L Acher

D Chartier

A Dannoux-Papin

J Haas

M Courtial

M-N De Noirfontaine

F Dunstetter

D Gorse-Pomonti

Radioactive waste conditioning: the choice of the cement matrix versus irradiation

The aim of this study is to compare the behavior of Portland and Ciment Fondu® cement under irradiation taking into account both real cement pastes and synthetic hydrates. First, γ-irradiations were performed using a 60 Co source (dose rate: 0.17 -0.25 Gy.s-1, dose: up to 500×10 3 Gy). Thermogravimetric analysis measurements were performed in order to determine the amount and the type of water involved. H2 gas production was measured by gas chromatography. Regardless of the water to cement ratio (W/C) chosen (0.2, 0.4 and 0.6), it is shown that Ciment Fondu® pastes produce less H2 under irradiation. Moreover, the H2 production of portlandite and gibbsite, constituent hydrates of Portland and Ciment Fondu® cements respectively, shows that the amount of gas produced depends on the hydrate nature. Secondly, portlandite and gibbsite were electron-irradiated up to 300 MGy and 3 GGy using the LSI SIRIUS accelerator platform. X-Ray Diffraction analyses were performed before and after irradiation in order to investigate structural damage. Only limited structural disorder was observed, which confirms the good stability of both hydrates under present irradiation conditions.

INTRODUCTION

Nowadays, Portland cement based matrices are widely used for conditioning and embedding nuclear waste. The literature reports a large number of studies on the impact of radiations on this type of material in order to demonstrate the validity and the sustainability of this solution [START_REF] Bibler | Radiolytic gas generation in concrete made with incinerator ash containing transuranium nuclides[END_REF][START_REF] Soo | The effect of gamma radiation on the strength of Portland cement mortars[END_REF][START_REF] Noshita | Generation mechanism of hydrogen gas from hardened cement paste by γ-irradiation[END_REF]. The interaction between the ionizing radiation and the matrix leads to (i) radiolysis gas production, mainly H2, which has to be minimized (ii) mechanical, textural and mineralogical modifications. Furthermore, due to the multiplicity and the complexity of the types of nuclear waste to be treated, alternative matrices to Portland cement are required. Recent unpublished results show a factor of three in the H2 radiolytic yield between Portland and Fondu® cement. Our aim is to compare the behavior of these two cements under irradiation taking into account both real cement pastes and synthetic hydrates. Two aspects are considered: H2 production and structural damage. In first approximation, two hydrates are considered: portlandite Ca(OH)2, one of the main constituent of Portland cement and gibbsite Al(OH)3, one of the main constituent of Ciment Fondu® cement (part of the Calcium Aluminate Cements (CAC)). Throughout the paper, in order to simplify the chemical formula of the various compounds discussed below, we use the shorter oxide abbreviations: C = CaO, S = SiO2, A = Al2O3, F = Fe2O3, T = TiO2, H = H2O.

EXPERIMENTAL Sample Preparation and Characterization

Portland (60 % C3S, 20 % C2S, 19 % C4AF and 1 % others) and Ciment Fondu® (50 % CA, 8 % C4AF, 8 % β-C2S, 8 % C3FT, 7 % Fe3O4 and 19 % others) cements were used. Cements were mixed with distilled water with a W/C ratio equal to 0.2, 0.4 and 0.6. Samples will be referred to as Portland-0.2, Fondu-0.2 and so on increasing the number according to the W/C ratio. Portland paste maturation occurred in sealed tubes, at room temperature, in order to limit atmospheric exchanges. Ciment Fondu® samples were cured at room temperature under 98 % of relative humidity during one week and then heated at 50 °C during one more week in order to ensure the total conversion of the metastable hydrates. Thermal Gravimetric Analysis (TGA, Netzsch STA 409 instrument, heating rate: 10 K.min -1 under nitrogen atmosphere, from room temperature to 1000 °C) were performed in order to determine the amount and type of water. Portlandite CH (VWR Chemicals Prolabo®, 96 %) and gibbsite AH3 (Merck, 99,6 %) commercial samples were used. For gas measurements, these hydrates had the advantage of only containing hydroxyl groups, consequently a heat treatment up to 150 °C during 48 hours in order to eliminate adsorbed water is possible. The amount of water was checked by TGA; a plateau is observed for both hydrates up to 200 °C. X-Ray Diffraction analysis were performed before and after electron irradiation in order to investigate any possible structural damage. Powder XRD analysis were performed using a PANalytical diffractometer, with a fast detector (X-celerator), in the Bragg Brentano geometry (CuKα radiation, λKα1 = 1.540596 Å and λKα2 = 1.544410 Å). All the data were collected in the same conditions, in the angular range 5° < 2θ < 90°, with step intervals of 0.02° (2θ) and scan set time of 1.5 hours. Rietveld refinements were performed using the TOPAS software (version 4, Bruker-AXS, Karlsruhe, Germany, 1996-2007) based on the fundamental parameters approach [START_REF] Cheary | A fundamental parameters approach to X-ray line-profile fitting[END_REF].

Irradiation Experiments

Two types of irradiation experiments were performed:

(i) gamma irradiation at low doses: Irradiations were conducted using a 60 Co source of the Gammatec facility (Steris, France). Cement pastes, CH and AH3 were irradiated up to 600 kGy at 900 Gy/h and up to 200 kGy at 600 Gy/h respectively in order to determine their hydrogen radiolytic yield.

(ii) electron irradiation at "high" doses: Small pellets (13 mm diameter and 1 mm thickness) of CH and AH3 were irradiated using the LSI SIRIUS accelerator platform. Electrons of 2.5 MeV were used. At this energy, all electrons pass through the sample (projected range was 4 mm). Irradiation conditions are summarized in table 1. Adsorbed doses were estimated using ESTAR code [START_REF] Berger | Stopping Powers and Range Tables for Electrons, Protons and Helium Ions[END_REF].

H2 Determination

Hydrogen production was measured by gas chromatography (Varian CP-3800 instrument equipped with a thermal conductivity detector and a molecular sieve-type column, furnace and detector temperature: 35 °C and 120 °C respectively). Argon was used as carrier gas. About 10 mL of gas were manually injected for each measurement. The radiolytic yield in H2, G(H2), is given by the slope of the linear regression of the number of moles of hydrogen (per kilogram of material), plotted versus the dose.

RESULTS

Low doses gamma irradiation Portland and Ciment Fondu® pastes

The hydrogen production of Ciment Fondu® pastes irradiated under γ-rays was measured. The impact of the type of matrix and the water content (related to the W/C ratio) on the hydrogen production are both explored.

The radiolytic yields in H2, G(H2) as a function of the W/C ratio is sketched in Figure 1. It appears that H2 production depends on the type of cement. Up to W/C = 0.4, Fondu® cement pastes produce three times less than Portland cement. At W/C = 0.6, the gap between the G(H2) values is not significant ; the type of matrix seems to not matter anymore. These observations are consistent with TGA results (Figure 2). At W/C equal to 0.2, Ciment Fondu® paste only contains adsorbed water whereas Portland cement contains free water, in particular due to the presence of Calcium Silicate Hydrates (C-S-H). Note that the presence of adsorbed water was confirmed by washing Fondu-0.6 sample with isoproponal and heating it up to 60 °C in order to eliminate residual water. The TGA curve obtained is the same as the one obtained for Fondu-0.2 sample. At W/C equal to 0.6, the amount of free water is important in both matrices, which should explains the lower gap between G(H2) values.

Portlandite CH and gibbsite AH3 samples

The hydrogen production of portlandite CH and gibbsite AH3 samples irradiated under γ-rays and heated up to 150 °C was measured. Their water content was measured by TGA (Figure 3). No adsorbed water is detected in both hydrates. CH and AH3 contains respectively 21.8 % and 29 % water as hydroxyls groups. The radiolytic yields in H2 measured on both hydrates are the following: G(H2)(CH) = (0.042 ± 0.004) 10 -7 mol.J -1 ; G(H2)(AH3) = (0.009 ± 0.005) 10 -7 mol.J -1 ; When normalized to the total amount of water contained in CH and AH3, 21.8 % and 32.9 % respectively, radiolytic yields are equal to 0.19 mol.J -1 and 0.027 10 -7 mol.J -1 . In comparison, the primary yield of bulk water is equal to 0.45 10 -7 mol.J -1 . So, it appears that (i) both hydrates produce hydrogen under irradiation, and (ii) this production is different between CH and AH3 whereas the same type of water is engaged.

Concluding remark

The radiolytic yield results obtained on cement pastes and synthetic hydrates are consistent. Both Portland cement paste and CH produce more hydrogen under gamma irradiation than Ciment Fondu® paste and AH3 respectively. For future studies, it appears that the study of the hydrates should really help us to improve the understanding of the H2 production of cement matrices.

High doses electron irradiation

Portlandite CH and gibbsite AH3 structural resistance under electron irradiation was investigated by XRD. Not irradiated, irradiated up to 270 (310) MGy and up to 3.5 (3.0) GGy CH (AH3) results are shown in Figure 4 and Figure 5.

Powder XRD patterns give intensity, width, position and also shape of each individual Bragg peaks, which can be associated to a structural arrangement of the material under study. The main results of Figure 4 and 5 are the following: In portlandite, (i) the intensity decreases following electron irradiation; (ii) there is an asymmetric broadening of some Bragg lines and (iii) an anisotropic shift of the Bragg lines positions. In gibbsite, similar effects are observed, but less pronounced. However, due to the more complex atomic structure of gibbsite (monoclinic) compared to portlandite (rhombohedral), the interpretation of the results is made more difficult.

Finally experimental results clearly show that Portlandite and gibbsite are both resistant to electron irradiation at high doses (no amorphization, not even a beginning of amorphization). As for portlandite a slight Crystallization water increase of interlayer spacing is seen with no consequence on the overall structural integrity. Work is in progress (using Electron Paramagnetic Resonance spectroscopy) in order to estimate the proper role of electron irradiation on the hydrogen bonding in these compounds.

CONCLUSIONS

This study on Portland and Fondu® cements highlights (i) a significant dependence of the composition of the hydrates on the H2 production and (ii) a rather low impact of electron radiations on the structure. A complementary study on other hydrates is currently underway.

Figure 1 .

 1 Figure 1. Portland and Ciment Fondu® radiolytic yield versus the water to cement ratio

Figure 2 .

 2 Figure 2. Portland and Ciment Fondu® pastes water content. TGA shows three types of water: 1) adsorbed water below 250 °C in Fondu-0.2, 2) free water below 250 °C in Portland-0.2, Portland-0.6 and Fondu-0.6, 3) crystallization water for all samples above 250 °C.

Figure 3 .

 3 Figure 3. Portlandite (CH) and gibbsite (AH3) water content (after heat treatment up to 150 °C during 48 hours). TGA shows an absence of adsorbed water for both hydrates.

Figure 4 .

 4 Figure 4. X-Ray diffraction pattern of portlandite Ca(OH)2: before irradiation and after electron irradiation at two doses (270 MGy, 3.5 GGy).

Figure 5 .

 5 Figure 5. X-Ray diffraction pattern of gibbsite AH3: before irradiation and after electron irradiation at two doses (310 MGy, 3 GGy).

Table 1 .

