Julia Wiktor

Gérald Jomard

Marc Torrent

Marjorie Bertolus

First-principles calculations of momentum distributions of annihilating electron-positron pairs in defects in UO 2

We perform first-principles calculations of momentum distributions of annihilating electronpositron pairs in vacancies in uranium dioxide. We take into account the full atomic relaxation effect (due to both electronic and positronic forces) and use self-consistent two-component density functional theory schemes. We present one-dimensional momentum distributions (Doppler-broadened annihilation radiation line shapes) along with line-shape parameters S and W . The effect of krypton incorporation in the vacancy is also considered and it is shown that it should be possible to observe the fission gas incorporation in defects in UO2 using positron annihilation spectroscopy.

I. INTRODUCTION

Uranium dioxide (UO 2 ) is currently the most widely used fuel material in pressurized water reactors (PWR). During the reactor operation the fission of actinide nuclei causes the creation of large amounts of defects, what leads to the evolution of the physical and chemical properties of UO 2 . To understand the behavior of the fuel material during reactor operation, it is essential to study the effects of the irradiation on the thermomechanical and thermochemical properties of UO 2 caused by defects creation and their interaction with fission products.

Positron annihilation spectroscopy (PAS) 1,2 is one of the non-destructive methods that can be used to study vacancies. There are two positron annihilation features that allow one to characterize defects in solids: the positron lifetime, mostly sensitive to the open volume of defects, and the Doppler broadening of the annihilation radiation, carrying information on the chemical environment in which positrons annihilate. Since PAS results do not provide a direct link between the signal and the type of the defect, comparisons with other experimental techniques or with electronic structure calculations are often required in the interpretation of experimental data.

In a recent study we performed fully self-consistent calculations of positron lifetimes for defects in uranium dioxide 3 and used the computational results to identify defects in α-irradiated UO 2 samples. We observed that in some cases different vacancies exhibit similar positron lifetimes and that it can be difficult to distinguish them based on this characteristic itself. In the present work we perform calculations of the second positron annihilation characteristic, the Doppler broadening of the annihilation radiation, which is often measured in experimental positron studies on UO 2 [4][5][6][7][8][9] and can bring complementary information on defects. This paper is organized as follows: In Sec. II we briefly present the computational methods. In Sec. III we present the calculated Doppler spectra and S and W parameters and discuss the results. Finally, we conclude the paper in Sec. IV.

II. METHODS

We use the implementation of the two-component density functional theory (TCDFT) 1,10,11 within the projector augmented-wave (PAW) [12][13][14][15] framework, available in the ABINIT code [16][17][18] . The methods are described in Ref. 19 and we only recall them briefly here.

In this work we use the so-called 'state-dependent' 20 scheme to calculate the momentum distributions of the annihilating electron-positron pairs. In this method the momentum distribution ρ(p) is expressed as:

ρ(p) = πr 2 e c ij γ j dr e -ip•r Ψ + (r)Ψ - j (r) 2 , (1)
where Ψ + (r) is the positron wavefunction, Ψ - j (r) is the wavefunction of the electron state j, p is a given momentum, r e is the classical electron radius and c is the speed of light. In the above equation γ j is equal to λ j /λ IPM j , where λ j is the total annihilation rate calculated for the electronic state j,

λ j = πr 2 e c dr n - j (r)n + (r)γ(n -), (2)
and λ IPM j is the annihilation rate calculated for the same state within the IPM, using γ = 1. n + (r) is the positron density and n - j (r) is the density corresponding to the electron state j.

To calculate the Doppler spectra of the perfect lattice we use the conventional (CONV) scheme, in which the LDA zero-positron density limit of the electron-positron correlation functional, parametrized by Boroński and Nieminen 11 using the data provided by Arponen and Pajanne 21 , is taken. In momentum distribution calculations for vacancies, we perform fully self-consistent calculations, using a full LDA electron-positron correlation functional provided by Puska, Seitsonen, and Nieminen 22 and an enhancement factor depending on both the electron and the positron densities, g(n -, n + ). This method corresponds to the so-called PSN scheme, in which case Eq. ( 2) is replaced by:

λ j = πr 2 e c dr n - j (r)n + (r)g(n -, n + ), (3)
The calculations are performed as self-consistent loops on the electronic and positronic densities: during each subloop, one of the two densities is kept constant while the other is being converged. In the calculations we allow the atomic positions to relax, according to the electronic and positronic forces, since it has been shown that the relaxation effect can affect strongly the calculated positron annihilation characteristics [23][24][25] . Both electronic and positronic wavefunctions are described using the same mixed basis (planewaves and atomic orbitals) in the framework of the PAW method. The PAW data sets are generated using a modified version of the atompaw code 14 . For oxygen we included 8 electrons (1s, 2s and 2p) and for uranium 14 electrons (5f , 6s, 6p, 6d and 7s) in the valence state. Additionally, to achieve a correct description of the positron wavefunction, we add 5s and 5p states in the U basis set (see Ref. 19 for the explanation of the dataset generation and discussion on the PAW data set completeness for the positron description).

We use the generalized gradient approximation (GGA) as parametrized by Perdew, Burke, Ernzerhof (PBE) 26 to describe the exchange-correlation interactions. Moreover, a Hubbard-like term (U ) is added in order to take into account the strong correlations between the 5f electrons of the uranium atoms. The Liechtenstein scheme 27 of the DFT+U method is used. The values of the U and J parameters are set to 4.5 eV and 0.51 eV respectively, in agreement with earlier DFT+U calculations [28][29][30][31][32] and the values extracted from experiments 33 . In order to avoid the convergence to one of the numerous metastable states yielded by the DFT+U method and ensure that the ground state is reached, we used the occupation matrix control scheme 31,34,35 . We consider a 1k antiferromagnetic ordering, which is an approximation of the noncollinear 3k order, since the two exhibit only small differences in energy 36 . We did not take into account the spin-orbit coupling (SOC) due to the too high computational cost. Extensive investigations of the SOC influence on the properties of actinide compounds 37,38 suggest that it does not affect the properties of defects 39 .

Calculations for defects are performed using 96 atom supercells (2×2×2 repetitions of the fluorite unit cell). We use the equilibrium lattice parameters of UO 2 yielded by the set of parameters described above, a = b = 5.57 Å and c = 5.49 Å. The positron wavefuntion and density are calculated at two k-points, the Γ point and another one chosen to lie on the edge of the Brilloun zone, to avoid the delocalization of the positron due to the small supercell, as proposed by Korhonen et al. 40 . The same k-points are used in the electronic calculations. The momentum distributions have been calculated using the wavefunctions corresponding to the Γ point only. We used the cut-off energy of 680 eV, since we found it was enough to obtain Doppler spectra converged up to 40 mrad. The atomic relaxation is performed until the forces acting on atoms become smaller than 0.03 eV/ Å.

For comparison with experiments we calculate one-dimensional projections (Doppler spectra) of the threedimensional momentum densities in three different directions. This is done by integrating the momentum distribution along two remaining directions, as:

ρ(p z ) = dp x dp y ρ(r). (4)
In the present study we calculate projections in three different directions and average the results. To obtain the best quality of the Doppler spectra, we choose p z to be normal to the dense (001), ( 011) and (111) planes. Additionally, to mimic the finite resolution of experimental measurements we convolve the theoretical results with a Gaussian function with the FWHM (full width at half maximum) equal to 4.7 mrad. We further interpolate the one-dimensional spectra on a grid with 0.1 mrad spacing and normalize the spectra to unity.

III. RESULTS AND DISCUSSION

A. Comparison of calculation schemes

In this work we use the PSN scheme to calculate the momentum distributions of annihilating pairs in vacancies in UO 2 . We decided to study, however, the effect of the choice of the calculation method on the Doppler spectra of defects in UO 2 . We perform, therefore, calculations using two other schemes, CONV and GGGC (see for instance Ref. 22 or 19 for the description of various schemes). In Fig. 1 we compare the ratio curves (normalized Doppler spectrum of the defect divided by the normalized Doppler spectrum of the lattice) calculated for the uranium monovacancy using the CONV, GGGC and PSN schemes. The vacancy was relaxed using the PSN and GGGC schemes. In the case of the CONV method we compare results calculated first for unrelaxed atomic positions and then taking the relaxed positions from the GGGC calculation. We can observe that the general shapes of the ratio curves calculated using different schemes are similar. For all methods a peak at p=0 is observed, with GGGC yielding the largest amplitude and the CONV method with unrelaxed positions the lowest. A second peak can be observed around p = 15 mrad, while around p = 27 mrad a shoulder or a peak, depending on the method used, appears.

