Guillaume Pillot

Eléonore Frouin

Emilie Pasero

Anne Godfroy

Yannick Combet-Blanc

Sylvain Davidson

Pierre-Pol Liebgott
email: pierre-pol.liebgott@mio.osupytheas.fr

Specific enrichment of hyperthermophilic electroactive Archaea from deep-sea hydrothermal vent on electrically conductive support

Keywords: Hyperthermophilic exoelectrogens, Deep-sea hydrothermal vent, Microbial electrolysis cell, External Electron Transfer

While more and more investigations are done to study hyperthermophilic exoelectrogenic communities from environments, none have been performed yet on deep-sea hydrothermal vent.

Samples of black smoker chimney from Rainbow site on the Atlantic mid-oceanic ridge have been harvested for enriching exoelectrogens in microbial electrolysis cells under hyperthermophilic (80 °C) condition. Two enrichments were performed in a BioElectrochemical System specially designed: one from direct inoculation of crushed chimney and the other one from inoculation of a pre-cultivation on iron (III) oxide. In both experiments, a current production was observed from 2.4 A/m² to 5.8 A/m² with a set anode potential of -0.110 V vs Ag/AgCl. Taxonomic affiliation of the exoelectrogen communities obtained on the electrode exhibited a specific enrichment of Archaea belonging to Thermococcales and Archeoglobales orders, even when both inocula were dominated by Bacteria.

Introduction

Since the discovery of the first deep-sea hydrothermal vent in 1977, many studies have expanded our understanding of extremophilic life forms in those environments. Considered as primordial environments similar to the early Earth conditions [START_REF] Martin | Hydrothermal vents and the origin of life[END_REF][START_REF] Takai | Microbial ecology of midocean ridges and back-arc basins[END_REF], the deep-sea hydrothermal ecosystems are regarded as a good model to study the origins and evolution of life on Earth [START_REF] Takai | Microbial ecology of midocean ridges and back-arc basins[END_REF]. In addition, in recent years many authors have focused on the great potential of extremophilic marine microbes for their use as prolific producers of bioactive substances (enzymes, metabolic products...) [START_REF] Poli | Microbial diversity in extreme marine habitats and their biomolecules[END_REF].

The "black smoker" deep-sea hydrothermal vents, located along the ridges of the Atlantic, Pacific and Indian oceans, are the result of volcanic activities that generate hydrothermal chimneys composed of polymetallic sulfide minerals (heterogeneous pyrite) [START_REF] Dick | The microbiology of deep-sea hydrothermal vent plumes: ecological and biogeographic linkages to seafloor and water column habitats[END_REF]). Those environments exhibit dynamic habitats that are characterized by large steep thermal and chemical gradients. These gradients provide a wide range of growth conditions for many extremophilic microorganisms growing as biofilms and being the base of these specific deep-sea ecosystems [START_REF] Flores | Microbial community structure of hydrothermal deposits from geochemically different vent fields along the Mid-Atlantic Ridge[END_REF]; [START_REF] Kristall | Growth history of a diffusely venting sulfide structure from the Juan de Fuca Ridge: A petrological and geochemical study[END_REF]). Thermophilic microorganisms from the Archaea domain, mainly belonging to the orders Thermococcales, Methanococcales, and Archaeoglobales have been identified in these environments, as well as mesophilic and thermophilic microorganisms from the Bacteria domain belong to Epsilon-proteobacteria [START_REF] Huber | Isolated communities of Epsilonproteobacteria in hydrothermal vent fluids of the Mariana Arc seamounts: Epsilonproteobacteria in vents of the Mariana Arc[END_REF][START_REF] Vetriani | Deep-sea hydrothermal vent Epsilonproteobacteria encode a conserved and widespread nitrate reduction pathway (Nap)[END_REF]) and to the orders Aquificales and Thermotogales [START_REF] Miroshnichenko | Recent developments in the thermophilic microbiology of deep-sea hydrothermal vents[END_REF].

Considering the mineralogical composition of these hydrothermal chimneys (polymetallic massive sulfide), it appears likely that a significant proportion of its microbial populations is dependent on energetic metabolisms based on the dissimilatory reduction of insoluble "metals" or sulfur compounds [START_REF] Cao | Microbial sulfur cycle in two hydrothermal chimneys on the Southwest Indian Ridge[END_REF][START_REF] Konn | The production of methane, hydrogen, and organic compounds in ultramafic-hosted hydrothermal vents of the Mid-Atlantic Ridge[END_REF].

As the microbial cell envelope is neither physically permeable to insoluble minerals nor electrically conductive, microorganisms have evolved strategically to exchange electrons with insoluble extracellular minerals, a mechanism known as the extracellular electrons transfer (EET) [START_REF] Hinks | Microbial electron transport in the deep subsurface[END_REF][START_REF] Shi | Extracellular electron transfer mechanisms between microorganisms and minerals[END_REF]). The first described EET capable bacteria were Shewanella and Geobacter [START_REF] Shi | Respiration of metal (hydr)oxides by Shewanella and Geobacter: a key role for multihaem c-type cytochromes[END_REF]). The role of membrane bound electron transport chains in carrying out EET was well acknowledged, but the exact mechanisms are still not completely understood [START_REF] Kumar | The ins and outs of microorganismelectrode electron transfer reactions[END_REF]). Most of the knowledge about EET in microbes is derived from studies in bioelectrochemical systems [START_REF] Allen | Microbial fuel-cells[END_REF]; [START_REF] Logan | Microbial fuel cells : Methodology and technology[END_REF][START_REF] Schröder | Microbial electrochemistry and technology: terminology and classification[END_REF] which helped to define a novel group of microorganisms called exoelectrogens. These exoelectrogenic microorganisms are capable of extracellular electron transfer to a solid electrode, which are used in Microbial Electrochemical Technologies (METs) such as Microbial Fuel Cells (MFC) and microbial electrolysis cells (MEC) [START_REF] Doyle | Methods for enrichment of novel electrochemically-active microorganisms[END_REF]. In the past years, exoelectrogenic activity has been reported in almost 100 microbial species which are mostly affiliated with the bacterial phylum Proteobacteria [START_REF] Koch | Is there a specific ecological niche for electroactive microorganisms?[END_REF]. All these microorganisms are mesophilic and grow optimally at moderate temperatures, ranging from 20 °C to 45 °C.

To date, only four thermophiles isolated from extreme natural environments, Thermincola ferriacetica [START_REF] Marshall | Electrochemical evidence of direct electrode reduction by a thermophilic Gram-positive bacterium, Thermincola ferriacetica[END_REF], Thermincola potens strain JR [START_REF] Wrighton | Evidence for direct electron transfer by a gram-positive bacterium isolated from a microbial fuel cell[END_REF]), Calditerrivibrio nitroreducens [START_REF] Fu | A thermophilic gram-negative nitrate-reducing bacterium, Calditerrivibrio nitroreducens, exhibiting electricity generation capability[END_REF]) and Thermoanaerobacter pseudethanolicus [START_REF] Lusk | Characterization of electrical current-generation capabilities from thermophilic bacterium Thermoanaerobacter pseudethanolicus using xylose, glucose, cellobiose, or acetate with fixed anode potentials[END_REF], were shown to generate electricity in MFCs operating at a temperature higher than 50°C. Moreover, it is only very recently that three hyperthermophilic strains, Pyrococcus furiosus, Geoglobus ahangari and Ferroglobus placidus have been shown to have the capacity to produce electricity in MFC or MEC [START_REF] Sekar | Electricity generation by Pyrococcus furiosus in microbial fuel cells operated at 90°C[END_REF][START_REF] Yilmazel | Electrical current generation in microbial electrolysis cells by hyperthermophilic archaea Ferroglobus placidus and Geoglobus ahangari[END_REF]). This would be the three first hyperthermophilic archaeon strains described having the capacity of EET. Several studies reported the enrichment of mixed cultures of efficient thermophilic exoelectrogens on the anode of METs [START_REF] Ha | Treatment of alcohol distillery wastewater using a bacteroidetes-dominant thermophilic microbial fuel cell[END_REF][START_REF] Mathis | Electricity generation by thermophilic microorganisms from marine sediment[END_REF][START_REF] Wrighton | A novel ecological role of the Firmicutes identified in thermophilic microbial fuel cells[END_REF]. More recently, two exoelectrogenic biofilms have been enriched at 70 °C from a high-temperature petroleum reservoir [START_REF] Fu | Bioelectrochemical analysis of a hyperthermophilic microbial fuel cell generating electricity at temperatures above 80 °C[END_REF] and at 80 °C from Red Sea brine pools [START_REF] Shehab | Enrichment of extremophilic exoelectrogens in microbial electrolysis cells using Red Sea brine pools as inocula[END_REF]) on the anode of MFC systems.

To the best of our knowledge, no exoelectrogenic biodiversity enrichment from deep-sea hydrothermal vents has been achieved yet, while it seems likely that some microbial populations require this type of energy metabolism to expand in these particular environments. Interestingly, a MFC was installed at a hydrothermal vent field [START_REF] Girguis | On the potential for bioenergy and biofuels from hydrothermal vent microbes[END_REF] showing for the first time, the in situ electricity generation in those extreme ecosystems. More recently it has been demonstrated that there is a widespread and distant electron transfer through the electrically conductive hydrothermal chimney by the internal oxidation of the hydrothermal fluid coupled to the reduction of oxygenated seawater at the external side of the chimney [START_REF] Yamamoto | Spontaneous and widespread electricity generation in natural deep-sea hydrothermal fields[END_REF]). This electricity generation in deep-sea hydrothermal systems must affect the surrounding biogeochemical processes and the development of microbial communities through potential EETcapable microorganisms.

The aim of this study was to promote and identify a part of the exoelectrogenic microbial community from a hydrothermal chimney of the Rainbow site on the Atlantic mid-oceanic ridge.

For this investigation, two experiments were carried out using a semiautomatic two-chamber BioElectrochemical System Stirred-Reactor (BES) prototype (graphical abstract), operating at high temperatures (80 °C). The first one was performed to enrich microbes after direct inoculation of the BES with a chimney fragment. The second enrichment in BES was carried out from an inoculum obtained by a microbial enrichment culture in flask on Fe (III) oxide particles as electron acceptor using the same hydrothermal sample. This was done in order to pre-cultivate potential exoelectrogenic microbes on iron oxide and observing the impact on biodiversity obtained subsequently in BES. The evolution of current production, of microbial diversity and biomass during the different enrichments were studied through electrochemical method and molecular biology survey.

