Laetitia Van Schoors
email: laetitia.van-schoors@univ-eiffel.fr

Thomas Cadu

Sandrine Moscardelli

Loïc Divet

Stéphane Fontaine

Olivier Sicot

Laetitia Van

Why cyclic hygrothermal ageing modifies the transverse mechanical properties of a unidirectional epoxyflax fibres composite?

Keywords:

The development of composites based on plant fibres has considerably grown in last decades; however, their high sensitivity to moisture limits their use in structural applications. The objective of this study is to determine and understand the impact of moisture variations during one-year cyclic hygrothermal ageing i.e. 52 cycles on the transverse properties of a unidirectional epoxy flax composite. A cycle consists of 3.5 days at 90% RH followed by 3.5 days at 40% RH. Compared to the studies usually carried out to determine the impact of ageing on the longitudinal properties of unidirectional composites, the determination of the transverse mechanical properties during this type of ageing allowed to focus on the contribution of the matrix and the interface on the evolution of the composite properties. The multi-scale analyzes provided identification of the phases responsible for the evolution of transverse mechanical properties induced by ageing. The transverse ultimate tensile strength drops by about 20% after the first week of ageing and slightly decreases up to 2 months. This evolution seems to be induced by the creation of flaws, in particular the phenomena of fibre-fibre and matrix-fibre debonding and the creation of cracks in the fibres initiated at the lumen level, revealed by SEM. The transverse modulus also strongly drops after 2 the first week by about 18% to reach about 45 % loss after one year of ageing. These evolutions are mainly linked to the physical plasticization of the epoxy matrix demonstrated by the reversible change of its glass transition temperature, but analyses showed that water does not lead to chemical degradation of the matrix.

Introduction

For many years, government directives have aimed at limiting the use of fossil resources in favour of materials that have less impact on the environment (Le Duigou and Baley, 2014). In the field of composites, one of the alternatives is the use of vegetable fibres such as flax, hemp, sisal, miscanthus... The flax fibres widely used as reinforcement fibres in thermosetting matrix have interesting properties, such as their lightness and their specific mechanical properties making them able to compete with glass fibres [START_REF] Amiri | Standard density measurement method development for flax fiber[END_REF][START_REF] Baley | Analysis of the flax fibres tensile behaviour and analysis of the tensile stiffness increase[END_REF][START_REF] Berges | Influence of moisture uptake on the static, cyclic and dynamic behaviour of unidirectional flax fibre-reinforced epoxy laminates[END_REF][START_REF] Cadu | What are the key parameters to produce a high-grade bio-based composite? Application to flax/epoxy UD laminates produced by thermocompression[END_REF][START_REF] Jeyapragash | Mechanical properties of natural fiber/particulate reinforced epoxy composites -A review of the literature[END_REF][START_REF] Poilâne | Polymer reinforced by flax fibres as a viscoelastoplastic material[END_REF]. However, these fibres also have the specificity of being hydrophilic, of having limited thermal stability and of being made up of photosensitive compounds such as lignin [START_REF] Azwa | A review on the degradability of polymeric composites based on natural fibres[END_REF]. To increase the development and use of these composites, a better understanding of the ageing mechanisms of these materials is necessary.

Today the vast majority of studies on the ageing of composites reinforced with flax fibres have been carried out by immersing these materials in water [START_REF] Assarar | Influence of water ageing on mechanical properties and damage events of two reinforced composite materials: Flax-fibres and glass-fibres[END_REF][START_REF] Dhakal | Effect of water absorption on the mechanical properties of hemp fibre reinforced unsaturated polyester composites[END_REF]; A Le Duigou et al., 2014;[START_REF] Duigou | In-situ evaluation of flax fibre degradation during water ageing[END_REF][START_REF] Li | Hydrothermal ageing mechanisms of unidirectional flax fabric reinforced epoxy composites[END_REF][START_REF] Yan | Effect of water, seawater and alkaline solution ageing on mechanical properties of flax fabric/epoxy composites used for civil engineering applications[END_REF]. This kind of ageing can lead to a huge drop of mechanical properties i.e. ultimate tensile strength and modulus especially caused by irreversible degradations of the composite. These damages mainly come from the differences in hydrophilicity, at the micro-scale, between the different flax constituents and, at the macro-scale, between the flax fibres and the epoxy matrix. This ageing can also lead to a decrease in modulus only, without variation in tensile strength explained mainly by a reorientation of the microfibrils and a plasticization of the inter-fibre bonds [START_REF] Sodoke | Hygrothermal effects on fatigue behavior of quasi-isotropic flax/epoxy composites using principal component analysis[END_REF].