The effect of the atomic relaxation on the calculated ratio curve can be analyzed by comparing the results obtained using the CONV method for two different geometries (blue lines in Fig. 1). We can observe that when the uranium vacancy relaxes outwards, the low-momentum contribution increases, since the electronic density moves further from the maximum of the positron density. At the same time, the ratio curve at higher momenta decreases.

The localized shape of the ratio curve calculated using the GGGC scheme is consistent with the overestimation of the positron localization yielded by this method, which was already discussed in previous studies 3,22,23,25 . As for the PSN scheme, the ratio curve obtained using this method is the flattest. Additionally, we can see that at low momenta the results yielded by this method are in good agreement with the ones calculated using the CONV scheme in the relaxed geometry. The agreement is, however, not as good above p = 10 mrad. In the calculations presented below, we use the PSN scheme since this method yields the best description of the positron localization in the defect.

B. Vacancies in UO2

We performed calculations of the momentum distributions for several vacancy defects in UO 2 . The ratio curves found for neutral V U , V U +V O , the three configurations of V U +2V O and one configuration of 2V U +4V O vacancies are presented in Fig. 2. We can see that all the calculated ratio curves are rather similar, with a maximum at p = 0 and two peaks, one around p = 15 mrad and one around p = 27 mrad. The curve calculated for the neutral 2V U +4V O complex is the most distinct from the others, it is more flat and has much lower values at high momenta. The similarity between for instance the monovacancy and the trivacancies can be explained by the fact, that while oxygen -2 ions are removed from the neighborhood of V U , the remaining ones can attract the positron and shift its density toward them (see positron isodensities in Ref. 3). As a result, even though there are less oxygen atoms surrounding the positron, the annihilation rate with the remaining ones increases and the two effects cancel each other out, leading to rather small changes in the ratio curves. Even though it will be probably possible to observe these changes in the S and W parameters, it could be difficult to distinguish defects based on them.

In the study of the positron lifetimes 3 we observed that the positron localization in the hexavacancy depends on p (mrad) Intensity ratio to UO2 lattice the charge state of this defect. In the (2V U +4V O ) 2- complex the positron density was centered between the uranium sites and not inside them, as in the other defects (see Ref.

V U V U +V O V U +2V O (011) V U +2V O (111) 2V U +4V O V U +2V O (
3). We performed, therefore, a momentum distribution calculation for this defect and present it in Fig. 3d, along with the ratio curves of the V O and V U monovacancies. In the negative hexavacancy, the positron occupies a large open volume, which is reflected in the high value of the maximum at p = 0, around 1.2. This is consistent with the long positron lifetime (365 ps) calculated for this defect. The curve at higher momenta has a shape similar to that of V U , peaks are observed around p = 15 and p = 27 mrad. However, the absolute values at high momenta between 10 and 30 mrad are closer to those calculated for V O .

C. Effect of the charge state

We verified the effect of the charge state on the momentum distribution for the uranium monovacancy. In Fig. 4 we present the ratio curves calculated for V U and V 4- U . There are only slight differences between the two charge states. For the negative monovacancy we can observe a small increase in the maximum at p = 0 and a decrease for momenta above p = 5 mrad. These results suggest that the change of the charge state has an almost negligible effect on the ratio curves, unless it changes the site at which the positron is localized, like in the case of the hexavacancy discussed before.

D. Krypton incorporation

Incorporation of gaseous fission products in vacancies in UO 2 is an important issue in the studies of fuel behavior under irradiation. The momentum distribution of the annihilation radiation is especially sensitive to the chemical environment of the defect. We have studied, therefore, the effect of a Kr atom on the Doppler spectrum of V U +2V O (110). The calculated ratio curve is presented in Fig. 5 and the positron isodensity in this defect in Fig. 6. We can see that the Kr incorporation has a significant effect on the ratio curve. The maximum at p = 0 is decreased, since krypton increases the electron density and decreases the free volume available to the positron, as seen in Fig. 5. Additionally, the peak around p = 15 mrad decreases and the one around p = 27 mrad increases. The high sensitivity of the momentum distribution of the annihilation radiation to the presence of krypton atoms suggests that such measurement can be very useful in studies of fission products incorporation in UO 2 .

V O V U V O (a) V U V O V O Kr (b)
FIG. 6. (Color online) Positron isodensities (70% of the maximum density -solid and 30% -transparent), in red, found in the VU+2VO(110) defect, empty (a) and containing a Kr atom (b). Uranium atoms are presented in gray, oxygen atoms in blue and krypton in green. White and yellow spheres represent oxygen and uranium vacancies, respectively. Figures were generated using the xcrysden 41,42 program.

E. S and W parameters

In experimental PAS studies integrated low-and highmomentum contributions to the momentum distribution are often considered. These contributions are calculated as so-called S (low-momentum) and W (highmomentum) parameters, being defined, respectively, as the ratio of counts in the regions close to and far from the 511 keV value to the total number of the counts. These parameters are usually presented as values relative to the perfect lattice and defined as:

S rel = S defect S lattice (5)
and

W rel = W defect W lattice . (6)
We calculated the S rel and W rel parameters for the considered vacancies in UO 2 , using the integration windows of S ∈ (0, 2.8) mrad and W ∈ (10.61, 26.35) mrad, as in Ref. 6 , and present them in Fig. 7. We can see that the points corresponding to V U , V U +V O , the three configurations of V

F. Comparison with experiments

In Fig. 7 we compare the calculated relative S and W parameters with the trend in measured parameters observed in Ref. 6 (dotted line). In this study UO 2 samples were irradiated with electrons with various energies (1 and 2.5 MeV) at various fluences (5×10 17 cm -2 and 5×10 18 cm -2 ). The positron lifetime observed in these samples was equal to 310±5 ps. We can clearly see that there is no agreement between the calculated and measured S rel. and W rel. parameters. We suppose that it is due to the fact that the comparison between the calculated and experimental S rel. and W rel. is only meaningful if the reference samples, considered as free of defects, exhibit positron annihilation characteristic close to those of a perfect lattice. The uranium dioxide samples taken as reference in Ref. 6 (annealed during 24 hours at 1700 o C under ArH 2 ) are hyper-stoichiometric and probably con-tain nonnegligible concentrations of defects, such as negative oxygen interstitials. These defects, even though having positron lifetimes close to that of the lattice, can give rise to significantly different momentum distributions of annihilating positron-electron pairs. This means that the denominators adopted in Eq. ( 5) and ( 6) in the present work and in the experimental study do not correspond. It is worth noting that the comparison between the absolute values of S and W would not solve this problem, since they depend strongly on, for instance, the detector geometry, resolution and calibration and, therefore, are meaningless 2 . We conclude that further experimental studies, with a careful control of the defects concentration in the reference samples and their stoichiometry, could enable an insightful comparison with calculations and a more advanced interpretation of the Doppler broadening measurements on UO 2 .

IV. CONCLUSIONS

We performed first-principles calculations of momentum distribution of the annihilation radiation for various vacancy defects in uranium dioxide. Self-consistent twocomponent density functional theory schemes were used and the full atomic relaxation (due to both electronic and positronic densities) was taken into account. We studied the effect of the choice of the calculation scheme, charge state and krypton incorporation on the calculated ratio curves.

We observed that in the case of the majority of considered vacancy defects, except for V O and (2V U +4V O ) 2-, calculations yield rather similar relative S and W parameters and hence they could only be distinguished in high precision experimental measurements. In the case of the uranium monovacancy we observed a negligible effect of the charge state on the calculated ratio curve. Our calculations for the bound Schottky defect containing a krypton atom indicate that the incorporation of this fission product affects strongly the Doppler spectrum of the defect and, therefore, could be successfully studied using PAS.

We did not observe a clear agreement between the calculated and measured S rel and W rel parameters. We suppose that this can be related to the fact that the reference samples may contain nonnegligible concentrations of negative oxygen interstitials. Additional experiments on samples with controlled stoichiometry could be performed to verify the influence of the reference data on the S(W ) plots.

  FIG. 1. (Color online) Ratio curves of the calculated momentum distributions of annihilating electron-positron pairs in VU using different schemes. All spectra are convoluted with a Gaussian function with FWHM=4.7 mrad and divided by the lattice spectrum.

FIG. 3 .

 3 FIG. 3. (Color online) Ratio curves of the calculated momentum distributions of annihilating electron-positron pairs in various defects in UO2. All spectra are convoluted with a Gaussian function with FWHM=4.7 mrad and divided by the lattice spectrum.