 1 Electron irradiation conditions

		CH		AH3
	Current (μA)	20	25	29	24
	Flux (×10 13 e -.cm -2 .s -1 )	7.0	8.8	10	8.5
	Dose (MGy)	300	3 000	230	2500
	Temperature (°C)	<43	<49	41	41

ACKNOWLEDGMENTS

This work was performed with financial support of CEA Project « MAD-DEM SPF-AVM ». We thank the French EMIR network for supporting this research. We are greatly indebt to B. Boizot and O. Cavani (Ecole Polytechnique, Palaiseau, France) for their help during the irradiations.


domain: chim phys

text:
Dr Olivier Bardagot
email: olivier.bardagot@dcb.unibe.ch

Cyril Aumaître

Anthony Monmagnon

Jacques Pécaut

Pierre-Alain Bayle

Dr Renaud Demadrille
email: renaud.demadrille@cea.fr

Revisiting doping mechanisms of n-type

2

Recently, remarkable progress of conducting polymers in terms of electrical properties opened up the field of thermoelectricity to organic semiconductors (OSCs). 1,2 For thermoelectric applications organic materials reveal some unique advantages such as low thermal conductivity, low cost, and ease of process on flexible substrates. 3,4 Since pioneer works dating from the last century, 5,6 molecular engineering and optimization of the doping process allowed to significantly improve the thermoelectric performances of doped OSCs reaching electrical conductivity (σ) beyond 2 x 10 5 S cm -1 (equivalent to platinum). 7 One of the most popular doping method of OSCs implies ion-pair formation via direct electron transfer. 8,9 This mechanism has been extensively studied for p-doped materials using various organic and inorganic dopants (halogens 10 , strong Lewis acid 11 (e.g. FeCl3 7 ), or π-conjugated accepting molecules (e.g. F4TCNQ 12 ), affording σ over 100 S cm -1 for many p-type polymers. 13 Comparatively, no n-doped OSC is reported with σ over 20 S cm -1 to date. One reason for the delayed development of highly conductive n-doped systems is their lower air-stability. 14 For p-doping via direct electron transfer, electrons are transferred from the OSC-HOMO to the dopant-LUMO, while for n-doping, electrons are transferred to the OSC-LUMO from the dopant-HOMO, therefore involving energy levels of much higher energies (lower ionization potentials). 9 If these levels are above the reduction potential of O2/H2O, n-doped systems are chemically unstable at air.

To tackle air-instability of n-dopants, the solution-processable small molecule (4 (1,3 dimethyl-2,3-dihydro-1H-benzoimidazol-2-yl)phenyl)dimethylamine (N-DMBI, named N-DMBI-H in this manuscript to emphasize the presence of the labile hydrogen atom) has been introduced as n-dopant precursor (Figure 1). 15 It was associated with various hosts such as carbon nanotubes 16 , conductive polymers 17 , and fullerene derivatives which led to the highest figure of merit ever reported for single-host organic thermoelectrics (ZT = 0.34 at 120°C). 18 We summarized some recent uses of N-DMBI-H in the organic thermoelectric field in Table S1. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637

N-DMBI-H doping mechanism is remarkable as, in most cases, it does not involve direct electron transfer but a two-step process comprising an activation step. 13 The doping pathways currently admitted are presented in Figure 1. The essential role of the -H atom was confirmed by the lost of the doping ability when substituting -H by a methyl group. 19 In 2013, spontaneous doping of PC61BM via heterolysis bond cleavage (pathway I) was evidenced in solution (chlorobenzene) without heating. 20 The postulated mechanism involves a two-step process with (i) a bimolecular hydride transfer from N-DMBI-H to the fullerene, followed by (ii) an electron transfer from the hydride-reduced PC61BM-H -to the unreduced PC61BM to form the PC61BM •-radical anion. Nonetheless, a hydrogen atom transfer was not completely ruled out in this study. Such mechanism remains an exception in the field and has never been evidenced with n-type polymers. In contrast, recent density functional theory (DFT)-supported mechanistic studies suggest that pathway II is the dominant mechanism when thermal annealing is performed on solid-state films. 21,22 Pathway II is characterized by an homolysis bond cleavage of the weak C-H bond, forming the neutral N-DMBI • radical with a singly occupied molecular orbital (SOMO) level DFT-calculated at ca. -2.4 eV 19,23 .

In this work, we found a SOMO level lying at -2.70 eV based on bond dissociation energy (BDE) calculations starting from coordinates obtained by single-crystal X-Ray diffraction (XRD) (.cif files in SI). The doping effect then occurs by spontaneous electron transfer from the unstable radical-SOMO to the host-LUMO. Lastly, pathway III involves the direct electron transfer from the N-DMBI-H-HOMO (at -4.4 eV 23,24 ) to the host-LUMO. Only few exceptions were reported 23,25 as such pathway is thermodynamically non favourable for most of host materials due to LUMO levels superior to -4.4 eV (Table S1). Note that, in all reports, the doping procedure involves a thermal activation step (Table S1). Previously reported examples of n-doping with N-DMBI-H in the solid state involve post-deposition thermal treatments (Table S1). This thermal step is claimed to activate the dopant, suggesting that the Gibbs free This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637

energy is positive at RT (with ΔH > 0 and ΔS > 0). 19 Providing external energy seems therefore primordial to trigger activation of N-DMBI-H dopant precursor. Herein, we demonstrate a convenient way to activate N-DMBI-H using UV-light in solution at room temperature (RT). We bring experimental evidences for unravelling the photo-activation mechanisms of N-DMBI-H, and we highlight the influence of the dielectric constant of the media in the prevalence of pathway I and II. In this study, we also disclose degradation pathways and clearly show the crucial importance of working in anoxic environments with degassed solvents to avoid parasitic O2-mediated side reactions.

The photo-activation of the dopant has been speculated but never demonstrated. 15,20 As a first approach, we monitored the evolution of absorbance spectra of N-DMBI-H solutions under diffuse daylight exposure and under dark conditions (Figure 2). The analysis of crystal 1 confirms the presence of the hydrogen atom (H1) on the sp3 carbon (C1) which induces a strong torsion angle between the benzimidazole and the benzene dimethylamine plane (~97°, Table S2). Exposing N-DMBI-H in acetonitrile to daylight at air leads to N-DBMI + cation (crystal 2, Table S3). This conclusion is supported by: (i) the disappearance of the H1 hydrogen atom, (ii) the partial planarization of the molecule suggesting that C1 turned into a sp2 carbocation, (ii) the shorter C1-N1 and C1-N2 bond lengths characteristic of C-N double bonds (~1.34° Å vs 1.47 Å) (Figure S3). The structure of the counter-anion could not be solved (Table S2), however a similar structure stabilized by chloride ions (Cl -) was found when reproducing the experiment in chloroform (crystal 2', Figure S3). In this case, chlorine ions are available from traces of HCl usually present in CHCl3 because of its decomposition into toxic phosgene and HCl when exposed to molecular oxygen and UV-light.

The presence of Cl -increases the overall dielectric constant of pure chloroform (apolar, ε = This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. In presence of a host, the stability of the doped system is therefore expected to be dominated by the stability of the reduced host (polymer or small molecule).

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Interestingly, performing the same experiment in apolar solvents revealed a radically different behaviour. Exposing N-DMBI-H in toluene to daylight at air results in the formation of an amide derivative of N-DMBI (crystal 3, Table S4, Figure 3). The same result was obtained in chlorobenzene. Such DMBI-derived amide structure was already reported as side product obtained during the synthesis of DMBI-dimers. 26 We speculate a radical-induced 3 O2-mediated degradation pathway, which argues in favour of the preferential homolysis of the C-H bond in apolar media (pathway II). A mechanism explaining the formation of the DMBI-derived amide is proposed in Figure S6 (referred to as pathway IV). On the contrary, in polar media, N-DMBI + cation is favourably formed, likely through a hydride release stabilized by the polarity of the medium (pathway I).

To support our speculations and gain insights on the energetics of the competing I and II activation pathways, the Gibbs free energy changes of the following rate-limiting reactions were calculated by DFT:

N-DMBI-H ⇋ N-DMBI + + H - (heterolysis, cf. pathway I) N-DMBI-H ⇋ N-DMBI • + H • (homolysis, cf. pathway II)
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637

The molecule geometries were optimized using the B3LYP-D3/TZ2P approach starting from the experimental set of Cartesian coordinates obtained by single-crystal XRD. The geometry of the neutral N-DMBI • radical was DFT-optimized starting from the cation structure. Solvation effects were investigated by performing the same calculations in different continuum polarizable models set for acetonitrile (polar) and toluene (apolar). The Gibbs free energy changes of the reactions of heterolysis and homolysis were calculated as follow: ΔG298 = G(products) -G(reactant), with G=H-TS, and reported in Table 1. The H and S values calculated for each reactants and products are reported in Table S5. All ΔG298 are positive, confirming that these reactions are not spontaneous at RT neither in acetonitrile nor in toluene. In acetonitrile, the heterolysis is found thermodynamically more favourable than the homolysis, hence supporting our previous statement and in accordance with the enthalpy change reported. 27 By opposition, ΔG298 heterolysis and ΔG298 homolysis are similar in toluene, thereby suggesting a competition between these two reactions. Note that ΔG300 ≈ 20.3 kcal/mol (84.9 kJ/mol) was found experimentally in toluene in presence of fullerene. 20 In comparison to Table 1, this lower value underlines the decrease of the activation energy barrier due to host:N-DMBI-H dipolar interactions and the propensity of the host to form C-H bond, as suggested by Naab and coworkers. 20 However, our calculations strongly suggest that the dielectric constant of the medium has an influence on the prevalence of the activation mechanism of N-DMBI-H: pathway I being dominant in polar media, whereas pathway II is slightly favoured in apolar media.

Solvent
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637

We believe that these different mechanisms can take place when N-DMBI dopes organic semiconductors of different polarity in the solid state. This might explain why polar side chains facilitates molecular doping leading to increased doping efficiency and electrical conductivity. 28 The thermal activation of N-DMBI is well established; however, the required temperature remains uncertain. Post-deposition thermal annealing ranging from 80°C to 150°C is generally applied, depending on the experimenter and the host material without a clear rationale (Table S1). In the literature, thermogravimetric analysis (TGA) has revealed that N-DMBI is a stable compound up to 200°C under inert atmosphere (N2) before decomposition 21 . In another article, a slight gain of mass above 90°C was evidenced and assigned to oxidation. 18 To shed light on the behaviour of N-DMBI upon thermal annealing, we heated up N-DMBI-H powder at 120°C for 2 hours in ambient conditions and analysed the residue without purification. The UV-Vis absorbance and NMR spectra of the residue are compared to the signatures of the neat N-DMBI-H, the N-DMBI + cation and the crystal 3 mainly composed of the amide derivative (Figure 4). This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637

gain is found at 100°C, reaching a maximum of +4.8% at 180°C. We can therefore conclude that: (i) the temperature to trigger N-DMBI activation is ~100°C, and (ii) the dominant mechanism is pathway II (cf. pathway IV). The C-H homolysis leads to the generation of unstable N-DMBI • radical that readily reacts with 3 O2 to form the amide derivative. In other words, the presence of molecular oxygen during N-DMBI-H activation leads to the formation of an amide degradation product that decreases the doping efficiency and acts as a morphological impurity, thus likely reducing the overall doped layer conductivity.

