Anna Bolzan
email: bolzan.anna92@gmail.com

Jeanne Benoit
email: benoit.j@chu-nice.fr

Francesca Pizzo
email: francesca.pizzo@ap-hm.fr

Julia Makhalova

Nathalie Villeneuve
email: nathalie.villeneuve@ap-hm.fr

Romain Carron
email: romain.carron@ap-hm.fr

Didier Scavarda

Fabrice Bartolomei
email: fabrice.bartolomai@ap-hm.fr

Dr Stanislas Lagarde
email: stanislas.lagarde@ap-hm.fr

Bartolomei Fabrice

Lagarde Stanislas
email: stanislas.lagarde@univ-amu.fr.

Agnes Trebuchon

Francesca Bonini

Geraldine Daquin

Lisa Vaugier

Marie Arthuis

Maxime Guye

Isabelle Lambert

Angela Marchi

Nada El Youssef

Sandrine Aubert

Anne Lépine

Mathieu Milh

seizure onset patterns in patients with MRI-negative drug-resistant focal epilepsy

Keywords: focal epilepsy, drug resistant epilepsy, epilepsy surgery, SEEG, scalp-EEG, seizure onset pattern

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Methods: We analysed retrospectively 41 patients without visible lesion on brain MRI who underwent video-EEG followed by SEEG. We defined five types of SOPs on scalp EEG and eight types on SEEG. We examined how various clinical variables affected scalp EEG SOPs.

Results:

The most prevalent scalp SOPs were rhythmic sinusoidal activity (56.8%), repetitive epileptiform discharges (22.7%), and paroxysmal fast activity (15.9%). The presence of paroxysmal fast activity on scalp EEG was always seen without delay from clinical onset and correlated with the presence of low-voltage fast activity in SEEG (sensitivity = 22.6%, specificity = 100%). The main factor explaining the discrepancy between the scalp and SEEG SOPs was the delay between clinical and scalp EEG onset. There was a correlation between the scalp and SEEG SOPs when the scalp onset was simultaneous with the clinical onset (p=0.026). A significant delay between clinical and scalp discharge onset was observed in 25% of patients and featured always with a rhythmic sinusoidal activity on scalp, corresponding to similar morphology of the discharge on SEEG. The presence of repetitive epileptiform discharges on scalp was associated with an underlying focal cortical dysplasia (sensitivity = 30%, specificity = 90%). There was no significant association between the scalp SOPs and the epileptogenic zone location (deep or superficial), or surgical outcome.

Significance:

In patients with MRI-negative focal epilepsies, scalp SOP could suggest the SEEG SOP and some aetiology (focal cortical dysplasia) but has no correlation with surgical prognosis. Scalp SOP correlates with the SEEG SOP in cases of simultaneous EEG and clinical onset, otherwise scalp SOP reflects the propagation of the SEEG discharge.

24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

PLAIN LANGUAGE SUMMARY

We looked at the correspondence between the electrical activity recorded during the start of focal seizure using scalp or intracerebral electrodes in patients with no visible lesion on MRI.

If there is a fast activity on scalp, it reflects similar activity inside the brain. We found a good correspondence between scalp and intracerebral electrical activity for cases without significant delay between clinical and scalp electrical onset (seen in 75% of the cases we studied). Visualizing repetitive epileptic activity on scalp could suggest a particular cause of the epilepsy: a subtype of brain malformation called focal cortical dysplasia. The SEEG thus provides a high spatial resolution and a more precise detection of spatially limited discharges, as well as an improved signal-to-noise ratio thanks to considerable reduction of artefacts (e.g., ictal movements which often obscure scalp EEG recording).

However, unlike the non-invasive whole-brain electrophysiological approaches such as electro-magnetic source imaging, SEEG ability to detect the EZ is limited by the number and position of the implanted electrodes (incomplete spatial sampling). To optimize the EZ localization through scalp EEG in a given patient, it is thus essential to take the advantages of both techniques and search for correlations between the electrical activities recorded on SEEG and on the scalp during seizures.

In recent decades, increasing attention has been drawn to the scalp [START_REF] Foldvary | The localizing value of ictal EEG in focal epilepsy[END_REF][START_REF] Lee | The Clinical Usefulness of Ictal Surface EEG in Neocortical Epilepsy[END_REF][START_REF] Pelliccia | Ictal EEG modifications in temporal lobe epilepsy[END_REF][START_REF] Risinger | Ictal localization of temporal lobe seizures with scalp/sphenoidal recordings[END_REF][START_REF] Worrell | Focal ictal β discharge on scalp EEG predicts excellent outcome of frontal lobe epilepsy surgery[END_REF] and SEEG [START_REF] Perucca | Intracranial electroencephalographic seizure-onset patterns: Effect of underlying pathology[END_REF][START_REF] Lagarde | The repertoire of seizure onset patterns in human focal epilepsies: Determinants and prognostic values[END_REF][START_REF] Singh | Ictal onset on intracranial EEG: Do we know it when we see it? State of the evidence[END_REF] seizure onset pattern (SOP). However, only a few studies have examined the relationships between them [START_REF] Ebersole | Localization of temporal lobe foci by ictal EEG patterns[END_REF][START_REF] Lieb | A Comparison of EEG Seizure Patterns Recorded with Surface and Depth Electrodes in Patients with Temporal Lobe Epilepsy[END_REF][START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF][START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF][START_REF] Ferrand | Intracerebral Correlates of Scalp EEG Ictal Discharges Based on Simultaneous Stereo-EEG Recordings[END_REF] , mostly in cases of temporal lobe epilepsy. One study assessed such correlations in patients with MRI-visible lesion [START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF] , showing that the scalp SOP could inform on the SEEG SOP, the underlying lesion, as well as the depth of the EZ location. In the present work, we aimed to assess the correlations between the scalp and SEEG SOPs in patients with negative MRI, known to be particularly challenging candidates for epilepsy surgery. Additionally, we aimed to identify factors that explain cases of discrepancy between scalp and SEEG SOP.

MATERIALS AND METHODS

Patients selection

We retrospectively analysed all patients with a brain MRI without visible lesion (reviewed in multidisciplinary meeting) who underwent SEEG in our department as part of their presurgical evaluation for focal drug-resistant epilepsy from March 2011 to September 2021. All patients had a complete presurgical work-up, including medical history, neurological examination, brain MRI, cerebral positron emission tomography, and scalp video-EEG recording. We included patients with at least one typical spontaneous seizure recorded on both scalp EEG and SEEG. The study was approved by the Institutional Review Board of the APHM (NHLS4Y), and the included patients provided written informed consent.

Scalp and SEEG recordings

Scalp EEGs were recorded using the international 10-20 system with additional electrodes exploring the basal temporal regions and temporal poles (FT9, TP9, FT10, and TP10). SEEG recordings were performed using intracerebral multiple contact electrodes (DIXI© or Alcis©, 10-15 contacts with length 2 mm, diameter 0.8 mm, and 1.5 mm apart [START_REF] Lagarde | Interictal stereotactic-EEG functional connectivity in refractory focal epilepsies[END_REF] ). SEEG electrodes were implanted for each patient based on EZ localization hypotheses inferred from noninvasive evaluation. Pre-implantation MRI and post-implantation CT were fused to locate each electrode contact within the brain [START_REF] Medina Villalon | A software suite for presurgical brain mapping in epilepsy: Intracerebral EEG[END_REF] . Signals were recorded on a 128-or 256-channel Natus© system, sampled at 256, 512, or 1024 Hz depending on EEG/SEEG modalities and year of recording. Partial or complete antiseizure medication withdrawal was performed to facilitate the recording of seizures.

Matching scalp and intracerebral ictal recordings

Only spontaneous clinical and electrographic seizures were analysed, and not those induced by electrical stimulation in SEEG. The SOP was considered as the first sustained electrographic change clearly distinguishable from background activity. All recorded seizures were evaluated by two trained electroencephalographers blinded to patients' clinical data (AB, SL). Since scalp and intracerebral EEG were not recorded simultaneously, we used previously published methodology to match scalp EEG and SEEG recorded seizures [START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF] . For each individual seizure, whether recorded with scalp-EEG or SEEG, we defined three main features 1) topography (with lobar precision (e.g., temporal) in EEG and sublobar precision (e.g., mesio-temporal) in SEEG), 2) morphology of the SOP (see paragraph 2.4) and 3) semiology. Subsequently, for each patient we compared these criteria across all seizures of a same modality (scalp-EEG or SEEG).

If these seizures did not present the exact same features, we defined different seizure types (specific to a modality). For instance, if a patient exhibited independent multifocal EZ, seizures arising from distinct EZ were considered as different seizure types due to their localization. Additionally significant differences in semiology between two seizures, even without clear difference in topography, resulted in their classification as different seizure types. Finally, seizure types between scalp-EEG and SEEG were matched based on the comparison of two criteria: 1) topography and 2) semiology. A match required similar semiology and a scalp-EEG projection that concurred with the SEEG data. This matching process was relatively straightforward in cases with bilateral EZ or multiple seizure semiology. However, it was more challenging in other scenarios such as a patient with a posterior EZ identified on SEEG but exhibiting a projection on anterior temporal in scalp-EEG; in such instances, a mismatch was acknowledged. Disagreements between experts were solved by discussion and seizure types that could not be confidently matched were excluded from subsequent analyses (details about matching procedure can be found in supplementary figure 1).

Seizure onset pattern analysis

For each scalp and SEEG seizure type, the SOP was determined through visual and timefrequency analysis.

