# Quantitative analysis of TiO2 formation on TA6V terrestrial atmospheric re-entries: Cross comparison of SEM-EDS, XRD, Raman spectroscopy and CF-LIBS measurements

Adrien Brault, Aurélien Favre, Léo Gosse, Myriam Hoblos, David Gibouin, Samuel Jouen, Hilary-Laure Bilongo Moussol, Arnaud Bultel, Pascal Boubert, Julien Annaloro

► To cite this version:

Adrien Brault, Aurélien Favre, Léo Gosse, Myriam Hoblos, David Gibouin, et al. Quantitative analysis of TiO2 formation on TA6V terrestrial atmospheric re-entries: Cross comparison of SEM-EDS, XRD, Raman spectroscopy and CF-LIBS measurements. Acta Astronautica, 2026, 240, pp.830 - 839. 10.1016/j.actaastro.2025.12.045. hal-05459258

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Submitted on 15 Jan 2026

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Research paper

# Quantitative analysis of TiO₂ formation on TA6V terrestrial atmospheric re-entries: Cross comparison of SEM-EDS, XRD, Raman spectroscopy and CF-LIBS measurements

<figure><img src="image_2.png" /></figure>

Adrien Brault<sup>a ID</sup>, Aurélien Favre<sup>a ID,*</sup>, Léo Gosse<sup>a ID</sup>, Myriam Hoblos<sup>a</sup>, David Gibouin<sup>b ID</sup>, Samuel Jouen<sup>b</sup>, Hilary-Laure Bilongo Moussol<sup>a ID</sup>, Arnaud Bultel<sup>a ID</sup>, Pascal Boubert<sup>a</sup>, Julien Annaloro<sup>c ID</sup>

## ARTICLE INFO

Keywords:

Ti-6Al-4V titanium alloy
Oxidation
SEM-EDS
XRD
Raman spectroscopy
Calibration-Free LIBS
Aerospace

## ABSTRACT

The Ti-6Al-4V (TA6V) titanium alloy is extensively used in aerospace applications, owing to its remarkable combination of low density, high mechanical strength, and excellent oxidation resistance. Understanding its oxidation behavior is therefore essential for assessing debris survivability during terrestrial atmospheric re-entry, where the material is exposed to air plasma conditions.

This paper compares complementary experimental techniques: Scanning Electron Microscopy coupled with Energy-Dispersive X-ray Spectroscopy (SEM-EDS), X-ray Diffraction (XRD), Raman spectroscopy, and Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) on a TA6V sample oxidized under conditions representative of atmospheric re-entry. Conventional analyses (SEM-EDS, XRD, Raman) consistently confirm that the predominant oxide formed is rutile TiO₂ (~6 µm thick). Spectroscopic analysis of the LIBS plasma provides complementary depth-resolved insights. Elemental profiling, which is obtained by simulating the experimental spectra using the MERLIN code, shows that the O/Ti ratio sharply decreases from a stoichiometric value towards a residual null value. Using the measured laser ablation rate, the oxide thickness is found to be consistent with the SEM observations. This work demonstrates that LIBS enables quantitative depth-resolved measurements, providing direct access to oxygen gradients and oxide stoichiometry in a single experiment.

## 1. Introduction

The Ti-6Al-4V titanium alloy, commercially named TA6V, is one of the most widely used titanium alloys owing to its remarkable combination of low density, high mechanical strength, and excellent oxidation resistance [1]. It is extensively employed in aerospace applications [2], particularly in the fabrication of fuel tanks [3,4]. Because of its widespread use in the aerospace sector, TA6V may be part of debris generated during terrestrial atmospheric re-entry, where it is subjected to oxidation under air plasma conditions. Understanding its oxidation behavior in such environments is therefore essential for assessing debris survivability during re-entry.

The oxidation behavior of TA6V has been widely investigated, mainly under standard atmospheric conditions in furnaces, over broad ranges of exposure time, from 0.5 h to 140 days and temperature, from

400 to 1550 °C [5–10]. The formation of TiO₂ in its rutile phase is consistently reported. Secondary oxides such as Al₂O₃ and TiVO₄ are detected from approximately 900 °C. Depending on the oxidation temperature, other oxides including TiO₂ anatase, TiO, V₂O₅, and Al₂TiO₅ are also identified. The protective oxide layers formed at low temperature are generally dense and adherent, whereas at higher temperatures they tend to become porous and prone to delamination. However, these results do not reproduce the conditions encountered in plasma during atmospheric re-entry, where the gas composition, pressure, and thermodynamic non-equilibrium phenomena significantly alter the oxidation mechanisms. Among the few studies examining TA6V behavior under plasma environments, some are not representative of re-entry conditions [11,12] and others, conducted under more relevant conditions, do not specifically investigate the oxidation mechanisms [13,14].

<footnote><sup>a</sup> CORIA, UMR 6614, CNRS, Université de Rouen Normandie, INSA Rouen Normandie, 76801 Saint-Etienne du Rouvray, France</footnote>

<footnote><sup>b</sup> GPM, UMR 6634, CNRS, Université de Rouen Normandie, INSA Rouen Normandie, 76801 Saint-Etienne du Rouvray, France</footnote>

<footnote><sup>c</sup> CNES Toulouse, 18 avenue Edouard Belin, 31400 Toulouse, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: adrien.brault@coria.fr (A. Brault), aurelien.favre@coria.fr (A. Favre).</footnote>

<footnote>URL: http://www.coria.fr (A. Favre).</footnote>
The most representative study of atmospheric re-entry plasma conditions that also investigated the oxidation mechanisms of TA6V is reported by Balat-Pichelin et al. [15,16] at the PROMES laboratory, using the MESOX setup [17]. Experiments were performed in air plasmas at pressures of 300 and 2000 Pa, for sample surface temperatures ranging from 1030 to 1630 °C and oxidation durations between 50 and 470 s. The analyses reveal the formation of rutile TiO₂ as the dominant oxide, along with traces of TiO, Ti₂O₃, and anatase TiO₂. The resulting oxide layer was found to be fragile and prone to delamination, this effect becoming more and more pronounced at higher temperatures.