As a take-home message, N-DMBI-H activation must be triggered in a strictly anoxic environment to maximize the doping effect and the conductivity enhancement. It is interesting to note that crystal 3 is not only composed of the amide but also of N-DMBI + cation (absorption band at ~350 nm, NMR doublet of doublet at ~7.65 ppm, Figure S7). The presence of both species demonstrates the competition of hetero-and homolysis pathways in toluene, in accordance with the small difference of Gibbs free energy found by DFT (Table 1).

To illustrate the extreme sensitivity of N-DMBI-H to O2 in a practical n-doping example, we blended N-DMBI-H with P(FBDOPV-2T-C12), a polymer recently synthesized in our laboratory (Figure 5 a). 24 An electrical conductivity of 4.2 x 10 -2 S cm -1 after thermal annealing can be achieved with this system. Doped films of P(FBDOPV-2T-C12) exhibit thermoelectric properties, with a negative Seebeck coefficient of -265 μV K -1 and a thermoelectric power factor (PF) of 0.30 μW m -1 K -2 at 303 K that rises up to 0.72 μW m -1 K -2 at 388 K.

In This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637 The blend system exhibits an ESR signal at RT, indicating unpaired radicals. Interestingly, heating up the solution induced a decrease of the ESR signal linewidth (Figure 5 c). In biological studies, the correlation of the ESR signal linewidth with the O2 content is common. 29,30 Heisenberg spin exchanges with paramagnetic O2 cause a broadening of the linewidth. 31 We can therefore correlate the decrease of the signal linewidth with the consumption of O2 in the solution over time. A sudden drop of the number of radicals is observed after 5 minutes at 100°C (Figure 5 d), suggesting a first step in which N-DMBI • is consumed through O2-mediated reactions according to the mechanism proposed for pathway IV (Figure S6). In a second step, the progressive consumption of O2 goes on (Figure 5 c) but an increase of radicals is observed (Figure 5 d). We can conclude that the effective doping of the polymer backbone is competing with side reactions involving O2 reduction. Considering the low polarity of chlorobenzene (apolar, ε = 5.69), this finding is consistent with the prevalence of pathway II in apolar media.

O2-mediated reactions are detrimental for the overall doping efficiency and should be considered when hot processing is required for material deposition, or when pre-activation in solution is performed. In apolar media (e.g. chlorobenzene or toluene): homolysis bond cleavage is dominant, indicating SOMO-mediated doping after H • release, however a non-negligible contribution of heterolysis should be considered. Alternatively to thermal activation, we demonstrate that photo-activation of N-DMBI-H is possible under UV-light irradiation, even at fluences as low as diffuse daylight. To illustrate the practical benefit of this finding, we show that P(FBDOPV 2T C12) thin films can be doped with N DMBI using UV-light irradiation only (Figure S12).

This result opens up the way to high-resolution doping patterning using shadow masks. Our findings bring important guidelines for the development of N-DMBI-H doped systems applicable in thermoelectrics and organic electronics.

Supplementary Material

See supplementary material for UV-Vis absorption spectra, Single-crystals X-ray diffraction data, ESR and NMR spectra, DFT calculation, and thermogravimetric analysis of the compounds, detailed doping and degradation mechanisms, and photo-induced n-doping experimental data in thin films.

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637

Figure 1 :

 1 Figure 1: Different n-doping pathways reported for N-DMBI-H dopant precursor. The neat molecule is named N-DMBI-H to emphasize the presence of the labile hydrogen atom, while the neutral imidazoline radical is written N-DMBI • . Italic: Energy levels (DFT).

Figure 2 :

 2 Figure 2: Evolution of UV-Vis absorbance spectra of neat N-DMBI-H over time when kept in dark and exposed to ambient diffuse daylight in solution in chloroform (stabilized by ethanol).

Figure 3 :

 3 Figure 3: Crystallographic data of neat N-DMBI-H (crystal 1) and photo-induced products obtained from acetonitrile (crystal 2) and from toluene (crystal 3) solutions. Simplified reaction pathways highlighting the impact of the dielectric constant of the medium. ϴ is the dihedral angle between the average planes formed by the benzimidazole moiety (green plane) and the phenyl ring (red plane).

  DOI: 10.1063/5.00476374.81) which can hence be compared to acetonitrile. The formation of N-DMBI + cation in CDCl3 upon UV-light irradiation (λ=[315-435 nm]) was confirmed by the complete assignment of the NMR signals for this molecule (based on 1 H and13 C NMR experiments, FigureS7, FigureS8and FigureS9) and the comparison with the ones of N-DMBI-H. The disappearance of the NMR signal of H1 (4.8 ppm) and the absence of electron spin resonance (ESR) signal (FigureS4), confirmed the cationic nature of this specie. The carbocation is stabilized by donating mesomeric effect (+M) exerted by the two tertiary amines of the benzimidazole and the phenyl ring.

Figure 4 :

 4 Figure 4: (a) UV-Vis absorbance spectra and (b) corresponding 1 H NMR spectra in CDCl3 of (from top to bottom): N-DMBI-H under dark conditions, after UV-light irradiation (λ=[315-435 nm], F1-30W/15 min, N-DMBI + cation), crystal 3 (from toluene), and the residue of N-DMBI-H heated at 120°C for 2 hours under ambient conditions.

  an argon-filled glovebox, aliquots of a freshly prepared P(FBDOPV-2T-C12):N-DMBI-H (62 mol%) anhydrous chlorobenzene solution stirred at RT (t0), 100°C (5, 10, 30, 60, 90 minutes) and allowed to cool down to RT (1080 minutes) were collected and analysed by ESR at RT (Figure 5 b).

Figure 5 :

 5 Figure 5: (a) Chemical structures of the n-type polymer (regiorandom x+y with x: R1=C12H25, R2=H; y: R1=H, R2= C12H25) and N-DMBI used to evidence O2 consumption. (b) ESR spectra of doped-P(FBDOPV-2T-C12), stirred at RT at t0 (black line), 100°C from 5 to 90 min, RT after (red line), in solution in anhydrous chlorobenzene (ESR tubes prepared in Ar-filled glovebox, O2 < 10 ppm, dark conditions). Evolution of the signal (c) linewidth and (d) intensity (double integration) as a function of the stirring time at RT at t0, 100°C from 5 to 90 min, RT after.

  Thought this study of the single molecule dissociation of N-DMBI-H combining UV-Vis absorption, single-crystal XRD, DFT, NMR, TGA and ESR experiments, we clarified the necessary conditions to thermo-and photo-activate N-DMBI-H for n-doping. We determined that, in the solid state, a temperature superior to 100°C is required to trigger N-DMBI-H This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0047637activation via C-H homolysis bond cleavage. We evidenced the prompt oxidation of the resulting N-DMBI • radical, forming an inactive amide by-product. We highlight that molecular oxygen should be strictly avoided during N-DMBI-H doping process, even for hosts considered as air-stable in their doped state. Therefore, for a better control of the doping process, N-DMBI-H and N-DMBI-H:host blend solutions should be prepared in dark conditions using degassed solvents and post-deposition activation should also be performed in inert atmosphere.Finally, we show that the doping mechanism in solution (C-H heterolysis versus C-H homolysis) is influenced by the dielectric constant and the nature of the solvent used. In polar media (e.g. acetonitrile or e.g. acetonitrile or chloroform containing Cl -from degradation):heterolysis bond cleavage is largely dominant, indicating direct doping via hydride H -transfer.

Table 1 :

 1

	model ΔG298 heterolysis ΔG298 homolysis
	Acetonitrile	+29.19 kcal/mol	+75.40 kcal/mol
	Toluene	+78.92 kcal/mol	+74.97 kcal/mol

Summary of Gibbs free energy changes to release a hydride anion (pathway I) or a hydrogen atom (pathway II) at T = 298.15K.

The data that supports the findings of this study are available within the article and its supplementary material.

The authors acknowledge the ANR for funding through the HARVESTERS project (ANR-16-CE05-0029-01) and the LABEX Laboratoire d'Alliances Nanosciences-Energies du Futur (LANEF, ANR-10-LABX-51-01). O.B acknowledge CEA for financial support through a PhD Grant.


Marie-Noëlle De Noirfontaine

Loren Acher

Mireille Courtial

Frederic Dunstetter

Dominique Gorse-Pomonti
email: dominique.gorse-pomonti@polytechnique.edu

Frédéric Dunstetter

Dominique Gorse -Pomonti

5 MeV SIRIUS accelerator

Introduction

Brucite Mg(OH)2 and portlandite Ca(OH)2 are isomorphous [START_REF] Petch | The Hydrogen Positions in Portlandite, Ca(OH)2, as Indicated by the Electron Distribution[END_REF][START_REF] Chaix-Pluchery | Structural prereactional transformations in Ca(OH)2[END_REF][START_REF] Catti | Static Compression and H Disorder in Brucite, Mg(OH)2, to 1l GPa: a Powder Neutron Diffraction Study[END_REF]. They belong to the family of CdI2 type hydroxides with a layered structure, giving them interesting physico-chemical and electronic properties for a large number of industrial applications. The M (M = Ca, Mg) cations are placed at the centre of edge-sharing [MO6] octahedra (Fig. 1): they are bonded to six neighboring hydroxyl ions and the hydroxyl ions are bonded to three M cations. The space group is P m1 (n°164).

The cell parameters are respectively a = 3.5918 Å and c = 4.9063 Å (c/a = 1.3659) in portlandite [START_REF] Chaix-Pluchery | Structural prereactional transformations in Ca(OH)2[END_REF] and a = 3.1497 Å and c = 4.7702 Å (c/a = 1.5145) in brucite [START_REF] Catti | Static Compression and H Disorder in Brucite, Mg(OH)2, to 1l GPa: a Powder Neutron Diffraction Study[END_REF]. The cell parameters of the refined structure model proposed by Chaix-Pluchery et al. are used for portlandite [START_REF] Chaix-Pluchery | Structural prereactional transformations in Ca(OH)2[END_REF], since their neutron diffraction study specifies accurately the H atoms positions and the O-H bond lengths. The octahedra are said flattened, compared to regular octahedra formed with close-packed spheres for which an higher c/a ratio of 1.633 is calculated [START_REF] Brindley | Structural and IR relations among brucite-like divalent metal hydroxides[END_REF]. The interlayer spacing h(inter), defined by Brindley et al. [START_REF] Brindley | Structural and IR relations among brucite-like divalent metal hydroxides[END_REF], decreases from h(inter) = 2.689 Å in brucite to h(inter) = 2.616 Å in portlandite, after Desgranges et al. [START_REF] Desgranges | Interlayer interactions in M(OH)2: a neutron diffraction study of Mg(OH)2[END_REF]. The recently calculated electronic structure of brucite and portlandite reveals only slight differences between them [START_REF] Pishtshev | Materials properties of magnesium and calcium hydroxides from first-principles calculations[END_REF].