The hydrophilicity differences generate a differential swelling responsible of internal stresses inside cell-wall layers [START_REF] Baley | Influence of drying on the mechanical behaviour of flax fibres and their unidirectional composites[END_REF][START_REF] Duigou | In-situ evaluation of flax fibre degradation during water ageing[END_REF][START_REF] Roudier | Analyse multi-échelle du comportement hygro-mécanique des fibres de lin[END_REF] and at the fibre-matrix interface [START_REF] Chilali | Analysis of the hydro-mechanical behaviour of flax fibre-reinforced composites: Assessment of hygroscopic expansion and its impact on internal stress[END_REF]. In addition, and as mentioned in the literature, this swelling can lead to the formation of micro-cracks in the fibre initiated in the lumen area [START_REF] Duigou | In-situ evaluation of flax fibre degradation during water ageing[END_REF] and within the matrix [START_REF] Azwa | A review on the degradability of polymeric composites based on natural fibres[END_REF][START_REF] Li | Hydrothermal ageing mechanisms of unidirectional flax fabric reinforced epoxy composites[END_REF] that facilitate the diffusion of water into the composite. Water can also cause the dissolution of some fibre constituents such as pectin and hemicellulose, thereby accentuating the degradation of the interface [START_REF] Li | Hydrothermal ageing mechanisms of unidirectional flax fabric reinforced epoxy composites[END_REF]. These degradation mechanisms are further accentuated by immersion/drying cycles, due to an increase in the diffusion kinetics of water at the fibre-matrix interface with the number of cycles [START_REF] Kim | Effect of water absorption fatigue on mechanical properties of sisal textile-reinforced composites[END_REF][START_REF] Newman | Auto-accelerative water damage in an epoxy composite reinforced with plain-weave flax fabric[END_REF]. However, despite the phenomena of swelling and hydrolysis of pectin and hemicellulose, Sodoke et al. [START_REF] Sodoke | Wetting/drying cyclic effects on mechanical and physicochemical properties of quasi-isotopic flax/epoxy composites[END_REF] have demonstrated a good preservation of tensile strength and modulus even after 7 ageing cycles of an epoxy / cyaniethylated flax fibre composite, linked to the fact that the humidification drying cycle would promote recrystallization of the cellulose chains. Thus, the drop in mechanical properties linked to the swelling and hydrolysis of the fibres would be counterbalanced by the increase in the crystallinity index of flax fibres. The immersion / drying cycles can have also favored the phenomenon of hornification which causes a modification of the microstructure of the fibres, the formation of new hydrogen bonds in the fibre wall structure resulting in an increase of fibres strength and modulus [START_REF] Mendes | Influence of Water Amount and Immersion Time on the Sisal Fibers Hornification Process[END_REF].

However, according to the chosen application, these materials can be subjected to environmental variations of humidity and will not be in contact with liquid water. Few studies deal with the hygrothermal ageing of epoxyflax composites. Berges et al. and Scida et al. (Berges et al., 2016;[START_REF] Scida | Influence of hygrothermal ageing on the damage mechanisms of flax-fibre reinforced epoxy composite[END_REF] have studied the impact of an ageing at constant humidity, with cycles between 85 and 90% RH, on the mechanical properties of epoxy/flax composite.

They showed a strong decrease in modulus (> 50% after 38 days at 40°C). The ultimate tensile strength seems to be not or much less impacted (0 and 12% after 38 days at 40°C). These changes in mechanical properties have been attributed to physical plasticization phenomena of the fibres and the resin.