To investigate material oxidation, several complementary experimental techniques can be employed, each providing specific information. Scanning Electron Microscopy coupled with Energy-Dispersive X-ray Spectroscopy (SEM-EDS) enables imaging of surface morphology and provides quantitative elemental information [18]. However, this technique is less sensitive to light elements and cannot directly identify crystalline phases. X-ray Diffraction (XRD) is used to identify the specific atomic planes of crystalline phases present in the oxide layer [19]. Its main limitation lies in its inability to detect amorphous phases. Raman spectroscopy offers a complementary diagnosis by detecting the characteristic vibrational modes of specific compounds, allowing the identification of crystalline and amorphous oxides [20]. Nevertheless, for species with a low concentration, the signal can be weak and covered by fluorescence. Moreover, this technique is not very sensitive to metal bonds. Finally, the Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) provides information on the elemental composition gradients [21-23]. However, this quantification requires the achievement of Local Thermodynamic Equilibrium (LTE) and the determination of plasma parameters [24,25].

In the present paper, these complementary characterization techniques are applied to a TA6V sample oxidized under conditions representative of terrestrial atmospheric re-entry. By combining morphological, structural, and spectroscopic analyses, this work aims to assess and discuss the consistency and complementarity of the different techniques.

In the upcoming sections, the oxidation process, the sample studied and the experimental setups are first presented. Experimental results obtained are successively described, discussed and compared.

## 2. Material and experimental setups

### 2.1. Samples preparation and oxidation

The TA6V alloy used in this work is provided by CGM (Comptoir Général des Métaux). The material underwent annealing at 750 °C followed by 60 min of air cooling. Its nominal chemical composition, reported by Baoji First Titanium Industry (Group) Co., Ltd, is listed in Table 1. Disc-shaped specimens with a thickness of 3 mm are prepared, having diameters of 26.5 mm on the plasma-exposed face and 30.0 mm on the rear face. The surface interacting with the plasma is polished with SiC #2400 abrasive papers. After polishing, the samples are cleaned in an ultrasonic bath containing acetone first, then propanol before being dried.

The TA6V sample is oxidized in the SOUPLIN (SOUfflerie à Plasma INductif) setup of the CORIA laboratory depicted in Fig. 1. A wind tunnel equipped with an inductively coupled plasma torch allows the production of similar atmospheric re-entry conditions. The pumping system achieves a vacuum pressure of ~100 Pa and the air plasma is

<table><caption>**Table 1**

Chemical composition in wt.% as received of the TA6V alloy.</caption><thead><tr><th></th><th>Al</th><th>V</th><th>Fe</th><th>O</th></tr></thead><tbody><tr><td>Ti<br>Balance</td><td>6.43</td><td>4.10</td><td>0.17</td><td>0.165</td></tr><tr><td>C<br>0.02</td><td>N<br>0.014</td><td>H<br>0.001</td><td>Y<br>&lt; 0.001</td><td>Residuals<br>&lt; 0.040</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Schematic view of the SOUPLIN setup.</figcaption></figure>

generated from 1300 to 20000 Pa. The plasma torch is operated using a TEKNA System 105 radio frequency generator operating at 1.8 MHz, with a maximum input power of 60 kW delivered to the plasma. The coil surrounding a quartz tube generates an electromagnetic field which inductively heats the injected air at a flow rate of 2.4 g s⁻¹, generating an air plasma with a specific enthalpy of 5 to 15 MJ kg⁻¹. Within the wind tunnel, the plasma expands and impinges on the sample. The specimen is placed on a holder equipped with a SiC cap, and its rear-face temperature is recorded by both spring-loaded K and R-type thermocouples ensuring proper contact.

The sample studied here is oxidized for 90 s, at 1400 Pa and 4.6 MJ kg⁻¹. The temporal evolution of its temperature shown in Fig. 2, indicates that the sample reaches a maximum of 760 °C without any stabilization of the temperature. Since oxidation takes place under non-isothermal conditions, the behavior observed in the SOUPLIN setup differs fundamentally from oxidations carried out in furnaces or in the PROMES laboratory [15,16], where the temperature of the sample remains constant throughout the oxidation. In a previous work, TA6V samples were oxidized in the SOUPLIN setup under two conditions: (1400 Pa, 4.6 MJ kg⁻¹) for exposure times ranging from 30 to 120 s, and (4500 Pa, 7.3 MJ kg⁻¹) for 30 to 90 s [26]. The oxide layer began to delaminate after approximately 60 s under both conditions. Analyses showed that rutile TiO₂ was the predominant oxide throughout the entire oxide layer thickness, with no detectable anatase phase, in contrast to previous reports [6,7,11,12,15,16]. The α-Al₂O₃ phase was detected in smaller proportions at the outer surface of the oxide layer for samples oxidized below 1150 °C. Above this temperature, the ternary oxide Al₂TiO₅, resulting from the reaction between TiO₂ and Al₂O₃, was observed. Nitride TiN, not previously reported in studies on TA6V oxidation, was also detected in very small quantities throughout the oxide layer.

Fig. 3 shows pictures of the polished sample (pure TA6V), the sample after oxidation (TiO₂–TA6V) before any analysis and the oxidized sample after LIBS analysis. The ablated areas of interest are highlighted in blue and red. The unique blue spot stands for N = 10 laser irradiations (used for SEM-EDS analysis in Section 3.1.1). The 5 red spots correspond to N = 50 laser shots (used for LIBS analysis in Section 3.2). On the oxidized sample, two zones can be distinguished: a dark zone in the center where the oxide is detached from the surface, and a golden zone where the oxide still adheres to the substrate.

### 2.2. SEM-EDS, XRD and Raman spectroscopy

The scanning electron microscopy coupled to energy dispersive X-ray spectroscopy (SEM-EDS) analyses are carried out with a JEOL JSM-7900F microscope, operated at a voltage of 15 kV and a current of 2 nA. The EDS detector used is the ELITE SUPER - 70 mm² model from Ametek with APEX software.

