# Compared SIMS and NanoSIMS Analyses of Duplex Oxide Layers Growth After Sequential Oxidation Tests Using Oxygen Isotope Tracers

Sergio Diez Mayo, Fabien Rouillard, François Jomard, Maximilien Verdier

Paoletti, Laure Martinelli

► To cite this version:

Sergio Diez Mayo, Fabien Rouillard, François Jomard, Maximilien Verdier Paoletti, Laure Martinelli. Compared SIMS and NanoSIMS Analyses of Duplex Oxide Layers Growth After Sequential Oxidation Tests Using Oxygen Isotope Tracers. High Temperature Corrosion of Materials, 2026, 103 (1), pp.13. 10.1007/s11085-025-10372-0 . hal-05497227

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# Compared SIMS and NanoSIMS Analyses of Duplex Oxide Layers Growth After Sequential Oxidation Tests Using Oxygen Isotope Tracers

Sergio Diez Mayo¹,² · Fabien Rouillard² · François Jomard³ · Maximilien Verdier Paoletti⁴ · Laure Martinelli²

Received: 17 December 2025 / Revised: 19 December 2025 / Accepted: 29 December 2025
© The Author(s) 2026

## Abstract

A precise methodology for determining the growth mode of oxide layers on metallic materials at high temperatures is proposed. The approach combines sequential isotopic oxidation tests (using ¹⁶O and ¹⁸O isotopes) with secondary ion mass spectrometry (SIMS and nanoSIMS) analyses. NanoSIMS provides high-resolution localisation of oxygen diffusion pathways and oxide growth zones. However, its limited accessibility and specialised instrumentation can pose practical constraints. In contrast, dynamic SIMS offers broader accessibility and the ability to directly quantify oxygen isotope ratios across depth profiles. The detection of both conventional atomic (O⁻) and diatomic (O₂⁻) oxygen signals in dynamic SIMS analysis proved highly effective in offering insights on oxide growth mode, closely replicating nanoSIMS results. The diatomic signal analysis complements the atomic signal data by improving the understanding of oxidant transport within the oxide layer. The methodology was validated through its application to a Co-10Cr alloy oxidised at 900 °C in O₂, under sequential exposures to ¹⁶O and ¹⁸O isotopes. Both SIMS and nanoSIMS revealed the formation of a duplex oxide layer, consisting of an outer layer formed by outward Co cation diffusion and an inner layer growing by inward oxygen penetration, particularly in the grain-boundary regions of the outer oxide layer. The alloy is proposed to oxidise according to the Available Space Model.

**Keywords** Isotopic labelling · SIMS · NanoSIMS · Co-Cr alloy · Duplex layers · Oxygen diffusion
Introduction

Understanding the mechanism leading to oxide growth is essential for predicting
the long-term degradation of alloys under oxidising environments. The oxide layer
formed on most metals and alloys at high temperatures commonly follows para-
bolic oxidation kinetics [1, 2]. According to Wagner's theory, this behaviour occurs
because the growth rate is limited by the diffusion of reactants (metallic cations or
oxygen anions) through the film [3, 4]. To determine the dominant diffusing species
and the growth mode of oxide layers, inert markers have been historically employed,
beginning with Pfeil's work [5]. By analysing the localisation of markers after oxi-
dation tests, conclusions can be drawn about the formation of the oxide layer. Plat-
inum [6–8] and gold [9–11] are the most frequently used inert markers, typically
deposited on the sample surface via physical vapour deposition before the oxidation
stage. In order to provide reliable information, these markers must remain immobile
relative to the system, without interfering in the oxidation process. However, sev-
eral studies show random potential displacement during oxidation as well as uncer-
tainties regarding their inert properties, probably having an effect on the oxidation
mechanism [12–15]. An alternative approach to address this issue and approximate
the initial surface would be to use regions where the oxide layer is very thin as it was
done for the oxidation of Ni [16]. However, this option is not always feasible. To
address these limitations, sequential oxidation tests employing isotopically labelled
molecules have been introduced, offering a more robust and precise analysis of
oxide layers growth modes [17–19].

Sequential oxidation experiments involving isotopic tracers enable the precise identification of the oxidant within the oxide layer. Conventionally, the experimental procedure begins by subjecting the sample to a ¹⁶O-rich environment, typically natural O₂. Subsequently, the sample is exposed to an ¹⁸O-rich environment. The resulting oxide layers are then analysed by a mass-sensitive technique such as Secondary Ion Mass Spectrometry (SIMS) [20–23]. The detection of the different oxygen isotopes, based on their mass-to-charge ratio (m/z), provides information about their distribution within the oxide layer. By examining the shape of the ¹⁸O atomic species profile relative to the ¹⁶O profile from the first oxidation stage, the oxide growth mode (external/internal growth, lattice/short-circuit diffusion) can be determined [20, 24–29].

Traditional SIMS analyses of oxygen atomic signals (O⁻ and O⁺) may fall short
in providing sufficient information. In response, Atkinson et al. [30–32] and Moon
et al. [29, 33, 34] advanced the use of SIMS by proposing the simultaneous analysis
of diatomic (O₂⁻) signals, thereby enhancing the understanding of the oxide growth
process. This approach is based on the assumption that the detected diatomic oxygen
signals result from neighbouring oxygen atoms within the oxide layer, rather than
from plasma recombination of oxygen isotopes during sputtering [30]. The detec-
tion of this diatomic species provides valuable insights into the incorporation of the
oxygen tracer (¹⁸O) into the oxide film, whether through lattice, grain boundaries, or
cracks. The effectiveness of this approach has been demonstrated through studies on
the high-temperature oxidation of pure Ni [29–32, 34] and Ni with minor additions
of Cr [30] or Al [33]. Although valuable information is obtained, the interest on dia-
tomic signals in the literature remains quite limited beyond the cited publications of
Atkinson et al. and Moon et al.

Despite its utility, a key limitation of conventional SIMS is the averaging of
signals over a large analysis area (about 30 µm), which can limit the detection of
minimal or highly localised isotopic enrichments [35]. The high-energy sputtering
employed during depth profiling can also cause interface roughness or a non-flat
analysis area, compromising depth profile accuracy. NanoSIMS, an advanced vari-
ant of SIMS, overcomes many of these limitations by offering superior depth and
lateral spatial resolution (between 50 and 200 nm, depending on analysis condi-
tions). Their application in analysing oxide layer cross sections after sequential iso-
topic oxidation tests enables precise determination of the tracer (¹⁸O) incorporation
into the oxide layer. However, the accessibility of NanoSIMS remains restricted for
many laboratories due to its complexity and small number of instruments currently
available worldwide.

This study aims to compare the ability of conventional SIMS to replicate the
findings of nanoSIMS. The final objective is to propose a clear, general, and robust
methodology for analysing sequenced oxidation experiments, maximising the infor-
mation extracted to understand oxide growth mechanisms. To this end, a cobalt/
chromium alloy (Co-10Cr) was oxidised at 900 °C in O₂. According to literature,
the oxidation of Co-10Cr at temperatures close to 900 °C results in the formation
of a duplex oxide layer. This structure consists of a relatively dense outer layer of
columnar grains (composed of CoO) and a fine-grained inner layer (composed of
CoO, Cr₂O₃, and CoCr₂O₄) [36–40]. Such oxide morphologies and structure are
very similar to those observed in the oxidation of Ni [30, 41–44], Ni–Cr alloys [40,
45–47], and Fe–Cr alloys [48–52]. Extensive studies on these previous systems
have proposed that the inner oxide scale is formed by gas diffusion of O₂ molecules
through the oxide scale via short-circuit paths, followed by reaction with fresh metal
at the oxide/metal interface [53–55]. While the presence of short circuits is widely
acknowledged in the literature, their formation mechanism remains a subject of
debate. Two main scenarios of formation have been proposed: formation through
oxide dissociation [53, 56–62] and formation by mechanical cracking of the oxide
[29–31, 63]. The present work aims to investigate the development of a duplex oxide
layer in a system other than pure and slightly alloyed Ni, extensively studied in the
past by Atkinson et al. [30, 31]. In the present study, particular attention is given
to identifying the transport pathways of the oxidising species responsible for form-
ing the internal oxide layer. For this purpose, the Co-10Cr alloy was selected, as
inward oxygen ingress has also been suggested by several authors in the oxidation of
Co-Cr alloys [36, 37, 64–66]. A deeper understanding of the oxidation mechanism
and the associated oxidant transport processes is critical to fully elucidate its high-
temperature oxidation behaviour. In this study, oxide layers formed after sequential
oxidation experiments with ¹⁶O and ¹⁸O isotopes are first analysed using nanoSIMS.
In the second phase, the potential of conventional dynamic SIMS is explored by uti-
lising atomic (O⁻) and diatomic (O₂⁻) signals, with the objective of obtaining com-
parable information to that achieved with nanoSIMS. Similar studies have also been
carried out on Fe–Cr and Ni–Cr binary alloys, but the results of these experiments will be reported in a forthcoming publication.

