# A Reference Hydride Ratio Method for the Resolution of Al/Fe Peak Overlapping in Atom Probe Tomography Experiments

Aidar Zakirov, Yann Le Bouar, Frédéric Fossard, Williams Lefebvre

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Aidar Zakirov, Yann Le Bouar, Frédéric Fossard, Williams Lefebvre. A Reference Hydride Ratio Method for the Resolution of Al/Fe Peak Overlapping in Atom Probe Tomography Experiments. Microscopy and Microanalysis, 2025, 31 (3), pp.ozaf030. 10.1093/mam/ozaf030. hal-05233956

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# A reference hydride ratio method for the resolution of Al/Fe peak overlapping in Atom Probe Tomography experiments

A. Zakirov¹, Y. Le Bouar², F. Fossard², W. Lefebvre¹

¹ Univ Rouen Normandie, CNRS, INSA Rouen Normandie, Groupe de Physique des Matériaux UMR 6634, 76000 Rouen, France

²Université Paris-Saclay, ONERA, CNRS, Laboratoire d'étude des microstructures, 92322 Châtillon, France

## Abstract

Precise Fe concentration measurements are essential to understand the kinetics of precipitation and evolution of mechanical properties in Al-Fe alloys. Moreover, with the increase proportion of recycled metals, it is mandatory to rely on techniques capable of tracking impurities in Al-alloys to elucidate their effects on microstructure and properties. Atom Probe Tomography is a powerful material analysis tool capable of precise composition measurements. As it relies on time-of-flight mass spectrometry, the quality of the composition measurements is highly dependent on the proper peak identification and solving peak overlapping. The complexity of peak decomposition multiplies if molecular ions such as hydrides or oxides are present in the mass spectrum. Al-Fe is one of these systems, where three out of four peaks of Fe isotopes are overlapping with Al, AlH and AlH₂ mass intervals. To solve this complex peak overlapping case, an approach has been developed here. It is based on acquiring the Al-hydride formation ratio from APT analyses of standard materials, where no overlap with Fe peaks is observed. This simple method aims to improve the precision of Fe concentration measurements in Al-Fe system.

## Keywords

Atom Probe Tomography, Peak Decomposition, Aluminum Alloys, Hydrides

## Introduction

Al is an important industrial material due to its light weight, low-cost, high oxidation and corrosion resistance and high electric conductivity (ASM Handbook Committee 1990). To improve mechanical properties, various alloying elements are usually added to Al (Murashkin et al. 2023; Nie 2014). Fe has until recently been little used as an element for precipitation hardening in Al-alloy. Fe is mostly an impurity inherited from the minerals from which Al is extracted (bauxite mostly) (Donaldson & Raahauge 2016). In cast and wrought aluminum alloys, Fe atoms form intermetallic compounds (Narayanan et al. 1994; Westengen 1982), leading to alloy embrittlement. Furthermore, Fe content in recycled aluminum is higher than in primary Al and its
interaction with other elements may lead to the multiplication of intermetallic compounds and to increased embrittlement (Görner 2009; Raabe et al. 2022).

Nevertheless, owing to the emergence of innovative solid-state processing (Medvedev et al. 2018) or to the extremely fast cooling rates achievable via additive manufacturing (Hooper 2018; Kotadia et al. 2021), it becomes possible to form Al-solid solutions supersaturated in Fe. Owing to the low solubility limit of Fe in Al-matrix (0.05 wt.%), application of Fe as an element to produce precipitation hardening in Al-alloys can now be foreseen in addition to solid-solution hardening (Shuai et al. 2021; Wu et al. 2022). Fe-rich precipitates are typically $Al_6Fe$ and $Al_{13}Fe_4$ (Ding et al. 2019; Medvedev et al. 2018; Shuai et al. 2021; Wu et al. 2022). Generally, to evaluate composition and number density of large precipitates techniques such as X-Ray diffraction (XRD) and Transmission Electron Microscopy (TEM) are used. Meanwhile, to precisely evaluate the effect solid solution hardening, meticulous composition measurements should be performed. To do so Atom Probe Tomography (APT) is the most appropriate microscopy technique.