  FIG. 4. (Color online) Ratio curves of the calculated momentum distributions of annihilating electron-positron pairs in VU and V 4- U . All spectra are convoluted with a Gaussian function with FWHM=4.7 mrad and divided by the lattice spectrum.

FIG. 5 .

 5 FIG. 5. Ratio curves of the calculated momentum distributions of annihilating electron-positron pairs in the VU+2VO(110) trivacancy (Bound Schottky Defect), empty and containing one Kr atom. All spectra are convoluted with a Gaussian function with FWHM=4.7 mrad and divided by the lattice spectrum.

FIG. 7 .

 7 FIG. 7. (Color online) S rel parameter as a function of the W rel parameter plotted for various defects in UO2, using windows S ∈ (0, 2.8) mrad and W ∈ (10.61, 26.35) mrad. The results were obtained using spectra convoluted with a Gaussian function with FWHM=4.7 mrad. The arrow indicates the effect of krypton incorporation. The dotted line indicates the trend in the experimental measurements presented in Ref. 6.

  U +2V O and neutral 2V U +4V O are close to each other. However, they could probably be distinguished in high precision experimental measurements. The points corresponding to V O and to negative 2V U +4V O lay far from the other points, hence could be easily identified if detected in Doppler broadening measurements. By comparing the S rel and W rel parameters calculated for the empty V U +2V O (110) defect and when containing a Kr atom, we can conclude that for the set of integration windows used, the krypton incorporation leads to a clear shift in the measured signal, which should be easily observed in experiments.

		1.18
		1.14 1.16	9
		1.12
	S/S lattice	0.98 1 1.02 1.04 1.06 1.08 1.1	0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 W/W lattice 2 3 7 10 1.lattice 2.VO 3.VU 4.VU+VO 10.VU+2VO+Kr 9.(2VU+4VO) 2-8.2VU+4VO 7.VU+2VO(111) 6.VU+2VO(011) 5.VU+2VO(001) Kr ex p.	6	5 8 1	1 4

ACKNOWLEDGMENTS

The authors are grateful to Marie-France Barthe and Ilja Makkonen for fruitful discussions.This research was supported by the basic research program on nuclear materials of the Nuclear Energy Division at CEA, RCOMB. This work was partly performed using HPC resources from GENCI-CCRT (Grant x2015096008).


Virginie Benavent

Fabien Frizon

Arnaud Poulesquen
email: arnaud.poulesquen@cea.fr

Effect of composition and aging on the porous structure of metakaolin-based geopolymers

Keywords: Geopolymer, porosity, aging

A combination of intrusive and small-angle scattering techniques is used to characterize the porous structure of metakaolin-based geopolymers. The influence of the geopolymer paste composition and the aging time in a 100% relative humidity environment at 20°C are studied.

The effect of the alkali activator, the water amount and the silica amount were investigated. The results show a strong "ink-bottle" effect indicating a two-level pore structure: a meso-and macroporous network. Both alkali activator and water amount have a significant impact on porosity and microstructure in the studied formulation range. After a period of one month, the pore structure is stable over a period of one year except for a small closure of porosity, revealed by nitrogen sorption and small-angle neutron scattering (SANS). These results highlight the geopolymer stability in the curing conditions. For the first time, SANS combined with the contrast matching technique was used to determine a fraction of closed porosity in geopolymer pastes. It was found that the geopolymer porosity is mainly open, the closed porosity representing less than 5% of the pore volume after six months of aging.

Introduction

Geopolymers are aluminosilicate materials having an amorphous structure, obtained by alkali activation of an aluminosilicate source (here metakaolin) at room temperature [START_REF] Duxson | Geopolymer technology: the current state of the art[END_REF] . The geopolymer formation takes place according to a well-accepted mechanism of dissolution/restructuring/polycondensation, called geopolymerization, which leads to a solid material with water trapped in the pores [START_REF] Xu | The geopolymerisation of alumino-silicate minerals[END_REF][START_REF] Dimas | Polymerization in sodium silicate solutions: a fundamental process in geopolymerization technology[END_REF] . Many studies highlighted their potential applications in several fields, such as civil engineering or waste management [START_REF] Duxson | Geopolymer technology: the current state of the art[END_REF][START_REF] Provis | Geopolymers: structures, processing, properties and industrial applications[END_REF][START_REF] Palomo | Alkali-activated cementitous materials: Alternative matrices for the immobilisation of hazardous wastes: Part I. Stabilisation of boron[END_REF][START_REF] Palomo | Alkali-activated cementitious materials: Alternative matrices for the immobilisation of hazardous wastes: Part II. Stabilisation of chromium and lead[END_REF][START_REF] Rooses | Encapsulation of Mg-Zr alloy in metakaolin-based geopolymer[END_REF][START_REF] Roy | Alkali-activated cements Opportunities and challenges[END_REF][START_REF] Cantarel | Solidification/stabilisation of liquid oil waste in metakaolin-based geopolymer[END_REF] .

According to literature, geopolymers are mesoporous materials [START_REF] Duxson | Understanding the relationship between geopolymer composition, microstructure and mechanical properties[END_REF][START_REF] Glad | Optimization of Gas Adsorption Porosimetry for Geopolymer Analysis[END_REF] , with a wide pore size distribution and a non-well defined pore form [START_REF] Maitland | Characterization of the pore structure of metakaolin-derived geopolymers by neutron scattering and electron microscopy[END_REF] . Several authors report a pore volume between 30% and 50% [START_REF] Bell | Nanoporosity in Aluminosilicate, Geopolymeric Cements[END_REF][START_REF] Fernandez-Jimenez | Immobilization of cesium in alkaline activated fly ash matrix[END_REF][START_REF] Skvara | Microstructure of geopolymer materials based on fly ash[END_REF] . Moreover, the porous network characteristics are highly dependent on the alkali activator (NaOH or KOH), on the alkali solution composition and on the aluminosilicate source. Typically, when potassium is used instead of sodium as the alkali activator, the pore size decreases and leads to higher specific areas [START_REF] Bell | Nanoporosity in Aluminosilicate, Geopolymeric Cements[END_REF][START_REF] Steins | Effect of aging and alkali activator on the porous structure of a geopolymer[END_REF] . It has also been proven that variations in the Si/Al ratio in the alkali solution has a strong influence on the geopolymer microstructure [START_REF] Duxson | Understanding the relationship between geopolymer composition, microstructure and mechanical properties[END_REF] and the amount of water initially introduced in the mixture has a huge impact on pore volume, which increases when the amount of water increases [START_REF] Lloyd | Spatial distribution of pores in fly ash-based inorganic polymer gels visualised by Wood's metal intrusion[END_REF][START_REF] Steveson | Relationships between composition, structure and strength of inorganic polymers[END_REF] . The porosity controls a lot of properties, such as mechanical and transport properties [START_REF] Boher | Influence of the pore network on hydrogen diffusion through blended cement pastes[END_REF][START_REF] Boher | Experimental investigation of gas diffusion through monomodal materials. Application to geopolymers and Vycor® glasses[END_REF] , directly linked to the material durability. The evolution of the pore structure has already been investigated at early age [START_REF] Rovnaník | Effect of curing temperature on the development of hard structure of metakaolin-based geopolymer[END_REF][START_REF] Steins | Structural Evolution during Geopolymerization from an Early Age to Consolidated Material[END_REF] while only a few studies focused on the long-term evolution of geopolymer materials [START_REF] Steins | Effect of aging and alkali activator on the porous structure of a geopolymer[END_REF][START_REF] Melar | The Porous Network and its Interface inside Geopolymers as a Function of Alkali Cation and Aging[END_REF] .

The aims of this work are to characterize the porous structure of metakaolin-based geopolymer and study the influence of aging, by the means of a multi-technique approach. Similarly to a previous study [START_REF] Steins | Effect of aging and alkali activator on the porous structure of a geopolymer[END_REF] , nitrogen sorption, small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) were used. In addition, mercury intrusion porosimetry (MIP) and water porosimetry were performed in order to determine the pore volume and the geopolymer microstructure was observed directly by scanning electron microscopy (SEM). Difficulties have been reported about porosity characterization by intrusive techniques such as nitrogen sorption or MIP. Large mesopores cannot be probed by nitrogen sorption. Significant errors can be obtained on materials having random porosity or when large-diameter pores are accessible only via smallerdiameter pores: this is known as the "ink-bottle effect". SAXS and SANS are commonly used to characterize porous materials [START_REF] Ramsay | Surface and pore structure characterisation by neutron scattering techniques[END_REF][START_REF] Gouze | How hexagonal mesoporous silica evolves in water on short and long term: Role of pore size and silica wall porosity[END_REF] , including geopolymers [START_REF] Steins | Structural Evolution during Geopolymerization from an Early Age to Consolidated Material[END_REF][START_REF] Melar | The Porous Network and its Interface inside Geopolymers as a Function of Alkali Cation and Aging[END_REF] . Contrary to nitrogen sorption, they present the advantage of being non-intrusive techniques and the sample preparation does not require any special treatment which could damage the structure. Both techniques can be used to found the mean pore size. However, the information provided by SAXS and SANS are limited by the range of the scattering vector. In the present study, a combination of these techniques is used to get a full description of the geopolymer porous network. The influence of aging time and of the activation solution chemistry on the porosity is also deeply investigated: nature of the alkali activator, Si/Al ratio and water H 2 O/Na 2 O molar ratio are considered. Finally, the proportions of open and closed porosity were estimated by SANS using the contrast matching technique, which consists in exchanging the pore solution by the geopolymer solid network extinction mixture made of water H 2 O and heavy water D 2 O. The pore solution composition was analysed as a function of time and the porosity evolution was followed for a period of one year by nitrogen sorption.