# Experimental Procedures

## Specimen Preparation

The alloy with the nominal composition Co-10Cr (%wt) was manufactured at the Institut Jean Lamour (Nancy, France), using high-purity cobalt and chromium pellets (1–5 mm, 99.99% purity). The impurity contents of the starting materials are summarised in Table 1. These pellets were placed in a metallic water-cooled crucible of a high-frequency inductive furnace (CELES), which allowed to obtain a chemical and microstructural homogeneous material [67, 68]. Rectangular parallelepiped samples with approximate dimension of 10 × 8 × 1 mm³ were cut from the ingot. Both faces of the samples were later ground with SiC paper up to grade P1200. The samples were later cleaned for 5 min in an ultrasonic bath using acetone and ethanol.

## Sequential Isotopic Oxidation

The Co-10Cr specimen was sequentially oxidised at 900 °C in a gas-phase analysis facility presented in the literature [69, 70]. The sample was introduced in the isothermal zone of the reaction chamber, which was later evacuated down to 10⁻⁴ mbar. The oxidation test required two sequential stages: a first oxidation in a ¹⁶O-rich atmosphere (natural oxygen) followed by a second oxidation under a ¹⁸O₂-rich atmosphere. The ¹⁶O₂ gas employed on the first stage was admitted to a total pressure of 200 mbar. The preheated furnace was then moved into position to heat the sample to 900 °C, thereby initiating the first stage of the oxidation process. When transitioning from the first stage to the second stage, all the ¹⁶O₂ was pumped for 5 minutes before the introduction of the ¹⁸O₂. Throughout this period, the sample was kept at the oxidation temperature to prevent any oxide layer spalling due to mechanical stresses during cooling. After this pumping phase, the ¹⁸O₂ gas employed on the second stage was admitted to a total pressure of 200 mbar, starting the second stage of the oxidation process. The gas-phase analysis facility was also equipped with a Quadrupole Mass Spectrometer (QMS). Prior to conducting these sequential isotopic oxidation experiments, QMS analysis was performed on each oxidising environment to measure the isotopic ratios of the supply gases. Both ¹⁶O₂ and ¹⁸O₂ gases were injected separately in the facility and the presence of the respective

<table><caption>**Table 1** Quantity (in ppm by mass) of impurities in the pellets used for alloy synthesis, according to the supplier Neyco</caption><thead><tr><th></th><th>Ag</th><th>Al</th><th>Cu</th><th>Fe</th><th>Mn</th><th>Ni</th><th>Si</th></tr></thead><tbody><tr><td>Co (99.99% purity)</td><td>0.93</td><td>0.06</td><td>13.70</td><td>3.87</td><td>—</td><td>24.5</td><td>0.27</td></tr><tr><td>Cr (99.99% purity)</td><td>—</td><td>20</td><td>5</td><td>30</td><td>5</td><td>5</td><td>20</td></tr></tbody></table>

<figure><img src="image_3.png" /></figure>
minor isotope was analysed. As determined by the analysis, the ¹⁸O₂ supply bottle contained a small amount of ¹⁶O as impurity, approximately 4.35 vol%. In contrast, the ¹⁸O content in the ¹⁶O₂ bottle corresponded to its natural abundance (0.2 vol%) but could not be accurately quantified by QMS due to its too low concentration.

The samples subjected to oxidation tests are summarised in Table 2. The Co-10Cr sample was oxidised following the conventional sequencing in isotopic tests (oxidation is firstly done under ¹⁶O₂ and then under ¹⁸O₂). In addition to the alloy sample, two reference samples of Co oxidised at 600 °C exclusively in ¹⁸O₂ or ¹⁶O₂, respectively, were included to strengthen the reliability of the proposed SIMS analysis methodology (see results in Appendix B). The duration of the oxidation tests was determined from the parabolic oxidation kinetics reported in the literature [64, 71, 72]. The objective was to achieve an oxide layer thick enough (2–10 µm) for reliable SIMS and nanoSIMS analyses while avoiding excessive thickness that would prolong SIMS measurements.

## SIMS and NanoSIMS Analyses

Dynamic SIMS analysis was conducted on the surface of the oxidised Co samples, using a Cameca IMS 7F instrument at the Groupe d'Étude de la MATière Condensée (GEMAC) of the Université de Versailles Saint-Quentin-en-Yvelines. The interaction of the sample surface with a primary ion beam (typically Cs⁺ or O⁻) enables the sputtering of extreme surface atoms as secondary ions, which are then accelerated by an electromagnetic field. Depth profiles were acquired using a 10 keV Cs⁺ primary ion beam. A voltage of −5 keV was applied between the sample and the extraction electrode to facilitate the extraction of negative secondary ions. Cs⁺ primary ions were selected due to their lower ionisation energy and increased secondary ion production for electronegative species like oxygen. The size of the analysed region was set at 33 µm, with a raster size of 150 µm. The primary ion current was established at 40 nA. This ensures a sufficiently high current density to minimise the influence of adsorbed water molecules from the SIMS chamber vacuum on the oxygen signal intensity [73]. The position of the metal/oxide interface was determined as the inflexion point of the ⁵⁹Co signal between the metal and oxide values. Subsequently, the sputtering time scale was converted to a depth scale using the average film thickness values observed on cross-sectional image by SEM and by considering an even sputtering rate throughout the oxide layer. All analyses using the negative secondary ions polarity were performed at high mass resolution in order to discard any possible interferences between neighbouring masses. The mass resolution, defined as M/ΔM (where M is the mass of the ion and ΔM is the minimum detectable

<table><caption>**Table 2** Oxidation tests carried out on the different samples used for this study</caption><thead><tr><td>Sample</td><td>Oxidation environment</td></tr></thead><tbody><tr><td>Co-10Cr</td><td>¹⁶O₂ (1.5 min) + ¹⁸O₂ (15 s), 900 °C</td></tr><tr><td>Co ref. ¹⁸O₂</td><td>¹⁸O₂ (50 min), 600 °C</td></tr><tr><td>Co ref. ¹⁶O₂</td><td>¹⁶O₂ (50 min), 600 °C</td></tr></tbody></table>
mass difference between two peaks), characterises the instrument's ability to distinguish between ions of nearly identical mass-to-charge ratios (m/z). To accurately distinguish between the analysed oxygen species and their main possible interferences (for instance, the ¹⁸O isotope and the H₂O molecule, both with a m/z of 18), a mass resolution of 2,000 was employed. Finally, the background levels of ¹⁸O in ¹⁶O₂ supply gas and ¹⁶O in ¹⁸O₂ supply gas were determined by analysing the oxide films of the respective reference samples.

Characterisations using Secondary Ion Mass Spectrometry at the nanoscale (nanoSIMS) were performed on a nanoSIMS N50 CAMECA instrument at the Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie at the Musée National d'Histoire Naturelle. The functioning of the nanoSIMS is similar to that of a conventional SIMS, with the exception that a coaxial lens configuration ensures that the primary and secondary beams are perpendicular to the sample surface. This geometry significantly reduces the focal distance and, consequently, the probe diameter at the sample surface can reach, theoretically, 50 nm for the employed Cs⁺ source [74]. The effective probe diameter during our measurements was determined to be approximately 150 nm (details of the measurement procedure are given in Appendix A). Prior to analysis, the samples were mechanically cut transversely and embedded in epoxy resin. The cross-section faces were polished to a 1-µm finish diamond suspension. To ensure surface conductivity, a nanometer-thin gold coating was applied to the polished sections. Five electron multipliers were assigned to detect ¹⁶O, ¹⁸O, ⁵⁹Co, ⁵⁹Co¹⁶O, and ⁵²Cr masses in combined analysis mode. Before analysis, the samples were pre-sputtered for 5 minutes using a 200 pA current over a 30 µm² area to achieve stable count rates in an area with minimal surface contamination. Nanoscale-resolution maps of the oxide layer cross sections were realised, allowing for the precise localisation of isotopes both laterally and in depth. An ion beam current of 1 pA was employed for analysis, and the raster size was limited to a central cleaned region of 20 µm². NanoSIMS images were acquired at 256 × 256 pixels resolution and were processed with the LImage software by the Carnegie Institution of Washington. As for dynamic SIMS analysis, a high mass resolution is employed to effectively discriminate any potential interferences from our masses of interests. Furthermore, this capability also complements SEM imaging, enabling direct observation of the nanoSIMS-analysed region by SEM. This facilitates the direct correlation of microstructural and isotopic data for a more comprehensive analysis of oxide growth modes.