For scalp recordings we found five SOPs (Figure 1): Hz) and with high amplitude 6. Sharp theta/alpha activity with sinusoidal activity of low frequency (lower than LVFA, median = 9.5 Hz), median initial amplitude (higher than LVFA), and progressively increasing amplitude 7. Sharp beta activity with sinusoid activity of beta-band frequency (lower than LVFA), median initial amplitude (higher than LVFA), and progressively increasing amplitude 8. Delta-brush, with bursts of low-amplitude rapid activity (within gamma frequency bands) superimposed upon low-frequency (delta) sinusoidal activity For patients presenting different SOPs for the same seizure type, we retained the predominant SOP both for scalp EEG and SEEG. In patients with a scalp EEG SOP occurring after clinical onset (delay = t), we additionally analysed the morphology of the SEEG ictal discharge at the time t, equal to the delay between clinical and scalp EEG onset.

Clinical variables

The EZ was defined using visual analysis of SEEG seizures, complemented by a quantitative method (epileptogenicity index [START_REF] Bartolomei | Epileptogenicity of brain structures in human temporal lobe epilepsy: A quantified study from intracerebral EEG[END_REF] ). We classified patients in ten subgroups, according to their EZ location: mesio-temporal, temporal lateral, mesio-lateral temporal, temporal plus, 24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License bitemporal, frontal, frontal plus, operculo-insular, parietal, and occipital plus. Each patient's EZ was further defined as deep (mesial part of the brain hemispheres, orbitofrontal region, and insula) or superficial (other locations or association of both deep and superficial EZ). The neuropathological diagnosis of patients who underwent resective surgery was reported according to current International League Against Epilepsy classifications [START_REF] Blümcke | The clinicopathologic spectrum of focal cortical dysplasias: A consensus classification proposed by an ad hoc Task Force of the ILAE Diagnostic Methods Commission[END_REF][START_REF] Blümcke | International consensus classification of hippocampal sclerosis in temporal lobe epilepsy: A Task Force report from the ILAE Commission on Diagnostic Methods[END_REF] . Surgical outcome was assessed regularly during post-operative follow-up and rated according to Engel classification [START_REF] Engel | Update on surgical treatment of the epilepsies. Summary of the Second International Palm Desert Conference on the Surgical Treatment of the Epilepsies[END_REF] . Engel score from the last available follow-up was used for statistical analyses.

Statistical analysis

We computed sensitivity and specificity for some specific scalp SOP to assess their predictive value for certain variables (e.g., SEEG SOP, depth of EZ, aetiology). We started by testing the significance for the overall association between scalp-EEG and SEEG SOP. Then, we focused on this association 1) for patients without delay between clinical and scalp-EEG onset, and 2) between the scalp SOP and the morphology of the discharge on SEEG after a time equal to the delay between clinical and scalp EEG onset. We also looked for any statistically significant differences between patients with / without such delay. Additionally, we examined the influence of the depth of the EZ on the scalp SOP, and whether there was any significant association between scalp-EEG and SEEG SOP in the subgroups with deep and superficial EZ.

Finally, we tested the association between scalp-EEG SOP and others clinical variables: aetiology, patients' eligibility for surgery, Engel's scores, age at SEEG, duration of epilepsy before SEEG, EZ localisation, and sex. Fisher's exact test was used for categorical data, and Kruskal-Wallis test for continuous data. Statistical significance was set at p-value < 0.05.

Statistical analyses were performed with the software SPSS Statistics for Mac, version 22 (IBM).

RESULTS

Population

Matching scalp and intracerebral SOP

Forty-nine seizure types were identified on scalp-EEG (47 clinical and two electrographic), and 53 on SEEG (48 clinical and five electrographic). Eight SEEG-recorded seizure types showed SOP variation from one seizure to another. The predominant SOP was retained for further analysis. Four scalp-EEG seizure types (three clinical and one electrographic) and eight SEEG seizure types (four clinical and four electrographic) could not be matched and were excluded from the analysis. A total of 45 pairs of SOPs were matched between scalp EEG and SEEG seizures. One of the remaining scalp SOP was categorized as an obscured pattern (corresponding to a sharp beta activity as SOP on SEEG), precluding it from further analysis (Figure 2A).

Association between Scalp-EEG and SEEG SOP

The most frequent scalp SOP was RSA (56.8 %), followed by RED (22.7 %), PFA (15.9 %), and attenuation (4.5 %) (Figure 2B). The most frequent SEEG SOP was slow wave or baseline shift followed by LVFA (34.1 %), followed by rhythmic spikes or spike-waves and LVFA (18.2% both), preictal spiking followed by LVFA (13.6 %), sharp theta-alpha activity (1.4 %), burst of

Impact of the delay of appearance of the scalp SOP

Ten patients (24.4%) presented a delay between clinical and scalp EEG onset. The time t equal to the delay between clinical and scalp EEG onset was in median of 9.75 seconds (range 5-32.5 seconds). All these patients featured RSA as scalp EEG SOP (p=0.03, sensitivity = 100% and specificity = 70% to predict the existence of a delay). All types of SEEG SOP were observed in these patients, except burst of polyspikes followed by LVFA. Regarding patients without such delay, all types of scalp-EEG SOP (14 RSA, 10 RED, 7 PFA and 2 attenuation), and SEEG SOP, except delta-brush (10 slow-wave followed by LVFA, 7 rhythmic spikes, 6 LVFA, 5 preictal spiking, 5 sharp theta-alpha activity and 1 burst of polyspikes) were observed. The existence of a delay between clinical and scalp EEG onset was not significantly associated with the following factors: SEEG SOP, depth of the EZ, type of epilepsy, histology, or surgical outcome. However, we found that 80% of patients with delayed scalp EEG SOP had a SEEG SOP including LVFA (compared to 68% in those without delayed scalp SOP). At the time t, most patients (n=8, 80%) showed slow SEEG ictal discharge (theta-alpha activity in five patients, rhythmic spikes in three). In six of these eight patients (75%), the initial SEEG SOP involved LVFA (preceded by a slow wave or baseline shift for five of these patients), which slowed down and increased in amplitude at the time t. For the two patients whose LVFA was still visible on SEEG at the time t, the LVFA was spatially limited to only a few SEEG contacts (Heschl gyrus for one, planum temporal and amygdala for the other), with concomitant slowing of background activity on the surrounding contacts. In patients with scalp SOP starting without delay from clinical onset, we found a statistically significant association between scalp and SEEG SOPs (p = 0.026, Figure 3B). Then, paroxysmal fact activity on scalp was associated in more than 70% of cases with slow wave followed by LVFA on SEEG. Repetitive 24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License epileptiform discharge on scalp was associated in 40% with rhythmic spikes and spikes-waves on SEEG. The distribution was more balanced for rhythmic sinusoidal activity (associated with SEEG SOP including or not LVFA) and attenuation as scalp-EEG SOP (always associated with SEEG SOP including LVFA). We also found a statistically significant association between the scalp SOP and the morphology of the SEEG ictal discharge at the time t (p = 0.003).

Impact of the depth of the EZ

Among the 44 matching seizure types, the EZ had a superficial location in 22 and deep locations in 22. A scalp EEG onset starting after the clinical onset was seen in 21.7% of seizures with a deep EZ and in 27.2% of those with a superficial EZ. Attenuation SOP on scalp EEG was only observed in seizures with a superficial EZ (n=2). A slight majority of PFA on scalp was seen in the cases with superficial EZ (57.1%, sensitivity = 13.6%, specificity = 81.8%), most of RED were seen in the cases with deep EZ (70%, sensitivity = 31.8%, specificity = 86.3%), and RSA was seen as often in case of deep or superficial EZ (48/52%, sensitivity = 54.6%, specificity = 40.9% for superficial) (supplementary figure 2). Statistically, scalp SOPs were not significantly associated with the depth of the EZ (p=0.32).

The distribution of the SEEG SOPs matched to the scalp SOP depending on the depth of the EZ is shown in supplementary figures 3. Among the 22 pairs of matched seizure types with a superficial EZ: attenuation on scalp matched with slow wave followed by LVFA and LVFA patterns on SEEG; PFA with pre-ictal spiking and slow wave followed by LVFA; RED with preictal spiking, rhythmic spikes and sharp theta alpha activity; and RSA with all types of SEEG SOPs. Among the 22 analysed pairs of matching seizure types with a deep EZ: PFA on scalp matched only with slow wave followed by LVFA on SEEG; RED with rhythmic spikes, slow wave followed by LVFA, pre-ictal spiking and sharp theta alpha activity; and RSA with slow wave followed by LVFA, LVFA, rhythmic spikes and sharp theta alpha. Statistically, there was no significant association between scalp and SEEG SOPs, neither within the superficial (p = 0.82) nor the deep (p = 0.45) EZ sub-groups. Out of the 20 patients operated, it was observed that scalp EEG REDs were mostly found in patients with an underlying FCD (75% of patients with RED, sensitivity = 30%, specificity = 90%, p=0.228). However, it is worth noting that some patients with FCD also had other types of scalp SOPs. The other scalp EEG SOPs were not explicitly linked to specific histological subgroups (Figure 4). There was no significant association between scalp SOPs and the following variables: patients' eligibility for surgery (conclusion of multidisciplinary meeting following SEEG, p=0.246, supplementary figure 4), Engel scores (p=0.378, supplementary figures 5), age at SEEG (p=0.659), duration of epilepsy before SEEG (p=0.352), EZ localisation (p=0.227), and sex (p=0.216). Conversely, SEEG SOPs were associated with the patients' Engel scores: patterns involving LVFA were associated with better outcomes (41.7% of seizure-freedom vs. 25% in patients with SOPs without LVFA, p=0.017).