Materials and methods

Geopolymer synthesis and curing.

Metakaolin-based geopolymers were prepared from the Pieri Premix MK from Grace Construction, which composition can be found elsewhere Samples were stored at 298 K and 100% relative humidity during all the curing period to prevent them from drying.

Pore solution characterization.

A high-pressure device similar to the one of Cyr et al. [START_REF] Cyr | High Pressure Device for Fluid Extraction from Porous Materials: Application to Cement Based Materials[END_REF] was used to extract the pore solution. At different aging times (1, 7, 14, 30, 90, 180 and 365 days), about 200 g of geopolymer paste were crushed into fragments of 2-5 cm each and were introduced in the extraction device. A loading rate of 0.6 kN.s -1 was applied up to a pressure of 300 MPa. This pressure was maintained for three minutes. About 5-10 mL of pore solution was collected this way, depending of the water molar ratio of the geopolymer paste. The pH value was measured with a dedicated high pH electrode calibrated with buffer solutions between 9 and 13. Part of the pore solution was kept under N 2 atmosphere to prevent from further carbonation, while the other part was acidified with nitric acid (2% v/v) for cation chemical analysis by Inductively Coupled Plasma (ICP). Chemical analyses of the anions were performed by anionic chromatography.

Scanning Electron Microscopy.

SEM imaging was performed on polished sections with a Supra 55 microscope (ZEISS, UK).

Prior to analysis, carbon coating was performed to prevent the accumulation of charge at the sample surface. The analysis was performed with 15kV acceleration voltage.

Porous network characterization by intrusive techniques.

Water porosimetry gives an estimation of the pore volume, for pore sizes from 2 nm up to 2 mm.

Samples were saturated in water and under vacuum for at least 72 hours. After complete saturation, the underwater weight and the saturated sample mass were measured. Then, the samples were dried in an oven at 80°C until equilibrium (mass loss less than 0.05% in 24 consecutive hours) and weighted again. Porosity 𝛷 was finally estimated according equation ( 1):

(1) 𝛷 (%) = 𝑚 𝑠𝑎𝑡 -𝑚 𝑑𝑟𝑦 𝑚 𝑠𝑎𝑡 -𝑚 𝑤𝑎𝑡 * 100

where 𝑚 𝑠𝑎𝑡 is the mass after saturation, 𝑚 𝑑𝑟𝑦 the mass after drying and 𝑚 𝑤𝑎𝑡 the underwater weight.

To determine the pore size distribution, mercury intrusion porosimetry (MIP) and nitrogen sorption porosimetry were performed, allowing the characterization of pore radius ranging from 3 nm to 400 µm and from 2 to 400 nm, respectively. Before the tests, the samples were freeze-dried, this technique supposing to be less damageable for the microstructure than another drying method in the case of cementitious materials [START_REF] Gallé | Effect of drying on cement-based materials pore structure as identified by mercury intrusion porosimetry: A comparative study between oven-, vacuum-, and freeze-drying[END_REF] .

Nitrogen sorption measurements were performed on a Micromeritics ASAP 2020 instrument at 77 K in the relative pressure range P/P 0 of 5.10 -6 -0.99. Because the water in the materials was not fully eliminated by the freeze-drying, all samples were degassed for 2 hours at 90°C and for 10 hours at 350°C under vacuum prior to analysis in order to eliminate the impurities at the material surface. The specific area was determined using the Brunauer-Emmet-Teller (BET) method, and the pore size distribution was calculated on the basis of the desorption branch of the isotherm using the Barret-Joyner-Halenda (BJH) model, which implies a strong approximation on the pore form supposed cylindrical. Pore volumes were calculated from the amount of adsorbed nitrogen at the relative pressure P/P 0 of 0.99.

A Micromeritics Autopore IV 9500 was used for the MIP experiments. Pore size distribution was calculated using the Washburn law with a contact angle of 130° and surface tension of 0.485 N/m.

First, a low pressure test is practiced to evacuate the gases and fill the sample holder with mercury, and the high pressure test reaches pressures up to 414 MPa.

Small-angle neutron scattering and Small-angle X-ray scattering.

Porosity was also investigated by the means of scattering techniques, allowing the estimation of the average pore size, the pore volume and the specific area.

SAXS measurements were carried out at the laboratory LIONS (Laboratoire Interdisciplinaire sur l'Organisation Nanométrique et Supramoléculaire, CEA Saclay, France) on thin geopolymer plates of about 500 µm. The X-ray radiation was generated by a Cu rotating anode (λ Kα-1 = 0.154 nm) and the covered q range was between 0.7 × 10 -3 and 0.4 Å -1 . On some samples, complementary SAXS experiments were made at the ESRF (European synchrotron facility, Grenoble, France) using a USAXS instrument in order to extend the covered q range from 2 × 10 -4 to 1 Å -1 . The radiation wavelength was 0.995 Å and the sample-detector distance was 0.76 m and 30.7 m for SAXS and USAXS, respectively.

SANS measurements were performed on the PACE spectrometer at the Laboratoire Léon Brillouin (Orphée Nuclear Reactor, Saclay, France), using two configurations (wavelength λ = 6 Å and sample-detector distance = 4.7 m, or λ = 17 Å and sample-detector distance = 3 m) to cover the q range between 2.4.10 -3 and 1.1.10 -1 Å -1 . Thin geopolymer plates of about 1 mm were placed between two quartz windows in a sealed cell and the measurements were realized at room temperature on saturated samples with solvents. The data treatment was carried out using the software Pasinet developed at the LLB [START_REF] Brûlet | Improvement of data treatment in smallangle neutron scattering[END_REF] . Typically, the obtained signal was corrected for the sample transmission and thickness, the contribution of the empty cell, and normalized by the water scattering to correct for the inhomogeneity of the detector response. At the higher wave vectors, incoherent diffusion due to the solvent was observed and a correction was applied to the diffusion profile in region III in order to get a q -4 evolution, considering the Porod regime observed in SAXS experiments, shown in Fig. 1. Further details on the data treatment are given in the Supporting Information in section SI.1.

Corrected SANS and SAXS diffusion profiles can be divided in three regions:

(I) At low q, the first region where the intensity decreases as a function of q -D , and where the exponent D represents the mass fractal dimension of the solid network structure. D is close to 2.7 in USAXS. This fractal dimension is actually very similar to the one of the metakaolin [START_REF] Steins | Effect of aging and alkali activator on the porous structure of a geopolymer[END_REF] . Differences in D value obtained with SANS are explained in the section SI.1 of the supporting information.

(II) A transition region between region I and region III, corresponding to the diffusion of the mesoporous network.

(III) At higher q, the intensity varies as q -4 (Porod regime 29 ), which is characteristic of a smooth interface between the solid network and the pores containing the pore solution.

From SAXS and SANS measurements, a characteristic size of the porous network can be estimated using a strong approximation on the pore form, i.e. a sphere model convoluted with a lognormal distribution of radii. The form factor 𝑃(𝑞) for a sphere of radius 𝑅 is given by equation ( 2).

(

) 𝑃(𝑞) = { 3[sin(𝑞𝑅)-𝑞𝑅𝑐𝑜𝑠(𝑞𝑅)] (𝑞𝑅) 3 } 2 2
The function 𝑓(𝑅, 𝑅 0, 𝑞) of a lognormal distribution for polydisperse spheres of radius 𝑅, with a median radius 𝑅 0 , and a standard deviation 𝜎, is given by equation ( 3).