Material and methods

Sample collection and preparation

The inoculum used for all the experiments was collected on the Rainbow hydrothermal vent field (36°14′N, MAR) by the Remote Operated Vehicle VICTOR 6000 during EXOMAR cruise in 2005 led by IFREMER (France) on board RV L'Atalante [START_REF] Godfroy | EXOMAR cruise, RV L'Atalante[END_REF]. Sample (EXO8E1) was collected from the breaking off of a piece of a high temperature active black smoker using the arm of the submersible and bring back to the surface into a decontaminated insulated box. On board, chimney fragments were anaerobically crushed into an anaerobic chamber (La Calhene, France) and stored into flasks under anaerobic conditions (anoxic seawater at pH 7 with 0.5 mg/L of Na 2 S and N 2 :H 2 :CO 2 (90:5:5) gas atmosphere) and kept at 4 °C. Prior to the experiment, pieces of hydrothermal chimney were removed from the sulfidic seawater flask, crushed in a sterile mortar and pestle in an anaerobic chamber (Coy Laboratories Inc.) and distributed in anaerobic tubes for use in various experiments.

Enrichment on iron oxide in flask

To obtain enrichment of electro-active microbes on insoluble Fe (III) oxide as electron acceptor, 2.5 g of crushed hydrothermal chimney was inserted in 500 mL flask with butyl rubber stopper under nitrogen gas atmosphere filled with 250 mL of anaerobic mineral medium at pH 7 containing 30 g/L NaCl, 0.65 g/L KCl, 0.5 g/L NH 4 Cl, 0.3 g/L KH 2 PO 4 , 0.3 g/L K 2 HPO 4 , 0.1 g/L MgCl 2 , 0.1 g/L CaCl 2 , 0.35 g/L Cysteine HCl, 0.2 g/L of yeast extract and 10 mL/l of Balch trace mineral solution [START_REF] Uzarraga | New cultural approaches for microaerophilic hyperthermophiles[END_REF]). The media was supplemented with 10 g/L of Fe (III) oxide, 10 mM of acetate and 4 g/L of yeast extract as electron donor and carbon source. The flasks were incubated at 80 °C in static condition until a dark coloration of iron oxide was observed. Two subcultures were performed in the same condition with 1% of inoculum from the previous culture.

Semi-Automated Bioelectrochemical Systems

A prototype of semi-automated BioElectrochemical System in Stirred-Reactor (BES) has been developed to assess the enrichment of hyperthermophilic electroactive microorganisms. The system was composed of a two-chamber jacketed glass reactor (Verre Labo Mula, France) with a 1.5 L working volume, thermostated with a Heating Circulator (Julabo SE 6, France) at 80 °C ± 1 °C, and separated by an Anion Exchange membrane (Membrane International Inc.). The working electrode was a 20 cm² carbon cloth (PaxiTech SAS, France) with a 3 M Ag/AgCl reference electrode and the counter electrode a 20cm² carbon cloth coated with platinum [START_REF] Hogarth | The development of the direct methanol fuel cell[END_REF].

The bioelectrochemical system was connected to a semi-automated platform previously described [START_REF] Boileau | Hydrogen production by the hyperthermophilic bacterium Thermotoga maritima part I: effects of sulfured nutriments, with thiosulfate as model, on hydrogen production and growth[END_REF] to control the composition and rate of gas input (H 2 , CO 2 , O 2 , N 2 ) with mass flowmeters (Bronkhorst, Netherlands). A continuous monitoring of output gas composition (H 2 , N 2 , CH 4 , O 2, CO 2 ) were performed using a micro-GC equipped with a catharometric detector (MS5A, SRA Instrument, France) and a CARBOCAP CO 2 probe (Vaisala GMT 221, Finland). To ensure anaerobic condition, the culture medium was continually sparged with a 50 mL/min flow of N 2 .

The pH was maintained at 7 ± 0.1 by the addition of sodium hydroxide (NaOH 0.5 mM) or hydrochloric acid (HCl 0.5 mM). The stirring, driven by two axial impellers, was set to 150 rpm.

All the parameters, as pH and ORP (Mettler Toledo InPro 3253, Switzerland), temperature (Prosensor pt 100, France), stirring speed, gaseous H 2 , N 2 , CH 4 , O 2 and CO 2 concentration and NaOH and HCl consumption, were measured and managed by the BatchPro software (Decobecq Automatismes, France). SP-240 potentiostats and EC-Lab software (BioLogic, France) were used to poise the electrodes at a fixed potential and measure current. All the measured currents are expressed in ampere per square meter of electrode area.

Operating conditions in BES

Before each experiment, the BES was dismantled, washed, and sterilized by autoclaving at 120 °C for 20 min. Then, the system was connected to the platform and 1.5 L of mineral medium was injected and supplemented with 10 mM acetate and 0.15 g/L of Yeast Extract (YE). The liquid media was set in the operational condition for a few hours prior to perform a cyclic voltammetry (CV, 20 mV/s). First, the system (BES1) was inoculated with 15 g of crushed hydrothermal chimney in anaerobic condition. A chronoamperometry was carried out by the potentiostat to poise the electrode at -0.110 V vs Ag/AgCl (+0.05 vs Standard Hydrogen Electrode), and a measurement of the current was taken every 10 s. A cyclic voltammetry was also performed at the end of the experiment. Secondly, a new system (BES2) was inoculated in the same condition with 1% of the last enrichments in flask on Fe (III) oxide on yeast extract. An abiotic control and an inoculated but non-polarized control have been performed in the same conditions to exhibit the exoelectrogenic specificity of the biofilm on the polarized electrode.

Taxonomic and phylogenetic classification

Taxonomic affiliation was performed according to [START_REF] Zhang | Bacterial and archaeal communities in the deep-sea sediments of inactive hydrothermal vents in the Southwest India Ridge[END_REF]. DNA were extracted from 1g of the crushed chimney and at the end of each experiment (BES-1 at 14 days and BES-2 at 11 days): on the scrapings from half of the 20 cm² of working electrode and from 50 mL of the liquid media of the BES and flask enrichments, which were centrifuged and suspended in 1 mL of sterile water. The DNA extraction was carried out using the MoBio PowerSoil DNA isolation kit (Carlsbad, CA USA). The V4 region of the 16S rRNA gene was amplified using the universal primers 515F (5′-GTG CCA GCM GCC GCG GTA A-3′) and 806R (5′-GGA CTA CNN GGG TAT CTA AT-3′) [START_REF] Bates | Examining the global distribution of dominant archaeal populations in soil[END_REF] with Taq&Load MasterMix (Promega) and PCR reactions were carried out using C1000 Thermal Cycler (BioRad) with the following conditions: initial denaturation at 94 °C for 3 min followed by 30 cycles of denaturation at 94 °C for 30 s, primers annealing at 50 °C for 30 s and extension at 72 °C for 90 s, followed by a final extension step of 5 min at 72 °C. The amplified gene regions were sequenced on Illumina MiSeq 2500 platform (GeT-PlaGe, France) to generate paired-end 150 bp reads. The reads were merged using the FLASH software. The taxonomic affiliation was performed with the QIIME software package v 1.9.1.

Chimera were removed from the merged sequenced using UCHIME Algorithm. Then, the filtered sequences were clustered into OTUs using the RDP method with a minimum bootstrap confidence of 0.8 and OTUs were affiliated using the Silva database as reference. To analyze the alpha diversity, the OTU tables were rarified to a sampling depth of 10770 sequences per library and two metrics were calculated: the richness component represented by the number of OTUs observed, and the Pielou's index representing the evenness component of our biodiversity. The raw data of barcoding analysis were deposited in the European Nucleotide Archive with the accession number PRJEB24019. The construction of clone library was performed by amplifying the 16S rRNA genes by previously described PCR method with a FD1 (5'-AGAGTTTGATCCTGGCTCAG-3') and R6

(5'-TACGGCTACCTTGTTACG-3') primer set [START_REF] Brosius | Gene organization and primary structure of a ribosomal RNA operon from Escherichia coli[END_REF] using Taq&Load MasterMix (Promega). The amplicons were cloned into the pGEM-T easy vector (Promega) and transformed into E. coli JM109 competent cells that were grown overnight in LB agar at 37 °C. Fragment of 16S rRNA gene (~1300 bp) of the clones were sequenced by ABI3730xl (GATC Biotech) sequencers. The nucleotide sequences obtained from clone library were deposited in the GenBank database with the accession numbers MG694212 through MG694233

Quantitative PCR of archaeal and bacterial 16S rRNA gene copies

Bacterial and archaeal quantification was carried out by qPCR with SsoAdvanced™ Sybr Green Supermix on a CFX96 Real-Time System (C1000 Thermal Cycler, Bio-Rad Laboratories, CA, USA) with the primers GML5F (5'-GCC TAC GGG AGG CAG CAG-3') and Univ516 (5'-GTD TTA CCG CGG CKG CTG RCA-3') specific to Bacteria [START_REF] Michotey | Spatio-temporal diversity of free-living and particle-attached prokaryotes in the tropical lagoon of Ahe atoll (Tuamotu Archipelago) and its surrounding oceanic waters[END_REF] and Arc931F (5'-AGG AAT TGG CGG GGG AGC A-3') and m1100R (5'-BTG GGT CTC GCT CGT TRC C-3') for Archaea [START_REF] Einen | Enumeration of Archaea and Bacteria in seafloor basalt using real-time quantitative PCR and fluorescence microscopy[END_REF]. The PCR program was composed of a 10 s denaturation step at 94 °C, a hybridization step of 10 s at 55 °C (Bacteria) or 62 °C (Archaea) and a 10 s elongation step at 72 °C, with melting curves performed at the end of each reaction to ensure product specificity. A standard curve from 10 2 to 10 10 16S rRNA gene copies was obtained by diluting pGEM-T plasmids harboring hyperthermophilic bacterial or archaeal rRNA gene fragment obtained from microbial community of interest. The results were expressed in copies number of 16s rRNA gene per gram of crushed chimney, per milliliter of liquid media or per cm² of surface of electrode.

Results and discussion

Microbial diversity of hydrothermal chimney from Rainbow site of Atlantic Ocean

Prior to study specifically the electroactive community putatively present on a chimney of the hydrothermal Rainbow site, an analysis of the total microbial diversity present in our crushed chimney inoculum was done by using the Illumina method. The chimney biodiversity (Fig. 1) was composed of 160 OTUs representing a high richness of species. As indicated by the Evenness index (0.677), the sequences were distributed relatively equally in the different OTUs.

