Quantification of ferric iron content in minerals via the STEM-EELS-mapping method

Abstract

The oxidation state of iron (Fe) in minerals is crucial for Earth and planetary sciences. Accurate determination of the oxidation state of Fe aids in the estimation of redox conditions during mineral formation and thus the reconstruction of the evolutionary history of Earth and other solid celestial bodies. Compared to conventional methods that provide the average bulk Fe³⁺/ΣFe ratio in minerals, the recently developed scanning transmission electron microscopy electron energy loss spectroscopy (STEM-EELS) technique enables the accurate determination of Fe oxidation states at sub-micrometer scales. However, the focused electron beam in STEM mode can induce the generation of Fe³⁺ and consequently introduces uncertainty in the quantification of Fe³⁺ in minerals. In this study, a calibration relationship was established between the relative ratios of the Fe-L₃ and Fe-L₂ peak areas in the EELS spectra and the Fe³⁺/ΣFe ratio based on the characterization of a series of pyroxene reference materials with varying Fe³⁺ contents. The EELS spectra were collected in the STEM-EELS-mapping mode using focused ion beam (FIB)-derived sections. The impacts of sample preparation, data acquisition, and data processing procedures on the determination of the Fe³⁺ contents in minerals were examined and discussed to gain insights into the constraints of parameters for accurate quantification of Fe³⁺ in minerals. The obtained calibration relationship was further validated for the accurate determination of Fe³⁺ content in other Fe-bearing minerals, suggesting its promising applicability in the quantification of Fe³⁺ in precious nanoscale terrestrial and extraterrestrial materials.

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1. Introduction

Iron (Fe) is the fourth-most-abundant element in the Earth's crust and occurs in Fe-bearing minerals in diverse terrestrial and planetary environments. It predominantly exists in three distinct oxidation states: elemental iron (Fe⁰), ferrous iron (Fe²⁺), and ferric iron (Fe³⁺) in different minerals. The relative proportions of these oxidation states relative to the total iron (ΣFe) vary with the evolution of redox conditions, and accordingly, an accurate determination of the relative proportions of Fe oxidation states in minerals can be used to assess the redox states of different geological environments. For instance, the Fe³⁺/ΣFe ratios in minerals and silicate glasses have been used to study the oxygen fugacity of the mantle.^1–4 The Fe³⁺/ΣFe ratios were also employed to estimate the depth to which oxygenated groundwater penetrates bedrock in climate change studies.⁵ In planetary science, the Fe oxidation states can record the redox conditions of planetary evolution processes, providing key evidence for in-depth research on planetary evolution.^4,6–8 The widespread Fe³⁺ on the Moon that might have resulted from micrometeorite impacts^9,10 may challenge the traditional view of the Moon's extremely reducing environment.¹¹

The conventional methods for the quantification of Fe³⁺ in minerals primarily include wet chemical analysis, Mössbauer spectroscopy, and electron probe microanalysis (EPMA).^12–14 These techniques are limited by their large sample consumption and low spatial resolution, making them unsuitable for in situ characterization of small or microsamples. X-ray photoelectron spectroscopy (XPS) and X-ray absorption spectroscopy (XAS) have enabled the measurement of Fe³⁺ content at the micrometre scale in individual mineral grains.^15–17 However, these micro-scale (with beam spot sizes generally ranging from tens to hundreds of micrometres) in situ examination methods still fall short of meeting the demands at the nanoscale.¹⁸

Electron energy loss spectroscopy (EELS) coupled with transmission electron microscopy (TEM) allows for the quantification of Fe³⁺ in tiny samples with exceptionally high spatial resolution.^19–25 The Fe-L_2,3 electron energy loss near-edge structure provides chemical information about the specific multiple structures of iron valence states, which can be used as valence state fingerprints. The L_2,3 edges of Fe exhibit sharp energy loss peaks that appear as two white lines on the recording camera and are thus referred to as the “white line” peaks. The Fe-L_2,3 white lines correspond to the transitions from 2p to unoccupied 3d orbitals,²⁶ and the distinct features of Fe-L₃ and Fe-L₂ edges are due to the spin–orbit splitting of the Fe-2p hole, with an energy separation of approximately 13 eV. The EELS spectra of Fe²⁺ and Fe³⁺ in minerals demonstrate distinct Fe-L_2,3 edge features. Therefore, the accurate quantification of Fe³⁺ in minerals can be achieved using TEM-based Fe-L_2,3 EELS.²²

The quantitative determination of Fe³⁺ content in minerals using EELS was proposed by van Aken et al. in 1998,²¹ and a modified method with a universal curve was set up in 2002.²² The universal curve was derived by synthesizing a series of minerals with varying Fe³⁺ contents and further analysing the correlation between the EELS-Fe-L_2,3 edge “white line” ratios and the Fe³⁺/ΣFe ratios measured using Mössbauer spectroscopy. The measurements were operated with the electron beam in a parallel beam condition (i.e., TEM mode), in which only the EELS spectrum is obtained without simultaneously capturing an image of the examined area, thus making it impossible to determine the exact location of the analyzed region.