(

) 𝑓(𝑅, 𝑅 0 , 𝑞) = 1 𝑁𝑜𝑟𝑚 𝑒 {- 1 2𝜎 2 [ln ( 𝑅 𝑅 0 )] 2 } 3
One fit is shown in Figure .2.

Pore volume and specific area were estimated only from SANS data because it was not possible to control the sample saturation in the SAXS experiments. This can induce errors in the intensity level and false the data analysis. The quantity of interface Σ (m -1 ) is given by the Porod limit (4):

(4) 𝛴 𝑝𝑜𝑟𝑒𝑠 = lim 𝑞 →∞ 𝐼(𝑞)𝑞 4 2𝜋𝛥𝜌 2
where 𝛥𝜌 2 is the contrast between the scattering length densities of the solid network and of the pore fluid. The specific area was obtained from the quantity of interface by dividing by the volume fraction of solid 𝛷 𝑠 and by the solid density d, which has been measured with the helium pycnometer Micromeritics AccuPyc II 1340 (d Na-geo = 2.3 ± 0.05 g.cm -3 and d K-geo = 2.4 ± 0.05 g.cm -3 ). 𝛷 𝑠 have been calculated from the water porosimetry measurement by:

(5) 𝛷 𝑠 = 1 -𝛷 SANS experiments were also realised to found out the proportions of closed and open porosity in the geopolymer pastes, using the contrast matching method. The principle of the experiment is illustrated in Fig. 3 and explained below.

Prior to analysis, the pore solution of the samples have been exchanged by immersing the geopolymer plates for at least 72h in pure water (Fig. 3a) or in the extinction mixture (Fig. 3b), which is an isotopic mixture of H porosities are filled with an aqueous solution, and the contrast 𝛥𝜌 2 between the solid network and the solvent inside the porosity leads to the diffusion signal, as described by equation ( 6):

(6) 𝐼(𝑞) = 𝜑𝑉𝛥𝜌 2 𝑃(𝑞)𝑆(𝑞)
where 𝜑 is the volume fraction of the solute, 𝑉 the volume fraction of the diffusing entities, 𝛥𝜌 the difference in scattering length densities, 𝑃(𝑞) is the form factor describing the size and shape of the diffusing entities, and 𝑆(𝑞) is the structure factor describing the interactions between entities.

The extinction mixture penetrates only in the open porosity, the closed porosity remaining inaccessible. Since it has the same scattering length density as the geopolymer solid network, there is no contrast between the open porosity and the solid. As a consequence, the diffusion profile results only from the contrast between the solid network and the closed porosity.

Results and discussion

Effect of the alkali activator.

Nitrogen sorption isotherms obtained on different geopolymer pastes are shown in Fig. 4. The isotherms of the geopolymer pastes Na-3.6-11.5 and K-3.6-11.5 are type IV isotherms according to the IUPAC classification [START_REF] Rouquerol | Recommendations for the characterization of porous solids (Technical Report)[END_REF] , attributed to mesoporous materials and characterized by: an inflexion point at low P/P 0 corresponding to the completion of the first adsorbed layer and the beginning of multi-layer sorption, and a rapid increase of nitrogen sorption, attributed to capillary condensation in the mesopores at higher P/P 0 .

The pore volume and the specific area of the potassium geopolymer are higher than the ones of the sodium geopolymer with the same nominal composition, whatever the experimental technique employed as reported in Table 1 andTable 2. These results are in agreement with Steins et al. [START_REF] Steins | Effect of aging and alkali activator on the porous structure of a geopolymer[END_REF] , who showed that the use of the potassium activator leads to higher porosity and smaller pore sizes, when the alkali silicate solution is prepared with the same silicate source, i.e. in both cases with precipitated silica or with a commercial silicate solution.

In our case, Fig. 5a shows that the sodium and the potassium geopolymer have about the same pore size distribution. The very first peak between 30 and 40 Å is an artifact [START_REF] Lu | Nanoporous materials: science and engineering[END_REF] . However, the potassium activating solution have been prepared from amorphous silica and KOH pellets, while the sodium geopolymer have been prepared from a ready-to-use commercial sodium silicate solution, in which NaOH pellets and water were added to obtain the desired composition. This demonstrates that bigger pore sizes are obtained by making the silicate solution from amorphous silica, probably because the dissolution of silica particles was not complete, leading to a lower condensation degree in the aluminosilicate network of the final material. This result highlights the importance of the raw materials in the composition of the alkali silicate solution to control the pore sizes.

Effect of the formulation molar ratios.

The formulation molar ratios of the geopolymer pastes have an impact on pore volume, pore size distribution, and specific area. The effect of the H 2 O/M 2 O ratio is significant on both pore volume and pore size, while the impact of the SiO 2 /M 2 O ratio is less important.

An increase in the water ratio H 2 O/M 2 O from 10 to 15 leads to an increase in the geopolymer paste porosity and in the mean pore size. The pore volume increases whatever the experimental technique, as reported in Table 1. BJH calculations on nitrogen sorption isotherms presented in Fig. 5a show that the pore size distribution broadened and was centered on higher pore sizes. In the SANS experiments, the position of the transition region is characteristic of the mean size the pores. This position is roughly designated in Fig. 5 by a dotted line and is shifted towards lower q values, meaning the mean pore size increases by increasing the amount of water in the geopolymer pastes. Results obtained from the sphere model are reported in Table 2 together with the results from the other techniques. All techniques show the same trend, but as expected MIP was less appropriate to differentiate the geopolymer paste mesoporosity for low water contents, i.e. for small pore sizes. Although in most cases the specific area was increasing slightly with water content, this trend was not confirmed by SANS results.

These results show that the water initially introduced in the mixture during the geopolymerization reactions plays an important role in the formation of the porous network. As water remains trapped in the final material, it is responsible for the geopolymer pore volume and mean pore size.

Increasing the water ratio H 2 O/M 2 O up to 20 leads to a macroporous geopolymer, as it can be seen in Fig. 5b. This geopolymer nitrogen sorption isotherm was attributed to a type II isotherm according to the IUPAC classification (see Fig. 4) and the BJH calculation in Fig. 5a does not have any meaning.

The SiO 2 /Na 2 O ratio had only a small influence on pore volume and pore sizes, which decrease slightly by increasing SiO 2 /Na 2 O from 3.6 to 4. The highest impact was observed on the nitrogen sorption isotherms in Fig. 6, when H 2 O/Na 2 O was equal to 10.

Open and closed porosity.

The fractions of closed and open porosity of the solid geopolymer were estimated using the contrast variation technique on seven formulations.

The scattering patterns of the one-month geopolymer Na-3.6-11.5 in water (H100) and in the extinction mixture (H30D70) in Fig. 7 are an example of results. In the case of the sample in the isotopic mixture, the scattered intensity is more than one order of magnitude lower, because of the extinction of the open porosity. The pore volume 𝑉 𝐻30𝐷70 found by fitting with a sphere model the scattering pattern of the geopolymer paste immersed in the extinction mixture (H30D70) is attributed to closed porosity, while the pore volume 𝑉 𝐻100 estimated from the scattering pattern of the same geopolymer paste in water (H100) is attributed to the total pore volume.

The fraction of closed porosity 𝛷 𝑐𝑙𝑜𝑠𝑒𝑑 is the ratio between the two pore volumes 𝑉 𝐻30𝐷70 /𝑉 𝐻100 .

𝛷 𝑐𝑙𝑜𝑠𝑒𝑑 (%) is reported in Table 3 for all the samples. At the age of one month, the porous network of all the geopolymer pastes is mainly connected, since only a small proportion of closed porosity was determined, representing less than 5 % of the total pore volume.

3.4

Evidence regarding a two-level pore structure: a meso-and macroporous network.

Contrary to materials with a well-defined pore structure (MCM-41 [START_REF] Naono | Porous Texture and Surface Character of Dehydroxylated and Rehydroxylated MCM-41 Mesoporous Silicas-Analysis of Adsorption Isotherms of Nitrogen Gas and Water Vapor[END_REF][START_REF] Neimark | Pore Size Analysis of MCM-41 Type Adsorbents by Means of Nitrogen and Argon Adsorption[END_REF][START_REF] Kruk | Characterization of Highly Ordered MCM-41 Silicas Using X-ray Diffraction and Nitrogen Adsorption[END_REF] and SBA-15 [START_REF] Ravikovitch | Characterization of Micro-and Mesoporosity in SBA-15 Materials from Adsorption Data by the NLDFT Method[END_REF] mesoporous silica, etc..), no clear saturation plateau was observed on the nitrogen isotherms in Fig. 4, after the capillary condensation had happened in the mesopores, probably because of the so-called "inkbottle effect" [START_REF] León Y León | New perspectives in mercury porosimetry[END_REF] happening when large-diameter pores are accessible via small-diameter pores.

