Bastien Radola

Maxence Giraudet

Igor Bezverkhyy

Jean Marc Simon

José-Marcos Salazar

Mathieu Macaud

Jean Pierre Bellat
email: jean-pierre.bellat@u-bourgogne.fr

New force field for GCMC simulation of D2/H2 quantum sieving in pure silica zeolites

We report a study on adsorption and coadsorption of H2 and D2 in FAU, MFI and CHA pure silica zeolites having different pore size and shape. Adsorption capacities, selectivities, enthalpies and entropies are determined by combining experiments and GCMC simulations. We show that the force fields available in the literature cannot predict the adsorption equilibria below 77 K with sufficient accuracy. Here we propose a new force field adjusted by using our experimental data obtained for pure silica MFI zeolite at 65 K and 77 K. With this new force field, it is possible to predict adsorption and coadsorption equilibria on the three zeolite structures in a temperature range between 47 and 77 K with satisfactory precision. We corroborate that the step appearing on the single adsorption isotherms in CHA is the result of a molecular rearrangement of the adsorbed phase due to the apparition of a new adsorption site characterized by weaker interactions of H2 with the adsorbent. We conclude that the quantum sieving of H2 and D2 does not depend only on the pore size but also on the pore shape, in particular, at high loading when the confinement effects become important.

Introduction

Over the last two decades, the interest in adsorption of hydrogen isotopes at cryogenic temperature has considerably growth in the nuclear industry. The development of new sources of energy based on nuclear fusion (ITER) will use and produce considerable amounts of hydrogen isotopes, which need to be recycled 1 . A promising way to recover and separate these isotopes at low cost is physisorption on nanoporous solids at cryogenic temperature (20 -100 K). One of the driving force for hydrogen isotopes separation is quantum sieving, which appears when the size of the adsorbed molecule (diameter of hydrogen = 0.28 nm) is close to the pore diameter. This phenomenon occurs at low temperature (below 100 K) and makes that heavier molecules are strongly adsorbed and diffuse faster in the nanoporosity. As shown by Beenakker et al. 2 , the smaller the pore radius, the higher the adsorption selectivity for the heaviest isotope is. The separation processes of hydrogen isotopes by adsorption that we are developing are based on the TSA (Temperature Swing Adsorption) technology [START_REF] Ruthven | Principles of adsorption & adsorption processes[END_REF] . They use a fixed bed adsorbent column working between 30 and 80 K under a pressure close to 10 5 Pa.

From a practical point of view, these separation processes require a porous adsorbent with two main properties: (1) the pores have to be small enough to be selective towards the heavier isotope and (2) the adsorption capacity has to be high enough in order to use a reasonable volume of adsorbent and then reduce the size of the adsorbent column under cryogenic temperatures. Therefore, the choice of the adsorbent is based on a subtle balance between adsorption selectivity and adsorption capacity in the operating conditions of separation process.

Numerous potential nanoporous materials able to separate hydrogen isotopes by quantum sieving have been already identified either from adsorption experiments or by molecular simulations, namely: carbons, zeolites and MOFs. These last, have attracted a particular attention [START_REF] Kim | [END_REF] and have been the subject of a considerable number of studies for estimating their capacity to selectively trap the isotopes. However, it is still difficult to establish a ranking of these adsorbents as a function of their selective adsorption properties towards hydrogen isotopes. The reason is just the lack of accurate experimental data at cryogenic temperatures (T < 77 K).

Carbons nanotubes and sieves show interesting D2/H2 adsorption selectivities, with values up to 16 at 40 K under 10 5 Pa, when using small pores ( < 0.56 nm) 5,6 . It has also been shown that the selectivity greatly depends on the pore geometry. Moreover, significant differences have been observed between slit pores and nanotubes. However their adsorption capacity, around 0.005 mol.g -1 under these conditions [7][8][9] , are too small for being used in industrial applications.

MOFs are very interesting adsorbents due to their well-defined pore structure which can be tuned by changing the length of the organic chains linking the inorganic units 10 . It is also possible to enhance their selective adsorption properties by changing the chemical nature of linkers or metal. In addition, the adsorption of heavier isotopes can be improved by taking advantage of their specific properties like multimodal porosity and framework flexibility. Some MOFs present excellent D2/H2 adsorption selectivity with value around 10 at 40 K like for the well-known flexible MIL-53(Al) 11 . Even the partially fluorinated metal-organicframework, so-called FMOFCu, can show selectivity values up to 14 at 25 K. This is a result of their capacity to open or close the pores as a function of temperature 12 . Unfortunately, the adsorption capacities of these materials are very low: 0.002 mol.g -1 for MIL-53 (Al) at 40 K and only 0.0005 mol.g -1 for FMOFCu at 25 K under 10 3 Pa. Like for carbon materials, such adsorption capacities are insufficient for industrial applications. Moreover, the use of organic material could be hazardous for nuclear applications due to possible isotope exchanges with the matrix. As a consequence, the use of inorganic porous materials is strongly suggested.

Among them, zeolites are promising adsorbents. Owing to their tunable chemical composition and regular porosity, they get both large hydrogen adsorption capacities and interesting adsorption selectivities in favor of deuterium. These properties are strongly dependent on the pore structure and nature of compensation cations [13][14][15][16][17] . For cationic FAU zeolites, D2/H2 selectivity can vary from 3 to 6 according to the compensation cation at 77 K and low pressure (a few hPa) corresponding to low loading 18 . However, under 10 5 Pa, which is close to the operating pressure of an adsorption process, the selectivity value is rather low, it does not exceed 2 whatever may be the chemical composition. Although it could seem insufficient in comparison with other materials (MOF, carbon). This is compensated by large adsorption capacities (up to 0.009 mol.g -1 at 77 K under 10 5 Pa with NaX 18 ), such that this material is a good candidate for separation processes. Recent Monte-Carlo simulations have shown that non-cationic zeolites could present very high adsorption selectivity 19 . In this work, the authors performed a systematic screening of H2/D2 mixtures over a large variety of synthesized and hypothetical pure silica zeolites of different topologies. For example, the BCT zeolite shows an adsorption selectivity towards deuterium of around 80 at 40 K under 10 5 Pa, conditions which are close to those of a separation process. This zeolite is made of a one-dimensional pore system formed by 8-membered oxygen ring (8MR) parallel channels of 0.38 nm diameter. However, the adsorption capacity of BCT is low, around 0.003 mol/g, which is almost ten times lower than for the NaX zeolite at 40K. Such an adsorption capacity is not enough to consider the development of a viable adsorption process with this type of adsorbent.

It may be noted that (i) the predictions obtained by molecular simulations have not been yet validated by coadsorption experiments and (ii) the pure silica BCT zeolite is not thermodynamically stable 20 . Anyhow, this study shows that high silica zeolites having very small pore composed of 8-membered oxygen rings could be potentially selective adsorbents for the separation of hydrogen isotopes. Henceforth, it appears relevant to study in more details the coadsorption of hydrogen isotopes in pure silica zeolites by combining adsorption experiments and molecular simulation.

Molecular simulations based on Monte Carlo method are a very useful tool for studying the adsorption properties and for the development of a separation process by adsorption 21 . First, as mentioned above, it allows screening of potential selective adsorbents without having to do long and tedious coadsorption experiments. Second, it gives rich information about the coadsorption mechanism at a molecular level, rather difficult to access at cryogenic temperatures. Third, it allows the prediction of coadsorption equilibria of radioactive isotopes like T2 or HT which can hardly been investigated experimentally. Nonetheless, the choice of the molecular model and the force field must be validated by accurate adsorption and coadsorption experimental data obtained with H2 and D2 on well characterized adsorbents.

Concerning the zeolites, several molecular simulations of adsorption and diffusion of hydrogen and deuterium are described in the literature [22][23][24][25][26][27] . They have been performed with Monte Carlo or Molecular Dynamics methods using different force fields including the Feynman-Hibbs variational approach to take into account quantum effects. Different force fields are used in the literature to describe the adsorption of hydrogen and deuterium in cationic and pure silica zeolites. However, these simulations are compared only with adsorption data of single components measured on few zeolites (NaX, Rho, silicalite-1, Si-LTA) at 77 K or higher temperatures. As far as we know, only few works report a comparison of simulated and experimental adsorption selectivities below 77 K. Probably this is due to the lack of coadsorption experimental data 22,28,[START_REF] Radola | Chemical Communications[END_REF] . Therefore, the achievement of new coadsorption experiments of hydrogen isotopes below 77 K is also an opportunity to test the force fields presented in the literature and their transferability among zeolitic structures having different pore geometry, but the same chemical composition.

The present work deals with the adsorption and coadsorption of hydrogen and deuterium in three pure silica zeolites: FAU, MFI and CHA. These zeolites differ by their pore geometries (form and aperture) but have the same surface chemistry. Single gas adsorption isotherms and adsorption selectivities of binary H2 + D2 mixtures have been measured between 35 and 77 K under 10 5 Pa. Experimental data are compared with the Grand Canonical Monte-Carlo (GCMC) simulations performed with different force fields to verify if the models describe accurately the zeolite, the gas and their interactions and if necessary to improve them.

Experimental

High silica Zeolites

Three framework types of high silica zeolite were studied: FAU, MFI and CHA. These zeolites can be elaborated at the industrial scale. All were pulverulent and free of binder.

Silica FAU was purchased from Degussa (Germany) under the reference DaY. It was obtained by dealumination of the NaY zeolite. Silica MFI was the silicalite-1 elaborated by the company Zephir-Alsace (Mulhouse, France). It was synthesized in fluoride media according to the procedure described by Guth et al. [START_REF] Guth | Studies in Surface Science and Catalysis[END_REF] . Silica CHA was kindly provided by J.

Patarin from IS2M laboratory (Mulhouse, France). The zeolite was prepared using the method described by Díaz Cabañas et al. [START_REF] Díaz-Cabañas | [END_REF] . These materials have been extensively characterized by XRD, FTIR, SEM, NMR and N2 adsorption in our previous works [START_REF] Radola | Chemical Communications[END_REF]32,33 . Silica MFI is perfectly crystallized with right morphology and microporosity and without silanol defects.

