Phuoc Hoang Ho

Vivian V Lofty

Altaf H Basta

Philippe Trens
email: philippe.trens@enscm.fr

Designing microporous activated carbons from biomass for carbon dioxide adsorption at ambient temperature. A comparison between bagasse and rice by-products

Keywords: Agrowaste, Pulping, CO2, Adsorption

Pulping in agro-waste processes are known to affect the chemical constituents of the materials obtained. In this study, activated carbons (ACs) were prepared using precursors based on rice straw, rice husks and bagasse. The composition of these precursors was first determined in order to study the influence of the components of each of these precursors on the sorption properties of the ACs obtained. The ash content was determined by calcination of the precursors as the main component present in ashes is silica, which is known to play a role on sorption processes. The surface chemistry of the ACs was assessed by ammonia thermodesorption (NH3-TPD), before being tested for carbon dioxide capture. ACs obtained from bagasse were capable of capturing up to 14 wt % at atmospheric pressure and 25°C, regardless of the pulping process applied to the precursor. Rice-husks based AC gave a similar result when the precursor was pulped with a 12% soda solution. Rice straw based ACs were less interesting in terms of CO2 capture. These differences were rationalized in terms of composition and textural properties.

Introduction

Increase of environmental pollution and amounts of waste matters caused by expansion of human activity is a continuingly growing and serious issue. [START_REF] Atkinson | Atmospheric chemistry of VOCs and NOx[END_REF][START_REF] Behera | Ammonia in the atmosphere: A review on emission sources, atmospheric chemistry and deposition on terrestrial bodies[END_REF]"Toxic Industrial Chemicals," 2002) Thus, social concerns on environmental problems and more rigorous regulations on strengthening the environmental protection have promoted the development of waste treatment technologies to enhance precursors as valuable products. [START_REF] Gupta | Chemical treatment technologies for waste-water recycling-an overview[END_REF][START_REF] Ioannidou | Agricultural residues as precursors for activated carbon production-A review[END_REF][START_REF] Rouquerol | Preparation of Activated Carbon from Acacia (Vachellia seyal) Tree Branches and Application to TreatWastewater Containing Methylene Blue Dye[END_REF] As a sustainable and renewable low cost precursor, biomass (natural or by-product such as agrolignocelluloses) has been used for the production of several efficient, eco-friendly, and costeffective lignocellulosic products, e.g. hydrogels for reclamation of sandy soils, (Basta et al., 2013a) functional paper sheets, agro-wood composites [START_REF] Basta | Performance assessment of deashed and dewaxed rice straw on improving the quality of RS-based composites[END_REF]Basta et al., 2013b) and carbon nanomaterials with distinctive functionalities. [START_REF] Guo | Adsorption of Cr (VI) on microand mesoporous rice husk-based active carbon[END_REF][START_REF] Lotfy | Novel approach for synthesizing different shapes of carbon nanotubes from rice straw residue[END_REF]. These latter promoted materials can be used, in turn, for applications in wastewater decontamination, (Basta et al., 2013a;[START_REF] Ozer | Removal of methylene blue from aqueous solutions using phosphoric acid activated carbon produced from hazelnut husks[END_REF] as well as for fuel production. [START_REF] Abdeshahian | Production of Biofuel using Biomass as a Sustainable Biological Resource[END_REF][START_REF] Siddiqui | Promising prospects of nanomaterials for arsenic water remediation: A comprehensive review[END_REF] If some studies focused on the inorganic part of these by-products, namely silica, [START_REF] Megawatia | Synthesis of Silica Powder from Sugar Cane Bagasse Ash and Its Application as Adsorbent in Adsorptive-distillation of Ethanol-water Solution[END_REF] they were mostly used as precursors for activated carbons. Clearly, most of the literature related to the preparation of activated carbons (ACs) from agro-wastes focuses on their application for removing pollutants from aqueous media. However, the application of porous carbon materials for removing noxious gases is also important to maintain the environment and life.

It is very common to say that these porous carbons are versatile. Indeed, they can be also used as supports in catalytic processes. This is already widely documented in the literature, for instance, Cu supported ACs catalysts were found to have an improved activity to remove SO2, compared to Cu supported alumina. [START_REF] Tseng | Carbon materials as catalyst supports for SO oxidation: catalytic activity of CuO-AC[END_REF] Additionally, ACs are used in Fischer Tropsch synthetic fuels, for converting gasses (carbon monoxide and hydrogen) to liquid hydrocarbons, as well as for reducing the effects of poisoning of FTS fuels. (Salinas-Martínez de [START_REF] Salinas-Martínez De Lecea | Improvement of activity and sulphur resistance of Pd complex catalysts using carbon-coated γ-Al2O3 and activated carbon supports[END_REF][START_REF] Van Steen | Fischer-Tropsch catalysts for the Biomass-to-Liquid (BTL)-Process[END_REF] ACs can be used as supports for different purposes; however, they can be functionalized to improve their activity. Classically, enhancing the functionalities of ACs is carried out by physical or chemical treatments. [START_REF] Fathy | Properties of Lignin, Cellulose, and Hemicelluloses Isolated from Olive Cake and Olive Stones: Binding of Water, Oil, Bile Acids, and Glucose[END_REF][START_REF] Guan | Physical preparation of activated carbon from sugar cane bagasse and corn husk and its physical and chemical characteristics[END_REF][START_REF] Mangun | Adsorption of sulfur dioxide on ammoniatreated activated carbon fibers[END_REF][START_REF] Matzner | Influence of nitrogen doping on the adsorption and reduction of nitric oxide by activated carbons[END_REF][START_REF] Ramangkoon | Preparation of rice straw activated charcoal by 2-step H3PO4 activation[END_REF] If agro-based activated carbons are demonstrated to have a high potential for removing noxious gasses, this would address a major concern in overcoming simultaneously both pollution and waste problems, which would be a great improvement regarding climate change. In the literature, different approaches have been envisaged for CO2 sequestration. If in the former studies this sequestration was performed at high pressure, [START_REF] Djeridi | Study of methane and carbon dioxide adsorption capacity by synthetic nanoporous carbon based on pyrogallol-formaldehyde[END_REF] more recently standard pressure conditions have been tested. [START_REF] Nachtigall | Understanding CO(2) Adsorption in CuBTC MOF: Comparing Combined DFT-ab Initio Calculations with Microcalorimetry Experiments[END_REF][START_REF] Phan | Synthesis, structure, and carbon dioxide capture properties of zeolitic imidazolate frameworks[END_REF][START_REF] Zárate | CO2 capture under humid conditions in NH2-MIL-53(Al): The influence of the amine functional group[END_REF] This can be understood by the fact that in nature, CO2 is present at low partial pressure. Investigating the potential of materials in the latter conditions therefore seems more relevant. Additionally, it must be remembered that water moisture is usually present in air. This explains why even if CO2 sequestration was first tested using dried porous materials, more recently raw porous materials were thoroughly studied [START_REF] Ding | Partitioning MOF-5 into Confined and Hydrophobic Compartments for Carbon Capture under Humid Conditions[END_REF][START_REF] Ding | Adsorption of CO2 from flue gas by novel seaweed-based KOHactivated porous biochars[END_REF][START_REF] Phan | Synthesis, structure, and carbon dioxide capture properties of zeolitic imidazolate frameworks[END_REF][START_REF] Zárate | CO2 capture under humid conditions in NH2-MIL-53(Al): The influence of the amine functional group[END_REF]. The regeneration of the adsorbents is of crucial importance, even with rather low cost materials such as pyrolysed wood based materials. As CO2 capture is usually performed at low temperature, or high pressure, it can be deduced that CO2 has mild interaction with most of functionalized surfaces. This is why TSA, PSA or VSA are interesting strategies that have been tested for this goal [START_REF] Raganati | CO2 Capture by Temperature Swing Adsorption: Working Capacity As Affected by Temperature and CO2 Partial Pressure[END_REF][START_REF] Riboldi | Evaluating Pressure Swing Adsorption as a CO2 separation technique in coal-fired power plants[END_REF]. In these studies, it is demonstrated that an appropriate adsorption/desorption balance must be reached in order to find a steady state allowing for a large number of cycles to be run, also described as the CO2 working capacity.

In many countries, rice by-products (rice straw and rice husks) or bagasse are regarded as the most available agro-wastes. These by-products were therefore investigated in many aspects, the main being their potential as carbon sources for making ACs. Because of their intrinsic differences, in terms of composition (lignin, cellulose, hemicellulose and silica), their application to depollution has been investigated and proved successful. (Basta et al., 2019a(Basta et al., , 2013a;;[START_REF] Guo | Adsorption of Cr (VI) on microand mesoporous rice husk-based active carbon[END_REF][START_REF] Megawatia | Synthesis of Silica Powder from Sugar Cane Bagasse Ash and Its Application as Adsorbent in Adsorptive-distillation of Ethanol-water Solution[END_REF] In these works, the adsorbents have been studied as powders because they are readily obtained after pyrolysis. They are characterized by a particle size lower than 50 microns which is a clear drawback for their use in dynamic sorption processes such as PSA or TSA [START_REF] Schöny | A multi-stage fluidized bed system for continuous CO2 capture by means of temperature swing adsorption -First results from bench scale experiments[END_REF]. Even though such fine particles can be easily used and tested for characterization in static analysis systems (TG, gas sorption analyzer, etc.), their applicability in actual dynamic systems even at lab-scale, such as fixed/fluidized bed reactors, is very challenging [START_REF] Raganati | Effect of Temperature on Fluidization of Geldart's Group A and C Powders: Role of Interparticle Forces[END_REF]. Clearly, a fixed bed system allows studying powdered sorbents but in this case, a high pressure drop maybe observed even for a fine bed of adsorbent. A pelletization step of the powders is usually required to avoid this pressure drop but in this case, the shaping process usually negatively affects the sorption performance, either by the loss of porosity, due to the high pressure undergone by the powders, or by the use of binders which may block the porosity. An alternative that has been envisaged is the Spark Plasma Sintering (SPS) densification, which can be performed without any binders at low pressure [START_REF] Dibandjo | Silica, carbon and boron nitride monoliths with hierarchical. porosity prepared by spark plasma sintering process[END_REF][START_REF] Grossin | Biomimetic apatite sintered at very low temperature by spark plasma sintering: Physico-chemistry and microstructure aspects[END_REF]. This will be a very interesting issue to study in the near future. Bagasse being highly regarded, compared to rice by-products, our goal is to assess some ACs prepared from rice by-products or bagasse as potential adsorbents for carbon dioxide. The promoting approach used for changing the chemical functionalities of these precursors is discussed with respect to the sequestration of carbon dioxide. The role of the silica content is also investigated.