Association with other variables

DISCUSSION

The purpose of this study was to assess the correlation between the scalp and SEEG SOPs in patients with focal drug-resistant epilepsy and negative MRI. This research builds upon previously published data about lesional epilepsy [START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF] . Our main findings are:

1. The most frequently observed scalp SOP is RSA (less than 13 Hz), which is consistent with findings in patients with lesional MRI [START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF] and temporal lobe epilepsies [START_REF] Ebersole | Localization of temporal lobe foci by ictal EEG patterns[END_REF][START_REF] Lieb | A Comparison of EEG Seizure Patterns Recorded with Surface and Depth Electrodes in Patients with Temporal Lobe Epilepsy[END_REF][START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF] .

2. There is a correlation between scalp EEG and SEEG SOPs in patients without delay between clinical and scalp EEG onset.

3. PFA is seen in about 16% of the patients on scalp, always simultaneous to clinical onset, and always reflecting a SEEG SOP including an LVFA. 4. In a quarter of patients there is a delay between clinical and scalp EEG onset (always presenting with RSA) corresponding to the evolution of the SEEG ictal discharge.

RED on scalp are evocative of an underlying FCD.

Our analyses suggest that scalp SOP is correlated with the morphology of the ictal discharge on SEEG at the time t equal to the delay between clinical and scalp EEG onset. Not surprisingly, we also found that PFA could be seen on scalp EEG in about 16% of the patients, simultaneously to clinical onset and was associated with SEEG SOPs including an LVFA. We did not find a significant over-representation of PFA on scalp in case of superficial EZ, conversely to previous studies [START_REF] Tao | The impact of cerebral source area and synchrony on recording scalp electroencephalography ictal patterns[END_REF][START_REF] Foldvary | The localizing value of ictal EEG in focal epilepsy[END_REF][START_REF] Pelliccia | Ictal EEG modifications in temporal lobe epilepsy[END_REF][START_REF] Worrell | Focal ictal β discharge on scalp EEG predicts excellent outcome of frontal lobe epilepsy surgery[END_REF] . This could be explained by the relatively low number of PFA in our cohort (n=7). Indeed, the amplitude of the EEG signal is inversely proportional to the square of the source-to-surface distance [START_REF] Cosandier-Rimélé | A physiologically plausible spatiotemporal model for EEG signals recorded with intracerebral electrodes in human partial epilepsy[END_REF] and low frequencies increase while high frequencies decrease with this distance 2 . It is essential to pay attention to the timing of scalp SOP appearance from clinical onset in patients with scalp SOPs other than PFA, because some delayed scalp SOP might reflect the evolution of the intracerebral discharge to slower frequencies and higher amplitudes. In our cohort, a significant delay was found in about a quarter of the patients without PFA, with a mean lag of 10 seconds.

These delayed scalp discharges were always RSA on scalp and mostly correlated with similar discharges on SEEG, possibly reflecting a propagation from the EZ. Actually, theta/alpha activity is a frequent propagation pattern in SEEG, observed in more than 50% of cases [START_REF] Perucca | Intracranial electroencephalographic seizure-onset patterns: Effect of underlying pathology[END_REF][START_REF] Schiller | Characterization and comparison of local onset and remote propagated electrographic seizures recorded with intracranial electrodes[END_REF] .

It has been explained in computational models by the combination of gradual recruitment of the local cortex (ictal wavefront) and sensor-to-source projection [START_REF] Sip | Evidence for spreading seizure as a cause of theta-Alpha activity electrographic pattern in stereo-EEG seizure recordings[END_REF] . This delayed appearance reflects the intracerebral dynamic and is probably due to several factors influencing the visibility of the electrical brain activity on the scalp. First, a sufficient cortical area (6-10 cm 2 ) needs to be activated by the ictal discharge 2,5 , as largely described for mesio-temporal seizures propagating to basal and lateral temporal areas [START_REF] Foldvary | The localizing value of ictal EEG in focal epilepsy[END_REF][START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF][START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF][START_REF] Caboclo | Correlation between temporal pole MRI abnormalities and surface ictal EEG patterns in patients with unilateral mesial temporal lobe epilepsy[END_REF][START_REF] Ebner | Noninvasive electroencephalography and mesial temporal sclerosis[END_REF][START_REF] Pataraia | Ictal scalp EEG in unilateral mesial temporal lobe epilepsy[END_REF][START_REF] Sirin | A Quadruple Examination of Ictal EEG Patterns in Mesial Temporal Lobe Epilepsy With Hippocampal Sclerosis[END_REF][START_REF] Ray | Localizing value of scalp EEG spikes: A simultaneous scalp and intracranial study[END_REF] .

Second, the magnitude of the ictal discharge, particularly the ratio over the background amplitude, significantly impacts its visibility due to the attenuation by the skull and scalp, especially for fast, low-voltage activities [START_REF] Cosandier-Rimélé | Recording of fast activity at the onset of partial seizures: Depth EEG vs. scalp EEG[END_REF][START_REF] Koessler | Catching the Invisible: Mesial Temporal Source Contribution to Simultaneous EEG and SEEG Recordings[END_REF] . Third, high synchrony is needed to generate ictal patterns visible on scalp EEG [START_REF] Cosandier-Rimélé | Recording of fast activity at the onset of partial seizures: Depth EEG vs. scalp EEG[END_REF][START_REF] Tao | The impact of cerebral source area and synchrony on recording scalp electroencephalography ictal patterns[END_REF][START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF] . Conversely, decreased synchrony has been demonstrated through functional connectivity analysis during intracerebral LVFA [START_REF] Wendling | Epileptic fast intracerebral EEG activity: Evidence for spatial decorrelation at seizure onset[END_REF][START_REF] Bartolomei | Pre-ictal synchronicity in limbic networks of mesial temporal lobe epilepsy[END_REF] , which might explain the "attenuation" scalp discharge sometimes correlated with intracerebral LVFA on the neocortex [START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF][START_REF] Ferrand | Intracerebral Correlates of Scalp EEG Ictal Discharges Based on Simultaneous Stereo-EEG Recordings[END_REF][START_REF] Sakai | Localization of epileptogenic zone in temporal lobe epilepsy by ictal scalp EEG[END_REF] . Other factors influencing the delayed appearance of the scalp ictal discharges may be the difficulties in distinguishing small PFA on the scalp from physiological (e.g. rhythms of frontocentral area) or muscular activities, as well as the curved geometry of some generators such as hippocampus, amygdala or bottom of sulcus, that could lead to electrical field cancellation [START_REF] Lagarde | Focal epilepsies and focal disorders[END_REF] . All these factors explain how some electrical seizures of short duration and confined to limited brain volume may be missed on scalp recordings in a significant number of cases [START_REF] Lieb | A Comparison of EEG Seizure Patterns Recorded with Surface and Depth Electrodes in Patients with Temporal Lobe Epilepsy[END_REF][START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF][START_REF] Ferrand | Intracerebral Correlates of Scalp EEG Ictal Discharges Based on Simultaneous Stereo-EEG Recordings[END_REF][START_REF] Casale | The Sensitivity of Scalp EEG at Detecting Seizures-A Simultaneous Scalp and Stereo EEG Study[END_REF] . This delayed appearance should be considered as an important confounding factor for ictal electrical source imaging (i.e., proceeding to signal analysis before the visible scalp discharge) [START_REF] Van Mierlo | Ictal EEG source localization in focal epilepsy: Review and future perspectives[END_REF] .

24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Another interesting finding is the association between RED and an underlying FCD. Despite improvements in imaging techniques and computer-assisted postprocessing [START_REF] Huppertz | Enhanced visualization of blurred gray-white matter junctions in focal cortical dysplasia by voxel-based 3D MRI analysis[END_REF][START_REF] Hong | Multimodal MRI profiling of focal cortical dysplasia type II[END_REF][START_REF] Desarnaud | F-FDG PET in drug-resistant epilepsy due to focal cortical dysplasia type 2: additional value of electroclinical data and coregistration with MRI[END_REF] , a significant percentage of FCD (especially type I) remains undetected in clinically used imaging. Because some FCD subtypes (particularly type II) are associated with favourable surgical outcome [START_REF] Baud | European trends in epilepsy surgery[END_REF][START_REF] Lamberink | Seizure outcome and use of antiepileptic drugs after epilepsy surgery according to histopathological diagnosis: a retrospective cohort study[END_REF] , the effort to find a neurophysiological biomarker that could suggest their presence in patients with negative MRI is essential. Some studies have suggested evocative interictal EEG patterns [START_REF] Bautista | Focal cortical dysplasia and intractable epilepsy in adults: Clinical, EEG, imaging, and surgical features[END_REF][START_REF] Epitashvili | Scalp EEG biomarkers in epilepsy patients with focal cortical dysplasia[END_REF][START_REF] Tassi | Focal cortical dysplasia: neuropathological subtypes, EEG, neuroimaging and surgical outcome[END_REF][START_REF] Noachtar | Interictal regional polyspikes in noninvasive EEG suggest cortical dysplasia as etiology of focal epilepsies[END_REF] but less is known about their scalp SOPs. Tanaka and colleagues have suggested that fast-frequency scalp SOPs could help the clinician suspect a cortical development malformation (not limited to FCD) [START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF] . This RED SOP probably corresponds to the pre-ictal spiking or burst of polyspikes prior to LVFA patterns observed in SEEG [START_REF] Lagarde | Seizure-onset patterns in focal cortical dysplasia and neurodevelopmental tumors: Relationship with surgical prognosis and neuropathologic subtypes[END_REF] . This scalp SOP should help clinicians to motivate SEEG because of a high suspicion of FCD and a potentially favourable surgical outcome.