For conventional materials requiring solely EELS spectral acquisition, particularly homogeneous single-mineral specimens, parallel-beam illumination with single-spectrum acquisition may suffice. However, with recent advancements in analytical techniques, geological research has progressively focused on nanoscale investigations, particularly for ultra-rare samples such as those from deep mantle environments and extraterrestrial sources. These precious specimens necessitate in situ characterization at sub-micron scales to resolve complex mineralogical compositions and structural heterogeneities. Consequently, conventional TEM specimen preparation protocols and parallel-beam spectral mapping approaches fall short in addressing these advanced analytical requirements.

In contrast to the TEM mode, the scanning transmission electron microscopy (STEM) mode allows for the collection of EELS spectra along with imaging information of the test location, enabling precise positioning of the analyzed area. The STEM mode in transmission electron microscopy, utilizing a focused electron beam, offers distinct advantages over conventional TEM mode with parallel illumination. Specifically, STEM enables simultaneous acquisition of both imaging data and EELS spectra, allowing precise localization of the analyzed area. This integrated capability contrasts with TEM-EELS, which only provides spectral information without spatial context for the measurement position. Spectral mapping enables direct visualization of redox heterogeneity, which is essential for deciphering paragenetic sequences.

However, the highly focused electron beam in STEM mode (with a nanometre-scale beam spot) inevitably induces electron beam damage to the sample, particularly in electron-beam-sensitive materials, causing significant deviations in the measured Fe³⁺ content. Acquiring high-quality EELS spectra requires the samples to be sufficiently thin, often 30–50 nm or even thinner. Consequently, the spectra collection mode and parameters must be carefully selected to accurately measure the Fe³⁺ content. EELS data collection can be performed in three modes: point, line, and mapping scan. The point and line scan modes involve continuous data collection at a single point. Shorter dwell times result in inferior data quality; however, extending the dwell time may cause damage to electron-beam-sensitive samples, consequently introducing bias in the data. For instance, using the point scan mode, Gu et al. observed an increase in the Fe³⁺/ΣFe ratio with the increase of the dwell time at a single point, when measuring the Fe³⁺ content in the Chang'e 5 impact glass.²⁷ In contrast, the mapping scan mode can ensure data quality even with a short dwell time at each point. The operation principle of the mapping scan mode involves using a scanning probe to collect parallel spectral data at (x, y) positions and sequentially acquiring image pixels by changing the (x, y) positions. This enables the simultaneous collection of EELS and annular dark field (ADF) signals and performs spatial drift correction, thus obtaining the EELS spectra and spatial image of the sample. The mapping scan mode distributes the number of electrons across multiple pixels within a given time, allowing for pixel stacking in data processing, which can yield higher-quality signals even with a shorter dwell time at each point. Consequently, the mapping scan mode is expected to effectively reduce the potential electron beam damage to the sample.

Sample preparation is another factor that may affect the measurements of Fe³⁺ content using EELS. Techniques including powder ultrasonic dispersion, ultra-thin sectioning, and ion milling are commonly used for preparing TEM specimens. Ultrasonic dispersion requires samples to be ground to particles that are finer than 200 mesh. Ultra-thin sectioning necessitates complex pre-treatments such as resin embedding and thus is unable to achieve precise micro-cutting at target sites. In ion milling, the sample must be pre-processed to a disc with a diameter of 3 mm and thickness of a few micrometres. These techniques are inadequate for samples in the Earth and planetary science community, which preferentially involve natural minerals, rocks, meteorites, interstellar dust, and space mission returns. These samples are characterized by their varied, heterogeneous, and complex nature, and can be irreproducible due to age or scarcity. Alternatively, the focused ion beam-scanning electron microscope (FIB-SEM) dual-beam system has emerged as a promising alternative, allowing SEM-guided selection of regions of interest, with FIB then used to extract precise sections for further TEM observations.²⁸

Although van Aken et al. (2002) established a “universal curve” for the quantification of Fe³⁺ in minerals through the analysis of powder samples in TEM mode,²² the applicability of this curve to FIB specimen preparation in conjunction with STEM-EELS mapping remains to be confirmed. In the present study, we conducted a methodological investigation using FIB-STEM-EELS-mapping to determine the Fe³⁺ content in a series of pyroxene reference materials. Additionally, we investigated the influence of FIB specimen preparation and experimental settings on the accurate quantification of Fe³⁺ in minerals.