Experimental section

Preparation and characterization of AC-precursors

Rice by-products (Rice husks and Rice straw) and sugarcane bagasse were subjected to pulping and biological processes in order to change their chemical constituents as well as their textural properties. These processes are known to change the lignin, cellulose, hemicellulose as well as silica contents of the agro-waste, (Basta et al., 2019b), or preserve one component while having significant effect on the others.

• Pulping processes: The pulping agents were sodium hydroxide, sodium sulfite and a sodium sulfite -sodium carbonate blend. Pulping processes were carried out by setting the percentage of Na2O in the pulping agent as 6.5%. They were performed at 140°C for 2h, using volume dilution ratio liquor / pulping agent of 5. An additional experiment was carried out for preserving the organic components of the material during the removal of silica from rice byproducts using the alkaline pulping. This process was carried with 12% NaOH, at 60 o C for 1 h, and a ratio liquor / pulping agent of 5.

• Biological process: The enzymatic treatment was achieved by exposing the rice straw to cellulosase and peroxidase enzymes (produced by fungi Rhizopus oryzae and Aspergillus awamor, pre-isolated from rice husks), under static conditions. The biological activation was performed during 2 weeks at 27 ºC using a concentration of 1/20 liquor ratio.

The obtained samples were named according to Table 1 in which their chemical compositions are also reported. These compositions (lignin, hemicellulose, α-cellulose) were estimated by standard methods. (Institute of Paper Chemistry, 1951;[START_REF] Jayme | Über die quantitative bestimmung von pentosen mittels bromwasserstosature[END_REF][START_REF] Krause | Prüfung von Papier, Pappe, Zellstoff und Holzstoff[END_REF] The ash content was determined by total oxidation of the materials in a muffle furnace.

Non-isothermal thermogravimetric measurements were performed to gain information about the thermal stability of the evaluated materials upon different activation procedures. It is then expected to find out appropriate methods able to reduce the formation of levoglucosan (carbon-containing volatile substance), and consequently lower the volatilization stage. The behaviour of the precursor through the volatilization stage and its effect on the sorption performance of the produced AC will be specified. This thermogravimetric analysis (TGA) was performed on untreated and treated materials by using a Perkin-Elmer Thermal Analysis Controller AC7/DX TGA7. Analysis was performed with a heating rate of 10°C min -1 and nitrogen flow rate of 50 mL s. -1 Interestingly these analyses also allowed assessing the temperature of pyrolysis which could be applied for the preparation of activated carbons.

Ammonia temperature-programmed desorption (NH3-TPD)

Temperature-programmed desorption of NH3 (NH3-TPD) was performed using a chemisorption analyzer (Micromeritics AutoChem II 2920) equipped with a thermal conductivity detector (TCD). Typically, about 50 mg of material was activated at 150 o C (after a ramp of 10 o C min -1 ) for 30 minutes in 30 mL min -1 of He flow. The material was further cooled down to 100 o C under a 30 mL min -1 He flow. Subsequently, the adsorption of NH3 was carried out at this temperature by switching to a flow of 5% NH3/He (30 mL min -1 ) for 1 h. The sample was further purged with He for 30 min to remove weakly adsorbed NH3.

The TPD was performed from 100 to 550 o C with a temperature ramp of 10 o C min -1 in a 25 mL min -1 He flow.

Textural properties and morphology

The textural properties of the activated carbons were determined by nitrogen sorption measurements at 77 K using a Tristar 3000 Micromeritics. About 80 mg of material were degassed under secondary vacuum at 150 o C for 12 h. A typical mass loss after thermal treatment was found to be ~20 weight percent which shows that these samples are hydrophilic, likely due to oxygenated functions on the carbon surface (phenols, lactones, aldehydes, etc). The equivalent specific surface areas were calculated using a BET linearization of the sorption isotherms around the monolayer, while the pore volume and the external surface area were assessed using the αs method, taking a non porous carbon as a reference [START_REF] Rouquerol | Preparation of Activated Carbon from Acacia (Vachellia seyal) Tree Branches and Application to TreatWastewater Containing Methylene Blue Dye[END_REF].

The morphology of the investigated activated carbons (ACs) was examined by scanning electron microscopy (SEM). The samples were exposed to gold coating (Edwards Sputter Coater, UK) using a quanta FEG250 microscope running at 20 kV.

CO2 adsorption measurements

CO2 adsorption isotherms were performed at 25 o C by using a home-made adsorption apparatus based on manometric measurements, equipped with two capacitive pressure gauges (10 mbar and 1000 mbar). Detailed information of the setup was described elsewhere [START_REF] Ramsahye | Influence of the organic ligand functionalization on the breathing of the porous iron terephthalate metal organic framework type material upon hydrocarbon adsorption[END_REF][START_REF] Trens | Adsorption and separation of xylene isomers vapors onto the chromium terephthalate-based porous material MIL-101(Cr): An experimental and computational study[END_REF]. In brief, the adsorbed amount is determined by measuring the equilibrium pressure difference before and after each sorption step. A precise amount of gas is introduced in a calibrated volume where the initial equilibrium pressure is measured. The gas is then allowed to expand in the sample cell where the pressure is also monitored. When the pressure is stable, the equilibrium pressure is recorded and the amount adsorbed can be calculated. In commercial sorption machines, target equilibrium pressures are set in the sorption programme. In our sorption device, we preferred to allow the sample itself to monitor how many data will allow to cover the whole sorption isotherm [START_REF] Trung | Hydrocarbon adsorption in the isostructural metal organic frameworks MIL-53(Cr) and MIL-47(V)[END_REF]. Indeed, after each data, additional gas is introduced in the calibration volume for the next data. If after adsorption, the equilibrium pressure is very low, the initial pressure of the following point will be very close to that set for the former point. In this way, any specific behaviour will be disclosed as we could exemplify it in the past [START_REF] Boudjema | A Switch in the Hydrophobic/Hydrophilic Gas-Adsorption Character of Prussian Blue Analogues: An Affinity Control for Smart Gas Sorption[END_REF][START_REF] Trung | Adsorption of C5-C9 hydrocarbons in microporous MOFs MIL-100(Cr) and MIL-101(Cr): A manometric study[END_REF]. Prior to measurements, about 250 mg of material were degassed at 150 o C for 12 h under secondary vacuum.

Results and Discussion

Precursor's analyses of CO2 adsorbents

Proximate analysis

The composition of the rice by-products (Rice Straw (RS) and Rice Husks (RH)) and sugarcane bagasse (B) is shown in Table 1 along with that of the processed materials. The figures given in Table 1 are subjected to the variations of quantities organic extractives in the samples used for these analyses. The difference between 100% and the sum of the percentages for each composition is therefore due to the amount of extractives in the samples. The chemical treatments (soda, sulfite and neutral sulphite) are known to remove the noncellulosic constituents of rice by-products (RS & RH) and bagasse (silica, hemicellulose and lignin). Accordingly, these treatments lead to an increase of the proportion of α-cellulose in the residual materials. The biological treatments are more specific according to the enzymes employed (cellulase and peroxidase) which yield a selective removal of RS and RH constituents. As expected, the cellulase enzyme shows a high activity towards cellulose, while peroxidase affects lignin in the precursors. In proportion, both treatments therefore lead to increase the silica content. From Table 1, it can be seen that the untreated RS and RH have very high ash contents (15.6% and 18.5% respectively). These can be related to silica content of the precursors, which is likely to enhance the sorption capabilities of activated carbons. [36] In the case of bagasse, the ash content is 4.7 % which confirms the low concentration of silica in the latter, as usually documented. [START_REF] Guo | Porous activated carbons derived from waste sugarcane bagasse for CO2 adsorption[END_REF][START_REF] Megawatia | Synthesis of Silica Powder from Sugar Cane Bagasse Ash and Its Application as Adsorbent in Adsorptive-distillation of Ethanol-water Solution[END_REF]. These differences highlight the specificity of the sorption properties of the carbon materials investigated. The ash content, being made of silica, is therefore related to the chemical treatment. As expected, soda treatment decreases the ash content by solubilizing the silica contained in the precursors (15.6 down to 11.1% and from 18.5 down to 11.3%, for RS and RH respectively). However, a low NaOH % pulping agent (6.5% as Na2O) has a rather limited influence on the ash content, and therefore the silica content. This can be evidenced on rice by-products which have high silica content. In the case of bagasse, the soda pulping eliminates almost the whole amount of silica present in the precursor, as its content is already very low (4.7%). The reduction in silica contents in the precursors subjected to pulping by alkaline agent has another effect, which is a decrease of the lignin content which in turn, increases the α-cellulose proportion. This can be seen with RS4, RS7, RH4 and B2.

Table1. Chemical constituents of the precursors of CO2 adsorbents

Subjecting the RS precursor to neutral sulphite pulping and enzymatic treatments provide the reverse trend. Such pre-treatments, except cellulase treatment, lead to increase in holocellulose. The alkali and peroxidase treatments are more efficient for increasing the αcellulose, as compared to pristine RS and RH. Indeed, the increase in α-cellulose reaches 36-39%, and 36-45%, for RS and RH precursors. Moreover, these treatments, especially by enzymes, lead to increase the ash content up to ~22%.

Pyrolysis of Precursor-based ACs

The prepared precursors were subjected to thermogravimetric analysis (TGA) in order to identify their thermal stability which is related to the chemical constituents. In general terms, the thermal decomposition of any biomass occurs via three-stages, namely: the desorption of moisture, the degradation and evolvement of the constitutive biopolymers, and finally carbonisation of the residue. The TGA and DTGA curves of the RS, RH and B materials are presented in Figure 1. Concerning the removal of water, it can be noticed that this phenomenon occurs at temperatures below 100°C, which is the indication that water is loosely bound to the biopolymeric structures. Depending on the material, the extent of water removal differs, which is the indication of different textural properties. The main degradation stage due to depolymerisation, volatilisation and (inter-and intra-molecular) dehydration occurs at temperatures higher than 200°C. This stage is complete at 400°C and at higher temperature, full carbonization of the materials can be observed. Focusing on the pristine materials (untreated), it can be noticed that bagasse (B1) leaves a lower percentage of ashes (~9.9%), compared to RH1 and RS1 (31.2% and 26.2% respectively). These results are expected as they are in line with the silica content of these materials, which was determined by their carbonization. The lower weight remain (free from ash) of volatilization stage of raw bagasse (8.9%) than rice by-products (13.7% and 13.2%) is probably ascribed to the higher content of α-cellulose.