In contrast to SEEG, scalp SOPs showed no significant association with our patients' surgical eligibility and outcome. Similar findings were reported in temporal lobe epilepsy [START_REF] Pelliccia | Ictal EEG modifications in temporal lobe epilepsy[END_REF] . Indeed, scalp SOPs are not very specific to a particular EZ localization [START_REF] Ferrand | Intracerebral Correlates of Scalp EEG Ictal Discharges Based on Simultaneous Stereo-EEG Recordings[END_REF] , and other more critical factors might have a more significant impact on the outcome [START_REF] Kim | Surgical treatment of nonlesional neocortical epilepsy: Long-term longitudinal study[END_REF] . Another explanation may be low statistical power due to the limited number of patients operated on in our study (n=20).

Our study has some limitations, the first being that scalp EEG and SEEG were recorded separately. Given a certain intra-individual variability in electrical seizure organization, the scalp SOP that would have been recorded simultaneously during SEEG monitoring might differ from the one recorded during video-EEG monitoring. However, a previous study has shown that scalp SOPs do not vary significantly between scalp-EEG only and simultaneous scalp-SEEG recordings in the same patient [START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF] . Our mean delay between clinical and scalp EEG onset may also be an underestimation of the delay between SEEG and scalp EEG discharge onset (that could only be estimated using simultaneous recordings), and we may have underestimated the number of patients with such a delay between SEEG and scalp EEG onset (higher in another study [START_REF] Casale | The Sensitivity of Scalp EEG at Detecting Seizures-A Simultaneous Scalp and Stereo EEG Study[END_REF] ). That could lead to underestimating the concordance between scalp and SEEG ictal discharge morphology at the time of scalp visibility. However, the delay of appearance of the scalp SOP in our study is similar to previous studies using simultaneous recordings [START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF][START_REF] Casale | The Sensitivity of Scalp EEG at Detecting Seizures-A Simultaneous Scalp and Stereo EEG Study[END_REF] . A recent study on SEEG correlates of scalp EEG ictal discharges used simultaneous recordings [START_REF] Ferrand | Intracerebral Correlates of Scalp EEG Ictal Discharges Based on Simultaneous Stereo-EEG Recordings[END_REF] , and described six different clusters that Theta/delta temporal scalp discharges were mainly associated with prolonged mesiotemporal discharges (starting with or without LVFA on SEEG) but more rarely with frontal, parietal, or insulo-opercular EZ (reflecting propagation). Alpha/slow waves posterior scalp discharges were associated mainly with LVFA coming from temporal, parietal and occipital EZ (but also seen in multilobar and insulo-opercular EZ). Paroxysmal fast activity and preictal spiking over frontal scalp electrodes were associated with LVFA originating mainly from frontal dorsal EZ (although also seen in temporal or parietal EZ). Finally, diffuse suppression on the scalp was associated with LVFA on SEEG and was particularly frequent in the case of temporal or insulo-opercular, mesial and/or ventral EZ. Overall, the scalp SOP frequently reflected the propagation of the ictal discharge and lacked specificity concerning EZ localization, which is in concordance with our findings.

Secondly, a subset of our patients either did not undergo resective surgery or did not achieve seizure-freedom after SEEG-guided resection. Several factors may account for these outcomes, including an excessively broad EZ or its overlap with eloquent cortices.

Notably, it cannot be excluded that in some of these patients, the EZ was not perfectly delineated by the SEEG, especially in this population of patients with negative MRI. This could explain the observed absence of significant association between scalp-EEG SOP and the depth of the EZ, and may have influenced our analysis of SEEG ictal activity at the delay between clinical and scalp-EEG onset. A third limitation is the relatively small sample size of our cohort due to our focus on the challenging population of patients with negative MRI aiming to complement previous findings on MRI-visible lesional epilepsy [START_REF] Tanaka | Association between scalp and intracerebral electroencephalographic seizure-onset patterns: A study in different lesional pathological substrates[END_REF] . It limits the statistical power of our analyses, and might explain the low prevalence of attenuation as scalp SOP in our cohort compared to others, particularly concerning mesio-temporal seizures [START_REF] Pacia | Intracranial EEG substrates of scalp ictal patterns from temporal lobe foci[END_REF] . For instance, we only analysed seven patients with frontal epilepsy that could explain the low prevalence of attenuation as scalp SOP, and the absence of significant association between deep EZ and these SOP. Additionally, we only found three patients with FCD and RED as scalp SOP. Consequently, the association between these two variables necessitates validation through subsequent investigations involving a larger patient cohort.

To ensure a thorough characterization of electrophysiological data, we opted for a detailed categorization of both scalp-EEG and SEEG SOP. This approach resulted in limited numbers of observations in some subcategories, thereby limiting statistical power. To overcome this

CONCLUSION

Low frequency RSA are the most frequent scalp SOPs in patients with focal MRI-negative epilepsy. A good correlation exists between the scalp and the SEEG SOP if there is no significant delay between clinical and scalp EEG onset. However, in about a quarter of patients, RSA appeared on the scalp several seconds after clinical onset, reflecting the evolution and/or propagation of the SEEG discharge at that time. REDs on the scalp may be evocative of an underlying FCD even in patients with negative MRI. Our findings may help clinicians facing the challenging population of patients with negative MRI. They may be the premise of future studies on ictal electrical source imaging with an improved methodology.

Number of text page: 25 ; 4 ;

 254 figures: 4; Number of tables: 2.

Keyword:

  focal epilepsy, drug resistant epilepsy, epilepsy surgery, SEEG, scalp-EEG, seizure onset pattern KEY POINTS • The most prevalent scalp SOPs were rhythmic sinusoidal activity, repetitive epileptiform discharges, and paroxysmal fast activity • Paroxysmal fast activity on scalp was always seen without delay from clinical onset and was highly specific of low-voltage fast activity in SEEG • There was a significant delay between clinical and scalp onset in 25% of patients with always a rhythmic sinusoidal activity on scalp • There was a correlation between the scalp and SEEG SOPs when the scalp onset was simultaneous with the clinical onset • Repetitive epileptiform discharges on scalp suggested an underlying focal cortical dysplasia MAIN BODY 1. INTRODUCTION For patients with focal epilepsy who do not respond to antiseizure medication, epilepsy surgery is the most effective treatment. To achieve a successful surgical outcome, it is important to accurately identify the epileptogenic zone (EZ) through a comprehensive presurgical evaluation that includes clinical, electrophysiological, and imaging data. During this evaluation, video-EEG recording of seizures is crucial for building hypotheses about the EZ, based on the analyses of ictal semiology and associated EEG changes. Several factors can influence the detectability of ictal discharges on scalp EEG: size, depth and orientation of the cortical sources of ictal activity, level of synchronization of neuronal populations, features of physiological background activity, and skull conductivity 1-5 . Thus, the diagnostic and localizing performances of scalp EEG are limited. Conversely, intracerebral electrodes can directly record local field potentials from the brain structures generating and propagating seizures.

1 .

 1 Rhythmic Sinusoidal Activity (RSA) <13 Hz 2. Repetitive Epileptiform Discharges (RED): (pseudo-)periodic spike-and-wave or sharpand-wave or spikes <13 Hz, without rhythmic sinusoidal activity 3. Paroxysmal Fast Activity (PFA): low amplitude fast discharges ≥13 Hz24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

4 .

 4 Attenuation: reduction of > 50 % of the background activity with a voltage ≤ 10 µV 5. Obscured: no visible EEG pattern because of artifacts at seizure onset For the statistical analysis, we excluded scalp seizures categorized as obscured SOP.For SEEG recordings we used the eight previously published SOP[START_REF] Lagarde | The repertoire of seizure onset patterns in human focal epilepsies: Determinants and prognostic values[END_REF] : 1. Low-voltage fast activity (LVFA): rhythmic fast oscillations (>14 Hz) of low amplitude (<30 μV) starting without other initial apparent changes 2. Preictal spiking with rhythmic spikes of low frequency (classically ≤3 Hz), high amplitude, and prolonged duration (>5 seconds, median = 20 seconds) followed by LVFA (usually of lower frequency than isolated LVFA) 3. Burst of polyspikes of high frequency (typically >12Hz) with high amplitude and short duration (<5 seconds) followed by LVFA 4. Slow wave or baseline shift (equal to DC shift) followed by LVFA 5. Rhythmic spikes or spike-waves, of low frequency (usually >6 Hz and constantly <14

  We identified 59 patients fitting our inclusion criteria. Among those,16 were excluded because their scalp EEG was performed outside our centre. Two more patients were excluded as they did not present spontaneous seizure on SEEG and/or scalp EEG monitoring. A final number of 41 patients (20 women, median age at scalp EEG = 27 years), with 279 habitual seizures (136 on scalp EEG, 143 on SEEG) were analysed. Patients' demographic data are summarized in Table 1. Almost all EZ localization were represented. Twenty patients underwent surgery with histology being focal cortical dysplasia (FCD) type I in six cases (30%), FCD type II in three (15%), FCD type III in one (5%), hippocampal sclerosis in one (5%), aspecific in four (20%) and gliosis in five (25%). At the latest available follow-up (mean = 66 months, SD = 44), seven patients were Engel class I, two Engel class II, three Engel class III and eight Engel class IV. The remaining 21 patients (51%) did not undergo surgery after SEEG because of contraindications (bilateral EZ or involving eloquent structures, n=15, 36.6%) or other reasons (personal preference, improvement after thermocoagulation).

  polyspikes followed by LVFA and delta brush(2.3 % both). Associations between matched scalp and SEEG SOPs are shown in Figure3A. Scalp PFA was only observed when a LVFA was visible on SEEG SOP, but some cases with LVFA on SEEG SOP did not exhibit a PFA SOP on scalp EEG (p= 0.086, sensitivity = 22.6%, specificity = 100%). Only 68% of RSA and 40% of RED on scalp were associated with SEEG SOP including an LVFA. Scalp RSA and RED further matched with almost all types of SEEG SOPs. Overall, scalp SOPs were not significantly associated with SEEG SOPs (p = 0.161).

  combine morphology and EZ localization (including "normal" and "blurred" EEG clusters).

  limitation, potential strategies include adopting a simpler classification scheme or focusing on specific SOP subtypes in larger cohort. Finally, the added value of signal analysis methods such as independent component analysis might be worth future investigation, to improve the relevance of scalp SOP[START_REF] Barborica | Extracting seizure onset from surface EEG with independent component analysis: Insights from simultaneous scalp and 24709239[END_REF] .

