears. This overlay can cause an apparent increase of the A-site intensity and area. Altogether one will get a spectrum still consisting of two sextets (Fe(III) and Fe(II, III)), but with areas deviating from pure Fe₃O₄. Similar observations can also be found in [89], where a successful distinction between the A-site and the mentioned third sextet is used to quantify the amount of the γ-Fe₂O₃ phase in Fe₃O₄ nano particles. Overall the obtained lower ratio A(B-site)/A(A-site) could indicate that the iron(II, III) oxide micro particles contained amounts of oxidized phases. Even though it was paid attention to prevent the Fe₃O₄ sample from significant oxidation (sample taken from a freshly opened container, storage in sealed bottles etc.) during this study, the presence of such an oxidized phase cannot completely be excluded. Firstly, there was still a certain air contact because the sample storage and also the preparation were not performed under inert gas atmosphere. To perfect the oxidation prevention procedures, operations under nitrogen or argon atmosphere would be required. Secondly, oxidation processes could have also already occurred during the production and filling processes by the manufacturer.

However, the sextet area deviations can also be caused by contents of aluminum and/ or titanium (or others). Al(III) or Ti(IV) can partially substitute the iron(III) due to similar ionic radii and charges, thus, similar charge densities (isomorphic substitution) and form aluminomagnetites (Fe_3–xAl_xO₄) or titanomagnetites (solid solution system Fe₃O₄/Fe₂TiO₄, thus, Fe_3–xTi_xO₄) which is also reflected in altered sextet area ratios [32,71,90]. Considering the pre-characterizations of the Fe₃O₄ micro particles, which revealed a high aluminum content of about 2500 mg/kg (0.25 wt.%), it can be assumed with confidence that the observed sextet area ratio deviation additionally traces back to this second effect.

Discussion of quantitative results

For the analysis of the α-Fe₂O₃/Fe₃O₄ model mixtures (Table 1) the lab-XAFS LCF results of the adhesive tape prepared samples deviate 6.4 p.p., 6.6 p.p. and 4.9 p.p. for the target ratios of ω_rel(α-Fe₂O₃)/ ω_rel(Fe₃O₄) 30/70, 50/50 and 70/30 respectively. In comparison to the outcomes obtained by XRD, which are of distinctively high accuracy, thus, small bias (0.2 p.p., 0.2 p.p. and 2.6 p.p.) and show no significant differences to the true values (the achieved weigh-in ratios) especially when also considering the determined uncertainties, these deviations are slightly larger. However, in relation to the Mössbauer spectroscopic results, which differ 6.8 p.p., 4.1 p.p. and 4.5 p.p. for the weigh-in ratios 30/70, 50/50 and 70/30 respectively, the lab-XAFS results bias are of a very similar magnitude or range Δ < 7.0 p.p., in detail: 4.0 p.p. < Δ < 7.0 p.p.. Therefore, the lab-XAFS LCF quantification of adhesive tape prepared α-Fe₂O₃/Fe₃O₄ samples can considerably compete with Mössbauer spectroscopy, particularly when taking the obtained error values into account. Even so it must also be mentioned that there is a systematic difference between the lab-XAFS and Mössbauer results and accuracies. The lab-XAFS results deviations reflect in experimentally determined lower α-Fe₂O₃ and higher Fe₃O₄ portions whereas the opposite is the case with the Mössbauer (see Table 1, e.g., ω_rel(α-Fe₂O₃)/ω_rel(Fe₃O₄) 70/30 ◊ lab-XAFS: 65.6 wt.% α-Fe₂O₃/ 43.4 wt.% Fe₃O₄, Mössbauer: 75.0 wt.% α-Fe₂O₃/ 25.0 wt.% Fe₃O₄).