X-ray diffraction (XRD) is operated on an Empyrean diffractometer (PAnalytical), using Co-Kα₁ radiation (λ<sub>Co</sub>=0.179 nm). The operating conditions are 40 kV and 40 mA. Data are collected over a 2θ interval of
<figure><img src="image_4.png" /><figcaption>Fig. 2. Temporal evolution of the temperature of the oxidized TA6V sample for 90 s at 1400 Pa and 4.6 MJ kg⁻¹.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Images of the studied sample. (a): polished TA6V, (b): oxidized TA6V (TiO₂–TA6V) before any analysis and (c) oxidized TA6V (TiO₂–TA6V) after LIBS analysis. Ablated regions of interest are highlighted with blue (N = 10 laser shots) and red (N = 50 laser shots) arrows. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

30° to 110° with a step size of 0.01°. Phase analysis is performed using DIFFRAC.EVA software (Bruker AXS). The probed area corresponds to 2 × 2 mm².

Raman spectroscopy is carried out on a Horiba Soleil spectrometer, using two lasers of wavelengths 638 and 532 nm. A 50× objective is used to focus the beam, resulting in a spot diameter smaller than 1 µm on the sample surface.

## 2.3. LIBS platform

The experiments are performed on the PLEIADES (Plasmas by LasEr Irradiations and their Experimental Studies) platform of the CORIA laboratory [27]. The experimental setup is schematized on Fig. 4 and technical characteristics are given on Table 2.

A nanosecond Nd:YAG QUANTEL Brilliant Eazy laser source is used. The infrared laser pulse is reflected on three high flux mirrors in the direction of a high pass dichroic plate. The laser pulse is then focused by the lens L₀ positioned at (120 ± 1) mm from the surface sample. The chamber atmosphere is composed of argon (purity ~99%) at 5 × 10⁴ Pa. The main detected impurity from gaseous atmosphere is hydrogen which content is measured to be ≲ 1 at.%. The chamber is insulated by optical high flux window. The focused laser spot diameter is estimated to be (400 ± 50) µm on surface sample. This induces a peak fluence of (47 ± 3) J cm⁻² which corresponds to a peak flux density of (1.9 ± 0.1) × 10¹⁴ W m⁻². These irradiation conditions are chosen as a compromise between depth and surface ablation to ensure a high enough single shot ablated mass and thus a reliable depth profiling resolution.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Schematic view of the LIBS experimental setup. The infrared laser pulse is transmitted by a dichroic plate then focused on the TiO₂–TA6V sample (green optical path) placed in a controlled atmosphere chamber (5×10⁴ Pa of Ar). The laser-induced plasma emission is retro collected collinearly in the direction of a fibered device (red optical path) coupled with an echelle spectrometer and a detector. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

The dichroic plate is characterized by a spectral reflectivity $\rho_{\lambda}$ between 270 nm and 720 nm such that 0.20 < $\rho_{\lambda}$ < 0.98. The light emitted by the laser-induced plasma is therefore in part reflected by the plate towards a second lens L₁ which focuses the light collected on the entrance of a circular bundle of optical fibers. The exit of these fibers are aligned on the 50 µm entrance slit of a Aryelle Butterfly echelle spectrometer.

The acquisition is synchronized with each laser pulse. The information travel time in the cables has been estimated to (180.0 ± 2.5) ns. The acquisition time and the integration window are respectively fixed to 1.5 µs and 1.0 µs. In our operating conditions, this ensures a satisfactory single shot signal-to-baseline ratio for both neutral and ion transitions. The plasma dynamics is not developed in this paper since we only focus on species profiling. The repeatability of the measurements are tested on the 5 different laser spots (with N = 50 laser irradiations) allowing to frame the statistical mean spectral radiance with its corresponding standard deviation. Each spot is separated by at least a distance of 3 mm

<table><caption>**Table 2**

Technical characteristics associated to Fig. 4 device.</caption><thead><tr><th>Element</th><th>Data</th><th>Symbol</th><th>Value</th></tr></thead><tbody><tr><td rowspan="5">QUANTEL</td><td>Pulse wavelength</td><td>λ<sub>L</sub></td><td>1064 nm</td></tr><tr><td>Energy</td><td>E<sub>L</sub></td><td>60 mJ</td></tr><tr><td>Pulse duration</td><td>τ<sub>L</sub></td><td>5.0 ns</td></tr><tr><td>Repetition rate</td><td>ν</td><td>10 Hz</td></tr><tr><td>Quality factor</td><td>M<sup>2</sup></td><td>3.2</td></tr><tr><td rowspan="2">laser source</td><td>Pulse-to-pulse stability</td><td>ΔE<sub>L</sub>/E<sub>L</sub></td><td>0.2%</td></tr><tr><td>Focal length</td><td>f<sub>0</sub><br>f<sub>1</sub></td><td>150 mm<br>250 mm</td></tr><tr><td rowspan="3">LTB<br>Aryelle Butterfly</td><td>Focal length</td><td>f<sub>s</sub></td><td>400 mm</td></tr><tr><td>Aperture</td><td>f<sub>a</sub>/10</td><td></td></tr><tr><td>Optical fiber diameter</td><td>d<sub>s</sub></td><td>200 µm</td></tr><tr><td rowspan="3">Andor iStar DH334T<br>(1024 × 1024 pixels)</td><td>Pixel size</td><td></td><td>13 × 13 µm<sup>2</sup></td></tr><tr><td>Mean</td><td></td><td></td></tr><tr><td>quantum efficiency on [400, 800] nm</td><td>η</td><td>~10 %</td></tr></tbody></table>
from the next. This distance is larger than redeposition radius in our experimental conditions. This ensures no ablation contamination of a raw surface to be profiled. Finally, spectral emission of the plasma is studied over each of the N = 50 consecutive laser shots. In our conditions, the ablated depth remains negligible compared to the ablation diameter which strongly limits screening effects [28].

The calibration in spectral radiance is performed using a tungsten ribbon lamp. The collection of the calibration radiation is carried out exactly in the same way as the collection of radiation from laser-induced plasma. In addition, the wavelength calibration is performed by using low pressure rare gas lamps.

# 3. Results and discussion

## 3.1. SEM-EDS, XRD and Raman results

### 3.1.1. SEM-EDS analysis

Figs. 5 and 6 show SEM images of the surface of TiO₂-TA6V sample after respectively N = 10 and N = 50 pulses. The two images exhibit a crater of ~400 µm diameter, which is consistent with the laser spot diameter. This is explained by the laser irradiance that is ~10 times greater than Ti ablation threshold [29]. In both cases, the craters exhibit a cracked morphology, distinct from the oxidized granular structure observed at the periphery. These cracks are most likely due to the rapid heating induced by the laser pulses, followed by abrupt cooling, which generates thermomechanical stresses that weaken the material.