Upon treatments, the thermal behaviour of the materials is changed. Indeed, both biological and chemical pulping lead to an enhancement of the thermal stability, compared to raw rice by-products and bagasse. This can be seen by focusing on the values of initial temperature and DTG peak temperature of depolymerization and volatilization stage which both increase upon treatment (2 nd degradation stage). The thermal stability of these materials is known to be improved for increased percentages of lignin and/or α-cellulose contents. Conversely, hemicellulose is known to have a rather low thermal stability (Basta et al., 2019b). Sulfite and neutral sulfite pulping treatments provide precursors with higher thermal stability (increase of Ti), compared to treatments by enzymes (cellulose and peroxidase). However, the latter treatments are preferred as they provide high carbon yields (free from ash). These results are gathered in Table 2.

Concerning RH precursors, the volatilization stage is observed at lower temperature range if the precursor results from the cellulase treatment (RH2) (Tf-Ti :152 o C). Furthermore, RH2 has a higher residual weight (16.6% free from residue), compared to RH 3 and RH4. This trend can be explained by the rather low cellulose content in RH2. The treatment of bagasse by pulping processes lead to an increase of the α-cellulose and a decrease of the lignin content. Sulfite and neutral sulfite pulping are less effective on removing the lignin than pulping by alkali. The higher weight remain (free from residue) of volatilization stage can be observed in case of the precursor resulting from sulfite pulping (B3), with relatively lower cellulose and higher hemicellulose and lignin contents versus soda pulping agent.

This suggests a slow pyrolytic degradation related to the higher lignin and pentosan contents which decompose at higher temperatures than low content of α-cellulose. Pyrolysis of neutral sulfite pulp (B4) behaves in a similar fashion to sulfite pulping material (B3). From all the foregoing data, we can conclude that there is a good relationship between the constituents of carbon precursor, especially low cellulose and high silica contents, with the weight remain of volatilization stage and consequently the carbon yield.

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Textural analysis.

The textural properties of the ACs evaluated by nitrogen adsorption at 77 K are shown in The shape of the sorption isotherm is changed according to the treatment. In the case of chemical treatments by pulping process, the RS-ACs and B-ACs follow the type I sorption isotherm according to the IUPAC classification, which is typical for microporous materials [START_REF] Rouquerol | Preparation of Activated Carbon from Acacia (Vachellia seyal) Tree Branches and Application to TreatWastewater Containing Methylene Blue Dye[END_REF] high relative pressure in some cases, which is indicative of some interparticular porosity or macroporosity. This is particularly true in the case of enzymatic treatments applied on RS and RH. This feature is interesting for favouring gas diffusion. Their equivalent specific surface area have been determined using the BET model in the relative pressure range 0.05 < p/p° < 0.25. They are gathered in Table 3 along with other textural properties obtained using the αs method, taking a non porous carbon material as reference [START_REF] Cabiac | Influence of textural properties of activated carbons on Pd/carbon catalysts synthesis for cinnamaldehyde hydrogenation[END_REF][START_REF] Cabiac | Controlled preparation of Pd/AC catalysts for hydrogenation reactions[END_REF][START_REF] Rouquerol | Preparation of Activated Carbon from Acacia (Vachellia seyal) Tree Branches and Application to TreatWastewater Containing Methylene Blue Dye[END_REF]. The pulping processes have impacts on two main aspects of the textural properties of the materials (i) equivalent specific surface areas and (ii) microporous volumes. These parameters are of prime influenced, as ACs should be more efficient if they have (i) large surface extents, and (ii) large pore volumes favouring CO2 diffusion. In general terms, the specific surface areas of the materials are higher after pulping processes of the raw materials. While the influence of other pulping processes is more specific on the textural properties of the materials, the most efficient pulping process is soda which allows the specific surface area to increase from 413 up to 547 m 2 .g -1 (RS1 and RS4 respectively). It is even more pronounced in the case of concentrated soda which allows the surface to double (812 m 2 g -1 for RS7). Other treatments have more limited impacts on the surface area of RS-based activated carbons. Soda pulping leads to an increase in the case of RH and B-based ACs. It must be emphasized that in the latter case, AC obtained from raw bagasse has already a high specific surface area. This could explain some of the published results which highlight the efficiency of bagasse for producing highly effective ACs [START_REF] Alabadi | Highly porous activated carbon materials from carbonized biomass with high CO2 capturing capacity[END_REF][START_REF] Guo | Porous activated carbons derived from waste sugarcane bagasse for CO2 adsorption[END_REF]. Bagasse is also very sensitive to sodium sulphite pulping, as its specific surface area increases from 655 up to 1614 m 2 g -1 . It can be concluded that depending on the raw material used, pulping processes have different impacts on the specific surface areas of the obtained ACs, due to their composition.

The general increase of the specific surface area upon soda treatment can be interpreted using Table 1. Indeed, the ash content (mainly made of silica) drastically decreases upon soda treatment. It can be deduced that silica is dissolved using concentrated basic aqueous solutions with two consequences (i) leaving voids in the structure and (ii) materials alleviating. The generation of voids in the structures has a direct impact on the pores volumes.

Indeed, it can be noticed that, compared to RS1, RH1 and B1, the pores volumes of the ACs obtained with pulped materials strongly increase. It can be deduced that pulping induces an enlargement of the pores, which favors gas diffusion and therefore sorption kinetics.

Our activated carbons compare well with materials already published in terms of their textural properties. Some are gathered in the following table (Table 4) and other may be found in the literature [START_REF] Álvarez-Gutiérrez | Kinetics of CO2 adsorption on cherry stone-based carbons in CO2/CH4 separations[END_REF][START_REF] Ammendola | Fixed bed adsorption as affected by thermodynamics and kinetics: Yellow tuff for CO2 capture[END_REF][START_REF] Monazam | Fluid bed adsorption of carbon dioxide on immobilized polyethylenimine (PEI): Kinetic analysis and breakthrough behavior[END_REF][START_REF] Raganati | Kinetic study and breakthrough analysis of the hybrid physical/chemical CO2 adsorption/desorption behavior of a magnetite-based sorbent[END_REF]. Bagasse based activated carbons have higher specific surface area compared to all the materials studied here, or in the literature. This can explain the great interest for this material. [START_REF] Fierro | Rice straw as precursor of activated carbons: Activation with ortho-phosphoric acid[END_REF] Sugar-cane bagasse 1075 -1254 [START_REF] Chen | Preparation of phosphoric acid activated carbon from sugarcane bagasse by mechanochemical processing[END_REF] Thevetia peruviana 862 [START_REF] Baseri | Preparation and characterization of activated carbon from Thevetia peruviana for the removal of dyes from textile wastewater[END_REF] Orange peel 1090 (Fernández-Bolaños et al., 2014) hazelnut husks 770 [START_REF] Ozer | Removal of methylene blue from aqueous solutions using phosphoric acid activated carbon produced from hazelnut husks[END_REF] Rice straw 967.72 [START_REF] Sun | Preparation of Rice Straw Activated Carbon by Phosphoric Acid[END_REF] Baslsamodendron caudatum wood waste 505 [START_REF] Sivakumar | Preparaction and characterization of activated carbon prepared from Baslsamodendron caudatum wood waste through various activation processes[END_REF] Peanut hulls 813 [START_REF] Zhong | Preparation of peanut hull-based activated carbon by microwave-induced phosphoric acid activation and its application in Remazol Brilliant Blue R adsorption[END_REF] Banana leaves 798 -1228 [START_REF] Martin-Gonzalez | Preparation of activated carbons from banana leaves by chemical activation with phosphoric acid[END_REF] Apple pulp 1103 [START_REF] Hesas | Preparation and Characterization of Activated Carbon from Apple Waste by Microwave-Assisted Phosphoric Acid Activation: Application in Methylene Blue Adsorption[END_REF] Acacia (Vachellia seyal) Tree 762 [START_REF] Rouquerol | Preparation of Activated Carbon from Acacia (Vachellia seyal) Tree Branches and Application to TreatWastewater Containing Methylene Blue Dye[END_REF] Xerogel-based ACs 567-839 [START_REF] Basta | Comparative evaluation of xerogel-based activated carbons synthesized from aliphatic aldehydes of different chain lengths[END_REF] WordCount = 8188

Morphology.

Scanning Electron Microscope (SEM)

The morphology of the investigated activated carbons (ACs) was examined by scanning electron microscopy (SEM) (Figure 3). The morphology of representative produced ACs shows that, the pulping process was effective for converting the surface from heterogeneous surface, (irregular shaped particles which are aggregated together), which observed in case of using raw RS or bagasse as precursor for ACs, to porous materials, even though the microporosity cannot be observed here. This observation is supported from texture analysis data. As can be noticed, due to presence of silica/and or extractives in raw precursors, cracks and crevices did form during the activation process likely, due the use of phosphoric acid (Basta et al., 2019a).

Sorption studies.

The aim of the present study is to compare rice by-products and bagasse as precursors for activated carbons in the CO2 capture. Apart from the extent of surface of the sorbents, a key feature is the surface chemistry of the sorbents surface. Acid sites can be explored using ammonia adsorption whereas carbon dioxide will have a known affinity for basic sites.

Ammonia adsorption was first investigated to characterize the acid sites of the ACs surface, that is, before thermodesorption. This classical method allows determining not only the strength of the acid sites, but also their quantity. The temperature at which desorption occurs is an indication of the strength of the acid site/ammonia whereas the quantity of ammonia released can be determined using a catharometer after calibration. Indeed, a lower temperature will be required for ammonia to desorb on the weak acidic sites compared to stronger acidic sites. The Temperature Programmed Desorption (TPD) of ammonia profiles obtained with the different activated carbons were deconvoluted in order to yield the populations of weak, mild and strong acidic surface sites of the sorbents. The NH3 TPD results are presented in Figure 4. We differentiated the materials in terms of the acid strength. The weakly bound ammonia could be desorbed in the range 138-150°C for all the materials. In the case of the mildly bound ammonia, the temperature range was located between 171 and 237 °C. In the case of the desorption of ammonia from the strong acidic sites the temperature range was found to be between 235°C and 335°C. All the TPD profiles along with the deconvolution curves can be found as supplementary information (ESI1).