Moreover, the values of total porosity evaluated from neutron scattering were much smaller than the porosity determined from the other characterization techniques (see Table 1). However, in the SANS experiments, the probed pore volume is the one whose characteristic pore size is located in the available wave vector range: that is to say mesoporosity. If the geopolymer pastes had another characteristic pore size not detectable in this q range, then the pore volume have been underestimated from the experiments. This "missing" pore volume could be either microporosity or macroporosity. The hypothesis of microporosity is ruled out in section SI.2 of the Supporting Information after t-plot calculations. Thus, the difference in pore volume between SANS and the other technique is attributed to macroporosity.

These observations are in agreement with literature [START_REF] Lloyd | Spatial distribution of pores in fly ash-based inorganic polymer gels visualised by Wood's metal intrusion[END_REF][START_REF] Provis | X-ray microtomography shows pore structure and tortuosity in alkali-activated binders[END_REF] . Provis et al. [START_REF] Provis | X-ray microtomography shows pore structure and tortuosity in alkali-activated binders[END_REF] conducted X-ray microtomography with a resolution of 0.75 µm on alkali activated binders and reported a pore volume between 25% and 35%. Such big porosity should be observable by SEM and two zones are clearly identified on the micrographs of a polished section of the geopolymer paste Na-3.6-13

in Fig. 8. The microcracks are probably due to the under vacuum drying during the carbon coating phase. The first smooth-looking zone is the dense amorphous and mesoporous geopolymer paste, while the second one is attributed to a porous region resulting from the partial dissolution of metakaolin, which leaves the print of metakaolin grains in the microstructure. The size of these pores can reach several tenths of micrometers, similarly to metakaolin grains. Fig. 8c is a picture of the inside of a pore, which shows the irregular pore surface. Macropores are not connected together, which could explain that the MIP data did not show any macroporosity. They would be connected by the means of the mesoporous network. A similar conclusion was drawn by Lloyd et al. [START_REF] Lloyd | Spatial distribution of pores in fly ash-based inorganic polymer gels visualised by Wood's metal intrusion[END_REF] on observations made on alkali activated fly ashes. They suggested that a large part of the pore volume exists in the cavities left by the dissolution of fly ash particles. Contrary to all the other formulations, SEM observations on the geopolymer paste Na-3.6-20 in Fig. 9 show a porous microstructure fully made of agglomerated entities, and the two different zones cannot be identified anymore. Some carbonation was observed on the sample surface.

Geopolymer paste evolution.

Both nitrogen sorption and SANS highlighted the great stability of the geopolymer pastes kept at 20°C in a 100% relative humidity environment for a period of one year.

Nitrogen sorption was performed at different aging time (7, 30, 90, 180 and 365 days) and the isotherms obtained on four formulations are shown in Fig. 10. A significant evolution is observed between 7 and 30 days, showing that the porous network formation was not completed even 7 days after the macroscopic setting time of the material. After 30 days of aging time, there is only a slow evolution of the geopolymer pastes. For some samples, like K-3.6-11.5 in Fig. 10a, there is almost no evolution. For other samples, in Fig. 10b and Fig. 10c, the pore volume becomes slightly lower and the capillary condensation phenomenon shifts towards higher P/P 0 . As a consequence, the pore size distribution calculated with BJH method moves towards bigger pore sizes. These small evolutions are attributed to the partial closure of porosity over time. The strongest evolution is observed for the geopolymer Na-4-10 in Fig. 10d.

To confirm the closure of the porosity and to quantify it, SANS experiments were performed again on the geopolymer pastes aged of six months, and the results were compared with the ones previously obtained at one month. The results, reported in Table 3, show a slight increase in closed porosity after six months, for all the sodium geopolymers, but not for the potassium geopolymer. Still, it is important to notice that in the nitrogen sorption experiments, the variation in the pore volume was sometimes visible only after a period of one year, and that there was no evolution for the potassium geopolymer. This can explain there is no difference for the potassium geopolymer in the SANS experiments either. In all cases, the closure phenomenon is small and the geopolymer paste porosity remains mainly opened after a period of six months.

The mechanism responsible for the closure of porosity is still unknown but four assumptions can be formulated:

(1) The geopolymerization reactions are still ongoing after 30 days and there is consumption of ionic species in the pore solution.

(2) There is a phase precipitation in the pore solution at the pore surface.

(3) There is a densification of the solid network.

(4) A dissolution-reprecipitation mechanism occurs at the pore wall/pore solution interface.

The two first assumptions could explain the closure of the smallest pores but not the enlargement of the biggest pores observed by nitrogen sorption. Moreover, the extraction and the chemical analysis of the pore solution at different times have been realized. The results are shown in Fig. 11 for the geopolymer pastes Na-3.6-11.5 and K-3.6-11.5 and no significant change in the pore solution composition or in the pH value is observed after 7 days. The pore solution composition evolves clearly only between 1 and 7 days. No densification of the solid network has been highlighted. However, porosity evolution due to a dissolution-reprecipitation process has been previously observed in porous silica MCM-41 [START_REF] Gouze | How hexagonal mesoporous silica evolves in water on short and long term: Role of pore size and silica wall porosity[END_REF] filled with water, causing similar consequences on nitrogen sorption results: decrease in pore volume and modification of the pore size distribution. Although confirmation is needed, it is possible that this kind of mechanism happens in the geopolymer porosity. Dissolution would happen in the larger part of the pores and precipitation in the smaller pores, causing pore clogging.

Conclusion

This study concerns the impact of the geopolymer paste chemistry on porosity and on their evolution at 20°C in a 100% relative humidity environment.

In agreement with previous literature data, the alkali activator choice has an impact on pore volume and specific area, but the raw materials have an impact on the pore size distribution. The effect of the molar ratio H 2 O/M 2 O is significant on both pore volume and pore size, while the SiO 2 /M 2 O ratio has almost no impact in the studied range. Increasing the water ratio up to a certain point can lead to a macroporous geopolymer. Besides, a significant part of the pore volume is due to cavities of several micrometers left by the partial dissolution of metakaolin particles.

From SEM observations, these macropores do not seem connected together, which implies a strong "ink-bottle effect" on the nitrogen sorption isotherms and on MIP results.

Between seven days and one month of aging, the nitrogen sorption results show a strong evolution of the porous network. It was clear that the geopolymer network is not completely formed even one week after the macroscopic setting time. After a period of one month, the evolution is much lower. The results highlight the durability of the geopolymer pastes in terms of their evolution in a 100% relative humidity environment for a period of one year. In most cases, the pore size distribution remains unchanged or is slightly shifted towards bigger pore size. In addition, a slight

,E-03 1,E-02 1,E-01 1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 1,E+09 1,E+10 1,E+11 0

FiguresFigure 1 -Figure 2 -

 12 Figures

Figure 3 -

 3 Figure 3 -Schematic diagram illustrating the measurement of closed porosity by smallangle neutron scattering with the contrast matching method.

Figure 4 -

 4 Figure 4-Effect of the water ratio H 2 O/M 2 O and alkali activator on the nitrogen sorption isotherms of geopolymer pastes.

Figure 5 -

 5 Figure 5 -Effect of water ratio H 2 O/M 2 O and alkali activator on the pore size distribution of different geopolymer pastes obtained by (a) nitrogen sorption porosimetry, (b) MIP, and (c) SAXS.

Figure 6 -

 6 Figure 6 -Effect of the silica ratio SiO 2 /M 2 O on the nitrogen sorption isotherms of onemonth aged geopolymer pastes and H 2 O/Na 2 O = 13, 11.5 or 10.

Figure 7 - 3 . 6 - 11 . 5 .

 736115 Figure 7 -Small-Angle Neutron Scattering patterns of the one-month geopolymer paste Na-3.6-11.5. The black points stand for the sample in water (H100), and the grey points stand for the sample in the extinction mix (H30D70).

Figure 8 -Figure 9 -Figure 10 -

 8910 Figure 8 -SEM micrographs of the one-month aged geopolymer paste Na-3.6-13 at different scales.

Figure 11 -

 11 Figure 11 -Evolution of the pore solution chemical composition and pH value of the geopolymer paste (a) Na-3.6-11.5 and (b) K-3.6-11.5.

