Origins of the hydrogen signal in atom probe tomography

Atom Probe Tomography (APT) analysis is being actively used to provide near-atomic-scale information on the composition of complex materials in three-dimensions. In recent years, there has been a surge of interest in the technique to investigate the distribution of hydrogen in metals. However, the presence of hydrogen in the analysis of almost all specimens from nearly all material systems has caused numerous debates as to its origins and impact on the quantitativeness of the measurement. It is often perceived that most H arises from residual gas ionization, therefore affecting primarily materials with a relatively low evaporation field. In this work, we perform systematic investigations to identify the origin of H residuals in APT experiments by combining density-functional theory (DFT) calculations and APT measurements on an alkali and a noble metal, namely Na and Pt, respectively. We report that no H residual is found in Na metal samples, but in Pt, which has a higher evaporation field, a relatively high signal of H is detected. These results contradict the hypothesis of the H signal being due to direct ionization of residual H$_2$ without much interaction with the specimen's surface. Based on DFT, we demonstrate that alkali metals are thermodynamically less likely to be subject to H contamination under APT-operating conditions compared to transition or noble metals. These insights indicate that the detected H-signal is not only from ionization of residual gaseous H$_2$ alone, but is strongly influenced by material-specific physical properties. The origin of H residuals is elucidated by considering different conditions encountered during APT experiments, specifically, specimen-preparation, transportation, and APT-operating conditions by taking thermodynamic and kinetic aspects into account.

I. INTRODUCTION Understanding the effect that the lightest and smallest atom, hydrogen (H), has on the physical properties of materials is of paramount importance. For instance, H triggers changes in the mechanical properties of metallic materials, such as a sudden and unpredictable loss of ductility and toughness, which is commonly referred to as hydrogen embrittlement [1,2]. H also plays for instance a key role in modifying electronic properties in semiconductors [3,4].
Despite its importance, the direct imaging of H has remained extremely challenging thereby limiting our understanding of its influence on materials.
Atom probe tomography (APT) has the ability to detect all elements irrespective of their mass [5], and provides three-dimensional compositional mapping with sub-nanometer resolution [6]. This unique combination of high spatial resolution and chemical sensitivity is necessary to enable observations and quantification of hydrogen at specific microstructural features within complex materials. In recent years, these abilities have triggered a surge of interest in the use of the technique to study hydrogen [7][8][9][10].
Interestingly in APT measurements, it has been known that characteristic peaks at 1, 2, and 3 Da, corresponding to H + , H + 2 , and H + 3 species respectively, are always produced under high-fields at the surface of many metals. This was studied in detail by Tsong and coworkers in the 1980s [11] who introduced low pressures of H 2 inside of the vacuum chamber of the atom probe. Using more modern instrument setups, similar observations have been reported for metals [12], semiconductors [13,14] and insulators [15] with a signal originating either from residual gases from the chamber or H 2 from the specimen itself. The H-related peaks can be minimized by reducing the hydrogen content by heat treatment in vacuum [9], or by modifying the surface of the specimen by oxidation of the deposition of H-barrier thin films (e.g., TiN [16]).
The study of hydrogen in materials by APT has hence often involved isotope labeling, i.e., using deuterium instead of hydrogen, in order to facilitate identification of the trapping sites for hydrogen in the microstructure [17], with an emphasis on steels [7,18].
In spite of a consensual perspective that H-related species detected by APT are unavoidable, there has been a long-standing debate regarding the origin of detected H atoms.
Gaseous H 2 molecules are present within the analysis vacuum chamber even in extremely low pressure and temperature (e.g., 10 −14 bar and 90 K). These H 2 molecules can be ionized during the measurement either under the effect of only the electric field or, possibly, in combination with the laser pulse, and dissociate, leading to the detection of atomic H + ions.
This detected H is considered as noise in the analysis of the mass spectrum, having nothing to do with the actual distribution of the hydrogen within the microstructure of the sample.
Kolli hypothesized controlling the relative amplitude of hydrogen peaks in mass spectra that the hydrogen originates only from the residual hydrogen [19]. In contrast, Breen et al. proposed that a substantial fraction of the detected H was inside the specimen itself [9], in line with observations by Chang et al. [12]. There are important differences between these two mechanisms. For instance, in the former case, H is initially in the form of gaseous H 2 that becomes ionized away from the specimen's surface. In the latter case, hydrogen can be already in its atomic form inside the material or chemisorbed on the surface, and must be desorbed and ionized from the specimen surface itself, potentially following surface diffusion.
This uncertainty about the origin limits our ability to precisely quantify H concentration in materials by using APT. It is therefore necessary to enhance our fundamental understanding of the origin and behavior of H in APT in order to elucidate numerous open questions regarding H-involving mechanisms in physics, chemistry, and materials science, including hydrogen trapping or grain boundary segregation of H in the context of hydrogen embrittlement.
From a theoretical perspective, the high reactivity of H and its strong impact on the electronic structure of materials hinders theoretical investigations with approximate methods, such as interatomic potentials. The use of first-principle calculations has enabled the significant progress achieved in theoretical understanding of materials with H within the last 25 years [4,18,20]. Furthermore, the state-of-the-art approach combining density-functional theory (DFT) with ab initio atomistic thermodynamics [21][22][23][24] allows us to predict the environment-dependent (e.g., temperature and pressure dependent) binding behavior of H both on solid surfaces and in the bulk of a material employing (periodically repeated) supercells for impurities (e.g., H) contained within a finite volume of the host material. Increasing computer power and continuous improvement of the methodology facilitate a high accuracy of the predictions.
Here, we investigate the origin of the APT-measured H residuals by combining DFT calculations on a selection of metals (Na, K, Pd, and Pt) and APT experiments on pure Na, a metal with a low-evaporation field, and pure Pt, a metal with a relatively high-evaporation field. Across several datasets, the Na APT measurements exhibit no H-related peaks, in contrast to Pt. Thermodynamic analysis based on DFT calculations allows us to determine the temperature-and pressure-dependent stability of metal surfaces in contact with H gas at the relevant vacuum conditions. Our study sheds light on the origins of H residuals in APT measurements, i.e., the detected H mainly originate from H located at the metal surface, either from contamination during specimen preparation and transfer, or during the APT measurement from adsorption of residual H 2 from the chamber onto the surface and migration towards the specimen's apex, making this highly dependent on the analysis conditions. These insights are critical to further optimize experimental workflows enabling the quantification of hydrogen in materials by APT.