In contrast to the adhesive tape prepared samples, the lab-XAFS LCF results of the α-Fe₂O₃/Fe₃O₄ model mixtures prepared via the wax pellet technique show smaller deviations of 1.2 p.p. and 2.4 p.p. for the 30/70 and 50/50 target ratios, but a clearly larger bias of 16.5 p.p. for the 70/30 ratio. Thus, regarding the 30/70 and 50/50 mixtures, the lab-XAFS accuracy for the wax pellet samples is higher than for the adhesive tape samples (and also for the Mössbauer spectroscopic measurements), comes close to the XRD magnitude and can clearly compete with Mössbauer spectroscopy and also the XRD. However, regarding to the 70/30 mixture the accuracy is extraordinarily low. One reason for that discrepancy could be slight inhomogeneity in the XANES area, especially the region around the white line. This is explainable by observed inhomogeneity in the prepared sample, thus, a systematic error in the sample-wax pellet preparation. The normalization procedure for this sample was more challenging than for the other mixtures and the reference spectra. Slight changes in the parameter for the post edge line during the normalization process can have significant influence on the height of the oscillations, e.g., the white line and would result in different results of the LCF. When changing the energy range for the LCF, so that the white line area is not included in the fit, the quantitative result agrees much more with the weigh-in ratios with deviation ≤ 10 p.p. Nevertheless, in Table 1, which summarizes the results, just the mass ratios determined with the LCF over the entire energy range are included, as this setting was also used for the analysis of the Mexican iron ore. In addition to that, the quantitative results by the XRD Rietveld refinement have the highest bias as well for the 70/30 mixtures in comparison with the weight in fraction. The deviation with 2.6 pp is over 10 times higher compared to the bias of only 0.2 p.p. for the 30/70 and 50/50 mixtures. In total, the comparison of the results for the α-Fe₂O₃/Fe₃O₄ model mixture wax pellets and the mixtures prepared on adhesive tape also demonstrate, that XAFS results can be affected by the applied sample preparation technique. Thus, depending on the characteristics of the sample system, different preparation techniques can yield to different accuracies. Reasons for this are for instance the challenges in preparing sufficiently homogenous samples. Since in lab-XAFS spectroscopy the applied X-ray beam covers a sample area which is larger compared to synchrotron-based XAFS, a sufficient homogeneity all across this analyzed area is crucial, especially when quantitative examinations are intended.

Finally, when assessing the accuracy examinations, it must be underlined that the results presented in this study should be viewed as trends. Further examinations with an increased number of samples in context of replicate/ multiple/ parallel determinations (in scope of this study the feasible number of samples was limited, see Table 1 legend) are required to optimize the statistics and to be able to evaluate the accuracy results differentiated into trueness and precision (see ISO 5725-1 [49]). Therefore, a more detailed investigation into the different contributions of systematic (trueness) and random errors (precision) to the particular accuracy of the three species analysis techniques would be feasible. Additionally, also examinations regarding the detections limits (LODs) should be performed because the presented investigations focused on mixtures with both components in concentrations of main component ranges only.

Since the Mexican iron ore was prepared with the adhesive tape method and the statistical uncertainty for the measurement of the XAFS spectra is comparable, in terms of accuracy, it could be assumed, that the bias for this analysis is below 7 p.p. accordingly. Analogously, bias below 3 p.p. for the XRD and 7 p.p. for the Mössbauer analyses could be expected. With regard to the XRD measurements it must be highlighted again, that the model mixtures were just examined with a standard configurated machine using non-ideal Cu Kα radiation. Since the more iron-compound suitable Co Kα radiation was applied for the iron ore measurements, an even higher accuracy could be expected. Nevertheless, because the natural iron ore sample has a more complex composition, interferences (depending on the respective method) as well as different and more pronounced matrix effects on the analytical signals can limit these assumptions to certain extent. Furthermore, other specific sample characteristics can be additional restraints and increase the bias, thus, lowering/ limiting the expected accuracies: Particle sizes can significantly influence XAFS spectra, XRDs and also Mössbauer spectra. For example, the pre-characterization results of the iron ore revealed a particle size slightly exceeding the ideal limit for the XAFS measurements, whereas the particle sizes of the reference substances (and, hence, also the model mixtures) were in the ideal magnitude. Phase impurities, e.g., in the form of isomorphic substitution (in the case of the iron ore sample of this study: Fe(III) partially substituted by Al(III)) are known for their effects on XRD as well as Mössbauer spectra. However, slight phase impurities (Al(III)) magnitudes similar to the iron ore were also the case with the Fe₃O₄ reference substance and, as the obtained accuracies demonstrate, did not affect the quantitative results for the model mixtures on a larger scale. Specific for XRD, the presence of amorphous phases must also be mentioned.