FAU and CHA have also a good crystallinity though they contain a few mesopores and a few sodium cations are present in FAU.

These silica materials differ by their pore geometries: FAU has quasi-spherical cages (Ø = 1.1 nm) with an aperture diameter of 0.74 nm (12MR), MFI has interconnected cylindrical channels of around 0.56 nm diameter (10MR) and CHA has cylindrical shaped cages (~ 0.8 x 1.1 nm) interconnected with windows of 0.37 nm diameter (8MR). Some physical-chemical characteristics of these silica zeolites are given in Table 1.

Adsorption and coadsorption manometric devices

Adsorption isotherms of single components were measured with a ASAP 2020 Micromeritics sorptometer equipped with a Gifford -McMahon He cryocooler. Adsorption experiments were performed between 47 and 77 K for pressures ranging from 0.1 to 10 5 Pa. Prior to adsorption, the sample (~ 100 mg) was outgassed at 673 K under secondary vacuum overnight.

H2 and D2 (purity > 99.9 %) gases were purchased from Air Liquide (France) and were additionally dried using zeolite filled cartridges.

Adsorption selectivity of deuterium with respect to hydrogen was measured from coadsorption experiments performed with a home-made manometric device coupled with a quadrupole mass spectrometrer OmniStar from Pfeiffer Vacuum. This apparatus and the procedure used have been described in our previous works 13,18 . The adsorption temperature was controlled with the cryocooler from Micromeritics. D2/H2 selectivities were measured for 25%D2 + 75%H2 mixture in the same conditions (temperature, pressure, outgassing…) as for single components. The relative precision of the measurements is of 5 % for the adsorbed amount and 15 % for the adsorption selectivity.

We remind that the adsorption selectivity of D2 with respect to H2 is defined by the relation:

𝛼𝐷 2 𝐻 2 ⁄ = 𝑥 𝐷 2 𝑦 𝐻 2 𝑥 𝐻 2 𝑦 𝐷 2 = 𝑁 𝐷 2 𝑎 𝑁 𝐻 2 𝑎 𝑃 𝐻 2 𝑃 𝐷 2 (1)
with x and y the mole fractions in the adsorbed and gas phase, respectively, N a the adsorbed amount expressed in molecules per unit cell (molec.uc -1 ) and P the partial pressure at equilibrium.

Molecular simulations

Grand Canonical Monte Carlo (GCMC) simulations were performed with the DL_MONTE package 34,35 . The applied conditions were similar to those of the experimental situations.

Under these conditions (47 ≤ T ≤ 77 K and P ≤ 10 5 Pa) the gas can be considered as ideal and, in this case, the fugacity is equivalent to the pressure. For convenience we fixed the fugacity instead of the chemical potential, in the GCMC input data.

The quantum effects arising at cryogenic temperature (T < 100 K) with hydrogen isotopes are included by using the Feynman-Hibbs approach [START_REF] Feynman | Quantum Mechanics and Path Integrals[END_REF][START_REF] Sesé | [END_REF] :

𝑉 𝐹𝐻 (𝑟 𝑖𝑗 ) = ( 6𝑀 𝑖𝑗 𝜋𝛽ℏ 2 ) 3 2 ∭ 𝑉(|𝑟 𝑖𝑗 + 𝑢|) +∞ -∞ 𝑒 -𝑢 2 ( 6𝑀 𝑖𝑗 𝛽ℏ 2 ) 𝑑𝑢 (2)
where Mij = mimj(mi + mj) -1 is the reduced mass of the interacting particles,  = (kBT) -1 with kB the Boltzmann constant, u the path involved and V(rij) is the classical interaction potential between a pair of particles. The analytical integration of this equation is practically infeasible.

To overcome this difficulty, the potential V(rij) is expanded in a Taylor series around r up to the 4 th order. After integration we obtain 38 :

𝑉 𝐹𝐻 (𝑟 𝑖𝑗 ) = 𝑉(𝑟 𝑖𝑗 ) + 𝛽ℏ 2 24𝑀 𝑖𝑗 ( 2 𝑟 𝑖𝑗 𝜕𝑉(𝑟 𝑖𝑗 ) 𝜕𝑟 𝑖𝑗 + 𝜕 2 𝑉(𝑟 𝑖𝑗 ) 𝜕𝑟 𝑖𝑗 2 ) + 1 2 ( 𝛽ℏ 2 24𝑀 𝑖𝑗 ) 2 ( 4 𝑟 𝑖𝑗 𝜕 3 𝑉(𝑟 𝑖𝑗 ) 𝜕𝑟 𝑖𝑗 3 + 𝜕 4 𝑉(𝑟 𝑖𝑗 ) 𝜕𝑟 𝑖𝑗 4 ) (3)
For a classical Lennard-Jones potential V(rij), Eq. ( 2) becomes:

𝑉 𝐿𝐽-𝐹𝐻 (𝑟 𝑖𝑗 ) =
The calculation of Feynman-Hibbs approach is implemented in the DL_MONTE Monte Carlo simulation package only to the 2 nd order. It has been shown that the expression given in Eq.( 4) (4 th order) is more accurate for confined fluids at cryogenic temperature 22 . For this reason we incorporated this correction in the DL_MONTE code.

For single gas adsorption, the insertion-deletion movements correspond to 50 % of the total moves and other movements correspond to translations. For mixtures, only 45 % insertiondeletion moves were used, the remaining 5 % being converted to identity-swap moves to accelerate the equilibration phase. Between 5 to 15 million Monte Carlo cycles, depending on the pressure, were necessary for reaching the equilibrium. And for data analysis 3 million simulation cycles were carried out. For each adsorption isotherm a total of 21 simulations were performed.

Zeolites and hydrogen isotopes

GCMC simulations were performed on pure silica FAU, MFI and CHA zeolites. Their structure was considered as rigid. Cell parameters and atomic positions were those given in the database of zeolite structures of the International Zeolite Association (IZA). The positions of the atoms inside the unit cell were relaxed by DFT (density functional theory) calculations namely with the VASP package, using the PBE-D3 exchange-correlation functional with dispersion corrections. The cut-off radius, above which the molecular interactions are neglected, was 1.5 nm. The simulation box was built with 8 (2x2x2), 12 (2x2x3) and 27 (3x3x3) unit cells for FAU, MFI and CHA zeolites, respectively.

Hydrogen isotopes were represented by a single sphere model with only one van der Waals interaction site per molecule and without electrical charge.

Force fields for adsorbate-adsorbate and adsorbate-adsorbent interactions

Two force fields given in the literature were used to describe the adsorbate -adsorbent (H2zeolite) and adsorbateadsorbate (H2 -H2) interactions. The first one was proposed by Deeg et al. 39 . It allowed a satisfactory modeling of the adsorption isotherm of hydrogen in all-silica ITQ-27 and MFI zeolites at 77 K. The second one, taken from Pantatosaki et al. 24 , gave a good prediction of adsorption isotherms of H2 and D2 in NaX zeolite at 77 K. Note that this latter force field uses only the H2 -O potential to describe the adsorbateadsorbent interactions. Then, we have developed a new force field, called here ASP (Adsorption sur Solides Poreux), by using the potential of Buch 40 for the H2 -H2 interactions and by adjusting the Lennard-Jones parameters of the H2-O and H2-Si potentials on our experimental data obtained below 77 K. In table 2 are given the parameters for the potential mentioned above.

Accuracy evaluation of the simulations

The deviation between the molecular simulations and the experiments is assessed by mean of the relative average deviation (RAD) defined by:

%𝑅𝐴𝐷 = 100 𝑁 ∑ | 𝑋 𝑒𝑥𝑝,𝑖 -𝑋 𝑠𝑖𝑚,𝑖 𝑋 𝑒𝑥𝑝,𝑖 | 𝑁 (5)
with 𝑋 𝑒𝑥𝑝,𝑖 and 𝑋 𝑠𝑖𝑚,𝑖 the values (adsorbed amount N a or adsorption selectivity 𝛼𝐷 2 𝐻 2 ⁄ ) measured and simulated in the same conditions. N is the number of computed values. We consider that values of RAD higher than 30 % are not acceptable. This upper limit is based on our experience in the field. We have performed a number of selectivity predictions from single adsorption isotherms by using the Ideal Adsorbed Solution Theory or extended Langmuir model for several binary systems (p-xylene and m-xylene in FAU, linear and branched paraffins in MFI, toluene and mercaptans in FAU, water and formaldehyde in FAU…). The accuracy of the selectivity determination is strongly dependent on the precision at which the adsorption isotherms are measured, simulated by GCMC or described by a classical adsorption model. Our results show that with a RAD above 30 % on single adsorption isotherm, the predicted adsorption selectivities are too much far from the experimental ones, with average deviation exceeding 100 % in some cases.

Results and discussion

Previous Force fields

Figure 1a shows the adsorption isotherms of H2 in FAU at 77 K and 47 K simulated with the force fields of Pantatosaki and Deeg (Table 2). The simulations are compared with our experimental data. The potential of Pantatosaki does not allow the prediction of the adsorption isotherms of H2 since they present a RAD of 82 % and 76 % at 77 and 47 K, respectively.

This force field does not take into account the H2 -Si interactions, which can explain in part the observed discrepancy. Similar results were obtained for D2. An enhanced agreement was obtained by using the force field proposed by Deeg. However, the relative average deviations are still high (RAD of 42 % and 30 % at 77 K and 47 K, respectively). The relative deviations are particularly large at low pressure (P < 10 4 Pa) where the GCMC simulations underestimate the adsorbed amounts but the fitting is better above this pressure. The difference could be attributed to the fact that our FAU zeolite is not completely siliceous since few sodium cations remain in the structure. Moreover, the dealumination treatment used to elaborate this material has created a few mesopores which can have hydroxyl groups on their surface. Cations and hydroxyl groups are known to be strong adsorption sites for hydrogen isotopes 18 .