More recently, Cadu et al. [START_REF] Cadu | Cyclic hygrothermal ageing of flax fibers' bundles and unidirectional flax/epoxy composite. Are bio-based reinforced composites so sensitive?[END_REF] and [START_REF] Koolen | Interface modification and the influence on damage development of flax fibre -Epoxy composites when subjected to hygroscopic cycling[END_REF] have carried out hygrothermal ageing cycles in order to stimulate the differential swelling inside the epoxy/flax composite. These ageing cycles seem to lead to less dramatic damage evolution. After 52 cycles (one cycle is composed of a 3.5 days step at 90% RH followed by a 3.5 days step at 50% RH) of ageing at 55°C, i.e. one year, Cadu et al. [START_REF] Cadu | Cyclic hygrothermal ageing of flax fibers' bundles and unidirectional flax/epoxy composite. Are bio-based reinforced composites so sensitive?[END_REF] have determined a slight decrease in longitudinal mechanical performance of a unidirectional composite. The modulus and ultimate tensile strength respectively drop by 12% and about 13%. These little evolutions are mainly attributed to fibre-fibre, and fibre-matrix debonding phenomena. [START_REF] Koolen | Interface modification and the influence on damage development of flax fibre -Epoxy composites when subjected to hygroscopic cycling[END_REF] were interested in the evolution of the three-point bending properties of unidirectional epoxy/flax composite subjected to an ageing at 80°C with humidity cycles at 78% RH and drying cycles at 25% RH. After 6 ageing cycles, the transverse tensile strength decreases from 28 MPa to 25 MPa. As in the previous study, performance losses are explained by a fibrematrix debonding phenomenon and failure of the internal interfaces of the fibres bundles. Note that these authors emphasize the fact that the degradation is much less dramatic than the ageing in water and may be more representative depending on the intended application.

To determine the interface and matrix qualities of the unidirectional composites, transverse tensile properties are one of the commonly used methods. Thus, this paper aims at determining the influence of a long (up to one year) hygrothermal ageing consisting of cycles on the transverse mechanical properties of an epoxy/flax composite in order to better assess the effects of this ageing on the interface and the matrix. Then, based on a multi-scale analysis, we try to identify the phases (i.e. interface, fibres and matrix) responsible of the changes in mechanical properties observed during ageing cycles and to improve understanding of these ageing mechanisms of this type of composites.

Materials and methods

Materials

The matrix is a DGEBA epoxy resin (SR 8500) reticulated by an amine hardener (SZ 8525) produced by Sicomin©. The flax fibres (Linum usitatissimum) are pure unidirectional reinforcements FlaxTape™ 110 produced by Lineo©. The area weight and density respectively are 96 g.m -2 and 1.45 [START_REF] Cadu | What are the key parameters to produce a high-grade bio-based composite? Application to flax/epoxy UD laminates produced by thermocompression[END_REF].

12-plies unidirectional composite has been manufactured by thermocompression, using optimized parameters [START_REF] Cadu | What are the key parameters to produce a high-grade bio-based composite? Application to flax/epoxy UD laminates produced by thermocompression[END_REF]. A first curing step was carried out at 80 ° C, for 1 hour under a pressure of 3 bars, followed by a cooling at 1 ° C per minute to 20 ° C. Then a post-curing was performed at 80 ° C for 2 hours without pressure. This composite (figure 1) contains approximately 47% by volume of fibres and 2.5% of voids. Unidirectional tensile specimens conforming to geometry 4 of ISO 527, having dimensions of 250 ± 0.5 mm long, 25 ± 0.5 mm wide and 1.8 ± 0.1 mm thick, were prepared. The edges of the composite samples were coated prior to the postcuring step with the same resin used for the fabrication.

Ageing Method

The ageing method consists of performing humidification/drying cycles in a climatic chamber to simulate the phenomena of differential swelling linked to the differences in hydrophilicity within the fibres and between the fibres and the matrix. Each cycle lasts one week and consists of a 3.5 days humidification phase at 90 ± 1% RH and a 3.5 days drying phase at 40 ± 1% RH. This ageing was carried out at 55°C to accelerate the kinetics of water diffusion but without generating melting of the waxes (60°C) on the surface of the fibres while limiting the optimal development of microorganisms which is around 30°C [START_REF] Gradeci | Mould growth criteria and design avoidance approaches in wood-based materials -A systematic review[END_REF]. Ageing durations are 1 week, 1 month, 2 months, 6 months and 1 year for the composite, and 1 week, 1 month, 2 months, 6 months for the epoxy matrix without fibres.

Aged samples are taken from the climatic chamber after the 40% RH phase. Before each characterization, all samples were conditioned at 23 ± 1°C and 50 ± 1% RH for 7 days in a climatic chamber (CTS® CP + 10/600).

This conditioning was carried out in order to get all the materials in the same water state [START_REF] Cadu | What are the key parameters to produce a high-grade bio-based composite? Application to flax/epoxy UD laminates produced by thermocompression[END_REF].