2. Experimental

2.1. Samples

A series of natural pyroxene grains with varying Fe³⁺ contents were collected and selected as reference samples in this study. A portion of these pyroxene mineral grains were finely ground into powders with particle sizes of ∼150 mesh, with the aim of determining the Fe³⁺/ΣFe ratios in these reference samples. Pyroxene grains with a size of 200–500 μm were embedded in epoxy resin (Fig. 1a), and were then coated with ∼20 nm of conductive carbon layers. Subsequently, the samples in the resin targets were precision-cut into thin sections (Fig. 1b) using FIB, to enable FIB-STEM-EELS mapping data acquisition.

Fig. 1 Optical (a) and high-angle annular dark field (HAADF) images (b) of the pyroxene reference samples with varying Fe³⁺ contents. The optical images were acquired of the samples embedded in epoxy resin, while the HAADF images were acquired on thin sections sampled using the focused ion beam (FIB) technique.

2.2. Characterizations

The sample characterizations were conducted at the Key Laboratory of Mineralogy and Metallogeny at the Guangzhou Institute of Geochemistry, Chinese Academy of Sciences. The major elements of the pyroxene samples were determined using a JEOL JXA-8230 electron probe microanalyzer (EPMA) at 15 kV and 20 nA with a beam spot size of 1 μm. The Mössbauer spectra were recorded in transmission mode using a WissEL GmbH WSS-10 Mössbauer spectrometer. All spectra were calibrated against a 7 μm α-Fe foil at room temperature and fitted using the MossWinn program (version 4.0) with least-square fitting to obtain the Mössbauer parameters. The FIB sections were prepared using a Ga⁺ ion beam operating at 30–5 kV and 9.3–0.6 nA in a Thermo Scientific FEI Helios 5 CX dual-beam system. A protective layer of tungsten was deposited prior to the FIB processing.

The prepared FIB thin sections were subjected to STEM-EELS measurements in a Thermo Scientific FEI Talos F200S TEM. The EELS data acquisition was performed in STEM mode using the Gatan Continuum 1077 EELS spectrometer, with a TEM camera length of 98 mm and EELS entrance aperture of 5 mm. The zero-loss and core-loss peaks were simultaneously acquired using the STEM SI Dual mode, with a core-loss range of 580–980 eV. To explore the impacts of the experimental conditions on the EELS data, spectra were acquired using various channel energy dispersion (0.05, 0.15, and 0.3 eV) and pixel time (0.01, 0.02, 0.04, 0.06, 0.08, and 0.1 s) values. The acquisition area size was set to 300 × 15 pixels for single-point dwell times of ≤0.02 s, but to 200 × 15 pixels for dwell time >0.02 s. As the ionization edges of the inner shells typically occur at energy losses higher than 100 eV, the electron excitation process can overlay a monotonically decreasing background signal onto the ionization edge signal of the inner shell. Consequently, it is necessary to subtract this background signal from the intensity of interest at the energy loss for quantitative elemental analysis. In this study, the following steps were taken in the Digital Micrograph software for accurate processing of the EELS spectra: (1) a background was fitted to the original spectrum using the least squares method at the 15–30 eV front of the Fe-L₃ edge at 708 eV, which yielded the subtracted spectrum (Fig. 2a). (2) Due to the multiple scatting effects, a broad hump may exist at the inner shell ionization edge due to the merging of higher-order satellite peaks and secondary scattering peaks, which can significantly influence the shape of the loss peak and eliminate fine structure. This multiple scatting impact could be neglected in the case of extremely thin samples (th/λ ≤ 0.3), but in thick samples, a Fourier-ratio deconvolution method was applied to eliminate the multiple scattering from the loss spectrum, which generated the deconvolved spectrum (Fig. 2a). (3) All spectrum intensities were normalized using a double arctan function.²² To establish the numerical proportionality between the white-line intensity ratio I(L₃)/I(L₂) and the ferric iron concentration Fe³⁺/ΣFe, the white lines must be isolated from the background intensity, which is due to transitions to unoccupied states in the continuum, using a double arctan function (Fig. 2b). Instead of calculating the total integral intensities of the L₃- and the L₂-white lines, Van Per et al. (2002)²² developed a method based on changes in the I(L₃)/I(L₂) intensity ratio, chemical shift, and near-edge structure, depending on the mean iron valence state. Two integrating windows of 2 eV width were applied to the L_2,3-edges from 708.85 eV to 710.85 eV and from 719.85 eV to 721.85 eV centered around the maximum at the L₃-edge for Fe³⁺ and at the L₂-edge for Fe²⁺, respectively. In our work, the background-function step sizes were scaled to the minima behind the L₃- and the L₂-edge with fixed inflection points at 709.85 eV and 720.95 eV (Fig. S1†).