APT is a destructive quantitative material analysis tool that provides a three-dimensional (3D) reconstruction of an analyzed volume at the atomic level (Gault et al. 2012; Larson et al. 2013; Lefebvre-Ulrikson et al. 2016; Miller & Forbes 2014). APT combines the ability to reconstruct objects in small volumes (generally $10^{-4}$ to $10^{-3}$ cubic micrometers), with a rare chemical sensitivity (down to parts per million) (Gault et al. 2021). In APT experiments, chemical composition data is obtained from a mass-to-charge ratio spectrum (further referred to as mass spectrum for simplicity). For the Al-Fe system however, detailed measurement of Fe concentration by APT is limited by the occurrence of peak overlapping. Indeed, three out of four isotopes of Fe ($^{54}$Fe, $^{56}$Fe and $^{58}$Fe) are superimposed on the mass spectrum with $AlH$, $AlH_2$ and Al (peaks at 27, 28 and 29 Da respectively). To obtain a reliable measurement of Fe content within the Al-matrix, assumptions have to be made to apply a peak decomposition Insofar as Al presents a single isotope and as the ratio between $AlH^+$, $AlH_2^+$ and $Al^+$ is not known, there is no possibility to identify which proportion of the main isotopes of Fe contribute to these peaks.

In this article, a simple approach is presented to solve peak overlapping which is inspired by the methodologies generally adopted in geology community (Gopon et al. 2022). It is based on the comparison with measurements on a standard material. The method is applied to a binary Al-4wt%Fe alloy prepared by additive manufacturing. In this alloy, the Laser Powder Bed Fusion (L-PBF) process results in solidification far from equilibrium, which can lead to solute trapping (Smith & Aziz 1994). As a result, the composition of the phases may differ significantly from that expected at equilibrium. In particular, the aluminum solid solution may contain an iron concentration well above the solubility limit, resulting in significant solid solution
strengthening (Uesugi et al. 2006). Measuring the Fe composition in this alloy is therefore essential for the understanding of its mechanical behavior.

## Materials and Methods

An Al-4Fe sample was produced during a research project at ONERA by L-PBF process in the shape of a cylinder of 46 mm in height and 11 mm in diameter. The nominal composition of the powder is 4 wt.% of Fe and Al in balance. The average composition of the as-built sample, measured by Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) is given in Table 1. The microstructure of the as-built Al-4Fe samples is multi-scale (Cook & Murphy 2020): it is characterized by melt pools about 200 microns wide wherein elongated grains have solidified. Inside the grains, a cellular structure is formed, ranging in size from 1 micron at the edge of the melt pool to about 50 nm inside the pool.

<table><caption>Table 1 - Bulk compositions of investigated Al alloys. Values given in weight and atomic percents (Lefebvre et al. 2021; Neyco 'Vacuum Deposition Grade Pellets').</caption><thead><tr><th>Material</th><th>Unit</th><th>Al</th><th>Fe</th><th>Zr</th><th>Mg</th><th>Si</th><th>Mn</th><th>Other</th></tr></thead><tbody><tr><td rowspan="2">Al-Fe</td><td>wt. %</td><td>95.29</td><td>4.39</td><td>-</td><td>-</td><td>0.19</td><td>0.07</td><td>0.06</td></tr><tr><td>at. %</td><td>97.58</td><td>2.17</td><td>-</td><td>-</td><td>0.18</td><td>0.04</td><td>0.03</td></tr><tr><td rowspan="2">Al-Zr</td><td>wt. %</td><td>99.25</td><td>0.24</td><td>0.39</td><td>-</td><td>0.02</td><td></td><td>0.09</td></tr><tr><td>at. %</td><td>99.64</td><td>0.12</td><td>0.12</td><td>-</td><td>0.02</td><td></td><td>0.09</td></tr><tr><td>Pure Al</td><td>at. %</td><td>99.999</td><td>1.5x10<sup>-4</sup></td><td></td><td>0.45x10<sup>-4</sup></td><td>2.6x10<sup>-4</sup></td><td></td><td>3.5x10<sup>-4</sup></td></tr></tbody></table>

The first reference for Al-matrix consists in APT data sets obtained from an Al-Zr alloy. The Al-Zr sample was produced by combined casting and rolling (C-R). Then, the sample was prepared in the shape of a thin disk which was subjected to high pressure torsion (HPT) by Prof. Tatiana S. Orlova at St. Petersburg State University (Lefebvre et al. 2021; Mohammadi et al. 2021; Orlova et al. 2019, 2018). Further, the sample underwent a heat treatment (HT) at 230 °C for 3 hours. During the HT, due to the high concentration of vacancies created during HPT and to the small grain size, Al<sub>3</sub>Zr precipitates are mainly formed at grain boundaries and the Al-matrix is depleted in Zr (Lefebvre et al. 2021). Finally, a pure Al specimen is also analyzed as a standard material. It was produced by "Neyco Vacuum and Materials" by vacuum deposition. The purity given by the manufacturer us 99.999% (Neyco, 'Vacuum Deposition Grade Pellets'). The bulk compositions in weight and atomic percentages of all studied alloys are shown in Table 1.
APT experiments were performed on a CAMECA LEAP 5000 XR atom probe using high-voltage (HV) mode at a temperature of 40 K. Pulse repetition rate (PR) and pulse fraction (PF) are set to 250 kHz and 20 % respectively. The detection rate was set to detect from 3 to 5 ions per 1000 HV pulses (i.e. 0.3 to 0.5 %). APT specimen preparation was done with a Thermo Fisher Helios 5 PFIB DualBeam microscope equipped with focused ion beam (FIB) setup. For the first step of data mining, a commercial Integrated Visualization and Analysis Software (IVAS) software (version 3.8.16) is used to create a 3D reconstruction. Reconstruction parameters are adjusted to fit angles between crystallographic poles and interplanar distances of APT reconstruction with a reference values (Gault et al. 2012). Further, GPM_3dSAT software developed at the Group de Physique de Materiaux (IDDN.FR.001.430017.000.S.P.2020.000.10000) is used to perform chemical composition measurements.