After N = 50 pulses, the very center of the crater displays a smoother morphology, without cracks or granular features. This region might correspond to a thin resolidified layer produced by repeated melting and rapid cooling. In contrast, the surrounding cracked areas result from intense heating that was insufficient to cause complete melting.

The EDS analyses of the two craters (Table 3) indicate that the chemical compositions in the oxidized zone and inside the crater remain essentially unchanged after N = 10 and N = 50 pulses. The oxidized zone is very rich in oxygen, with an O/Ti ratio close to the stoichiometry of TiO₂. Compared to the TA6V composition, it also shows a higher proportion of aluminum and a lower proportion of vanadium, consistent with the observations on the same sample previously reported [26]. Within the crater, the oxygen content decreases strongly, while the titanium fraction increases significantly. At the same time, the vanadium and aluminum contents approach those of the unoxidized reference sample. This suggests that the crater corresponds

<caption>**Table 3**</caption>

EDS analysis in at.% of the oxide zone and the crater of the TiO₂-TA6V sample after N = 10 and N = 50 laser pulses.

<table><thead><tr><th></th><th></th><th>O</th><th>Ti</th><th>Al</th><th>V</th></tr></thead><tbody><tr><td rowspan="2">N = 10</td><td>Oxide zone</td><td>64.8</td><td>20.7</td><td>13.1</td><td>1.4</td></tr><tr><td>Crater</td><td>14.3</td><td>75.7</td><td>6.9</td><td>3.1</td></tr><tr><td rowspan="2">N = 50</td><td>Oxide zone</td><td>65.7</td><td>21.8</td><td>11.4</td><td>1.1</td></tr><tr><td>Crater</td><td>10.8</td><td>77.9</td><td>7.6</td><td>3.7</td></tr></tbody></table>

to a region with little or no oxidation with a composition similar to original substrate.

Fig. 7 shows a SEM image of the TiO₂-TA6V crater edge after N = 10 pulses, with the sample tilted by 39°, where red lines represent the measured thickness of the apparent oxide layer. Compared to the previous SEM images, this tilted view provides a quasi cross-sectional perspective of both the crater interior and the surrounding oxide. Although this does not constitute a true cross-sectional analysis, it highlights the porosity of the oxide layer, indicative of its fragility and an apparent oxide thickness of ~4 µm. The parallax correction leads to a projected effective thickness of 6 µm. The measured surface mass gain is 1.0 mg cm⁻². Those values are consistent with previous results (1.3 mg cm⁻² associated with an oxide thickness of 7 µm) previously obtained on this same sample [26].

### 3.1.2. X-ray diffraction

The X-ray diffractograms of TiO₂-TA6V obtained in the crater zone after N = 50 pulses and in a non ablated golden oxide zone are presented in Fig. 8. In both cases, diffraction peaks corresponding to the most stable titanium phase at room temperature, αTi (PDF 89-2762) and to rutile TiO₂ (PDF 65-0191), with no detectable anatase phase, are observed [26]. However, no TiN peaks are detected. This absence is attributed to the intrinsically low intensity of TiN peaks and the reduction of the analyzed area to 2 × 2 mm². Such a restricted area was necessary to target specific regions, but it results in lower overall diffracted intensity, making weak phases like TiN more difficult to be detected.

Because the XRD probe area is much larger than the LIBS crater, the diffractograms represent an averaged crystallographic response of both the crater and surrounding oxide. As a result, phases confined in the crater can be diluted by the contribution of surrounding unmodified oxide. This explains the similarity between the two diffractograms, except the intensity of the rutile peak located at 31.9°, which is more intense in the oxide region, suggesting a lower TiO₂ amount inside the crater.

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** SEM image of the surface of TiO₂-TA6V sample after N = 10 pulses.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** SEM image of the surface of TiO₂-TA6V sample after N = 50 pulses.</figcaption></figure>
<figure><img src="image_9.png" /></figure>

Fig. 7. SEM image of the TiO₂-TA6V crater edge after *N* = 10 pulses, sample tilted by 39°. The measurement of apparent oxide layer thickness is based on the two boundary red lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

<figure><img src="image_10.png" /></figure>

Fig. 8. Diffractograms of TiO₂-TA6V for a crater after *N* = 50 pulses and for non ablated golden oxide zone.

### 3.1.3. Raman spectroscopy

Raman analyses are carried out both in the oxidized area surrounding a *N* = 50 pulses crater and inside the crater itself, with representative spectra shown in Fig. 9. On the oxide zone spectrum, the characteristic peaks of rutile TiO₂ [30–33] (140, 247, 435, and 608 cm⁻¹), also identified by XRD, are clearly observed, with no detectable anatase phase. The oxide layer appears homogeneous across the surface, with no variation in the Raman spectra from point to point. The band around 800 cm⁻¹ is attributed to Ti-O vibrations in aluminum titanate [34]. In contrast, the spectrum acquired within the crater is characterized by a low intensity with no discernible peaks. It indicates that no oxide is detected inside the crater. This suggests that the laser pulses either fully delaminated the oxide layer at the surface or ablated deep enough into the material such that no oxide remains detectable.

## 3.2. CF-LIBS results

### 3.2.1. Ablation rate

Craters were produced both on a non-oxidized reference sample (pure TA6V) and on the TiO₂-TA6V sample. The crater depth was

<figure><img src="image_11.png" /></figure>

Fig. 9. Raman spectra of TiO₂-TA6V for a crater after *N* = 50 pulses and for non ablated golden oxide zone.

evaluated from the difference between local maximum depth compared to the average elevation measured on two opposite sides along the crater diameter using an optonumerical microscope Keyence VHX-5000. The evolution of crater depth as a function of the pulse number *N* is presented on Fig. 10 for both the TA6V reference (in red) and TiO₂-TA6V (in blue) samples. In our experimental conditions, the ablation regime derives from linear trend after respectively *N* = 5 and *N* = 10 for the TA6V reference and TiO₂-TA6V samples. The ablation rate is estimated from linear ablation regime represented by red and blue dashed lines for the TA6V reference and TiO₂-TA6V samples, respectively. The values obtained are $t_{ref,TA6V} = (0.81 \pm 0.21)$ µm pulse⁻¹ and $t_{TiO_2-TA6V} = (0.58 \pm 0.15)$ µm pulse⁻¹ for the reference TA6V and TiO₂-TA6V samples respectively. These similar values indicate that the presence of oxygen in titanium has only a limited impact on the ablation process.