Furthermore, the taxonomic affiliation of the 160 OTUs showed that 66% were assigned to Bacteria and 33% to Archaea domains. This was consistent with the quantitative Polymerase Chain Reaction (qPCR) assays which showed a dominance of Bacteria compared to Archaea (6.38 ± 0.05 vs 4.77 ± 0.19 log of 16S rRNA gene copies per gram of chimney, respectively). The difference of ratio obtained can be explained by the overestimation of the bacterial quantification by 16S rRNA gene qPCR, because of the high number of gene copies per cells compared to Archaea (generally equal to 1 per cell) (cf. rrnDB, [START_REF] Stoddard | rrnDB: improved tools for interpreting rRNA gene abundance in bacteria and archaea and a new foundation for future development[END_REF]). Within the bacteria domain, the OTUs were mainly assigned to 5 phyla: Proteobacteria (58%), Firmicutes (3%), Aquificae (1%), Bacteroidetes (1%) and Thermodesulfobacteria (1%) whereas the archaeal OTUs were only identified as Euryarchaeota represented by Thermococcales (23%) and Archaeoglobales (11%). This taxonomic profile was substantially similar to those previously reported on Rainbow chimneys (

Enrichment of anode-respiring community in BES from crushed chimney

To assess the diversity of hyperthermophilic exoelectrogenic microbes from deep hydrothermal vent on conductive electrode, a fraction of a crushed chimney from the Rainbow site was used to inoculate the BES1. To mimic the hydrothermal vent conditions in the BES, a synthetic seawater medium, containing acetate and yeast extract as carbon and energy sources, was used. Indeed, in hydrothermal vent fluid, acetate can be chemically synthesized through Fischer-Tropsch Type (FTT) reaction from H 2 and CO 2 , both produced otherwise during serpentinization reaction [START_REF] Schrenk | Serpentinization, carbon, and deep life[END_REF]. Acetate can also be biologically produced during fermentative metabolisms.

It should be noted that acetate is not fermentable in the absence of acetoclastic methanogens and needs an exogenous electron acceptor to be used as energy source for microorganisms' growth. On the other hand, YE mimicked here the organic compounds produced by autotrophic and heterotrophic communities of hydrothermal chimney available for the fermentative/respiratory growth of microorganisms.

While no notable current was observed during the 10 days of experiment in the control experiments (abiotic and killed inoculum), a raise of current density was observed after 6 days of incubation in the BES1 inoculated with crushed chimney (Fig. 2). The maximum current density reached 5.9

A/m² at 8.7 days and remained stable for few hours. The 3 mM of acetate consumed during this period as attested by HPLC measurements (data not shown) was in good agreement with the current production assuming a maximum faradic efficiency at 95-100%, as previously obtained in literature [START_REF] Sengodon | Microbial fuel cells[END_REF]. After this period the current density decrease progressively probably due to the exhaustion of growth factors present in the medium and necessary to the biofilm metabolic activity. Indeed after 10 days of culture, the renewal of the medium led again to a current increase of up to 6 A/m² at maximum current density. Similarly, the current decreased after a few hours but remained stable in absence of medium renewal.

Cyclic voltammetries (Fig. 3) have been performed after inoculation and at the end of experiment in polarized condition to observe the electrochemical profile of ElectroActive Biofilms (EAB) as catalyst of the bioelectrochemical oxidation of acetate. The anode showed the apparition of an oxidation peak with a midpoint potential at -0.100 V (vs. Ag/AgCl) at the end of the experimentation. No oxidation peak was observed for the spent media with a new sterile electrode, suggesting that EET mechanisms were not involving mediators (data not shown). Moreover, the capacitive current (vertical distance between oxidation and reduction waves) increasing between beginning and end of the culture experiments reports an increase of the electrochemical double layer and suggests the presence of a biofilm on the surface of the electrode. Thus, these results suggest the development of EAB with direct EET using acetate as electron donor.

In contrast to the non-polarized culture conditions, microscopic observations over time have revealed the presence of planktonic microorganisms (in the liquid medium) after 9 days of incubation in the polarized electrode culture condition. In addition, the microbial quantification by qPCR of the enrichment in BES1 shows 7.3 ± 0.18 and 9.23 ± 0.04 log of bacterial and archaeal 16S rRNA gene copies per milliliter of liquid media and 7.28 ± 0.53 and 9.73 ± 0.06 log per square centimeter of electrode, respectively. On the contrary, in the non-polarized control, quantification of 16S rRNA copies was under the 2 log of sensitivity threshold of the method, indicating that no significant growth was observed under these conditions in liquid media or on the non-polarized electrode. Thus, the polarization of the electrode (-0.110 V vs Ag/AgCl), which served as an obligatory electrons acceptor to allow the oxidation of acetate or the weak amount of YE, seems essential also for the planktonic microbial growth.

To identify the microbes present on the electrode (Electrode BES1) and in liquid medium (Liquid BES1), a microbial diversity study through sequencing of the hypervariable V4 region of 16S rRNA gene (Fig. 1) have been performed at the end of the enrichment (day 14). 61 OTUs were obtained on Electrode 1 and 58 OTUs in Liquid Media 1, indicating of a loss of biodiversity from environmental chimney (160 OTUs). The sequences obtained are distributed in the different OTUs with however some OTUs more represented than in environmental sample (evenness at 0.452 on Electrode 1 and 0.331 in Liquid Media 1). This can be explained by our selective conditions of enrichment with high temperature and substrate specificity. Based on average abundance analysis, the microbial diversity of enrichment culture was dominated by Euryarchaeota phyla (> 70%), either on electrode or in liquid medium. Interestingly, at the genus level, the dominating archaeal OTUs on electrode were closely related to Geoglobus spp. (45.2%) and Thermococcus spp.

(25.6%) whereas the planktonic microbial diversity in liquid medium is especially dominated by uncultured Thermococcus spp. (64.1%) rather than Geoglobus spp. (13.3%). The bacterial diversity on the electrode and in liquid media were mainly assigned to Thermodesulfatator spp. (15.6% and 18% respectively), while the remaining were distributed between members of Bacillaceae and Micrococcaceae families. These specific enrichments of Archaea compared to Bacteria demonstrate a shift in initial microbial community structure from the crushed chimney, surely driven by the specific BES characteristics (i.e., polarized electrode, hyperthermophilic condition).

Due to the limitation for taxonomic affiliation at species level of the Illumina techniques on 290 bp 16S fragments, we performed 16S rDNA clone libraries on ~1300 bp 16S sequence. It allowed identifying the Thermococcus spp. as closely related to Thermococcus thioreducens, T. coalecens, T. barossi, T. peptonophilus, T. celer (98% similarities with them) and an unidentified Thermococcus species (95% similarity with Thermococcus thioreducens). However, because of the high levels of similarity between species of the genus Thermococcus, the taxonomic affiliation through the coding gene for 16S rRNA is not sufficient to determine the Thermococcus species present in enrichments.

However, among the Geoglobus spp. the taxonomic affiliation from clone libraries has allowed to identify two species: Geoglobus ahangari (99% similarity) and a novel genus or species of the Archaeoglobaceae family (MG694212 and MG694224: 95 % of similarity vs Geoglobus ahangari). This novel taxon is exclusively found on the electrode surface. Interestingly, this affiliation has been possible only through near full 16S rRNA gene sequence (1300 bp) alignment. Indeed, the hypervariable V4 region of the rRNA gene (~290 bp), used to the study of microbial diversity by Illumina-based analysis, did not allow to phylogenetically differentiate this novel taxon from Geoglobus ahangari. Differences are remarkable at level of hypervariable V6 to V8 regions.

The discovery of Geoglobus species enrichment on the electrode is remarkable. The two species of Geoglobus described so far (G. ahangari and G. acetivorans) are known to grow autotrophically using H 2 or heterotropically using a large number of organic compounds with in both cases soluble or insoluble Fe (III) oxide as a final electrons acceptor (Manzella et al. 2013). More recently, it has been shown that Geoglobus ahangari was exoelectrogenic by direct contact when placed in onechamber microbial electrolysis cells at 80 °C. In contrast to our results, the current produced was particularly weak probably due to its use as an axenic culture, and its lack of enzymatic component to resist to oxidative stress on electrode [START_REF] Yilmazel | Electrical current generation in microbial electrolysis cells by hyperthermophilic archaea Ferroglobus placidus and Geoglobus ahangari[END_REF]).

Phylogenetic analysis of 16S rRNA clone libraries has led to the identification of taxon

Thermodesulfatator atlanticus among the Thermodesulfatator spp. previously identified in high throughput sequencing. This bacterium, also isolated from a Rainbow site chimney, is known to be chemolithoautotrophic, sulfate-reducing obligate bacterium that uses H 2 as electron donor and CO 2 as carbon source. Alternatively, it is able to use methylamine, peptone or yeast extract as carbon sources [START_REF] Alain | Thermodesulfatator atlanticus sp. nov., a thermophilic, chemolithoautotrophic, sulfatereducing bacterium isolated from a Mid-Atlantic Ridge hydrothermal vent[END_REF]. A close related species, Thermodesulfobacterium commune has already been identified in EAB on electrode of a MFC (Fu et al. 2015)

Enrichment of hyperthermophilic microorganisms on crystalline Fe (III) oxide

In parallel of the first BES previously described, flask enrichments with insoluble metallic electron acceptor were done. Crushed chimney was inoculated in anaerobic mineral medium added with 10 g/L of crystalline Fe (III) oxide (α-Fe 2 O 3 : hematite) as electron acceptor (Wahid and Kamalam, 1993), acetate (10 mM) and yeast extract (4 g/L) as energy and carbon source. After 2 days of static incubation at 80 °C, the hematite was completely reduced to black compounds (magnetic particles) and the head space of the flask contained 32% of CO 2 , 0.2% of H 2 and 10% of CH 4 . A production of acetate was also observed in the liquid media, reaching 12 mM at the end of the experiment. The next subcultures reached the black coloration in less than 24 hours with similar concentration of each gas in the headspace of the flasks and same profile of metabolites in the liquid media. The presence of a thin biofilm could be observed on the surface of the agglomerated iron oxide. An abiotic control with a mix of acetate, yeast extract, H 2 , CH 4 and CO 2 didn't show black coloration of iron oxide after one month of incubation at 80 °C. These results suggest the development of a community of both fermentative organisms, producing acetate, and electroactive microorganisms, able to oxidize organic compounds brought by the YE (peptides, carbohydrates, etc.) and acetate in the culture medium for the reduction of crystalline Fe (III) oxide.