For the MFI and CHA zeolite structures, the force field of Pantatosaki does not accurately describe the adsorption of hydrogen isotopes (RAD > 80 % at 77 K). This is illustrated in Figure 1b for the adsorption of H2 in CHA at 47 K (RAD > 42 %). The force field of Deeg can correctly predict the adsorption of H2 and D2 in MFI zeolite between 77 (RAD < 23 %)

and 47 K (RAD < 11 %). For CHA zeolite, it gives also reasonable predictions at 77 K (RAD = 31 %) but overestimates the adsorbed amounts at lower temperature when the pressure increases. Moreover, it does not reproduce the step in the adsorption isotherm, which appears at 47 K above 100 Pa despite a RAD of 27 % (Figure 1b).

These results show that the force fields described in the literature should be used with precaution. Notice that they have been validated with experiments performed essentially at 77 K or above and only for few zeolitic structures. Their use for lower temperatures and other zeolitic structures requires to be validated by experimental data at the same conditions.

Henceforth, the transferability of these force fields is questionable. This state of the art led us to develop a new force field to predict the adsorption and coadsorption of hydrogen isotopes in pure silica zeolites below 77 K.

New force field ASP

In our force field, called ASP, the H2 -H2 interactions are described with the L-J potential of Buch 40 . As can be seen in figure 2, this potential correctly describes the bulk fluid properties (density versus fugacity) of hydrogen between 40 K and 200 K, at the conditions that the Feynman-Hibbs corrections are used. The L-J parameters of potentials for the H2 -O and H2

-Si interactions have been adjusted on the adsorption experimental data of hydrogen on the silica MFI zeolite (Silicalite-1) measured at 65 K and 77 K (Table 2). We have chosen this zeolite because it is free of defects as hydroxyl groups or mesopores and these temperatures rather than 47 K because they are better controlled with our He cryocooler. Adsorption measurements at these temperatures are therefore more accurate. Figure 3a shows the best fitting of the adsorption isotherm of H2 in silica MFI zeolite at 65 K and 77 K obtained by GCMC after adjustment of the ASP force field (Table 2). The figure shows a remarkable agreement with experiments with RAD = 1 % at 65 K, and 4 % at 77 K. Moreover, the adsorption of D2 is nicely reproduced (RAD < 7 %) and indicates that the Feynman-Hibbs approach expanded to the 4 th order reproduces coherently the differences between H2 and D2 at cryogenic temperature. In Figure 3b, we can see that the prediction is less accurate at 47 K, notably at high pressure, nonetheless it is acceptable with a RAD around 10 %. As can be verified in Figure 4, when the new force field is applied to other zeolites such as FAU or CHA, the potential gives acceptable predictions. For silica FAU, the RAD values lie however between 20 % and 30 % according to the temperature. This could be due to the presence of residual cations in our FAU sample as discussed above. For silica CHA, it is noticeable that the steps observed at 47 K with the adsorption H2 and D2 are well reproduced. RAD values are lower than 15 % independently of the temperature. These results allow us to confidently say that we have to our disposal a force field reproducing the single adsorption of H2 and D2 below 77 K in high silica zeolites of various structures (FAU, MFI, CHA) with a good accuracy. Hence, we can use this potential for the prediction of coadsorption equilibria of hydrogen isotopes.

Adsorption selectivities

The coadsorption isotherms and the adsorption selectivities of D2 with respect to H2 have been simulated with the ASP force field for a mixture containing 75 % of H2 and for pressure ranging from 10 to 10 5 Pa. Results obtained with FAU, MFI and CHA zeolites at 47 and 77 K and for different loadings are compared with experimental data in Figure 5. The simulations obtained for silica MFI at 77 K are in very good agreement with experimental data, they present RAD values of 10 %. The ASP force field gives also satisfactory predictions of selectivity for silica CHA with RAD of 19 and 10 % at 77 and 47 K, respectively. The simulations of the adsorbed amounts are however less accurate (RAD around 30 %). The increase of the selectivity observed at 47 K above 18 molec.uc -1 is well reproduced. In contrast, the agreement between experiments and simulation for the silica FAU zeolite have a RAD of 38 %. Here again, the impossibility to obtain good prediction with this type of silica zeolite could be due to the presence of defects in our sample.

Singular behavior of silica CHA zeolite

Among the three zeolites studied in this work, the silica CHA zeolite shows a particular behavior with a step on the single adsorption isotherm appearing at 47 K (Figure 4b). Notice that the step is more pronounced with H2 than with D2. The step appears at different pressures, 15 000 Pa for H2 and 1 000 Pa for D2, but at the same filling of ~ 18 molec.uc -1 , from GCMC simulations. Worth noticing that the adsorption selectivity of D2 towards H2 sharply increases from the same filling, as shown on figure 5. In a recent communication [START_REF] Radola | Chemical Communications[END_REF] , we have shown, by analyzing the density profiles of molecules adsorbed in the cages calculated by GCMC, that this step is the result of a molecular rearrangement of the adsorbed phase induced by confinement effects. Below 18 molec.uc -1 , the H2 and D2 molecules are adsorbed in the middle of the cages with a low selectivity (i.e., in similar proportion as in the gas phase).

Above this filling, molecules are also adsorbed on a second site located in the octagonal window separating two cages with a selectivity largely in favor of D2. This result may suggest that the difference in adsorbate-adsorbent interactions between H2 and D2 is more important on this second adsorption site. For corroborating this hypothesis, here we present a thermodynamic interpretation of our GCMC simulations.

For the adsorption of a single component, the equality of chemical potentials of adsorbed and gas phases at equilibrium leads to the relation:

𝑙𝑛 ( 𝑃 𝑃°) 𝑁 𝑎 = 𝛥𝐻 𝑎 𝑅 1 𝑇 - 𝛥𝑆 𝑎 𝑅 ( 6
)
where H a and S a are the molar adsorption enthalpy and entropy at the filling N a . They are considered as independent on the temperature.

The adsorption enthalpy can be calculated at a given filling from the GCMC simulations by means of the relation:

∆𝐻 𝑎 = <𝐸𝑁>-<𝐸><𝑁> <𝑁 2 >-<𝑁> 2 -𝑘 𝐵 𝑇 (7)
with N the number of particles, E the configurational energy and kB the Boltzmann constant.

This adsorption enthalpy is the opposite of the well-known isosteric heat of adsorption (H a = -Qst). If the value of H a is known, the adsorption entropy can be easily calculated at different filling by means of the equation ( 6) and the adsorption isotherm N a = f(P)T.

The adsorption enthalpies and entropies for pure H2 and D2 in silica FAU, MFI and CHA are given in Figure 6 as a function of filling at 47 K.

For CHA zeolite, the adsorption enthalpies extrapolated at zero filling are slightly lower for D2 than for H2 (-5.7 against -5.5 kJ.mol -1 ) indicating that the adsorbate-adsorbent interactions are stronger with D2. This is along with the quantum sieving theory, which states that the heavier isotopes are more strongly adsorbed. The values of adsorption enthalpies are of the same order of magnitude as those determined from the experimental adsorption isotherms which lies between -5 and -6 kJ.mol -1 . As filling increases, the molecules are adsorbed in the middle of CHA cages. For H2 as for D2, the adsorption enthalpy decreases continuously because of the interactions between adsorbed molecules which are more and more confined.

At a filling of 18 molec.uc -1 , the level of confinement is so important that molecules have to be adsorbed on another site near the octagonal window 8MR separating two cages. At this filling, a sharp increase of 1 kJ.mol -1 (around 20 %) of the adsorption enthalpy is observed with H2 while D2 exhibits a plateau. After this jump, the adsorption enthalpy decreases with the same slope as before the jump. This suggests that the adsorbate-adsorbate interactions increase in the same way before and after the step. From these results we can consider that the jump in the adsorption enthalpy curve is due to the adsorption of H2 with more repulsive adsorbate-adsorbent interactions than with D2. This explains why the adsorption selectivity of D2 towards H2 increases after 18 molec.uc -1 . The increase of D2/H2 selectivity occurs when the molecules are adsorbed near the octagonal windows. This is in agreement with the quantum sieving theory established by Beenakker 2 which states that the selectivity increases as the pore diameter decreases. Below 18 molec.uc -1 , the molecules are adsorbed in the middle of CHA cages of 0.74 nm diameter while above this filling they are adsorbed near the 8MR windows of 0.37 nm diameter.

In figure 6 are also reported the evolution of adsorption entropies of hydrogen isotopes with filling and similar behaviors are observed with H2 and D2. The adsorption entropies continuously decrease in the same way along the filling. We just observe with H2 a small jump of entropy at 18 molec.uc -1 , like for the enthalpy. This jump of both entropy and enthalpy clearly indicates that the step on the adsorption isotherm associated with an increase of D2/H2 selectivity is entropy driven, in agreement with a molecular rearrangement of the adsorbed phase. This conclusion is, however, less obvious for D2 since no increase of entropy is observed. Notice that the adsorption entropies decrease down to values largely below to the deposition entropies. This indicates that molecules adsorbed in the CHA cages are extremely confined. Clearly, they are in a physical state that is more organized than in a compressed gas or in a liquid as it is currently admitted, but more like a solid phase.

Comparison of FAU, MFI and CHA silica zeolites

Among the three silica zeolites studied in this work, the silica CHA appears as the most efficient adsorbent for the separation of H2 and D2 by quantum sieving. This is the material which exhibits the best adsorption selectivity in favor of D2 at 47 K and high filling (Figure 5).

Figure 6 reports the comparison of adsorption enthalpies and entropies of H2 and D2 in the three silica zeolites. First, it can be noticed that the adsorption enthalpies are lower for D2 than for H2, whatever the zeolites. As mentioned above, this is in agreement with the quantum sieving theory. Second, for each zeolite at low filling the adsorption entropies of H2 and D2 are identical, indicating that the confinements of the two isotopes are similar. As filling increases, adsorption entropy decreases more for H2 than for D2, in particular with FAU and MFI. As the presence of other molecules reduces the available pore space, H2 is more confined than D2 because its effective kinetic diameter is greater at cryogenic temperatures. This is the consequence of the quantum effect that is applied in the simulation through the Feynman-Hibbs correction of the interaction potential.