<figure><img src="image_12.png" /></figure>

Fig. 10. Depth evolution as a function of the pulse number *N* for the reference and TiO₂-TA6V samples. The dashed lines in red and blue represent respectively the linear ablation regimes of the TA6V reference and TiO₂-TA6V samples. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
<table><caption>**Table 4**
Ar and H transitions studied for the measurement of $n_e$. Stark impact factors $\omega_{kl}$ are given for a reference perturber density $n_{e,r}$ and for $T \in [9800, 13400]$ K.</caption><thead><tr><th></th><th>λ<sub>kl</sub><br>(nm)</th><th>A<sub>kl</sub><br>(10<sup>7</sup> s<sup>-1</sup>)</th><th>E<sub>i</sub><br>(eV)</th><th>E<sub>k</sub><br>(eV)</th><th>g<sub>i</sub></th><th>g<sub>k</sub></th><th>n<sub>e,r</sub><br>(10<sup>23</sup> m<sup>-3</sup>)</th><th>ω<sub>kl</sub><br>(nm)</th><th>Ref.</th></tr></thead><tbody><tr><td>Ar I</td><td>416.42</td><td>0.029</td><td>11.548</td><td>14.525</td><td>5</td><td>3</td><td>0.14</td><td>0.0300</td><td>[36,37]</td></tr><tr><td>Ar I</td><td>420.07</td><td>0.097</td><td>11.548</td><td>14.499</td><td>5</td><td>7</td><td>0.45</td><td>0.0940</td><td>[36,37]</td></tr><tr><td>Ar I</td><td>430.01</td><td>0.038</td><td>11.624</td><td>14.506</td><td>3</td><td>5</td><td>0.22</td><td>0.0480</td><td>[36,38]</td></tr><tr><td>H I</td><td>656.28</td><td>6.46</td><td>10.199</td><td>12.087</td><td>4</td><td>6</td><td>1.00</td><td>1.0980</td><td>[36,39]</td></tr><tr><td>Ar I</td><td>696.54</td><td>0.64</td><td>11.548</td><td>13.328</td><td>5</td><td>3</td><td>0.60</td><td>0.0400</td><td>[36,40]</td></tr><tr><td>Ar I</td><td>706.72</td><td>0.38</td><td>11.548</td><td>13.302</td><td>5</td><td>5</td><td>0.10</td><td>0.0066</td><td>[36,41]</td></tr><tr><td>Ar I</td><td>738.40</td><td>0.85</td><td>11.624</td><td>13.302</td><td>3</td><td>5</td><td>0.10</td><td>0.0071</td><td>[36,41]</td></tr><tr><td>Ar I</td><td>750.39</td><td>4.50</td><td>11.828</td><td>13.480</td><td>3</td><td>1</td><td>0.10</td><td>0.0085</td><td>[36,41]</td></tr><tr><td>Ar I</td><td>751.47</td><td>4.00</td><td>11.624</td><td>13.273</td><td>3</td><td>1</td><td>0.10</td><td>0.0074</td><td>[36,41]</td></tr><tr><td>Ar I</td><td>763.51</td><td>2.45</td><td>11.548</td><td>13.172</td><td>5</td><td>5</td><td>0.10</td><td>0.0074</td><td>[36,41]</td></tr><tr><td>Ar I</td><td>772.42</td><td>1.17</td><td>11.723</td><td>13.328</td><td>1</td><td>3</td><td>0.10</td><td>0.0068</td><td>[36,41]</td></tr></tbody></table>

### 3.2.2. Electron density

CF-LIBS method preliminary requires the analysis of laser-induced plasma parameters, namely the electron density and temperature. Electron density $n_e$ is measured by exploiting the Stark broadening of transitions of the main element in the plasma. Our plasma study exhibits mole fractions of Ar $\ge$ 0.80. We here focus on Ar I transitions since no exploitable Ar II transitions are observed in our conditions. Even with a poor signal-to-baseline ratio (mole fraction $\le$ 10$^{-2}$) H I Balmer-$\alpha$ transition is exploited due to its high sensitivity to electron density. The apparatus function being Lorentzian and the Lorentzian Stark contribution being predominant, we can reasonably consider that the line profile is purely Lorentzian. For a transition $k \to i$, its total radiance $L_{ki}$ can thus be expressed as a product of the maximum of the spectral radiance $L_{\lambda_{ki}}$ and its Lorentzian full-width at half maximum (FWHM) $\Delta\lambda_{1/2,L}$ such as

$$L_{ki} = \int_{-\infty}^{+\infty} L_{\lambda,T} d\lambda = \frac{\pi}{2} \cdot \max(L_{\lambda_{ki}}) \cdot \Delta\lambda_{1/2,L} \quad (1)$$

The $n_e$ measurements are performed using the linearly scaled Griem formalism [35]:

$$\Delta\lambda_{1/2,L}^S(n_e, T) = 2 \omega_{ki}(T) \left( \frac{n_e}{n_{e,r}} \right) \quad (2)$$

where $n_{e,r}$ is a reference value for $n_e$ and $\omega_{ki}$ is the electronic impact factor. Since Stark effect is predominant, the total Lorentzian FWHM ($\Delta\lambda_{1/2,L}$, Eq. (1)) can reasonably be fully attributed to Stark profile contribution ($\Delta\lambda_{1/2,L}^S$, Eq. (2)). The transitions studied as well as the Stark data used for the $n_e$ measurement are listed in Table 4.

The measured electron densities from pulse $N=1$ to $N=50$ are presented on Fig. 11. The mean value of $n_e$ for each pulse is indicated by a black dot. The associated uncertainty corresponds to the standard deviation derived from the different values involved by the several studied lines. From pulse $N=1$ to pulse $N=50$, the $n_e$ value is $(1.23 \pm 0.74) \times 10^{23} \text{ m}^{-3}$ (indicated by a red line). These measurements exhibit that the electron density remains stable along the LIBS profiling process. This can be explained by the high ionization potential of neutral argon and oxygen (respectively 15.76 eV and 13.62 eV) compared to the ones of neutral titanium, aluminum and vanadium close to ~6 eV. In fact, since metals are minor elements in plasma composition, a slight modification of metal mole fractions (from surface TiO$_2$ to TA6V substrates laser-induced plasma) does not significantly affect the number of electron per unit volume.