II. METHODOLOGY
A. APT specimen preparation from Na Performing APT analysis requires a needle-shaped specimen in order to generate the intense electrostatic field necessary to initiate the field evaporation of the surface atoms.
There are challenges inherent to the sample preparation of alkali metals (e.g., Li, Na, and K), in comparison to transition metals (e.g., Pt). Alkali metals are reactive when in contact with moisture and air (i.e., oxygen), leading to severe oxidation during the sample transfer to form NaO, which is unstable and soon reacts with H to form NaOH. These issues have so far hindered the characterization of alkali metals by APT. Here, we used a specific setup to prepare and transfer specimens that is described in detail in Ref. 25.
First, a Na sample (> 99 %, Sigma Aldrich) submerged in kerosene oil was prepared inside an N 2 -filled glovebox (Sylatech GmbH, Walzbachtal, Germany) to avoid oxidation [ Fig. 1(a)]. The Na sample was first sliced into a small piece (0.5 × 0.75 × 0.3 cm 3 ) and the piece of bulk Na was attached to a flat Cu stub with adhesive carbon tape. The stub was placed in a CAMECA cryogenic APT puck (CAMECA Instruments, Madison, USA) [ Fig. 1 Alkali metals, and particularly Na, were reported to react strongly with the Ga used in conventional FIBs [26], and the heating and radiation damage caused by the ion-beam milling can lead to melting of the sample [27]. This explains our choice of a Xe-plasma FIB to limit the ion-beam damage and the reactivity of the implanted ions, as Xe is more inert compared to Ga [28,29]. Moreover, the cryo-stage is implemented to avoid uncontrolable melting of the Na sample during the FIB process (see Fig. S1 in the Supporting Information). wedge-shaped lamella from the Na bulk was prepared using the lift-out protocol described in Ref. 30. Clean trenches were milled on the Na surface for the lift-out process. In order to prevent the condensation of gaseous platinum deposition precursor molecules from the lift-out process (e.g. methylcyclopentadienyl trimethyl platinum), the stage was warmed up to room temperature to weld the wedge onto the micromanipulator.
Scanning electron micrographs, taken at 5 kV and 1.6 nA, for each of the successive steps of the preparation are shown in Fig. 2(a-j). A low-electron-dose image was taken since the alkali material is also sensitive under electron beam (e.g., Li battery reacts with the electron beam [31]). After the milling process, no open pores or cracks were observed in the SEM and the back-scattered electron (BSE) image in Fig. 2 After the final milling, the cryo-prepared specimens were transferred from the PFIB chamber to the UHV suitcase and subsequently transferred into the CAMECA LEAP (local electrode atom probe) 5000 HR [ Fig. 1(g)]. To summarize, the overall process is shown in Fig. 1(h).
For the Pt specimen, the same protocol was conducted as for Na. The only difference was that Pt bulk was loaded through the FIB intermediate chamber, not the N 2 glovebox.