Silica FAU presents the highest adsorption enthalpies and entropies. This is also the adsorbent which has the largest cages (1.1 nm) and consequently the greatest adsorption capacity.

Adsorbate-adsorbent interactions are relatively weak, and confinement is moderate (S a > Sdeposition). Its adsorption selectivity for D2 is low whatever the filling is (about 1.5).

With cylindrical channels of smaller diameter (0.56 nm), the MFI zeolite presents lower adsorption enthalpies and entropies. Adsorbate-adsorbent interactions are stronger, and the confinement degree is more important than in FAU. According to the quantum sieving theory, this zeolite should be more selective for D2, at least at low filling where the theory is valid.

Surprisingly, the selectivity is the same as for FAU (Figure 5). Nevertheless, the adsorption selectivity increases with the filling in particular above 20 molec.uc -1 , when the confinement becomes important (S a < Sdeposition).

Silica CHA exhibits an intermediate behavior. At low filling, the molecules are adsorbed in the middle of cages. The adsorption enthalpy lies between those of FAU and MFI, but the adsorption entropy is slightly lower than for MFI. The adsorbate-adsorbent interactions are weaker than in MFI but the confinement is more important despite the fact that the molecules are adsorbed in larger pores (0.74 nm diameter). The adsorption selectivity is the same as for the other two zeolites. As the filling increases, the confinement becomes so important that a molecular rearrangement takes place, and the selectivity becomes in favor of D2, as explained above. Thus, despite the fact that these three zeolites have the same surface chemical features, they exhibit a different behavior from the energetic point of view. These results show that the quantum sieving does not depend only on the pore diameter. The shape of pores is also a parameter which can influence the separation especially at high filling when confinement effects are enhanced.

Estimation of the size of H2 and D2 molecules at different temperatures

Given the description of hydrogen isotopes adsorption in silica zeolites by the developed ASP potential, we used it to estimate the size of H2 and D2 molecules at different temperatures. This information is crucial for hydrogen isotope separation, however the size estimation currently used in some works raises serious questions. For instance, Cao et al. 41 propose to use the de Broglie wavelength of molecules () as a measure of their "swelling" which is added to the "hard core" to obtain the molecular sizes at different temperatures. The physical basis of this approach is not clear, since the de Broglie wavelength does not characterize any "swelling", but the wave-like behavior of a quantum particle [START_REF] Atkins | Physical Chemistry[END_REF] . In this sense the value of the de Broglie wavelength of H2 or D2 at low temperature was applied to the analysis of quantum sieving in the work of Beenakker et al. 2 . Under cryogenic conditions  and D are comparable with the difference between the pore diameter and the molecular size, this difference is used as a criterion (of necessity) to take into account quantum effects. This approach by no means justifies the use of the de Broglie wavelength as a measure of molecular "swelling" under low temperature.

Here, we propose to estimate the molecular size of H2 and D2 by using the shape of LJ-FH potential. Indeed, in LJ potential the distance corresponding to the minimum in the potential curve () corresponds to the equilibrium separation between two molecules and can therefore be used as estimation of their size. In the case of LJ potential it can be shown that = 2 1/6 , but for the combined LJ-FH potential no simple expression can be obtained. Nevertheless, the LJ-FH potential has a minimum whose position depends on temperature and on the molecular mass, as illustrated by the data calculated at 30 K (Figure 7). The distance corresponding to the minimum can be considered as the size of D2 or H2 molecules. Obviously, the molecular sizes obtained in this way should not be considered as some absolute values since they are calculated in the particular framework used in this study (spherical D2 and H2 molecules interacting via LJ-FH potential). Despite this limitation, we consider that the obtained values can be used as a physically sound estimation of the temperature effect on the size of D2 and H2.

The values of H2 and D2 sizes at different temperatures obtained using the described approach are presented in Table 3 and in Figure 8. As expected, the size of both D2 and H2 increases by lowering the temperature, but not to the same extent. This effect results in a significant increase of the size difference from 0.0056 nm at 100 K to 0.0148 nm at 40 K. Moreover, this difference appears to vary linearly with the inverse of the temperature (Figure 8). It is instructive to compare the calculated size differences with the same parameter for other couples of molecules being separated by adsorption on porous solids. According to the classification proposed by Adil et al. [START_REF] Adil | [END_REF] , D2/H2 separation would be of the highest (3 rd ) level of complexity concerning the separation of molecules with size difference of 0.01 -0.025 nm. In the same class we find N2/CH4 or N2/O2 couples whose size difference (~ 0.015 nm) is similar to that calculated for D2 and H2 below 40 K. Despite the small size difference, N2/CH4 or N2/O2 couples can be separated by molecular sieving, i.e., using a material adsorbing only one component. This result suggests that the same process can be realized for hydrogen isotopes by using adsorbents with the appropriate pore size.

Conclusion

Our adsorption experiments of H2 and D2 in FAU, MFI and CHA silica zeolites below 77 K were used to test the force fields proposed in the literature. These force fields have been adjusted mainly for measurements performed at 77 K and because of the lack of experimental data at lower cryogenic temperature. We clearly showed that they do not predict accurately the adsorption equilibria below 77 K. We propose a new force field adjusted with data obtained at 65 K with high silica MFI zeolite. This force field, named ASP, is able to predict the adsorption isotherms at other temperatures (40 -100 K) and to reproduce with high accuracy the D2/H2 adsorption selectivities. A particularity of this force field concerns its transferability to other silica zeolites having different structures, namely: FAU and CHA zeolites. Moreover, it nicely reproduces the step observed on the adsorption isotherm with CHA at 47 K. This step is concomitant with a sharp increase of the adsorption selectivity towards D2 observed experimentally at 18 molec.uc -1 which is well reproduced with the proposed potential. The thermodynamical analysis of our GCMC data confirms that the particular behavior of CHA is the results of a molecular rearrangement of the adsorbed phase induced by confinement. A second adsorption site appears where the adsorbate-adsorbent interactions are weaker with H2 than with D2.

The three silica zeolites have the same surface chemical properties, but different pore structures. Our results show that the quantum sieving is not only dependent on the pore diameter, but it is also influenced by the pore geometry. According to the pore shape, new adsorption sites can appear due to molecular rearrangement induced by confinement. These sites are more or less selective, as shown with CHA. This particular phenomenon explains why CHA is more efficient than FAU and MFI zeolites for the separation of H2 and D2 by quantum sieving.

We dispose now of an efficient force field to study by GCMC simulation the separation of hydrogen isotopes by quantum sieving in pure silica zeolites. This force field is a useful tool to perform a screening of zeolites in order to identify, from GCMC simulations, which adsorbent presents the best selectivity. This will permit to avoid fastidious coadsorption experiments at cryogenic temperature which are very time consuming. It allows also to study the adsorption of tritiated radioactive isotopes (T2, HT, DT…) which cannot be manipulated in conventional laboratories. Our results show that the CHA zeolite is a promising adsorbent for hydrogen isotopes separation by quantum sieving. Therefore, it could be interesting to use our force field to simulate the adsorption of hydrogen isotopes on other zeolitic structures having pore diameter below 0.4 nm, i.e. pores formed with 8-membered oxygen ring (8MR) as in CHA. Among the 252 zeolite structures listed in the database of the International Zeolite Association, some structures as LTA, RWR, CDO, RRO, TON, NSI or ITW have 8MR pore windows and can be synthesized in the pure silica form 20 . It could be relevant to test these structures in particularly at very low temperature in order to know if the molecular rearrangement favorable to the adsorption of deuterium could be observed for these zeolites as it was observed for CHA.

In order to increase the accuracy of our GCMC predictions in these high silica zeolites, more efforts have to be done to describe the interactions between the zeolites and the hydrogen.

They must be more realistic by taking into account: (i) the zeolite structure at cryogenic temperature (cell parameters) in particular its flexibility with the temperature and the loading (particularly with zeolite like CHA showing a negative thermal expansion), (ii) the hydrogen molecules which should be described by a more realistic model like dumbbell with partial electrical charges, (iii) the electrostatic interactions between adsorbate and adsorbent, since the hydrogen isotopes can be polarized by the strong electrical field present in the silica nanopores.

FiguresFigure 1 :

 1 Figures

Figure 3 :

 3 Figure 3: Adsorption isotherms of H2 and D2 on silica MFI simulated with the ASP force

Figure 4 :

 4 Figure 4: Adsorption isotherms simulated with the ASP force field: a) H2 in silica FAU at 47

Figure 5 :

 5 Figure 5: Coadsorption isotherms (left) and adsorption selectivities (right) for a 75% H2 +

Figure 6 :

 6 Figure 6: Adsorption enthalpies (open symbols) and entropies (full symbols) of D2 (squares)

Figure 7 :

 7 Figure 7: L-J and FH-LJ potentials of interaction for H2 and D2 as a function of the distance at

  4ℇ 𝑖𝑗 (

	𝜎 𝑖𝑗 12 𝑟 𝑖𝑗 12 -	𝜎 𝑖𝑗 6 𝑟 𝑖𝑗 6 +	𝛽ℏ 2 24𝑀 𝑖𝑗	(132	𝜎 𝑖𝑗 12 𝑟 𝑖𝑗 14 -30	𝜎 𝑖𝑗 6 𝑟 𝑖𝑗 8 ) +	1 2	( 24𝑀 𝑖𝑗 𝛽ℏ 2	) 2	(24024	𝜎 𝑖𝑗 12 𝑟 𝑖𝑗 16 -1680	6 𝜎 𝑖𝑗 𝑟 𝑖𝑗 10 ))

Table 2 :

 2 Lennard-Jones interaction parameters used to describe the adsorbate-adsorbate and adsorbate-adsorbent interactions. The parameters for D2 are the same as for H2.