Fig. 2 EELS data processing for calculation of the integral white-line intensity ratio I(L₃)/I(L₂). (a) Subtraction of the ionization background and multiple scattering, (b) spectrum normalization and integral area calculation of the 2 eV width windows for determining the white-line intensity ratio I(L₃)/I(L₂).

The height of the two arctan functions (h₁ and h₂) were scaled to the minimum behind the Fe-L₃ and the Fe-L₂ edge, respectively, with fixed inflection centres at E₁ = 709.85 eV and E₂ = 720.95 eV and fixed widths of w₁ = w₂ = 1 eV. Two integration windows of 2 eV in width were applied to the Fe-L₃ and the Fe-L₂ edges, respectively, to calculate the integral areas and I(L₃)/I(L₂) ratios (Fig. 2b). The rationale for selecting a 2 eV integration window lies in the chemical shift of ∼2 eV between Fe²⁺ and Fe³⁺. While integration windows narrower than 2 eV could theoretically be applied, excessively small widths amplify measurement errors due to reduced signal intensity. To balance data integrity and measurement reliability, we adopted a 2 eV integration window as the optimal threshold (Fig. S2†).

3. Results and discussion

3.1. Chemical composition and Fe³⁺/ΣFe reference values

The EPMA results suggested a distinct Fe content in the selected pyroxene samples that contained ∼50 wt% of SiO₂ (Table 1). More than 20 wt% FeO was detected in Hed1904, XWT-1, and Age1903, but only 6–7 wt% of Fe was observed in HYP-1, GAZ-F, and CL-R. A small amount of TiO₂ (<2%) was identified in most samples except for Hed1904, while it contained a higher manganese content (∼5% MnO). The contents of CaO, Na₂O, and Al₂O₃ in these samples decreased with increasing Fe content. The calculated crystal chemical formulas of the six pyroxene references based on the anion method and the charge-balance rule using the EPMA data are provided in Table 2.

Table 1 Chemical composition (wt%) of six pyroxene samples based on the EPMA results and the Fe³⁺/ΣFe ratios derived from the Mössbauer spectroscopic analyses^a

Sample	Hed1904	HYP-1	GZF-A	CL-R	XWT-1	Age1903
a bdl denotes data below detection limit of EPMA. b All the valence states of iron are calculated as FeO. Based on EPMA analytical results and reference material certifications, total compositions within the range of 98.5% to 101.5% are considered analytically acceptable.
Data points	12	5	5	4	5	12
SiO2	48.93	51.96	48.74	46.93	49.31	51.31
TiO2	bdl	0.47	1.16	1.64	0.83	1.83
Al2O3	0.01	3.59	8.89	9.12	4.15	0.15
FeO	21.84	6.5	7.43	6.31	23.16	29.16
MnO	5.14	0.07	0.13	0.11	0.51	0.51
MgO	1.61	14.5	13.67	12.44	0.03	0.03
CaO	23.64	21.17	17.24	20.82	13.54	0.54
Na2O	0.02	1.61	1.73	1.31	6.99	12.99
K2O	bdl	bdl	0.01	0.01	0.01	0.01
Cr2O3	bdl	1.04	bdl	0.01	bdl	bdl
Total^b	101.19	100.91	99.01	98.69	98.53	96.52
Fe^3+/ΣFe Mössbauer	0.00	0.16	0.21	0.36	0.54	1.00

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Table 2 Crystal chemical formulas of six pyroxene reference samples

Sample	Chemical formula
Hed1904	(Ca1.025Fe^2+0.675Mn0.176Mg0.097Fe^3+0.040Na0.002)Σ2.015(Si1.980Fe^3+0.020)Σ2.000O6
HYP-1	(Ca0.872Mg0.788Na0.114Fe^2+0.17Fe^3+0.06Cr0.030Ti0.0132Mn0.002)Σ2.005(Si1.894Al0.106)Σ2.000O6
GZF-A	(Ca0.685Fe^2+0.144Mn0.004Mg0.756Ti0.032Al0.196Fe^3+0.084Na0.124)Σ2.025(Si1.807Al0.193)Σ2.000O6
CL-R	(Ca0.820Fe^3+0.228Mg0.696Al0.122Na0.093Fe^2+0.076Ti0.045Mn0.003)Σ2.070(Si1.726Al0.274)Σ2.000O6
XWT-1	(Ca0.573Na0.523Fe^3+0.480Fe^2+0.300Al0.090Ti0.025Mn0.017Mg0.002)Σ2.010(Si1.903Al0.189)Σ2.092O6
Age1903	(Fe^3+0.959Na0.948Ca0.022Mn0.016Mg0.002Ti0.052)Σ1.999(Si1.932Fe^3+0.061Al0.007)Σ2.000O6