The biodiversity enriched in flask was composed of 29 OTUs, and the sequences were relatively concentrated in dominant OTUs (evenness at 0.292). At the family level, the microbial diversity was dominated by bacterial OTUs related to Clostridiaceae (73%), and Thermodesulfobacteriaceae (3%). The archaeal OTUs represented only 24% of the biodiversity distributed between Thermococcaceae (20.5%), Methanococcaceae (3%) identified as Methanotorris igneus species and Archaeoglobaceae (0.5%). The quantification showed an enrichment of 9 log of bacterial and 7 log of archaeal 16S rRNA gene copies which demonstrated a shift of enrichment toward the preferential bacterial growth in opposition with BES enrichment. Interestingly, the taxonomic affiliation showed that members of the Clostridiaceae OTUs were closely related in clone libraries to Caloranaerobacter ferrireducens (97% of identity)This later microorganism is known to use crystalline Fe (III) reduction as a minor pathway for electron flow while fermenting sugars or amino acids to a mixture of volatile fatty acids (acetate, butyrate) and hydrogen (Zheng et al.

2015)

. Archaeoglobaceae accounted for only 0.5% of the microbial communities in this enrichment and have been closely related from clone libraries analysis to Geoglobus ahangari (99% of identity). As mentioned above, Geoglobus ahangari is known to reduce amorphous Fe (III) oxide but these culture conditions with crystalline form do not seem to favor its growth (Wahid & Kamalan, 1993). All these results could suggest the organization of a kind of trophic chain in our flask enrichment. The new iron reducing species close to Caloranaerobacter ferrireducens would have used organic compounds from yeast extract to reduce crystalline Fe (III) oxide. The Thermococcus would have grown on peptides or carbohydrates from yeast extract or partly produced by Firmicutes, and both would have produced H 2 . The methanogens such as Methanotorris igneus would then have used the H 2 to produce methane.

Solid electron acceptor determine the microbial ecology of electroactive enrichment

In this context, a new BioElectrochemical System (BES2) was inoculated with the flask enrichment on YE/acetate to assess the specificity of the microbial community obtained on the electrode with a different initial microbial composition in the inoculum. Experimental conditions were exactly the same as for BES1. Contrary to BES1, a lag time of 3 days (Fig. 2) has been observed before the increase of the current. After 4.5 days the current has reached 2.4 A/m² and stayed stable during about 1 day before decreasing rapidly. Phase contrast microscopic observations before the culture medium renewal in BES2 have shown the only presence of irregular coccoid cells. Thereafter, the current density reached a maximum of 3.4 A/m² at 4 days after the renewal of the culture medium. This phase of current production came along with a decrease of acetate as observed in the BES1 (data not shown). Cyclic voltammetry (Fig. 3) exhibited oxidation peak appearing between initial time and final time with a midpoint potential at -0.107 V (vs. Ag/AgCl), slightly offset compared to the one obtained with BES1.

The biodiversity indexes between YE enrichment in flask and BES2 showed a loss of richness of species from 29 to 26 OTUs, and evenness from 0.292 to about 0.17, indicating a loss of biodiversity dominated only by a few OTUs. Furthermore, only Archaea were detected in BES2, when they were trivial in Flask enrichment. The dominating OTUs (Fig. 1) were closely related to Thermococcaceae uncultured species at 87.2% on electrode and 95.4% in liquid media of total OTUs. The remaining archaeal diversity was composed of Archaeoglobaceae spp. (12.7% and 4.5%), with clones affiliated to Geoglobus ahangari (99% identity) and unknown species belonging to Archaeoglobaceae family (95% identity with Geoglobus ahangari) similarly found on BES1 electrode. No Caloranaerobacter spp. or Thermodesulfobacteriaceae spp. growth was observed on the BES2 neither on electrode nor in liquid media. This is supported by the qPCR, which has shown a drastic difference of 4 log between archaeal (9 log) and bacterial (5 log) 16S rRNA copies per milliliter of liquid media and square meter of electrode.

It should be pointed out that the flask YE enrichment did not promote growth of Archaeoglobales or Archaea in general, whereas they seemed to be re-enriched in the BES2 conditions. These results suggest the specific enrichment on polarized electrode of Archaea belonging to Thermococcales and Archeoglobales in our BES condition. It is noteworthy that the biodiversity indexes showed a loss of biodiversity in BES compared to crushed chimney due to selective condition of our experiment to enrich preferentially the electroactive microorganisms. However, in each BES, the richness and the evenness are more important on polarized electrode than in liquid media, suggesting a specific enrichment of more diverse species and better distribution of microbial population on polarized support. According to the absence of growth in non-polarized electrode and the more important diversity on electrode than in liquid, the microbial diversity found in liquid media would arise from EAB which develop on the electrode. This is supported by the really low H 2 production in BES (data not shown) -H 2 being normally produced by Thermococcus sp. during fermentative metabolisms -which could be explained by a lack of carbon and energy source in liquid media. Thus, in absence of possible known metabolism for Thermococcus species in liquid, we would suggest Thermococcus cells to be in quiescent conditions after it is released from EAB.

Its growth would thus have an obligatory dependence on the polarized electrode.

If the presence of Geoglobus species is consistent with its known capacity to transfer EET with acetate as electron donor [START_REF] Yilmazel | Electrical current generation in microbial electrolysis cells by hyperthermophilic archaea Ferroglobus placidus and Geoglobus ahangari[END_REF]), Thermococcus species abundance on polarized electrode is more surprising. Thermococcales are known to share an energetic peptidic or carbohydrate metabolisms, associated necessarily or not with the reduction of elemental sulfur (Bertoldo and Antranikian, 2006). In addition, it was shown that some species have the capacity to grow by using Extracellular Polymeric Substances (EPS) of microbial origin (dextran, pullulan, peptides, etc.) [START_REF] Legin | Production of thermostable amylolytic enzymes by Thermococcus hydrothermalis[END_REF]. So far, no respiration ability on electrode or direct EET mechanism have been reported about this archaeal genus, even if some Thermococcus species have been shown to reduce amorphous Fe (III) oxide. However, the mechanism is still unclear and could We can therefore suppose a potential role of these nanotubes in EET. Thus, Thermococcus sp. could potentially be exoelectrogenic microorganisms through a still unknown mechanism.

Remarkably, the obligatory presence of both Thermococcus and Geoglobus species found in each BES on the polarized electrode did not seem fortuitous. Assuming that the Thermococcus species found in our enrichment are heterotrophic, after consumption of YE traces, their only carbon source available would be the EPS or organic compounds produced by Geoglobus spp. present on polarized electrode. Then, their fermentative metabolism would lead to the production of acetate, H 2 and CO 2 which could then be used by Geoglobus species to grow using the electrode as the ultimate electrons acceptor. However, recent data have shown the inability of Geoglobus to transfer electrons to an electrode from H 2 [START_REF] Yilmazel | Electrical current generation in microbial electrolysis cells by hyperthermophilic archaea Ferroglobus placidus and Geoglobus ahangari[END_REF]. Previous studies have shown that some electroactive bacteria are also able to grow syntrophically with other microorganisms via direct interspecies electron transfer (DIET) [START_REF] Shrestha | Plugging in or going wireless: strategies for interspecies electron transfer[END_REF]. As explained previously, Geoglobus ahangari has shown a weak electron transfer capacity when grown in pure culture. The higher current density obtained in our conditions would suggest that the Geoglobus sp. and Thermococcales enriched on our polarized electrodes live syntrophically to improve their growth, and subsequently increased the quantity of electrons transferred to the electrode. Thus we would suggest that there is a syntrophic mechanism, with potentially DIET, between Thermococcus and Geoglobus in deep hydrothermal vents.

Conclusion

This study is the first to report on the enrichment of electroactive consortium in ex-situ conditions that mimic the conductive chimney of a hydrothermal vent with polarized carbon cloth in anaerobic artificial seawater at 80 °C. Moreover, we demonstrate the specificity of enrichment of Bacteria on Fe (III) oxide compared to the enrichment of Archaea (mainly Thermococcus sp. and Geoglobus sp.) on BES, where the biodiversity is more conserved. These results support the hypothesis of electroactivity as a well-represented metabolism in this type of environment by confirming the presence of exoelectrogenic microorganisms capable of external electron transfer to conductive support. E-supplementary data of this work can be found in online version of the paper

  Cerqueira et al. 2017; Flores et al. 2011), except for the proportion of methanogens and Desulfurococcales found significantly lower in our samples. Despite a recognized stability in the conservation of hyperthermophilic microorganisms at low temperature (Wirth, 2017), our samples have been conserved more than 12 years at 4 °C, this could mostly explain the decrease in Archaea diversity.

  be mediated through electron transfer to humic substances and other extracellular quinones (Lovley et al. 2000, Slobdokin et al. 2001). Furthermore, a recent study has highlighted the possibility of hydroquinone for microbial electron transfer to electrically conductive minerals, especially with pyrite composing hydrothermal chimney, or electrode (Taran, 2017). Nevertheless, no current was obtained with replacement of electrode with spent media, indicating no mediated electron transport in our condition. However, species of Thermococcus genus have been reported to produce nanopods or nanotubes by budding of their cellular envelope but their function have not been fully understood (Marguet et al. 2013). As suggested by the authors, these archaeal nanopods or nanotubes could be used to expand the metabolic sphere around cells, promote intercellular communication or act in sulfur detoxifying mechanisms (Gorlas et al. 2015).

Figure 1 :

 1 Figure 1: Dominant taxonomic affiliation and biodiversity indices of microbial communities from Crushed Chimney, Flask enrichment on iron (III) oxide, Electrode and Liquid media from BES1 and BES2. OTUs representing lower than 0.5% of total sequences of the sample was grouped as Rares OTU. Biodiversity indexes of Richness and Evenness represent the number of observed OTU and the Pielou's J' evenness index respectively.

Figure 2 :

 2 Figure 2: Current monitoring (A/m²) of BES1 Enrichment inoculated with crushed hydrothermal chimney (blue line), BES2 Enrichment inoculated with flask subculture (green line) and abiotic control (orange line). Electrode potential was poised at -0.110V vs Ag/AgCl. Arrows represent the renewal of the liquid media.

Figure 3 :

 3 Figure 3: Cyclic Voltammetries between -0,6V and +0,6V at 20mV/s of Working Electrode at initial time (dot lines) and final time (full line) in BES1 (blue line), BES2 (green line) and abiotic control (orange line).