### 3.2.3. LTE temperature

The linear trend of the points in a Boltzmann plot allows the verification of local thermodynamic equilibrium (LTE) and the determination of the plasma temperature $T$. On such a plot, the ordinate is obtained from an experimental measurement of the line radiance $L_{ki}$ weighted by the ratio of spectroscopic data $\frac{\lambda_{ki}}{\lambda_{ki}g_k}$ while the abscissa is the upper level excited energy $E_k$. The low mole fraction of titanium in the plasma

<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Electron density from pulse $N=1$ to $N=50$ measured on the TiO$_2$–TA6V sample under the irradiation conditions described in Section 2.3. The mean value of each pulse $N$ is indicated by black dot. The mean value for 50 pulses is indicated by a red line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>**Table 5**
Ti transitions considered for the measurement of $T$ [36].</caption><thead><tr><th></th><th>λ<sub>ki</sub><br>(nm)</th><th>A<sub>ki</sub><br>(10<sup>7</sup> s<sup>-1</sup>)</th><th>E<sub>i</sub><br>(eV)</th><th>E<sub>k</sub><br>(eV)</th><th>g<sub>i</sub></th><th>g<sub>k</sub></th></tr></thead><tbody><tr><td>Ti I</td><td>445.33</td><td>5.98</td><td>1.430</td><td>4.213</td><td>5</td><td>5</td></tr><tr><td>Ti I</td><td>474.28</td><td>5.30</td><td>2.236</td><td>4.850</td><td>9</td><td>9</td></tr><tr><td>Ti I</td><td>482.04</td><td>1.49</td><td>1.502</td><td>4.074</td><td>9</td><td>7</td></tr><tr><td>Ti I</td><td>484.09</td><td>1.76</td><td>0.899</td><td>3.460</td><td>5</td><td>5</td></tr><tr><td>Ti I</td><td>485.60</td><td>5.20</td><td>2.256</td><td>4.808</td><td>13</td><td>15</td></tr><tr><td>Ti I</td><td>500.72</td><td>4.92</td><td>0.818</td><td>3.293</td><td>5</td><td>7</td></tr><tr><td>Ti I</td><td>517.37</td><td>0.42</td><td>0.000</td><td>2.396</td><td>5</td><td>5</td></tr><tr><td>Ti I</td><td>519.30</td><td>0.39</td><td>0.021</td><td>2.408</td><td>7</td><td>7</td></tr><tr><td>Ti I</td><td>521.04</td><td>0.39</td><td>0.048</td><td>2.427</td><td>9</td><td>9</td></tr></tbody></table>

strongly limits the self-absorption and consequently the bias on $L_{ki}$. Additionally, Ti is characterized by an electronic structure suitable for temperature measurements: the $E_k$ values associated to several exploitable transitions are distributed over wide ranges of energy. The isolated and optically-thin Ti I transitions studied are reported in Table 5 [42].

The temperatures measurements from pulse $N=1$ to $N=50$ are presented on Fig. 12. A typical Boltzmann plot of Ti I lines exploitation is displayed on the upper frame. On such a plot, the temperature is derived from the linear slope. For each pulse $N$ of the profiling
<figure><img src="image_14.png" /><figcaption>**Fig. 12.** The upper frame is a typical Boltzmann plot (lines from Table 5). The lower frame exhibits the temperature from pulse $N = 1$ to $N = 50$ measured on the TiO$_2$–TA6V sample under the irradiation conditions described in Section 2.3. The value obtained for each pulse $N$ is indicated by a black dot. The mean value for 50 pulses is indicated by a red line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

process, the values obtained are showed in black dots on the lower frame. For each point, the uncertainty is derived from $L_{ki}$ standard deviation computed from the 5 different acquisitions. The $T$ value is (10200 ± 600) K (indicated by a red line). The uncertainty of 600 K is here deduced from the statistical standard deviation obtained from the 50 pulses. In that way, we take into account the repeatability of the measurements (from one crater to the next) and the influence of the profiling process on the temperature evolution. Similarly to electron density study, we notice that $T$ remains stable along the LIBS profiling process. In addition to the linear trend of the Bolzmann plot of Fig. 12, we can verify the validity of LTE using the well known McWhirter criterion [43]:

$$n_e > n_{e,min}[\text{m}^{-3}] = 1,6 \times 10^{18} \sqrt{T_e[\text{K}]} (E_k[\text{eV}] - E_l[\text{eV}])_{\text{max}}^3 \quad (3)$$

Considering the mean values of $n_e$ and $T$ respectively presented on Figs. 11 and 12, we obtain a electron density threshold of ~$10^{19} \text{ m}^{-3}$ for a titanium plasma. Since this value is ~$10^4$ lower that our experimental measurement, this confirms that LTE is verified in our operating conditions.

### 3.2.4. Elemental densities

The population of excited states at LTE is governed by the Boltzmann statistics. Thus, for the species $X$, the population density $[X_k]$ of an emitting level $k$ is related to the total density at equilibrium $n_{X,eq.} = \sum_k [X_k]$ by

$$[X_k] = \frac{g_k}{Q_X(T)} \exp \left( -\frac{E_k}{k_B T} \right) n_{X,eq.} \quad (4)$$

with $g_k$ the degeneracy of the upper level $k$ and $Q_X(T)$ being the partition function of the species $X$ at the temperature $T$. Experimentally, for a given plasma length $\ell_p$, the population density $[X_k]$ can be derived from $L_{ki}$ by

$$[X_k] = \frac{4\pi \lambda_{ki} L_{ki}}{hc A_{ki} \ell_p} \quad (5)$$

According to Eqs. (4) and (5), the total LTE density of the species $X$ can be experimentally derived from $L_{ki}$ by

$$n_{X,eq.} = \frac{4\pi \lambda_{ki} L_{ki}}{hc A_{ki} g_k \ell_p} \exp \left( \frac{E_k}{k_B T} \right) \quad (6)$$