## Methodology of SIMS Analysis

After the sequential oxidation experiments, the distribution of oxygen isotopes within the oxide layer is analysed using Secondary Ion Mass Spectrometry (SIMS). The intensity profiles of the ¹⁶O and ¹⁸O isotopes as a function of depth provide valuable information about the oxide growth mode [20, 24–29]. The interpretation of the possible growth scenarios is based on the ideal distributions of the ¹⁸O isotope (from the second oxidation stage) within the pre-existing ¹⁶O enriched oxide layer. The theoretical scenarios are illustrated in Fig. 1:
<figure><img src="image_4.png" /><figcaption>**Fig. 1** Theoretical schematic representation of the correlation between the in-depth intensity profile of the ¹⁸O tracer and the growth mode of the layer formed during a conventional two-stage oxidation experiments. The first oxidation stage (forming the “old oxide”) is conducted in a ¹⁶O-rich environment and the second stage (forming the “new oxide”) in an ¹⁸O-rich environment (partially adapted from [20, 24, 28])</figcaption></figure>

* The oxide layer grows exclusively by outward transport of the metal (Fig. 1A). The ¹⁸O isotope is solely present in the new oxide layer created at the oxide/gas interface, placed above the ¹⁶O-rich oxide layer (“old layer” in the scheme). The ¹⁸O isotope from the oxidising environment reacts with the metal diffusing to the external interface (creating the “new oxide”). When profiling from external to internal interfaces, the intensity of the ¹⁸O profile will decrease sharply at the depth corresponding to the ¹⁸O/¹⁶O interface. The outward diffusion of metal cations proceeds either through the oxide lattice, along oxide grain boundaries, or via alternative short-circuit diffusion pathways.

* The oxide layer grows exclusively by inward transport of oxygen (Fig. 1B). In the case of transport via the lattice (Fig. 1B1), the ¹⁸O anions diffuse into the lattice of the pre-existing ¹⁶O-rich oxide layer (“old layer”). As ¹⁸O is incorporated into the oxide, the ¹⁶O atoms are progressively displaced towards the metal/oxide interface, where they react with the underlying metal to form the “new oxide”. As a consequence of this displacement, a diffusion profile of ¹⁸O develops within the ¹⁶O-oxide. Consequently, the ¹⁸O-rich oxide layer overlays the pre-existing oxide layer despite overall internal oxide growth. Notably, this is the only scenario in which the newly formed oxide is not predominantly composed of ¹⁸O atoms.

* In the case of transport along oxide grain boundaries (Figure 1B2), the ¹⁸O oxide layer forms beneath the pre-existing oxide layer. Consequently, the intensity of the ¹⁸O profile exhibits a sharp increase at the ¹⁶O/¹⁸O interface, similar to the
case of outward growth, but with an inverted ¹⁶O/¹⁸O sequence. During the rapid ¹⁸O transport along grain boundaries (short circuits) of the pre-existing layer, isotopic exchange with the surrounding grains may occur. This scenario leads to the formation of a diffusion profile within the ¹⁶O-oxide layer, as represented by the solid line. In contrast, if no isotopic exchange occurs during ¹⁸O transport, diffusion will proceed at an even faster rate, facilitated by pathways such as mechanical-induced cracks or fissures along grain boundaries. In this case, the resulting diffusion profile will correspond to the dashed line.

* The oxide layer grows by the counter-current transport of both reactants, metal and oxygen (Fig. 1C). In the case of the diffusion of reactants by using different pathways, the new oxide forms at both internal and external interfaces (Fig. 1C). The outward diffusion of metal results in the formation of a new ¹⁸O-rich oxide layer at the oxide/gas interface, while the simultaneous inward diffusion of oxygen results in a new ¹⁸O-rich layer at the metal/oxide interface. A minimal isotopic exchange may exist during the transport of the species within the old ¹⁶O-rich oxide layer inducing slight ¹⁸O enrichment. Conversely, in the case of the diffusion of both reactants by using the same pathways, the new oxide forms within the pre-existing ¹⁶O-rich oxide layer (Fig. 1). The feasibility of this last scenario has been a subject of debate. For instance, Clarke [75] argued that, in the case of alumina, the lateral growth strain generated by such internal oxide formation would suppress further growth, rendering this process unlikely. However, Atkinson [76] demonstrated that whether new oxide is formed or consumed within the film depends critically on the nature of cation and anion defects diffusing. This dependency applies to oxide growth occurring both within the crystal lattice and along grain boundaries.

Therefore, the analysis of the ¹⁶O and ¹⁸O intensity profiles after sequential oxidation tests not only enables the identification of the oxide growth mode but also provides initial insights into oxidant transport processes. To further characterise this transport within the oxide layer, Atkinson et al. [30–32] and Moon et al. [29, 33, 34] proposed complementary analyses of oxygen diatomic species. Their approach focuses on mass numbers 32, 34, and 36, corresponding to the ¹⁶O₂, ¹⁶O¹⁸O, and ¹⁸O₂ species, respectively. The underlying hypothesis motivating the analysis of the oxygen diatomic species is the observation that these signals exist exclusively if two oxygen atoms are near-neighbours in the solid phase, forming an oxide unit. This implies that the detection of a diatomic signal does not result from the recombination of the oxygen atoms within the plasma of the analysis chamber (this result will be confirmed in the Results section). Thus, following this observation, the detection of the ¹⁸O₂ or ¹⁶O₂ species is only possible if two ¹⁸O atoms or two ¹⁶O are close neighbours within the oxide layer, forming a M¹⁸O–M¹⁸O or M¹⁶O–M¹⁶O oxide units within the MO (M is the cation) oxide layer for instance, respectively. In a scenario where both ¹⁶O and ¹⁸O isotopes are mixed in a specific region, the ¹⁶O¹⁸O species would be detected by SIMS, corresponding to the presence of M¹⁶O–M¹⁸O oxide units.

In a conventional sequential isotopic test, where oxidation sequence is ¹⁶O₂ followed by ¹⁸O₂, the isotope of interest for SIMS analysis is ¹⁸O. Due to the

<figure><img src="image_5.png" /></figure>
methodology's particularity to analyse diatomic species, particular attention is given to the mass number 36 signal, corresponding to the ¹⁸O₂ species. This signal provides sensitive information about the distribution of neighbouring M¹⁸O–M¹⁸O oxide units throughout the ¹⁶O-rich oxide layer formed during the first stage. In that respect, the objective of this methodology is to compare the intensity of the measured s₃₆ signal obtained via SIMS analysis with the two calculated extreme scenarios: s₃₆ “fully mixed” and s₃₆ “two phases”. This comparative approach allows for the identification of the distribution of the ¹⁸O tracer within the oxide layer, thereby revealing the predominant oxygen transport mechanism (whether lattice diffusion in a random distribution case; or via short-circuits diffusion in a localised distribution case). Ultimately, it provides valuable insights into the growth mode of the oxide layer. Hence, based on the tracer transport mechanism within the pre-existing oxide layer, two extreme isotopic distribution scenarios are considered:

Random distribution (“Fully mixed” [30]): the diffusion of the ¹⁸O isotopes occurs randomly within the oxide volume. In this scenario, the inward diffusion of oxygen to the metal/oxide interface occurs exclusively via defects in the crystallographic lattice of the M¹⁶O oxide. During this process, the ¹⁸O isotopes are arbitrarily distributed throughout the oxide layer. The detection of the m/z=36 signal will arise from the presence of two neighbouring ¹⁸O isotopes forming oxide units after this random diffusion.

In this scenario, the intensities of all the diatomic species (¹⁶O₂, ¹⁶O¹⁸O, and ¹⁸O₂) depend on their formation probabilities, dictated by the ¹⁶O and ¹⁸O isotopes concentrations. Regarding this assumption, the intensity of the relative diatomic signals can be related to the fractional concentration of ¹⁸O isotope within the oxide layer through the following relationship (1):

$$c = \frac{[^{18}\text{O}]}{[^{18}\text{O}] + [^{16}\text{O}]} \quad (1)$$

Here, the constant c represents the probability of finding an ¹⁸O isotope among all oxygen isotopes, and (l-c) represents the probability of finding a ¹⁶O isotope. The expressions for the diatomic signal intensities s₃₂, s₃₄, s₃₆ are obtained as follows:

* The signal s₃₂ corresponds to a diatomic species formed by two ¹⁶O isotopes. The probability of forming of such species depends on the probability of independently finding two ¹⁶O isotopes, (l-c) and is expressed as:

$$s_{32} = \alpha(1 - c)^2 \quad (2)$$

* The signal s₃₄ corresponds to a diatomic species formed by one ¹⁶O and one ¹⁸O isotope. The probability of forming of such species depends on the combination of finding one ¹⁶O isotope (l-c) and one ¹⁸O isotope (c). The probability is double since there are two possible configurations (either ¹⁶O followed by ¹⁸O or vice versa):

$$s_{34} = 2\alpha c(1 - c) \quad (3)$$
* The signal $s_{36}$ corresponds to a diatomic species formed by two $^{18}$O isotopes. The probability of forming such a species depends on the probability of independently finding two $^{18}$O isotope (c) and is expressed as:

$$s_{36} = \alpha c^2 \qquad (4)$$

The presence of the $\alpha$ factor establishes a relationship between the measured raw intensity by the apparatus and the probability of forming each diatomic species, related to the isotope atomic fraction within the oxide layer. This factor accounts for the instrument's characteristics and the analysis parameters (such as sputtering rate, crater size, employed intensities, lenses settings, etc.). By combining the expressions for the different diatomic signal intensities, the expression of the $m/z=36$ signal under a random isotopic distribution can be obtained. It is important to note that the theoretical signal in this scenario is derived from two SIMS measured signals, $s_{34}$ and $s_{32}$:

$$s_{36 \text{ fully mixed}} = \frac{s_{34}^2}{4 s_{32}} \qquad (5)$$

Localised distribution (“Two phases” [30]): the diffusion of the $^{18}$O isotope is exclusively made within localised zones. Consequently, the probability of encountering two $^{18}$O isotopes as near-neighbours within these localised zones is higher than in the previous case. In this scenario, two different oxide phases exist: the M$^{18}$O oxide units surrounded by the lattice of M$^{16}$O oxide units (for a MO oxide layer). As a result, the proportion of the $^{18}$O isotope relative to the total isotopes is identical in both atomic and diatomic form. Thus, the $m/z=36$ signal, normalised by the sum of the $s_{32}$ ($^{16}$O$_2$) and $s_{36}$ ($^{18}$O$_2$) intensities, is proportional to the intensity of the $s_{18}$ signal (atomic $^{18}$O) normalised by the sum of the $s_{16}$ (atomic $^{16}$O) and $s_{18}$ intensities, as proposed by Atkinson et al. [30].