Acknowledgements

This work was financially supported by the National Interdisciplinary Program of CNRS "Initiative structurante EC2CO" (MICROBIEN). The authors thank Erwan Roussel (LM2E, IFREMER Brest) for helpful suggestions, Françoise Lesongeur (LM2E, IFREMER Brest) for clone libraries and the GeT-PlaGe platform (GenoToul, France) for DNA sequencing.

Highlights

• Development of a new semi-automatic hyperthermophilic bioelectrochemical system.

• Enrichment of hyperthermophilic exoelectrogen community in MEC system

• Specific enrichment of Archaea in MEC system

• Potential exoelectrogenic capability of Thermococcus spp.


D Di Caprio

J Stafiej

G Luciano

L Arurault

3D cellular automata simulations of intra and intergranular corrosion

Keywords:

A simple mode! for the effect of intergranular corrosion on overall corrosion processes is investigated using a cellular automata approach. The corroding polycrystalline material consists of domains and their boundaries. The domains represent the monocrystalline cores while their boundaries represent the inter granular defects. Either, a periodic pattern or randomly generated domains of Voronoï tessellation are used to represent the polycrystalline structure. The parameters of the mode!, taking into account the polycrystalline aspect of corrosion, are the domain density and the corrosion probabilities of metal grain core and grain boundary sites. The corrosion probability for grain boundary is set to a value higher than it is for the grain core. A complex surface structure appears with a high geometrical roughness when defects are not too dense. A strong correlation is established between the roughness evolution, the metal crystalline properties and the corrosion mechanism ofmetal dissolution. This work concerns simulations in 3D and extends the previous work limited to 2D simulations.

Introduction

Physical properties of materials e.g. mechanical properties are strongly dependent on structural features, such as grain sizes of the polycrystalline material [START_REF] Stoudt | The relationship between grain size and the surface roughening behavior of Al-Mg alloys[END_REF]. This is also true for suscep tibility/resistivity to corrosion. It is known, for instance, that susceptibility to corrosion increases with the roughness [START_REF] Alvarez | Corrosion relationships as a function of time and surface roughness on a structural AE44 magnesium alloy[END_REF][START_REF] Sasaki | The generation of surface roughness during slurry erosion-corrosion and its effect on the pitting potential[END_REF] related with the presence of intergranular material and granuiar junctions at the outer surface of the material.

A common type of corrosion attack, for which the grain structure is important, is intergranular (IGC) or intercrystalline corrosion. IGC is defined [START_REF] Davis | Corrosion of aluminum and aluminum alloys[END_REF] as a selective corrosion of grain boundaries or closely adjacent regions without considerable attack on the grains or crystals themselves. In IGC, the grain boundaries become anodic and the bulk material between the grain boundaries is not affected and therefore becomes cathodic. Due to its nature, IGC penetrates more quickly than pitting corrosion and it has drastic effect as a stress riser, in comparison to pitting corrosion, reducing the num ber of cycles required to initia te a fatigue crack [START_REF] Ra Berge | Corrosion Inspection and Monitoring[END_REF]. The same kind of subsurface fissure can be produced by transgranular corrosion where a small volume of metal is removed in preferential paths that proceed across or through the grains. Alloys with enhanced resistance to corrosion as well as methodologies to analyze, predict corrosion development and avoid corrosion failures remain a very active field of research. This is confirmed by a selection of recent articles found on the topic [START_REF] La Fontaine | Martensitic transformation in an intergranular corrosion area of austenitic stainless steel during thermal cycling[END_REF][START_REF] Stratulat | Grain boundary structure and intergranular stress corrosion crack initiation in high temperature water of a thermally sensitised austenitic stainless steel, observed in situ[END_REF][START_REF] Dhondt | Effects of microstructure and local mechanical fields on intergranular stress corrosion cracking of a friction stir welded aluminum-copper-Iithium 2050 nugget[END_REF][START_REF] Egbewande | Transgranular crack growth in the pipeline steels exposed ta near-neutral pH soit aqueous solutions: discontinuous crack growth mechanism[END_REF][START_REF] Sharma | A microscopie study on the corrosion fatigue of ultra-fine grained and conventional Al-Mg alloy[END_REF][START_REF] Sun | Correlations between stress corrosion cracking susceptibility and grain boundary microstructures for an Al-Zn-Mg alloy[END_REF][START_REF] Spencer | The initiation and propagation of chloride-induced transgranular stress-corrosion cracking (TGSCC) of 304L austenitic stainless steel under atmospheric conditions[END_REF][START_REF] Zhou | The intergranular corrosion of mild steel in C02 + NaN02 solution[END_REF][START_REF] Tachibana | Effect of hot rolling and cooling conditions on intergranular corrosion behavior in alloy625 clad steel[END_REF][START_REF] Li | The intergranular corrosion susceptibility of a heavily overaged Al-Mg-Si-Cu alloy[END_REF][START_REF] Li | Intergranular corrosion of Zn-free and Zn-microalloyed Al-xCu-yLi alloys[END_REF][START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF][START_REF] Shi | Improving intergranular corrosion resistance in a nickel-free and manganese-bearing high-nitrogen austenitic stainless steel through grain boundary character distribution optimization[END_REF].

Cellular automaton models (CA) based on discretized descrip tion of time, space and states, have been applied successfully for modelling pitting corrosion and passivation/depassivation events [START_REF] Meakin | Simple passivation and depassivation mode! for pitting corrosion[END_REF][START_REF] Balazs | Two-dimensional pitting corrosion of aluminium thin layers[END_REF][START_REF] Li | Computational simulation of metastable pitting of stainless steel[END_REF][START_REF] Di Ca Pria | Morphology of corroded surfaces: contribution of cellular automaton modelling[END_REF][START_REF] Di Caprio | Simulations of passivation phenomena based on discrete lattice gas automata[END_REF][START_REF] Di Caprio | The raie of adsorption in passivation phenomena modelled by discrete lattice gas automata[END_REF][START_REF] Bartosik | Cellular automata approach ta corrosion and passivity phenomena[END_REF][START_REF] Lan | Simulation of the growth of oxide layer of stainless steels with chromium using cellular automaton mode!: verification and parameter study[END_REF][START_REF] Wang | Simulation of metastable corrosion pit development under mechanical stress[END_REF][START_REF] Van Der Weeën | Modeling pitting corrosion by means of a 3D discrete stochastic mode![END_REF][START_REF] Pérez-Brokate | Overview of cellular automaton models for corrosion[END_REF][START_REF] Wang | Computational simulation of corrosion pit interactions under mechanochemical effects using a cellular automaton/finite element mode![END_REF][START_REF] Pérez-Brokate | Three dimensional discrete stochastic mode! of occluded corrosion cell[END_REF]. The present study is an extension in 3D of a previous 2D numerical mode! [START_REF] Taleb | Numerical simulation of the effect of grain size on corrosion processes: surface roughness oscillation and cluster detachment[END_REF][START_REF] Lishchuk | A cellular automaton mode! for predicting intergranular corrosion[END_REF][START_REF] Igarashi | Simulations of intergranular corrosion feature for stainless steel using cellular automata method[END_REF][START_REF] Ueno | Study on the effect of phosphorous concentration on intergranular corrosion of stainless steel in boiling nitric acid solution[END_REF][START_REF] Igarashi | Three dimensional computational modelling and simulation of intergranular corrosion propagation of stainless steel[END_REF] simulating the effect of the grain size on the corrosion processes by using a CA mode! focusing on intra and intergranular corrosion (IGC). It adds to recent findings published in this field [START_REF] Guérin | Identification of the metallurgical parameters explaining the corrosion susceptibility in a 2050 aluminium alloy[END_REF].

In this work, both surface properties and internai bulk struc ture of the material are investigated. The focus of this paper is on geometrical effects of the grain shape and their spatial organiza tion in the system. The objective is to study how fast corrosion can penetrate into material and besides chemical dissolution of the corroded material determine the effect of pure mechanical detachment of chunks of material. These chunks are nearly always parti ail y dissolved grains of polycrystalline material when their link to the bulk material becomes corroded by the faster intergranular corrosion. The chunk effect may also occur in random dissolution of the material when the external medium grows as in the Eden mode! [START_REF] Vautrin-Ul | Mesoscopic modelling of corrosion phenomena: coupling between electrochemical and mechanical pro cesses, analysis of the deviation from the faraday law[END_REF]. Originally, the medium is defined a connected set. However, the material may form peninsulas detached as islands when a straight corrosion cuts the peninsula from the mainland. This chunk effect gives a plausible explanation for non-faradaic material Joss in some electrode processes. The inhomogeneous granular structure leads to an enhancement of this scenario [START_REF] Taleb | Numerical simulation of the effect of grain size on corrosion processes: surface roughness oscillation and cluster detachment[END_REF]. The modelling is very simple. The grain cores are embedded in intergranular material. Both the core and intergranular materials are homogeneous and isotropie. Cores are more resistant to corro sion therefore the corrosion proceeds by dissolving intergranular material at grain boundaries. Ultimately, grain cores "fall off' when the intergranular material around them gets corroded. The progres sion of the corrosion front is to some degree delayed, compared to "pure intergranular material", by the sinuosity effect of the lines of "steepest descent" from the surface. These lines can be described as the "shortest path" within the intragranular space connecting two points on a line normal to the surface. There is a sinuosity coef ficient due to the fact that the line cannot go through the cores. Imagine a signal is sent from one of the points to another propa gating isotropically and with constant speed. Compare the time of arrivai in two cases. In the first event, the signal is allowed to propa gate only in intergranular space and in the second case it propagates in both cores and intergranular spaces ignoring the difference. The ratio between the two Iengths of time is the sinuosity coefficient. In our mode!, the sinuosity coefficient is the main consequence of the granular structure of the material. It is isotropie for the Voronoï tessellation but, in general, it is direction dependent.