FIGURES LEGENDSFigure 1 .

 1 FIGURES LEGENDS

Figure 2A .

 2A Figure 2A. Flow chart showing the inclusion of the patients and the process of defining and matching seizure type on scalp and on SEEG.

Figure 2B .

 2B Figure 2B. Pie chart representing the prevalence of scalp-EEG SOP. SOP: Seizure Onset Pattern.

Figure 3A .

 3A Figure 3A. Histogram showing the overall repartition of the SEEG SOP according to scalp EEG SOP. LVFA = Low Voltage Fast Activity, SOP: Seizure Onset Pattern.

Figure 3B .

 3B Figure 3B. Histogram showing the repartition of the SEEG SOP according to scalp EEG only in cases without delay between clinical and scalp onset. LVFA = Low Voltage Fast Activity.

Figure 4 .

 4 Figure 4. Histogram showing the repartition of the scalp SOP according to the underlying histology. FCD = Focal Cortical Dysplasia, SOP: Seizure Onset Pattern.

Figures 1A_R1.tiff

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Figures 1C_R1.tiff

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Figures 1D_R1.tiff

  Figures 1D_R1.tiff

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Table 1 . Patients' demographic characteristics Total population (n=41)

 1 24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License TABLES FCD = Focal Cortical Dysplasia 24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

	Gender, male, n

Table 2 . Patients with delayed discharge on scalp (n=10) SEEG SOP Delay (t) between clinical and scalp onset (in seconds) Scalp EEG SOP Morphology of the SEEG discharge after a time = t

 2

	SW	15	RSA	RS
	STA	32.5	RSA	STA
	LVFA	15	RSA	STA
	DB	7.5	RSA	LVFA
	SW	9.5	RSA	STA
	SW	7.5	RSA	RS
	LVFA	5.1	RSA	LVFA
	RS	5	RSA	RS
	SW	12.1	RSA	STA
	SW	10	RSA	STA

SW = Slow wave or baseline shift followed by LVFA; DB = Delta Brush; STA = Sharp theta/alpha activity; RSA = Rhythmic sinusoidal Activity; LVFA = Low Voltage Fast activity; RS = Rhythmic Spikes.

  24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

24709239, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/epi4.12886 by Cochrane France, Wiley Online Library on [02/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

ACKNOWLEDGMENTS

We thank all colleagues involved in our epilepsy centre (Neurology: Agnes Trebuchon, Francesca Bonini, Geraldine Daquin, Lisa Vaugier, Marie Arthuis, Maxime Guye, Isabelle Lambert, Angela Marchi, Nada El Youssef, Sandrine Aubert; Neuropaediatry: Anne Lépine, Mathieu Milh, Beatrice Desnous; all paramedical staff of the above departments). We thank Serge Vulliemoz and Nicolas Roehri for suggestions and comments on this work. We thank the patients.

SL is supported by grants from the LFCE (Ligue Française Contre l'Épilepsie, french chapter of the ILAE) and PHOCEO.

DISCLOSURE OF CONFLICT OF INTEREST

None of the authors has any conflict of interest to disclose. We confirm that we have read the Journal's position on issues involved in ethical publication and affirm that this report is consistent with those guidelines.

FUNDINGS

SL is supported by grants from the LFCE (Ligue Française Contre l'Épilepsie, french chapter of the ILAE) and PHOCEO. Institutional Review Board of the APHM (NHLS4Y), and the included patients provided written informed consent.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

SUPPORTING INFORMATION


A Zuber
email: axel.zuber@univ-poitiers.fr

V Gauthier-Brunet

J Roger

J Gonzalez-Julian

T Ouisse

S Dubois

Cr 2 AlC high temperature oxidation under dry and wet air: understanding of the oxidation mechanism

Keywords: Cr 2 AlC, high-temperature oxidation, microstructure, gas emission, thermodynamic calculations

Cr 2 AlC is one of the most interesting MAX phase compositions to operate under aggressive environments up to 1400 °C, but the effect of humidity at high temperatures is still poorly investigated. Cr 2 AlC high-temperature oxidation tests under controlled humidity are carried out on fined-grained samples for 40 hours in the [1000-1400 °C] temperature range and compared to a previous study performed on single-crystals, fine and coarse-grained samples oxidized under dry air. Oxidation products are characterized and mass gain curves are analysed using both cubic and paralinear oxidation models to extract kinetics and characterize gas emission during the oxidation tests. These experimental data are supported by thermodynamic calculations in order to propose a quite complete oxidation mechanism for Cr 2 AlC. The nature and the arrangement of the oxidation products formed during wet and dry air oxidation tests are similar -a continuous Al 2 O 3 layer and a Cr 7 C 3 sublayer with pores-which demonstrates that the water vapor does not affect significantly the high-temperature oxidation of Cr 2 AlC. The acceleration of the oxidation process during wet air tests is correlated to the higher partial pressure of gaseous species produced in the presence of humidity which is associated with the chromium carbide's volatilization in the form of carbon oxide.

Introduction

Cr 2 AlC is one of the most studied and attractive MAX phases (M transition metal, A p-block element and X nitrogen and/or carbon), a well-known class of nanolamellar compounds with an unique combination of metallic and ceramic properties [START_REF] Sokol | On the Chemical Diversity of the MAX Phases[END_REF]. Cr 2 AlC was first discovered in 1963 by Jeitschko et al. [START_REF] Jeitschko | Kohlenstoffhaltige ternäre Verbindungen (H-Phase)[END_REF], but its interest has mainly arisen in the last 10-15 years for its corrosion resistance properties [START_REF] Tallman | A Critical Review of the Oxidation of Ti 2 AlC, Ti 3 AlC 2 and Cr 2 AlC in air[END_REF]. The structure of Cr 2 AlC, first imaged at atomic resolution by Lin et al. [START_REF] Lin | Atomic scale characterization of layered ternary Cr 2 AlC ceramic[END_REF], is typical of MAX phases: it crystallizes in the P6 3 /mmc hexagonal space group and is composed of a stack of M 6 X chromium carbide octahedrons layers and aluminium planes. As for other MAX phases such as Ti 2 AlC and Ti 3 AlC 2 , Cr 2 AlC is an alumina-forming phase which oxidizes slowly with diffusion based (parabolic, cubic) kinetics and a resulting activation energy typically above 300 kJ.mol -1 [START_REF] Tallman | A Critical Review of the Oxidation of Ti 2 AlC, Ti 3 AlC 2 and Cr 2 AlC in air[END_REF] [START_REF] Smialek | Oxygen diffusivity in alumina scales grown on Al-MAX phases[END_REF]. These properties make MAX phases comparable to other typical high temperature alloys such as aluminides and superalloys while having higher mechanical properties, as shown in figure 1 [START_REF] Tallman | A Critical Review of the Oxidation of Ti 2 AlC, Ti 3 AlC 2 and Cr 2 AlC in air[END_REF][START_REF] Tossey | High temperature oxidation of corrosion resistant alloys from machine learning[END_REF][START_REF] Ashby | The CES EduPack Resource Booklet 2: Material and Process Selection Charts[END_REF].

Figure 1: A) Comparison of MAX phases parabolic kinetic constant and activation energy with high-temperature oxidation resistant alloys ones [START_REF] Tallman | A Critical Review of the Oxidation of Ti 2 AlC, Ti 3 AlC 2 and Cr 2 AlC in air[END_REF][START_REF] Lin | Atomic scale characterization of layered ternary Cr 2 AlC ceramic[END_REF][START_REF] Smialek | Oxygen diffusivity in alumina scales grown on Al-MAX phases[END_REF][START_REF] Tossey | High temperature oxidation of corrosion resistant alloys from machine learning[END_REF]. B) Ashby diagram of materials strength vs. Young's modulus reproduced from [START_REF] Ashby | The CES EduPack Resource Booklet 2: Material and Process Selection Charts[END_REF] with MAX phases's position added to it.