In general terms, it can be noted that the acidic sites contents decreases upon pulping processes. When comparing the amount of acidic sites, the ACs obtained have low concentrations of weak surface acidic sites, whereas these materials have higher concentrations of medium surface acidic sites. It can be noted that pulping processes have little impact on their amount. Indeed, it decreases by 10% for RS and RH-based ACs. The changes in surface acidic sites in case of RS versus type of treatment is more clear in case of RS than RH, especially in case of strong surface acidic site on treatment by peroxidase enzyme. Where it provides higher values of ammonia adsorption (RS3: ~ 6.5 mmol g -1 ) than that observed in case of RH3 (~ 3 mmol g -1 ). This is ascribed to great increasing in silica content with moderate decreasing in lignin content in treated RS, and consequently more

Acidic sites

WordCount = 8188 number of chemisorption sites is created to enhance the physical adsorption of ammonia with free OH groups on the silica surface and formation of hydrogen bonded to one another. Acidic and basic surface sites can be present on the surface of the prepared ACs. It is therefore ambitious to deduce that the lower the amount of acidic surface sites, the higher will be the amount of basic sites. CO2 adsorption was therefore performed to evidence a possible correlation, but also to highlight particular pulping processes that would favour CO2 adsorption.

The CO2 sorption isotherms are presented in Figure 5. They exhibit the same rather linear shape, up to the atmospheric pressure. At atmospheric pressure, these materials are able to adsorb up to 14% in weight in the case of B-based materials, which compares well with recent published results. [START_REF] Ding | Adsorption of CO2 from flue gas by novel seaweed-based KOHactivated porous biochars[END_REF] Indeed, amongst many studies dealing with carbon dioxide sequestration, Ding and Liu recently claimed a maximum uptake of 1.05 mmol g -1 of seaweed based biochars, which corresponds to 4.62% weight uptake. Alabadi et al found a very high CO2 uptake using a carbonized biomass material.

[43] However, the CO2 uptake of 7.49 mmol.g -1 was reached at 0°C, which strongly favors sorption processes. Comparing the influence of the pulping processes applied on bagasse, it is clear that raw bagasse is as efficient as the pulped bagasse based ACs for CO2 adsorption. In the case of RH-based ACs, the CO2 uptake for RH1 is rather high (13 mmol.g -1 ), however it is lower (6 wt% at atmospheric pressure) for the other materials which shows that the nature of the waste is of importance for favouring the CO2 sorption. It can be concluded that, depending on the biomass investigated, the chemical activation procedure can be of importance for producing efficient sorbents. To a fundamental point of view, it is therefore interesting to derive sorption isotherms per nm 2 instead of weight % uptake in order to better understand the influence of the chemical treatments that all the samples have undergone. The corresponding sorption isotherms are reported in In the case of the RS and RH-based materials, the results do not allow selecting a particular material which would adsorb more CO2 per nm 2 . The sorption curves are very linear up to 700

Torr, which suggests that the sorption process is ruled by the Henry's law. This can be interpreted by considering the sorbents as homogeneous towards CO2 sorption, thus behaving like ideal surfaces for CO2. RH1 is slightly different in the sense that it adsorbs CO2 to a greater extent which suggests that this material has a higher content in basic surface sites. This is consistent with the shape of the curve, which is not linear, but slightly curvy. In contrast, bagasse based ACs have different CO2 sorption properties. In those cases, pulping processes induce different surface properties towards CO2 capture. Soda and sodium sulphite pulping processes yield homogeneous materials without any specific sites that could be detected by sorption. Sulphite pulping yields an intermediate treatment in the sense that the CO2 adsorbed amount are higher, compared to B2 and B4. However, its sorption capacity is lower compared to AC the obtained using raw bagasse precursor (B1).

More importantly, the affinity of the latter material for CO2 is higher compared to the pulped materials B2, B3 and B4. B1 therefore has a clear affinity for CO2 as the sorption curve exhibit a knee at around 100 torr. This can be interpreted by a stronger interaction between CO2 and the basic sites of this particular sorbent. Once these sites are saturated (above ~250 torr), the sorption proceeds according to a Henry's law, like for any other material studied here. The particular behaviour of B1 compared to RH1 and RS1 can be evidenced at low pressure where the affinity of the different activated carbons towards CO2 can be better seen (Figure 6, bottom right). It appears that a curvy shape is more apparent in the case of B1, which confirms that AC produced from raw bagasse has a greater affinity, compared to the other materials. To confirm this point, the Henry's constants have been derived as the slope of the sorption isotherms at p = 0 torr. For the materials B2, B3, B4 and B1, the following Henry's constants (in molec.nm 2 .torr -1 ) were obtained respectively: 0.0021; 0.0044; 0.0020 and 0.0073. These results confirm the difference between B1 and the other materials. From these results, it can be concluded that based on the efficiency of CO2 sequestration, the materials issued from bagasse are very promising, B1 developing stronger interaction with CO2.

Conclusion

Rice by products and bagasse have been used for producing activated carbons after pulping processes and pyrolysis. The obtained ACs were characterized by TGA, elemental analysis, nitrogen adsorption and surface chemistry. Ammonia TPD was performed for characterizing the acid sites, in terms of strength and amounts. Bagasse-based ACs were found to have less acidic sites compared to rice-based ACs. Pulping processes resulted in an increase of the specific surface areas of the corresponding ACs, especially in the case of bagasse-based ACs.

These materials were therefore found to be the most efficient for CO2 adsorption in terms of quantities. Additionally, they compared well with recent published results. A focus was given to the influence of the surface sites towards the affinity of CO2 for ACs. While rice based ACs yielded similar sorption isotherms, clear differences could be observed in the case of bagasse based ACs. In that case, the highest affinity was observed for the activated carbon obtained from the raw bagasse, that is without any pulping process. The pulping processes applied on raw bagasse strongly increased the specific surface area of the corresponding ACs at the expense of their affinity for CO2. The efficiency of ACs for the sorption of carbon dioxide can be seen as a balance between the uptake and the strength of the interaction involved in the sorption process. Strong interaction favours a selectivity towards CO2 while high specific surface areas favours the amounts adsorbed. In this sense, raw bagasse as precursor for activated carbons seems a sensible choice amongst the materials investigated in this study.

Figure 1 .

 1 Figure 1. Thermogravimetric analysis of the different materials. (top) Rice straw materials (RS), (middle) Rice husks materials (RH), (bottom) Bagasse materials (B).

  Figure 2.

Figure 2 .

 2 Figure 2. Nitrogen adsorption isotherms of the different activated carbons.

Figure 3 .

 3 Figure 3. Representative micrographs of the activated carbons studied in this work. Top left, RS1 ; Top right RS6 ; Bottom left B1 ; Bottom right, B4.

Figure 4 .

 4 Figure 4. Acid properties of the prepared activated carbons derived after NH3-TPD.The impact is more obvious on bagasse based ACs. Compared to AC prepared with raw bagasse, the concentration of weak acidic sites is decreased, up to 4 times in the case of B2 (soda treatment). It is also the case for medium and strong acidic sites. Bagasse therefore undergoes a clear lowering of the acidic surface sites upon pulping, as demonstrated by the sum of the acidic sites reported in Figure4.

Figure 5 .

 5 Figure 5. CO2 uptakes performed at 298 K, reported as wt%.

Figure 6 .Figure 6 .

 66 Figure 6.

Table 2 .

 2 TGA analyses of AC precursors

		Ti /°C Tf /°C Tpeak/°C Tf-Ti	Wt remain,	Residue	wt remain free ash,
						%	%	%
	RS1	159	408	320	249	39.9	26.2	13.7
	RS2	231	394	351	163	36.7	18.9	17.8
	RS3	226	392	346	166	30.4	12.00	18.4
	RS4	250	385	350	134.7	34.5	26.2	8.3
	RS5	245	386	351	141.3	32.3	21.1	11.2
	RS6	245	390	351	145.1	31.6	21.1	10.5
	RS7	223	392	352	169	22.2	7.3	14.9
		Ti /°C Tf /°C	Tpeak/°C Tf-Ti Wt remain, % Residue	wt remain free ash
							%
	RH1	223	381	333	158	44.4	31.2	13.2
	RH2	245	397	354	152	42.9	26.3	16.6
	RH3	217	403	355	186	42.3	27.5	14.8
	RH4	234	392	349	158	30.9	18.5.	12.4
		Ti /°C Tf /°C	Tpeak/°C Tf-Ti	Wt remain,	Residue,	wt remain free ash,
						%	%	%
	B1	220.1	385.2	350	165.1	18.8	9.9	8.9
	B2	250.4	388.4	350	138	17.0	8.6	8.4
	B3	242.3	390.6	356	148.3	27.6	17.5	10.1
	B4	236.5	385.9	347	149.4	26.3	17.0	9.3

Table 3 .