The $s_{18}^\circ$ and $s_{36}^\circ$ signals correspond to the background intensities for the atomic and diatomic $^{18}$O isotopes, respectively. These signals were determined by analysing the presence of the $^{18}$O isotope as impurities in the reference sample which underwent oxidation exclusively in $^{16}$O$_2$ gas (“Co ref $^{16}$O$_2$”). During its oxidation, these impurities were randomly distributed (“fully mixed”) within the oxide lattice. A similar situation arises during the first oxidation stage of a conventional sequential isotopic oxidation test ($^{16}$O$_2$ then $^{18}$O$_2$). Based on these assumptions, the theoretical expression for the $s_{36}$ signal in the case of diffusion via localised zones derives from that proposed by Atkinson [30]:

$$s_{36 \text{ two phases}} = \frac{A(s_{32} - s_{36}^{\circ}) + s_{36}^{\circ}}{1 - A} \qquad (6)$$

$$\text{from} \frac{(s_{36} - s_{36}^{\circ})}{(s_{32} + s_{36} - s_{36}^{\circ})} = \frac{(s_{18} - s_{18}^{\circ})}{(s_{16} + s_{18} - s_{18}^{\circ})} \text{ with } A = \frac{(s_{18} - s_{18}^{\circ})}{(s_{16} + s_{18} - s_{18}^{\circ})} a$$
It is important to highlight that it is necessary to eliminate potential interferences with impurities of identical mass numbers to ensure reliability of the calculations. This is essential to confirm that the measured $s_{36}$ diatomic signal arises exclusively from the oxygen tracer. As a result, the use of high mass resolution is crucial. Before examining the SIMS analyses of the Co-10Cr oxidised sample, nanoSIMS analyses of the cross-sectioned oxidised sample were performed.

# Results

## Characterisation of the Oxide Layer Formed on Co-10Cr

Cross-sectional images of the oxide film formed on the Co-10Cr sample oxidised at 900 °C under 200 mbar of pure oxygen were obtained using a Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM). To prevent surface damaging during ion milling, a ~ 0.2-µm carbon layer and a ~ 0.5-µm platinum protective layers were deposited prior to sectioning. Analysis of the oxide layer revealed a duplex structure composed of an outer and an inner layer, with a total average thickness of 6.3 ± 0.5 µm. The outer layer measured 4.0 ± 0.2 µm, while the inner layer measured 2.3 ± 0.3 µm. Thickness values were determined at 2-µm intervals along the width of the FIB cross section shown in Figure 2. The microstructural difference between these outer and inner layers (distinguished using a golden dashed line in Figure 2) suggested the existence of different formation mechanisms for each sublayer in the duplex structure.

The outer oxide layer exhibited large columnar grains, surmounted by a thin surface oxide film (placed above the white dashed line in Figure 2). Several macropores were observed within this region, particularly at the interface between the outer

<figure><img src="image_6.png" /><figcaption>**Fig. 2** FIB-SEM secondary electron (SE) cross-sectional micrograph of the oxide film grown on the Co-10Cr sample. The golden dotted line delineates the boundary between the outer and inner layers of the duplex structure. The white dashed line indicates the interface between the columnar CoO layer and the thin $Co_3O_4$ layer at the extreme surface. Points A, B, and C mark the locations where Raman spectroscopy was performed</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 3 XRD and Raman analysis of the oxide film grown on the Co-10Cr sample</figcaption></figure>

and inner layers. The application of micro-Raman spectroscopy on this outer layer
revealed two distinct oxide phases: a predominant CoO phase (point B in Figure 2,
corresponding spectrum<fnref n="1" /> in Figure 3), and a thin surface layer of Co₃O₄ layer located
above the CoO grains (point C in Figure 2, corresponding spectrum in Figure 3).
The columnar CoO grains are clearly discernible due to the grain orientation con-
trast provided by the FIB imaging. The interface between CoO and Co₃O₄ is marked
by a white dashed line in Figure 2. The average columnar grain width, determined
through SEM measurements using the different crystallographic orientations, was
about 2 µm in average. As shown in Figure 4, energy-dispersive X-ray spectroscopy
(EDX) was also performed in a different region of the oxide layer in order to com-
plement the microstructural and spectroscopic data. Both elemental mapping and
linescan profiles revealed that the outer oxide layer predominantly contains cobalt
and oxygen in agreement with the formation of Co oxides mentioned previously. In
contrast, the inner layer characterised by very fine equiaxed grains and the presence
of micro-porosity, contains cobalt, chromium, and oxygen. Chromium was confined
exclusively to the inner layer and was absent from the outer layer. Micro-Raman
analysis of this region did not yield a spectrum that matched any standard reference
compounds. However, the spectral features shared similarities with Raman spectra
reported in the literature for synthetically produced CoCr₂O₄ particles [78], suggest-
ing the presence of spinel-type CoCr₂O₄ phase in the inner layer. The analysis of the
different phases present in the oxide layer agrees with the results obtained by XRD,
as shown in Figure 3. These results align with previously reported data on the mor-
phology and structure of oxide layers formed on Co-Cr alloys at high temperatures
[36–40, 64, 66, 72].

<figure><img src="image_8.png" /></figure>

<footnote n="1">¹ The spectrum of the point B in Fig. 2 exhibited three characteristic broadened peaks at approximately 540, 690, and 1050 cm⁻¹. These broad peaks are attributed to CoO, especially given their similarity to spectra reported in the literature [77].</footnote>
<figure><img src="image_9.png" /><figcaption>**Fig. 4** Energy-dispersive X-ray spectroscopy (EDX) linescan (red arrow) and cartography of the oxide film grown on the Co-10Cr sample</figcaption></figure>

## NanoSIMS Analysis

Figure 5 illustrates the nanoSIMS analyses of the oxide layer grown on the Co-10Cr sample after sequential oxidation test ($^{16}$O$_2$ for 1.5 min then $^{18}$O$_2$ for 15 s, at

<figure><img src="image_10.png" /><figcaption>**Fig. 5** NanoSIMS isotopic mapping of the analysed region on the oxide film grown on the Co-10Cr sample after the sequential oxidation test: first stage in $^{16}$O-rich atmosphere (1.5 min) + second stage in $^{18}$O-rich atmosphere (15 s); a individual isotopic mapping of the intensities corresponding to the species $^{16}$O, $^{18}$O in linear scale and $^{18}$O in logarithmic form, respectively. b Mapping obtained by superposing the intensities of both $^{16}$O (in linear scale) and $^{18}$O (in logarithmic scale)</figcaption></figure>
900 °C). The intensities of the ¹⁸O and ¹⁶O isotopes obtained in the nanoSIMS mapping provide detailed information about their distribution within the oxide layer. The combined “¹⁶O + Log ¹⁸O” image (Figure 5b) reveals the formation of a thin ¹⁸O-enriched oxide layer above the pre-existing oxide layer formed during the first oxidation stage (¹⁶O, shown in green). This indicated that the growth of the oxide layer on Co-10Cr at 900 °C is at least partially external. It is important to highlight that the second oxidation stage lasted only 15 s, yet resulted in the formation of an approximately 0.7-µm-thick oxide layer at the gas/oxide interface, demonstrating the rapid oxidation of Co-10Cr at this temperature (Figure 5a, ¹⁸O linear scale).

Furthermore, the inner part of the oxide scale is enriched in ¹⁸O, indicating a significant contribution of inward oxygen ingress to the growth of the inner oxide layer (Figure 5a, ¹⁸O linear scale). Notably, the ¹⁸O tracer is detected throughout the entire inner part of the ¹⁶O-enriched layer, in localised regions as precipitates. Furthermore, the employ of a logarithmic intensity scale in the ¹⁸O image (Figure 5a, ¹⁸O logarithmic scale) allowed the visualisation of localised ¹⁸O-enriched zones distributed throughout the outer part of the ¹⁶O layer, nearly indistinguishable when employing a linear scale. Their spatial distribution, localisation and morphology suggested that this ¹⁸O enrichment occurred along grain boundaries of the ¹⁶O outer layer. Quantitative analysis of inter-distances between distinct localised zones of oxygen penetration (white arrows in the Figure 5a, ¹⁸O logarithmic scale) showed an average spacing of 1.9 µm, which closely corresponded to the average grain width of the columnar grains determined from SEM micrographs (about 2 µm).