Model

As in [START_REF] Taleb | Numerical simulation of the effect of grain size on corrosion processes: surface roughness oscillation and cluster detachment[END_REF], let us consider a simplified mode! of intergranu Iar corrosion. The grain boundaries are assumed to be the only defect of the crystalline structure susceptible to enhance corrosion rate. The intergranular region has chemical and physical prop erties distinct from that of the grains. A common occurrence is segregation or depletion of some components of the alloys in the intergranular region [START_REF] Grabke | Grain boundary segregation of impurities in iron and steels and effects on steel properties[END_REF][START_REF] Briant | The effect of grain boundary segregation on intergranular failures[END_REF][START_REF] Vargel | Chapter B.2 -types of corrosion on aluminium[END_REF][START_REF] Kim | Effect ofchromium content on intergranular corrosion and precipitation ofTi-stabilized fe rritic stainless steels[END_REF][43][START_REF] Kumar | Methods for making alloy 600 resistant to sensitization and intergranular corrosion[END_REF][START_REF] Lejcek | Grain Boundary Segregation in Metals Springer Series in Materials Science[END_REF][START_REF] Kim | Investigation of the sensitization and intergranular corrosion of tube-to-tubesheet welds of hyper duplex stainless steel using an electrochemical reactivation method[END_REF][47]. For instance, in the case of sensi tized stainless steels, chromium carbide precipitates fragilize the intergranular region [START_REF]Aciers inoxydables critères de choix et structure, Techniques de l'ingénieur: Aciers inoxydables[END_REF]. In general, several different compo nents can segregate at the grain interface, such as phosphorous, tin, silicium, nickel, Ieading by different mechanisms to a higher susceptibility to corrosion of the material [START_REF] Seah | Grain boundary segregation[END_REF][START_REF] Christien | Phosphorus grain boundary segregation in steel 17-4 PH[END_REF]. In this paper, the focus is on the difference in corrosion kinetics between intra and intergranular corrosion. Consequently, the dependence of cor rosion on crystalline orientation is not taken into account. The grains of polycrystalline material are presented as homogeneous isotropie domains arranged as adjacent polyhedra in three dimen sional space. The material, in the thin intergranular spaces of the polygonal faces of the polyhedra, is regarded as more susceptible to corrosion than the grain cores.

Let us look at regular structured fillings of three dimensional space analogous to those shown in [START_REF] Taleb | Numerical simulation of the effect of grain size on corrosion processes: surface roughness oscillation and cluster detachment[END_REF] in two dimensions. The first case, referred to as cube piling (CP), is a regular piling with cubes one above the other with matching edges. The second case, referred to as brick piling(BP), is a regular piling, with the edges of the cubes shifted by half a lattice dimension in the two directions parallel to the metal surface with respect to the plane below. Finally, three dimensional Voronoï tessellation is considered as an example of non periodic irregular structures.

The Voronoï tessellation is obtained by randomly generating a number of vertices with uniform distribution corresponding to a given density or, conversely, to the average domain volume. Peri odic boundary conditions in ail directions are used for the vertices to avoid deformation of the Voronoï tessellation at the facets of the simulation cube. The domains start growth at the vertices. Initially they form vertex centred spheres. Gradually, the domains grow by slightly incrementing the radius and including points which do not belong to another sphere. The growing domains meet ultimately at the faces ofVoronoï polyhedra if growth starts simultaneously and growth rate is identical at ail vertices. The two nearest neighbouring sites, each belonging to different domains, are marked as intergra nular sites in our lattice version of the growth process. lt is possible to represent this system on a discrete, three dimensional lattice, Nx x Ny x Nz where Ni, i =x, y, z are the integer dimensions of the lattice in the three directions. In our mode!, there are three types of lattice sites corresponding to the inter, the intra granular material and the solution. The solution corresponds to an aggressive, corrosive environment -acidic solution for instance. The top z plane is composed of solution sites and below lies the bare metal made of granular and intergranular material. Hence, the direction z is the direction perpendicular to the metal surface, which also corresponds to the main direction in the propagation of corrosion. Periodic boundary conditions are used in the plane parai lei to the x and y directions. The cellular au toma ta Iattice approach adopts a mesoscopic viewpoint. As in [START_REF] Lucas | Cellular automata modeling of scanning electrochemical microscopy (SECM) experiments[END_REF][START_REF] Pérez-Brokate | Cyclic voltammetry simulations with cellular automata[END_REF], to relate the simula tion to the real world, space and time equivalence for our pixel size and simulation time step must be set in terms of real dimensions. In this paper, a cube of Iateral dimension a= 0.2 µm is chosen for the pixel size, a size sufficiently small for a typical grain dimension as chosen in this paper [START_REF] Whang | Nanostructured Metals and Alloys[END_REF][START_REF] Tian | Intergranular corrosion of spark plasma sintering assembled bimodal grain sized M7075 aluminum alloys[END_REF]. The time scale is set considering a cor rosion process for the intergranular material of 1 mm/y. With the above value of a, the simulation time step corresponds to of 6310 s.

Such value is comparable to that illustrated in [START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF]. In this paper, the authors find that in one instance a period of 1000 h corresponds to the detachment of one layer of grains of characteristic dimension 84 µm. In one year, the corrosion rate corresponds approximately to 0.74mm/y. The round value of 1 mm/y adopted here is consis tent with the above experimental value, and simplifies discussion for the case studies discussed in this paper.

The intergranular region has a width of two lattice sites. This value is a minimal value chosen in order to ensure a regular prop agation of corrosion in the intergranular region. The characteristic dimensions of the intragranular domains will be specified in more detail later, as grains may not be isotropie. Typically, they are between 6 and 24 µm, which is in the range of a micrometre to 100 µm found in the literature [START_REF] Whang | Nanostructured Metals and Alloys[END_REF][START_REF] Tian | Intergranular corrosion of spark plasma sintering assembled bimodal grain sized M7075 aluminum alloys[END_REF], although smaller than the grains studied in [START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF]. Clearly, the order of magnitude is only indicative, as real systems may have grains of different dimensions depending on the metallurgical treatment or the "history of the sample". The corrosion rates of inter and intragranular material depend on the treatment and also on aggressiveness (temperature, pressure, composition) of the external environment in contact with the metal.

In our simulation, the active sites susceptible to corrosion are those which have a neighbouring solution site. It means that during a time step they are converted to the solution site with a certain probability. The intergranular material can corrode with a prob ability Pig which can be set to Pig = 1. Choosing a different value rescales the correspondence between the simulation time step and the real corrosion rate. The choice is arbitrary in the sense there are many possible sets of values of simulation time step and Pig cor responding to the same corrosion rate. This means that Pig = 1 and time step of 6310 s can also be simulated by Pig = 0.5 a time step of 3155 s. In terms of computational efficiency Pig = 1 is the better choice, as each computational time step results in an intergranu lar corrosion, whereas the second choice would require double the number of simulation steps. In both cases the physical corrosion rate is identical.

The grain material can corrode with a probability p g , With the choice of Pig = 1, the corrosion rate for the grain is seen as relative to the corrosion rate of the grain boundaries and p g < 1 is assumed.

At each time step, the lattice sites in contact with the aggressive environment dissolve according to the probabilities P ig and Pg• Fur thermore, any metal material disconnected from the main piece is removed. By convention, the main piece is connected to the lowest bottom part of the metal. Corrosion proceeds downwards and the connectivity check starts from the bottom up to the top surface. The top surface is exposed to solution and susceptible to corrosion.

The average height at a time step t is given as:

Nx,Ny - 1 � h(t) = N x N y L... hx ,y (t) x,y=0 (1)
where hx,y(t) is the height (z-coordinate) of the topmost site of the material column over the site referenced by x and y in the xy plane. The mean squared deviation of hx,y(t) averaged over the (x, y) surface is denoted a(t)

1 X, y [ N N l 1/2 a(t) = N x N y x�O (hx,y(t) -ii(t)l
and it serves as a measure for surface roughness.

Results

Mode! grains: cube and brick pilings

(2)

In the following, results of simulations performed with grain size of 64 lattice units for the cube and brick pilings are presented. stops when corrosion reaches the plane next to the bottom ( one above the bottommost layer of sites). Hence, the simulation time with Pi g = 1 is of the order of 4000 time steps corresponding to approximately 7000 h i.e. 290 days at the chosen corrosion rate for intergranular material of 1 mm/y. The curves show that the average height follows a step like behaviour. They remain almost constant and drop abruptly when the layer of cubes detaches. The linear regression lines for bath models are quasi identical, the expression is h 1r (t) =4141 -0.9994t, the slope is around -1 in bath cases. This is in contrast to what has been shown for the two dimensional systems and will be discussed further on. In this specific case, the effective corrosion rate of the sample remains 1 mm/y, i.e. the nominal corrosion rate of the inter granular material multiplied by the coefficient in front of t which is almost 1.

Fig. 2 shows the roughness of the surface plotted as a function of time. The regular oscillations of roughness correspond to the corrosion and detachment of an entire layer of grains. The mechanism is detailed later on. Before detachment the roughness increases gradually to drop sharply at the time of detachment of a layer of grains. Due to symmetry of the system, in the absence of intragranular corrosion, detachment takes place simultaneously for ail grains across the metal surface. Once ail the grains in a layer detach, the layer becomes smooth again and the roughness is at its minimum. The roughness oscillations are similar for bath CP and BP geometries although they do not have exactly the same magnitude. The maximum roughness for BP geometry is lower than the roughness for CP geometry, while the BP minimum is higher than the CP minimum.

System cross sections.

To better understand the differences between the two geometries, we show horizontal and vertical cross sections of the material at different time steps -characteristic of grain detachment. The vertical cross sections are chosen for planes spaced Jess than half the grain size, as there are symmetries across half of the grain in the x and y directions. First, the CP in a configuration three time steps after detach ment is described. The characteristic sections are shown in Fig. 3. The intergranular material fills the horizontal and vertical planar slits between the cubes up to the horizontal level reached by cor rosion. As a consequence, the horizontal sections above and below differ in that above the corrosion level the vertical slits are filled with solution and below the corrosion level they are filled with intergranular material. Another scenario occurs in the horizontal slit above the corrosion level just before the detachment. Sorne of the intergranular material remains in the slit and keeps the top cubes attached to the rest of the corroded piece. This is illustrated in Fig. 4 corresponding to three time steps before detachment. The cross sections show that once the corrosion level attains the hor izontal slit, the corrosion can proceed horizontally inwards from the edges to the centre of the facets. The top level grains remain "glued" to the system by contacts until they undergo corrosion and the layer of grains detaches. This horizontal corrosion phase takes time and, just after grain detachment, the corrosion is already well below the new material surface -as seen in Fig. 3.

Intergranular corrosion, p g = 0 for BP

The phenomenon is quite different in the BP structure despite the quasi identical evolution in corrosion (Fig. 1 ).

In Fig. 5, planar cross sections are shown at three time steps after detachment of a layer of cubes, i.e. just after the rugosity minimum. Fig. 5 shows that at this time step corrosion proceeds downwards, mostly from the top layer of cubes, along the slits between the cubes. The combined horizontal and vertical corrosion leads to the sawtooth pattern visible in the figures.