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Most of the Mössbauer spectra of the pyroxene samples exhibited tall and thin doublets, suggesting similar occupation status of Fe in the mineral structures (Fig. 3). The occurrence of hyperfine magnetic doublets indicates poor magnetic ordering of these pyroxene samples at room temperature, which is consistent with the typical features of Fe-bearing silicates. The quadrupole doublet derived from the spectral fitting mainly originates from the presence of Fe²⁺, particularly at the M₁ (weakly distorted octahedral) positions in the pyroxene structures. Two quadrupole doublets were observed in the Hed1904, suggesting that Fe²⁺ occupies both M₁ and M₂ positions in the mineral structure (Fig. 3a), which is consistent with the absence of Fe³⁺ based on the spectrum fitting (Table 1). In contrast, only one quadrupole doublet was observed in samples with low Fe content (Fig. 3b–d), suggesting that the small amount of Fe preferentially exists as Fe²⁺ at the M₁ positions in the mineral structures. The spectrum of XWT-1 was different from those of the other samples (Fig. 3e), likely because the Fe³⁺ occupies not only the octahedral M₁ positions but also tetrahedral positions in the pyroxene structure. Only a narrow quadrupole splitting was identified in Age1903, which is because of the presence of Fe³⁺ at the M₁ position in the pyroxene structure (Fig. 3f). The Fe³⁺/ΣFe reference values of the pyroxene samples were calculated based on the Mössbauer spectra fitting and are provided in Table 1.

Fig. 3 Mössbauer spectra and their fittings for the pyroxene reference samples. The experimental data were recorded in transmission mode against a 7 μm α-Fe foil at room temperature, and fitted in the MossWinn 4.0 program. D1 and D2: doublet; S: singlet.

3.2. Impacts of dwell time on the Fe-L_2,3 EELS spectrum and the quantification of Fe³⁺/ΣFe

The samples HYP-1 (Fe³⁺/ΣFe = 0.16) and Age1903 (Fe³⁺/ΣFe = 1) were selected to investigate the impacts of dwell times of t = 0.01, 0.02, 0.04, 0.06, 0.08, and 0.10 s, using a channel energy dispersion of d = 0.05, 0.15, or 0.3 eV (Fig. 4). The spectra of Age1903 acquired at d = 0.15 eV and different dwell times completely overlap (Fig. 4a), suggesting that the dwell time does not affect the Fe-L_2,3 EELS spectrum of Age1903, or, consequently the quantification of its Fe³⁺ content. However, significant rightward shifts from 708 eV to 709 eV were observed in the Fe-L₃ peak in HYP-1 with the increase in dwell time from 0.01 to 0.10 s (Fig. 4b). Particularly, at t ≥ 0.08 s, a distinct shoulder peak relevant to the occurrence of Fe³⁺ arose at ∼710 eV in the spectrum of HYP-1 (Fig. 4b). The rightward shifts of the Fe-L₃ peak position and the emerge of the shoulder peak at ∼710 eV with increasing dwell time indicate that the increase in dwell time induces the generation of Fe³⁺ in HYP-1.

Fig. 4 Fe-L_2,3 spectra of reference samples Age1903 and HYP-1 acquired under different conditions with various dwell times and electron energy resolutions. (a) Spectra of Age1903 (Fe³⁺/ΣFe = 1) acquired at d = 0.15 eV and various dwell times, (b) spectra of HYP-1 (Fe³⁺/ΣFe = 0.16) acquired at d = 0.15 eV and various dwell times, (c) spectra of HYP-1 acquired at d = 0.05 eV and various dwell times, and (d) spectra of HYP-1 acquired at d = 0.3 eV and various dwell times.