The solidification velocity at the edge of the melt pool is lower than that in the inner region. Therefore, iron atoms are expected to be trapped to a greater extent in the inner region than at the edge. Consequently, it is decided to study these regions separately. The edge of the melt pool, located at the interface between two melt pools, is now referred to as the interface region (I). For simplicity, the inner region of the melt pool is now referred to as the melt pool (MP).

As mentioned before, the composition data of APT experiment is extracted from a mass spectrum. The position of ions on mass spectrum is set as atomic mass divided by charge state of each ion. This means that $ ^{56}Fe^+ $ will be positioned at 56 Da, and $ ^{56}Fe^{++} $ will be located at 56/2=28 Da. Lighter and heavier ions may be evaporated in different charge states and hence potentially having the same mass-to-charge ratio, and therefore being located in the same area of mass spectrum ( $ ^{27}Al^+ $ and $ ^{54}Fe^{++} $ at 27 Da). Al exists as a single isotope, therefore the peak decomposition should be based on Fe. Additional complexity comes with the detection of Al-hydrides (AlH and $AlH_2$), which both overlap with Fe isotopes ( $ ^{28}AlH^+ $ / $ ^{56}Fe^{++} $ and $ ^{29}Al_2H^+ $ / $ ^{58}Fe^{++} $). This is what is showcased by the APT experiments detailed hereafter.

## Results

Two lift-outs from each region of interest (I and MP) are performed (Fig. 1). From each lift-out five or six APT needles of Al-Fe alloy are prepared.
<figure><img src="image_2.png" /><figcaption>Fig.1 - Scanning Electron Microscopy (SEM) images of lift-out areas. (a) Melt pool interface. (b) Inside of melt pool.</figcaption></figure>

In both regions of interest, several Fe-rich regions are intercepted, which are most likely cell boundaries but could also be Fe-rich precipitates. Due to their size, these iron-rich regions are usually only partially intercepted by APT volumes. Therefore, their number density and volume fraction cannot be determined quantitatively with APT and another technique such as TEM should be used. Also, the scale of bulk metallurgical heterogeneities is larger than the total size of studied volume (~10⁻³ cubic micrometers), and therefore, bulk composition cannot be quantitatively measured with APT. Hence, the term "global" will be used to describe an entire APT volume, and the term "matrix" will be used to describe a region excluding Fe-rich regions. Typical examples of APT reconstructions obtained with this material are presented in figure 2. Only a thin slice (10 nm) of the volume is given to limit the effect of coincidence between Fe-rich regions and Al-matrix.

Among the maps presented in figure 2, only one allows representing only Fe ions (on the right). All others are built with a mass interval eventually selecting both Fe and Al ions. However, we clearly distinguish two types of regions: Fe-rich regions and the Al-matrix. What is more interesting is that the majority of ions selected at 28 Da are associated with Fe-rich regions, and are therefore most likely Fe ions in reality. On the contrary, ions selected at 29 Da are not associated with precipitates and are more abundant in the Al-matrix. Nevertheless, owing to the very low solubility of Fe in the Al-matrix, it is mandatory to establish a reliable methodology of peak decomposition to extract Fe ions from AlH⁺ in the Al-matrix.
<figure><img src="image_3.png" /><figcaption>Fig. 2 - Atom maps from an APT experiment performed on the Al-Fe alloy. This tip is lifted-out from a region inside a melt pool. The slices are ten nanometers in thickness.</figcaption></figure>