The detection of ¹⁸O-enriched zones in the grain-boundary regions of the outer part of the ¹⁶O-enriched oxide layer implies that O₂ molecules or O atoms were transported preferentially along these specific regions. Thus, a supplementary analysis was carried out to better characterise these ¹⁸O-enriched regions. In this context, a horizontal intensity profile was plotted across the totality of the ¹⁸O-enriched zones within the outer part of the ¹⁶O-enriched oxide layer, as depicted in Fig. 6. A single grain boundary was selected for detailed analysis. The experimental ¹⁸O isotope profile in the vicinity of this grain boundary, extending approximately about 200 nm on each side of the maximum ¹⁸O peak, is significantly larger than the typical grain-boundary widths (approximately 1 nm) [55]. Additional calculations will be presented in the Discussion section to identify which mechanism could account for this presence of ¹⁸O in the grain-boundary regions.

Additionally, an average bandscan of the nanoSIMS-analysed region was performed, as presented in Figure 7a, to enable comparison of the cross-sectional nanoSIMS data with the dynamic surface SIMS results. A wide area of 150 pixels (accounting for ~ 12 µm), represented by the dashed white rectangle, was selected. This area is relevant for characterising the oxygen penetration along grain boundaries as in both techniques the signal is averaged over a spatial extent significantly larger than the size of an individual grain. Figure 7b shows the intensity-depth profiles of each oxygen isotope from the external interface to the substrate, in the direction indicated by the arrow, providing information about their distribution within the oxide layer. As expected, the intensity profile of the ¹⁸O isotope (shown in red) exhibits a distinct peak in the external part of the oxide layer accounting for external growth, extending less than 1 µm before decreasing sharply. This sharp drop at

<figure><img src="image_11.png" /></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 6** Horizontal profile of the ¹⁸O signal of the oxide film grown on the Co-10Cr sample obtained by nanoSIMS mapping. A zoom has been made in a selected grain boundary to compare the experimental intensity with the literature values, assuming lateral diffusion</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 7** a NanoSIMS bandscan on the cross section of the oxide layer grown on the Co-10Cr sample after a sequential oxidation test: first stage in ¹⁶O-rich atmosphere (1.5 min) + second stage in ¹⁸O-rich atmosphere (15 s). The rectangle outlined by the dashed white lines corresponds to the 150 pixels wide analysis area, the arrow representing the bandscan sense of analysis. b Depth atomic profiles of the nanoSIMS bandscan realised on the oxide layer grown</figcaption></figure>

the interface between the ¹⁶O and ¹⁸O oxide layers demonstrated the absence of any large isotopic interdiffusion zone. Nevertheless, the $s_{18}$ signal remained detectable throughout the outer part of the initial ¹⁶O layer, forming a plateau region ending at
a bandscan depth of 5 µm. At this point, an increase in ¹⁸O intensity marks the transition to the inner part of the original oxide layer, where a more homogeneous distribution of ¹⁸O-rich precipitates is observed. The relatively high intensity of the ¹⁶O signal in this inner part, compared to the outer part of the oxide layer, was initially unexpected, given that no additional ¹⁶O should accumulate during the second oxidation stage. The presence of ¹⁶O impurities in the ¹⁸O₂ supply gas did not account for the observed s₁₆ signal (the impurity content was approximately 4.35 vol% by QMS analysis, represented in the graph by s₁₆°). The elevated observed ¹⁶O intensity may primarily be attributed to nanoSIMS analysis conditions. Due to the low ion beam intensity required for high-resolution imaging, the technique is susceptible to interference from residual adsorbed water (H₂O) molecules, present in the vacuum chamber during analysis [73]. Since water adsorption is a dynamic process, removing its contribution to the analysis requires an abrasion rate faster than the adsorption rate. The applied current density for nanoSIMS analysis (<1 µA/cm²) was well below the ~20 µA/cm² threshold needed to effectively remove adsorbed water which leads to an overestimation of the ¹⁶O signal. Furthermore, the fine-grained microstructure of the inner oxide layer increases the specific surface area available for adsorption, amplifying the effect in this region compared to the outer layer. This overestimation of the ¹⁶O signal compared to the ¹⁸O signal measured by nanoSIMS has already been observed [79] but has not been well interpreted.

The volumes of oxide formed externally and internally were quantified from the areas under the ¹⁸O profile obtained from the bandscan in Figure 8. For the determination of these zones, the mid-points between the inflection points of the ¹⁸O profile were used as a reference. The area corresponding to external oxide growth (A<sub>EXT</sub>) was about 28 % of the total area corresponding to the oxide growth occurring during the second oxidation stage (A<sub>TOT</sub>). Meanwhile, the internal region of ¹⁸O accumulation at the inner part of the original oxide layer (A<sub>INT</sub>) accounted for ~ 64 % of the total growth during the second oxidation stage (A<sub>TOT</sub>). These results suggested that

<figure><img src="image_14.png" /><figcaption>**Fig. 8** Depth atomic profiles of the nanoSIMS bandscan on the cross section of the oxide layer grown on the Co-10Cr sample after a sequential oxidation test. The calculation of the internal, external, and intermediate areas of the ¹⁸O intensity profile account for the oxide growth in the internal part (A<sub>INT</sub>), external part (A<sub>EXT</sub>) or grain boundaries (A<sub>GB</sub>) of the oxide</figcaption></figure>
oxide growth in the inner layer played a significant role in the overall oxide formation. Furthermore, the findings lead to the conclusion that ~ 8 % (A<sub>GB</sub>/A<sub>TOT</sub>) of the oxide growth during the second oxidation stage occurred in the grain-boundary regions of the <sup>16</sup>O-rich outer oxide layer.

## Dynamic SIMS Analyses

SIMS depth profiles of <sup>16</sup>O and <sup>18</sup>O signals for the Co-10Cr sample are presented in Figure 9. To ensure the reliability of the interpretation and quantification of the SIMS results obtained from sequential isotope exposure, reference samples oxidised exclusively with a single oxygen isotope were prior analysed. This approach enabled the determination of the background signal for each species (s<sub>16</sub>° for <sup>16</sup>O and s<sub>18</sub>° for <sup>18</sup>O), by analysing the minority isotope present under the form of impurities in each reference sample (see Table 2). The background values (Appendix B) were subsequently subtracted from the measured s<sub>16</sub> and s<sub>18</sub> signal in Figure 9. The correction applied to the <sup>18</sup>O signal is negligible (corresponding to only about 0.2 % of the intensity of the <sup>16</sup>O signal) and does not affect the profile shape or its quantitative interpretation. In the conventional oxidation sequencing, the primary focus was on signals containing the <sup>18</sup>O isotope which corresponds to the isotope employed during the second oxidation stage. As observed in Figure 9, two main zones of <sup>18</sup>O enrichment were detected. A first zone was located at the oxide/gas interface to an approximate depth of 0.7 µm then a second zone, in the inner part of the O<sup>16</sup>-rich oxide scale from 2.5 µm to the metal/oxide interface. A third zone of nonzero <sup>18</sup>O intensity was detected as well between these two zones with an average intensity of about 2.8 × 10<sup>6</sup> cnt/s. From Fig. 1, such <sup>18</sup>O profile suggests mixed diffusion of metal and oxygen employing different paths (Fig 1 C).

<figure><img src="image_15.png" /><figcaption>**Fig. 9** Depth atomic SIMS profiles of the oxide film grown on the Co-10Cr sample. The percentages of each isotope relative to the total oxygen content throughout the entire oxide layer are presented as an inset graph</figcaption></figure>
To better illustrate the extent of the ¹⁸O penetration throughout the ¹⁶O original layer, the isotopic percentages of each species relative to the total oxygen content throughout the entire oxide layer are presented as an inset graph (% O vs depth) in Figure 9. This analysis revealed that in the inner part of the original oxide layer, the ¹⁸O content varies between 25 and 50 % of the total oxygen isotopes. Quantification of oxide growth was achieved by calculating the different areas under the ¹⁸O signal curve in a similar method that was employed for nanoSIMS analysis, as shown in Figure 10. The area corresponding to external oxide growth ($A_{EXT}$) was found to represent approximately ~43% of the total oxide growth during the second oxidation stage ($A_{TOT}$). Meanwhile, the area associated with the ¹⁸O region in the inner part of the initial ¹⁶O layer ($A_{INT}$) accounted for approximately part of the total oxide growth during the second oxidation stage (~48%). Finally, the percentage of ¹⁸O in the “high diffusion” path region, ($A_{GB}$), demonstrated to be the grain boundaries region by nanoSIMS, accounted for ~9% of the total oxide growth during the second oxidation stage. The calculated proportions of oxide growth were in good qualitative agreement with the measured values through nanoSIMS mapping (Figure 8). The SIMS signals from the inner and outer layers can be compared under the assumption that there is no matrix effect, despite the two layers consisting of different oxides.