Oxidation of bulk Cr 2 AlC has been studied in dry and ambient air in a large temperature range, from 700 °C to 1400 °C for various oxidation durations [START_REF] Lee | Oxidation of Cr 2 AlC at 1300 °C in air[END_REF][START_REF] Lin | High-temperature oxidation and hot corrosion of Cr 2 AlC[END_REF][START_REF] Lee | Oxidation of Cr 2 AlC between 900 and 1200 °C in air[END_REF][START_REF] Tian | Oxidation behavior of Cr 2 AlC ceramics at 1,100 and 1,250[END_REF][START_REF] Lee | Cyclic oxidation of Cr 2 AlC between 1000 and 1300 °C in air[END_REF][START_REF] Lee | Long-time oxidation of Cr 2 AlC between 700 and 1,000 °C in air[END_REF][START_REF] Li | Oxidation and crack healing behavior of a fine-grained Cr 2 AlC ceramic[END_REF][START_REF] Li | Influence of grain size on high temperature oxidation behavior of Cr 2 AlC ceramics[END_REF][START_REF] Gonzalez-Julian | Environmental resistance of Cr2AlC MAX phase under thermal gradient loading using a burner rig[END_REF][START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF]. The usual observations made on oxidized Cr 2 AlC samples report the formation of an α-Al 2 O 3 layer and a Cr 7 C 3 chromium carbide sublayer. We recently showed that oxidation in dry air of bulk Cr 2 AlC, independently of the grain size, ineluctably involves, for short/mid-term oxidation, the formation of a continuous α-Al 2 O 3 layer and a Cr 7 C 3 sublayer with pores; whereas very high temperature or long-term oxidation tests lead to the formation of chromia rich corundum's [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF]. The pores formation in the carbide sublayer could be caused by Kirkendall effect but it is often explained to be due to carbon and chromium oxides volatilization [START_REF] Lee | Oxidation of Cr 2 AlC at 1300 °C in air[END_REF][START_REF] Lin | High-temperature oxidation and hot corrosion of Cr 2 AlC[END_REF][START_REF] Lee | Cyclic oxidation of Cr 2 AlC between 1000 and 1300 °C in air[END_REF]. Carbon oxides volatilization was indeed characterized in a unique reference [START_REF] Lin | High-temperature oxidation and hot corrosion of Cr 2 AlC[END_REF] but stays a minor concern in dry air oxidation studies.

Gas volatilization becomes a major concern when performing high-temperature oxidation in wet air due to the water vapor reaction at the oxide surface, which evaporates the oxide scale by forming volatile oxyhydroxides [START_REF] Opila | Alumina volatility in water vapor at elevated temperatures : application to combustion environments[END_REF][START_REF] Opila | Volatility of Common Protective Oxides in High-Temperature Water Vapor: Current Understanding and Unanswered Questions[END_REF]. Presence of water vapor can have critical other effects on the global behaviour during the oxidation such as composition and arrangement changes of the oxide scale, oxidation rates increase or oxide scale brittleness [START_REF] Douglass | International Workshop on High-Temperature Corrosion[END_REF]. Alumina is usually poorly affected by volatilization in the 1300-1400 °C temperature range, contrary to chromia which undergoes a significant volatilization at temperature as low as 800°C [START_REF] Saunders | The oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: A review[END_REF]. The influence of water vapor onto the oxidation of MAX phases has been poorly investigated, except in one study of Lin et al. on the wet oxidation of Ti 2 AlC and Ti 3 AlC 2 . The authors mention an oxidation rate increase of these MAX phases in presence of water vapor [START_REF] Saunders | The oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: A review[END_REF].

In this study, we report the first Cr 2 AlC high-temperature oxidation tests under controlled humidity conditions as well as practical and theoretical evidence of carbon oxide volatilization in dry and wet air via paralinear oxidation kinetic model and thermodynamic calculations. For this purpose, finegrained samples were oxidized in wet air for 40 hours at 1000, 1200 and 1400 °C under three water vapor partial pressures (P H2O = 1700, 3400, 5100 Pa). For wet oxidation tests, oxidation products were characterized and mass gain curves were treated using both cubic and paralinear models to extract kinetics and oxidation mechanism information for fine-grained samples. Thermodynamic calculations were performed to support the experimental data. Results are compared with a previous study performed on single-crystals, fine and coarse-grained samples oxidized under dry air for 100 hours at temperatures ranging from 800 to 1400 °C [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF].

Method

Synthesis method

For the synthesis of fine-grained samples, chromium (Alfa Aesar, purity: 99%, D 50 = 28.0 µm), aluminium (Alfa Aesar, purity: 99.5%, D 50 = 9.1 μm) and graphite (Alfa Aesar, purity 99%, D 50 = 6.9 μm) powders were mixed in a Cr:Al:C=2:1.02:0.97 molar ratio and further with a ball to powder mass ratio of 1:1 during 24h in ethanol using planetary milling. Reactive sintering was performed using a Field Assisted Sintering Technology/Spark Plasma Sintering (FAST/SPS, FCT-HPD5, FCT System GmbH, Germany) under vacuum at 1200°C/30MPa for 15 minutes [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF].

For the synthesis of coarse-grained samples, chromium (Alfa Aesar, purity >99%, <44µm), aluminium (Alfa Aesar, purity >99.5%, <44µm) and chromium carbide (Alfa Aesar, purity >99,5%, <44µm) powders were mixed with a Cr:Al:Cr 3 C 2 =0.525:1.2:0.475 molar ratio and uniaxially cold-pressed. The pellet was then encapsulated into a glass container before being isostatically pressed at 1400 °C/150MPa during 4 hours using a Hot Isostatic Press (ACB-HIP6) [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF].

To synthesize the single crystals, aluminium and chromium pellets were melted in an alumina crucible in an induction-heated growth reactor. At 1650°C, a carbon rod was actuated through a hole made in the alumina cover, and dipped at a pre-selected depth into the flux until the dipped part totally dissolved. After carbon dissolution, the flux was cooled down to 1200°C in one week, and then let to cool down freely. Crystals were extracted from the solidified flux by etching in concentrated HCl [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF].

Oxidation processes

For the dry air oxidation tests, the polycrystalline and single crystal samples were cut into parallelepipeds (10x2x2 mm 3 ) and triangles (half a centimeter square sized plates), respectively. Both were polished with silicon carbide abrasive disks and finished on felt disk with diamond paste of 0.25 µm particles. The polished samples were placed into a thermogravimetric analysis chamber (TGA, SETARAM EVOSYSTEM) and heated under argon flow at 20°C/min. The subsequent isothermal oxidation treatment was performed under dry air flow at T=[800;1500] °C during 100 h. Since previous results related to dry air oxidation tests showed that the oxidation process is independent of the microstructure [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF], wet air oxidation tests were carried out only on fine-grained samples. Tests were performed using the same thermogravimetric analysis system, for 40 hours at 1000, 1200 and 1400 °C after heating under dry air. The three water partial pressures used were calculated from the wet gas temperature to be 1700, 3400 and 5100 Pa.

Kinetic models and data exploitation

Oxidation kinetic constants consist in describing the mass gain over time t, associated to the oxide growth, using a law depending on the reaction mechanism (associated to an order n=1,2,3…) according to , with S the sample's surface. For the parabolic and cubic treatments, the normalized mass gain curves were raised to the power 2 and 3 respectively. The slope of the resulting straight line gives the parabolic kinetic constant k p (kg 2 .m -4 .s -1 ) and the cubic kinetic constant k c (kg 3 .m -6 .s -1 ) at a given temperature.

The paralinear model is used when the mass gain curve is flawed by species volatilization. In the paralinear model, the normalized and smoothed mass gain curve is usually plotted as f( [START_REF] Berthod | Kinetics of High Temperature Oxidation and Chromia Volatilization for a Binary Ni-Cr Alloy[END_REF]. While the parabolic (n=2) and cubic (n=3) models are only diffusion driven growth kinetic models, the paralinear model contains a growth term and a volatilization term expressed as . The intercept of the curve with the y axis is homogeneous to a parabolic kinetic constant and it is further called paralinear kinetic constant k pl (kg 2 .m -4 .s -1 ). The slope of the curve, called volatilization kinetic constant k v (kg.m -2 .s -1 ), corresponds to a linear kinetic constant. The volatilization kinetic constant k v can be used to estimate the partial pressure of the volatilized gas P v according to P v α , with P tot and v gas the total gas pressure and the gas velocity respectively [START_REF] Opila | Volatility of Common Protective Oxides in High-Temperature Water Vapor: Current Understanding and Unanswered Questions[END_REF].

For all models, the kinetic constants calculated for each temperature can then be used to obtain the ln(k)=f(1/T) Arrhenius plots and determine the activation energy of the associated oxidation mechanism.

Thermodynamic calculations

To support the experimental investigations, thermodynamic analyses of Cr 2 AlC equilibrium in air were performed with Thermo-Calc software [START_REF] Andersson | Thermo-calc and dictra[END_REF]. The thermodynamic equilibria calculated from this software were based on the CALculation of PHAse Diagrams (CALPHAD) methodology [START_REF] Sundman | Computational thermodynamics: the calphad method[END_REF]. The relevant thermodynamic descriptions of the Cr-Al-C and CrO 2 -Al 2 O 3 systems reported, respectively by Y. Liang et al. and by T. M. Besmann et al., were used for the equilibrium calculations of the system [START_REF] Hallstedt | Thermodynamic evaluation of the Al-Cr-C system[END_REF][START_REF] Besmann | Thermochemical analysis and modelling of the Al 2 O 3 -Cr 2 O 3 , Cr 2 O 3 -SiO 2 , and Al 2 O 3 -Cr 2 O 3 -SiO 2 systems relevant to refractories[END_REF]. The thermodynamic descriptions of the gaseous species considered for the calculations result from the NIST Chemistry WebBook and the work of B.B. Ebbinghaus [START_REF] Linstrom | NIST chemistry webbook[END_REF][START_REF] Ebbinghaus | Thermodynamics of gas phase chromium species: The chromium oxides, the chromium oxyhydroxides, and volatility calculations in waste incineration processes[END_REF].