B. APT measurement
Atom probe data were acquired in laser-pulsing mode with a pulse energy of 70 pJ and rate of 50 kHz at 1 % evaporation rate by adjusting an applied DC voltage. The base temperature was set throughout the measurement to 30 K and 90 K, respectively. The Na and Pt specimens that were field evaporated at 90 K base temperature are labelled as Na 90K and Pt 90K whereas the Na specimen at 30 K is labeled as Na 30K . The chamber pressure was in the 10 −14 bar. The 3D data reconstruction, data analysis, and visualization were performed using AP SUITE software version 6.1. (VASP) [32,33] with the projector augmented wave (PAW) approach [34]. The kineticenergy cutoff employed for the plane-wave basis set is 500 eV. The generalized gradient approximation (GGA) is used for the exchange-correlation approximation [35][36][37] (see Ta-ble S1 in the Supporting Information for details of the used approximations). Electronic and ionic relaxations are carried out until the total energy convergence is less than 10 −5 eV, respectively, 10 −4 eV.
A repeated slab approach is used to study the most favorable surface planes for bodycentered cubic (BCC) and face-centered cubic (FCC) metals, specifically Na(110), K(110), Pd(111) and Pt(111). The periodically repeated slabs are decoupled by adding a vacuum region and applying the dipole correction scheme [38]. A detailed description of the computational setup for each metal surface calculation (e.g., vacuum thickness, supercell size, k-point mesh, and slab thickness) is given in Table S1 in the Supporting Information. We employ surface cells larger than the p(1 × 1) cell to account for various coverages (Θ) up to 1 ML (monolayer) (e.g., from Θ = 1/12 ML to 1 ML for H on Pt (111)). Defining the coverage as the ratio between the number of adsorbate atoms and the number of metal atoms in the top surface layer, 1 ML is reached for an equal number of adsorbate and surface metal atoms.

D. Surface thermodynamics
The binding energy of hydrogen on the metal surface, E b , with respect to a H 2 molecule is calculated as where , and E H 2 tot are the DFT calculated total energies of a metal surface with and without (i.e., of a clean metal surface) adsorbed H and the H 2 molecule, respectively. N H is the number of hydrogen atoms adsorbed on the surface.
To account for the stability of the metal surface in a H atmosphere as a function of the temperature and pressure, the change in the Gibbs free energy of each surface phase with respect to a H-free metal surface is calculated as, where µ H (T, p) is the chemical potential of hydrogen, which is a function of temperature (T ) and pressure (p), A is the area of the surface cell and S conf is the configurational entropy of the surface atoms. The later is approximated by where k B and Θ are the Boltzmann constant and the coverage of the adsorbates, respectively.
The H chemical potential [µ H (T, p)] is evaluated as follows [21,22,39], where 1 2 E H 2 tot and E H 2 ZPE are the total energy at T = 0 K and the zero-point energy of a hydrogen molecule. Our calculated value for E H 2 ZPE is 0.273 eV. ∆µ H (T, p) contains the temperature-and pressure-dependent free energy contributions. Assuming that H 2 gas behaves like an ideal gas, the temperature dependence at standard pressure (i.e., p 0 = 1 atm) is evaluated using tabulated values for enthalpy (H) and entropy (S) at finite temperature [40] and the relationship, G = H − T S.