A common way to obtain chemical composition from the APT experiments is to employ the commercial Cameca software (IVAS®, AP Suite). Unfortunately, to the authors' knowledge, the detailed procedure of the peak decomposition procedure performed by the commercial software is not publicly available. A detailed custom procedure for peak decomposition has been proposed by London and is accessible via a MATLAB® script named AtomProbeLab (London 2019). This script was applied to six APT experiments in the present study. From this method, the predicted Fe concentration inside the Al-matrix ranges from 0.04 to 0.35 at.%. Furthermore, for one of the volumes, the script gave a wide range of uncertainty - the predicted value of 0.17 at.% with the lower bound of 0.03 at.% and the higher of 0.31 at.% of Fe. For the particular case of Al-Fe system, the use of AtomProbeLab script is found to be inappropriate. Hence, it was decided to use a simple peak decomposition approach based on the natural abundances of the isotopes. The natural abundances of Al and Fe isotopes are given in Table 2 (de Laeter et al. 2003).
<table><caption>Table 2 - Natural abundances of Al and Fe isotopes in 27-29 Da range of mass spectrum (de Laeter et al. 2003).</caption><thead><tr><th>Da</th><th>Al<sup>+</sup></th><th>Fe<sup>++</sup></th></tr></thead><tbody><tr><td>27.0</td><td>100</td><td>5.85</td></tr><tr><td>28.0</td><td>-</td><td>91.75</td></tr><tr><td>28.5</td><td>-</td><td>2.12</td></tr><tr><td>29.0</td><td>-</td><td>0.28</td></tr></tbody></table>

The simple peak decomposition approach is to calculate the number of Fe ions in the overlapping peaks (27, 28, 29 Da) from the isotopic abundance in comparison with unbiased peak <sup>57</sup>Fe<sup>++</sup> at 28.5 Da. For example, the number of Fe ions in the main peak at <sup>56</sup>Fe<sup>++</sup> is (Gault et al. 2012):

$$nb.ions^{++}_{56}Fe = (nb.ions^{++}_{57}Fe/abun^{++}_{57}Fe) * abun^{++}_{56}Fe$$

where *abun* stands for the abundance of the isotope considered and *nb.ions* is the number of ions of the isotope in the mass interval considered. It should be mentioned that some amount of Fe in a single-plus charge is also observed (Sup. fig. 1). Yet, the number of counts of <sup>56</sup>Fe<sup>+</sup> (56 Da) is around twice the number of counts of <sup>57</sup>Fe<sup>++</sup> (28.5 Da). Based on the natural abundances, the ratio of Fe evaporated in a single-charge state is around 5% of the total number. Therefore, the peak decomposition procedure for Fe in two-plus charge state is essential.

The straightforward procedure peak decomposition procedure is accurate if the non-overlapping peaks have a high abundance or if the total concentration of the element of interest is high. None of these conditions are fulfilled for the analysis of Fe in the Al-solid solution. Additionally, it should be noted that a high fraction of multi-hit events can limit the accuracy of the chemical composition measurements (Meisenkothen et al. 2020). The fraction of single-hit events is above 90 percent for pure Al, Al-Zr and Al-Fe alloys.

In figure 3, mass spectra containing one million ions each are plotted for comparison in the interval of Al-hydrides for pure Al, Al matrix of Al-Zr, Al-matrix of Al-Fe MP and global volume of Al-Fe MP. Mass spectra of each condition separately are available in supplementary data (Sup. fig. 2).
<figure><img src="image_4.png" /><figcaption>Fig. 3 - (Left) Section of mass spectrum of pure Al, matrix of Al-Zr, matrix of Al-Fe MP and global volume of Al-Fe MP. The size of selected volumes is one million ions. (Right) Close-up of the peak at 28.5 Da. Alloys are analyzed in the same conditions (T=40K, HV, 250kHz repetition rate, 20% pulse fraction).</figcaption></figure>

<figure><img src="image_5.png" /></figure>

As we can see from figure 4, in the case of the Al-matrix of Al-Fe MP, a small number of ions are found at 28.5 Da due to the low natural abundance of $^{57}$Fe$^{++}$ (2.12 %), which makes noise subtraction unreliable. At the same time, we can see that the number of ions at 28 Da is larger in Al-Fe MP than in pure Al, because it overlaps with the main peak of $^{56}$Fe$^{++}$. In addition, the height of the peak at 29 Da is similar for pure-Al and Al-Fe MP matrix, because the abundance of $^{58}$Fe$^{++}$ isotope is very low (0.28 %).