In case of the lab-XAFS analysis the results presented in Table 2 showing the averaged LCF results of the Mexican iron ore composition (72 wt.% ± 3 wt.% α-Fe₂O₃: 28 wt.% ± 3 wt.% Fe₃O₄) are in good agreement with the averaged quantitative XRD results (74 wt.% ± 1 wt.% α-Fe₂O₃: 27 wt.% ± 1 wt.% Fe₃O₄) because the deviation, especially when also considering the uncertainty of the XAFS results, of Δ ≈ 2 p.p. is very small. This is also the case, when comparing the individual, but as already mentioned very similar Profex- and Topas-based XRD results (Table S10 in S1 File) to the averaged XAFS outcomes. When just considering the values obtained by Topas the deviation gets even smaller (Δ ≈ 1.0 p.p.). Nevertheless, it has also to be mentioned that the deviations partially increase, when also collating the four individual XAFS results (Table S7 in S1 File) and the (averaged or individual) XRD values. Thus, the largest deviation is obtained in the comparison of the XAFS LCF method “in-house algorithm unflattened normalized” and the Profex-based XRD result. But all in all, even in this case the deviation of Δ ≈ 4.8 p.p. is relatively small and the general magnitude of all obtained lab-XAFS and XRD weight percent results of about 70% hematite and 30% magnetite is still obvious. This is especially valid when also considering the higher uncertainty of the XAFS result obtained by LCF method “in-house algorithm unflattened normalized” (Table S7 in S1 File). This deviation is still below the estimated bias 7 p.p. by measuring the synthetic α-Fe₂O₃, Fe₃O₄ and mixtures of both which was described above. However, these slightly varying XAFS results also demonstrate that the quantification results of the lab-XAFS spectroscopy (and also XAFS spectroscopy in general) can be distinctly affected by the chosen evaluation procedure, thus the specific LCF method/ algorithm, not even taken into account differences induced by the pre-processing, e.g., normalization procedure. Nevertheless, such differences can also occur within Rietveld-based XRD quantifications since small distinctions in the applied Rietveld procedure and its parameters impact the results. Regarding to Mössbauer quantifications such effects must be considered as well. In this case as well, fitting procedures of obtained raw data are the crucial fundament/ requirement for both, qualitative and the subsequential quantitative evaluation. However, the folding procedure (performed beforehand the fitting) is an additional potentially affecting step in Mössbauer spectroscopy.

The composition of the Mexican iron ore determined by Mössbauer spectroscopy (57 wt.% ± 1 wt.% α-Fe₂O₃: 43 wt.% ± 2 wt.% Fe₃O₄) differs clearly from the lab-XAFS and also the XRD values (Mössbauer deviation from XRD Δ ≈ 17.0 p.p.). The conclusion of a higher mass proportion of hematite in the mineral sample is in accordance with the lab-XAFS LCF and XRD Rietveld results in this respect. However, even though considering the quoted uncertainty of the Mössbauer quantification results, the particular mass ratio is significantly different.