The thermal decomposition of Mg(OH)2 into MgO under the electron beam and of isotructural compounds like Ca(OH)2, has been largely studied for over fifty years by neutron diffraction, X-ray diffraction and electron microscopy [2, 7 -12]. It was finally concluded that the thermal and electronbeam-induced transformation are identical and that this transformation is pseudomorphic and topotactic in spite of a huge volume reduction between the initial and final phase, involving the proton mobility, formation of H2O molecules from hydroxyl ions sites OH -and elimination along the 00l cleavage planes followed by the "final" structural transformation. Note that the complete decomposition of Mg(OH)2 into MgO at "high" flux under the 80 keV electron beam of a microscope has been reported as early as 1958 by Goodman [START_REF] Goodman | The decomposition of magnesium hydroxide in an electron microscope[END_REF] and was said to proceed in a highly ordered manner, topotactically, by simple rearrangement of the atoms of the parent crystal, already by Goodman [START_REF] Goodman | The decomposition of magnesium hydroxide in an electron microscope[END_REF] and later by Dahmen and coworkers [START_REF] Dahmen | Microstructural evolution during the decomposition of Mg(OH)2[END_REF].

The NEC Pelletron accelerator of the SIRIUS platform is used here to study the radiation damage effects caused by electron irradiation to portlandite Ca(OH)2 and brucite Mg(OH)2. Portlandite enters in the composition of the Portland cement pastes today proposed for the conditioning of nuclear wastes [START_REF] Acher | Radioactive waste conditioning: the choice of the cement matrix versus irradiation[END_REF]. It is thus essential to determine its structural stability and resistance under (somehow) representative irradiation conditions, while brucite is being studied here for comparison purposes.

There is today a substantial literature on electron radiation damages in ceramics, including complex ceramics proposed for nuclear waste disposal, as a function of the irradiation conditions, especially energy, dose and temperature [START_REF] Hobbs | Application of transmission electron microscopy to radiation damage in ceramics[END_REF][START_REF] Hobbs | Radiation effects in ceramics[END_REF][START_REF] Weber | Radiation effects in crystalline ceramics for the immobilization of high-level nuclear waste and plutonium[END_REF]. The dependency with respect to radiation flux was clearly far less studied for the obvious reason that two experimental techniques are necessary to cover a wide range of flux values, a Transmission Electron Microscope (TEM) for "high" electron fluxes (from ~10 17 to a few 10 22 e -.cm -2 .s -1 ) and a linear electron accelerator for "low" electron fluxes (in the range of 10 13 to a few 10 14 e -.cm -2 .s -1 ), with no overlap between them. The influence of electron irradiation at low flux on the structural properties of ceramics has been scarcely studied to date and it is often said that no significant electron radiation damage could be created at low electron flux and dose and that exposure to the intense electron beam of a TEM is required to seriously damage ceramic materials. We shall see later that brucite and porlandite are sensitive to electron irradiation for a flux of order 10 14 e - .cm -2 .s -1 and an absorbed dose of a few hundred MGy.

The slowing down of electrons through matter, as for other types of projectile and it is not different actually from other light or not projectiles (with exception of swift heavy ions), is caused by both electron excitations or ionizations of target atoms and subsequent radiolytic reactions (referred to as inelastic electronic energy loss) and ballistic collisions with target nuclei giving rise to atomic displacements (referred to as elastic nuclear energy loss) [START_REF] Balanzat | Basic phenomena of the Particle-Matter interaction[END_REF][START_REF] Hobbs | Radiation effects in analysis of inorganic specimens by TEM[END_REF]. When changing the projectile nature and velocity, only the balance between the two energy loss mechanisms will be affected. As for electron irradiation, two contradictory statements can be found in the literature. On the one hand, it is widely accepted that the contribution of ballistic collisions to an incident electron slowing down is negligible compared to that of the electronic excitations generated by its passage, and that over a wide energy range in excess of 1 MeV or above. But on the other hand if we go a little further, it appears that there are some radiation damages effects following electron irradiation which cannot be fully explained without taking into account some atomic displacements in the crystal lattice. This has been shown in rather recent studies dealing with ceramics foreseen for nuclear waste immobilization [START_REF] Aubin-Chevaldonnet | Paramagnetic defects induced by electron irradiation in barium hollandite ceramics for caesium storage[END_REF].

To the best of our knowledge, nothing is known about electron-radiation damage effects in Ca(OH)2 and Mg(OH)2, but only in CaO and MgO crystals. It was stated in 1984 by W. Hayes and A.M.

Stoneham that radiolysis of oxides such as CaO and MgO does not result in production of vacancies and interstitials [START_REF] Hayes | Defect and defect processes in nonmetallic solids[END_REF]. Since then this statement has apparently not been contradicted. It is also known that the threshold displacement energies, both cationic and anionic, are high in CaO and in MgO [START_REF] Zinkle | Defect production in ceramics[END_REF], which would not be in favour of a significant contribution of ballistic collisions to the electron radiation damage in both oxides and hydroxides. To be clear there is no indication in the literature about the possible cause of electron radiation damages in both brucite and portlandite. Coming back to the comparison between CaO and MgO, it is noteworthy that in 1966, Matzke and Whitton studied the ion-irradiation effects on a series of cubic single crystals (among them CaO and MgO) and non-cubic single crystals and in doing so that they have shown by electron diffraction that among the cubic crystals only MgO is damaged under 40 keV rare gas ion irradiation up to a dose of 2 x 10 16 ion cm -2 , with lattice disorder observed without phase change (as mentioned by the authors) in MgO, in contrast with other cubic crystals, like CaO, that all remain undamaged [START_REF] Matzke | Ion-bombardment-induced radiation damage in some ceramics and ionic crystals[END_REF].

In this paper, Powder X-ray Diffraction is used to analyze the irradiated hydroxides. Beyond identification of (perfect) crystalline phases and unit cell dimensions (peak positions and indexation), XRD is sensitive to deviations from perfect crystals taking the form of any structural disorder (whatever its origin, induced by irradiation, ball-milling …), provided that the defects are correlated at long distance and that the defective structure exhibits a long range correlated disorder [START_REF] Guinier | Théorie et technique de la radiocristallographie[END_REF]. Information on this point is contained in the shape of the diffraction spectra and the structured background between the diffraction peaks. However the point is that electron irradiation does not give rise to displacement cascades, but only to isolated point defects. So a priori one might wonder whether XRD is the suitable tool to study electron radiation damages. Moreover we are also well aware of the fact that hydrogen is a weak scatterer and that the charge density distribution of hydrogen in both compounds is not directly accessible by XRD. However, in this paper, and in spite of these non negligible drawbacks, significant changes in the XRD patterns of brucite and portlandite are observed following electron irradiation at low flux and doses in the range of 0.3 to 3 GGy. And a substantial difference in behavior under electron irradiation between the two compounds is highlighted.

Experimental

Materials

Commercial powders of portlandite Ca(OH)2 (Prolabo, 96 wt.% purity) and of brucite Mg(OH)2 (Prolabo, 99,7 wt. % purity) were used in this study. The impurity content was determined by X-ray fluorescence. For brucite, the impurities are: SiO2: 0.845 wt.%, SO3: 0.068 wt.%, CaO: 0.061 wt.%, Fe2O3: 0.008 wt.%, TiO2: 0.002 wt.%, K2O: 0.001 wt.%, P2O5: 0.001 wt.%. For porlandite, the main impurities are: MgO: 0.838 wt.%, SiO2: 0.406 wt.%, Al2O3: 0.084 wt.%, Fe2O3: 0.071 wt.%, SO3: 0.048 wt.%, MnO: 0.022 wt.%, Cl: 0.005 wt.%, TiO2: 0.001 wt.%. In ambient air, some unavoidable carbonation of the portlandite powder occurs according to the reaction Ca(OH)2 + CO2  CaCO3 + H2O. Consequently the presence of a significant amount of calcite or/and vaterite will be found by XRD in the portlandite sample [START_REF] López-Arce | Influence of relative humidity on the carbonation of calcium hydroxide nanoparticles and the formation of calcium carbonate polymorphs[END_REF]. For irradiation experiments the powders are pressed in order to make discs of 13 mm diameter (1.33 cm 2 ) and about 1 mm thickness.

Electron irradiation conditions and energy loss in the target

The irradiation conditions are reported in Table 1. The accelerator NEC Pelletron of the SIRIUS platform (Ecole Polytechnique, Palaiseau, France) was used for electron irradiation at 2.5 MeV. At this energy all electrons pass through the sample, the projected range being in the order of 4 mm. The values of average beam current are 20 A and 25 A, the corresponding fluxes are equal to 9.5 x 10 13 e -.cm - 2 .s -1 and 1.2 x 10 14 e -.cm -2 .s -1 respectively. The fluence  ranges from 7.4 x 10 17 e -.cm -2 to 9.6 x 10 18 e - .cm -2 .

The energy loss in the target is then estimated. The total inelastic energy loss is calculated using the ESTAR code [START_REF] Berger | Stopping Power and Range Tables for Electrons, Protons and Helium Ions[END_REF], based on the Bethe theory that gives an expression of the stopping power for fast electrons due to inelastic collisions events with electrons in a target of electron density 𝑁𝑍 2 (N atoms per unit volume of material of atomic number 𝑍 2 ) [START_REF] Rohrlich | Positron-Electron differences in energy loss and multiple scattering[END_REF]. The average energy loss per unit path length writes as:

-[ 𝑑𝐸 𝑑𝑥 ] 𝑖𝑛𝑒𝑙 = 2𝜋𝑒 4 𝑚 𝑒 𝑣 1 2 𝑁𝑍 2 {ln ( 𝑚 𝑒 𝑣 1 2 𝐸 1 2𝐼 2 (1-𝛽 2 ) ) + 𝐹(𝛽 2 )} (1)
With:

𝐹(𝛽 2 ) = 1 -𝛽 2 -(2√1 -𝛽 2 -1 + 𝛽 2 ) ln 2 + 1 8 (1 -√1 -𝛽 2 )
where 𝑚 𝑒 , 𝑣 1 and 𝐸 1 refer respectively to the electron mass, velocity and total energy, and with 𝛽 = 𝑣 1 𝑐 ⁄ (c = speed of light in vacuum) to take into account the relativistic character of the electrons.

Appearing in equation (1) as a logarithm, I refers to the mean excitation energy of the target [START_REF] Balanzat | Basic phenomena of the Particle-Matter interaction[END_REF]. A value of about 44 eV, almost the same for both portlandite and brucite, is used. This choice could be justified according to recent electronic structure calculations of both hydroxides [START_REF] Pishtshev | Materials properties of magnesium and calcium hydroxides from first-principles calculations[END_REF], revealing only slight differences in electronic density distribution between Mg(OH)2 and Ca(OH)2. Consequently, the inelastic energy loss, and in fine the structural damages, should be comparable in the two materials. The total inelastic stopping power is reported in Table 2. The absorbed doses (in Gy) are then deduced:

[ 𝒅𝑬 𝒅𝒙 ] 𝒊𝒏𝒆𝒍
x /using 1Gy= 1J/kg (Table 1). Energy loss via elastic collisions between electrons and target nuclei also contributes to the stopping power, giving rise to atomic displacements and possibly in fine well separated point defects. If sufficient energy is transferred to target nuclei, small cascades are possible. We have reported in Table 3 the maximum transferrable energy, 𝑇 𝑚𝑎𝑥 in eV, by electrons to the target atoms of atomic mass 𝐴 during a head-on collision at 2.5 MeV, and 100, 200 keV for comparison, using:

𝑇 𝑚𝑎𝑥 = 𝐸 1 (𝐸 1 + 2𝑚 𝑒 𝑐 2 ) 𝑀 2 𝑐 2 ⁄ (2)
or equivalently using 𝑚 𝑒 𝑐 2 = 511 𝑘𝑒𝑉, 𝑇 𝑚𝑎𝑥 = 2147.7 × 𝐸 1 (𝐸 1 + 1.022) 𝐴 ⁄ , with 𝐸 1 being the incident electron energy expressed in MeV.