<figure><img src="image_6.png" /><figcaption>Fig. 4 - Slices of atom maps for ions ranged at 27, 28 and 29 Da. Thickness of slices is 10 nanometers. All APT experiments were performed in the same conditions, namely: T=40 K, HV mode (RR=250 kHz, PF=20%). (a) Pure-Al. (b) Al-matrix of Al-Fe MP case. (c) Global volume of Al-Fe MP containing Al<sub>13</sub>Fe<sub>4</sub> regions.</figcaption></figure>
Considering the distribution of ions on the atom maps in Fig. 2 and the respective heights of peaks on the mass spectra (Fig. 3), it is concluded that peak at 29 Da is fully composed of AlH<sub>2</sub> ions. Therefore, it should have the same intensity in the case of pure Al and Al-matrix of Al-Fe. At the same time slightly more ions are detected at 29 Da in the case of Al-Zr. Yet, number of events in the peak at 28 Da is also larger in that alloy. The potential reason for a higher fraction of Al-hydrides in Al-Zr alloy is the affinity of H to Zr atoms (Jenkins et al. 2023). Indeed, a higher number of H and H<sub>2</sub> counts are observed in Al-matrix of Al-Zr than in pure Al (Sup. fig. 3).

In order to propose an alternative method for identifying the respective contribution of Fe and Al-hydrides in overlapping peaks, it is suggested to evaluate how the relative proportions of AlH⁺ and AlH₂⁺ peaks vary for standard Al alloys. The first choice is an Al-Zr system, which was already analyzed earlier. Based on the OES measurements (Table 1) Al-Zr alloy contains 0.12 at. % of Fe. Yet, no peaks related to Fe (28.5, 56 and 57 Da) are observed with APT (Sup. fig. 4). Therefore, it is considered that Al-matrix of Al-Zr alloys is Fe-free. Further, a proper standard of a pure Al is also analyzed. Before going further with calculation, we should check that Al-hydrides are distributed in a random way inside the APT volumes. Additional top-view atom maps are represented in figure 4. From these maps, we can see that distribution of <sup>27</sup>AlH+, <sup>27</sup>AlH+ and <sup>27</sup>AlH<sub>2</sub>⁺ ions are also dependent on the local crystallography. For example, we can see less Al-hydrides around low-index pole [111]. In the case of Al alloys prepared by FIB, several poles are always located inside the volume. To limit the user-related bias associated with the selection of ROI less affected by zone lines and poles, we decide to work around the whole APT volumes. The result of a student's test on the volume-to-volume distribution of <sup>27</sup>AlH⁺ / <sup>27</sup>AlH<sub>2</sub>⁺ ratios randomly split in two categories for both Al-Zr and pure Al show that there is not statistically meaningful difference between tips with different crystallographic orientations.

The standard materials and the Al-Fe system are analyzed in APT, while paying attention to keep the same acquisition parameters (HV mode, RR=250 kHz, PF=20 % at T=40 K). To confirm that evaporation conditions are akin between Al-Fe and standard materials, an estimation of post-ionization field based on Kingham curves is performed (Fig. 5).
<figure><img src="image_7.png" /><figcaption>Fig. 5 - Kingham curve for pure Al replotted from the literature (Gault et al. 2012; Kingham 1982). Pure Al, matrix of Al-Zr, matrix of Al-Fe I and matrix of Al-Fe MP, are represented in cyan, olive, blue and fuchsia respectively.</figcaption></figure>

As we can see from the Kingham curves in all analyzed materials, the evaporation field of Al-matrix is similar and around 19.5 V/nm. This value is close to the expected evaporation field of Al of 19 V/nm (Tsong n.d.). Detailed information is given in Table 3. At the same time, it should be noticed that the average evaporation field generally increases with the enlargement of the tip radius. In the case of two APT experiments of pure Al and Al-Zr the average evaporation field grows by around 0.2 V/nm from the beginning to the end of APT analysis (voltage ranges from 2.5 to 3.8 kV).

<table><caption>Table 3 - The average ratio of Al ions in two-plus charge state over all detected Al ions and estimation of post-ionization field based on Kingham curves.</caption><thead><tr><th>ID</th><th>Al<sup>++</sup> (13.5 Da) over all Al<br>(13.5 and 27 Da) [%]</th><th>f<sub>ev</sub> [V/nm]</th></tr></thead><tbody><tr><td>Al-Fe I</td><td>5.87</td><td>19.5</td></tr><tr><td>Al-Fe MP</td><td>6.51</td><td>19.6</td></tr><tr><td>Al-Zr</td><td>4.97</td><td>19.4</td></tr><tr><td>Pure Al</td><td>5.15</td><td>19.4</td></tr></tbody></table>