Characterization Methods

Fourier transform infrared spectroscopy (FTIR) was used to monitor the chemical evolution of the resin and composite surface ( 10 μm) during ageing cycles. Analyses were performed on a Nicolet ™ impact 380 spectrometer in attenuated total reflectance (ATR) mode, using a Durascope diamond. For each measurement, 32 scans were realized, with a resolution of 4 cm -1 over a wavelength range of 400 to 4000 cm -1 . The spectra were normalized relatively to the peak present at 1508 cm -1 , which corresponds to the aromatic groups (C = C) that do not normally evolve under the ageing conditions described in section 2.2 [START_REF] El Yagoubi | Thermomechanical and hygroelastic properties of an epoxy system under humid and cold-warm cycling conditions[END_REF]. For each ageing period, 5 measurements were carried out. Modulated Differential Scanning Calorimetry has been used to determine the glass transition temperatures (Tg) of the matrix, Tg measurements were performed on reversible signals and crosslinking enthalpies on non-reversible signals. For the composite specimens, the crosslinking enthalpy measurements were also corrected by the mass of resin present in the composite sample. These analyses were carried out using a TA Instrument DSC 250 differential scanning calorimeter. The temperature profile used is a ramp from 25 to 200°C at a rate of 1°C/min and a modulation of ± 0.16°C during 60 seconds. Furthermore, the total enthalpy of reaction (ΔHT) was measured on the non-crosslinked resin using a ramp from -70°C to 280°C at a rate of 10°C/min. For each deadline, at least two tests were carried out for the composite and the resin. The masses of the composite samples are approximately of 30mg and those of the resin of 20mg.

Dynamic Vapor Sorption (DVS) analyses were performed using a DVS-Advantage SMS. The DVS measurements achieve very accurate measures of the changes in mass of a sample based on the relative humidity of the environment. The DVS analyses are composed of a wet phase (3.5 days at 90% RH) and a dry phase (3.5 days at 40% RH) under similar humidity conditions to those of an ageing cycle. The samples used are in the form of small balls of about 0.5 cm 3 for the fibres and squares of about 1 cm side for the composite and the resin.

Secondary Electron (SE) mode scanning electron microscopy (SEM) was used to assess the morphological changes associated with ageing. The composite samples were coated in an epoxy resin (EpoFix ©) and were then polished to a mirror finish using the Struers © LaboForce-100 polisher. To limit the effect of lubricant on the swelling of the fibres, the polishing was not carried out with water but with ethanol. Then they were covered with a thin layer of carbon to avoid sample loading during observations. The mechanical properties were determined by monotonic tensile tests.

The tensile tests were performed on fibre bundles at room temperature on an Instron 5969 tensile machine equipped with a 2 kN force transducer at a speed of 1mm/min. The specimens analysed were conditioned and aged, then cut into strips with the following dimensional characteristics: width of 5 ± 0.5 mm, length between tabs of 150 ± 0.5 mm, thickness of 0.2 µm. Steel tabs were glued using Loctite® to realize tensile tests. As the dispersion of the measurements can be important due to the variability of the intrinsic characteristics of the fibres, 40 specimens have been tested for each deadline.

The tensile tests on dumbbell-shaped type 5A epoxy resin specimens (ISO527-2, 2012) were also carried out at room temperature on a Shimadzu AGS-X tensile machine equipped with a 10 kN force sensor and an integrated video extensometer system. They were performed at a speed of 1 mm/min. For each ageing period, 10 specimens were tested.

The tensile tests on the unidirectional composite material were carried out at room temperature on a MTS 100 kN Criterion C45 tensile machine, equipped with a 10 kN force transducer (precision 1/500 th or ±0,02kN) and a MTS 634.31F-24 mechanical extensometer, with a 50mm gauge length. The tests were carried out at a speed of 1 mm/min. For each ageing period, 5 composite specimens were tested.

Results and discussion

Chemical, physicochemical, morphological and mechanical analyses have been realized to determine the mechanisms taking place in the composite throughout ageing. Firstly, the evolution of mechanical properties will be presented.

Mechanical properties of the composite

The initial mechanical properties of the composite, in the transversal direction (90°), were determined by tensile tests on non-aged samples. The properties measured are as follows: σmax = 20.4 ± 1.2 MPa and E = 4.1 ± 0.2 GPa.