III. RESULTS
A. Atom probe results Figure 3(a) and (b) show the 3D atom maps and corresponding mass spectra acquired from the Na 90K and the Pt 90K , respectively. All samples were in the laser pulsing mode (background levels < 10 ppm/nsec). While the Pt measurement was smooth, there were several micro-fractures during the Na measurement. We tried high voltage pulsing for both materials, however the level of background signals was higher than would be acceptable (> 1000 ppm/nsec) and the Na specimens failed after the collection of only less than 52,000 ions at a pulsed voltage of 10-percentage. The sizes of acquired dataset for Na 90K and Na 30K APT measurements were > 10 M ions. In the acquired mass spectrum of the Na 90K , strong peaks appear at 23, 62, and 63 Da correspond to Na, Na 2 O, and Na 2 OH, respectively. These peaks associated to residual -O and -OH are frequently observed in experiments following cryo-UHV transfer and can be also associated to low level of frosting on the specimens following preparation [25,41]. The composition of the whole Na 90K sample is 99.006 % Na, 0.987 % O, and 0.007 % H following peak decomposition [42]. Figure 3(c), (d) and (e) display the section of the mass spectrum for the hydrogen peaks of the analyses of Pt 90K , Na 30K , and Na 90K , each dataset containing 2.5 × 10 6 identified ions.
No peak pertaining to H species, at 1, 2 or 3 Da, is visible above the level of background in the mass spectrum from the analysis of the Na 90K plotted in Figure 3(e), which corresponds to the lowest electric field conditions across the data reported herein. For the Na 30K analysis, a small peak at 1 Da is visible, whereas for Pt, strong peaks at 1 and 2 Da are clearly resolved. reports for FCC metals [e.g., Pd(111) [43,44] and Pt(111) [45]] we consider in the following the FCC-hollow sites (i.e., a triply coordinated binding site, on which a next layer metal atom in the continuation of an FCC-stacking sequence would be found) for Pd and Pt.
For Na(110) and K(110) we tested various binding sites, specifically top, long-bridge, shortbridge, and hollow sites, because of a lack of previous studies. Increasing the surface coverage from of H 0.11 ML to 1 ML, we consistently find that H prefers to bind to the hollow sites.
Having identified the most favourable adsorption sites, we calculate the H binding energy (E b ) on each of the metal surfaces using Eq. 1. The result is shown in Fig. 4   explaining bonding between H and transition metal surfaces, the so-called d-band model [50].
In the case of the Na system [the bottom panel of Fig. 4  It is commonly accepted that residual H 2 molecules are still present in a vacuum chamber even at extremely low pressure and temperature. This is in part due to the relatively high content of hydrogen within the stainless steel most vacuum chamber are made of. Residual H 2 molecules can then ionize and dissociate due to the intense electric field and/or laser pulse during APT operation. This leads to the detection of H species without any direct interaction with the specimen, simply associated to typical field ionization as encountered in field-ion microscopy for instance. The ionization potential of H 2 is 15.4 eV, and it has been used as an imaging gas, in particular for silicon [51,52].
H species present inside the specimen are detected during APT measurements. Even if the presence of H atoms in a sample can be undesired, contamination may occur during the specimen preparation and transport, or during the measurement itself. The importance of controlling the temperature during specimen preparation was recently pointed out for several alloy systems [12,53], and in particular for materials systems that are known hydrideformers [10]. Breen et al. demonstrated the strong ingress of hydrogen arising from the specimen preparation by electrochemical polishing [9].
Here, we prepared specimens either at 90 K or at 300 K, but at a fixed pressure of approx.
10 −9 bar inside the focused ion beam. The specimens were then transported into the atom probe by using an ultra-high vacuum transfer suitcase, being maintained at approx. 300 K and 10 −11 bar. According to our phase diagram [ Fig. 5(a)], both the Na and Pt surfaces will not become covered by H during this process, because the respective H-free clean surfaces are thermodynamically favored. However, Pt samples can become contaminated by H atoms when the specimen is created in the vacuum chamber, especially at the conditions of 90 K and 10 −9 bar, while this is unlikely for a Na surface under similar conditions. Furthermore, given the high affinity of H and Pt discussed in the previous section, we cannot neglect the possibility of H diffusion from a H contaminated surface of a Pt sample into either its sub-surface or bulk region. This mechanism was pointed out to be responsible for the large ingress of H in titanium specimens during specimen preparation [12] under similar preparation conditions. Therefore, there is a high likelihood that the Pt specimen has already absorbed H atoms even before the APT measurement commences, which can be excluded in the case of Na.
An alternative scenario in which surfaces of samples are contaminated during the actual APT measurement is also conceivable, assuming that the metallic specimen is initially devoid of H. The detected H-related signal can originate from the binding of H to the specimen's surface during the APT measurement as a consequence of interactions between the H 2 gas and the surface metal atoms. First we note that from a thermodynamic perspective H-covered Pt surfaces are more stable than the clean surface at the conditions of our APT experiments (i.e., 10 −14 bar and 30 90 K). This is shown in Fig. 5(a) and suggests a high possibility of contamination. However, the Na phase boundary [red line in Fig. 5(a)] intersects the region of specified APT conditions. This means that the clean Na surface is stable against H chemisorption even at the relatively higher temperatures, e.g., 90 K, whereas Hcovered surfaces are expected to form at the lower temperature, e.g., 30 K. This is supported qualitatively by the APT measurements reported in Fig. 3.