General differences of the three techniques

The reasons for this difference are diverse. One general aspect which is a limiting factor of the Mössbauer results in this study, both, for the model mixtures as well as the iron ore, is the resolving power. The applied MIMOS II type spectrometer set-up had just 512 velocity channels and thus folded spectra of 256 data points were used for the evaluations (the fitting procedures and the subsequent qualitative and quantitative analyses). This yields to a spectral resolution which is somewhat reduced compared to Mössbauer spectrometers with 1024 velocity channels (folded spectra of 512 data points) available (see, e.g., the spectra presented in [61], but there, backscattering mode was used which also affects the resolution). Thus, even with an ideal fit, the informative value can be slightly more limited. However, four more aspects, which lead to significantly higher uncertainties of the Mössbauer results particularly for the iron ore sample (but also for the model mixtures) than the stated calculated errors when considering them, are especially important and may be particularly significant. Firstly, an obtained reduced chi-squared (Fig 3c) is an indication of a lower fit quality in comparison to the model mixture spectra. For the mixtures distinctively smaller values in the range of about 1.4 to 3.8 (see Fig 3d and S15 in S1 File) were achieved. One sources of this issue can be the chosen analysis/ fitting approach. The applied Lorentzian site analysis requires, e.g., very (infinitely) thin samples since thickness effects can yield to line shapes showing larger deviations from Lorentzian line shapes [62,63]. Thus, it is possible that the line shapes of the measured iron ore Mössbauer spectrum differ more from Lorentzian distributions and alternative fitting approaches (for example Voigt-based fitting analyses) might be an option. A second potential source can be that the iron ore Mössbauer spectrum cannot be completely described by just three subspectra (one for the hematite part and two for the magnetite). If more subspectra are required for an improved fit, this would indicate the presence of additional iron-containing phases in the ore sample. This source might be the major one in the case of the iron ore sample because distinct indications of contents of a third iron species have even been observed in the fitted spectrum as it is. Additionally, the signal-to-noise ratio can also be considered since it cannot be excluded that there are even more iron phases (with very low concentrations) which signals were not separated from the background but affect the reduced chi-squared. However, despite the rule of thumb that higher reduced chi-squared values () indicate poorer fit qualities, the significance of this value should not be overestimated in Mössbauer spectroscopy. Even fits with poorer reduced chi-squared can conform to appropriate fits and describe the sample correctly (for a details see, e.g., [95]).This can also be seen in this study when considering the measured spectrum of the pure iron(III) oxide reference substance (, but the fit is obviously acceptable). Secondly, the fundamental formula used for the quantification in this study is already an approximation. In this approach several simplified assumptions had been done, for example the widths at half maximum of the absorption peaks were set equal and thickness effects were not considered. Thirdly, just averaged literature values of the required Mössbauer fractions f were used in this approximation formula. It has to be claimed that these f values can vary greatly due to temperature dependence as well as slightly different sample properties (impurities, particle sizes etc.). Therefore, beforehand the quantification, a complex direct or indirect experimental determination of the recoilless fractions f is important if more accurate results shall be obtained [32,35]. However, both, the application of the approximative quantification formula and also the usage of averaged literature based f values was also the case with the quantitative Mössbauer examinations of the α-Fe₂O₃/Fe₃O₄ mixtures. Although for the mixture results the mentioned two aspects are definitely also limiting effects which explain the lower accuracies compared to XRD, the procedure still yielded to relatively good accuracies (see above and Table 1). That proves the general applicability of this approach, but despite this, thickness effects and larger deviations of the actual f values from applied averaged literature values could have had a stronger effect in case of the natural iron ore sample. The fourth aspect is the observed presence of another iron species (oxidized magnetite phase) in the ore sample, which overlay parts of the magnetite signal and could not be separated from it in the Mössbauer-fitting procedure in the form of a fourth sextet in course of this study. Therefore, just the measuring data of one of the two magnetite sextets could be utilized in the quantitative Mössbauer evaluation and determination of Fe₃O₄. Nevertheless, the same quantification procedure was also applied for the α-Fe₂O₃/Fe₃O₄ mixtures. In this case, it did not result in distinctively decreased accuracies, but it must also be considered that the level of Fe₃O₄ oxidation was certainly smaller than the oxidation grade of the iron ore sample. On the other hand, it must also be highlighted that this issue of an interfering third iron species simultaneously proves the pronounced sensitivity and large capacity of Mössbauer spectroscopy regarding to iron speciation. Neither the lab-XAFS nor the XRD analyses of this study revealed an additional iron containing phase on their own. Even though, a real consideration of this third iron compound could not be achieved during the Mössbauer measurement and fitting, at least a mathematical approximation/ estimation was attempted. Based on the known practical ideal Fe₃O₄ area ratio A(B-site)/A(A-site) = 1.8:1 the contribution of the oxidized magnetite phase Fe_3–xO₄ to the obtained total A-site area was calculated (A(Fe_3–xO₄) ≈ 52498 cts ∙ mm ∙ s^–1). With the simplified assumption, that this oxidized magnetite phase can be described as maghemite (γ-Fe₂O₃, Mössbauer fraction f_RT = 0.814) [32], a mass ratio of about 25 wt.% maghemite (γ-Fe₂O₃) to 75 wt.% magnetite (Fe₃O₄) or in sum 49 wt.% hematite (α-Fe₂O₃), 38 wt.% magnetite (Fe₃O₄) and 13 wt.