  Rhodia, purity > 98%), and a sodium silicate solution (Betol 52T, Woellner; 30.2 wt % SiO 2 , 14.7 wt % Na 2 O and 55.1 wt % H 2 O). Nine geopolymer pastes were prepared by mechanically mixing at 800 rpm metakaolin with a sodium or a potassium silicate solution. A molar ratio Al/M of 1 (M = Na or K) and molar ratios H 2 O/M 2 O of 10, 11.5, 13, 15 or 20 and SiO 2 /M 2 O of 3.6 or 4 (corresponding to Si/Al of 1.8 and 2, respectively) were studied. The alkali silicate solution had the nominal composition 𝑥SiO 2 M 2 O𝑤H 2 O, with 𝑥 equal to 1.2 or 1.4 and 𝑤 equal to 10, 11.5, 13, 15 or 20. Below, we denote for example Na-4-13 the sodium geopolymer formulation with a molar ratio SiO 2 /Na 2 O of 4 and H 2 O/Na 2 O of 13.

[START_REF] Steins | Effect of aging and alkali activator on the porous structure of a geopolymer[END_REF]

(d 10 = 1.8 µm, d 50 = 10.3 µm, d 90 = 48.2 µm), NaOH (Normapur, Prolabo), KOH (Normapur, Prolabo), amourphous silica (Tixosil 331,

Acknowledgments

This work benefited from SasView software, originally developed by the DANSE project under NSF award DMR-0520547. The authors thank Olivier Diat (ICSM), Olivier Tache (LIONS), Sylvain Prevost (ESRF) and Jacques Jestin (LLB) for their help with small-angle X-ray and smallangle neutron scattering measurements, Karine Ressayre for ionic chromatography and Adrien Gerenton for MIP experiments.


V Garric

P Donnadieu

F Leprêtre

M Loyer-Prost

B Kapusta

K Colas-Leroux

Effect of simultaneous triple beam irradiation to reproduce in-situ radiation damage of an aluminum alloy

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

EMIRUM 2018

Effect of simultaneous triple beam irradiation to reproduce in-situ radiation damage of an aluminum alloy

Abstract

Aluminum alloys have been widely used in nuclear research reactors since 1960. Even though many data on their mechanical behavior are available, few studies focus on the understanding of void swelling. Indeed, the density measurements of aluminum samples before and after irradiation allow to assess the total swelling but don't discriminate the contributions of thermal and fast neutrons. In the material testing reactors, the higher fast neutron flux (E>1MeV) is expected to impact the relative contributions to total swelling. Therefore, this study aims to reproduce reactor irradiation conditions using a simultaneous triple beam irradiation to simulate the materials damage observed in aluminum components. Aluminum specimens were irradiated with different ions: helium ions, simulating the production of alpha particles inside the reactor, silicon ions to reproduce the aluminum transmutation and tungsten ions to enhance the DPA rate. Using the proper energy and flux conditions, a 200 nm wide area of interest was obtained (figure 1a) and TEM specimens were prepared in this specific zone. TEM examinations show multiple defects and a unique microstructure. A wide area with helium bubbles (figure 1b) is present, thus modifying the initial microstructure (precipitates and dispersoïds).

Comparing the current results with previous single beam studies using gold ions, we strive to explain and understand the peculiar role of helium and silicon in the void swelling process.

Figure 1 :

 1 Figure 1: (a): ion beam profile, (b): helium bubble at the implantation peak seen in TEM

  V. Garric 1 , P. Donnadieu 2 , F. Lepretre 3 , M. Loyer-Prost 3 , B. Kapusta 1 , K.Colas 1

	1 DEN-Service d'Etudes des Matériaux Irradiés, CEA Université Paris-Saclay, F-91191, Gif-sur-Yvette
	2 Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMaP F-38000 Grenoble
	3 DEN-SRMP-JANNuS, CEA Université Paris-Saclay, F-91191, Gif-sur-Yvette
	Presenter's e-mail address: victor.garric@cea.fr


Maxime M Bonney

Maxime Zabiégo

Zabiégo Validation

Pirat

Validation of PIRAT, a Novel Tool for Beam-Like Structures Subject to Seismic Induced Misalignment of Guiding Sleeves

teaching and research institutions in France or abroad, or from public or private research centers.

BACKGROUND

• Typically comprised on non-uniform beam-like structures that can be modeled as beam with several sections • A typical RCS, in particular control rod assembly, is comprised of 3 main components:

1. A Mobile Part (MP) that contains neutron absorbing material 2. A Lower Sleeve (LS) that is considered a rigid boundary 3. An Upper Sleeve (US) is considered a quasi-rigid boundary (within calculations treated as rigid, but equilibrium is checked)

• Shape and materials can change greatly between designs, analysis tools need to be adaptable • Leads to development of a tool for simplified analysis for design phase consideration • Interaction between components is treated as point forces and each component has linear-elastic material properties • While this can give a "worst-case scenario", it is important to know how the system reacts during the actual earthquake • First step is to look at dynamic effects to verify if they can be neglected (only the maximum deflection to be used) or if they contribute to resonance based motion that might cause failure

  Systems (RCS) are critical components for any nuclear reactor • These systems control the output of reactor core • Seismic vibrations represent the most challenging situation for RCS design • Fukushima: RCS worked, melt-down caused by Tsunami • This work focuses on RCS used in Sodium-cooled Fast Reactors, such as Super-Phénix and ASTRID project (currently being designed by CEA, Framatome, and others)

  Euler-Bernoulli Implementation for Seismic Events tool • SIKI -Step-by-step Insertion Kinetic Implementation tool • Currently in development with StaBI completed and current work on DEBSE • Uses Python for calculations and Excel for geometry/materials

•

  Similar method to get FRF data • Replace [0] with a forced excitation using stepped-sine • Used as verification check that all modes are included •

INVESTIGATION INTO CORRELATION

• Both situations have a 1-to-1 matching of a single mode with other modes being correlated • Free-Clamp : Mode 11 seems to have some axial stretching near 20% along the length of beam

CONCLUSIONS

• PIRAT is a novel toolbox to analyze RCS designs, but can also be used for any beam that is deformed by guiding sleeves • StaBI uses static deformations and DEBSE uses dynamic deformation to determine: Contact forces and beam deflection • The use of these tools is to perform preliminary evaluations during the design phase of a new nuclear reactor, particularly focused for applications to the ASTRID reactor project • This is thought of as a method to reject and rank possible design configuration for future in depth computational analysis and prototype testing • The use of Python and Excel greatly increase the ease-of-use and allows for simple and rapid changes to geometric and material properties


• 40 installations de neutronographie dans le monde (réacteurs)

• 2000 100 installations de neutronographie (réacteurs), surtout sur objets non irradiants Le design du système s'est focalisé sur l'optimisation des performances et la maintenance :

• Convoyeur pour le transfert de la feuille de dysprosium dans sa cassette. Réduction significative de la durée du processus et optimisation du flou géométrique.

• Design de la chambre arrière abritant la cassette d'irradiation et le dispositif expérimental en examen incluant un système d'étanchéité de la chambre (en air) durant l'examen.

• Système de positionnement des dispositifs en azimuth et en altitude assurant une course verticale de 100 cm et une rotation sur 360°pour les différents types de dispositifs expérimentaux envisagés.

• Technologie de détection (formation de l'image à partir du convertisseur). La technologie de référence au démarrage du SIN sera la même que celle utilisée précédemment sur OSIRIS (films radiographiques à couche simple) mais leur pérennité incertaine et leurs inconvénients (faible sensibilité, non-linéarité, processus chimique) amènent à rechercher une alternative du type Imaging Plate, dont des premiers tests ont été menés en 2016-2017.