The elastic scattering cross sections, or displacement cross sections 𝜎 𝑑 , as a function of the electron projectile energy were then calculated up to 2.5 MeV for Mg, Ca and O atoms, using the SMOTT/ POLY code based on the model proposed by D. Lesueur [START_REF] Caulfield | Point defects in electron-irradiated oxide single crystals[END_REF]. This model takes into account elastic collisions with atoms of different atomic mass and number and possible displacement cascades (primary elastic collisions due to the incident electrons and also secondary elastic collisions due to recoil nuclei with all target elements), neglects the electronic slowing down, and also both long range and local order in the solid target considered as amorphous. As input data, the threshold displacement energies 𝐸 𝑑 are required. We used the 𝐸 𝑑 values measured for magnesium and oxygen in an MgO crystal (𝐸 𝑑 (Mg)

= 52 eV and 𝐸 𝑑 (O) = 54 eV [START_REF] Hayes | Defect and defect processes in nonmetallic solids[END_REF][START_REF] Zinkle | Defect production in ceramics[END_REF][START_REF] Cheary | A fundamental parameters approach to X-ray Line-Profile Fitting[END_REF]), and that measured for calcium and oxygen in a CaO crystal (𝐸 𝑑 (Ca) = 50 eV and 𝐸 𝑑 (O) = 50 eV [START_REF] Hayes | Defect and defect processes in nonmetallic solids[END_REF][START_REF] Zinkle | Defect production in ceramics[END_REF][START_REF] Cheary | A fundamental parameters approach to X-ray Line-Profile Fitting[END_REF]), considering that the local octahedral environment is unchanged, or only slightly distorted from CaO to Ca(OH)2, and from MgO to Mg(OH)2. This is not an unreasonable assumption. The displacement cross sections of oxygen atoms in both brucite and portlandite are comparable above 1 MeV, this is less the case for the metal cations (Fig. 2). The displacement cross section of hydrogen is even not mentioned, which would be found very similar in the two compounds so long as the effective positive charge on the hydrogen atoms and effective negative charge on the OH -anions [START_REF] Pishtshev | Materials properties of magnesium and calcium hydroxides from first-principles calculations[END_REF] are not taken properly into account. The 𝜎 𝑑 values should vary between about 20 and 50 barn for Ca and Mg atoms for 2.5 MeV electrons depending on the 𝐸 𝑑 values. The maximum doses, expressed in dpa, estimated as the product 𝜎 𝑑 , are reported in Table 1 for two values of displacement cross sections.

Powder X-ray diffraction

X-ray diffraction (XRD) data were collected using a powder X-ray diffractometer (X'Pert Pro Model, MPD, Panalytical) in the Bragg-Brentano geometry (/). The experimental configuration is as follows: the incident X-ray beam (Cu radiation, 45 kV, 40 mA) passes through a 0.5° divergence slit, a 0.02 rad Soller slit, a 1° anti-scatter slit, and a 10 mm beam mask before sample, and the diffracted beam through a 5.5 mm anti-scatter slit, a Ni K filter, a 0.02 rad Soller slit before entering a fast X'Celerator detector of 2.546° (2) aperture. The instrument is operated in step-scan mode between 5° and 90° (2), with 0.02° (2) per step and 200 s step-time at room temperature.

Rietveld refinements are performed using TOPAS software (TOPAS, version 4.2, Bruker-AXS, Karlsruhe, Germany, 1999-2009) based on the fundamental parameters approach [START_REF] Klug | X-ray diffraction procedures: for polycrystalline and amorphous materials[END_REF][START_REF] Maslen | Electron Density and Optical Anisotropy in Rhombohedral Carbonates. III.* Synchrotron X-ray Studies of CaCO3, MgCO3 and MnCO"3[END_REF]. The line profile of the Bragg peaks is represented as the convolution of the instrumental function, which is calculated as the convolution of the source function and all optical elements on the incident beam trajectory, and of an intrinsic diffraction profile representing the sample contribution with its specific microstructure.

For all adjustments, the refined parameters are the following: phase scale factor, zero-shift error, coefficients of the background described as a fifth order Chebychev polynomial combined with a 1/X term, unit cell parameters and crystallite size. The atomic positions and temperature factors are kept constant in the crystal structures. The structural data respectively reported by Chaix-Pluchery et al. [START_REF] Chaix-Pluchery | Structural prereactional transformations in Ca(OH)2[END_REF] for Ca(OH)2, by Catti et al. [START_REF] Catti | Static Compression and H Disorder in Brucite, Mg(OH)2, to 1l GPa: a Powder Neutron Diffraction Study[END_REF] for Mg(OH)2, by Maslen et al. [START_REF] Maslen | Electron Density and Optical Anisotropy in Rhombohedral Carbonates. III.* Synchrotron X-ray Studies of CaCO3, MgCO3 and MnCO"3[END_REF] for calcite and by Kahmi [START_REF] Kamhi | On the structure of vaterite, CaCO3[END_REF] for vaterite were used. Preferred orientation along the [001] axis is corrected using the March-Dollase algorithm [START_REF] Dollase | Correction of intensities for preferred orientation in powder diffractometry: application of the March Model[END_REF].

Here, crystallite means a coherent scattering domain, which can be smaller than the grain size because of extended structural defects (grain boundaries or dislocations), resulting in a loss of coherency. Electronirradiation may cause displacements of atoms from their ideal position, giving rise to lattice microstrains, and also change the crystallite size.

To go deeper inside the microstructural analysis and get some quantitative information, two analyses were performed, one assuming a monodispersed distribution of spherical (or quasi-spherical) crystallites (resulting in an isotropic line broadening) and a second one always assuming a monodispersed distribution of crystallites but taking into account a possible shape anisotropy (resulting in an anisotropic line broadening).

Integral-breath method

This first method is used for determining the volumeweighted crystallite size and lattice microstrain, which are varying in 2 as a function of 1/cos and tan respectively [START_REF] Balzar | Voigt-Function Modeling in Fourier Analysis of Size-and Strain-Broadened X-ray Diffraction Peaks[END_REF]. The integral breadth  is given by the line profile area divided by the peak maximum intensity for each hkl reflection: 2) I( 2I max [START_REF] Catti | Static Compression and H Disorder in Brucite, Mg(OH)2, to 1l GPa: a Powder Neutron Diffraction Study[END_REF] where refers to the truncation of the Bragg peak profile at position of maximum intensity 0 2 . It is used to define the peak width. Then, according to Scherrer, the apparent volume-averaged crystallite size   in the direction normal to the reflecting plane (hkl) writes:

            0 0 2 2 1 ) d(
     cos  ( in radians) (4)
In fact   is just the volume -averaged mean thickness of the crystallites measured perpendicularly to the reflecting planes [START_REF] Wilson | X-ray Optics: The Diffraction of X-rays by Finite and Imperfect Crystals[END_REF][START_REF] Langford | Scherrer after sixty years: a survey and some new results in the determination of crystallite size[END_REF].   is also written as Vol L or IB LVOL  , the so-called volume -weighted column height in TOPAS-4. Assuming a monodispersed system of spherical crystallites, after Wilson [START_REF] Wilson | X-ray Optics: The Diffraction of X-rays by Finite and Imperfect Crystals[END_REF], we deduce the diameter of the sphere D (in nm) using:

  3 4    V D (5)
Now let 0 be the maximum lattice deformation (or strain). The interplanar spacing d will vary

of 0  ( dd 0   
). Directly deduced from the Bragg law, the reflections will be appreciable over an angular range equal to 4  tan, in 

2 . An upper limit of the lattice deformations in the crystallites is thus obtained, using:

( tan )

0 4     (6)
where  is the integral breadth defined above.

In TOPAS, the intrinsic diffraction profile is represented by a Voigt function, as a result of the convolution of two Voigt functions, one for the crystallite size and the other for lattice microdistortions [START_REF] Balzar | Voigt-Function Modeling in Fourier Analysis of Size-and Strain-Broadened X-ray Diffraction Peaks[END_REF]. Both crystallite size and strain parameters are refined, giving access to an apparent volumeaveraged crystallite size Vol L (in nm) and a mean microstrain value 0 (in %).

Variance method

This second method allows for determining an average surface-weighted crystallite size [START_REF] Wilson | X-ray Optics: The Diffraction of X-rays by Finite and Imperfect Crystals[END_REF][START_REF] Langford | Scherrer after sixty years: a survey and some new results in the determination of crystallite size[END_REF][START_REF] Wilson | On Variance as a measure of line broadening in diffractometry general theory and small particle size[END_REF]. The projected surface of the crystallite volume in the direction [hkl] is directly calculated in real space. In case of anisotropic shape, there will be different apparent crystallite sizes

) hkl ( k



for the corresponding Bragg peaks, defined as:

) hkl ( ) hkl ( k A V   (7)
where V is the crystallite volume and ) hkl ( A its area projected on a plane parallel to the reflecting planes (hkl). There will be also different Scherrer constants

) hkl ( k K defined as: 𝐾 𝑘(ℎ𝑘𝑙) = √𝑉 3 𝜀 𝑘(ℎ𝑘𝑙) ⁄ = 𝐷 𝐴 𝜀 𝑘(ℎ𝑘𝑙) ⁄ , using 𝐷 𝐴 = √𝑉 3 (8)
Now we use an expression of the surface-weighted crystal size proposed by Sanchez-Bajo [START_REF] Sanchez-Bajo | Analytical formulation of the variance method of line-broadening analysis for Voigtian X-ray diffraction peaks[END_REF],

assuming a purely lorentzian line profile:

   cos H K D L ) hkl ( K A 2 180    (9)
where L H is the Lorentzian full width at half maximum.

Based on the above formalism, the so-called "AnisoCS" routine, developed by Ectors et al. [START_REF] Ectors | A generalized geometric approach to anisotropic peak broadening due to domain morphology[END_REF][START_REF] Ectors | Routine (an)isotropic crystallite size analysis in the double-voigt approximation done right?[END_REF], was implemented into the TOPAS software. This approach has proven to be effective in the case of different geometric models of crystallite. Note that no lattice distortions are taken into account in this model, the line broadening being supposed entirely due to a crystallite size effect. In other words, the crystallites are supposed strain free.

In the present work, the crystallites are assumed cylindrical, with the flat cylindrical face normal to the [001] direction. The averaged dimensions of the cylinders D001 (height in nm) and D100 (diameter in nm) are then refined. Details are given in section 3.3.

