Understanding atom probe's analytical performance for iron oxides using correlation histograms and ab initio calculations

To ascertain the extent of oxygen loss in each iron oxide sample during field evaporation, we conducted atom probe analyses on hematite (α-Fe₂O₃), magnetite (Fe₃O₄), and wüstite (FeO). Figure 1 insets, illustrate the reconstructed atom maps. To ensure precise comparisons, three specimens were meticulously prepared during FIB, with specimen geometries closely matching each other, approximately 50 nm in diameter at the tip. In the reconstructed 3D atom maps, iron and oxygen atoms are denoted by pink and cyan dots, respectively.

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The stoichiometric fraction in atomic percent of oxygen in hematite, magnetite, and wüstite are 60% (3/5), 57.1% (4/7), and 50% (1/2), respectively, as derived easily from the oxygen/(oxygen + metal) stoichiometric ratio. A quantitative analysis of the APT data reveals that the observed ratio of oxygen to iron generally decreases as the oxidation state of the iron oxide decreases, as summarized in figure 1(a), but always falls short of the ideal ratio by a factor that sensitively depends on the measurement parameters. During field evaporation, there is a preferential loss of oxygen atoms compared to iron atoms, resulting in a decrease in the O-to-Fe ratio, a phenomenon documented in the analysis of various other oxides and nitrides [13, 33–36]. We ignore the overlap of O2++ and O+ as a possible loss channel of oxygen as it was shown to be negligible by Bacchev et al [35] The highest oxygen concentrations observed in each sample are approximately 55, 52, and 45 at.%, representing a loss of approximately 5 at.% of oxygen across the three oxides. Notably, there is an overlapping range of oxygen concentrations between 50–52 at.% for hematite and magnetite samples, as well as between 47–43 at.% for magnetite and wüstite.

To facilitate comparison and enhance the reproducibility of our experiments, we chose to map the experimental parameters by measuring the charge-state ratio (CSR) of Fe. The CSR is defined as the ratio of the number of ions in the peak of ⁵⁶Fe⁺ to the number of ions in ⁵⁶Fe⁺⁺. While acknowledging its imperfections as a descriptor [37], the CSR serves as an indication of the electrostatic field intensity near the field emitter, with higher laser energy resulting in lower electric fields (e.g. lower CSR). Figures 1(b)–(d) depict the oxygen contents in hematite, magnetite, and wüstite, respectively, plotted against the CSR. Notably, the oxygen contents increasingly deviate from the stoichiometric compositions as the field (and CSR) increases. The observed decay in oxygen with intensity of the electrostatic field is consistent with previous reports [13, 15].

To complement the experimental findings on molecular ion dissociation, we have employed DFT calculations to perform energetic analyses. The purpose of the DFT calculation was to highlight that some fragmentation pathways with neutral products are energetically favorable from a ground-state perspective, and thus could occur from a quasi-thermalized initial state. We do not consider any dynamical effects as done in [11] for ZnO crystals. We considered all experimentally identified (ranged) molecular ion and theoretically possible combinations. A comprehensive scan over all possible spin configurations was undertaken to identify the most stable spin state of the molecule. Systematically varying spin multiplicities allowed us to determine the relative stability of different spin states. The spin state with the lowest energy was designated as the most stable configuration for the molecule. Detailed results, encompassing formation energies and ionization energies of the most stable spin state, are provided in the supplementary material (table S1). For the formation energies the chemical potential of Fe, O and H in Fe₂O₃, O₂ and H₂ molecules are chosen as reference. With formation energy then being ${E_f} = {\text{ }}{E_{\text{DFT}}} - {n_s}{\mu _s}$, where $n$ and $\mu$ correspond to the number and chemical potential of each element $s$=(Fe, O, H) found in the molecule. Using these energies, we explored all energetically possible dissociation reactions for each molecular ions in charge states + and ++. Of course, molecular ions could evaporate in vibrationally or electronically excited states, thereby enabling additional fragmentation pathways. Yet, exploring which excited states are likely to occur—possibly as a function of experimental parameters—is beyond the scope of the present work. Our predicted fragmentation patterns are thus a subset of possible reactions.