An additional study was conducted to quantify the oxide growth during the second oxidation stage (Co-(Cr)¹⁸O) relative to the oxide formed during the first oxidation stage (Co-(Cr)¹⁶O). The integrated areas under the ¹⁸O and ¹⁶O profile were compared separately for both the outer and inner parts of the ¹⁶O-enriched oxide layer, as shown in Figure 11. Analysis of the outer part revealed that oxide growth within the ¹⁶O oxide grain boundaries (diagonal red pattern in Figure 11a) accounted for approximately 6% of the total oxide growth relative to the surrounding oxide lattice formed during the first oxidation stage (green area in Figure 11a). In contrast, analysis of the inner part of the ¹⁶O layer indicated that internal ¹⁸O-rich oxide

<figure><img src="image_16.png" /><figcaption>**Fig. 10** Depth atomic SIMS profiles of the oxide film grown on the Co-10Cr sample, allowing the quantification of external, internal, and grain boundaries by calculating the specific areas under the ¹⁸O intensity profile</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Fig. 11** Depth atomic SIMS profiles of the oxide film grown on the Co-10Cr sample after a sequential oxidation test. Calculation of the area under the ¹⁸O profile (diagonal pattern) and area under the ¹⁶O profile (green area) enables the quantification of the oxide grown within grain boundaries and internally, respectively, relative to the surrounding oxide lattice</figcaption></figure>

growth accounted for approximately 39% of the total oxide growth relative to the surrounding ¹⁶O-rich oxide matrix (Figure 11b). This type of quantitative analysis is a key advantage of dynamic SIMS over nanoSIMS, where the direct comparison of the ¹⁶O and ¹⁸O signals intensities was not possible due to residual water adsorption during analysis (leading to the previously discussed overestimation of ¹⁶O). Dynamic SIMS, on the other hand, utilises a sufficiently high primary ion current density to overcome this limitation, enabling more accurate quantification of oxygen isotope distributions within oxide layers, particularly valuable when distinguishing oxide growth from sequential oxidation stages.

To go further on the understanding of oxygen transport during this test from dynamic SIMS, the diatomic O₂ signals were analysed; their intensities are presented in both linear (Figure 12a) and logarithmic (Figure 12b) scales. Analysis of the measured s₃₆ signal indicated a strong correspondence with the calculated s₃₆ signal of the “two phases” scenario. Thus, the diffusion and the distribution of the ¹⁸O isotope within the oxide layer occurred through localised regions, where two close-neighbouring ¹⁸O isotopes created oxide units within the ¹⁶O-rich oxide layer. This result was consistent with nanoSIMS observations, which revealed ¹⁸O-enriched oxide precipitates within the inner region of the pre-existing ¹⁸O-enriched oxide layer, as well as along the grain boundaries region in its outer part.

## Discussion

The oxidation behaviour of a Co-10Cr alloy at 900 °C was investigated using sequential isotopic oxidation combined with SIMS and nanoSIMS analyses. The oxide scale consisted of an outer columnar CoO layer topped by a thin Co₃O₄ film, and an inner porous layer composed of a complex mixture most likely containing CoO,
<figure><img src="image_18.png" /><figcaption>Fig. 12 Depth diatomic SIMS profiles of the oxide films grown on the Co-10Cr sample in: a linear scale; b logarithmic scale</figcaption></figure>

CoCr₂O₄, and nanoscale porosity. Both nanoSIMS (Fig. 5 and Fig. 7) and SIMS (Fig. 9 and Fig. 12) clearly demonstrated that scale growth proceeds by outward Co cation diffusion and by inward oxygen ingress. The high lateral resolution of nanoSIMS further revealed that, during the second oxidation stage, the inner oxide grows through the formation of new, finely dispersed oxide precipitates throughout the whole pre-existing porous Co-Cr-rich inner layer. Thus, inner-layer growth does not occur exclusively at the metal/oxide interface, as it could be expected first, but proceeds heterogeneously across the entire inner region. In addition, nanoSIMS identifies the grain-boundary regions of the outer columnar CoO layer as the dominant fast-diffusion paths for oxygen penetration. Similar conclusions regarding the oxidation mechanism and oxygen transport were also obtained through SIMS analysis of the oxide scale based on both atomic and di-atomic species. However, the SIMS analyses were not able to demonstrate that the “high diffusion” pathways were created exactly in the oxide grain boundaries region and that the inner oxide growth was finely dispersed since no high spatial resolution is possible by SIMS.
Based on the evidence that ¹⁸O isotopes are concentrated at the oxide grain boundaries regions of the outer oxide layer, a critical question arises: how is oxygen transported through these oxide grain boundaries to reach the inner layer? Several mechanisms may be considered, including the diffusion of neutral or ionised oxygen species, or the transport of molecular O₂. The following analysis explores these possibilities.

## Transport of Oxygen Through the Oxide Scale

Two possible scenarios for oxygen transport at the grain-boundary regions of the outer columnar CoO layer were considered: anionic diffusion along the grain-boundaries and molecular diffusion within the grain boundaries regions. For the latter case, the diffusion coefficient of oxygen molecules was calculated assuming a Knudsen-type diffusion regime (details of the calculations are provided in Appendix C). In this regime, the grain boundaries are treated as nanochannels, and oxygen transport is governed by collisions with the nanochannel walls. The assumed nanochannel width corresponds to the lower limit typically proposed for oxide grain-boundary width, yielding the minimum possible gas diffusion coefficient. The resulting gas diffusion coefficient was compared with an estimated diffusion coefficient of oxygen anion along oxide grain boundaries, which is commonly assumed to be 10⁵ times higher than in the lattice [42, 47, 80, 81] ($D_{O}^{lattice} inCoO \sim 1 \times 10^{-16} cm^2/s$ at 900 °C [82, 83]). Using these values, the maximum penetration depth of the isotope during the second oxidation stage was estimated for each scenario. The results obtained at 900 °C for the employed second oxidation stage of 15 s, are summarised in Table 3. This relatively short exposure time for the second oxidation stage was chosen deliberately to evidence that oxygen is transported extremely fast through the oxide scale.

The results presented in Table 3 clearly show that anionic transport of ¹⁸O²⁻ along grain boundaries cannot account for its observation at such intensity level in the inner oxide scale. Indeed, the maximum penetration depth is about 240 nm for grain-boundary diffusion, whereas nanoSIMS mapping revealed penetration of ¹⁸O to the metal/oxide interface at a depth of approximately 6.3 µm. In contrast, gas-phase transport of O₂ molecules can reach a depth of 4.2 mm which is high enough for explaining the inner oxide growth. For anionic diffusion along grain boundaries

<table><caption>**Table 3** Values of the different diffusion coefficients and penetration depth of oxygen (taken as $2\sqrt{Dt}$) as a function of the diffusion regime considered (Knudsen, diffusion in the lattice or in the grain boundaries) in a short circuit 1 nm in diameter and at 200 mbar and 900 °C, for 15-s duration of the second oxidation stage</caption><thead><tr><th></th><th>GB diffusion (Knudsen)</th><th>GB diffusion (anionic)*</th></tr></thead><tbody><tr><td>D (cm²/s)</td><td>2.94 × 10<sup>-3</sup></td><td>1.0 × 10<sup>-11</sup></td></tr><tr><td>x (µm)</td><td>4200</td><td>0.24</td></tr></tbody></table>

<footnote>*: The additional driving force induced by the two negative charge of oxygen, if present as anions, is not considered here, but the given diffusion distance must be multiplied by 3 if it is the case [84]</footnote>
to allow ¹⁸O to reach the inner interface, the diffusion coefficient along the grain boundaries would need to be more than 10⁷ times higher than the lattice diffusion coefficient (and not only 10⁵ as used in Table 3). Even if such an acceleration factor in oxide grain boundaries seems very high, it cannot be considered as unrealistic. Indeed, Atkinson et al. proposed such acceleration factor from studies on oxidation of Ni [80]. Indeed, in NiO, tracer diffusion measurements of oxygen show that grain-boundary diffusion coefficients of oxygen exceed lattice diffusion coefficients by more than five orders of magnitude at 1400 °C and this difference is expected to increase strongly at lower temperatures [16, 55, 85]. By analogy, it is therefore plausible that an acceleration factor exceeding 10⁷ for diffusion of oxygen in CoO grain boundary exists. Consequently, based solely on the inner oxide growth rate, it is not possible to discriminate between diffusion of atomic/ionic oxygen in CoO grain boundaries and diffusion of molecular O₂, as both could account for the rapid inner-layer growth.