Results and discussion

X-ray powder diffraction diagrams of brucite and portlandite before and after irradiation

The X-ray diffraction patterns seen in Figs. 3 and4 for brucite and portlandite respectively immediately show: i) an anisotropic shift of some diffraction peaks, ii) an asymmetric broadening of some diffraction peaks, iii) the appearance of a diffuse and continuous background between 10° and 90° (in 2) with a maximum around 40° (in 2) but only for brucite (Fig. 3.b). We remark the diffraction lines of CaCO3 (calcite and/or vaterite) in the portlandite diffractogram and also of the major 200 diffraction line of MgO at 42.8° in the brucite diffractogram, as announced earlier, all unchanged after irradiation. As a first remark, the overall hexagonal structure is preserved in both compounds at these radiation doses (up to 3.5 GGy).

The shift of the Bragg peaks is related to a change in lattice parameters. As an example the (001) line small shift toward a lower angle in Fig. 3.a for brucite is consistent with a slight increase of the caxis lattice parameter of the hexagonal lattice and an increase of the interlayer spacing. This effect is also well visible in the inset of Fig. 3a and4a showing a zoom of the XRD patterns between 60° and 85° for brucite and between 55 and 75° for portlandite.

The appearance of a diffuse background, concomitant with a decrease in the intensities of the Bragg peaks is compatible with a structural disorder induced by irradiation. Among the two compounds, this effect is only seen on brucite irradiated at 3.0 GGy (Fig. 3.b and 4.b). In the present case, diffuse scattering should be associated with some static structural disorder (random lattice displacements) following irradiation [START_REF] Krivoglaz | Chapter IV of "Theory of X-Ray and Thermal -Neutron Scattering by Real Crystals[END_REF].

All peaks appear more or less broadened after irradiation as seen in Figs. 3 and4. Such broadening could be consistent either with a reduction of the grains size, or with an increase of the inhomogeneous microstrains induced by irradiation, or both. An anisotropic broadening is here foreseen because of the layered structure of the studied compounds.

Electronradiation effect on structural parameters: changes in the interplanar distances and lattice parameters in damaged portlandite and brucite

The X-ray diffraction patterns were analyzed by the Rietveld method (Figs. 5 and6).

Quantitative phase analysis of the non irradiated powders gives 84.5 wt.% of portlandite and 15.5 wt.% of CaCO3 in the portlandite powder, 99.3 wt.% of brucite and 0.7 wt. % of MgO in the brucite powder.

We have reported in Tables 4 to 5 the calculated interplanar distances, the relative changes in the interplanar distances (in %) and the integrated intensities, prior to and following irradiation, for the two absorbed doses respectively per comparison with the non irradiated powders. The indices of the diffraction planes are sorted per increasing value of

d i -d 0 𝑑 0 ⁄ (i=1, 2).
Under present electron-irradiation conditions, the layered structure of brucite and portlandite is substantially affected, not only at "high" dose (~ 3.0 GGy for brucite and 3.5 GGy for portlandite) but also at the intermediate dose (~ 310 MGy for brucite and 270 MGy for porlandite). Electron irradiation leads to a shift of the peak positions for the two compounds. Unexpectedly, the analysis highlights significant differences between these two isostructural compounds. Two sets of scattering planes are clearly identified: i) For all planes parallel to the basal plane, namely (001), (002), (003) and (004), a dilatation along the c axis is observed with a stretching of the interplanar distances. This effect is very clearly visible on brucite, still visible for portlandite but the degree of stretching is reduced and delayed with respect of the absorbed dose. A zoom on the 001 diffraction line of portlandite and brucite together with a sketch of the crystal structure is seen in Fig. 7. Such a dilatation effect remains visible for all planes oriented close to the basal plane, like (112) and (113) planes. And this effect is not so small when compared to the variations of lattice parameter measured in some ceramic oxides following ion irradiation [START_REF] Sattonnay | Mechanical stresses induced in ceramic oxides by ion irradiation[END_REF][START_REF] Zinkle | Microstructure of Al2O3 and MgAl2O4 irradiated at low temperatures[END_REF].

ii) In contrast, for all planes perpendicular to the basal plane, or close to this orientation, electron irradiation highlights a net difference between the damaged structures of brucite and portlandite. A contraction of the interplanar distance is observed for the (110), (010) and (020) planes for instance in brucite, to be compared to the weak dilatation observed in irradiated portlandite. A zoom on the 110 diffraction line of portlandite and brucite is seen in Fig. 8.

The refined lattice parameters, their values, their relative change (in %), the unit cell volume and relative change (in %) and residues of the refinement, RB and Rwp, are noted in Table 6. The a and c unit-cell parameter values for the unirradiated compounds are the ones expected at room temperature [START_REF] Chaix-Pluchery | Structural prereactional transformations in Ca(OH)2[END_REF][START_REF] Catti | Static Compression and H Disorder in Brucite, Mg(OH)2, to 1l GPa: a Powder Neutron Diffraction Study[END_REF]. We have also noted in Table 6 the values of lattice parameters of deuterated brucite and portlandite powders measured by neutron diffraction at various temperatures, between 35°C (40°C) and 250°C [START_REF] Xu | Anisotropic thermal expansion and hydrogen bonding behavior of portlandite: A high-temperature neutron diffraction study[END_REF][START_REF] Xu | High-temperature neutron diffraction study of deuterated brucite[END_REF]. For both compounds, both a and c parameters increase with increasing temperature, and c faster than a by a factor of ~5 in Mg(OD)2 and of ~ 4.5 in Ca(OD)2. Their respective thermal expansion follows the same trend, referring to the decomposition temperature (~ 350°C for brucite and ~ 450°C for portlandite [START_REF] Acher | Etude du comportement sous irradiation  et électronique de matrices cimentaires et de leurs hydrates constitutifs[END_REF], depending on powder, heating rate and cover atmosphere). Now, for irradiated portlandite, both a and c lattice parameters increase with electron dose. At 3.5 GGy, they attain values comparable to that measured on a deuterated portlandite at 130°C. We are not saying that this is the "effective temperature" attained under irradiation, since we have no idea of the composition and structure fluctuations accompanying the damage process under present irradiation conditions (using electrons as projectiles). But we retain this temperature value for a simple minded description of the state of the irradiated powder.

Things are completely different for irradiated brucite, which undergoes structural changes similar to that observed in graphites following neutron irradiation in nuclear fission reactors [START_REF] Kelly | Dimensional changes in polycrystalline graphites under fast -neutron irradiation[END_REF]. Dilatation along the c axis occurs in brucite (c/c = +0.733 % at 3.0 GGy) as in portlandite. But in the basal plane, a decrease of the a lattice parameter is observed, attaining a/a = -0.273 % at 3.0 GGy. As a consequence of this, the volume change V/V (in %) remains limited even at the highest dose in brucite (~ + 0.18 %) whereas it is more significant in portlandite (~ + 0.74 %), as seen in Table 6. For brucite, because of the opposite irradiation effects along a axis (contraction) and c axis (dilatation), no effective temperature could be defined under electron irradiation, contrary to portlandite.It could be worth recalling that a shrinkage in the basal plane of brucite had already been observed according to an electron diffraction study of a Mg(OH)2 single crystal by Goodman in 1958 [START_REF] Goodman | The decomposition of magnesium hydroxide in an electron microscope[END_REF]. A shrinkage of order 4 % is mentioned by the author, but the irradiation conditions were different (80 keV electron beam delivered by the Siemens Elmiskop I microscope operating), suggesting a more advanced state of decomposition.

The curves representing the relative change in interplanar distance (d001) versus dose are reported in Fig. 9 for both compounds. Now we make the oversimplified assumption that brucite and portlandite transform under irradiation in a similar manner. In such case, the curve for portlandite should osculate the one for brucite around 15 GGy. In other words, portlandite should be much more radiation resistant.

Finally we note that there is a radiation dose effect on the integrated intensity for brucite (Fig. 10). For a given total scattered intensity depending only on the nature of the compound, the balance between Bragg scattering and diffuse scattering is related to the balance between coherent and incoherent scattering. Such an effect is clearly visible looking at Figs 3, 4 and 10. For brucite, the rather important diffuse scattering observed increasing with dose between 310 MGy and 3.0 GGy can be correlated with the decrease of the integrated intensity with dose seen in Fig. 10. At the opposite, no diffuse scattering is observed for portlandite (Fig. 4) and the integrated intensity remains unchanged at 3.5 GGy, an argument in favor of an higher radiation resistance of portlandite, compared to brucite.

Electronradiation effects on microstructure of portlandite and brucite: crystallite size and microdistortions

Both crystallite size and lattice disorder are responsible for the intrinsic peak profiles broadening. We used the isotropic integral breadth and anisotropic variance models detailed in section 2.3.The Rietveld refinements and refined model parameters are reported in Figs. 11 and12 and Tables 7 and8, assuming either spherical or cylindrical crystallites of same size.

For portlandite, whatever irradiated or not, the isotropic model provides a reasonably good fit but the best refinement is obtained when using the anisotropic variance model. The microstrain value is found negligible (0 ~0.033%), which fully justifies the assumption of strain free crystallites adopted in the variance model. Before irradiation, the crystallites of portlandite should have the shape of a flattened cylinder (Table 7). Their dimensions are almost exactly the ones found for the portlandite powder studied by Ectors et al. (D100 = 26 nm, D001 = 11 nm) [START_REF] Ectors | Routine (an)isotropic crystallite size analysis in the double-voigt approximation done right?[END_REF]. Then we remark that the crystallite size remains unchanged after irradiation at a dose of 270 MGy, and starts to decrease at a high dose (Fig. 11, Table 7).

Significant differences between brucite and portlandite appear, prior to and following irradiation. Prior to irradiation, the brucite crystallites should be rather spherical (Table 8). In brucite the size reduction under irradiation is significant, and already observed for an absorbed dose of 310 MGy (Fig. 12, Table 8). Therefore, it seems that electron irradiation induces a higher number of structural defects in brucite with a detrimental effect on crystallite size at 310 MGy. At 3.0 GGy, due to the presence of diffuse scattering, the fit is too poor to conclude. The peaks broadening and change in intensity following irradiation cannot be satisfactorily reproduced by a change in crystallite size (using Balzar model) or even a change in crystallite shape (using Ectors model).

Plausible damage mechanisms

Several hypotheses might be considered, related to the role of hydrogen, the one of ballistic collisions and/or electronic excitations. It is a fact that brucite is more seriously damaged than portlandite, here under electron irradiation, just as well as MgO was damaged under ion irradiation while CaO was not. It is also a fact that ballistic collisions are responsible for the lattice deformations (expansion in the c-axis and shrinkage in the a-axis) and reduced crystallite size in nuclear graphite under neutron irradiation, according Krishna et al. [START_REF] Krishna | An understanding of lattice strain, defects and disorder in nuclear graphite[END_REF]. In the present work, the idea is not to suggest that ballistic collisions are responsible for the degradation of the studied hydroxides, or that the network of [MO6] octahedra (M = Ca, Mg) is damaged by electron irradiation while the H-bond network would be left more or less undamaged.

Referring to the three-site split-atom model due to Desgranges et al. [START_REF] Desgranges | Hydrogen thermal motion in Calcium hydroxide: Ca(OH)2[END_REF], the consequences of electron irradiation on the hydrogen-bond network cannot be estimated. According to Hobbs, hydrogen could act as an intermediary: it would gain enough energy during collision with an incident electron to be able to displace other nuclei with higher threshold displacement energy [START_REF] Hobbs | Radiation effects in analysis of inorganic specimens by TEM[END_REF]. The appearance of some diffuse scattering in the XRD diagrams of irradiated brucite, but not of irradiated portlandite, suggests that the hydrogen bond network of brucite is perturbed here under irradiation.