Supplementary figure S2 illustrates the energies of 369 dissociation reactions constructed from DFT, with 65 reactions exhibiting negative energies, which indicates the metastability of the parent molecular ion with respect to the daughter ions (m₁, m₂). Table 1 provides a comprehensive compilation of the fragmentation energies of dissociation pathways observed in the experiments and those predicted by DFT to be likely to occur. By analyzing the dissociation energies associated with each pathway, we gain valuable insights into the energetics and the relative stability of their different fragmentation products. Across all oxides, two reactions involving the production of neutral O₂ are observed experimentally and predicted to have a negative reaction energy from DFT.

In figure 2(a), we illustrate one such reaction FeO₂ ⁺ → Fe⁺ + O₂ (reaction 1 in table 1), with ΔE = − 0.19 eV. The trace of this reaction is plotted with a dashed red line on the correlation histogram constructed from the Fe₂O₃ dataset. The detection of neutrals is discussed below. Figure 2(b) showcases another neutral oxygen emitting reaction, FeO₃ ⁺ → FeO⁺ + O₂ (reaction 4 in table 1), with ΔE = −1.1 eV. The traced reactions exhibit a slight deviation from the track observed experimentally. The reaction track aligns correctly if two H are added to the parent molecular ion. However, reaction involving two H is predicted to be positive from DFT for ground states. It is not clear from the current study whether any dissociation from excited states containing two H would be favorable. The hydrogen less reaction fits well for Fe₃O₄ dataset. One possible explanation is that the thermal pulse provided by the laser creates a surface configuration favorable for the field evaporation of FeO₂ ⁺ and FeO₃ ⁺. The time taken for the formation of such configurations leads to consistent delayed field evaporation of these ions. This can lead to increased mass-to-charge value for the parent, as evidenced from the experiment, indicating that mass-to-charge adjustment should be done only for the parent ion in both reactions. Further exploration of reasons for the deviation is not undertaken in this study.

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For both reactions, the counts along the track are extracted from the histogram and are plotted in figures 2(c)–(d). Both these reactions produce a relatively low cumulative count of 162 and 110, respectively, and this number of neutrals cannot fully explain the loss of oxygen or the underestimation of oxygen from these oxides. However, for neutral molecules to be detected by the multi-channel plate detector, they must possess a minimum kinetic energy. Research has demonstrated that ions with kinetic energy below 2 keV gradually diminish the electron cascade signal at MCPs, leading to reduced detection efficiency rather than registering as an event [38]. Consequently, neutrals produced from the dissociation of the parent molecular ions near the tip might not be registered, as the daughter neutral molecules may not have acquired sufficient kinetic energy for detection. This limitation is evident from the counts extracted from the track, where the cumulative hits reach a plateau (see figures 2(c) and (d)). There is also clear evidence of plateau like regions in figures 2(c) and (d), this indicates a consistent delayed dissociation of the parent molecular ion. Such features have been researched and attributed to emission of parent ions in an excited state which can survive for longer times [39], which later switch to the ground state. DFT studies shown here do not consider these effects.

Neutral molecules may additionally evade detection if their projected impact falls beyond the physical limits of the detector [15]. In a dissociation involving a neutral product, the charged molecular ions are consistently closer to the detector center compared to the neutral molecules. This is attributed to the compression of electric field lines caused by the shank of the specimen. Following dissociation, the neutral molecule is no longer guided by the field lines and its impact is consistently farther from the center of the detector than the charged ions. This is clearly illustrated in figures 2(e) and (f), where the impact positions of pairs corresponding to the reactions are displayed on the detector event histogram. The impact positions of each pair are color-coded based on their mass-to-charge difference, and an arrow is drawn from the lighter of the pair to the heavier ion's impact position. Most arrows for the reactions point outward, indicating that neutral molecules indeed impact outside the charged ions. This is shown schematically in figure 3. This results in a cutoff in the launch angle of ions from the tip, corresponding to the physical size of the detector, where dissociations leading to a neutral impact position outside the detector are not registered.