Microstructural characterization

Scanning electron microscopy (SEM -JEOL 7001-TTLS) and energy dispersive X-Ray spectrometry (EDXS, Oxford Instrument) techniques were used to observe the surface and cross-section of the samples and analyse the composition of the different contrasted regions, before and after oxidation. X-Ray Diffraction (XRD -BRUKER D8 diffractometer) with Cu-K α radiation was performed for crystalline structure identification of synthesized and oxidized samples.

Results and discussion

Microstructure characterization

As reported in [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF], Cr 2 AlC fine-grained (2 µm) samples contain small amounts of Al 2 O 3 and Cr 7 C 3 chromium carbide impurities as evidenced on the XRD pattern shown in Figure 2(a). After oxidation tests at 1000, 1200 and 1400°C during 40 hours under a water vapor partial pressure of 1700 Pa, the sample's surface consists of a continuous Al 2 O 3 layer which undergo buckling and cracking revealing the Cr 7 C 3 sublayer (Figure 3). At 1000 °C, θ-Al 2 O 3 whiskers have been observed, which is consistent for this oxidation time-temperature conditions. The corresponding cross-section SEM micrographs in back-scattered mode of the oxidized Cr 2 AlC fine-grained samples shown in Figure 4 confirm the presence of an external alumina layer and a chromium carbide sublayer, as reported in the case of dry air oxidation tests [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF]. The only difference is related to the existence of numerous and large porous areas in the Cr 7 C 3 sublayer and to an increase of the alumina scale thickness after wet oxidation tests implying an acceleration of the oxidation process. For brevity, the SEM micrographs related to samples oxidized at others water vapor partial pressures are not shown here since they exhibit similar features. Nevertheless, table 1 shows variation of the alumina thickness measured on the different micrographs. The alumina scale's thickness of the samples oxidized in dry air during 100 hours is the same as the one measured on samples oxidized in wet air for 40 hours, suggesting an acceleration of the oxidation process in the presence of water vapor.

However, the scale's thickness shows no obvious dependency on the water vapor partial pressure, suggesting that the water is an accelerating factor but doesn't significantly contribute to the oxidation process.

From the XRD patterns reported in Figure 2, the intensity of the peaks associated to Cr 7 C 3 and Al 2 O 3 phases increases with the oxidation temperature while the peaks associated to the Cr 2 AlC fades, indicating a substantial increase of the chromium carbide and alumina layers thickness with the oxidation temperature in good agreement with Table 1. These observations, related to a water vapor partial pressure of 3400 Pa, are also valid for other partial pressures. This first part shows that one of the features making Cr 2 AlC remarkable is its similar oxidation behaviour in the 800-1400°C temperature range in dry air and wet air. Indeed, the oxide layer formed during the wet and dry oxidation tests consists in a continuous external Al 2 O 3 layer and a Cr 7 C 3 porous sublayer in contact with the fine-grained Cr 2 AlC phase. Regarding the nature and the arrangement of the oxidation products, one can conclude that the water vapor does not affect the high-temperature oxidation of Cr 2 AlC in a significant way, at least for the investigated partial pressures and oxidation times. This statement has however to be confronted to other studies in similar conditions which are scarce in the literature.

Kinetics coupled with thermodynamic calculations

3.2.1.Mass gain curves

The mass gain curves are measured as a function of time during the wet air oxidation process for the three temperatures and water vapor partial pressures investigated (Figure 5). Compared to the dry conditions tests, the global behaviour under wet conditions shows a similar increase of the mass gain with temperature but does not reveal any clear tendency with the water vapor partial pressure. One can observe that the dry air oxidation curve's slope tilts more rapidly at 1400 °C than the one of the samples oxidized under wet air, highlighting the change of mechanism in the case of dry air oxidation tests compared to wet air tests. The exploitation of the mass gain curves for the Cr 2 AlC single-crystal, coarse-grained and fine-grained polycrystalline samples [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF] using the cubic, parabolic and paralinear models gives the kinetic constants listed in Table 2, for dry air and wet air oxidation tests. Independently of the microstructure, the k p parabolic and k pl paralinear kinetic constant values are close to each other, demonstrating that the oxide scale growth is well-described without considering species volatilization. Despite that, trying to take a volatilization phenomenon into account reveals differences between dry and wet air oxidation, as well as differences between oxidation tests performed below and above 1200 °C. The volatilization kinetic constant values, in the case of oxidation tests performed under dry air and below 1200°C, are quite low, in the range 5×10 -9 -5×10 -8 mg/mm²/s. In the case of oxidation tests performed under dry air above 1200 °C and under wet air, the volatilization kinetic constant values are higher, in the range 8×10 -8 -7×10 -7 mg/mm²/s. These features are valid whatever the microstructure of the Cr 2 AlC sample.

T (°C) P(H2O)

(Pa) Table 2: Kinetic constants deduced from the application of parabolic, cubic and paralinear models to mass gain curves under dry air and wet air for single crystal samples (SC), fine-grained (FG) and coarse-grained (CG) polycrystalline samples.

k c (kg 3 .m -6 .s -1 ) k p (kg 2 .m -4 .s -1 ) k pl (kg 2 .m -4 .s -1 ) k v (kg.m -2 .s -

Gas volatilization in dry and wet conditions

In figure 6-A, the gas partial pressure deduced from the volatilization kinetic constant k v [START_REF] Opila | Alumina volatility in water vapor at elevated temperatures : application to combustion environments[END_REF] in dry air shows that the paralinear model highlights gas species volatilization above 1200 °C for the Cr 2 AlC single-crystals, coarse-grained and fine-grained polycrystalline samples. According to literature [START_REF] Lin | High-temperature oxidation and hot corrosion of Cr 2 AlC[END_REF], this gas should be mostly composed of carbon oxides which is corroborated by the thermodynamic calculations shown in figure 6-B. Indeed, during the dry air oxidation process, the carbon oxides' partial pressure increases supposedly due to the oxidation of the carbides, prevailing on other gas products by far. In Figure 7-A, the gas partial pressure calculated from the volatilization kinetic constant in wet air shows that there is a significantly higher volatilization of species during wet air oxidation than during dry air oxidation for Cr 2 AlC fine-grained samples, at least for temperatures higher than 1000°C. Such a result may be associated to oxyhydroxide formation leading to the volatilization of the oxide scale [START_REF] Opila | Alumina volatility in water vapor at elevated temperatures : application to combustion environments[END_REF]. Nevertheless, alumina is the only oxide formed at this stage and it is not subject to volatilization at such temperatures [START_REF] Opila | Volatility of Common Protective Oxides in High-Temperature Water Vapor: Current Understanding and Unanswered Questions[END_REF]. Thus, gas volatilization indirectly confirms that the chromium carbide is oxidized. As a consequence, acceleration of volatilization is associated to the acceleration of the chromium carbide oxidation under wet air conditions. By extension, such a result proves the whole Cr 2 AlC oxidation process acceleration which is in good agreement with the thick alumina scale observed on the samples oxidized 40h in wet air. It is worth noting that the experimental carbon oxide partial pressure cannot be directly compared to the one predicted by thermodynamic calculations as the gas pressure depends on the kinetic factors.

In Figure 7-B, thermodynamic calculations show that the partial pressures of oxyhydroxide species are much lower than the carbon oxide ones. As a consequence, the gas formation mostly consists in carbon oxides due to the oxidation of the chromium carbide, whose oxidation rate increases in the presence of water vapor. Indeed, the presence of water vapor drastically increases the formed gas pressure as shown in Figure 7-A. Moreover, the gas pressure does not vary significantly with water vapor pressure which likely implies that water vapor is in excess during the chromium carbide oxidation. Thermodynamic calculation also predicts the reduction of the water vapor in parallel of the oxidation process, which produce dihydrogen gas, along with other gas state reactions producing NO X and H 2 O 2 gases. These reactions are disregarded since they are supposed to be of minor influence on the total mass variation.

Arrhenius plots

The ln(k c ) are plotted as a function of 1/T to determine the activation energy of the oxidation mechanism. The Arrhenius plots of the cubic model for the oxide growth are reported in Figure 8-A for Cr 2 AlC single crystals, fine and coarse-grained samples after 100 hours oxidation in dry air in the temperature range 800-1400 °C. It is the only model to be shown as it is commonly admitted that it is the one that best describes the oxide growth [START_REF] Tallman | A Critical Review of the Oxidation of Ti 2 AlC, Ti 3 AlC 2 and Cr 2 AlC in air[END_REF]. Moreover, it has been previously mentioned that gas volatilization has only a low influence on the mass gain curve for dry oxidation tests at temperatures below 1200°C.

The Arrhenius curves deduced from the cubic kinetic constants of the dry oxidation tests show a slope variation at low (below 900°C) and high (above 1200°C) temperatures independently of the microstructure. The slope change at 900°C likely results from the oxidation mechanism being, at least partially, driven by surface reactions. The slope change observed at high temperature results from a modification of the oxidation mechanism and is concomitant with the carbon oxide volatilization characterized for T>1200°C in dry air, confirming the oxidation of the chromium carbide sublayer. This chromium carbide oxidation explains the formation of the chromia-rich oxide scale for high enough temperature or oxidation duration in the case of dry air oxidation tests [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF].

