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Iterative energy self-calibration of Fe XANES spectra

Determining the oxidation state of Fe through parameterization of X-ray absorption near-edge structure (XANES) spectral features is highly dependent on accurate and repeatable energy calibration between spectra. Small errors in energy calibration can lead to vastly different interpretations. While simultaneous measurement of a reference foil is often undertaken on X-ray spectroscopy beamlines, other beamlines measure XANES spectra without a reference foil and therefore lack a method for correcting energy drift. Here a method is proposed that combines two measures of Fe oxidation state taken from different parts of the spectrum to iteratively correct for an unknown energy offset between spectra, showing successful iterative self-calibration not only during individual beam time but also across different beamlines.

1. Introduction

Iron is an abundant element with critical importance to many aspects of our lives, from steelmaking to the formation of red blood cells. Fe usually occurs in oxidized form, either as Fe²⁺ (ferrous iron) or Fe³⁺ (ferric iron), each with distinct chemical properties. The reaction involving reduction or oxidation of Fe is a fundamental process (Ilbert & Bonnefoy, 2013; McCammon, 2005; Potapkin et al., 2013; O'Neill et al., 2018) and quantifying the direction and extent of this reaction is a major goal in science.

Fe K-edge X-ray absorption near-edge structure (XANES) has become the method of choice for quantitative determination of Fe oxidation state, expressed as the concentration ratio Fe³⁺/ΣFe where ΣFe = Fe²⁺ + Fe³⁺, via empirical fitting of unknowns to a calibration curve developed from a suite of standards with independently determined Fe³⁺/ΣFe ratios. An Fe K-edge XANES spectrum can be parameterized via a number of methods, such as the centroid energy of the combined pre-edge peaks (Fiege et al., 2017; Berry et al., 2018, 2003; Cottrell et al., 2009; Dyar et al., 2012), the energy of a specific normalized intensity along the absorption edge (Berry et al., 2018; Nedoseykina et al., 2010; Dyar et al., 2012) or the ratio of normalized intensities at two post-edge energies (Berry et al., 2010; Dyar et al., 2012). The relationship between any of these points and the known Fe³⁺/ΣFe ratio of standards can be fitted, allowing the Fe³⁺/ΣFe ratio of an unknown specimen to be easily determined provided the composition and structure of standards and unknowns are similar; criteria easily satisfied by using synthetic glass standards. However, any error in the energy calibration feeds directly into the Fe³⁺/ΣFe quantification making empirical methods extremely sensitive to the scan-to-scan energy reproducibility. For example, the entire range of Fe³⁺/ΣFe from 0 to 1 in silicate glasses of basaltic composition results in a change of <6 eV in the absorption edge at a normalized intensity of 0.8 and an even smaller change of <2 eV in the pre-edge centroid (Fiege et al., 2017; Berry et al., 2018). The resolution and reproducibility of monochromators are therefore critical in making precise determinations of Fe³⁺/ΣFe.

At beamlines employing double-crystal monochromators, time-dependent changes in the relationship between the nominal incident energy and the true incident energy, herein termed energy drift, typically arise because of changes in the geometric relationship between the Bragg axis encoder and the lattice planes of the diffracting crystals. Energy drift is highly dependent on a combination of factors, including monochromator mechanical design, thermal management and storage-ring top-up frequency.

A typical method to correct energy drift and perform an absolute energy calibration during Fe³⁺/ΣFe determinations is to simultaneously collect the spectrum of an Fe foil. The Fe foil spectrum can then be calibrated by using the energy of the first derivative peak (Fiege et al., 2017) for example, with the calibration factor then applied to the simultaneously collected unknown spectra. However, in some cases this approach is impractical, either because of a specific experimental setup [e.g. simultaneously collecting ptychography data using the transmitted beam (Jones et al., 2016)] or because of beamline design [e.g. the X-ray Fluorescence Microscopy (XFM) beamline at the Australian Synchrotron (AS) (Paterson et al., 2011), which lacks the ability to simultaneously measure a reference standard]. Additionally, there may be occasions where reference foils were collected at intervals insufficient to develop a time-dependent expression for energy drift and, therefore, an alternate method is necessary to salvage the dataset.