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Lastly, our observations indicate that crystallographic facets play a pivotal role in determining the viability of specific dissociations. Notably, Fe₂O₃ has a rhombohedral centered hexagonal crystal structure, which is distinct from FeO and Fe₃O₄ showing a cubic lattice system. This results in variations in field distribution and the dissociation region on the surface. In figures 4(a)–(c), detector event histograms for each oxide are overlaid with the impact positions of dissociation products corresponding to reaction 4. Across all oxides, the impact positions are closely spaced, and the mass-to-charge ratio difference (median ≈ 18 amu) is smaller compared to reaction 1 displayed (median ≈ 130 amu) as seen from figures 2(e) and (f). This suggests that dissociation in reaction 4 occurs much closer to the detector across all analyzed oxides.

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Another distinction lies in the distribution of the dissociation products on the detector, which is contained in a small annular region for Fe₂O₃ and FeO. However, this distribution is relatively homogenous for the Fe₃O₄. The detector event histogram (shown as gray-scale background in figures 4(a)–(c)) suggests a low density of hits for Fe₂O₃ in the center, indicating a low field region. For Fe₃O₄ and FeO, the detector event histograms are more uniform, suggesting a homogenous field distribution. To validate the field distribution, we have also plotted the histograms of events corresponding to H ions (m/n ⩽ 3 amu) in figures 4(d) and (e). Total number of ions corresponding to each dataset are also shown. In Fe₂O₃, the hotspot of hydrogen impact positions on the detector indicates field inhomogeneity. This suggests an effect of crystallographic direction, leading to an inhomogeneous field or the adsorption of gas atoms. Consequently, this causes the preferential emission of FeO₃ ⁺ from certain crystallographic poles.

We can infer that for these oxides the dissociation reactions leading to neutral molecules are impacted by the electric field, the crystallographic orientation of the tip, and possibly the impact of thermal profile (for creating certain configurations, as indicated by consistent increase in m/n of parent molecular ions). Further insight was gained by analyzing mass spectra obtained from the low-density (inner, low field) and high-density (outer, high field) regions of the detector event histogram of Fe₂O₃. The mass spectra, depicted in supplementary figure S4, reveal that the high-field region mass spectrum includes additional peaks corresponding to heavier molecular ionic such as Fe₂O₃ ⁺, Fe₂O₂ ⁺ and FeO₄ ⁺. Our DFT calculations predict that some of these molecular ions should dissociate, as shown in supplementary table S2. The dissociation products then contribute to the molecular ions involved in further dissociating into neutrals, as illustrated in figure 2.

Beyond dissociations resulting a neutral, we also observed dissociation reactions into two charged, oxygen-containing molecules. These reactions are overlaid on each oxide's correlation histogram, as shown in supplementary figure S3. Dissociations involving charged ions manifest as curved lines with negative slopes on the correlation plot. One endpoint lies on the diagonal at the mass-to-charge ratio of the parent ion and corresponds to a late dissociation. The other endpoint occurs if the ion splits early on and yields coordinates corresponding to the fragmentation products. Since the reaction products in between these endpoints end up in the tails of the 1D mass spectrum, they are not accurately ranged. All the correlation histograms also exhibit strong correlation events during the tail of laser pulsing, leading to diagonal lines emanating from hotspots of corresponding correlated mass-to-charge ratios, which are also not correctly ranged. The fraction of multiple events in these oxides is significant, ∼55% in FeO, ∼51% in Fe₂O₃, and ∼54% in Fe₃O₄. Such a high fraction of multiples can introduce compositional biases due to improper ranging. Additionally, loss due to detector pile up is a possibility [40–42]. We have seen an increased propensity of oxygen to be detected as multiples as part of O⁺ and O₂ ⁺⁺ peaks. This seen for Fe₂O₃ and Fe₃O₄ oxides, as shown in supplementary figure S6. The effect of detector pile-up can be quantified by using the differences between measure and known isotopic abundance ratios [41, 42].