In Fig. 6, the sections correspond to three time steps before detachment of the grains, when maximum roughness is reached. Just before grain detachment, the sawtooth pattern is also present in the regions between grains but now in the top horizon tal intergranular planes there is a diagonal mesh-like structure.

�� ■■■■ • • • • • • • • • • • • • • • Fi g . 4.
Vertical and horizontal cross sections of the corroded metal. At the top, the vertical planes correspond ta planes in the vertical intergranular region between grains, on quarter of the grain size and in the middle of the grain. At the bottom, the horizontal planes are for planes situated half and a quarter grain size below the intergranular horizontal plane between cube layers. Then, across this plane and half the grain size above it.

Fi g . 5. Vertical and horizontal cross sections of the corroded metal. The first vertical section correspond ta a section across the vertical intergranular region of the middle layer of grains in the image then planes one quarter and half a grain size from this plane. The horizontal sections are for the top intergranular dividing plane. Then, for planes a quarter, half, three quarters and an approximately one grain size above this plane just above the sawtooth top.

Fi g . 6. Vertical and horizontal cross sections of the corroded metal. The first vertical section correspond to a section across the vertical intergranular region of the middle layer of grains in the image then planes one quarter and half a grain size from this plane. The horizontal sections are for one before the top intergranular dividing plane. Then, for planes half, three quarters, one grain size above this plane and finally just across the sawtooth top.

This structure results from the horizontal corrosion as previously described. However, the horizontal corrosion proceeds from the middle of the edges outwards. This location is the junction with the middle of the edges of the cubes above which are oriented per pendicularly. Conversely, for CP, the corrosion proceeds from the edges towards the middle of the facet. The intergranular material patterns, in the horizontal plane, slightly below the top layer of cubes, are distinctly different for the CP and BP geometries just before detachment. There are small spots of contact in the case of CP piling, while there is a mesh formation in the case of BP. This phenomenon could have a baring on the tendency to detachment of the grains, for instance, in the case of exfoliation.

Finally, the left and right vertical sections in Figs. 5 and6 show that there is a thin vertical line of intergranular material common to two successive layers of grains. Therefore in contrast to the two dimensional case, the corrosion can proceed vertically along this line, and no consecutive horizontal and vertical corrosion sequence is necessary. As a result, the same average corrosion rates and the slope -1 for corrosion advancement curves h(t) characterize bath CP and BP cases.

Meta! grains of the Voronoï tessellation form

Based on an experimental structure, Fig. 7, Voronoï tessel lation is now considered as a more realistic mode! for grains of Fi g . 7. Optical microscopic3D views of the M 7175T7351 substrate after degreasing and metallographic attack [START_REF] Goueffon | Black anodic coatings for space applications: study of the process parameters, characteristics and mechanical properties[END_REF]. polycrystalline material. An example of the initial system geometry (IVT) is shown in Fig. 8. From Voronoï tessellation an alternative case can be easily obtained corresponding to the rolled treatment of metals. To be specific, consider grains elongated by a factor 4 in one direction (L) and contracted by an equal factor 4 in one of the perpendicular directions, the short transverse direction (ST). The remaining direction, the long transverse direction (LT), is left unchanged. The elongation and contraction having the same ratio, the overall average volume of the grains is left unchanged compared to the reference IVT case. Now the material is inhomo geneous. Corrosion rates depend on the direction, and take the form of a symmetric tensor where the elongation, contraction and remaining direction are the tensor normal axes.

The height as a function of time is shown in Fig. 9.

The linear regression for the IVT is h 1 r(t) = 4151 -0.8090 t. Here, the effective corrosion rate of the material is 0.809 mm/y. The slope is lower than the slope for the CP, BP geometries. These are more "efficient", in bath geometries there are vertical straight paths which optimize the vertical corrosion process. In [START_REF] Taleb | Numerical simulation of the effect of grain size on corrosion processes: surface roughness oscillation and cluster detachment[END_REF], the angle of the si ope is also used as an added measure of corrosion oblique ness. The slope is a tangent to this angle. The corrosion is faster than it is for the brick and Voronoï geometries in two dimensions with a slope of 2/3. This is likely as the brick geometry has a slope 1 and Voronoï should be situated below this limit. The IVT geometry corresponds to a progression angle 0=37.8 ° degrees with respect to the vertical for the equivalent system with regular linear oblique corrosion.

When the corrosion is parallel to the elongation direction (L), the linear fit is h 1 r(t) = 4166 -0.9357 t. Here, the corresponding angle is 0 = 21.4 ° degrees with respect to the vertical. The effective corrosion rate of the material is now 0.9357 mm/y.

The case where the corrosion is parallel to the invariant (LT) axis, the linear fit is h 1 r(t)=4160-0.9260t. The corresponding angle is 0 = 22.5 ° degrees with respect to the vertical. The effective corrosion rate of the material is then 0.9260 mm/y.

And finally, when the corrosion is parallel to the transversal axis with contraction (ST), the linear fit is h 1 r(t)=4130-0.5193t. The corresponding angle is 0 = 58.7 ° degrees with respect to the verti cal and the corrosion is much slower than in ail other cases. The effective corrosion rate of the material is 0.5193 mm/y.

We draw attention to the fact that the fastest and slowest cor rosion rates -respectively the directions of corrosion parallel to (L) and (ST) axes -differ by a factor of approximately 1.8, a significant value.

The roughness is shown in Fig. 10. Obviously, the variations in roughness are no longer periodic as they are in the CP and BP structures.

Finally, Fig. 11 illustrates images of the system corroded in the (L), (LT) and (ST) directions. Note that corrosion rates in the directions (L) and (LT) have the same magnitude and show a corrosion rate faster than in the IVT. Conversely, corrosion in the (ST) direction is considerably slower and even slower than in the case of IVT. These tendencies can be explained if one bears in mind that the intergranular corrosion applies to phases where the corrosion evolves horizontally. The corrosion in the directions (L) and (LT) share the (ST) direction in the horizontal plane, which is related to a fast horizontal cor rosion process. On the other hand, corrosion in the (ST) direction involves slow horizontal corrosion processes along the (L) and (LT) directions. The roughness follows the same trend with comparable magnitude of roughness for the (L) and (LT) corrosion directions. Roughness is slightly larger for (L) direction due to larger expan sion rate in the corrosion direction. Smaller roughness is found for the IVT and even smaller for the (ST). x and finally y, x, z. The direction of the axis is the one given in Fig. 8.

For rolled material the grains are elongated and oriented in the rolling direction if no further thermal treatment is a pp lied.

The slowing down of corrosion in the (ST) case can be compre hended when we think of the brick geometry in two dimensions [START_REF] Taleb | Numerical simulation of the effect of grain size on corrosion processes: surface roughness oscillation and cluster detachment[END_REF], characterized by a slower corrosion rate than the square struc ture. In the brick structure, the system is forced into regimes of horizontal corrosion in order to successively find ways for the verti cal corrosion. The same occurs in three dimensions when the layers of"plaquettes" are organized parallel to the metal surface. Note that here plaquettes are more difficult to remove, and this for instance has repercussions on the kinetics of exfoliation.

For corrosion progress along (L) and (LT) directions of the grains, the corrosion rate is Iarger compared to IVf, as the steepest descent lines on the grain boundaries are longer than for !Vf by a coefficient equal to the elongation factor. The difference between corrosion along the (L) and (LT) directions appears to be relatively smalt.

Scantily faster corrosion and higher roughness occur when corro sion propagates in the (L) direction of the Iargest elongation.

The above results characterize corrosion for different materiaI structures and surface orientation in steady state conditions. The initial evolution can be described by considering examples of the surface morphologies at the initial stages of the corrosion process. Let us take the IVf case at two different stages in time. First, when corrosion has progressed on a length scale smaller than the average grain size -64 Iattice sites in our simulations. Second, when the corrosion progress is larger than the average grain size.

Fig. 12 shows the initial stages when grains start "falling out" from the initial flat surface. The images indicate that the cor roded spots where the grains have "fallen out" are not uniformly distributed. There are clusters of grains forming flat areas at the surface, with practically no grain detachment, and rough regions with detached surface grains. At the top surface, the initial distribu tion of grain sizes which results from the section of 3D tessellation with a plane, can differ from the distribution of grains sizes in the volume. The surface grains are more or Jess strongly embed ded into the substrate below. However, the initial detachment of a grain seems to facilita te the detachment of the neighbouring grains, leading to correlation between corroded and noncorroded surface areas. The simulated surface resembles the experimental image of intergranular corrosion shown in Fig. 13.

lntergranular and intragranular corrosion

In this section, the combined effect of intergranular and intra granular corrosion is considered. The intragranular corrosion rate value is P g = 0.25. This value corresponds to a corrosion rate smaller than for intergranular corrosion, yet of the same order of magni tude.

Cube piling

For the simple CP, two typical side views are given in Fig. 14, corresponding to a few time steps before and after detachment of a plane of grains.

The side views before detachment, in Fig. 15, show the peculiar shape of the grains just before detaching.

The typical V-shape corrosion groove is formed. It is characteris tic of the combined effects of faster intergranular corrosion (bottom pointed "V" shape) and the "V" shape opening due to intragranular corrosion [START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF][START_REF] Beaunier | A kinetical mode! for the electrochemical grooving of grain boundaries[END_REF][START_REF] Bague | Determination of the long-term intergranular corrosion rate of stainless steel in concentrated nitric acid[END_REF]. Peninsulas form as a combined effect of intra and intergranular corrosion. The last image of Fig. 15 resembles the scheme of Fig. 16 obtained by combining the main V-shape vertical corrosion groove with the V-shape horizontal corrosion groove.

The side views after detachment in Fig. 17 show grains at the beginning of their corrosion. The grains have the predictable shape of cubes eroded from the top edges downwards Ieading to the V reentrant shape.

These shapes resemble those illustrated in the 2D model in [START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF].

Brick piling

For the BP geometry, two typical side views are given in Fig. 18 corresponding to a few time steps before and after detachment of a plane of grains. The sections before detachment, in Fig. 19, show the peculiar shape of the grains before detachment, resembling canes with cross shaped sections. The sections after detachment are shown in Fig. 20. They have a shape similar to that of CP, but combined with emergence of a cross shaped section at the top. For the BP, we find that the possible shapes of the grains visible in Figs. [START_REF] Shi | Improving intergranular corrosion resistance in a nickel-free and manganese-bearing high-nitrogen austenitic stainless steel through grain boundary character distribution optimization[END_REF] and 19 just before detachment might in 3D have a larger variety than could be foreseen by extrapolating the 2D mode) in [START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF]. In particular, they need not have convex geometries.