The Arrhenius plots deduced from the cubic kinetic constants of the wet oxidation tests related to the fine-grained samples are shown in Figure 8-B. The linear shape is typical of a single oxidation mechanism in the investigated temperature range. The deduced activation energies, in the range 430-530 kJ.mol -1 , are higher than the activation energy in the linear regime of the dry oxidation tests on fine grained samples between 900 and 1300 °C, reaching a maximum of 400 kJ.mol -1 [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF]. These values are compatible with the highest values expected in the case of Cr 2 AlC oxidation process governed by oxygen diffusion at the grains boundaries [START_REF] Tallman | A Critical Review of the Oxidation of Ti 2 AlC, Ti 3 AlC 2 and Cr 2 AlC in air[END_REF][START_REF] Smialek | Oxygen diffusivity in alumina scales grown on Al-MAX phases[END_REF]. In this case, the oxide growth results from oxygen anions diffusion at the grain boundaries of alumina whereas a weak carbon oxide volatilization also occurs resulting from the Cr 7 C 3 carbide oxidation.

Long duration oxidation tests in wet air

A longer oxidation test (360 hours) at 1400°C with a higher water vapor content (P H2O = 20 kPa) was carried out on the Cr 2 AlC fine-grained sample to observe the gas volatilization. The mass gain curve, shown in Figure 9, can be fitted with an oxide growth part, represented by a cubic law and a volatilization part, represented by a linear law. The resulting kinetic constants (k c and k v ) match quite well the constants determined in the Table 2 for an oxidation test performed at 1400 °C during 100h under wet air. The small spacing between the experimental and theoretical curves starting at about 20000 s and remaining constant (green arrows) is due to anomalous mass variations associated with external factors (machine related), however one can observe a good match in the evolution of the curves. This experiment is proof of the volatilization phenomena previously determined with mass gain curve's analysis. The higher partial pressure of gaseous species produced during wet air oxidation tests is typical of an acceleration of the oxidation process as observed in numerous studies [START_REF] Opila | Volatility of Common Protective Oxides in High-Temperature Water Vapor: Current Understanding and Unanswered Questions[END_REF] and confirmed by the long-term oxidation test. This acceleration of the oxidation process is correlated to the presence of the numerous pores in the chromium carbide layer which may result from gas formation. The presence of pores could be also related to the well-known Kirkendall effect which corresponds to the accelerated diffusion of aluminium towards the surface in contact with air.

Oxidation mechanism of Cr 2 AlC

From the experimental data of the present and previous studies [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF] coupled with thermodynamic calculations, an oxidation mechanism is proposed and illustrated in Figure 10. As it was previously demonstrated, Cr 2 AlC high-temperature oxidation products' nature and arrangement are not sensitive to water vapor pressure -contrary to the reaction's rate which increases in presence of water vapor. The following mechanism can therefore be applied in both dry and wet conditions:

1) The oxygen reacts at the surface with aluminium atoms of the MAX phase to form an alumina scale and the Al-depleted Cr 2 AlC in contact with Al 2 O 3 transforms into chromium carbide Cr 7 C 3 .

2) The alumina scale thickens by inward diffusion of oxygen anions through alumina grain boundaries and the outward diffusion of aluminium cations through Cr 7 C 3 allows the alumina to be formed close to the Cr 7 C 3 /MAX phase interface

3) The alumina layer grows until the chromium carbide sublayer thickens enough to make significant the distance between Cr 2 AlC/Cr 7 C 3 and Cr 7 C 3 /Al 2 O 3 interfaces. At this stage, we assume that oxygen anions diffusion through the alumina scale up to the chromium carbide is faster than the Al cations diffusion from the inner Cr 2 AlC up to the Al 2 O 3 /Cr 7 C 3 interface. Thus, oxygen anions diffuse through alumina and reach the chromium carbide layer which is further oxidized, leading to the chromium carbide's volatilization as carbon oxide gaseous species 4) Then the carbon-depleted Cr 7 C 3 layer is further oxidized into chromia, along with some alumina due to the remaining aluminium cations from the MAX phase diffusing through the Cr 7 C 3 . These phenomena lead to an oxide scale composed of chromia and alumina (Cr,Al) 2 O 3 (see also ref.

Conclusion

Oxidation tests in dry air were carried out on single crystals, fine and coarse-grained polycrystalline Cr 2 AlC samples in the 800-1500 °C range up to 1000 hours [START_REF] Zuber | Towards a better understanding of the high-temperature oxidation of MAX phase Cr 2 AlC[END_REF] whereas oxidation tests in wet air were performed on fine-grained polycrystalline samples in the 1000-1400 °C range up to 360 hours. Thermodynamic calculations were also performed to support experimental investigations. It is demonstrated that oxidation products formed using wet and dry air conditions are similar. They consist in a continuous Al 2 O 3 alumina layer, a porous Cr 7 C 3 sublayer, as well as progressive gaseous carbon oxide emission due to Cr 7 C 3 oxidation, in good agreement with thermodynamic calculations. The water vapor partial pressure does not affect the nature and the arrangement of the oxidation products in the studied range, but it does modify its kinetics by increasing the oxidation rate. Such an increase, during wet air tests, is correlated to the higher partial pressure of carbon oxides produced in the presence of humidity. Lastly, based on thermodynamic calculations, kinetics and microstructural analyses related to wet and dry air oxidation tests, a complete oxidation mechanism has been proposed for pure Cr 2 AlC.

Acknowledgement

Special thanks to the Région Nouvelle-Aquitaine and the Ministère de l'Enseignement Supérieur et de la Recherche for funding this research. This work was supported by the French government program "Investissements d'Avenir" (EUR INTREE, reference ANR-18-EURE-0010). This work was supported by the European commission through the Horizon 2020 project IL TROVATORE (n° 740415).

Figure 2 :

 2 Figure 2: XRD patterns of fine-grained Cr2AlC samples: (a) before oxidation, and after oxidation at (b) 1000°C, (c) 1200°C, (d) 1400 °C during 40 hours under a water vapor partial pressure of 3400 Pa. The XRD patterns have been indexed with the theoretical structures available on the Materials Project website (Cr2AlC P63mmc mp-9956; Al2O3 3 c mp-1043; Cr7C3 P63mc mp-1196316) [30].

Figure 3 :

 3 Figure 3: SEM micrographs of fine-grained Cr2AlC sample's surface oxidized at: A) 1000 °C, B) 1200 °C, and C) 1400 °C during 40 hours under wet air (PH2O = 1700 Pa).

Figure 4 :

 4 Figure 4: Cross-section SEM micrographs, in back-scattered mode, of a fine-grained Cr2AlC sample oxidized at: A) 1000°C and B) 1200 °C during 40 hours under wet air (PH2O = 1700 Pa)

Figure 5 :

 5 Figure 5: Normalized mass gain curves of fine-grained Cr2AlC samples oxidized during 40 hours at T=[1000; 1200; 1400] °C and at PH2O =[1700; 3400; 5100] Pa. N.B.: In our previous article [16], the mass gain curves were not normalized (/100) ; these curves are the normalized ones.

Figure 6 :

 6 Figure6: A) Evaporated gas partial pressures deduced from the volatilization kinetic constant of Cr2AlC single crystal, fine and coarsegrained samples oxidized in dry air during 100 hours in the temperature range 800-1400 °C. The dashed line draws the limit between the temperature (T>1200°C) where gas volatilization occurs or not (T<1200°C). B) CALPHAD calculations of the oxidation product's partial pressures at 1200 °C under dry air.

Figure 7 :

 7 Figure 7: A-Evaporated gas partial pressures deduced from the volatilization constant of Cr2AlC fine-grained samples oxidized in wet air during 40 hours and in dry air during 100 hours in the temperature range 1000-1400 °C. B-CALPHAD calculations of the oxidation product's partial pressures at 1200 °C under wet air (PH2O=5100 Pa).

Figure 8 :

 8 Figure 8: A) Arrhenius plots of cubic kinetic constants of Cr2AlC single crystals, fine and coarse-grained samples after 100 hours oxidation in dry air in the temperature range 800-1400 °C; B) Arrhenius plots of cubic kinetic constants of Cr2AlC fine-grained samples after 40 hours oxidation in wet air in the temperature range 1000-1400 °C.

Figure 9 :

 9 Figure 9: Normalized mass gain curve of a fine-grained Cr2AlC sample oxidized 360 hours at 1400 °C under wet air (PH2O= 20 kPa) (red) with a theoretical fit (blue) composed of a cubic law for oxide growth (green) and a linear law for oxide volatilization (yellow).

). 5 )

 5 With respect to the progress of the chromia-alumina oxide formation, oxygen anions can reach Cr 2 AlC and lead to the formation of a new alumina layer and chromium carbide sublayer at the interface between Cr 2 AlC and the chromia-alumina oxide scale. Al atoms of Cr 2 AlC are oxidized in alumina and the outer Cr 2 AlC is transformed into chromium carbide Cr 7 C 3 .

Figure 10 :

 10 Figure 10: Schematic of the high-temperature oxidation mechanism of Cr2AlC in air with a final microstructure of a sample oxidized 1000 hours at 1000 °C for comparison.

Table 1 .

 1 Thickness of the alumina scale for several temperature and water vapor partial pressure conditions measured on Cr2AlC finegrained samples after 40 h and 100 h oxidation. The uncertainties are representative of the local variation of the alumina scale thickness measured on cross-sectional SEM micrographs.