Understanding the kinetics of iron reduction using hydrogen as an alternative reductant has been initiated by analyzing the microstructure and local chemistry of the ores at atomic-scale levels, such as through APT. During this process, the reduction proceeds from iron-ore hematite (Fe₂O₃) to magnetite (Fe₃O₄), then to wüstite (FeO), and finally to metallic iron (Fe). The mass loss due to the FeO to Fe transition is significant, and the sluggish reduction of the FeO becomes the dominant process. The final reduction step consistently generates non-stoichiometric oxides [43]. Revealing the effect of the presence of these pseudo-phases on the most sluggish step (i.e. wüstite reduction) is crucial for a thorough understanding of the reduction kinetics. However, this is rarely reported due to the detection resolution limits in most studies, which were conducted at the macro- and/or micro-scale rather at the near-atomic-scale [21]. Therefore, precise atomic compositional information of O must be provided to identify which stable/unstable oxides are present. However, a challenge arises as O depletion occurs during field evaporation of oxides; neutral O atoms do not contribute to the detector signal leading to apparent O loss, which means measurements of FeO phases could be mis-interpreted as meta-stable Fe_1−xO.

As described above, the determination of iron ores reduction from APT can be significantly affected by the measurement parameters of APT. For instance, considering CSR of Fe combined with the simulation results, it could provide insights into the field strength and the corresponding reduction state. As-received commercial iron ores were subjected to reduction using pure hydrogen gas in a custom-designed furnace at 700 °C for durations of 1, 5, and 120 mins (see the Methods). The pristine and H-reduced sample were prepared into APT specimen, with a focus on targeting the surface sites during specimen preparation, and subsequently measured with APT. After 120 min of reduction, the ores fully transformed into iron (O < 0.07 at.%). However, after the 1 min hydrogen reduction process of the commercial iron ore, the O level dropped to approximately 45%. It remains unclear whether this decrease resulted from partial reduction or the influence of laser energy. Additionally, following the 5 min hydrogen reduction process, two distinct phases with different O contents were detected. The first phase from the 5 min reduced sample contains approx. 45 at.% O while the second phase contains approx. 37 at.% O. However, solely based on the O ion counts from the acquired data, both the first and second phases might be misinterpreted as pseudophases of wüstite, since their correspondence cannot not be definitively determined without considering the fields that influence the O measurement.

Although the specimens were measured with the same laser pulse energy, each specimen experienced different field conditions depending on their geometry and corresponding field factor [44, 45], leading to different CSR. The O concentrations versus Fe⁺⁺/Fe⁺ CSR from each H-reduced sample were plotted along with the references of the hematite, magnetite and wüstite sample (see figure 5(a)). The as-received sample (iron ores) aligned with the hematite (red line) while the 1 min reduced sample (marked as 2) was closer to the magnetite regime (green). The two different phases (marked as 3 and 4) detected in the 5 mins reduced sample corresponded to magnetite and a lower wüstite regime, suggesting that the second phase is a partially reduced wüstite phase. From our previous discussion, we observe significant differences in the neutral dissociation reactions of hematite when compared to magnetite and wüstite, which behave similarly. This can be ascribed to different crystal structure and electrostatic field conditions. This gives us more confidence to associate the third phase to partially reduced wüstite. Similar trends were observed when plotting the O⁺/O₂ ⁺ CSR against O level in figure 5(b) [46, 47].

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A comprehensive investigation of the various measurement parameters with theoretical dissociation reactions is imperative to guarantee measurement precision in APT analyses of oxide materials. This empirical methodology is vital for both advancing the understanding of APT and its application in material characterization. A meticulous assessment of relevant factors, such as laser pulse energy (e.g. field strength), is essential to ensure the acquisition of reliable and meaningful concentration maps, which is a prerequisite for the analysis of new materials. The correlated event analysis shown here works only for instruments with no energy compensation mechanisms i.e., straight flight path machines. The Invizo 6000 series by CAMECA expands the field of view, thereby enhancing the detection of neutral atoms in oxides [48]. It is crucial to consider the location of dissociation concerning any additional lenses utilized. When molecular ion dissociation occurs nearer to the tip, neutral loss can still happen if the impact lies beyond the detector's range. However, with the Invizo 6000 series, dissociation along parallel field lines can increase the likelihood of detection. Any potential corrections based on the findings in this manuscript would require meticulous scaling in accordance with detection efficiency and loss channels.