Let us assume that ballistic collisions play a significant role in the damage process, a study as a function of the energy of the electron beam, decreased below 480 keV in order to immobilize the Mg ions, then below 330 keV in order to immobilize the oxygen ions, could confirm/infirm this assertion for brucite [START_REF] Hayes | Defect and defect processes in nonmetallic solids[END_REF][START_REF] Chen | Colour centres in electron irradiated MgO[END_REF]. With this same aim and without more data, a comparable study should be conducted in the case of portlandite, the minimum electron energy to displace atoms by collision being assumed of order 480 keV for Ca ions and 320 keV for oxygen ions [START_REF] Caulfield | Point defects in electron-irradiated oxide single crystals[END_REF]. Only at this point it would be known whether a change in electron flux could be pertinent, so far chosen in the range of that previously employed to study radiation damages in semiconductors or ceramics to avoid annealing effects during irradiation [START_REF] Balanzat | Basic phenomena of the Particle-Matter interaction[END_REF]. Now, we recall the values of swelling obtained here at the highest dose, in parallel with the estimated dpa levels: 0.183 % for 2.2 x 10 -4 dpa in brucite and 0.743 % for 3.7 x 10 -4 dpa in portlandite.

If we were assuming that ballistic collisions are responsible for the swelling, we would obtain extremely high values of swelling rate per dpa, of order ~8.3 x 10 2 %/dpa in brucite and even ~2 x 10 3 %/dpa in portlandite. These values are orders of magnitude higher than in spinel (~0.16 %/dpa) or alumina (~0.45 %/dpa) damaged by ballistic collisions as a result of irradiation with 4 MeV Ar + ions [START_REF] Zinkle | Microstructure of Al2O3 and MgAl2O4 irradiated at low temperatures[END_REF]. Such a hypothesis seems really unrealistic. This reasoning is clearly in favor of a non negligible role of electronic excitations on the observed swelling of the studied hydroxides.

Conclusions

We performed a comparative XRD study of electron radiation damages in brucite and portlandite, showing that both compounds remain stable under the beam up to high doses, in the range of 3 -3.5 GGy., However the study also reveals significant differences of behavior between them under irradiation.

In portlandite, there are some similarities between the structural modifications induced by electron irradiation and the early stages of its thermal decomposition, leading to a significant dilatation of the unit cell along the caxis, much less along the a -axis. In this case the structural disorder caused by irradiation at an electron dose of 3.5 GGy could be compared to the one attained at an "effective temperature" of 130°C (0.3 TD, with TD referring to the decomposition temperature of portlandite into lime). By contrast, in brucite, no "effective temperature" can be defined. The XRD study still reveals a reduced dilatation of unit cell along the c axis, but also a contraction of the cell parameter a in the basal plane, an effect never observed when heating. Moreover, in brucite, the intensity of the Bragg peaks decreases with increasing electron dose up to 3.0 GGy, while appears a diffuse scattering over a large angular range, compatible with the appearance of some static structural disorder under irradiation.

Crystallite sizes were determined. It is shown that they decrease under electron irradiation, only slightly in portlandite at the highest dose (3.5 GGy), apparently more rapidly with dose in brucite.

Finally portlandite should be considered more electron radiation resistant than brucite. This result is perhaps to be considered in the light of the conclusions of an early study of ion-irradiation effects in cubic oxides [START_REF] Matzke | Ion-bombardment-induced radiation damage in some ceramics and ionic crystals[END_REF], showing that CaO is more resistant than MgO under ion bombardment under comparable conditions. These results constitute a basis for a future work as function of electron flux and dose to go deeper inside the understanding of the damage process affecting the skeleton of [MO6] octahedra and/or solely the hydroxyl network until complete decomposition.

Table 1. Irradiation conditions using the SIRIUS platform for 2.5 MeV electrons. The electron doses are calculated without taking into account the contribution of backscattered electrons and the absorption effects along the trajectory. The absorbed doses are calculated using the inelastic stopping power values estimated using ESTAR [START_REF] Berger | Stopping Power and Range Tables for Electrons, Protons and Helium Ions[END_REF]. The cation displacements damages, in dpa, are given assuming two different values of 𝜎 𝑑 given in parenthesis (in barn), calculated using two threshold displacement energy values, 𝐸 𝑑 = 30 eV (low 𝜎 𝑑 ), or 𝐸 𝑑 = 50 eV (high 𝜎 𝑑 ).

Portlandite Ca(OH)2

Brucite

Mg(OH)2

Current (µA) [START_REF] Hayes | Defect and defect processes in nonmetallic solids[END_REF] 25 25 20 Flux (e -.cm -2 .s -1 ) 9.5 x 10 13 1.2 x 10 14 1.2 x 10 14 9.5 x 10 13

Dose (e -.cm -2 ) Table 2. Density , mean excitation energy I, inelastic stopping power and range R estimated using ESTAR [START_REF] Berger | Stopping Power and Range Tables for Electrons, Protons and Helium Ions[END_REF] for the two studied compounds and 2.5 MeV electrons.

Density  (g/cm 3 )

I (eV) (MeV/cm) R (

Figure 1 .

 1 Figure 1. Schematic illustration (VESTA software) of the trigonal structure of M(OH)2 hydroxide, with M=Ca, Mg. For portlandite Ca(OH)2 : a = 3.5918 Å, c = 4.9063 Å, d(Ca-O) = 2.370 Å, d(O-H) = 0.940 Å and d(Ca-Ca) = 4.906 Å, after [2] and for brucite Mg(OH)2: a = 3.1497 Å, c = 4.7702 Å, d(Mg-O) = 2.1003 Å, d(O-H) = 0.919 Å and d(Mg-Mg) = 4.7702 Å, after [3].

Figure 2 .

 2 Figure2. Displacement cross sections by elastic collisions for Mg (red curve with symbols), Ca (red curve with symbols) and O (black curves with symbols) in brucite Mg(OH)2 and portlandite Ca(OH)2, calculated using the SMOTT and POLY code due to Lesueur[START_REF] Caulfield | Point defects in electron-irradiated oxide single crystals[END_REF]. An Ed value between 30 eV and 70 eV is assumed for both Mg and Ca based on displacement energies measured in MgO and CaO respectively, according to W. Hayes and A. M. Stoneham[START_REF] Hayes | Defect and defect processes in nonmetallic solids[END_REF].

Figure 3 .

 3 Figure 3.a) X-Ray diffraction patterns of brucite Mg(OH)2 showing a shift and broadening of the Bragg lines following electron irradiation at two doses (310 MGy, 3.0 GGy); b) zoom on the continuous background.

Figure 4 .

 4 Figure 4.a) X-Ray diffraction patterns of portlandite Ca(OH)2 showing a shift and broadening of the Bragg lines following electron irradiation at two doses (270 MGy, 3.5 GGy); b) zoom on the continuous background.

Figure 5 .

 5 Figure 5. Rietveld refinement of an X-ray diffraction pattern collected on unirradiated portlandite. From top to bottom are represented: the observed (solid line), the calculated (dotted line) XRD patterns, the difference plot (grey line) between observed and calculated data, and the Bragg reflection markers. From top to bottom, these markers correspond to portlandite and calcite.

Figure 6 .

 6 Figure 6. Rietveld refinement of an X-ray diffraction pattern collected on unirradiated brucite. From top to bottom are represented: the observed (solid line), the calculated (dotted line) XRD patterns, the difference plot (grey line) between observed and calculated data, and the Bragg reflection markers. From top to bottom, these markers correspond to brucite and (residual) MgO.

Figure 7 .

 7 Figure 7. 001 diffraction lines of portlandite (a) and brucite (b) samples prior to and following irradiation at intermediate (270 MGy for portlandite, 310 MGy for brucite) and high (3.0 GGy for brucite, 3.5 GGy for portlandite) electron doses. (c) sketch of the crystal structure of the hydroxide (M=Ca, Mg) showing (001) planes and the stretching of the interlayer.

Figure 8 .

 8 Figure 8. 110 diffraction lines of portlandite (a) and brucite (b) samples prior to and following irradiation at intermediate (270 MGy for portlandite, 310 MGy for brucite) and high (3.0 GGy for brucite, 3.5 GGy for portlandite) electron doses. (c) sketch of the crystal structure of the hydroxide (M=Ca, Mg) showing (110) diagonal plane.

Figure 9 .

 9 Figure 9. Variation of interplanar distance versus dose for (00l) planes (l = 1 to 4) of brucite and portlandite.

Figure 10 .Figure 11 .

 1011 Figure 10. Variation of integrated intensities versus dose for some (hkl) planes of brucite and portlandite.

Figure 12 .

 12 Figure 12. Rietveld refinements of XRD data, in the angular window 2=48-64°, of brucite prior to and following irradiation at intermediate (310 MGy) and high (3.0 GGy) electron doses for crystallites supposed (a) spherical and (b) cylindrical. The anisotropic model doest not improve the refinement: the crystallites can be considered rather spherical. The crystallite size could not be satisfactory estimated for the high dose irradiated sample.

mm)

	Portlandite	2.24	44.3	5.1	4.5
	Brucite	2.39	43	5.5	4.2

Table 3 .

 3 Maximum energy (Tmax in eV) transferable to different target atoms as a function of their atomic mass and of the electron energy (E in MeV) during a head-on collision.

	E (MeV)	H (A=1)	O (A=16)	Mg (A=24.3)	Ca (A=40.08)
	0.1	241	15.1	9.9	6.0
	0.2	524	32.5	21.6	13.1
	2.5	18910	1182	778

Table 4 .