 3 Textural characterization of the samples.

		Sample	SBET/ m 2 g -1 Vp/ cm 3 g -1 Smicro / m 2 g -1 Vmicro/ cm 3 g -1
	RS1 RS-control	413	0.614	61	0.028
	RS2 Cellulase treatment	361	0.596	14	0.006
	RS3 Peroxidase treatment	372	0.703	16	0.008
	RS4 6.5% soda treatment	547	0.956	24	0.008
	RS5 6.5% sulfite treatment	489	0.785	47	0.021
	RS6 6.5% neutral sulfite treatment	507	0.709	30	0.012
	RS7 12% soda treatment	812	1.502	51	0.021
			SBET/ m 2 g -1 Vp/ cm 3 g -1 Smicro / m 2 g -1 Vmicro/ cm 3 g -1
	RH1 RH-control	317	0.509	26	0.011
	RH2 Cellulase treatment	585	0.848	48	0.020
	RH3 Peroxidase treatment	398	0.537	45	0.019
	RH4 12% soda treatment	709	0.929	18	0.007
			SBET/ m 2 g -1 Vp/ cm 3 g -1 Smicro / m 2 g -1 Vmicro/ cm 3 g -1
	B1	B-control	655	0.259	310	0.143
	B2	6.5% soda treatment	1576	2.083	148	0.062
	B3	6.5% sulfite treatment	1033	0.784	357	0.169
	B4	6.5% neutral sulfite treatment	1614	2.132	137	0.049

Table 4 . Comparison of specific surface area for different activated carbons

 4

	Adsorbent	SBET/ m 2 g -1	Reference
	B1 B4 B3 B2	1614 1033 1576 655	Present article
	RS1 RS7 RS6 RS5 RS4 RS3 RS2	812 507 489 547 372 361 413	Present article
	RH1 RH4 RH3 RH2	709 398 585 317	Present article
	Rice straw	529


Professor Eric Hug
email: eric.hug@ensicaen.fr

Clément Keller

Pierre-Antoine Dubos

Mayerling Martinez Celis

Size effects in cobalt plastically strained in tension: impact on gliding and twinning work hardening mechanisms

Keywords: cobalt, size effects, mechanical properties, dislocations, basal slip mechanisms, twinning

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Forming process of thin metallic parts of miniaturized systems used in medical or electrical devices remains an issue for obtaining desired performances in terms of structural and functional properties. The influence of free surfaces on the properties of the material becomes very sensitive when one or several characteristic length of the representative volume element becomes less than typically a few hundred of micrometers [START_REF] Arzt | Size effects in materials due to microstructural and dimensional constraints: a comparative review[END_REF]. Such intrinsic size effect is moreover strongly dependent on the grain size [START_REF] Armstrong | On size effects in polycrystal plasticity[END_REF][START_REF] Armstrong | 60 years of Hall-petch: past to present nano-scale connections[END_REF] and leads to an impact of thickness (t) to grain size (d) ratio t/d on the mechanical properties [START_REF] Fulop | Size effects from grain statistics in ultra-thin metal sheets[END_REF][START_REF] Janssen | An experimental assessment of grain size effects in the uniaxial straining of thin Al sheet with a few grains across the thickness[END_REF]. The flow stress, the work hardening mechanisms and the fracture properties are modified when t/d decreases below a critical value. This t/d threshold is linked to the stacking fault energy [START_REF] Miyazaki | Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes[END_REF], and some experimental conditions such as the temperature [START_REF] Hug | Size effects and temperature dependence on strain-hardening mechanisms in some face centered cubic materials[END_REF], the strain level [START_REF] Thompson | The dependence of polycrystal work hardening on grain size[END_REF], and the mechanical loading [START_REF] Dubos | Size effects in thin face centered cubic metals for different complex forming loadings[END_REF][START_REF] Keller | Effect of stress path on the miniaturization size effect for nickel polycrystals[END_REF]. The surface effect is quite well understood for face centered cubic (fcc) metals and alloys and is intimately related to a stress gradient of typically 30% between core and surface grains [START_REF] Hug | Intrinsic Effects due to the Reduction of Thickness on the Mechanical Behavior of Nickel Polycrystals[END_REF]. This was highlighted by transmission electron microscopy (TEM) and nanohardness experiments and confirmed by finite element simulations using strain gradient crystal plasticity models [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF]. Further decrease on the t/d ratio leads to the existence of a second critical ratio, around unity [START_REF] Janssen | An experimental assessment of grain size effects in the uniaxial straining of thin Al sheet with a few grains across the thickness[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF], related to a constant stress regime dependent of the thickness [START_REF] Fourie | The flow stress gradient between the surface and centre of deformed copper single crystals[END_REF][START_REF] Keller | Finite element investigation of size effects on the mechanical behavior of nickel single crystals[END_REF].

The progressive transition from a polycrystalline to a quasi-single crystalline state, through an intermediate so-called multicrystalline state, strongly modifies the mechanical properties and affects not only the forming performances of small metallic parts [START_REF] Geng | Effect of crystalline anisotropy and forming conditions on thinning and rupturing in deep drawing of copper single crystal[END_REF][START_REF] Raulea | Size effects in the processing of thin metal sheets[END_REF], but also their functional properties, such as the coercive field strength and magnetic behavior [START_REF] Hug | Size effects and magnetoelastic couplings: a link between Hall-Petch behaviour and coercive field in soft ferromagnetic metals[END_REF][START_REF] Mohri | Sensitive micro magnetic sensor family using magneto-impedance (MI) and stress-impedance (SI) effects for intelligent measurements and controls[END_REF], the electrical resistivity [START_REF] Chauhan | Probing thickness-dependent dislocation storage in freestanding Cu films using residual electrical resisitivity[END_REF][START_REF] Lim | Electrical resistivity of Cu films deposited by ion beam deposition: Effects of grain size, impurities, and morphological defect[END_REF] or the thermal conductivity [START_REF] Dong | Relative importance of grain boundaries and size effects in thermal conductivity of nanocrystalline materials[END_REF]. Such mechanisms associated with the strengthening of fcc materials are well documented in the literature but their characterization for others crystallographic structures remains, however, an issue. Many researches focused on the so-called "smaller is stronger" effect depicted by micropillar experiments on hexagonal closed packed (hcp) metals [START_REF] Byer | Effects of the initial dislocation density on size effects in single-crystal magnesium[END_REF][START_REF] Yu | Strong crystal size effect on deformation twinning[END_REF]. However, very few works concerning size effects in hcp crystallographic structures are available in the range of laminated part thickness. The grain size impact on the yield stress verifies a Hall and Petch (HP) relationship, as shown for instance for magnesium [START_REF] Qiao | Effects of grain size, texture and twinning on mechanical properties and work-hardening behaviors of pure Mg[END_REF], zirconium [START_REF] Ramani | Grain size dependence of the deformation behaviour of alpha zirconium[END_REF] and titanium [START_REF] Ghaderi | Sensitivity of deformation twinning to grain size in titanium and magnesium[END_REF]. Concerning magnesium, this law was found to be valid for higher values of plastic strains by Ono et al [START_REF] Ono | Effect of deformation temperature on Hall-Petch relationship registered for polycrystalline magnesium[END_REF], but only five grain diameter values were used to plot the HP graphs. Grain size was also found to influence twinning [START_REF] Meyers | The onset of twinning in metals: a constitutive description[END_REF] and fracture mechanisms [START_REF] Fan | The grain size dependence of ductile fracture toughness of polycrystalline metals and alloys[END_REF] of hcp metals. Twinning and gliding regimes exhibit their own HP relationship with higher slopes in twinning mechanisms as dislocation gliding is restricted in this case. HP plots with two or three distinct regimes were depicted [START_REF] Barnett | Influence of grain size on the compressive deformation of wrought Mg-3Al-1Zn[END_REF] depending on the plastic strain level and the dominant work hardening mechanism. For a given grain size, Lou et al [START_REF] Lou | Hardening evolution of AZ31B Mg sheet[END_REF] have shown that a decrease in thickness of Mg alloys leads to a decrease in the ultimate stress in tension and a corresponding decrease in the fracture strain. Same evolutions were obtained for titanium plastically strained in tension but also in shear [START_REF] Nasiri-Abarbekoh | Effects of thickness and texture on mechanical properties anisotropy of commercially pure titanium thin sheets[END_REF]. To the knowledge of the authors, only one major work was dedicated to the coupled effect of the grain size and t/d ratio for hcp materials. This study was devoted to zinc [START_REF] Ecob | Effect of grain size on flow stress of textured Zn alloy[END_REF], and a critical t/d ratio of 12 was found below that one a softening of the mechanical properties was observed. This effect was attributed to the impact of a strong basal texture which develops during plastic deformation. Among all hcp structures, cobalt has been much less studied but is of particular interest due to its specific mechanical and magnetic properties, which makes it a good candidate for miniaturized systems and components. Cobalt deserves also attention due to its higher melting point and very low stacking fault energy compared with others hcp metals [START_REF] Betteridge | The properties of metallic cobalt[END_REF]. Work hardening curves of polycrystalline cobalt exhibit two distinct stages in the plasticity regime. Basal dislocation glide on the crystallographic system 0001 〈12 10〉 is the dominant mechanism in the first stage of work hardening (labelled stage A in the following). Unlike magnesium, where prismatic or pyramidal slip systems can also be observed under specific experimental conditions [START_REF] Couret | An in situ study of prismatic glide in magnesium-I. The rate controlling mechanism[END_REF][START_REF] Máthis | The evolution of non-basal dislocations as a function of deformation temperature in pure magnesium determined by X-ray diffraction[END_REF], basal slip is the only activated mode in cobalt [START_REF] Marx | Straininduced phase transformation of a thin Co film on flexible substrates[END_REF][START_REF] Seeger | Theory of work-hardening of FCC and HCP single crystals[END_REF]. After an amount of plastic strain, because of the limited number of available slip systems, twinning process occurs in the second work hardening stage (stage B) as an alternative for plastic deformation. Several twinning modes occur in cobalt but twinning in the 101 2 planes was found to be the majority mode [START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF] due to its low corresponding twinning shear [START_REF] Partridge | The crystallography and deformation modes of hexagonal close-packed metals[END_REF]. The size effects in such metal, for instance the impact of the t/d ratio on gliding and twinning regimes, deserve attention.

The objective of this work is to contribute to the understanding of size effects in metallic materials by giving first new experimental results concerning high purity cobalt.

HP formalism and strengthening mechanisms were studied and size effects were depicted in the gliding regime below a critical t/d ratio related to the low stacking fault energy in a similar way than for fcc alloys. This behavior fades away when twinning occurs. Surface effects were highlighted by nanoindentation experiments completed by the application of a simple composite model [START_REF] Yang | Yield stress influenced by the ratio of wire diameter to grain size -a competition between the effects of specimen microstructure and dimension in micro-sized polycrystalline copper wires[END_REF]. The softening of the mechanical properties observed in the stage A of work hardening is finally discussed using the Kocks-Mecking formalism [START_REF] Keller | Kocks-Mecking analysis of the size effects on the mechanical behavior of nickel polycrystals[END_REF][START_REF] Kocks | Physics and phenomenology of strain hardening: the FCC case[END_REF] and the observation of dislocation pile-ups against boundaries in the gliding planes.