## Analysis of ¹⁸O NanoSIMS Profiles

To further investigate the transport mechanism, additional nanoSIMS data were analysed. Lateral ¹⁸O profiles across ¹⁸O-enriched grain boundaries (Fig. 6) exhibited widths far exceeding typical grain-boundary thicknesses (~1 nm) [55]. At first glance, this result might suggest lateral diffusion of ¹⁸O from the grain boundary into the adjacent ¹⁶O-rich oxide grains. However, such an interpretation was affected by the finite probe size used in the analysis (~150 nm, Appendix A), which limits the effective lateral resolution and broadens the apparent profile. Although the ¹⁸O distribution cannot be reliably fitted using a classical diffusion profile, the measured peak intensity can still be used to evaluate whether the enriched region could plausibly result from lattice diffusion. As shown in Fig. 6, the maximum peak intensity value expected in such a scenario corresponds to the total amount of ¹⁸O present within the ~150 nm wide analysed region. To estimate this value, the oxygen diffusion profile was simulated assuming that grain boundary acts as a constant planar source of ¹⁸O, and ¹⁸O diffuses into the adjacent oxide grains considered, here, as semi-infinite solid. The analytical solution of this system diffusion is given by expression (7) using intensity rather than concentration [86]:

$$I_{x,t} = I_S \text{erf} \left( \frac{x}{2\sqrt{D_O^{\text{lattice}} t}} \right) \quad (7)$$

For numerical application, the source intensity value of $I_S$ (which is proportional to the concentration) was set equal to 330 cnts/s, the ¹⁸O intensity value measured in the compact external ¹⁸O oxide scale in Fig. 7 and corrected by a factor of ¾ since the surface oxide was Co₃O₄ and the grain boundary was rather CoO. Moreover, $D_O^{\text{lattice}} \sim 10^{-16}$ cm²/s at 900 °C in CoO [82, 83]. The maximum expected peak intensity value was then calculated by integrating the ¹⁸O diffusion profile in the 75 nm wide oxide region on both side of the grain boundary and then by dividing
it by 150 nm, the size of the probe. The obtained value was about 3 cnt/s which is well below the measured peak values between 10 and 25 cnt/s in Fig. 6. Thus, the measured ¹⁸O peak intensity values in the grain-boundary region cannot be easily explained by the presence of ¹⁸O in grain boundaries and into the adjacent oxide grains due to lattice diffusion. To reproduce the measured peak intensity in the grain-boundary regions, the lattice diffusion coefficient proposed in literature [82, 83] would need to be increased by a factor of 50–100, or the I$_S$ would need to be increased by a factor of 5–10; neither of which is physically justified. It is therefore more likely that an ¹⁸O-rich oxide forms within the grain-boundary regions.

## Crack Healing Scenario

A mechanism consistent with the observed ¹⁸O peak intensities and profiles is therefore considered. As proposed by Atkinson et al. for the oxidation of Ni and dilute Ni–Cr alloys [30, 47, 55], oxygen may be transported as O$_2$ molecules in the gas phase along microcracks formed within grain boundaries. According to Atkinson et al., ¹⁸O enrichment would then result from subsequent crack healing by oxide formation. In this scenario, the measured peak intensity directly reflects the thickness of the healing oxide. With this scenario, the width of the healing oxide (w$_{healing}$) can be calculated from the measured peak ¹⁸O intensities according to the following expression:

$$w_{\text{healing}}(\text{nm}) = \frac{I_{\text{JdG}}^{18\text{O}}}{I_{\text{MAX}}} * 150\text{nm} \quad (8)$$

From the I$_{JdG}$ ¹⁸O peak intensities measured in Fig. 6 (I$_S$=10 to 25) and the I$_MAX$ intensity obtained from the 0.7 thick dense ¹⁸O-rich oxide present in the surface in Fig. 7 (about 330 counts/s), the inferred healing-oxide widths range from 5 to 11 nm.

A similar estimation of the healing-oxide widths can be obtained from SIMS data. Assuming that the plateau intensity in Fig. 9 at an approximate analysis depth of 2 µm obeys:

$$I^{18} = f I_{\text{healing}}^{18} \quad (9)$$

with I$_{healing}$, the intensity in the healing oxide (equal to 2.8 × 10⁶ cnt/s); I$_{bulk}$, the intensity in the lattice oxide (equal to 2.1 × 10⁸ cnt/s after correction from Co$_3$O$_4$ to CoO) and f, the fraction of the cross section occupied by the healing oxide.

By taking f = qw/σ with q between 2 and 3 to reflect realistic oxide grain shape [87], the resulting healing-oxide widths fall in the range of 9–13 nm. These values are in quite good agreement with those obtained previously from nanoSIMS. Such healing-oxide widths of cracks are entirely plausible [88]. Variations in measured peak ¹⁸O intensity shown in Fig. 6 would simply reflect differences in crack aperture.
All these calculations strongly suggest a scenario analogous to that proposed by Atkinson et al. for the oxidation of pure Ni and Ni containing small amounts of Cr or Al [30, 31], in which short circuits arise from a dynamic cracking and healing process. In this context, cracks are thus created by intergranular growth stresses (resulting from the combination of tensile and compressive forces in these regions) allowing molecular oxygen transport and are subsequently healed by oxide formation along grain boundaries during oxide growth. Despite this rapid oxidant supply, the overall oxidation kinetics remain parabolic, suggesting that the rate-controlling step is not the diffusion rate of the oxidising molecules. It is rather the outward diffusion of metal cations responsible for the outer oxide growth. The only mechanism capable of accounting for these observations is the “Available Space Model”, widely detailed in previous studies [30, 31, 43, 51, 52, 54–57, 62]. This mechanism is proposed to explain the formation of duplex oxide layers where the outer oxide layer grows at the external interface via outwards cation diffusion and the inner layer grows in the “available space” created by the formation of metallic vacancies by the reaction of metals and oxygen molecules which has diffused very fast through cracks.

## Conclusions

This study introduces a methodology for examining high-temperature oxide growth in metallic alloys using nanoSIMS and SIMS analyses following sequential isotopic oxidation experiments ($^{16}$O$_2$ + $^{18}$O$_2$). The results demonstrate that a significantly deeper understanding of the oxidation mechanisms can be achieved by employing very short $^{18}$O$_2$ exposure times during the second oxidation stage (on the order of a few seconds). The approach was validated through the investigation of oxide scales formed on a Co-10Cr alloy oxidised at 900 °C in O$_2$. The results show that both SIMS and nanoSIMS lead to consistent interpretations of the oxidation mechanism (oxide growth modes and oxidant transport pathways) although nanoSIMS provides superior resolving power due to its markedly higher spatial resolution.

For the oxidation behaviour of Co-10Cr, the main conclusions are as follows:

1. NanoSIMS revealed a duplex scale consisting of an outer layer of Co-rich columnar grains formed by outward Co diffusion and an inner layer of equiaxed Co-Cr-rich oxide grains with nanoporosity. The inner oxide layer does not form exclusively at the metal/oxide interface but develops heterogeneously throughout the entire inner region. NanoSIMS also directly evidenced inward oxygen ingress along grain boundaries regions in the outer oxide layer.

2. Conventional dynamic SIMS delivered comparable insights into the oxidation mechanism through the analysis of atomic (O$^−$) and diatomic (O$_2$$^−$) species:

1. Atomic O$^−$ signals elucidated oxide growth modes, confirming both outer and inner oxide formation mediated by short-circuit oxygen transport pathways.

2. Diatomic O$_2$$^−$ signals further clarified the nature of oxidant transport and oxygen enrichment within the inner oxide, enabling discrimination between random versus localised distributions.
3. Accurate interpretation of diatomic signals relied critically on reference samples oxidised in single-isotope atmospheres.

3. Critical analyses of the measured ¹⁸O enrichment peaks in the grain boundaries of the outer oxide layer suggests that the inner oxide layer develops through repeated crack formation and healing, which transiently enables O₂ molecular transport. This oxidation behaviour is consistent with the ‘Available Space Model’ proposed in literature.

# Appendix A

## NanoSIMS Probe Size Calculation

The effective lateral resolution of the NanoSIMS was estimated from a profile acquired in a region where no ¹⁸O diffusion is expected (Fig. 13). Since oxygen diffusivity in CoO is low and the oxide grows externally, no significant ¹⁸O penetration into the grains of the outer oxide layer is expected. A vertical profile was therefore realised from the external oxide layer towards a grain formed during the first oxidation stage, for which the apparent ¹⁸O distribution is governed primarily by the probe size rather than by diffusion. The probe size was determined by evaluating the ¹⁸O intensity profile and identifying the positions corresponding to 85% and 15% of the maximum intensity measured externally. From these values, the effective probe diameter was estimated to be ~150 nm ± 10 nm. This value exceeds the nominal theoretical probe size (~50 nm), highlighting the dependence of the effective spatial resolution on practical analysis conditions such as beam focusing, sample topography, and counting statistics.