 4 The hkl indices, diffraction peak positions (in 2), corresponding integrated intensities Ii (i = 0, 1, 2) and interplanar distances di (i=0, 1, 2) are reported for brucite Mg(OH)2 prior to irradiation (i = 0), following electron irradiation at an absorbed dose of 310 MGy (i= 1) and of 3.0 GGy (i = 2). The relative change in interplanar distance d i -d 0 𝑑 0 ⁄ (in %) are also mentioned. The indices of the diffraction planes are sorted per increasing value distance d i -d 0 𝑑 0 ⁄ . The values of Ii (i = 1, 2) are the calculated ones, not corrected for Lorentz polarization and preferential orientation.

	hkl	20	I0	d0	I1	d1	(d1-d0)%	I2	d2	(d2-d0)%
	110	58.5827	1283	1.57444	1253	1.57400	-0.028%	1088	1.57014	-0.273%
	010	32.81524	31	2.72702	30.8	2.72626	-0.028%	27	2.71956	-0.274%
	020	68.79598	71	1.36351	69	1.36313	-0.028%	60	1.35978	-0.274%
	021	71.9623	7	1.31110	7	1.31096	-0.011%	6	1.30850	-0.198%
	201	71.9623	680	1.31110	664	1.31096	-0.011%	577	1.30850	-0.198%
	111	62.01631	740	1.49526	724	1.49518	-0.005%	629	1.49263	-0.176%
	011	37.96607	1908	2.36805	1866	2.36872	0.028%	1626	2.36737	-0.029%
	101	37.96607	19	2.36805	18.6	2.36872	0.028%	16	2.36737	-0.029%
	022	81.17014	254	1.18402	248	1.18436	0.029%	216	1.18368	-0.029%
	202	81.17014	508	1.18402	497	1.18436	0.029%	433	1.18368	-0.029%
	112	71.75516	20	1.31438	19	1.31492	0.041%	16.73	1.31475	0.028%
	113	86.97096	113	1.11934	110	1.12030	0.086%	97	1.12181	0.221%
	102	50.78491	518	1.79634	507	1.79816	0.101%	443	1.80159	0.292%
	012	50.78491	1124	1.79634	1101	1.79816	0.101%	963	1.80159	0.292%
	013	68.16116	97	1.37465	95	1.37662	0.143%	83	1.38117	0.474%
	103	68.16116	879	1.37465	862	1.37662	0.143%	757	1.38117	0.474%
	104	89.56075	239	1.09357	235	1.09536	0.164%	207	1.09979	0.569%
	014	89.56075	8	1.09357	7.77	1.09536	0.164%	6.76	1.09979	0.569%
	002	37.64493	3	2.38751	3.23	2.39231	0.201%	3	2.40500	0.733%
	001	18.56686	269	4.77502	263	4.78463	0.201%	230	4.81000	0.733%
	003	57.88809	24	1.59167	23.70	1.59488	0.202%	21	1.60333	0.733%
	004	80.3724	167	1.19375	164	1.19616	0.202%	145	1.20250	0.733%

Table 5 .

 5 The hkl indices, diffraction peak positions (in 2), corresponding integrated intensities Ii (i = 0, 1, 2) and interplanar distances di (i=0, 1, 2) are reported for portlandite Ca(OH)2 prior to irradiation (i = 0), following electron irradiation at an absorbed dose of 270 MGy (i= 1) and of 3.5 GGy (i = 2). The relative change in interplanar distance d i -d 0 𝑑 0 ⁄ (in %) are also mentioned. The indices of the diffraction planes are sorted per increasing value distance d i -d 0 𝑑 0 ⁄ . The values of Ii (i = 1, 2) are the calculated ones, not corrected for Lorentz polarization and preferential orientation.

	hkl	20	I0	d0	I1	d1	(d1-d0)%	I2	d2	(d2-d0)%
	010	28.67304	43	3.11085	40.817	3.11211	0.041%	42.129	3.11501	0.134%
	020	59.37026	31	1.55542	29.145	1.55605	0.041%	30.114	1.55750	0.134%
	110	50.79359	273	1.79605	259.637	1.79678	0.041%	268.456	1.79845	0.134%
	210	81.85932	42	1.17579	39.58	1.17627	0.041%	40.914	1.17736	0.134%
	121	84.69778	175	1.14348	166.645	1.14397	0.043%	172.454	1.14522	0.152%
	211	84.69778	19	1.14348	17.837	1.14397	0.043%	18.433	1.14522	0.152%
	201	62.59398	158	1.48284	150.605	1.48351	0.045%	155.844	1.48528	0.165%
	021	62.59398	11	1.48284	10.918	1.48351	0.045%	11.275	1.48528	0.165%
	111	54.34373	175	1.6868	166.283	1.68759	0.047%	171.964	1.68973	0.174%
	101	34.08806	8	2.62805	7.943	2.62949	0.055%	8.177	2.63411	0.231%
	011	34.08806	411	2.62805	391.318	2.62949	0.055%	404.754	2.63411	0.231%
	202	71.77747	99	1.31402	94.604	1.31474	0.055%	98.011	1.31706	0.231%
	022	71.77747	77	1.31402	73.028	1.31474	0.055%	75.658	1.31706	0.231%
	112	64.1933	20	1.4497	19.196	1.45054	0.058%	19.829	1.45335	0.252%
	203	86.17358	16	1.12764	15.294	1.12837	0.065%	15.847	1.13096	0.294%
	023	86.17358	90	1.12764	85.921	1.12837	0.065%	89.163	1.13096	0.294%
	113	79.08445	62	1.20993	58.626	1.21075	0.068%	60.795	1.21379	0.319%
	102	47.11005	156	1.92753	148.378	1.92891	0.072%	153.792	1.93414	0.343%
	012	47.11005	202	1.92753	192.732	1.92891	0.072%	199.77	1.93414	0.343%
	013	64.23902	23	1.44878	22.044	1.44994	0.080%	22.842	1.45457	0.400%
	103	64.23902	158	1.44878	150.21	1.44994	0.080%	156.078	1.45457	0.400%
	104	84.82181	37	1.14212	35.511	1.14308	0.084%	36.919	1.14701	0.428%
	014	84.82181	12	1.14212	11.228	1.14308	0.084%	11.642	1.14701	0.428%
	001	18.04656	67	4.9115	64.018	4.91595	0.091%	66.147	4.93477	0.474%
	002	36.56126	3	2.45575	2.419	2.45798	0.091%	2.483	2.46738	0.474%
	003	56.13446	17	1.63716	16.076	1.63865	0.091%	16.682	1.64492	0.474%
	004	77.70873	35	1.22787	33.22	1.22899	0.091%	34.586	1.23369	0.474%

Table 6 .

 6 Refined parameters, based on the fundamental parameters approach[START_REF] Cheary | A fundamental parameters approach to X-ray Line-Profile Fitting[END_REF]: unit cell parameters, volume V, c/a ratio and respective change in %, prior to and following irradiation at two doses for brucite and portlandite. Comparison with unit -cell parameters deduced from a neutron powder diffraction study at high temperature of deuterated brucite[START_REF] Xu | High-temperature neutron diffraction study of deuterated brucite[END_REF] and of deuterated portlandite[START_REF] Xu | Anisotropic thermal expansion and hydrogen bonding behavior of portlandite: A high-temperature neutron diffraction study[END_REF]. The residues of the refinements are reported:

	R B =	∑|I exp,k -I cal,k | ∑ I exp,k
	with Iexp,k and Icalc,k the experimental and calculated intensities of the k th reflection.
	and R wp = √ ∑ [w i (I exp,i -I cal,i ] N i=1 ∑ [w i I exp,i ] 2 N i=1	2
	𝑤 𝑖 =	1 √ 𝐼 𝑒𝑥𝑝,𝑖	and N the number of points.
	Brucite		Unirradiated 310 MGy 3.0 GGy	[12]	40°C	70°C	150°C	250°C
	a (Å)			3.1489	3.1480	3.1403	a (Å)	3.15545 3.15700 3.16016 3.16419
	 a/a (%)	-	-0.028	-0.273	 a/a (%)	-	+0.049 +0.1493 +0.2769
	c (Å)			4.7750	4.7846	4.8100	c (Å)	4.77185 4.78311 4.80706 4.83668
	 c/c (%)	-	+ 0.201	+ 0.733	 c/c (%)	-	+0.306	+0.738	+1.359
	c/a			1.51641	1.51988	1.53171	c/a	1.51225 1.51591 1.52114 1.52857
	 c/a (%)	-	+ 0.229	+ 1.009	 c/a (%)	-	+0.2359 +0.5878 +1.0791
	V (Å 3 )		41.0034	41.0629	41.0783	V (Å 3 )	41.147	41.285	41.937
	V/V (%)	-	+ 0.145 %	+ 0.183 V/V (%)	-	+0.335	+1.919
	RB			3.320	4.121	5.105	 	3.28	4.52	-	3.94
	Rwp			7.29	9.54	11.92	Rwp	1.03	1.09	-	1.06
	Portlandite Unirradiated 270 MGy 3.5 GGy	[11]	35°C	130°C	190°C	250°C
	a (Å)			3.5921	3.5936	3.5969	a (Å)	3.60045 3.60483 3.60725 3.60966
	 a/a (%)	-	+ 0.040	+ 0.134	 a/a (%)	-	+0.121	+0.188	+0.256
	c (Å)			4.9115	4.9160	4.9348	c (Å)	4.9113	4.9345	4.9491	4.9642
	 c/c (%)	-	+ 0.091	+ 0.474	 c/c (%)	-	+0.472	+0.769	+1.077
	c/a			1.36730	1.36799	1.37195	c/a	1.36408 1.3688 1.37198	1.3752
	 c/a (%)	-	+ 0.050	+ 0.34	 c/a (%)	-	+0.346	+0.579	+0.819
	V (Å 3 )		54.8834	54.9776	55.2910	V (Å 3 )	55.136	55.532	55.77	56.016
	V/V (%)	-	+ 0.172% + 0.743 V/V (%)	-	+0.718	+1.149	+1.596
	RB			4.321	4.591	5.219	  	3.18	4.45	4.05	4.27
	Rwp			7.93	8.12	10	Rwp	1.13	0.82	0.79	0.76

Table 7 .

 7 Refined parameters for microstructural analysis of portlandite prior to and following irradiation at two doses, considering: (i) A monodisperse powder of spherical crystallites, after Balzar et al.[START_REF] Balzar | Voigt-Function Modeling in Fourier Analysis of Size-and Strain-Broadened X-ray Diffraction Peaks[END_REF]: volumeaveraged crystallite size Vol L , diameter D of the crystallites, and mean microstrain value 0 (%); (ii) Cylindrical crystallites, based on Ectors model[START_REF] Ectors | A generalized geometric approach to anisotropic peak broadening due to domain morphology[END_REF][START_REF] Ectors | Routine (an)isotropic crystallite size analysis in the double-voigt approximation done right?[END_REF]: D100 (diameter) and D001 (height) cylinder dimensions. The residues of the refinements R-weighted pattern Rwp and R-Bragg RB are reported.

	Portlandite Unirradiated	270 MGy	3.5 GGy
	Vol L (nm)	27 ± 2	27 ± 2	24 ± 2
	D (nm)	36	36	32
	0 (%)	0.033	0.044	0.112
	RB	4.32	4.59	5.22
	Rwp	7.93	8.12	10
	100 D	22	22	17
	001 D	11	11	7
	RB	3.25	3.58	4.11
	RWP	6.22	6.37	8.03

Table 8 .

 8 Refined parameters for microstructural analysis of brucite prior to and following irradiation at two doses,

	considering:
	(i) A monodisperse powder of spherical crystallites, after Balzar et al. [34]: volume -averaged crystallite size Vol L
	, diameter D of the crystallites, and mean microstrain value 0 (%);
	(ii) Cylindrical crystallites, based on Ectors model [39-40]: D100 (diameter) and D001 (height) cylinder dimensions.
	The residues of the refinements R-weighted pattern Rwp and R-Bragg RB are reported.
	Brucite	Unirradiated 310 MGy
	Vol L (nm)	67 ± 2	37 ± 2
	D (nm)	89	49
	0 (%)	0.092	0.111
	RB	3.32	4.12
	Rwp	7.29	9.54
	100 D	30	20
	001 D	26	13
	RB	3.11	4.73
	RWP	8.72	9.81

Acknowledgements

The authors would like to thank the EMIR French accelerator network for radiation beam time.

They are very much indebted to Olivier Cavani for irradiation experiments at the LSI SIRIUS beam line.

Many thanks are due to Sandrine Tusseau -Nenez for her help during XRD experiments on the DIFFRAX platform.