Reduced energy dispersion enhances the spectral resolution of the EELS-Fe-L-edges within narrower energy windows, although this improvement comes at the expense of increased filtration of inelastic scattered electrons through the spectrometer slit and concomitant SNR degradation. Systematic comparisons of spectral outcomes across dispersion settings (0.05–0.3 eV per channel) are being conducted to establish optimal acquisition parameters balancing edge definition and counting statistics. Increasing the dwell time from t = 0.01 to 0.02 s can improve the signal-to-noise ratio in the spectrum of HYP-1 while minimizing the electron beam damage on the sample (Fig. 4b). The electron beam damage on HYP-1 induced by the prolonged dwell time was also observed in the data acquired at d = 0.05 eV (Fig. 4c) but not that at d = 0.3 eV (Fig. 4d). This is because the low energy resolution of d = 0.3 eV is limited to revealing the changes in the fine electronic structure.

3.3. Impacts of integration time on the quantification of Fe EELS I(L₃)/I(L₂) ratio

The spectrum acquired at a single pixel with an integration time of 20 ms is insufficient for quantitative analysis of the Fe³⁺ contents in the samples, thus necessitating the stacking of multiple pixels to improve the spectrum quality. To gain intuitive insights into the impacts of integration time on the quantification of Fe³⁺, the parameter of total integration time, T, was defined as the product of the single-pixel dwell time t and the number of pixels n, i.e., T = t × n. The Fe EELS I(L₃)/I(L₂) ratio increased and plateaued with increasing total integration time (via accumulating signals of multiple pixels) (Fig. 5). The fluctuation of the Fe EELS I(L₃)/I(L₂) ratio at low T could be ascribed to the poor quality of the integrated spectra. A long integration time of T ≥ 45 s is required to obtain a stable EELS I(L₃)/I(L₂) value for HYP-1, which has low contents of total Fe and Fe³⁺ (Fig. 5a), while a shorter integration time of T ≥ 24 s is sufficient to acquire a stable EELS I(L₃)/I(L₂) value for Age1903, which possesses high contents of total Fe and Fe³⁺ (Fig. 5b).

Fig. 5 Impacts of the total integration time on the quantification of white-line intensity ratios I(L₃)/I(L₂) for the reference samples (a) HYP-1 and (b) Age1903. The total integration time was calculated by multiplying the single pixel dwell time and the number of pixels selected. The I(L₃)/I(L₂) rations were obtained via processing the spectrum generated from the stacking of multiple spectra in the selected pixels.

3.4. Impacts of thickness of the FIB section on the quantification of the Fe EELS I(L₃)/I(L₂) ratio

The approximate thickness (th) of the FIB section can be obtained through direct integration of the low-energy loss part of the EELS spectrum, because the thickness and the mean free path of inelastic scattering of the sample follows the specific relationship
where I_t is the total number of electrons in the low energy loss spectrum and I₀ is the number of electrons without energy loss. The relative thickness of the FIB section can be directly read and estimated using the built-in program in the Gatan software. Obviously, the Fe I(L₃)/I(L₂) ratio of the HYP-1 generally remains constant at thicknesses of 0.4–0.8 but trends downwards with further increasing the thickness (Fig. 6). This indicates that it is essential to section the sample to an optimal thickness to ensure precise quantification of the Fe³⁺ content in the samples. The recommended thickness for this purpose falls in the range of 0.4 to 0.8.

Fig. 6 I(L₃)/I(L₂) ratios with variation of the FIB section thickness. The I(L₃)/I(L₂) ratios were calculated based on the processing of spectra. The thickness values were directly read using the built-in program in the Gatan microscopy suite software.

3.5. Calibration curve for the quantification of Fe³⁺ using FIB-STEM-EELS mapping and its applicability

Based on the aforementioned Results and discussion of the impacts of dwell time, electron energy resolution (channel energy dispersion), and total integration time, Fe EELS spectra of the six selected pyroxene reference samples were acquired at t = 0.02 s, T = 45 s, and multiple electron energy resolution conditions of d = 0.05, 0.15, or 0.3 eV to obtain the Fe I(L₃)/I(L₂) ratio values of these samples. The Fe I(L₃)/I(L₂) ratio data versus the Mössbauer Fe³⁺/ΣFe ratio were subsequently plotted to generate calibration curves for determining Fe³⁺ content in minerals using the STEM-EELS mapping method (Fig. 7). Following van Aken et al. (2002),²² the curves of Fe I(L₃)/I(L₂) versus Mössbauer Fe³⁺/ΣFe can be described with the equation:
where I(L₃)/I(L₂) represents the parameter determining the content of Fe³⁺ using the STEM-EELS mapping. The parameter x represents the Fe³⁺/ΣFe ratios derived from the analysis of the Mössbauer spectra. The parameters a, b, and c can be determined through the fitting of curves. The curves were well fitted using the above equation (Fig. 7), suggesting that the channel energy dispersion had a limited impact on the quantification of Fe³⁺ in minerals compared to that of the dwell time and the total integration time. Despite the EELS data of the pyroxene reference samples being acquired at different electron energy resolutions of d = 0.05, 0.15, and 0.3 eV, fitting of the curves generated similar parameters of a, b, and c for the above equation, which are summarized together with the experimental conditions in Table 3.