Silicate melts, quenched to glass, are sensitive recorders of magmatic Fe³⁺/ΣFe and thus capture the oxygen fugacity of magmatic systems on eruption. The accurate quantitative determination of Fe³⁺/ΣFe in natural silicate glasses is essential in studying these systems, with uncertainty in the energy calibration potentially rendering an entire beam time dedicated to Fe K-edge XANES analysis worthless.

Here, we develop a method of iterative self-calibration of Fe XANES spectra that combines information from both the rising edge and the post-edge structure, allowing precise energy calibration of unknown spectra without a simultaneously measured reference foil. Furthermore, we apply this method to iteratively self-calibrate spectra between beamlines, opening the possibility for all researchers to use a single set of high-quality calibration standards for each system being investigated, making data collection more efficient and direct comparisons between beam times trivial.

2. Method

2.1. Sample description

The samples used were a mix of synthetic and natural samples collected at a variety of beamlines. Table 1 provides a summary of the samples used in this study.

Table 1
Samples used in the present study

Sample	Fe^3+/ΣFe	Beamline (facility)
11 × Basalt standards†	0.011–0.775†‡	XFM (AS)§
7 × Rhyolite standards¶	0.238–0.806‡††	X26A (NSLS)¶
MORB VG 3450†	0.132†‡‡	I18 (Diamond)
RGM-2§§	0.262¶¶	XFM (AS)§
Havre pumice†††	Unknown	XFM (AS)§

†As described by Berry et al. (2018).
‡Determined by Mössbauer spectroscopy.
§This study.
¶As described by Cottrell et al. (2009).
††Determined by wet chemistry.
‡‡Determined by XANES.
§§USGS natural rhyolite standard.
¶¶Values determined from USGS natural rhyolite standard RGM-1.
†††Sea-rafted rhyolitic pumice from the 2012 Havre eruption (Carey et al., 2018).

2.2. Data collection

Fe K-edge XANES data for this study were collected at the XFM beamline at the AS (Paterson et al., 2011) at 220 energies between 6.963 keV and 7.462 keV with non-uniform energy spacing (see Table S2 in the supporting information). For each of the 11 synthetic glass standards and the rhyolite RGM-2 standard, 200 individual pixel-wise spectra were collected with 10 ms per energy yielding an equivalent dwell of 2 s per energy across the sample. Similarly, the pumice sample was collected with a dwell of ∼32 s per energy. Excited fluorescent photons from a 2 µm full width at half-maximumX-ray focus formed by a Kirkpatrick–Baez mirror pair were collected using a Maia (Rev D) detector system positioned in its typical backscatter geometry (Siddons et al., 2014; Ryan et al., 2018). Fluorescent data were analysed using the dynamic analysis method (Ryan & Jamieson, 1993) implemented in GeoPIXE (Ryan et al., 2005) and quantified using known metallic foils (Micromatter, Canada). The Fe maps for each incident energy were exported as quantitative TIFF files yielding pixel-wise XANES spectra for each sample. All spectra had a constant pre-edge background subtracted and were normalized to an edge step of 1.

2.3. Iterative self-calibration

We generated two parameterizations of the relationship between spectral features of the standards and their independently determined Fe³⁺/ΣFe ratios for both the basalt and rhyolite glass standards. Method A involved determining the energy where the absorption edge reaches a normalized intensity of 0.8, while Method B involved determining the ratio of the normalized intensity of two post-edge energies (E₁ and E₂), with linear fits performed for each method against Fe³⁺/ΣFe. While the values (0.8, E₁ and E₂) are somewhat arbitrary, they were chosen to obtain maximum energy or intensity separation while maintaining a linear relationship to Fe³⁺/ΣFe concentration. E₁ and E₂ were taken as 7138.4 eV and 7161.7 eV, respectively, for the basalts as previously described by Berry et al. (2018), while E₂ was extended to 7175 eV for the rhyolites because of the poorly defined isosbestic point for the natural standards. The normalized spectra and the fits to both Methods A and B are shown in Figs. 1 and 2 for basaltic and rhyolite glasses, respectively. We note that the error bars in Fig. 1(b) are one standard deviation from the 200 individual measurements (this study), whereas in Fig. 2(b) the error bars indicate the extent of variability from the three individual measurements (Cottrell et al., 2009).