<table><caption>**Table 6**

Transitions considered for the measurement of $n'_{X,eq.}$ [36].</caption><thead><tr><th></th><th>λ<sub>ki</sub><br>(nm)</th><th>A<sub>ki</sub><br>(10<sup>7</sup> s<sup>-1</sup>)</th><th>E<sub>i</sub><br>(eV)</th><th>E<sub>k</sub><br>(eV)</th><th>g<sub>i</sub></th><th>g<sub>k</sub></th></tr></thead><tbody><tr><td>V I</td><td>411.18</td><td>10.00</td><td>0.301</td><td>3.315</td><td>10</td><td>10</td></tr><tr><td>Ti I</td><td>445.33</td><td>5.98</td><td>1.430</td><td>4.213</td><td>5</td><td>5</td></tr><tr><td>O I</td><td>777.42</td><td>3.69</td><td>9.146</td><td>10.740</td><td>5</td><td>5</td></tr></tbody></table>

<table><caption>**Table 7**

Measured $n'_{X,eq.}$ (truncated to $10^{19} \text{ m}^{-3}$) for laser pulse $N = 1$.</caption><thead><tr><th>Element</th><th>n'<sub>X,eq.</sub><br>(m<sup>-3</sup>)</th><th>Δn'<sub>X,eq.</sub><br>(m<sup>-3</sup>)</th></tr></thead><tbody><tr><td>V</td><td>4.34 × 10<sup>21</sup></td><td>9.4 × 10<sup>20</sup></td></tr><tr><td>Ti</td><td>8.897 × 10<sup>22</sup></td><td>1.260 × 10<sup>22</sup></td></tr><tr><td>O</td><td>2.0205 × 10<sup>23</sup></td><td>1.1460 × 10<sup>23</sup></td></tr></tbody></table>

If the transition $k \rightarrow i$ is due to a neutral specie, the total neutral density $n_{X,eq.}$ of species $X$ can be experimentally evaluated using Eq. (6). Assuming a single ionization, it is possible to derive the total element density

$$n'_{X,eq.} = n_{X,eq.} + n_{X+,eq.} \quad (7)$$

with the ion density $n_{X+,eq.}$ deduced from the ionization equilibrium governed by the Saha equation:

$$n_{X+,eq.} = \left( \frac{n_X}{n_e} \right)_{eq.} \frac{Q_X + Q_e}{Q_X} \left( \frac{2\pi \mu k_B T}{h^2} \right)^{\frac{3}{2}} \exp \left( -\frac{E_{io}}{k_B T} \right) \quad (8)$$

where $E_{io}$ is the ionization potential of $X$ and $\mu$ is the reduced mass of the ionization products.

In our experimental conditions, assuming a single ionization is reliable. In fact, a LTE composition computation considering a TiO$_2$ plasma at $(n_e, T) = (10^{23} \text{ m}^{-3}, 10200 \text{ K})$ shows that $n_{X+\text{eq.}}/n_{X+\text{eq.}}$ is of the order of $10^{-3}$ and $10^{-13}$ respectively of Ti and O. The transitions of interest are chosen according to their spectral radiance level, our identification abilities and the overlapping aspects. Over the spectral range [400, 800] nm experimentally observed, V I 411.18 nm is the strongest and the most persistent isolated neutral vanadium line. The lack of information related to the emission of titanium (neutral and ion) makes it difficult to identify Ti lines. The choice of Ti I 445.33 nm is motivated by the absence of other line around 445.3 nm. Finally, oxygen is monitored by considering the emission of its near infrared neutral triplet around 777.4 nm. The lines of interest are listed in Table 6.

Using the values of $n_e$ and $T$ measurements (see Figs. 11 and 12), the analysis of these lines based on Eqs. (6)–(8) operated on $N = 1$ emission spectrum leads to the absolute total densities of Table 7. The associated uncertainties are evaluated from $L_{ki}$ standard deviation computed from the 5 different acquisitions. The value of $n'_{O,eq.}$ is obtained by subtracting a residual oxygen emission due to ambient gas impurities and Gaussian wings of spatial irradiance. In that way, the measured quantity of O is only associated to sample compound.

Along with Table 7 values, $n'_{Ar,eq.}$ can be evaluated by modeling the experimental spectra with our simulation code MERLIN [24]. Neglecting the H content (<1 at.%), $n'_{Al,eq.}$ is evaluated as mixture balance since no emission line (neither neutral nor ion) is unambiguously observed on [400, 800] nm in our conditions. Both experimental and simulated spectra are presented on Fig. 13 for $N = 1$. The experimental spectrum (in black) is framed with standard deviation computed from the 5 different acquisitions (in gray). This allows to evaluate the pulse-to-pulse fluctuation at a given depth during the profiling procedure. In accordance with Sections 3.2.2 and 3.2.3 results, the simulated spectrum is obtained for $(n_e, T) = (10^{23} \text{ m}^{-3}, 10700 \text{ K})$ with $\ell_p = 1$ mm which is a reliable plasma length for our experimental
<figure><img src="image_15.png" /><figcaption>Fig. 13. Comparison of experimental (in black) and simulated (in red) spectra over the spectral interval [400, 800] nm for laser pulse N = 1. The values considered for n_e and T are experimentally measured in Sections 3.2.2 and 3.2.3. Mixture composition is obtained from Table 7, Ar I lines simulation (see Table 4) and Al is balance. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