B. Surface contamination during analysis
During an APT measurement, the surface atoms are progressively field evaporated from the specimen's surface, fly through the ultra-high vacuum and are collected by the particle detector, as illustrated in Fig. 5(b). Therefore, it is necessary to also consider kinetic scenarios, which can be involved in surface contamination by H. The field evaporation of the specimen's outermost surface layer, as illustrated in Fig. 5(c), exposes a new surface layer that was previously in the sub-surface region, as depicted in Fig. 5(d). This means that the space where the original surface layer was found has now become empty. Therefore, there is not only a lack of metal atoms in this region, but it is also void of H 2 molecules. The later (i.e., H 2 ) have to diffuse from the vacuum through this space towards the surface. The  Fig. 5(a), the chances for forming a H-contaminated surface will be much higher for Pt surfaces than for Na surfaces.

C. Influence of the electric field
Last but not least, since APT measurements are carried out in the presence of large electric fields (e.g., 1 4 V/Å)), the impact of such a large electric field on the surface stability has to be considered.
The electric field is known to have a substantial influence on the distribution of detected hydrogen [11,54,55]. The content of H, presumably originating from the residual gas from the chamber, is expected to increases as the electric field decreases [56]. In contrast, Andren and Rolander pointed to an influence of the electric field on the hydrogen adsorption behavior and hence suggest a change in the detection of H level as a function of the base temperature [57]. For relatively low fields, hydrogen adsorbed on the surface is field evaporated alongside one of the host-metal atoms forming, as reported for Al for instance, AlH, AlH 2 , AlH 3 [58]. The bonding of the metal atoms with gaseous species has been reported to favour the field evaporation at lower electric fields [59], and their detection should hence not be seen here.
The evaporation field of Na is estimated using the classical image hump model for field evaporation to be in the range of 1.1 V·Å −1 [60]. No experimental value was ever reported.
There are theoretical estimates of the evaporation field for Na adsorbates on Al and W that are also typically in this range of 0.6 0.8 V·Å −1 [61,62]. Under such low fields, typically peaks appear at 1, 2, and 3 Da in most analyses of metallic samples. These peaks are not observed here (cf. Fig. 3).
Although well-established approaches exist to explicitly include the electric field in DFT surface calculations [63], they come with large computational costs. Therefore, in the following we utilize as a first approximation to account for the thermodynamic effect of the electric field only free energy contributions, ∆U , due to the presence of an electric field and use the equation ∆U α = −∆µ α dipole E/A. Here ∆µ α dipole is the dipole moment difference of a surface phase α with respect to the H-free surface, E is the electric field applied during the APT measurement, in the range 0.5 5 V·Å −1 , and A is the surface area of the used slab models. By adding ∆U α to the Gibbs free energy changes calculated from Eq. 2, we can evaluate the field dependent phase boundary positions for Na and Pt, assuming fields of 2 and 4 V·Å −1 respectively, shown as dashed colored lines in Fig. 5(a). For both Na and Pt, the stronger surface dipole (compared to the pristine surface) due to the presence of bound H atoms at the surface leads to a reduction of ∆G by up to 10 meV/Å 2 for the highest H coverage. This results in a destabilization of H-covered surfaces. Therefore, the phase boundaries for the Na and Pt cases, shown as red and orange dashed lines in Fig. 5(a), are shifted towards the left, i.e., increasing the region in which the respective clean surface is stable. Comparison between the shifted phase boundaries and the actual conditions of the APT measurement consistently imply, from a thermodynamic standpoint, a low probability of H contamination of Na samples, even in the presence of a large electric field, in agreement with experimental results.