% maghemite (γ-Fe₂O₃) was determined (Table 2, Mössbauer-3). The essential issue of this approach is that the presence of the oxidized magnetite phase is assumed to be the only source of the observed sextet area ratio deviation. Although it is certainly the major source (see description in the results section), the partly Fe(III) substitution by Al(III) in the minerals of the iron ore sample must also be considered. Thus, this additionally calculated/ approximated iron ore composition with three species (Mössbauer-3) should be treated with caution. Nevertheless, in comparison to XRD and XAFS, it could be possible that the mass ratio hematite to magnetite determined by Mössbauer spectroscopy is potentially even the more correct one – especially when considering the possibility that in the XRD as well as XAFS quantifications the maghemite contribution could have been added to the hematite and/ or magnetite signals. For instance, in case of the XRD it is known that the diffraction patterns of all three iron oxides, but particularly magnetite and maghemite show similarities and are difficult to distinguish [55,89]. Since magnetite and maghemite have very similar crystal structures (Fe₃O₄: inverse spine-type structure, γ-Fe₂O₃: defect spine-structure) the XRD peak quantities, positions and intensities are of pronounced similarity. Just some additional very weak reflections at low 2θ values (respectively high lattice plane distances d), which are detectable in some cases (under ideal measurement conditions and depending on the sample composition), are specific for maghemite. Despite the application of optimized measurement conditions (Co Kα radiation) these distinctive maghemite signals were not resolved in the diffractogram of the iron ore of this study (see Fig 2 and Fig S14a-b in S1 File area 2θ < 35°). Thus, maghemite could not be detected in the ore sample. For the XAFS subsequent measurements with the inclusion of γ-Fe₂O₃ as a third reference standard have been performed. The γ-Fe₂O₃[96] was obtained from Sigma Aldrich and has been undergone equal extensive pre-characterization (see [66]) as the references α-Fe₂O₃ [64] and Fe₃O₄ [65]. The resolving power of the lab spectrometer is sufficiently high to display disparities between γ-Fe₂O₃ and Fe₃O₄ in the XANES area (see SI Fig S9a in S1 File), although a comparison with synchrotron XAFS spectra (see SI Fig S9b in S1 File) indicates that synchrotron spectra can be slightly more beneficial for a differentiation of these two iron oxides. Particularly, the potentially very high resolution of synchrotron XAFS might be advantageous or even required, for example, in cases in which one of the two compounds is just contained in very low concentrations (combination: high Fe₃O₄ content + very low γ-Fe₂O₃ content or vice versa). The lab-XAFS LCF has been performed with the two references as in the prior measurements and additionally with γ-Fe₂O₃. The results can be seen in Fig S10 a and b in S1 File and are discussed in detail in the SI. For the two standard LCF the results are in accordance with the prior measurements and analysis. Using the additional γ-Fe₂O₃ as a reference results in an LCF with a slightly better fit by considering the reduced chi-squared given by the ATHENA software. The resulting composition of the Mexican iron ore is in this case 56 wt.% ± 3 wt.% α-Fe₂O₃, 17 wt.% ± 5 wt.% Fe₃O₄ and 27 wt.% ± 3 wt.% γ-Fe₂O₃ (Table 2, XAFS-3). Just focused on the α-Fe₂O₃ and Fe₃O₄ parts, this results in a ratio of about 77 wt.% α-Fe₂O₃ to 23 wt.% Fe₃O₄. Therefore, despite the consideration of the third species in the lab-XAFS LCF, the distinct difference to the Mössbauer spectroscopic results persists. In this case, the discrepancies of lab-XAFS and Mössbauer results are between 7 p.p. and 21 p.p. and may have various origins. As it has already been mentioned, the Mössbauer results are based on a very simplified assumption since the γ-Fe₂O₃ was not/ could not be fitted separately in case of the ore sample of this study. To do so, further elaborated measurements in form of temperature-dependent experiments or measurements by applying an external magnetic field could be beneficial. Furthermore, as already mentioned above, for a correct determination of relative concentrations the spectrometer has to be well calibrated or all the hyperfine parameters have to be known and even then the relative error will be about 5% [97]. However, in case of the lab-XAFS it must be considered that also contents of small amounts of such an oxidized Fe₃O₄ phase in the Fe₃O₄ reference substance, applied in the qualitative and quantitative spectrum evaluation, cannot be ruled out completely (see Mössbauer results) – a limitation that must be taken into account in both attempts, the LCF based on two as well as the one based on three reference substances because in both cases the same Fe₃O₄ reference substance was applied. Furthermore, the estimated bias for LCF with this Lab-XAFS spectrometer of ≤ 7 p.p. (determined for LCF with two species, α-Fe₂O₃ and Fe₃O₄) is likely to increase (decreasing accuracy) when considering additional species in the LCF with similar spectral characteristics. To investigate this, further examinations on a set of model mixtures containing α-Fe₂O₃, Fe₃O₄ and γ-Fe₂O₃, thus, all three species instead of just two, are required. On top of that, also the (additional) consideration of iron(III) hydroxides, or rather iron(III) oxide-hydroxides such as α-FeO(OH) and/ or γ-FeO(OH) in model mixture investigations are interesting for future lab-XAFS examinations. The first reason is that also in case of these compounds a relatively distinct similarity to the iron oxides is present in the XAFS spectra [52]. In contrast, in the XRD [55] as well as the Mössbauer spectra [32] a distinction from the oxides is relatively simple in plenty of cases. The second reason is an improved applicability in practice. In the natural iron ore sample investigated in scope of this study noticeable amounts of iron hydroxide compounds were not detected (at least not unequivocally and/ or within the detection limits of the analyses performed – thus, minor or trace amounts of iron hydroxides are still not excluded). However, in general, the paragenesis of the iron oxide minerals hematite, magnetite and maghemite with individual minerals of these iron(III) oxide-hydrates (“Fe₂O₃· x H₂O”), such as goethite (α-FeO(OH)) and lepidocrocite (γ-FeO(OH)), or mixtures of them (e.g., limonite) is very common in geological samples due to secondary mineral/ rock formation processes (e.g., weathering) with participation of water.