Experimental details

Laminated sheets of high purity cobalt (higher than 99.9wt.%) of variable thicknesses t ranging from 125 to 700 µm, provided by GoodFellow company, were considered. As-received sheets were first annealed at 900 °C for 1 h and considered as the starting polycrystalline state. Samples were therefore subjected to heat treatments at 1100 °C with increasing times in order to modify the grain size d and the corresponding t/d ratio. For all heat treatments, the partial pressure of oxygen was maintained lower than 10 -7 mbar for limiting oxidation of the free surfaces during the annealing process. Cobalt exhibits an allotropic transformation at 376 °C during cooling, between the hcp phase and the fcc high temperature metastable structure. A slow cooling of samples inside the furnace during 24 h is mandatory in order to control the amount of remaining secondary fcc phase.

Values of d for different thicknesses and corresponding t/d ratios are given in Table I. (nominal tip radius of curvature of 20 nm) was employed and measurements were displacement-controlled up to a penetration depth of 500 nm. Spacing between each indent was set to 1 µm to avoid interaction between plastics zones. A calibration experiment on a fused quartz specimen was performed before each test to ensure reliable measurements.

Grain size, crystallographic texture and residual fcc phase fraction were systematically evaluated by electron back scattered diffraction (EBSD) working on a scanning electron microscope (SEM). Gliding mechanisms, dislocation features and pileups were studied by TEM with a microscope operating at 200 kV. To this aim, 3 mm diameter discs were first extracted from mid-thickness of the strained specimens and then thinned down by mechanical polishing and electropolishing using a twin jet electrolytic thinning apparatus (90% glacial acetic acid and 10% perchloric acid solution, working voltage of 50 V).

Experimental results

Microstructural evolution of cobalt samples with heat treatments

Fig. 1 presents a general overview of the microstructure of polycrystalline and multicrystalline samples after heat treatment. Independently of the t/d ratio, a well-defined hcp crystallographic structure is evidenced giving an isotropic grain size both through the thickness (Fig. 1(a)) and on the surface (Fig. 1(b)). Specimens also exhibit 71.4°/ 10 2 1 boundaries resulting from the martensitic transformation from fcc to hcp during cooling. -9 -

The retained fcc phase is mainly located at triple junctions of grain boundaries of the hcp phase as revealed by EBSD cartography (Fig. 1(c)). This secondary phase modifies the mechanical properties of cobalt for amounts of the order of 40-45 % [START_REF] Bouquet | Influence of the f.c.c. phase retained at room temperature on the mechanical properties of cobalt[END_REF] well higher than the values displayed in Fig. 1(d) (between 5 % and 25 %, depending on the t/d ratio).

We will consider in the following paragraphs that modifications of the mechanical properties of cobalt result to the behavior of the hcp phase only. -10 -

The initial microstructure is also characterized by the existence of numerous stacking faults, both in hcp and fcc phases (Fig. 3). These faults are bounded by partial dislocations and their occurrence reveals the low stacking fault energy of cobalt, typically in the range 23-31 mJ/m 2 [START_REF] Korner | Weak-beam study of glide dislocations in h.c.p. cobalt[END_REF]. In order to go further into the plasticity mechanisms, it is of major importance to consider the mechanisms linked to gliding and those due to twinning. In general for hcp -12 -metals, strain mechanisms in small grain specimens are driven by slip processes whereas for larger ones deformation twinning becomes predominant [START_REF] Stanford | Deformation twinning and the Hall-Petch relation in commercial purity Ti[END_REF]. These two deformation mechanisms can be evidenced and studied by considering work-hardening plots issued from monotonous tensile curves. It can be considered, in first approach, a linear relationship between θ and ε in stages A and B, represented by corresponding slopes ∆A and ∆B. Both slopes are negative highlighting the general decrease in work hardening rate with plastic deformation.

Mechanical behavior of cobalt in tension. Impact of the t/d ratio

However, this effect is much pronounced when slip mechanisms predominate. As shown in Fig. 5, ∆A also strongly decreases (in absolute value) with t/d ratio, together with the work hardening rate θ0 at the beginning of the plasticity (i.e. for a plastic strain of 0.002). In the twinning stage, ∆B remains more or less independent of t/d ratio.

Effect of the t/d ratio on the HP relationship

Based on the monotonous tensile curves exhibited in Fig. 4, HP plots are illustrated Fig. 6, for various plastic deformations and three thicknesses. Two distinct linear regimes are evidenced for the 0.5 mm thick specimens (Fig. 6 -15 -

The evolution of the ratio km/kp with the strain presents two distinct stages (Fig.

7(a)

). It remains constant until ε = 0.025 and strongly increases for higher values of the strain. This could be related to the modification of the straining mechanisms with the generalization of twinning process, more sensitive to grain size than slip mechanisms [START_REF] Ghaderi | Sensitivity of deformation twinning to grain size in titanium and magnesium[END_REF][START_REF] Kumar | Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study[END_REF]. The value of σ0 in the multicrystalline regime (called σ0m) is of the order of a few MPa at the yield stress, related to the critical resolved shear stress in the basal plane of hcp ideal structures [START_REF] Hutchinson | A minimum parameter approach to crystal plasticity modelling[END_REF]. The ratio σ0m/σ0p is always less than the unity, increases with the deformation (Fig. 7(b)), and tends to saturate at higher strain levels with the generalization of the twinning process. The difference between the mechanical behavior of multicrystals and polycrystals in slip regime is then reduced with strain in accordance to previous observations concerning nickel [START_REF] Keller | Hall-Petch behaviour of Ni polycrystals with a few grains per thickness[END_REF], aluminum [START_REF] Janssen | An experimental assessment of grain size effects in the uniaxial straining of thin Al sheet with a few grains across the thickness[END_REF], or copper [START_REF] Hug | Temperature dependence and size effects on strain hardening mechanisms in copper polycrystals[END_REF] and for surface and core regions of copper single crystals [START_REF] Fourie | The flow stress gradient between the surface and centre of deformed copper single crystals[END_REF]. -16 -HP plots for cobalt samples with a thinner thickness of 250 µm are displayed in Fig. 6(b) for several deformations. For this thickness, the t/d ratio ranges between 1 and 3.5

(Table I). Experimental results clearly show two distinct domains which correspond to the transition between multicrystalline and quasi single crystalline regimes. There are separated by a second t/d critical value of around 2.5, which is independent on the strain level. This second critical value was found around unity for nickel [START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF], and around 2 in Ni-20Cr alloy [START_REF] Rudloff | Etude des mécanismes de transition volume / surface du comportement mécanique d'un alliage Ni20Cr[END_REF], and seems to slightly increase with a decrease in stacking fault energy. The slope of HP plots is very weak for quasi single crystals. In these samples, grain boundaries are mainly normal to the tensile direction, forming a so-called "bamboo-like" microstructure [START_REF] Janssen | Processing induced size effects in plastic yielding upon miniaturisation[END_REF]. It was demonstrated that this grain boundary configuration does not act as strong obstacles to the dislocation slip mechanisms [START_REF] Sutou | Effect of grain size and texture on pseudoelasticity in Cu-Al-Mn-based shape memory wire[END_REF]. For 125 µm in thickness samples, t/d ratio is in the range 2.2-4.2. Despite a fewer number of experimental points concerning grain size, HP plots exhibit a single linear behavior independently of the deformation (Fig.

6(c))

, with slope values in agreement with the multicrystalline regime.

Fig. 8 displays an overview of the HP law at the yield stress for four thicknesses and a large range of grain size. The multicrystalline regime delimited by the two critical t/d ratio is clearly evidenced despite the scattering of the stress values. In this regime, cobalt experiences a strong softening of its yield stress, of around 40%-50% of the corresponding polycrystalline value. The transitions surprisingly appear for a given grain size, respectively around 30 µm for the first transition and 90 µm for the second one, independently of the thickness, leading therefore to different critical t/d ratio (see inset in Fig. 8).

Evolution of the strengthening parameters with t/d ratio

The initial work hardening rate θ0 at the beginning of the plasticity (i.e. for a plastic strain of 0.002, see Fig. 5) exhibits three distinct stages with a decrease in t/d ratio (Fig.

9(a)

). These stages are delimited by critical t/d ratio taking values in the same order than those depicted in HP plots. However, these critical parameters are independent of the thickness of the samples, highlighting a purely t/d effect on strengthening mechanisms of cobalt. In the polycrystalline regime (t/d higher than a critical value around 10-15), the slope ∆A of the first stage decreases when the grain size increases (Fig. 9(b)), due to the impact of the grain size on the basal slip mechanism in hcp crystals [START_REF] Britton | On the mechanistic basis of deformation at the microscale in hexagonal close-packed metals[END_REF]. ∆A decreases more These mobile dislocations were identified as <a>-type basal perfect dislocations. Sessile <c>-type dislocations in dipolar configurations, lying in the prismatic planes, are also sometimes observed [START_REF] Fleurier | Etude des transitions volume / surface des propriétés mécaniques du cobalt de haute pureté. Influence des mécanismes de glissement et de maclage[END_REF]. There are less frequently encountered than <a>-type ones. shows several twins with lenticular morphology. A typical selected diffraction pattern used for the identification of twins is also depicted in the same figure. The rotation between the hole of the thin foil in order to avoid artificial free surface effects. They are also single layers, with all dislocations in the same slip plane, and single-ended, with a source supposed close to a grain boundary and a pile-up against a grain or twin boundary [START_REF] Li | The role of dislocations in the flow stress grain size relationships[END_REF]. For each pile up, the total number of dislocations n and their length L were measured. Gliding mechanisms being only activated in the basal plane of cobalt, the value of L was computed taking into account the angle between the observation direction and the [0001] direction.

Despite the scattering of measurements, ∆τ is found slightly higher in multicrystals (60 ± 20 MPa on average) than in polycrystalline specimens (45 ± 20 MPa on average). For a similar value of strain in stage A, higher mechanical work is then necessary to pile-up dislocations against boundaries in multicrystals.

Surface effects in multicrystalline samples

Nanoindentation measurements performed across the thickness of multicrystalline samples plastically strained in stage A exhibit a strong decrease in hardness close to the free surfaces (Fig. 13(a)).