Then, the monotonous tensile tests carried out on the aged specimens enabled to follow the evolution of these properties during the ageing cycles (Figure 2). It appears that the ultimate tensile strength (σmax) (Figure 2) drops by 22% after the 1 st week of ageing and then decreases more slightly until the 9 th week (8%). Between 9 and 52 weeks, σmax seems to stabilize. Indeed, the decreases in σmax are less than 5% between these two ageing periods.

The Young modulus (E) (Figure 2) of the composite also decreases sharply after the 1 st week (-18%). The reduction in modulus continues until the 26 th week (23%) and almost seems to stabilize between the 26 th and 52 nd week (3%).

Therefore, the mechanical tests showed an evolution of the ultimate tensile strength and transverse Young modulus of the composite during the hygrothermal ageing cycles. Using a multi-scale analysis, we will first seek to understand whether the evolution of the ultimate tensile strength is related to the creation of defects in the different phases of the composite. Regarding the modulus, we will then try to identify whether the observed decrease is also related to the evolution of the resin, interfaces and/or fibres.

To identify the changes that take place within the composite during hygrothermal ageing cycles, several types of physicochemical analyses were carried out on composite and resin samples; the results are presented in the following sections.

Effect of cyclic hygrothermal ageing on the resin

In order to determine if the decreases of the mechanical properties of the composite are due to the degradation of the resin, analyses of Differential Scanning Calorimetry in modulated mode (mDSC) were carried out at each ageing period on composite and epoxy resin samples. The use of modulated mode makes it possible to dissociate the irreversible signal from the reversible signal. First, the irreversible signal was analysed to measure the residual crosslinking enthalpy (ΔHr) of the epoxy resin without fibres and composite (Figure 3). For the composite samples, ΔHr is recalculated based on the resin mass content in the sample. The analyses carried out on the non-crosslinked resin also made it possible to measure the total enthalpy of reaction ΔHT = 444 J/g; this value is consistent with the values found in the literature for epoxy resins DGEBA/amine for which ΔHT is between 400 and 500 J/g [START_REF] Corsetti | Modeling and estimation of parameters for the curing of an epoxy/amine system[END_REF][START_REF] Prime | Differential scanning calorimetry of the epoxy cure reaction[END_REF]. week Figure 3 shows that the residual crosslinking enthalpy (ΔHr) of the composite sharply decreases during the first 4 ageing weeks. Indeed, it decreases by 65% after the first week and by 25% between the first and the fourth week.

During this period, ΔHr varies from 20.2 ± 4.9 J/g to 8.3 ± 0.9 J/g, then to 2.8 ± 0.1 J/g. After the 4 th week, ΔHr evolves very slightly, less than 3% between each tested deadline, reaching 0.47 ± 0.03 J/g after 52 weeks of ageing.

Similarly, Figure 3 shows the evolution of ΔHr for the resin without fibres during ageing. As for the composite, this parameter decreases sharply during the cycles.

Thanks to these enthalpy measurements, the state of crosslinking of the resins can be evaluated and the degrees of progress of the resin crosslinking reaction (α) of the composite and of the epoxy resin without fibres were calculated based on the following relationship:

𝛼 = ∆H T -∆H r ∆H T (1)
With: α the progress rate of the crosslinking reaction; ΔHT the total enthalpy of the reaction and ΔHr the enthalpy of residual crosslinking.

Figure 4 shows the progress of the resin crosslinking reaction in the composite and in the epoxy resin without fibres. It appears that, for non-aged materials, the crosslinking of the matrix is not complete but high, either for the composite or for the resin without fibres. In addition, the epoxy network tends to be completely crosslinked during ageing. Figure 4 also shows that the progress rate of the crosslinking reaction is slightly greater for the composite than for the resin without fibres, under the same curing conditions. For non-aged materials, α is respectively 0.956 for the composite and 0.904 for the resin without fibres. Thus, either the Tg of the composite is slightly higher than the resin's one, or the fibres have an impact on crosslinking thereof.

To answer this question, the reversible signals obtained by the mDSC tests, i.e. Tg of the composite and resin without fibres, were analysed (Figure 5). Figure 5 shows that before ageing, the Tg of the composite (110.6 ± 1.0°C) and epoxy resin without fibres (111.4 ± 0.3°C) are very close. It therefore seems that the resin without fibres is not less crosslinked than the resin in the composite. The slight difference in residual crosslinking enthalpy can then be related to the presence of the fibres in the composite. The fibres could physically or chemically interact and limit the crosslinking, which would explain the lower crosslinking enthalpy measured for the composite. The composite ΔHT would therefore probably be lower than the ΔHT of the resin without fibres. The fibres would thus act as obstacles to the crosslinking of the matrix starting from a certain level of crosslinking of the polymer network.