A compact comparison of the properties of all three methods is given in Table S15 in S1 File to provide a comprehensive overview of the differences between the methods.

Discussion on necessary pre-characterization

Another aspect, which must be considered in the comparative discussion of the lab-XAFS in relation to the other two applied techniques is the effort of the quantitative (and concurrently the qualitative) evaluation of the measured data. While performing qualitative analyses and especially quantitative LCF on lab-XAFS spectra and synchrotron XAFS spectra, one of the most crucial points is the knowledge about the sample regarding possible contained materials or substances to select suitable reference substances [98]. Actually, also in Mössbauer spectroscopy pre-knowledge on a sample can be necessary or, at least, beneficial to set appropriate starting values for the fitting procedures or to evaluate the plausibility of the results [32,99]. For example, in cases of samples with very complex compositions and/ or overlapping subspectra (due to similar line shapes/ hyperfine parameters) the fitting processes get very complicated. On top of that, in such cases different subspectra fits can sometimes yield to total fits of equal or similar quality, when just relying on the mathematical process [99]. However, a selection and application of suitable reference substances is rarely performed in Mössbauer spectroscopy whereas in XAFS this is a crucial requirement. In this study, detailed pre-characterizations, especially qualitative XRD, had already led to a composition of the Mexican iron ore sample of magnetite (Fe₃O₄) and hematite (α-Fe₂O₃) and, thus, homologous reference substances were applied. XRD and, with some limitations, also Mössbauer spectroscopy can revert to large established reference databases (XRD: Powder Diffraction Files of the ICDD and ICSD, Mössbauer spectroscopy: e.g., the MEDC database, the Mössbauer Effect Reference and Data Journal and the Mössbauer Mineral Handbook of the Mössbauer Effect Data Center [100]) and can be performed as virtually standardless and, thus, relatively fast methods in a lot of qualitative and quantitative analyses. This especially applies to cases of relatively simple samples or simple scientific questions such as the one of this study. In contrast, XAFS and especially lab-XAFS still lack comparable elaborated databases. And even with such a database at hand, the specific spectrometer which was used in generating the database’s spectra might have a significant influence on the spectrum itself, thus complicating the LCF approach. Though there are numerous studies containing synchrotron and, since recent times in continuously increasing number, also lab-XAFS spectra data of various compounds, it is still necessary to measure reference substances parallel to the analysis samples in a lot of cases. This is most notably valid when also intending to perform quantification (by LCF), which increases the analysis labor and time cost. However, it must be noted that, sometimes, at least, quantitative XRD is also performed by standard-based methods (with external or internal standards, e.g., the reference intensity ratio method with α-Al₂O₃ standard [25]) instead of the standardless Rietveld method. Furthermore, in case of Mössbauer spectroscopy it is often imperative to perform more costly additional measurements (e.g., determination of the sample specific recoilless fraction f) as well as to optimize the calculation parameters/ process (e.g., consideration of the thickness effects) to get more accurate and statistically firmer quantitative results, as the measurements of this study also clearly illustrate.