The sample corresponding to polycrystalline state and strained in stage A presents an average hardness of 2.8 GPa all across the thickness with no pronounced surface effects (Fig. 13(b)). When it comes to multicrystal sample, in the core region, the same average value of hardness than in polycrystal is observed. However, a significant decrease in hardness on the 100 µm closer to the free surface is highlighted in Fig. 13(b). In this case, taken into account the sample characteristics (t/d = 5 and t = 500 µm), this feature suggests -25 -that the corresponding stress gradient is only observed in the grain emerging on the free surface. Surface effects can be captured using an analytical composite model, following previous works of Yang et al [START_REF] Yang | Yield stress influenced by the ratio of wire diameter to grain size -a competition between the effects of specimen microstructure and dimension in micro-sized polycrystalline copper wires[END_REF]. These authors considered that grains in the surface region behave differently than in the core leading to a mechanical softening of the material close to the free surface. Considering fs, the volume fraction of the material affected by the surface softening and fc the volume fraction of core region, not affected by surface effects, the overall stress σ applied to the transverse section can be computed, in first approximation, using the mixture rule between surface and core areas [START_REF] Fourie | Soft surface effect in copper single crystals oriented for multiple glide and in polycrystalline copper[END_REF]:

= -. . + -/ / (4)
σs and σc are the flow stress inside surface and core areas, respectively. For flat plate geometry samples [START_REF] Shin | Specimen size effects on the weakening of a bulk metastable austenitic alloy[END_REF], the ratio σ/σc can be written under the following form:

0 0 1 = 1 -
In this equation, α is the number of grains affected by surface effects, β is the ratio between the flow stress of the surface regions over the core ones (β = σs/σc) and w is the width of the specimen, see inset in Fig. 14(a). Eq. ( 5) was used to fit the evolution of the stress level with deformation and t/d ratio. Results are given in Fig. 14 where each value of stress was normalized by the higher value σmax representative of the polycrystalline stage. It is shown in Fig. 14(a) that surface effects occur for t/d ratio around 15, in agreement with previous results. Moreover, this critical ratio is weakly dependent on the deformation, as observed in HP plots [START_REF] Fleurier | Size effects and Hall-Petch relation in polycrystalline cobalt[END_REF].

For each t/d ratio and a given level of deformation, best fits of experimental values are obtained for specific values of α and β. Fig. 14(b) shows that for a polycrystal, α and β are close to 0 and 1, respectively, independent of the deformation, indicating that no surface effects occur. For multicrystals, α is maximal at the yield stress with values around 1.2 for t/d = 5 for instance. More than one grain is then affected by size effects when cobalt begins to deform plastically. Surface effects become less pronounced when the deformation increases (α decreases up to 0.5), in agreement with experimental results concerning work affected by the t/d ratio, with a critical value around 12, of the same order than that one found for HP law. Twinning mechanisms are not impacted by such size effects, even if twins are more present in large grain size specimens than in small ones [START_REF] Martinez | Characterization of deformation twinning in polycrystalline cobalt: A quantitative analysis[END_REF].

The size effects in fcc metals were previously closely linked to the stacking fault energy and the ability of cross slip mechanisms during the work hardening [START_REF] Hug | Size effects and temperature dependence on strain-hardening mechanisms in some face centered cubic materials[END_REF]. Precedent results concerning nickel [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF][START_REF] Keller | On the origin of the stress decrease for nickel polycrystals with few grains across the thickness[END_REF] and copper [START_REF] Hug | Size effects and temperature dependence on strain-hardening mechanisms in some face centered cubic materials[END_REF][START_REF] Hug | Temperature dependence and size effects on strain hardening mechanisms in copper polycrystals[END_REF] also underlined the role of internal stress gradients which develop across the thickness of samples with a decreasing in t/d ratio. This leads to a progressive softening of the surface at the origin of the decrease of stress levels for multicrystals. The softening of the mechanical properties of fcc multicrystals can be attributed to surface effects, the surface becoming progressively softer than the core as the plastic straining proceeds [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF]. The physical origin of this softening can be found in the variation of the diameter of cell dislocations between surface and core, higher in the former case than in the latter. The internal stress level being inversely proportional to the cell diameter [START_REF] Kuhlmann-Wilsdorf | Theory of plastic deformation: properties of low energy dislocation structures[END_REF], a gradient of internal stresses progressively takes place through the thickness leading to the overall softening of the mechanical properties.

The low stacking fault energy of cobalt combined with its restricted glide system number imply that this metal is very sensitive to the reduction of the t/d ratio. The composite model of Shin et al [START_REF] Shin | Specimen size effects on the weakening of a bulk metastable austenitic alloy[END_REF] coupled to nanohardness measurements also highlight an impact of the free surfaces for multicrystalline cobalt. Mechanical softening is mainly detectable during the stage A of work hardening, driven by slip mechanisms in the basal plane.

To better understand the modification of dislocation glide character between polycrystals and multicrystals, work hardening curves of cobalt can be modeled by a one--29 -parameter model such as that one developed by Mecking [START_REF] Mecking | Description of hardening curves of fcc single and polycrystals[END_REF], Kocks and Mecking [START_REF] Kocks | Physics and phenomenology of strain hardening: the FCC case[END_REF] or Estrin and Mecking [START_REF] Estrin | A unified phenomenological description of work hardening and creep based on one-parameter models[END_REF]. We have shown in previous works how this model can be successfully used for the study of size effects in fcc materials [START_REF] Keller | Kocks-Mecking analysis of the size effects on the mechanical behavior of nickel polycrystals[END_REF]. In this model, the work hardening is issued from a competition between the progressive storage of dislocations and their annihilation [START_REF] Sevillano | Flow stress and work hardening[END_REF]. Following the formulation given by Malygin [START_REF] Malygin | Dislocation Density Evolution Equation and Strain Hardening of f.c.c. Crystals[END_REF], the general equation of accumulation of dislocations in single crystals, represented by the dislocation density ρ, with the strain γ, takes the following form:

; < = = > + = ? @A -= B A (6)
κm = 1/(bΛ) is the coefficient of multiplication of dislocations in the easy glide stage, when all dislocations slip along one activated gliding system. b is the Burgers vector modulus and Λ the mean free path of mobile dislocations. The second term in the right side of Eq. ( 6) is an accumulation term related to the athermal storage of mobile dislocations, and the last one is an annihilation component associated with recovery mechanisms such as cross slip.

κf and κa are corresponding constant materials.

The use of this equation can be extended to the case of hexagonal materials if slip mechanisms predominate [START_REF] Qiao | Effects of grain size, texture and twinning on mechanical properties and work-hardening behaviors of pure Mg[END_REF][START_REF] Král | Softening during Deformation of Zr Alloys[END_REF]. The strain hardening of polycrystals can then be studied by the following relationship:

C -D EF = & G H I J K L M= > + = ? 6 0'0 N O4 9 -= B 6 0'0 N O4 9 P (7)
-30 -σy is the yield stress, αT is a material constant linked to the dislocation arrangement, M is the Taylor factor. The work hardening curves of cobalt can therefore be modeled by a three parameters (A, B and C) adjusted equation [START_REF] Fleurier | Etude des transitions volume / surface des propriétés mécaniques du cobalt de haute pureté. Influence des mécanismes de glissement et de maclage[END_REF]:

F = Q 0'0 N + R -SC -D E (8)
An example of such a fitting is given in Fig. 15

T = & G H I J KL = > (9)
This leads to an expression for the mean free path of mobile dislocations: µm. When t/d becomes lower than the critical ratio (t/d)c = 14, a strong increase of Λ is evidenced. This result is similar than that one reported in multicrystalline nickel [START_REF] Hug | Intrinsic Effects due to the Reduction of Thickness on the Mechanical Behavior of Nickel Polycrystals[END_REF], and numerically predicted by Kocks -Mecking analysis [START_REF] Keller | Kocks-Mecking analysis of the size effects on the mechanical behavior of nickel polycrystals[END_REF]. The slip characteristics in the stage A of work hardening are then deeply modified in the multicrystalline regime. Indeed, increasing the mean free path of dislocations would imply an overall softening of the mechanical properties.

Λ = O V 4 W # # Q (10)
To sum up, the mechanical softening in cobalt multicrystals strongly modifies the yield stress with a pronounced three stages on the HP law (Fig. 8). This softening is also evidenced by an initial strain hardening rate θ0 smaller for multicrystals than for polycrystals (Fig. 9 Cobalt multicrystals are then initially softer from a mechanical point of view. When plastic strain occurs, dislocation activity is more important, in good agreement with the increase of the mean free path below the critical t/d ratio (Fig. 15(b)). The internal stress generated around pile-ups by this dislocation activity is then slightly higher in multicrystals, as computed using TEM observations. The overall softening of the mechanical properties of cobalt multicrystals is then due to very strong surface effects, which compensate the small increase of internal stress in the volume. Such effects are the consequence of the greater dislocation mobility, as shown by the increase of the mean free path. Dislocations are able to escape through free surfaces, especially when the grain size is larger. With the generalization of twinning, twins develop also on the free surface of samples. These twins prevent the escape of dislocations. Mechanical behavior of multicrystals and polycrystals tend to become similar when the deformation level is enough for activating the second stage of the work hardening.

Conclusion

In this work, the mechanical properties of cobalt were reported for a wide range of grain size and for several sample thicknesses. The transition between polycrystalline and multicrystalline behavior has been demonstrated, occurring for critical number of grains through the thickness of the order of 13-15. The mechanical behavior of cobalt is strongly impacted for t/d ratio less than this critical value, both from the point of view of the hardening effect of the grains, related to a strong modification of the HP law, and of dislocation hardening mechanisms in the basal slip stage. It was also demonstrated that the size effects tend to disappear when twinning mechanisms become predominant.

As in fcc metals, the size effects depicted in cobalt traduce the existence of an important surface effect inside the samples with less than 13-15 grains through the thickness. The dislocation activity was found to be greater in cobalt multicrystals, leading to denser and smaller dislocation pile-ups, generating larger internal stresses. Surface effects, therefore, compensate these larger levels in multicrystals, leading to their overall softening in terms of mechanical properties.

The origin of the strong softening of cobalt at the beginning of plasticity, however, remains unclear. In particular, the role played by nonlinear elasticity during elastic loading and in the microyielding stage needs to be better understood and should be the subject of future research.

Figure 1 -

 1 Figure 1 -General overview of the microstructure of cobalt, unstrained state. (a) Grain size across the thickness, SEM, t/d = 14. (b) EBSD IPF map of the hcp phase, t/d = 14. (c) Cartography representing in red the hcp phase and in green the fcc one (t/d = 19). (d) Amount of residual fcc phase with the holding time of annealing at T = 1100 °C, for three thicknesses of cobalt samples.