The combined data on overlapping peaks ratios of Al-matrix of all APT experiments is presented in Table 4.
<table><caption>Table 4 – The ratio of ions detected in the overlapping peaks on the mass spectra of Al-matrix. All atoms at 27 Da range are defined as $^{27}$Al$^{+}$. The error margin is given by $2\sigma$ of the volume-to-volume variations.</caption><thead><tr><th>ID</th><th>28 Da (AlH<sup>+</sup> and <sup>56</sup>Fe<sup>++</sup>)<br>over 27 Da (~Al<sup>+</sup>) [%]</th><th>29 Da (AlH<sub>2</sub><sup>+</sup> and <sup>58</sup>Fe<sup>++</sup>)<br>over 27 Da (~Al<sup>+</sup>) [%]</th><th>28 Da (AlH<sup>+</sup> and <sup>56</sup>Fe<sup>++</sup>)<br>over 29 Da (AlH<sub>2</sub><sup>+</sup> and <sup>58</sup>Fe<sup>++</sup>)</th></tr></thead><tbody><tr><td>Al-Fe I</td><td>0.33 ± 0.8</td><td>0.3 ± 0.1</td><td>1.2 ± 0.4</td></tr><tr><td>Al-Fe<br>MP</td><td>0.41 ± 0.07</td><td>0.2 ± 0.1</td><td>2 ± 1</td></tr><tr><td>Al-Zr</td><td>0.30 ± 0.05</td><td>0.5 ± 0.2</td><td>0.6 ± 0.2</td></tr><tr><td>Pure Al</td><td>0.19 ± 0.03</td><td>0.33 ± 0.03</td><td>0.6 ± 0.1</td></tr></tbody></table>

As we can see from Table 4, Al-matrix of Al-Zr and pure Al have the same ratio of $^{27}$AlH$^{+}$ over $^{27}$AlH$^{2+}$ (28 / 29 Da). It should be mentioned that with an increase of the evaporation field (simultaneous with the tip radius), the ratio between $^{27}$AlH$^{+}$ and $^{27}$AlH$^{2+}$ becomes larger (Sup. fig. 5). Yet, in the case of APT tips prepared by FIB and evaporated up to the standing voltage of 5 kV, the field related trend is below the uncertainty value of $^{27}$AlH$^{+}$ / $^{27}$AlH$^{2+}$ ratio given in Table 4. Alternatively, in the case of Al-Fe I, more ions are detected at 28 Da, meaning that the difference most likely comes from additional ions of $^{56}$Fe$^{++}$. Furthermore, even more ions are detected at 28 Da in Al-Fe MP, which confirms the hypothesis that Fe-content inside Al-matrix is not the same at the interface and inside the melt pools of Al-Fe alloy produced by additive manufacturing.

Since it is confirmed that evaporation conditions are similar enough between Al-Fe and standard materials, the Al-hydride formation from Al-matrix is considered the same. Based on this observation, a reference hydride ratio (RHR) peak decomposition approach can be proposed, which breaks down as following:

* For the first step, all ions at 29 Da are defined as $^{27}$AlH$^{2+}$ owing to the low natural abundance of $^{58}$Fe$^{++}$ (~0.3 %);

* From the ratio between $^{27}$AlH$^{+}$ and $^{27}$AlH$^{2+}$ obtained from a standard material, number of $^{27}$AlH$^{+}$ at 28 Da is calculated based on the number of ions in the peak at 29 Da ($^{27}$AlH$^{2+}$);

* All the remaining ions of the peak at 28 Da are defined as $^{56}$Fe$^{++}$;
* Further, the number of <sup>54</sup>Fe<sup>++</sup> at 27 Da is evaluated from natural abundances based on the main isotope of <sup>56</sup>Fe<sup>++</sup> at 28 Da;

* Finally, all Fe ions are summed up and Fe concentration is calculated.

The comparison of the composition measurements based on this reference hydride ratio and the conventional approaches is presented in the following section.

Discussion

As mentioned above, the aim of this study is to evaluate Fe-content in Al-matrix in two different regions of an Al-Fe alloy produced by additive manufacturing. Accurate evaluation of these values can help to understand the precipitation kinetics in Al-Fe system and to evaluate the contribution of solid solution hardening to the mechanical properties of the Al-Fe alloy.

We start by presenting the results of the global Fe content measurements for both ROIs. The range of measured Fe contents for each case is also given. Fe content of global APT volumes calculated using conventional (based on natural abundance of non-overlapping <sup>57</sup>Fe<sup>++</sup>) and reference hydride ratio approaches is shown in Table 5. The error margins are given by 2σ of the volume-to-volume variations. The possible range on Fe-contents evaluated with RHR based on the error margin of the <sup>27</sup>AlH<sup>+</sup> / <sup>27</sup>AlH<sub>2</sub><sup>+</sup> ratio is also given.