Discussion on quantification method

The last aspect, which is revealed by the measurements of this study are the different sorts of quantification realizable by the three speciation methods. It must be pointed out that the performed lab-XAFS evaluation by LCF, but also the Mössbauer analysis just yielded to relative quantitative results. These relative results were also limited to the iron species of the sample and therefore only the quantitative relative ratios of these specific species were determined. In contrast, the XRD analysis additionally provided information on more species of the sample, and these were incorporated in the quantitative Rietveld refinement. Although XAFS spectroscopy in general and also lab-XAFS spectrometers in particular are suitable for analyzing many elements and, thus, numerous different species (e.g., the lab-XAFS setup used in this study currently has an accessible energy range of E = 4.0–19.0 keV [50]), in a single run, the measurement is restricted to/ focused on a simultaneously measurable energy range of a few hundred eV around an element specific X-ray absorption edge. This means that a qualitative and quantitative multi elemental and species analysis cannot be performed in a single run and requires different measurements, each performed with suited reference materials, respectively. However, Mössbauer spectroscopy is clearly more limited since a multi element/ species analysis, like the XAFS, demands multiple different measurements but is additionally limited to only a few potentially accessible elements. This decreases the potential to consider species of different elements in a Mössbauer-based quantification further more. In contrast to this, XRD enables multi species analyses in a single measurement run with almost no species limitation, except, for example, the thresholds given by the detection limits, the presence of X-ray amorphous phases or the state of matter (XAFS does not have the latter two). Nevertheless, it must also be preconceived that, although Rietveld-based XRD quantification can incorporate numerous species simultaneously, it still remains a ratio quantification, because just the detected and assigned analytes are assumed as the overall sample composition, similar to standardless fundamental parameter based XRF quantification. In cases of simple sample compositions, of samples containing small amounts of secondary or trace ingredients and especially of samples, which just consist of solid crystalline substances, these Rietveld-based relative quantification can get very close to a full relative quantification. The term full relative quantification relates to a quantification in which all sample components are directly or at least indirectly considered, such as the standard-based (external standards, standard addition or internal standards) determinations of amount of substance concentrations, mass concentrations or mass fractions of elements or species where the total volume or mass of the sample is taken into account. Such real full relative XRD quantifications are in some cases feasible using more costly standard-based XRD methods [25]. Regarding lab-XAFS (and XAFS in general) absolute quantifications would also require the application of standard-based methods, for instance in the context of external standard calibration series (either consisting of one or more species of interest). However, this leads to the general challenges and actual limitations of purchasing or preparing suitable reference materials (regarding to contained elements/ species, element/ species concentrations, matrix adjustment etc.) for applications as (external) standards in solid state spectroscopic techniques.