Furthermore, the decrease in the crosslinking enthalpy (Figure 3) and the increase in α (Figure 4) mean that the crosslinking rate of the epoxy network increases during ageing cycles. This is explained by the exposure of the composite to a temperature of 55°C, which may be characterized as "post-curing". This temperature allows the epoxy and amine groups, which could not react during the various stages of process, to react. As the increase in the crosslinking rate leads to a decrease in the mobility of the macromolecular chains of the polymer network, it week is therefore usually accompanied by a shift in the glass transition temperature (Tg) towards the high temperatures [START_REF] Danieley | Effects of curing on the glass transition temperature and moisture absorption of a neat epoxy resin[END_REF]. However, opposite to what is expected, the Tg of the materials decreases during the ageing cycles (Figure 5). Thus, the observed Tg evolutions result from other phenomena than the postcrosslinking mentioned previously.

The water in contact with the matrix during ageing can lead to chemical (non-reversible) and/or physical (plasticization) modifications, which would explain the decrease of Tg.

To identify the phenomena, related to water, that may be responsible for this evolution of the Tg, the evolution of the Tg as a function of the water intake of the composite during ageing was studied. To do so, the composite samples were weighed after each ageing time. As illustrated in Figure 6, the evolution of the Tg as a function of the water intake is linear. DVS analyses (Figure 7) have shown that the diffusion of water in flax fibres is faster than in the composite, which is itself faster than in the epoxy resin without fibres. Moreover, the final mass of the samples is greater than the initial mass for the composite and epoxy resin without fibres but not for the fibres alone. So, for the composite, we can assume that only the resin "stores" water molecules during ageing cycles, i.e. it is only the matrix which is responsible for the measured mass gain after hygrothermal ageing. Water intake (%)

Figure 7: DVS measures on flax fibres (----), epoxy resin ( ) and composite (…..)

To verify whether, in the composite, water is only stored in the resin, the empirical relationship of Gordon Taylor [START_REF] Gordon | Ideal copolymers and the second-order transitions of synthetic rubbers. i. noncrystalline copolymers[END_REF][START_REF] Hodge | Free Volume and the Mechanism of Plasticization in Water-Swollen Poly(vinyl alcohol)[END_REF] was used. Gordon and Taylor proposed an empirical relation to predict the evolution of a polymer Tg as a function of plasticization, according to the absorbed water:

1 𝑇𝑔 = 𝑓 𝑤𝑎𝑡𝑒𝑟 𝑇𝑔 𝑤𝑎𝑡𝑒𝑟 + 𝑓 𝑝𝑜𝑙𝑦𝑚𝑒𝑟 𝑇𝑔 𝑝𝑜𝑙𝑦mer, 𝑑𝑟𝑦 (2)
With: fwater and fpolymer respectively the mass fractions of water and of the polymer; Tgwater and Tg polymer dry respectively the Tg of water (134K) [START_REF] Jenniskens | Crystallization of Amorphous Water Ice in the Solar System[END_REF][START_REF] Sugisaki | Calorimetric Study of the Glassy State. IV. Heat Capacities of Glassy Water and Cubic Ice[END_REF]) and the Tg of the polymer in its dry initial state.

For this purpose, the mass fraction of water, calculated as a function of the mass gain of the composite, was reduced to the mass of resin using the mass proportion of resin in the composite, which is 47%.

The calculated Tg results and the experimental measurements performed on the composite are presented as a function of the ageing time (Figure 8). These different data are superimposed; it therefore appears that the Gordon-Taylor relationship enables to predict the evolution of the Tg of the composite for the ageing times up to 1 year.

Consequently, it seems that the decrease in Tg is mainly induced by a plasticization of the network, i.e. a rupture of the Van der Waals inter-chain forces and of the hydrogen bonds initially formed between the polymer chains, that increases the mobility of the macromolecular chains of the polymer. Finally, it therefore seems that the post-crosslinking of the resin in the composite has only a very negligible influence on the glass transition temperature, compared to the influence of the water intake.

Physical evolutions of the resin as a function of ageing time

In order to confirm that the decrease in Tg observed is mainly related to physical plasticization phenomena in the materials, samples of composite and resin without fibres, unaged and aged 9 and 26 weeks, were dried (Figure 9).