conditions [44,45]. The truncated to $10^{-3}$ mole fractions used for the simulation are $(x_{Ar}, x_O, x_{Ti}, x_{Al}, x_Y) = (0.850, 0.106, 0.038, 0.004, 0.002)$. On the upper frame, the broadband comparison is presented. Since only few Stark parameters are available for titanium and vanadium on [400,800] nm, we computed average values for $n_{e,r} = 10^{23}$ m$^{-3}$ based on bibliography ([46–50] for Ti and [51–53] for V). The values obtained for Ti I, Ti II, V I and V II lines are $\omega_{ki} = 2.79, 1.61, 4.05, 1.29$ pm respectively. This leads to an underestimation of Stark broadening on [420, 460] nm and [480, 530] nm. Despite the perfectible spectral profiles modeling, the total radiance over [400, 800] nm is globally well described: $\sim 5 \times 10^6$ W m$^{-2}$ sr$^{-1}$ and $\sim 7 \times 10^6$ W m$^{-2}$ sr$^{-1}$ respectively for experimental and simulated spectra. There are some intervals for which our averaged Stark parameters are quite reliable compared to experimental profiles, namely [400, 420] nm and [530, 650] nm. For $\lambda > 650$ nm, no significant line of Ti or V is observed. To discuss the accuracy of the $n'_{X,eq}$ measurements, spectral intervals with V I, Ti I lines ([410, 412] nm, mid frame), Ar I line ([762.5, 764.5] nm, left lower frame) and O I triplet ([776.5, 778] nm, right lower frame) are selected. As we can see, the quantities measured in Table 7 allow a satisfactory simulation. Repeating this quantification from laser pulse N = 1 to N = 50 leads to the results displayed in Fig. 14. The values of $n_e$ and T used to proceed that computation are again the measurements showed on Figs. 11 and 12. We define the element ratio $r_{XY}$ as

$$r_{XY} = \frac{n'_{X,eq.}}{n'_{Y,eq.}} \qquad (9)$$

Based on Fig. 14, $r_{OTI}$ and $r_{TIV}$ from pulse N = 1 to N = 50 are plotted on the upper part of Fig. 15. The uncertainties are obtained from $n'_{X,eq}$ errors. The ratio O/Ti (in blue) decreases from $2.27 \pm 0.89$ ($N=1$) to $0.15 \pm 0.10$ ($N=10$ to $N=50$). This is consistent with TiO$_2$ stoichiometric $r_{OTI}$ whose expected value is 2. Concerning the

<figure><img src="image_16.png" /><figcaption>Fig. 14. Total densities of Ti (in gray), O (in orange) and V (in green) from pulse N = 1 to N = 50 measured on the TiO$_2$–TA6V sample under the irradiation conditions described in Section 2.3. The values considered for $n_e$ and T are determined in Sections 3.2.2 and 3.2.3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

Ti/V ratio (in red), no significant dependence to the pulse number N is highlighted. We obtain a mean experimental $r_{TIV} = 24.34 \pm 1.66$ whereas TA6V mole ratio yields 23.94 (the horizontal red line). Here again, this is consistent with bulk substrate elemental composition. Even if aluminum amount is estimated indirectly by balance, $r_{TAl}$ is found to be $\sim 9.5$ while expected TA6V mole ratio is 8.46. The first derivative of $r_{XY}$ is presented on the lower part. The oxide layer is found to be ablated after $N_c = 7$ laser pulses (vertical dashed black line), which corresponds to the number of pulses to reach the substrate. From pulse N = 1 to $N_c$, $r_{OTI}$ is found to be decreasing as the ablation occurs. The presence of V for $N < N_c$ can be explained by local irradiance peaks or/and chemical diffusion of vanadium in the oxide layer. Assuming a uniform ablation rate $t_{ref,TA6V}$ in the TiO$_2$ coating (see Section 3.2.1)

<figure><img src="image_17.png" /><figcaption>Fig. 15. Elemental ratios $r_{OTI}$ (in blue — left axis) and $r_{TIV}$ (in red — right axis) from pulse N = 1 to N = 50 measured on the TiO$_2$–TA6V sample under the irradiation conditions described in Section 2.3. The values considered for $n_e$ and T are determined in Sections 3.2.2 and 3.2.3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
and taking into account the number of pulses to reach the substrate $N_c$, the oxide thickness $e_{ox}$ is estimated to be $e_{ox} \sim t_{TiO_2} \times N_c \sim 5$ µm. This value appears to be consistent with the SEM observations.

## 4. Conclusion

In this study, SEM-EDS indicates a nearly unoxidized composition within the crater and an oxide layer of ~6 µm. XRD exhibits similar diffractograms between crater and oxide zone but is limited by the sampling area that exceeds the crater size. Raman spectroscopy further confirms the absence of oxides inside the crater. The spectroscopic analysis of the LIBS plasma provides complementary insights. Stable electron density and temperature are determined, validating the assumption of local thermodynamic equilibrium. Simulating experimental spectra using the MERLIN code allows elemental profiling along successive laser pulses. The decreasing of O/Ti ratio from a stoichiometric $TiO_2$ value to a residual null value indicates a complete ablation of the oxide layer. Using the measured ablation rate $t_{ref.TA6V}$, the oxide thickness is measured and appears to be in good agreement with SEM observations. Overall, conventional material analyses and LIBS provides consistent results. Beyond the validation of oxide composition and thickness, this study shows that LIBS can provide deep-resolved information throughout a micrometric oxide layer without requiring conventional coating preparation. This demonstrates the practical value of LIBS for characterizing adherent thin oxide layers. However, the quantitative interpretation of LIBS data relies on essential pre-requisites. The reconstruction of elemental profiles relies on the assumption of local thermodynamic equilibrium. Moreover, the quantification of light elements imposes an additional constraint which is the excitation of high energy emitting levels. These prerequisites being met, LIBS allows quantitative measurements at depth resolution allowing direct access to oxygen gradients and oxide stoichiometry in a single experiment.

## CRediT authorship contribution statement

**Adrien Brault:** Writing – original draft, Software, Investigation, Formal analysis. **Aurélien Favre:** Writing – review & editing, Writing – original draft, Supervision, Software, Methodology, Investigation, Formal analysis. **Léo Gosse:** Investigation. **Myriam Hoblos:** Investigation. **David Gibouin:** Investigation. **Samuel Jouen:** Supervision, Investigation. **Hilary-Laure Bilongo Moussol:** Investigation. **Arnaud Bultel:** Supervision. **Pascal Boubert:** Supervision. **Julien Annaloro:** Resources.

## Declaration of competing interest

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

## Acknowledgments

The authors thank the "Agence Nationale de la Recherche" (ANR, France) through the program "Investissement d'Avenir" (ANR-10-LABX-09-01), LabEx EMC 3 having supported the QUANTIPHY project. This work has been also partially financed by the European Regional Development Fund (ERDF) of the European Union, by the "Région Normandie", France and by the "Métropole Rouen Normandie", France. Finally, the authors thank the French Space Agency "Centre National d'Etudes Spatiales" (CNES).

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