Fig. 2

 2 Fig.2represents the c-axis pole figures for cobalt specimens with various t/d ratio.

Figure 2 -

 2 Figure 2 -Pole figures for annealed cobalt samples with various t/d ratio.

Figure 3 -

 3 Figure 3 -Stacking faults observed in (a) hcp and (b) fcc phases of unstrained cobalt.

Figure 4 -Figure 4

 44 Figure 4 -Typical true stress -true strain curves obtained in cobalt with various t/d ratio and a thickness of (a) 700 µm, (b) 500 µm, (c) 250 µm and (d) 125 µm.

Figure 5 -

 5 Figure 5 -Examples of hardening curves for polycrystalline (t/d = 22), multicrystalline (t/d = 7) and quasi single crystalline (t/d = 3) cobalt with corresponding work hardening stages.

  Figure 5 displays typical work hardening curves θ(ε) = dσ/dε for polycrystalline, multicrystalline and quasi single crystalline specimens with θ the work hardening rate. All curves exhibit a nonlinear elasticity regime (not studied in this work) followed by two distinct hardening stages A and B, separated by a threshold stress σAB. These stages are traditionally encountered in hcp structures and are linked to gliding mechanisms and twinning processes, respectively.

  (a)), from the very beginning of the plasticity. The two regimes correspond to the polycrystalline and the multicrystalline -13 -behaviors. A linear regression on the two regimes allows us to compute the HP coefficients k and σ0 of the HP relationship, which links the flow stress σ to the strain level ε and the grain size d [49]: = + √ (1) σ0(ε) and k(ε) are material parameters and function of the strain. For the yield stress (εp = 0.002), when t/d ratio is higher than a critical value (t/d)c = 14, HP constants for cobalt in the polycrystalline regime take values kp = 245 MPa.µm 1/2 and σ0p = 211 MPa, in accordance with the few experimental results available in open literature [50]. When t/d < 14, k takes higher values (km = 1590 MPa.µm 1/2 ) than for polycrystalline specimens, indicating a much more pronounced grain size dependence of the stress in this so-called multicrystalline regime.

Figure 6 -

 6 Figure 6 -(a) HP plots for several deformations showing the transition between polycrystalline and multicrystalline behaviors (t = 500 µm) (following [51]). In inset, definition of the two distinct stages in HP plot at the yield stress. (b) HP plots for 250 µm in thickness cobalt for different deformation levels showing the transition between multicrystalline and quasi-single crystalline behaviors. (c) HP plots for 125 µm in thickness cobalt exhibiting a multicrystalline single regime in the overall studied ranges of grain size and plastic deformation.

Figure 7 -

 7 Figure 7 -Evolution of the HP coefficients with deformation for 0.5mm in thickness samples. (a) Ratio km/kp and (b) ratio σ0m/σ0p vs deformation ε.

Figure 8 -

 8 Figure 8 -Initial HP plots for four distinct thicknesses showing the existence of the three crystalline configurations. In inset, evolution of the critical t/d ratio between multicrystalline and polycrystalline stages in function of the thickness.

- 18 -

 18 significantly when t/d decreases below the first critical t/d ratio, revealing the size effect on slip process in the multicrystalline regime. By contrast, the slope ∆B of the second work hardening stage, driven by twinning mechanisms, remains roughly constant with t/d ratio (Fig.9(b)). Its value is very weak, around 5000 MPa, and the experimental dispersion does not allow highlighting several distinct stages.

Figure 9 - 3 . 5 .

 935 Figure 9 -Evolution of the hardening parameters with t/d ratio computed from Fig. 5. (a) Initial work hardening rate θ0, (b) absolute values of slopes ∆ in stages A and B, (c) stress transition σAB between stages A and B.

Figure 10 -

 10 Figure 10 -Microstructural features of gliding mechanisms in cobalt. (a) Slip lines against twins in the beginning of plastic strain, confocal microscopy observation of a multicrystal. (b) Two examples of dislocation pile-ups representative of slip mechanisms in stage A of cobalt polycrystals.

Figure 11 -

 11 Figure 11 -Microstructural features of twinning mechanisms in polycrystalline cobalt. (a) Twinning generalization in fractured samples observed in optical microscopy. (b) Image Quality map of twins in stage B, the extension twins highlighted in red represent the 101 2 mode. (c) TEM image of 101 2 twins, and identification by electron diffraction. The diffraction pattern of the matrix (represented in green) and the twin (represented in yellow) are superposed and show a rotation about the 〈12 10〉 axis of ∼ 86°.

Figure 13 -

 13 Figure 13 -(a) Normalized hardness values through the thickness of a multicrystal sample not deformed and strained in stage A. (b) Hardness profiles through the thickness of polycrystalline and multicrystalline samples plastically strained in stage A (t = 500 µm). Errors bars in Fig. 13(a) are of the same order of magnitude than in Fig. 13(b).

  (a). The fitting procedure is robust and stable, weakly dependent on the initial values of A, B and C. B and C are related to κf and κa, representing multislip gliding and twinning processes, respectively. In the first work hardening stage of cobalt, driven by basal slip mechanisms, the parameter A is especially of interest. It is related to the coefficient of multiplication of dislocation in single slip regime κm by the equation:

Figure 15 -

 15 Figure 15 -(a) Modeling of the work hardening curve of cobalt by using Eq. (8) (t/d = 13). (b) Evolution of the mean free path of dislocations in stage A with the t/d ratio for cobalt specimens of thickness 500 µm.

Fig. 15 (

 15 Fig. 15(b) displays the evolution of Λ with t/d for cobalt samples of 500 µm in thickness. Λ was computed using αT = 0.3, which holds for pile-ups configurations, M = 2.3, considering basal glide of a hcp material moderately textured [76], µ = 83.5 GPa and b = 0.25 nm. Λ remains constant for polycrystalline specimens, around a mean value of 1.5

  (a)) and remains present in the first work hardening stage (Fig. 9(b)).

Table I .

 I Extreme values dmin and dmax of mean grain sizes obtained by annealing of cobalt with various thicknesses t (standard deviation is about one-half of the grain size) associated with their corresponding t/d

	three and six mechanical tests were carried out for each metallurgical state and average
	stress values were reported on HP plots and work hardening curves. As mentioned in
	previous works of our group [18, 45], a	statistical test was systematically performed on
	the least square regression considering one or two different stages for HP plots. An error
	bar of 5% was associated with each stress measurement in agreement with the experimental
	scattering analysis. Supplementary interrupted tensile tests were performed at different
	stages of strengthening, to analyze the deformation mechanisms using optical and electron
	microscopy. Nanoindentation measurements through the thickness of some samples, using
	a staggered matrix, were performed with a MTS XP nanoindentation device to capture the
	ratio ranges.
	softening effect of free surfaces in multicrystalline specimens. Berkovich diamond tip
	t (µm)	dmin (µm)	dmax (µm)	t/d range
	125	30	57	2.2 -4.2
	250	72	248	1 -3.5
	500	10	119	4.5 -44
	700	10	112	6 -70
	Uniaxial monotonous tensile experiments were carried out up to fracture, using an
	Instron 5569 (Norwood, MA, USA) universal testing machine, on dog bone shaped samples
	with a gauge length of 20 mm. Strain measurements were achieved by a clip-on
	extensometer for all thicknesses except for the 125 µm thickness, for which a laser
	extensometer was used to avoid buckling and surface fracture initiator. The strain rate was
	maintained in the range (10 -4 -10 -3 ) s -1 using a constant crossing head speed of 1 mm/min.
	All tests were performed with the tensile axis aligned with the rolling direction. Between

Acknowledgments

Part of the experimental work was performed in the PhD work of Gwendoline Fleurier, Normandie Université, UNICAEN, 2016.

matrix and the twin about the 〈12 10〉 axis is 86°, so that this correspond to a 101 2 twin type.

Decreasing the t/d ratio clearly affect the gliding mechanisms in stage A as evidenced by the evolution of the work hardening parameters (Fig. 9). Such size effects are much less sensitive in stage B because twining mechanisms lead to a refinement of the microstructure and grain size is no longer the pertinent length scale. Pile-ups are the more frequent dislocation arrangement in stage A of polycrystals, due to the low stacking fault energy of cobalt. When the t/d ratio is reduced below the multicrystal critical value, pileups remain present as revealed by TEM observations, but are shorter in length and contain more dislocations in average. This feature suggests a significant different work hardening process operating in cobalt when t/d falls below the critical ratio.

In front of pile-ups, an internal stress develops, which can be roughly estimated based on the geometrical properties of the dislocation arrangement (Fig. 12). -23 -Knowing the length L of a pile-up and their number n of dislocations, the internal stress in front of pile-ups can be represented by the local activation shear stress ∆τ, computed with the relation [START_REF] Cai | Imperfections in crystalline solids[END_REF][START_REF] Friedel | Dislocations[END_REF]:

∆τ = τ -τi with τ the applied shear stress in the slip plane and along the slip direction, and τi the minimum internal stress needed to move dislocations along the slip direction. The constant K depends on the screw or edge character of the dislocations. For each pile-up, an image can be obtained using different diffraction vectors and the [0001] zone axis of the corresponding grain. The orientation of the Burgers vector of the dislocations inside pileups can be therefore identified. These dislocations are always of mixed character with an angle ϕ ≅ 30° between Burgers vector and unit line vector. For such mixed dislocation in an isotropic medium, K takes the following form [START_REF] Hirth | Theory of dislocations[END_REF]:

Discussion

The stronger reduction in stress depicted in HP plots with decreasing grain size when t/d is in the range 2.5-14 (multicrystalline range) is due to a size effect, which appears at the end of the elasticity. It was shown in a previous paper [START_REF] Fleurier | Size effects and Hall-Petch relation in polycrystalline cobalt[END_REF] that the transition between polycrystals and multicrystals takes place during the microyielding stage of loading. This transition was also recently highlighted by measurements of the magnetic coercive field [START_REF] Hug | Size effects and magnetoelastic couplings: a link between Hall-Petch behaviour and coercive field in soft ferromagnetic metals[END_REF]. Concerning strengthening, all parameters representative of gliding process are