<table><caption>Table 5 - Fe concentration measurements of global APT volume. Peak decomposition using simple and reference hydride ratio approaches using hydride formation ratios of Al-matrix of Al-Zr and pure Al are given. 2σ of the volume-to-volume variations is also presented. The uncertainty of RHR approach is derived from the uncertainty of <sup>27</sup>AlH<sup>+</sup>/<sup>27</sup>AlH<sub>2</sub><sup>+</sup> ratio represented in Table 4.</caption><thead><tr><th>ROI</th><th>Type</th><th>Average [at. %]</th><th>2σ [at. %]</th><th>Uncertainty range of RHR [at. %]</th></tr></thead><tbody><tr><td rowspan="3">Al-Fe I</td><td>Simple</td><td>2.9</td><td>2.9</td><td>-</td></tr><tr><td>RHR (Al-Zr)</td><td>2.8</td><td>2.8</td><td>2.7-2.8</td></tr><tr><td>RHR (Pure Al)</td><td>2.8</td><td>2.8</td><td>2.7-2.8</td></tr><tr><td rowspan="3">Al-Fe MP</td><td>Simple</td><td>1.7</td><td>1.1</td><td>-</td></tr><tr><td>RHR (Al-Zr)</td><td>1.7</td><td>1.1</td><td>1.6-1.7</td></tr><tr><td>RHR (Pure Al)</td><td>1.7</td><td>1.1</td><td>1.7-1.7</td></tr></tbody></table>
As we can see from Table 5, all three methods give equivalent results. Overall, it is promising that both approaches lead to the same results when the non-overlapping ion $^{57}$Fe$^{++}$ at 28.5 Da has enough counts. This condition is fulfilled only for a global Fe composition of several at. %, which is not the case in the Al-solid solution.

We now consider the results of the measurement of Fe content in Al-matrix, which are presented in Table 6 in the same way as for the global volume. Here, we can see that values obtained with the simple and the reference hydride ratio approaches are different. The conventional approach underestimates Fe content in Al-matrix because the $^{57}$Fe$^{++}$ peak at 28.5 Da has a low number of counts, making it difficult to distinguish from the background. Additionally, in the range from 27 to 30 Da, the background level is increased due to the tail of the main $^{27}$Al$^{+}$ peak. Therefore, after the background subtraction the number of ions of $^{57}$Fe$^{++}$ is underestimated, and total number of Fe ions, calculated from the abundance and number of ions of $^{57}$Fe$^{++}$ is also lower than in reality. In addition, the reference hydride ratio approaches obtained with reference derived from Al-matrix of Al-Zr alloy and pure Al lead to the same results since they have the same ratio between $^{27}$AlH$^{+}$ and $^{27}$AlH$_{2}^{+}$ of 0.6. The possible range of the predicted Fe content volumes varies more in the case of Al-Zr than of pure-Al, due to the higher volume-to-volume deviation of the measured $^{27}$AlH$^{+}$ (28 Da) and $^{27}$AlH$_{2}^{+}$ (29 Da) values.

<table><caption>Table 6 - Fe concentration measurements of Al-matrix. Peak decomposition using simple and reference hydride ratio approach using hydride formation ratios of Al-matrix of Al-Zr and pure Al are given. 2σ of the volume-to-volume variations is also presented. The uncertainty of RHR approach is derived from the uncertainty of $^{27}$AlH$^{+}$/ $^{27}$AlH$_{2}^{+}$ ratio represented in Table 4.</caption><thead><tr><th>ROI</th><th>Type</th><th>Average [at. %]</th><th>2σ [at. %]</th><th>Uncertainty range of RHR [at. %]</th></tr></thead><tbody><tr><td rowspan="3">Al-Fe I</td><td>Simple</td><td>0.12</td><td>0.04</td><td>-</td></tr><tr><td>RHR (Al-Zr)</td><td>0.18</td><td>0.04</td><td>0.12-0.23</td></tr><tr><td>RHR (Pure Al)</td><td>0.18</td><td>0.04</td><td>0.15-0.20</td></tr><tr><td rowspan="3">Al-Fe MP</td><td>Simple</td><td>0.25</td><td>0.10</td><td>-</td></tr><tr><td>RHR (Al-Zr)</td><td>0.31</td><td>0.06</td><td>0.28-0.35</td></tr><tr><td>RHR (Pure Al)</td><td>0.31</td><td>0.06</td><td>0.30-0.33</td></tr></tbody></table>
**Conclusions**

Atom Probe Tomography is one of few techniques capable of composition measurements on the level of ppm. Yet, this precision depends on the quality of the applied data treatment procedure. To more accurately evaluate the Fe content in Al matrix an alternative reference hydride ratio approach based on a reference ratio of Al-hydride formation has been developed. The main conclusions are the following:

* Both pure Al and Al-matrix of Al-Zr alloy are reliable references for estimating the hydride formation ratio;

* Both conventional and reference hydride ratio approaches give the same results when working with Fe concentrations greater than 1-3 at. %;

* In the case of Al-matrix where the Fe-content is low, the conventional approach significantly underestimates the Fe content;

* The range of the predicted with RHR values of Fe-content inside the Al-matrix based on the uncertainty of the Al-hydride ratio varies by ±33% for interfacial and ±13% for melt pool areas;

* The RHR measurement approach can be used for other cases where hydrides or oxides are formed and the information about their abundances is missing. Yet, the care should be taken with the possible evolution of the evaporation conditions and consequently the hydride / oxide formation ratio through the APT analysis. The possible variation of results between tips with different crystallography orientation should be also accounted for.

**Acknowledgements**

This project was financially supported by the « Région Normandie » and the European Union through RIN Tremplin FusionSATMET project. Europe invests in Normandy with the European Regional Development Fund (ERDF).

Experiments were performed on GENESIS platform instruments supported by the Région Haute-Normandie, the Métropole Rouen Normandie, the CNRS via LABEX EMC3 and the French National Research Agency as a part of the program "Investissements d'avenir" with the reference ANR-11-EQPX-0020. This work was partially supported by the CNRS Federation IRMA - FR 3095.

The authors acknowledge the financial support of the French Agence Nationale de la recherche and LABEX EMC3 through the project HydroSATMET.

YLB and FF acknowledge the CNRS network "Microscopie Electronique et Sonde Atomique" (METSA, FR CNRS 3507) for financial support.

AZ would like to express his thanks to Samba Ndiaye for productive discussions.
The authors would like to thank Eric Grévin, Jean-Sébastien Mérot and Louise Toualbi
for fruitful discussions.

CRediT authorship contribution statement

Aidar Zakirov – Conceptualization, Investigation, Methodology, Writing-original draft;

Yann Le Bouar – Conceptualization, Funding acquisition, Supervision, Writing-review
& editing;

Frédéric Fossard – Conceptualization, Funding acquisition, Writing-review & editing;

Williams Lefebvre – Conceptualization, Funding acquisition, Methodology, Supervision, Writing-review & editing.

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported in
this paper.

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Supplementary data

<figure><img src="image_8.png" /><figcaption>Sup. fig. 1 - Sections of mass spectra in the range from 55.5 to 58.5 Da. In each case only a section of the reconstructed volume containing one million ions is selected. The APT experiments were performed in the same conditions, namely: T=40 K, HV mode (RR=250 kHz, PF=20%). (a) Al-matrix of Al-Fe alloy (melt pool area). (b) Global volume of Al-Fe MP containing Al13Fe4 precipitate.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Sup. fig. 2 - Sections of mass spectra in the range from 26.5 to 29.5 Da. In each case only a section of the reconstructed volume containing one million ions is selected. All APT experiments were performed in the same conditions, namely: T=40 K, HV mode (RR=250 kHz, PF=20%). (a) Al-matrix of Al-Zr alloy. (b) Pure-Al. (c) Al-matrix of Al-Fe MP case. (d) Global volume of Al-Fe MP containing Al13Fe4 precipitate.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Sup. fig. 3 - Sections of mass spectra in the range from 0.5 to 2.5 Da. In each case only a section of the reconstructed volume containing one million ions is selected. The APT experiments were performed in the same conditions, namely: T=40 K, HV mode (RR=250 kHz, PF=20%). (a) Pure Al (b) Al matrix of al-Zr alloy.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Sup. fig. 4 - Sections of mass spectrum of Al-matrix of Al-Zr alloy in the ranges from 27.5 to 29.5 Da and 55.5 to 58.5 Da. Only a section of the reconstructed volume containing one million ions is selected. The APT experiment was performed at T=40 K in HV mode (RR=250 kHz, PF=20%).</figcaption></figure>
<figure><img src="image_12.png" /></figure>

Sup. fig. 5 – Evolution of the Al-hydride ratio ($^{27}$AlH$^+$ over $^{27}$AlH$_2$$^+$) as a function of the ratio of Al ions detected in a two-plus charge state over all detected Al ions. The experiments were performed at the voltage range from 2.5 to 3.8 kV in the case of pure Al, and from 2.6 to 3.4 kV for Al-matrix of Al-Zr. The ratio of Al in two-plus charge state is effectively represents the average evaporation field on our sample. In these two experiment the average evaporation field grows through the depth of APT volume (effectively with increase of the tip radius)