Fig. 7 Calibration curves for the quantification of Fe³⁺ contents in minerals at channel energy dispersions of d = 0.05, 0.15, and 0.3 eV per channel. The I(L₃)/I(L₂) ratios were derived from EELS spectra. The Fe³⁺/ΣFe ratios were obtained from the analyses of their corresponding Mössbauer spectra.

Table 3 Experimental conditions for the Fe I(L₃)/I(L₂) data acquisition at different electron energy resolutions, and the data fitting versus the Mössbauer Fe³⁺/ΣFe ratio derived parameters

d (eV)	t (s)	T (s)	R ^2	a	b	c
0.05	0.02	45	0.97	0.19 ± 0.06	−0.40 ± 0.08	0.30 ± 0.02
0.15	0.02	45	0.99	0.25 ± 0.05	−0.48 ± 0.07	0.33 ± 0.02
0.30	0.02	45	0.98	0.18 ± 0.05	−0.38 ± 0.06	0.30 ± 0.02

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Several Fe-bearing minerals, including two natural hornblende (labelled BD #4 and SC #1), one natural magnetite (Fe₃O₄_tw), one synthetic nano magnetite (Fe₃O₄_sy), and one synthetic hematite (Fe₂O₃_sy) sample, were selected to assess the reliability and applicability of the calibration curve established under the experimental condition of d = 0.15 eV. The EELS spectra were collected with parameters of d = 0.15 eV, t = 0.02 s, T = 50 s, and a sample thickness of th = 0.6 (Fig. 8a). The Fe³⁺ content in these samples, as determined by EPMA, was found to be 82% for SC #1, 32% for BD #4, 67% for the magnetite, and 100% for the hematite. The EELS spectra correspondingly displayed features that correlated with the Fe³⁺ contents in the samples (Fig. 8a). For instance, the peak maximum for Fe-L₃ was observed at 708.5 eV for BD #4, and at 710 eV for Fe₂O₃_sy, which is in line with the 32% Fe³⁺ content in BD #4 and the 100% Fe³⁺ content in hematite. The Fe³⁺ contents derived from the EELS analyses for these minerals aligned well with those obtained from the EPMA analyses (Fig. 8b), as indicated by the data points clustering around the 1 : 1 line. This alignment validates the high reliability and broad applicability of the calibration curves obtained under the data acquisition conditions of t = 0.02 s, T = 45 s, and d = 0.15 eV (as well as d = 0.05 and 0.3 eV).

Fig. 8 Reliability and applicability of the calibration curves evaluated by determining the Fe³⁺ contents in various Fe-bearing minerals, including natural hornblende (BD #4 and SC #1) and magnetite (Fe₃O₄_tw), and synthetic magnetite (Fe₃O₄_sy) and hematite (Fe₂O₃_sy). (a) Fe-L_2,3 EELS spectra of the Fe-bearing minerals, and (b) consistency analysis between the EELS- and EPMA-derived Fe³⁺/ΣFe ratios.

3.6. Error analysis

Errors inevitably occur during the quantitative analysis of Fe³⁺ contents in minerals, originating from the limitation of the energy resolution of the EELS instrument, the signal-to-noise ratio of the spectrum, potential electron beam damage to samples, and the post-processing of data, such as background subtraction, deconvolution of multiple scattering, and removal of the continuous background under the Fe-L_2,3 white lines, as well as the fitting of the EELS spectrum and subsequent calculations. Some of the post-processing errors can be minimized via optimizing the method and parameters for background subtraction. More attention should be paid to the procedure of arctan background subtraction, as the Fe I(L₃)/I(L₂) ratio is highly sensitive to the height (h) behind the Fe-L_2,3 edges. The point with the minimum intensity behind the Fe-L_2,3 edge peaks is commonly chosen to measure the height during the arctan background subtraction. However, it is hard to select an ideal height value for the arctan background subtraction from a spectrum at low signal-to-noise ratio, which may produce significant errors. Therefore, a comprehensive judgment of the spectrum is essential, and the average value within fluctuations could be the optimal one for background subtraction.