	Interaction	adsorbate -adsorbate		adsorbate -adsorbent
		H2 -H2	H2 -O	H2 -Si
	L-J parameter	 (nm)	 (K)	 (nm)	 (K)	 (nm)	 (K)
	Deeg et al. 39	0.2959	36.70	0.2890	66.06	0.1854	28.26
	Pantatosaki et al. 24	0.2820	36.50	0.2800	56.00	-	-
	ASP	0.2920	38.00	0.3080	47.00	0.2800	39.00

Table 3 :

 3 Effective size of D2 and H2 determined at different temperatures from the FH-LJ

	potential of interaction.
	T (K)	0(D2) (nm)	0(H2) (nm)	0(D2) -0(H2) (nm)
	100	0.3335	0.3391	0.0056
	90	0.3342	0.33403	0.0061
	77	0.3352	0.34230	0.0071
	70	0.3360	0.3436	0.0076
	60	0.3373	0.3460	0.0087
	50	0.3391	0.3493	0.0102
	40	0.3418	0.3539	0.0121
	30	0.3461	0.3609	0.0148

Acknowledgments

Calculations were performed using the resources of DNUM CCUB, the computing center of Université de Bourgogne. The authors thank J. Patarin from IS2M laboratory (Mulhouse, France) who kindly provided the sample of pure silica chabazite used in our experiments. B.

Radola thanks the CEA for its financial support.

Conflicts of interest

They are no conflicts to declare Tables Table 1: Some physical-chemical properties of high silica zeolites (the pore volume is the one accessible to nitrogen at 77 K).


Alicia Weibel

Andréas Flaureau

Adeline Pham

Geoffroy Chevallier

Jérôme Esvan

Claude Estournès

Christophe Laurent

One-step synthesis of few-layered-graphene/alumina powders for strong and tough composites with high electrical conductivity

Keywords:

The chemical vapor deposition of carbon onto a commercial α-Al 2 O 3 powder bed produces a pristine film of fewlayered-graphene (FLG) uniformly covering the α-Al 2 O 3 grains. This obviates both the manipulation of nanocarbons, lengthy mixing steps and the risk of damaging any pre-existing graphene platelets. The powders are consolidated to 99 % by SPS, producing samples where a FLG film is located along the grain boundaries of the submicron α-Al 2 O 3 . Compared to the pure α-Al 2 O 3 , the composites are moderately stronger and similarly tough and hard due to crack-deflection and crack-bridging and they are electrically conducting with a percolation threshold below 0.74 vol.% of carbon. The high conductivity values reflect the high quality of the thin FLG film and its continuous nature over very long distances. The samples are characterized by Raman spectroscopy, X-ray photoelectron spectroscopy, scanning and transmission electron microscopy.

Introduction

Graphene/ceramic composites [START_REF] Porwal | Review of graphene-ceramic matrix composites[END_REF][START_REF] Nieto | Graphene reinforced metal and ceramic matrix composites: a review[END_REF][START_REF] Miranzo | From bulk to cellular structures: a review on ceramic/graphene filler composites[END_REF][START_REF] Markandan | Recent progress in graphene based ceramic composites: a review[END_REF], notably Al 2 O 3 -matrix samples, have very attractive thermal [START_REF] Rutkowski | Thermal properties of pressure sintered alumina-graphene composites[END_REF], electrical [START_REF] Fan | Preparation and electrical properties of graphene nanosheet/Al2O3 composites[END_REF][START_REF] Fan | Highly Conductive few-layer graphene/Al 2 O 3 nanocomposites with tunable charge carrier type[END_REF][START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Çelik | Anisotropic mechanical and functional properties of graphene-based alumina matrix nanocomposites[END_REF], mechanical [START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Çelik | Anisotropic mechanical and functional properties of graphene-based alumina matrix nanocomposites[END_REF][START_REF] Liu | Mechanical properties of graphene platelet-reinforced alumina ceramic composites[END_REF][START_REF] Fan | The effect of homogeneously dispersed few-layer graphene on microstructure and mechanical properties of Al 2 O 3 nanocomposites[END_REF][START_REF] Liu | Preparation and mechanical properties of graphene nanosheet reinforced alumina composites[END_REF][START_REF] Porwal | Graphene reinforced alumina nano-composites[END_REF][START_REF] Porwal | Effect of lateral size of graphene nano-sheets on the mechanical properties and machinability of alumina nano-composites[END_REF][START_REF] Ahmad | Toughening mechanisms and mechanical properties of graphene nanosheetreinforced alumina[END_REF][START_REF] Meng | Microstructure and anisotropy of mechanical properties of graphene nanoplate toughened Al 2 O 3 -based ceramic composites[END_REF][START_REF] Alam | Effect of graphite nanoplatelets on the mechanical properties of alumina based composites[END_REF] and tribological [START_REF] Alam | Effect of graphite nanoplatelets on the mechanical properties of alumina based composites[END_REF] properties. Carbon is present in these samples as discrete particles of few-layered-graphene (FLG) platelets with 2-10 layers or in the form of thicker stacks (up to about 100 nm). Such platelets are denoted variously as graphene-nanosheets (GNS), -nano-platelets (GNP), -platelets (GPL) or graphite platelets. The composites are usually prepared by sintering graphene/Al 2 O 3 powders and the prior preparation of the powders is indeed regarded as the key step in the process. The reported methods, such as the salt precursor method, colloidal processing and molecular mixing, involve many successive steps. Most importantly they share the use of pre-existing graphene agglomerates prepared by chemical [START_REF] Hummers | Preparation of graphitic oxide[END_REF] or mechanical exfoliation [START_REF] Yi | A review on mechanical exfoliation for the scalable production of graphene[END_REF] of graphite. These are lengthy routes prone to introducing contamination and/or undesirable structural defects, as in graphene oxide or reduced graphene oxide. An alternative method has been reported, using the chemical vapour deposition (CVD) of a carbon-containing gas for the formation of graphene films on porous Al 2 O 3 ceramic substrates [START_REF] Zhou | Highly conductive porous graphene/ceramic composites for heat transfer and thermal energy storage[END_REF], foams [START_REF] Zhou | Heat transport enhancement of thermal energy storage material using graphene/ceramic composites[END_REF] and powders [START_REF] Rümmeli | On the graphitization nature of oxides for the formation of carbon nanostructures[END_REF][START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF][START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF]. Rümmeli et al. [START_REF] Rümmeli | On the graphitization nature of oxides for the formation of carbon nanostructures[END_REF] have reported the encapsulation of the oxide (Al 2 O 3 , MgO, SiO 2 and Ga 2 O 3 ) grains by 1-8 graphitic layers. Our group has recently reported the formation of FLG/MgO powders by the decomposition of methane on an MgO powder bed. Moreover, the so-obtained powders have been consolidated by spark plasma sintering (SPS), producing strong, hard and electrically conducting FLG/MgO composites [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF]. Here, we propose to extend this one-step fast route, which does not involve any mixing, to the synthesis of FLG/Al 2 O 3 powders, to consolidate the soobtained powders by SPS and to investigate the microstructure and the mechanical and electrical properties of the so-obtained fully dense composite samples. Such a study on FLG/Al 2 O 3 samples was reported very recently [START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF], building also on our previous work on FLG/MgO [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF]. There are several differences between the present study and [START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF], including a study of the powders by X-ray photoelectron spectroscopy and a report that the strength of the sintered composites is increased, not decreased, by the presence of moderate amounts of FLG. We also bring to light some reinforcement mechanisms including crack-deflection, crack-bridging and the debonding of the FLG film bridging two grains.

⁎ Corresponding author. E-mail address: laurent@chimie.ups-tlse.fr (C. Laurent). 1 Present address: LPCNO, Université de Toulouse, CNRS, UPS, INSA, 135 Avenue de Rangueil, F-31077 Toulouse cedex 4, France. https://doi.org/10.1016/j.jeurceramsoc.2020.06.029 T

Experimental methods

Raw materials

A commercial α-Al 2 O 3 powder (Baikowski BMA 15, > 99.9 %, 284 ± 112 nm) was divided into five batches. Four of them were submitted to a chemical vapor deposition (CVD) treatment performed in order to decompose methane (CH 4 ) and deposit carbon onto the α-Al 2 O 3 grains. The samples (12 g) were heated in argon (10 L/h) up to 900 °C (15 °C/min) and upon reaching this temperature, CH 4 was introduced (1, 4, 5, and 7 L/h, respectively, while keeping the total gas flow-rate equal to 10 L/h). A dwell time of 75 min was applied at 900 °C. Cooling down to room temperature was performed in the same CH 4 / Ar atmosphere. The flow-rates were monitored using mass-flow controllers.

Sintering

The powders were consolidated by SPS (SPS632LX, Fuji electronic Industrial Co., Japan). The samples (about 3.2 g) were loaded into a 20 mm inner-diameter graphite die. A sheet of graphitic paper was placed between the punch and the powder and between the die and the powder for easy removal. The tool was introduced in the SPS device and a uniaxial pressure of 50 MPa was applied at room temperature in 1 min. Then, the samples were sintered in vacuum (residual cell pressure < 5 Pa). A direct current with a pulse pattern of 40 ms on: 7 ms off was used. An optical pyrometer, focused on a little hole at the outer surface of the die, was used to control the temperature. A heating rate of 300 °C/min was used from room temperature to 600 °C. There is no temperature measurement from room temperature to 570 °C. The power is automatically and gradually increased until the temperature is detected by the pyrometer at 570 °C, which takes about 2 min. Then a 1 min dwell time is applied at 600 °C in order to offset any overshoot, which from experience is known to be very minor anyway, and stabilize the temperature of the SPS stack at 600 °C before the start of the controlled ramp. Then, the temperature was raised (100 °C/min) to 1375 °C (only 1300 °C for pure α-Al 2 O 3 ), where a 5 min dwell was applied. A uniaxial load was gradually applied during the first heating to, and stabilization at, 600 °C and then maintained during the second heating step up to 1375 °C. The corresponding pressure is equal to 100 MPa. Once the set-point of 1375 °C is reached, the pressure was increased to 150 MPa during the first minute and maintained until the end of the dwell. A cooling rate of 100 °C/min was applied down to room temperature and the uniaxial load was gradually released during the same time. The sintered specimens were in the form of pellets 20 mm in diameter and about 3 mm thick. The graphitic paper remaining on the surface was removed by polishing.