Figure 1 (a) Fe-XANES spectra from 11 synthetic basalt standards with Fe^3+/ΣFe between 0.011 and 0.775. The horizontal dashed line represents a normalized intensity of 0.8 (Method A) and the vertical dashed lines correspond to the points E1 = 7138.4 eV and E2 = 7161.7 eV, placed either side of the isosbestic point ip, with the ratio of the normalized intensity at E1 and E2 used to determine the Fe^3+/ΣFe concentration (Method B). (b) Results from Method A (orange solid line, lower axis) and Method B (blue dashed line, upper axis), where the error bars represent one standard deviation, calculated from the 200 individual measurements.

Figure 2 (a) Fe-XANES spectra from seven rhyolite standards with Fe^3+/ΣFe between 0.238 and 0.805 (Cottrell et al., 2009). The horizontal dashed line represents a normalized intensity of 0.8 (Method A) and the vertical dashed lines correspond to the points E1 = 7138.4 eV and E2 = 7175.0 eV, with the ratio of the normalized intensity at E1 and E2 used to determine the Fe^3+/ΣFe concentration (Method B). (b) Results from Method A (orange solid line, lower axis) and Method B (blue dashed line, upper axis). The error bars in (b) represent the limits of the range from three measurements (Cottrell et al., 2009).

Two methods are needed in tandem to constrain the energy calibration to a single solution. For example, a spectrum offset to lower energy will result in an under-reporting of the Fe³⁺/ΣFe concentration using Method A (edge moves to lower energy) and an over-reporting of the Fe³⁺/ΣFe concentration using Method B (I₂/I₁ increases as the spectrum shifts to the left). However, we can combine these two methods to adjust the energy offset in an iterative process converging on a single value for the Fe³⁺/ΣFe concentration,

where E is the energy scale and E_c is the final self-calibrated energy scale. , where Fe_A is the Fe³⁺/ΣFe ratio using Method A, is the mean Fe³⁺/ΣFe ratio using Methods A and B, and is the energy of the edge given the Fe³⁺/ΣFe ratio . In the present case the iterative process was stopped when ΔE < 10⁻⁴ eV. At this point, both methods report the same value for the Fe³⁺/ΣFe ratio and the energy, and therefore the Fe³⁺/ΣFe ratio, is calibrated.

We apply this method to three cases. Firstly, to a mid-ocean-ridge basalt (MORB) sample (VG 3450) spectra with a previously determined Fe³⁺/ΣFe ratio (Berry et al., 2018) using the basaltic glass standard reference spectra. Secondly, to a thin section of the USGS rhyolite standard RGM-2, and thirdly, to a thin section of rhyolitic pumice collected at the XFM beamline at the AS using the rhyolite glass standard reference spectra (Cottrell et al., 2009). Further details and an example Matlab code are presented in the supporting information.

3. Results and discussion

The results for the MORB sample, RGM-2 and the Havre raft pumice are presented in Figs. 3(a)–3(c), respectively. Here we observe that the proposed method of energy self-calibration successfully converges on the correct Fe³⁺/ΣFe ratio for the MORB sample, converging to a Fe³⁺/ΣFe concentration of 0.129 [Fig. 3(a)]. In addition, we observe that the self-calibration method can also be successfully applied to rhyolite samples, with the RGM-2 sample converging to a Fe³⁺/ΣFe ratio of 0.231 [Fig. 3(b)] and the previously unknown Havre pumice sample converging to a Fe³⁺/ΣFe ratio of 0.149 [Fig. 3(c)]. A summary of the results is presented in Table 2.