The total integration time has a pronounced impact on the accurate determination of Fe-EELS I(L₃)/I(L₂) ratios (Fig. 9a). Insufficient integration time can lead to spectra with inadequate signal-to-noise ratios, particularly in minerals with low Fe³⁺ contents. For example, the EELS I(L₃)/I(L₂) ratio error for HYP-1, which does not contain Fe³⁺, can be as high as 0.35 when the total integration time is less than 45 s. In contrast, the error for Age1903, which contains 100% Fe³⁺/ΣFe, is relatively modest at 0.3. Prolonging the total integration time to T ≥ 45 s can effectively reduce the error to a maximum of 0.14. Notably, the Fe-EELS I(L₃)/I(L₂) ratio does not vary linearly with Fe³⁺ content in the calibration curve (Fig. 7). Consequently, the error associated with quantifying Fe³⁺ content using the Fe-EELS I(L₃)/I(L₂) ratio can vary across samples with various Fe³⁺ contents. The error in Fe³⁺ content quantification initially decreases and then increases with the increasing Fe³⁺/ΣFe ratio, reaching a minimum of 0.012 at a Fe³⁺/ΣFe ratio of 0.7 (Fig. 9b). The error values for samples with 0% and 100% Fe³⁺ are 0.032 and 0.025, respectively, which are slightly lower than the 0.04 reported in the previous study by van Aken et al.²²

Fig. 9 Experimental error analysis considering the impacts of (a) the total integration time and (b) the nonlinear relationship between the EELS I(L₃)/I(L₂) ratio and the mineral Fe³⁺ contents.

Furthermore, in the microanalysis (EPMA) data and EELS-derived I(L₃)/I(L₂) ratios in Fig. 8b, we attribute these discrepancies primarily to two dominant sources of uncertainty: (1) systematic measurement errors inherent to EPMA instrumentation and (2) computational uncertainties propagated through the charge-balance oxygen modelling framework. We employed the conventional ZAF + standards routine of the JEOL JXA-8230 EPMA to determine the compositions of Fe-bearing minerals. Based on the analysis of an in-house monitor standard (chrome-diopside), the error was less than 3% for the major elements. The Fe³⁺/ΣFe ratios were determined through charge-balance oxygen calculation, a methodology intrinsically associated with computational uncertainties. When implementing the standard calibration curve established in this study for retrospective quantification, the methodological error was constrained to 4%. However, the combined uncertainty—accounting for both the inherent limitations of the charge-balance approach and the propagated uncertainties from the calibration protocol—may reach approximately 10%.

4. Conclusions

In the present study, accurate Fe-L_2,3 EELS spectra and images of the exact locations examined on the FIB thin sections were acquired at the sub-micro scale using STEM-EELS-mapping. A calibration curve of EELS I(L₃)/I(L₂) versus Fe³⁺/ΣFe with a minimum error of 0.014 was established, which can be used for accurate quantitative analysis of Fe³⁺ content in complex Fe-bearing materials from Earth and other planets. Recommendations regarding the sample preparation, experimental parameters, and data post-processing for accurate determination of Fe³⁺ content in samples under the STEM-EELS-mapping mode are as follows: (1) the dwell time for the single point spectrum acquisition should be reduced to t ≤ 20 ms to minimize potential electron beam damage. (2) The total integration time is recommended to be set at T > 45 s for samples with low total Fe content, but it can be slightly reduced for samples with a high content of total Fe. (3) The use of a sample thickness of th/λ ≤ 0.8 is recommended for the examination of FIB sections. (4) The obtained calibration curve is also applicable to the quantitative analysis of Fe³⁺/ΣFe ratio in diverse Fe-bearing minerals.

Data availability

Data of this paper are presented in the tables and ESI.†

Author contributions

Shan Li: sample collection, investigation, methodology, writing – original draft, review & editing. Ke Wen: writing – review & editing, data curation, visualization. Yiping Yang: investigation, methodology. Xiaoju Lin: investigation, methodology. Yonghua Cao: sample collection, methodology. Yao Xiao: investigation. Haiyang Xian: conceptualization, methodology, funding acquisition, formal analysis, supervision, writing – review & editing. Jianxi Zhu: writing – review & editing. Hongping He: writing – review & editing, supervision.

Conflicts of interest

The authors declare no competing interests.

Acknowledgements

This work was financially supported by the Bureau of Frontier Sciences and Basic Research, CAS (QYJ-2025-0102), the Youth Innovation Promotion Association CAS (2021353), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0840100), the Director's Fund of Guangzhou Institute of Geochemistry, CAS (2022SZJJZD-03), and the Science and Technology Planning Project of Guangdong Province, China (2023B1212060048). This is contribution no. IS-3665 from GIGCAS.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ja00002e

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