Characterization

The carbon content in the powders was measured by the flash combustion method with an accuracy of ± 2 %. The samples were investigated using X-ray diffraction (XRD, CuKα radiation, Bruker D4 Endeavor). Raman spectra were recorded at 532 nm (LabRAM 800, Horiba Jobin-Yvon) and they were averaged on three spectra. The X-ray photoelectron emission spectra were recorded using a monochromatised Al K α (hν = 1486.6 eV) source on a Thermo Scientific K-Alpha system. The X-ray spot size was about 400 μm. The pass energy was fixed at 30 eV with a step of 0.1 eV for core levels and 150 eV for surveys (step 1 eV). The spectrometer energy calibration was done using the Au 4f 7/2 (83.9 ± 0.1 eV) and Cu 2p 3/2 (932.8 ± 0.1 eV) photoelectron lines. XPS spectra were recorded in direct mode N (Ec) and the background signal was removed using the Shirley method. The flood gun was used to neutralize charge effects on the top surface. Selected samples were observed by field-emission-gun scanning electron microscopy (FESEM, JEOL JSM 6700F and 7800F) and transmission electron microscopy (TEM, JEOL JEM 2100 F). The samples were coated with platinum (a few nanometers thick) prior to FESEM observations, in order to increase the contrasts by enhancing secondary electrons emission of carbon. For a sintered sample, a thin foil for TEM observations was prepared using a routine involving grinding with SiC paper, dimpling (GATAN 656) with a 1 μm diamond suspension and cold ion milling at 4 kV (GATAN PIPS 691).

The density of the specimens was measured by Archimedes' method using a hydrostatic balance (Sartorius MSE224S-YDK03) with an accuracy of ± 1 %. The relative density was calculated using 3.98 g/cm . The values reported are the average of at least 20 measurements. The transverse fracture strength (σ f ) was measured, parallel to the SPS pressing axis, by the three-point bending method (Material Testing Systems MTS 1/M) on specimens about 1.8 × 1.8 × 18 mm 3 . The span between the two supporting pins is equal to 13 mm. Cross-head speed was fixed at 0.1 mm/min. The toughness (K Ic ) was measured, also parallel to the pressing axis, by the single-edged notched beam (SENB) method, on similar specimens notched with a diamond wire 0.17 mm in diameter. The notch depth/height ratio was verified to be slightly higher than 0.4. A calibration factor [START_REF] Brown | Plane Strain Crack Toughness Testing of High Strength Metallic Materials[END_REF] was used to calculate the SENB toughness from the experimental results. The values reported for σ f and K Ic are the average of measurements conducted on seven or eight specimens. Note that the present experimental setup and calibration factor were used for earlier works on carbon nanotube-Al 2 O 3 composites [START_REF] Flahaut | Carbon nanotube-metal-oxide nanocomposites: microstructure, electrical conductivity and mechanical properties[END_REF][START_REF] Kasperski | Multi-walled carbon nanotube-Al2O3 composites: covalent or non-covalent functionalization for mechanical reinforcement[END_REF]. The electrical conductivity was measured at room temperature with direct currents applied on (1.8 × 1.8 × 5 mm 3 ) specimens, parallel to their length and perpendicular to their length, i.e. perpendicular and parallel to the SPS pressing axis, respectively. A silver paste was applied in order to connect the conducting electrodes. The current densities used were lower than 160 mA/cm² (Keithley 2400).

Results and discussion

Powders

The carbon content (C n -Table 1) in the powders was measured as equal to 0.13, 0.39, 0.58 and 0.77 wt.% (i.e. 0.24, 0.74, 1.09 and 1.45 vol.%) for the samples prepared using 1, 4, 5 and 7 L/h of CH 4 , respectively, in line with other works [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF][START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF]. For the sake of brevity, the

Table 2

Curve fitting r esults o f t he X PS C 1s a nd A l2p s pectra o f t he p owders: binding energy (BE), full width at half-maximum (FWHM) and content.

powders will be denoted hereafter as G24, G74, G109 and G145, considering the carbon volume content. The XRD patterns (not shown) for all samples reveal only the peaks typical of α-Al 2 O 3 (corundum-type).

No peak for any form of carbon is detected because of the very low content.

The Raman spectra (Fig. 1) show the carbon D, G and 2D bands (ca. 1330, 1590 and 2688 cm -1 , respectively). For G24, a peak between the D and G bands is also observed (ca. 1470 cm -1 ), which could correspond to the D'' band that has been reported for samples containing disordered and/or amorphous carbon [START_REF] Sadezkya | Raman microspectroscopy of soot and related carbonaceous materials: spectral analysis and structural information[END_REF][START_REF] Jawhari | Raman spectroscopic characterization of some commercially available carbon black materials[END_REF]. In addition to these peaks, fluorescence peaks of α-Al 2 O 3 are also detected for G24.

The Raman spectra (Fig. 1) are normalized with the G band at 100 %. Despite some uncertainties, both the I D /I G and the I 2D /I G ratios (Table 1) decrease upon the increase in carbon content, which could traduce less disorder, i.e. less defects in the graphene layers and an increase in the number of layers, respectively [START_REF] Zhou | Heat transport enhancement of thermal energy storage material using graphene/ceramic composites[END_REF]. Note however that the spectra for G74, G109 and G145 are not much different from each other. The 2D band position, shape and intensity are by and large in agreement with values commonly observed for FLG with 5-10 layers [START_REF] Ferrari | Raman spectrum of graphene and graphene layers[END_REF] but they all result from the contribution of several parameters including the number of graphene layers, the defects, the stacking order, the presence of strains within the stacking [START_REF] Kasperski | Multi-walled carbon nanotube-Al2O3 composites: covalent or non-covalent functionalization for mechanical reinforcement[END_REF][START_REF] Tsoukleri | Subjecting a graphene monolayer to tension and compression[END_REF][START_REF] Nguyen | Excitation energy dependent Raman signatures of ABA-and ABC-stacked few-layer graphene[END_REF] and a more precise determination falls outside the scope of the present work.

The XPS spectra are presented in Fig. 2. α-Al 2 O 3 is used as a reference for Al environments. A graphene sample prepared elsewhere [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF] was used as a reference for C environments. The semi-quantification of each chemical group contribution is reported in Table 2. The range 280-294 eV shows the response of carbon C1s. The different C1s contributions in the spectra are denoted by A symbols: A': 284.3 eV for C]C, A'': 284.6 eV for CC, CH, A''': 286.0 eV for CO and A'''': 287.0-290 eV for CO and OCOeee]]e. The C1s signals for G74, G109 and G145 are similar to each other and show an asymmetrical carbon at low binding energy (A'), highlighting the presence of graphene (sp 2 carbon hybridization). Hydrocarbon (A''), CeO (A''') and carbonyl/ester groups (A''') contributions are detected too. No aluminum carbides (C-Al, C1s contributions < 282 eV) and no aluminum oxycarbides (C-Al-O-C, C1s contributions < 282.5 eV) are detected. The C1s response for G24 is similar to that for the α-Al 2 O 3 reference, which could indicate very thin and/or incomplete layers, similar in signature to carbon from atmospheric pollution. The 70-78 eV range describes the presence of aluminum Al2p. For all samples, only one chemical environment is found, Al-O-Al (73.6 eV, denoted B on the spectra), in comparison with the response of Al2p for the α-Al 2 O 3 reference. This is by contrast to a study [START_REF] Zhou | Heat transport enhancement of thermal energy storage material using graphene/ceramic composites[END_REF] where the formation of aluminum oxycarbide was reported. The latter samples were prepared at 1200 °C, thus significantly higher than for the present study (900 °C), and the formation mechanism of graphene were attributed to the carbothermal reduction occurring at the Al 2 O 3 surface, with a chemical bonding between graphene and Al 2 O 3 playing a significant role in the nucleation and growth of graphene. The present results do not point out the occurrence of the carbothermal reduction nor therefore to the necessity of such a mechanism for the deposition of carbon and the formation of FLG onto the α-Al 2 O 3 grains.

All powders were observed by FESEM and they look exactly the same. Typical FESEM images are shown for G74 (Fig. 3a) and G145 (Fig. 3b). They show α-Al 2 O 3 primary grains 100-500 nm in size. Graphene platelets or films were not observed on such images, probably due to their low thickness, even when using a higher-magnification as for G145 (Fig. 3c). TEM images of G74 (Fig. 4a), G109 (Fig. 4b) and G145 (Fig. 4c) reveal that for all three powders, the surface of the α-Al 2 O 3 grains is covered by a few (4-8) graphene layers. Disorganized carbon was not evidenced on TEM images but its presence at a very low amount cannot be ruled out. These observations are in agreement with results reported for other oxide powders [START_REF] Rümmeli | On the graphitization nature of oxides for the formation of carbon nanostructures[END_REF][START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF][START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF].

Dense samples

The sintered specimens are denoted like the corresponding powders. The relative density of all specimens is equal to or above 99 ± 1 % (Table 3). The Raman spectra (Fig. 5 and Table 3) do not show much change compared to those of the respective powders (Fig. 1), which could indicate no or little damage to the FLG upon sintering by SPS.