To account for the kinetic effect of the electric field, we note that Brandon and Southon [64,65] independently connected the gas kinetics theory with the high-electric field, allowing us to approximate the time for the field-ion imaging gas molecules (i.e., H 2 molecules) adsorption on the electrically charged surface of the APT specimen. The total adsorption of gas per unit area per time, Φ ( H 2 molecules m 2 ·sec ) can be obtained by combining the equation of the classical gas kinetics factor (see Eq. 5), electric-field enhancement factor (see Eq. 6), and probability, P , that a gas molecule is ionized on its way to the tip.
where Φ 0 is the gas kinetic arrival rate. We assumed P as zero to maximize the net adsorption rate of H. The flux of H that arrives at the surface of the Na nanosized tip in the absence of an electric field (E) is given by where p is the partial pressure of H 2 , M is the molecular mass of H 2 [2 atomic mass unit (amu)], and T is the base temperature of the specimen (i.e., 30 K). Since H is the predominant residual gas in metal vacuum chambers at low pressures, here we assume p equal to the analysis chamber pressure during the APT measurement that is 3.43 × 10 −14 bar. When an electric field is applied to the Na tip, the H supply is enhanced by a factor of ζ: where µ H 2 dipole is the permanent dipole moment of gas for a H 2 molecule and α is its polariz-ability. Assuming that µ H 2 dipole is zero and the error function gives a value of 1, the equation simplifies to Eq. 7: The following experimental and theoretical values used in our calculation, α H 2 = 5.314 [atomic unit (au)] [66] and assuming an electric field of E = 2 V/Å for Na, yield the total supply of gas Φ 0 ≈ 48 H 2 molecules m 2 ·sec and ζ = 11.5, which results in Φ = 549 H 2 molecules m 2 ·sec striking the Na tip. Assuming that an area of an APT specimen is π · (100 × 100) nm 2 , the approximate time to achieve a monolayer coverage of H molecules on the Na tip is over 1800 years.
This implies that the hydrogen detected over the course of an experiment is mostly supplied from chemisorbed or physisorbed hydrogen on the specimen's shank that surface-diffuses towards the apex, and has little to do with the direct chemisorption or ionisation of hydrogen at the apex itself. The field-free adsorption properties of the surface are hence likely the most critical parameter to consider.

D. Summary
Our discussions consistently suggest that the possible interaction between the residual H 2 gas in the UHV chamber and an APT specimen is both thermodynamically and kinetically almost negligible, which agrees with previous reports [67,68]. As illustrated in Fig and/or the specimen holders (i.e., Cu holder and Si coupon) [9,69] that were exposed to air before going into the UHV system. Subsequent surface diffusion indicated by blue arrows in Fig. 5(f), leads to a migration of the H at the surface towards the APT specimen apex to finally get desorbed and ionized as shown by the purple arrow in Fig. 5(f) [70]. Both processes (i.e., ad-/absorption) strongly depend on the material's properties.

V. CONCLUSIONS
In conclusion, we studied the origin of residual hydrogen in APT experiments by combin- specimen preparation and transport, involving cryogenic workflows and vacuum transfer, seem to be lower hanging fruits that can lead to substantial improvements in data quality.
The possible coatings of specimens and holders with materials on which hydrogen adsorption is not favourable should also be explored in the future.

VII. DATA AVAILABILITY STATEMENT
All DFT calculated data used in this work is available in the Pyiron repository and can be given access to upon request.