•

  a), (n,g), (n,t), … + Imageur 2D de faible épaisseur, sensible aux particules ionisantes produites neutrons • Feuille cellulosique (track etch) + 6 LiF ou 10 B + traitement chimique • Feuille Dy ou In + film argentique après transfert + développement • Scintillateur (ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S) + CCD • Imaging Plate dopée au Gd + numérisation • Feuille Dy ou In + Imaging Plate après transfert + numérisation • Scintillateur (ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S) + Flat panel aSi • Production de micro-traces (track etch) • Opacification de film argentique par ionisation (Ag + Br -) • Production de lumière de scintillation • Excitation d'états métastables photostimulables (PSL BaFBr:Eu 2+ ) • Ionisation dans un semi-conducteur 6 Li + n → 3 H + 4 He + 4,79 MeV 3 He + n → 3 H + p + 0,77 MeV 10 B + n → (7%) 7 Li + 4 He + 2,78 MeV 10 B + n → (93%) 7 Li * + 4 He + 2,30 MeV + γ (0,48 MeV) 155 Gd + n → 156 Gd + γ + électrons de conversion 157 Gd + n → 158 Gd + γ + électrons de conversion 113 Cd + n → 114 Cd + γ + électrons de conversion 164 Dy + n → 165 Dy + b -(activation) 115 In + n → 116 In + b -+ γ (activation) a), (n,g), (n,t), … + Imageur 2D de faible épaisseur, sensible aux particules ionisantes produites neutrons 6 Li + n → 3 H + 4 He + 4,79 MeV 3 He + n → 3 H + p + 0,77 MeV 10 B + n → (7%) 7 Li + 4 He + 2,78 MeV 10 B + n → (93%) 7 Li * + 4 He + 2,30 MeV + γ (0,48 MeV) 155 Gd + n → 156 Gd + γ + électrons de conversion 157 Gd + n → 158 Gd + γ + électrons de conversion 113 Cd + n → 114 Cd + γ + électrons de conversion 164 Dy + n → 165 Dy + b -(activation) 115 In + n → 116 In + b -+ γ (activation) Réactions exploitables Image numérique directe • Feuille nitrate de cellulose (track etch) + 6 LiF ou 10 B + traitement • Feuille Dy ou In + film argentique après transfert + développement • Scintillateur (ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S) + CCD • Imaging Plate dopée au Gd + numérisation • Feuille Dy ou In + Imaging Plate après transfert + numérisation • Scintillateur ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S + Flat panel aSi • Production de micro-traces (track etch) • Opacification de film argentique par ionisation (Ag + Br -) • Production de lumière de scintillation • Excitation d'états métastables photostimulables (PSL BaFBr:Eu 2+) a), (n,g), (n,t), … + Imageur 2D de faible épaisseur, sensible aux particules ionisantes produites neutrons 6 Li + n → 3 H + 4 He + 4,79 MeV 3 He + n → 3 H + p + 0,77 MeV 10 B + n → (7%) 7 Li + 4 He + 2,78 MeV 10 B + n → (93%) 7 Li * + 4 He + 2,30 MeV + γ (0,48 MeV) 155 Gd + n → 156 Gd + γ + électrons de conversion 157 Gd + n → 158 Gd + γ + électrons de conversion 113 Cd + n → 114 Cd + γ + électrons de conversion 164 Dy + n → 165 Dy + b -(activation) 115 In + n → 116 In + b -+ γ (activation) Réactions exploitables Image insensible au flux gamma • Feuille nitrate de cellulose (track etch) + 6 LiF ou 10 B + traitement • Feuille Dy ou In + film argentique après transfert + développement • Scintillateur (ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S) + CCD • Imaging Plate dopée au Gd + numérisation • Feuille Dy ou In + Imaging Plate après transfert + numérisation • Scintillateur ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S + Flat panel aSi • Production de micro-traces (track etch) • Opacification de film argentique par ionisation (Ag + Br -) • Production de lumière de scintillation • Excitation d'états métastables photostimulables (PSL BaFBr:Eu 2+) a), (n,g), (n,t), … + Imageur 2D de faible épaisseur, sensible aux particules ionisantes produites neutrons • Feuille nitrate de cellulose (track etch) + 6 LiF ou 10 B + traitement • Feuille Dy ou In + film argentique après transfert + développement • Scintillateur (ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S) + CCD • Imaging Plate dopée au Gd + numérisation • Feuille Dy ou In + Imaging Plate après transfert + numérisation • Scintillateur ZnS(Ag)-6 LiF ou Gadox Gd 2 O 2 S + Flat panel aSi • Production de micro-traces (track etch) • Opacification de film argentique par ionisation (Ag + Br -) • Production de lumière de scintillation • Excitation d'états métastables photostimulables (PSL BaFBr:Eu 2+) • Ionisation dans un semi-conducteur 6 Li + n → 3 H + 4 He + 4,79 MeV 3 He + n → 3 H + p + 0,77 MeV 10 B + n → (7%) 7 Li + 4 He + 2,78 MeV 10 B + n → (93%) 7 Li * + 4 He + 2,30 MeV + γ (0,48 MeV) 155 Gd + n → 156 Gd + γ + électrons de conversion 157 Gd + n → 158 Gd + γ + électrons de conversion 113 Cd + n → 114 Cd + γ + électrons de conversion 164 Dy + n → 165 Dy + b -(activation) 115 In + n → 116 In + b -+ γ (activation) Réactions exploitables Processus de production d'images Systèmes d'imagerie neutronique Pas d'image numérique directe sur des objets fortement irradiants Imagerie possible par conversion (n,g ou n,a) Hartmut Kallmann & Ernst Kuhn (Allemagne) • Neutronographie avec accélérateur Peter (Allemagne) • Première Neutronographie avec réacteur 10 9 n.cm -2 .s -1 Thewlis, Derbyshire @BEPO (Harwell, UK) • Neutronographie sur combustible irradié (méthode par transfert) Berger (US) et Barton (UK) • Premières installations : US, France, Canada, Allemagne, Japon • 1932 J.Chadwick Possible Existence of a Neutron. Nature 129 (27 février 1932).

Faisceau

  installations de neutronographie opérationnelles dans 40 pays (hors sources de spallation) Mianyang Research Reactor (CMRR), Mianyang, Chine 2) China Advanced Research Reactor (CARR), Beijing, Chine 3) Neutron Radiography Reactor (NRAD), Idaho National Laboratory, USA 4) SINQ (Paul-Scherrer Institute) (source de spallation), Suisse En 2017, seules 7 installations dans le monde proposaient une radiographie neutronique sur objets irradiants, toutes avec un faisceau sorti associé à une casemate blindée, convertisseur Dy ou In + film radiographique ou Imaging Plates : 5) High Flux Advanced Neutron Application Reactor (HANARO), Corée Sud 6) Kalpakkam Mini reactor (KAMINI), IGCAR, Inde 7) CIRUS reactor, Bhabha Atomic Research Centre, Inde 6 Grenoble, 1963 -1997) : 120 x 400 mm, L/D = 380 • Osiris (Saclay, 1966 -2015) : 100 x 650 mm, L/D = 150 • Orphée (Saclay, 1980 -) • Triton (Fontenay aux Roses, 1959-1979) • LDAC (Rapsodie, Cadarache, 1967 -1983) : source pulsée (solution fissile ~20 L nitrate d'uranyle) • Isis (Saclay) • Phenix (Marcoule, 1970 -2009) : source pulsée (solution fissile) • RJH (Cadarache, 2023 -) : 70 x 650 mm, L/D = 260 Mélusine en 1962. Yves Ballu "De Mélusine à Minatec 1956-2006 : 50 Ans d'histoires du CEA Grenoble", Éditions du Dauphiné Libéré, 2003 Orphée en 2013 (hall des guides) Osiris (CEA DEN)• MIRENE(Valduc, 1977) : source pulsée (solution fissile) nécessaire pour permettre la production d'une image neutronographique est de l'ordre de : 10 8 n th .cm -² sur le plan détecteur dans une méthode directe 10 10 n th .cm -² dans la méthode par transfert(1) La fluence au niveau du plan détecteur dépend de la géométrie du système : D L l La résolution spatiale est fortement impactée par sa contribution géométrique (flou géométrique U g ) : Fluence et flou géométrique sont liés via le paramètre géométrique L/D objet détecteu (1) Non Destructive and Analytical Techniques using Neutrons, Report of a Consultancy Meeting IAEA, Vienna, Austria, 26 -28 Nov 2008 Neutron Radiography, J.P Barton, Proceedings of the firs world Conference, Reidel Publishing, 1981 géométrique sont liés via le paramètre géométrique L/D objet détecteu Un gain en sensibilité d'un facteur 5 du détecteur permet un gain d'un facteur 2 sur le flou géométrique, via la réduction de D La neutronographie d'objets irradiants : méthode par transfert Imageur La neutronographie d'objets irradiants : méthode par transfert Méthode développée à partir de 1962 par H. Berger Irradiation avec des neutrons thermiques collimatés . Réacteur : faisceau sorti ou système immergé . Accélérateur : neutrons de spallation thermalisés exposition en labo (autoradiographie béta)Mise en contact avec le système imageur (film radiographique ou imaging plate, sous vide)

  La neutronographie d'objets irradiants : méthode par transfert Imageur IMAGEUR La performance d'un imageur dépend : De la géométrie de l'examen résolution spatiale (flou géométrique) Des systèmes utilisés -source (énergie, fluence) dynamique de signal, contraste -collimateur (qualité du faisceau) contraste -détecteur imageur résolution spatiale, sensibilité -qualité du transfert résolution spatiale

HaroldBerger and W.N. Beck , Neutron Radiographic Inspection of Radioactive Irradiated Reactor Fuel Specimens Nuclear science and engineering : 15 , 411-41 4 (1963)

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