The fracture surfaces of the samples (Fig. 6) were observed by FESEM. The average α-Al 2 O 3 grain size (d -Table 3), determined from such images, is equal to 0.89 μm for α-Al 2 O 3 (Fig. 6a). This relatively grain low size (i.e. submicron) for a dense α-Al 2 O 3 sample is achieved because the SPS process allows densification at relatively low temperatures, thus limiting grain growth [START_REF] Santanach | Spark plasma sintering of alumina: study of parameters, formal sintering analysis and hypotheses on the mechanism(s) involved in densification and grain growth[END_REF]. The average α-Al 2 O 3 matrix grain size for G24 (image not shown) is slightly lower (0.82 μm) and is about twice lower for the specimens containing more carbon: 0.51 μm for G74 (Fig. 6c andd), 0.47 μm for G109 (Fig. 6e andf) and 0.46 μm for G145 (Fig. 6g andh). This could indicate that the graphene layers around the α-Al 2 O 3 grains hamper the motion of grain boundaries during sintering and thus limit matrix grain growth, in line with other works [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF][START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF]. This effect is however much less pronounced than for the FLG/MgO samples where there was a 15-fold difference in MgO grain size [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF]. Note that the low magnification FESEM images of all three composites (Fig. 6c, e and g) reveal a very uniform matrix grain size, which reflects the very homogeneous dispersion of graphene at the matrix grain boundaries. This is a direct consequence of the very homogeneous dispersion of graphene around the grains in the powder, which is a key feature of the one-step synthesis route. Moreover, these images reveal a transgranular-intergranular mixed fracture mode for α-Al 2 O 3 (Fig. 6a) and an intergranular fracture mode for composites (Fig. 6c, e andg). For all composites, there are some areas where the partly debonded FLG film is observed in a transverse orientation (arrowed in Fig. 6d, f andh). Note that the Pt-coating a few nanometers thick used for the preparation of SEM samples results in an overestimation of the FLG thickness. There is no observed particular orientation of the FLG with respect to the pressing axis, as also noted elsewhere [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF][START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF] but unlike in composites prepared by mixing GNP or GNS with the matrix powder or precursor, where the GNP or GNS are mostly aligned in the plane perpendicular to the pressing direction [START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Çelik | Anisotropic mechanical and functional properties of graphene-based alumina matrix nanocomposites[END_REF][START_REF] Porwal | Graphene reinforced alumina nano-composites[END_REF][START_REF] Meng | Microstructure and anisotropy of mechanical properties of graphene nanoplate toughened Al 2 O 3 -based ceramic composites[END_REF]. TEM observations of the G145 specimen (Fig. 7a) show α-Al 2 O 3 grains about 200 nm in size separated by sharp grain boundaries. HRTEM images of the grain boundaries (Fig. 7b-d) reveal fringes corresponding to fairly well-organized FLG about 2-5 nm thick. The number of graphene layers at the grain boundaries is thus ranging from 6 to 12, i.e. roughly twice the number of graphene layers covering the α-Al 2 O 3 grains in the corresponding powder (Fig. 2c). These observations confirm the above Raman spectroscopy results revealing no or little damage to the FLG upon sintering by SPS.

The electrical conductivity for the α-Al 2 O 3 and G24 sample is not measurable, either in the direction perpendicular (σ e⊥ -Table 3) or parallel to the SPS pressing axis (σ e// -Table 3). For G74, G109 and G145, both σ e⊥ and σ e// increase upon the increase in carbon content, with σ e⊥ about 1.7-2.6 times higher than σ e// (Table 3). This could indicate that although not observed on the FESEM images, there is some degree of anisotropy induced by the uniaxial pressing during SPS. The maximum value measured (σ e⊥ = 1.84 S cm-1 for G145) is significantly higher than some values reported elsewhere for FLG/Al 2 O 3 samples, even for higher carbon contents [START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Çelik | Anisotropic mechanical and functional properties of graphene-based alumina matrix nanocomposites[END_REF]. They are in line with some others, 10.4 S. cm -1 for 2.35 vol.% of carbon dispersed as very thin FLG [START_REF] Fan | Highly Conductive few-layer graphene/Al 2 O 3 nanocomposites with tunable charge carrier type[END_REF] and 2.67 S. cm -1 for 1.74 vol.% of carbon prepared by the CVD route [START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF] (Table 3). This could reflect the high quality of the FLG film in the present samples and its continuous nature over very long distances, in line with results reported for carbon nanotube -oxide composites [START_REF] Rul | Percolation of singlewalled carbon nanotubes in ceramic matrix nanocomposites[END_REF][START_REF] Kasperski | Preparation-microstructure-property relationships in double-walled carbon nanotubes/alumina composites[END_REF], where the carbon nanotubes are significantly longer than the matrix grains. This is by contrast to samples where there are a great many of individual FLG platelets with submicron lateral dimensions along the conducting path, therefore contributing more to contact resistance. The change between G24 (conductivity not measurable) and G74 (σ e⊥ = 0.68 S cm -1 and σ e// = 0.27 S cm -1 ) could indicate that the electrical percolation threshold is between 0.24 and 0.74 vol.%. This is slightly lower than for FLG/Al 2 O 3 samples [START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF] with a similar microstructure but in line with data reported for FLG/MgO composites [START_REF] Weibel | Fast and easy preparation of few-layered-graphene/magnesia powders for strong, hard and electrically conducting composites[END_REF], other GNS/Al 2 O 3 samples [START_REF] Fan | Highly Conductive few-layer graphene/Al 2 O 3 nanocomposites with tunable charge carrier type[END_REF][START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF] and carbon nanotubeoxide composites [START_REF] Tsoukleri | Subjecting a graphene monolayer to tension and compression[END_REF]. However, it is markedly lower than for GNS/ Al 2 O 3 samples with thicker GNS (about 3 vol.% [START_REF] Fan | Preparation and electrical properties of graphene nanosheet/Al2O3 composites[END_REF] and 7 vol.% [START_REF] Çelik | Anisotropic mechanical and functional properties of graphene-based alumina matrix nanocomposites[END_REF]). Detailed discussions have been reported on the topic of the percolation threshold [START_REF] Fan | Highly Conductive few-layer graphene/Al 2 O 3 nanocomposites with tunable charge carrier type[END_REF][START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Çelik | Anisotropic mechanical and functional properties of graphene-based alumina matrix nanocomposites[END_REF] but here further work is warranted in order to get a better determination of the precise nature of the percolating system.

The Vickers microhardness (HV 0.2 -Table 3) is in the range 22.0-23.8 GPa, in line with [START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF], and is similar for all samples despite the admittedly decreasing size of the matrix grains upon the increase in carbon content. These values are however typical for α-Al 2 O 3 in the 0.3-1.2 μm size range [START_REF] Nguyen | Excitation energy dependent Raman signatures of ABA-and ABC-stacked few-layer graphene[END_REF]. Other authors [START_REF] Liu | Mechanical properties of graphene platelet-reinforced alumina ceramic composites[END_REF][START_REF] Fan | The effect of homogeneously dispersed few-layer graphene on microstructure and mechanical properties of Al 2 O 3 nanocomposites[END_REF][START_REF] Porwal | Graphene reinforced alumina nano-composites[END_REF][START_REF] Ahmad | Toughening mechanisms and mechanical properties of graphene nanosheetreinforced alumina[END_REF][START_REF] Meng | Microstructure and anisotropy of mechanical properties of graphene nanoplate toughened Al 2 O 3 -based ceramic composites[END_REF] have reported that the Vickers microhardness decreases slightly upon the increase in carbon content, when there is also only a minor decrease in the matrix grain size. The transverse fracture strength (σ f -Table 3) for α-Al 2 O 3 is equal to 435 MPa and is slightly higher for the FLG/Al 2 O 3 samples, in the range 482-551 MPa, by contrast to what has been reported by other authors [START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF]. The reinforcement achieved appears to be lower than what has been reported earlier [START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Liu | Mechanical properties of graphene platelet-reinforced alumina ceramic composites[END_REF][START_REF] Fan | The effect of homogeneously dispersed few-layer graphene on microstructure and mechanical properties of Al 2 O 3 nanocomposites[END_REF][START_REF] Alam | Effect of graphite nanoplatelets on the mechanical properties of alumina based composites[END_REF], but note that the present α-Al 2 O 3 is also stronger. In agreement with other results, the maximum reinforcement is obtained for very low carbon contents and a further increase is detrimental. The fracture toughness (K Ic -Table 3) for α-Al 2 O 3 is equal to 6.5 MPa.m 1/2 , a relatively high value. It is not markedly different for the composites, between 5.5 and 6.9 MPa.m 1/2 . Yao et al. [START_REF] Yao | Grain size dependence of fracture toughness for fine grained alumina[END_REF] have shown that the fracture toughness for fine grained (0.3-3 μm) α-Al 2 O 3 is not grain-size dependant. Other authors have reported no toughening [START_REF] Çelik | Anisotropic mechanical and functional properties of graphene-based alumina matrix nanocomposites[END_REF] or a moderate one [START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Liu | Mechanical properties of graphene platelet-reinforced alumina ceramic composites[END_REF][START_REF] Porwal | Graphene reinforced alumina nano-composites[END_REF][START_REF] Ahmad | Toughening mechanisms and mechanical properties of graphene nanosheetreinforced alumina[END_REF][START_REF] Meng | Microstructure and anisotropy of mechanical properties of graphene nanoplate toughened Al 2 O 3 -based ceramic composites[END_REF][START_REF] Alam | Effect of graphite nanoplatelets on the mechanical properties of alumina based composites[END_REF][START_REF] Hrubovčáková | Microstructure, fracture behaviour and mechanical properties of conductive alumina based composites manufactured by SPS from graphenated Al 2 O 3 powders[END_REF] but their reported value for α-Al 2 O 3 is lower than the present one. In addition, it is worth noting that many different methods are used to evaluate the toughness, such as Chevron Notch, Indentation, R-curve, Single Edge Notched Beam and Single Edge V-Notched Beam (Table 3). This has been found [START_REF] Wang | Contact-damage-resistant ceramic/singlewall carbon nanotubes and ceramic/graphite composites[END_REF] to be a source for conflicting results on toughening in the case of carbon nanotubeceramic composites. Therefore, it is clearly a field deserving more work, round-robin tests coming to mind.

Vickers indentations were performed on the surface of G145 using a deliberately high load (2 kg) in order to produce cracks, which were observed by FESEM (Fig. 8).

The path of the cracks is intergranular and quite tortuous, revealing

5.