Table 2
Summary of uncalibrated and self-calibrated values for the data presented in Fig. 2, where the uncalibrated, self-calibrated and expected Fe³⁺/ΣFe ratios are presented together with the required energy change (ΔE)

	Fe^3+/ΣFe
Sample	Uncalibrated	Self-calibrated	Expected	ΔE (eV)
MORB VG3450	0.591 (0.018)	0.129 (0.004)	0.132	0.8
RGM-2	0.535 (0.037)†	0.231 (0.016)	0.262 (0.015)‡	0.3§
Havre pumice	0.452 (0.031)†	0.149 (0.010)	—	0.4§

†Manually offset to be within calibration range.
‡RGM-1 values.
§After manual offset.

Figure 3 Demonstration of iterative energy calibration correction. (a) A MORB glass spectra (Smithsonian Institute sample number VG 3450), as collected by Berry et al. (2018) (orange dot–dashed line), iteratively self-corrected (solid black line) to the basaltic glass standards. Also shown for reference are the spectra for the 0.011 and 0.775 Fe^3+/ΣFe ratio standards (black dotted lines). The Fe^3+/ΣFe ratio (inset) for Method A (solid orange lines) and B (dashed blue lines) as a function of iteration number shows convergence to a single Fe^3+/ΣFe ratio. Similar treatment is shown for the RGM-2 reference standard (b) and an experimental section of pumice from the 2012 Havre eruption (c), both iteratively self-corrected to the rhyolite glass standards (Cottrell et al., 2009). Also shown for reference are the spectra for the 0.238 and 0.806 Fe^3+/ΣFe ratio standards (black dotted lines). The vertical dashed lines in (a)–(c) refer to the two points E1 and E2 in each case.

We have shown that the proposed method can accurately correct an unknown energy offset in Fe XANES data of isotropic non-crystalline materials. Furthermore, we have shown that the current method can not only be used for correcting an energy drift during a beam time but also for correcting discrepancies in the absolute energy calibration between multiple beam times or indeed between multiple beamlines, as highlighted by the successful calibration of the MORB spectra, where we identify an absolute energy offset of 0.8 eV between two independent beam times at beamlines I18 at the Diamond Light Source and XFM at the AS. In addition, we determine the calibrated value for the Fe³⁺/ΣFe ratio of the USGS RGM-2 standard sample to be 0.231 using a set of rhyolite standards. This represents the first estimation of Fe³⁺/ΣFe ratio for this new standard material that has been collected from the same locality as the previous block of rhyolite standard RGM-1 (Wilson, 2019).

Furthermore, we apply the method to a sample of sea-rafted rhyolitic pumice from the 2012 Havre eruption (Carey et al., 2018). We obtain a value for the Fe³⁺/ΣFe ratio of 0.149, the first reported value for pumice from this significant unobserved submarine eruption. Establishing the oxidation state and magmatic Fe³⁺/ΣFe ratio is often difficult for such crystal-poor rhyolites because of the lack of co-existing oxide minerals that are typically used to constrain oxygen fugacity of the magmatic system on eruption (e.g. Buddington & Lindsley, 1964; Ghiorso & Evans, 2008).

The ability to calibrate unknown samples to a set of reference spectra collected at a different time and place potentially allows for a single set of absolute reference spectra to be collected and used by researchers to calibrate their unknowns. This would not only allow results to be easily compared but could also remove the need to collect a set of reference spectra at every beam time, saving multiple hours of costly beam time and allowing additional unknown samples to be studied. The proposed method can in theory be used to correct any spectra from isotropic non-crystalline materials where two opposing oxidation-dependent trends can be identified, such as the rising edge energy, the intensity or energy of pre-edge features, or the ratio of the intensity of pre- or post-edge features, provided the same method is used for the known and unknown samples and each sample type is compositionally similar.