The overall corrosion rates for CP and BP geometries are not shown as they are similar to those in the absence of intragranular corrosion -the slope is of the order of -1. As long as intragran ular corrosion is slower than intergranular corrosion, the overall corrosion process is dominated by the grain detachment whose kinetics remains identical. The ratio ofintra to intergranular corro sion affects mainly the shape of the grains that "fall out" as well as the roughness shown in Fig. 21. The more complex grain shape, for the BP, results from the shifted grainjunctions in the vertical planes for successive layers. The roughness is lower than it is in the absence ofintragranular corrosion, because the top grains end up smaller as a result of the intragranular corrosion.Again, the roughness appears higher in BP geometry than in CP geometry.

Note that the intergranular rate Pg can be related to the groove angle a introduced in [START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF][START_REF] Beaunier | A kinetical mode! for the electrochemical grooving of grain boundaries[END_REF][START_REF] Bague | Determination of the long-term intergranular corrosion rate of stainless steel in concentrated nitric acid[END_REF]. Here the ratio of the intergranu lar corrosion rate to the intragranular corrosion rate is the ratio between the respective probabilities. This translates into the rela tion In [START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF]. the experimentaI values of the angles were distributed between 5 ° and 15 °, which can be roughly averaged at 10 °. This would approximately correspond, in the present mode!, to p g = 0.087. As for [START_REF] Bague | Determination of the long-term intergranular corrosion rate of stainless steel in concentrated nitric acid[END_REF]. the angle is close to 25 ° corresponding to p g = 0.22. Here, for numerical applications, the larger value of P g = 0.25 has been taken to evidence the effects ofintragranular cor rosion. The angle of approximately 29 ° corresponds to the angles observed at the tip of the grooves, in contact with the grain bound aries, as seen in Figs. [START_REF] Li | The intergranular corrosion susceptibility of a heavily overaged Al-Mg-Si-Cu alloy[END_REF][START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF][START_REF] Meakin | Simple passivation and depassivation mode! for pitting corrosion[END_REF], and 20.

Voronoï tessellation type grains

The anisotropie structure derived from Voronoï tessellation with three principal axes (L), (LT) and (ST) and elongation along these axes is the same as in the previous section. Configurations after corrosion progress are shown in Fig. 22.

In Fig. 23, two perpendicular vertical sections into the mate rial are shown. Again, the characteristic V-shaped groove is seen in CP and BP geometries and is also observed experimentally [START_REF] Bague | Determination of the long-term intergranular corrosion rate of stainless steel in concentrated nitric acid[END_REF][START_REF] Gwinner | Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media[END_REF].

Here the reentrant V-shape can have a larger number of orienta tions according to the direction of the intergranular region. We also point out the merging of two corrosion fronts that will likely lead to a grain detachment or the formation of cavities (Fig. 23 top-right).

The linear regressions for height and angles of the equivalent systems, are respectively h 1 r(t) = 4108-0.8107t, 0=35.8 ° for the IVT, h 1 r(t) = 4102-0.9369t, 0 = 20.5 ° for corrosion parallel to the (L) direction, h 1 r(t) = 4101 -0.9269 t, 0= 22.0 ° for corrosion parallel to the (LT) direction, h 1 r(t) = 4096 -0.5665 t, 0 = 55.5 ° for corrosion parallel to the (ST) direction. As in Section 3.2, the absolute value of the coefficient in front of t gives directly the effective corrosion rate in mm/y in our case where a corrosion rate of 1 mm/y and Pig = 1 is assumed for the intergranular material. The results are practically identical to the case in absence of intergranular corrosion, indi cating that the main mechanism of mass Joss is the mechanism related to the intergranular corrosion. The only noticeable differ ence concerns the (ST) case where the intragranular corrosion in the smaller dimension of the grains can more efficiently help the detachment of grains. The different kinetics are similar to those found in the absence of intragranular corrosion. As for CP and BP, the corrosion remains dominated by the detachment of grains related to the intergranular region corrosion. The only noticeable differ ence relates to the grain plaquettes oriented parallel to the surface. There, the corrosion rate is slightly higher than in the absence of intragranular corrosion.

The roughness is shown in Fig. 24. Note that in ail cases the roughness is much lower than in the absence of intragranular corrosion. The corrosion of the grains themselves levels out the surface. The effect is more pronounced for the (L) and (LT) direc tions, where plaquettes are perpendicular to the surface and show higher roughness values in the absence of intragranular corro sion. This leads to even smaller roughness than the IVT case. The corrosion parallel to (ST) direction also leads to a smaller rough ness as the largest surface of the plaquettes is parallel to the outer surface.

Conclusion

This paper presents a mode! investigating the effects of geom etry on intergranular corrosion as well as the combined effects of inter and intragranular corrosion. The approach generalizes previ ous 2D models. Various grain geometries, isotropie or anisotropie, and different layouts are examined.

Sinuosity of the corrosion paths is found to play a similar role as in 2D. The effective corrosion rate is much smaller when the grain geometries and their layout force long deviations from the shortest corrosion path i.e. the straight line perpendicular to the metal surface. The susceptibility of grains to detachment depends upon the anisotropy of the grains. Moreover, the 3D extension of the mode! shows a larger variety of grain geometries as well as scenarios of grain detachment compared to simple extrapolation of 2D geometries. The predicted corrosion is, in general, faster than in the 2D case as shown in this paper.

When both inter and intragranular corrosion are present, the characteristic V-shaped grooves, found experimentally, are formed and their angle indicates the ratio of inter to intragranular corro sion rates. However, owing to faster intergranular corrosion, the overall corrosion rate remains generally fixed by the intergranular corrosion.

  The simulation box size is 512 x 512 x 4096 sites. It is 512 x 512 in Iateral size (horizontal plane) and 4096 sites high. The simulation

3. 1 . 1 .

 11 Intergranular corrosion, p g = 0 for CP 3.1.1.1. Height and roughness. First, consider the corrosion of the intergranular region, leaving intact the grain cores p g = O. The aver age height as a function of time is shown in Fig. 1.

Fig. 1 .

 1 Fig. 1. Corrosion height as a function of time and on the right a detail of the plot. Full black line is for the cube piling and red dashed line for the brick piling. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

Fig. 2 .

 2 Fig. 2. Surface roughness as a function of time and on the right a detail of the plot. Full black line is for the cube piling and red dashed line for the brick piling. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

Fig. 8 .

 8 Fig. 8. Granular material with an isotropie Voronoï tessellation {!Vf) (top) and granular material from rolled treatment (bottom) where the elongation (L) is in the direction y, long transversal {LT) is in direction x and short transversal (ST) in direction z. The elongation and contraction factor for (L) and {ST) is 4 while for {LT) it is unchanged compared to the lVf. First each grain is marked with a distinct colour. Then only the intra and inter-granular materials are marked.

Fig. 9 .

 9 Fig. 9. Corrosion height as a function of time for the lVf (black line) and with elon gation/contraction in the z/x (red dotted line), with elongation/contraction in the y/x (green dashed line), with elongation/contraction in the y Jz (blue dot-dot-dashed line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

Fig. 10 .

 10 Fig.10. Roughness as a function of time t for the geometries used in Fig.9and with identical colour codes for the lines. Full lines are used because the curves are quite rough.

Fig. 11 .

 11 Fig.11. Side and top views of the corroded system with !Vf, with elongated grains and with (L), (LT ) and (ST) respectively directed along the following axis: z, y, x; y, z, x and finally y, x, z. The direction of the axis is the one given in Fig.8.

Fig. 12 .

 12 Fig. 12. Initial top view of the layer after 55 and 70 corrosion steps. Here larger planes oflateral dimension of2048 x 2048 are shown.

Fig. 13 .

 13 Fig. 13. SEM micrographs ofpolished AE44 coupons during immersion test subject ta intergranular corrosion. Reprinted from Ref. [2].

1

 1 Pig sin(a/2) Pg In our case, Pig = 1 and we have the simple relation sin(a/2) = p g --.� -• -� ' ' -:' ,_ ,, , _ -,, i_ ---- ,, Cl -, fJ -, .'.] ,-, :__.J ''..-, � -1 ,, 1 ,' ,_, -- . , ' . � \ 1,,

Fig. 14 .

 14 Fig. 14. Initial side and top views of the CP at two characteristic times before detachment and after detachment in presence of intragranular corrosion.

Fig. 15 .

 15 Fig. 15. Sections of the CP before detachment of the grains. To the exception of the first two images which show the intergranular plane and the next plane, ail other planes are spaced of 8 planes, which corresponds to an eighth of the grain size. The planes beyond the 32nd plane are not shown as they are symmetric with respect to the middle of the elementary cube.

Fig. 16 .

 16 Fig. 16. Pattern obtained from a combined inter and intragranular corrosion in two competing directions vertical and horizontal.

Fig. 17 .

 17 Fig. 17. Sections of the CP after detachment of the grains. The first two images are for the intergranular plane and the next plane. The following ones are for planes placed an eighth and across the middle of the elementary cube.

Fi g . 18 .

 18 Initial side and top views of the BP at two characteristic times before detachment and after detachment in presence of intragranular corrosion. Fi g . 19. Sections of the BP before detachment of the grains. To the exception of the first two images which show the intergranular plane and the next plane, ail other planes are spaced of 8 planes, which corresponds to an eighth of the grain size. The planes beyond the 32nd plane are not shown as they are symmetric with respect to the middle of the elementary cube. Fi g . 20. Sections of the BP after detachment of the grains. To the exception of the first two images which show the intergranular plane and the next plane, ail other planes are of 8 planes, which corresponds to an eighth of the grain size.

1 1200Fig. 21 .

 121 Fig. 21. Roughness for the CP and BP geometries identical colour code as in Fig. 2, detail of the curves on the right.

Fig. 22 .

 22 Fig. 22. Side and top views of the corroded system in the presence of intragranular corrosion for IVf and grains elongated as in Fig. 11.

Fig. 23 .

 23 Fig. 23. Two perpendicular vertical sections of the metal for the systems of Fig. 22.

oFig. 24 .

 24 Fig.24. Roughness as a function of time t for the geometries used in Fig.9, with combined inter and intragranular corrosion. The same colour codes as in Fig.10.