Raman spectra of the dense α-Al 2 O 3 and FLG/Al 2 O 3 samples (G24, G74, G109 and G145). The spectra of G74, G109 and G145 are normalized with the G band at 100 %.The dashed lines are guides to the eye. crack-deflection (Fig. 8a andb). Crack-bridging by the FLG film is observed. Some images also show the debonding of the FLG film as it bridges two grains (arrowed in Fig. 8c). The large surface area of graphene in contact with the α-Al 2 O 3 grain causes a large adhering surface, improving the anchoring to the sides of the crack and hampering crack propagation [START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF]. Other authors [START_REF] Centeno | Graphene for tough and electroconductive alumina ceramics[END_REF][START_REF] Liu | Mechanical properties of graphene platelet-reinforced alumina ceramic composites[END_REF][START_REF] Porwal | Effect of lateral size of graphene nano-sheets on the mechanical properties and machinability of alumina nano-composites[END_REF][START_REF] Ahmad | Toughening mechanisms and mechanical properties of graphene nanosheetreinforced alumina[END_REF][START_REF] Meng | Microstructure and anisotropy of mechanical properties of graphene nanoplate toughened Al 2 O 3 -based ceramic composites[END_REF] have also reported crackbranching, crack-deflection and crack-bridging as toughening mechanisms in the case of discrete graphene particles (GNS, GNP, ...) dispersed into α-Al 2 O 3 . A toughening mechanism involving a continuous wall of graphene along Si 3 N 4 grain boundaries has been reported [START_REF] Walker | Toughening in graphene ceramic composites[END_REF]. The graphene layers wrapping the Si 3 N 4 grains anchor themselves around them and show a resistance to pullout. These authors also proposed that the continuous wall of graphene along the grain boundaries forces the cracks to propagate in not just two but in three dimensions in order to continue to propagate through the material. The similarity with the present microstructure could make it a possibility, although admittedly no macroscopic toughening is observed for the present samples.

Conclusions

In conclusion, we have reported the preparation of graphene/Al 2 O 3 composite powders in a simple, one-step, route involving the chemical vapor deposition of carbon onto the α-Al 2 O 3 powder grains. This obviates both lengthy mixing steps and the risk of damaging any preexisting graphite or graphene platelets. It is shown that carbon is deposited in the form of pristine few-layered-graphene films (about 4-8 layers) wrapping the α-Al 2 O 3 grains. The samples are consolidated to 99 % by SPS. It is shown that a FLG film is located along the grain boundaries of the submicron α-Al 2 O 3 , as opposed to be dispersed as discrete particles. The so-obtained composites are moderately stronger and similarly tough and hard than the present pure submicron α-Al 2 O 3 . Crack-deflection and crack-bridging have been observed and it is proposed that the adhesion of a large surface area of graphene in contact with the α-Al 2 O 3 grain significantly improves the anchoring to the sides of the crack and hampers crack propagation. Moreover, the samples are electrically conducting with a percolation threshold below 0.74 vol.%. The study reveals that the conductivity values achieved (1.84 S cm -1 for 1.45 vol.% of carbon) reflect the high structural quality of the thin FLG film in the present samples and its continuous nature over very long distances. The proposed synthesis method for the direct preparation of FLG-containing powders is simple to perform, does not involve the manipulation of nanocarbons and is dependent on mature industrial technology and therefore prone to up-scaling. Interestingly, it can be used on almost any powder bed by fine-tuning the experimental conditions, such as using different carbon sources.

Fig. 1 .

 1 Fig. 1. Raman spectra of the α-Al 2 O 3 and FLG/Al 2 O 3 powders (G24, G74, G109 and G145). The spectra of G74, G109 and G145 are normalized with the G band at 100 %. The dashed lines are guides to the eye.

Fig. 2 .

 2 Fig. 2. XPS spectra of the α-Al 2 O 3 and FLG/Al 2 O 3 powders (G24, G74, G109 and G145). A' : C = C, 284.3 eV ; A'' : C-C, C-H, 284.6 eV ; A''' : C-O, 286.0 eV ; A'''' : C = O, O = C-O, 287 -290 eV; B : Al-O-Al, 73.6 eV.

Fig. 3 .

 3 Fig. 3. FESEM images of the a) G74, b) and c) G145 powders.

Fig. 4 .

 4 Fig. 4. High-magnification TEM images of the a) G74, b) G109 and c) G145 powders.

Fig. 6 .

 6 Fig. 6. FESEM images of the fracture surface of the specimens prepared by SPS a) and b) α-Al 2 O 3 , c) and d) G74, e) and f) G109, g) and h) G145. Arrows point to the FLG observed in a transverse orientation.

Fig. 7 .

 7 Fig. 7. TEM image a) of a thin foil of the G145 specimen sintered by SPS and HRTEM images b), c) and d) of the grain boundaries.

Fig. 8 .

 8 Fig. 8. FESEM images showing sample G145 with cracks made on purpose, revealing a) and b) crack-deflection a), b), c) and d) crack-bridging and c) the debonding of the FLG film bridging two grains.

Table 1

 1 CVD atmosphere (CH 4 /Ar) and characteristics of the powders: carbon content (C n and C v ), Raman I D /I G and I 2D /I G ratios for the powders and dense samples.

nm: not measurable.

Table 3

 3 Characteristics and properties of the sintered specimens: carbon content (C v ), relative density (ρ), Al 2 O 3 matrix grain size (d), Vickers microhardness (HV 0.2 ), fracture strength (σ f ), SENB toughness (K Ic ), electrical conductivity perpendicular (σ e⊥ ) and parallel to the SPS pressing axis (σ e// ).

	Specimen or Ref.	C v (vol.%)	ρ (%)	d (μm)	HV 0.2 (GPa)	σ f (MPa)	K Ic (MPa.m 1/2 )	σ e⊥ (S.cm -1 )	σ e// (S.cm -1 )
	α-Al 2 O 3	0	99	0.89 ± 0.28	23.1 ± 1.5	435 ± 125	6.5 ± 0.9	-	-
	G24	0.24	100	0.82 ± 0.26	23.1 ± 1.5	482 ± 64	6.9 ± 0.5	-	-
	G74	0.74	99	0.51 ± 0.17	23.8 ± 2.8	551 ± 47	5.5 ± 0.5	0.68	0.27
	G109	1.09	99	0.47 ± 0.16	22.1 ± 4.0	531 ± 57	5.8 ± 0.5	0.85	0.50
	G145	1.45	99	0.46 ± 0.15	22.0 ± 1.5	516 ± 37	6.5 ± 0.6	1.84	0.71
	[6]	3	100	< 0.5	-	-	-	0.03	-
	[7]	0.6	-	< 0.5	-	-	-	0.30	-
	[7]	2.35		< 0.5	-	-	-	10.4	-
	[8]	0	99	4	-	320	3.5 RC	-	-
	[8]	0.30	99	< 1	-	610	-	0.001	7.10 -5
	[8]	0.41	99	< 1	-	630	5.1 RC	0.067	0.013
	[8]	0.85	99	< 1	-	480	-	0.111	0.012
	[9]	0	100	2.39	18.4	-	2.9 IND	-	-
	[9]	5	99.4	1.27	15.1	-	2.6 IND	-	-
	[9]	7	98.7	1.31	13.1	-	2.8 IND	-	-
	[9]	9	99.2	1.31	11.8	-	3.0 IND	0.014	0.007
	[9]	15	98.5	1.33	9.8	-	3.2 IND	0.201	0.091
	[10]	0	100	3-4	18.04	400	3.53 SEVNB	-	-
	[10]	0.38	99.6	2-3	17.66	523	4.49 SEVNB	-	-
	[10]	0.76	99.9	2-3	17.46	485	4.11 SEVNB	-	-
	[10]	1.33	99.9	2-3	16.32	464	3.94 SEVNB	-	-
	[12]	0	99.6	2.4	18.8	348	3.11 IND	-	-
	[12]	0.3	98.9	-	23.7	708	3.89 IND	-	-
	[12]	0.6	97.4	-	21.5	597	3.58 IND	-	-
	[12]	2	96.7	0.2	21.6	584	3.40 IND	-	-
	[13]	0	99.8	0.53	22.9	-	2.9 CN / 2.8 IND	-	-
	[13]	0.2	99.9	-	21.3	-	3.7 CN / 3.5 IND	-	-
	[13]	0.8	99.9	-	21.6	-	3.7 CN / 3.9 IND	-	-
	[13]	2	98.9	0.52	22.1	-	3.0 CN / 2.9 IND	-	-
	[15]	0	100	1.5	17.2	-	3.3 IND	-	-
	[15]	0.47	99	1.2	17.9	-	4.1 IND	-	-
	[15]	0.94	99	0.9	18.3	-	5.7 IND	-	-
	[15]	2.81	99	1.0	16.1	-	3.2 IND	-	-
	[15]	5.54	99	1.0	14.3	-	2.5 IND	-	-
	[16]	0	99.5	1.17	22.3	-	3.2 CN	-	-
	[16]	0.8	97.4	1.23	21.9	-	4.3 CN	-	-
	[17]	0	-	-	-	290	3.9 IND	-	-
	[17]	0.25	-	-	-	384	5.7 IND	-	-
	[17]	0.75	-	-	-	461	6.2 IND	-	-
	[17]	1	-	-	-	406	5.5 IND	-	-
	[24]	0	99.9	2.5	21.9	500	2.8 IND	< 10 -12	-
	[24]	0.17	99.9	0.98	24.5	410	3.1 IND	< 10 -12	-
	[24]	1.03	99.8	0.35	21.3	400	3.6 IND	0.02	-
	[24]	1.74	98.2	0.27	20.1	310	3.3 IND	2.67	-

CN Chevron Notch; IND: Indentation; RC: R-curve; SEVNB: Single Edge V-notched beam.

Acknowledgments

The authors thank S. Huet for preliminary works on sample synthesis and characterization. Electron microscopy was performed at "Centre de microcaractérisation Raimond Castaing -UMS 3623" (Toulouse) and the authors thank L. Weingarten for help with the TEM observations. The SPS was performed at the Plateforme Nationale CNRS de Frittage-Flash (PNF², Toulouse).

Declaration of Competing Interest

None.