<figure><img src="image_19.png" /><figcaption>**Fig. 13** Depth diatomic logarithmic SIMS profiles of the oxide films grown on pure Co reference samples oxidised at 600 °C for 50 min: a Vertical profile realised employing the mapping of the ¹⁸O signal of the oxide film grown on the Co-10Cr sample. The probe size is obtained by analysing the width of the obtained profile b between the values corresponding to 85% and 15% of the IMAX</figcaption></figure>
# Appendix B

## Analysis of the Oxide Layer on the Reference Samples

The analysis of the reference samples, oxidised exclusively with a single oxygen isotope ($^{16}$O₂ or $^{18}$O₂ supply bottles), was conducted to strengthen the robustness of the interpretation and quantification of the SIMS analyses following the sequential oxidation tests using both isotopes. The primary objective was to accurately quantify the minority oxygen isotope within an oxide layer enriched in the major oxygen isotope, Figure 14 presents the isotopic ratio profiles as a function of depth, measured using monoatomic (O⁻) negative secondary ions for a fixed time of 2000 seconds. Initially, the isotopic ratio of the minor isotope was measured in both reference samples: $^{18}$O in the reference sample oxidised under $^{16}$O₂ (called “Co ref. $^{16}$O₂” in Table 2) and $^{16}$O in the reference sample oxidised under $^{18}$O₂ (called “Co ref. $^{18}$O₂” in Table 2):

* The $^{18}$O/O$_{TOTAL}$ intensities ratio of the sample oxidised in a $^{16}$O-rich atmosphere (“Co ref. $^{16}$O$_2$”) is presented in Fig. 14 a. The O$_{TOTAL}$ signal corresponded to the sum of the intensities of both $^{16}$O and $^{18}$O signals. The calculated ratio remained relatively stable throughout the measure, with an average value of 0.22 at%. This value was in good agreement with the natural isotopic abundance of $^{18}$O in natural oxygen (0.20 at%), confirming the accuracy of the SIMS for $^{18}$O quantification in an oxide formed in a $^{16}$O-rich environment. This value was used as the s$_{18}$° background signal in the calculation of Eq. 6.

* The $^{16}$O/O$_{TOTAL}$ intensities ratio of the sample oxidised in a $^{18}$O-rich atmosphere (“Co ref. $^{18}$O$_2$”) is presented in Fig. 14b. The calculated ratio remained stable throughout the measure, with an average value of 4.3 at%, which is consistent with the value of impurity levels of $^{16}$O isotopes measured by QMS in the $^{18}$O$_2$

<figure><img src="image_20.png" /><figcaption>Fig. 14 a Vertical profile realised employing the mapping of the $^{18}$O signal of the oxide film grown on the Co-10Cr sample. The probe size is obtained by analysing the width of the obtained profile b between the values corresponding to 85% and 15% of the I$_{MAX}$</figcaption></figure>
supply gas. This value was used as the $s_{16}^{\circ}$ background signal value in the calculation of Eq. 6.

The profiles of the diatomic species $^{16}\text{O}_2^-$ (m/z = 32), $^{16}\text{O}^{18}\text{O}^-$ (m/z = 34), and $^{18}\text{O}_2^-$ (m/z = 36) were analysed in both reference samples, as shown in Fig. 15. The results from the reference samples aligned with the expectation that the minority isotopes are randomly distributed within the oxide lattice, as they are present in the supply gas under the form of impurities. Consequently, the experimental profiles of the minority diatomic species in each reference aligned with the “fully mixed” theoretical profile calculated using equation 5. This applies to the $s_{36}$ signal (corresponding to the $^{18}\text{O}_2$ species) in the reference sample oxidised under $^{16}\text{O}_2$ and the $s_{32}$ signal (corresponding to the $^{16}\text{O}_2$ species) in the reference sample oxidised under $^{18}\text{O}_2$. The measured $s_{36}$ signal intensities in Figure 15 correspond to the background diatomic signals intensity ($s_{36}^{\circ}$) be used in equation 6 after the sequential oxidation tests.

<figure><img src="image_21.png" /><figcaption>Fig. 15 Isotopic ratios of the minority isotope obtained by dynamic SIMS of the oxide films grown on pure Co reference samples oxidised at 600 °C for 50 min: a under an $^{16}\text{O}$-rich atmosphere (“Co ref. $^{16}\text{O}_2$”); b under a $^{18}\text{O}$-rich atmosphere (“Co ref. $^{18}\text{O}_2$”)</figcaption></figure>
# Appendix C

## Flux Calculation for Gaseous Diffusion in Short Circuits of Diffusion

The diffusion regime in a short circuit of diameter $l$ (nm) can be characterised by the Knudsen number ($K_n$), defined by:

$$K_n = \frac{\lambda}{l} \qquad (10)$$

The mean free path ($\lambda$) represents the average distance travelled by a gas molecule of diameter $d$ between two successive collisions. When the relative motion of the molecules is taken into account, its expression is given by:

$$\lambda = \frac{1}{\pi d^2 n_v \sqrt{2}} = \frac{k_B T}{P \pi d^2 \sqrt{2}} \qquad (11)$$

With: $\lambda$ the mean free path (in nm); $d$ the short-circuit diameter (in nm); $n_v$ the number of molecules per unit volume (in mol/nm3). Its expression can be determined using Avogadro's number ($N_A$) and the ideal gas law ($PV = nRT$), leading to the following expression:

$$n_v = \frac{nN_A}{V} = \frac{PN_A}{RT} = \frac{P}{k_B T}$$

When the average diameter of the short circuit is significantly greater than the mean free path of the gas molecules ($K_n \ll 1$), the resistance to mass transfer is mainly governed by intermolecular collisions, characteristic of the pure molecular diffusion regime [89]. In contrast, when the average diameter of the short circuit is much smaller than the mean free path or comparable to the molecular size ($K_n \gg 1$) mass transfer is dominated by collisions between gas molecules and the walls of the short circuit. This situation corresponds to the Knudsen diffusion regime, where the behaviour of ideal gases dictates molecular interactions [90].

The diffusion coefficient in the Knudsen regime ($D_k$) is given by the following expression, according to the kinetic theory of gases:

$$D_k = \frac{l}{3} \sqrt{\frac{8RT}{\pi M}} \qquad (12)$$

With: $l$ the short-circuit diameter (in nm); $R$ the ideal gas constant ($R = 8,314 \text{ J.K}^{-1}\text{.mol.}^{-1}$); $T$ the temperature (in K); $M$ the molar mass of the considered molecule.

**Acknowledgements** We would like to express our gratitude to E. Loire and M.-A. Pinault-Thaury from GEMAC (Groupe d'Étude de la Matière Condensée) at Université de Versailles Saint-Quentin-en-Yvelines for assistance with SIMS analysis. We also extend our thanks to J. Aleon from the Institut de Méralogie, de Physique des Matériaux et de Cosmochimie at the Museum National d'Histoire Naturelle for his role as the scientific coordinator of the NanoSIMS. Additionally, we are grateful to P. Berthod and L. Aranda from the Institut Jean Lamour at Nancy for their contribution to the manufacturing of the alloys. Finally, we would like to thank D. Monceau for the enriching and insightful discussions on this article.
**Author Contributions** S.D.M. performed the sample preparation, the isotopic oxidation experiments and first analysed the results. S.D.M., L.M., and F.R. analysed the results and drew the conclusions. S.D.M. wrote the original draft of the manuscript, which was reviewed and edited by S.D.M., L.M., and F.R. F.J. carried out the SIMS analyses of the samples. M.V.-P. performed the nanoSIMS mappings. All authors approved the final version of the manuscript.

**Funding** Open access funding provided by Commissariat à l'Énergie Atomique et aux Énergies Alternatives. The authors received no financial support for the research, authorship, and/or publication of this article.

**Data Availability** No datasets were generated or analysed during the current study.

## Declarations

**Conflict of interest** The authors declare no competing interests.

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## Authors and Affiliations

Sergio Diez Mayo<fnref n="1" />,<fnref n="2" /> · Fabien Rouillard<fnref n="2" /> · François Jomard<fnref n="3" /> · Maximilien Verdier Paoletti<fnref n="4" /> · Laure Martinelli<fnref n="2" />

<figure><img src="image_23.png" /></figure>

Fabien Rouillard
fabien.rouillard@cea.fr

Sergio Diez Mayo
sergio.diezmayo@cea.fr

François Jomard
francois.jomard@uvsq.fr

Maximilien Verdier Paoletti
maximilien.verdier@mnhn.fr

Laure Martinelli
laure.martinelli@cea.fr

<footnote n="1">¹ Chimie Physique et Chimie Analytique de Paris-Centre (ED-388), Université Paris Sorbonne, 75252 Paris 05, France</footnote>

<footnote n="2">² Service de Recherche en Corrosion et Comportement des Matériaux, Université Paris-Saclay, CEA, 91191 Gif-sur-Yvette, France</footnote>

<footnote n="3">³ Groupe d'Étude de la MATière Condensée (GEMAC), Université de Versailles Saint-Quentin-en-Yvelines, 78035 Versailles, France</footnote>

<footnote n="4">⁴ Institut de Minéralogie, de Physique Des Matériaux et de Cosmochimie, CNRS UMR7590, 75231 Paris 05, France</footnote>