The drying, 9-weeks long i.e. up to constant masses, was carried out in a desiccator containing silica gel at room temperature, to limit the influence of the temperature on a possible resin post-crosslinking. The results for the composite are showed in Figure 9. It appears that the drying induces an increase in the Tg compared to the initial Tg (110.6 ± 1.0°C). This means that the shift of Tg towards the low temperatures caused by ageing is cancelled out once the water has been extracted and that the effect of post-crosslinking is then observable by increases in Tg.

For the epoxy resin (Figure 9), the increase in Tg after 2 months of drying is lower than for the composite and the Tg remains lower than the initial Tg. This can be explained by a quantity of residual water caused by a slower water extraction due to the absence of fibres: the fibres favour the diffusion and extraction of water out of the material.

Analyses of differential scanning calorimetry in modulated mode have therefore made it possible to note that the evolution of the resin Tg of the composite during ageing seems mainly linked to a matrix physical plasticization.

To confirm these interpretations, Fourier transform infrared spectroscopy (IRTF) analyses were carried out on the composite and resin without fibres samples to ensure that the decrease in Tg during ageing is not also related to a chemical evolution of the resin.

Chemical evolutions of the resin with the ageing time

The infrared spectra of the resin without fibres obtained in attenuated total reflectance mode (ATR), before and after ageing, are presented in Figure 10. It appears that the peak present at 908 cm -1 decreases over the ageing cycles. This peak is attributed to the epoxy groups of the prepolymer [START_REF] Corsetti | Modeling and estimation of parameters for the curing of an epoxy/amine system[END_REF][START_REF] González | Applications of FTIR on Epoxy Resins -Identification, Monitoring the Curing Process, Phase Separation and Water Uptake[END_REF].

Its decrease, during ageing, indicates a better crosslinking of the network, which is in agreement with the decrease in enthalpy (Figure 3) and the increase in the degree of progress of the crosslinking reaction (Figure 4). In addition, by comparison of the IRTF spectrograms, no other evolution is observed whatever the ageing, up to 1 year of exposure. Thus, these ageing processes do not lead to significant surface chemical degradation of the resin.

Figure 10: Infrared Spectra of the resin: 1) unaged, 2) aged 4 weeks and 3) aged 26 weeks.

IRTF spectrometer measurements were also carried out on the composite samples (Figure 11). Firstly, it appears that the spectra obtained for the composite samples are very close to those of the resin without fibres (Figure 10).

This can be explained by the attenuated total reflectance mode (ATR) which enables to characterize only the surface of the samples. Since in the composite, the fibres are coated with matrix and since the characterized thickness is of the order of 10μm, it is therefore the resin which is analysed. It appears that no significant chemical degradation was observed on the surface of the samples. Thus, the presence of flax fibres does not affect the chemical evolution of the polymer at the surface. IRTF analyses tend to confirm the physical origin, i.e.

plasticization, of the decrease in Tg already demonstrated by mDSC. The physicochemical analyses highlighted the phenomena of physical plasticization and post-crosslinking of the resin during ageing. To determine the influence of these phenomena on the mechanical properties of the epoxy matrix, tensile tests were carried out. Figure 12 shows the evolution of the ultimate tensile strength of the resin without fibres as a function of the degree of progress of the crosslinking reaction.

According to the standard deviations (Figure 12), it appears that σmax is mainly governed by network postcrosslinking and is sparsely impacted by water intake. Thus, unlike the composite (Figure 2), the ultimate tensile strength measured on the epoxy resin without fibres samples does not drop during ageing. The phenomena of physical plasticization and post-crosslinking of the resin within the composite, highlighted by physicochemical analyses, do not therefore seem to be responsible of the drop in the composite ultimate tensile strength. In addition, the tensile tests carried out on flax fibre bundles (Figure 13) indicate that the mechanical properties of the uncoated fibres are not damaged before 9 weeks of ageing. Therefore, the fibres do not seem to be directly responsible for this change of the composite propriety. In view of the results of the physicochemical and mechanical tests, the drop in the ultimate tensile strength of the composite observed after the first week of ageing is therefore not induced by changes in the resin or the fibres. It therefore seems that this drop is related to the interfaces within the material. In order to confirm this assumption, observations with a scanning electron microscope (SEM) were carried out on transverse sections of the composite specimens.

Figure 14 presents the observations of composite cross sections (90°) made on the unaged material, after 1 week and 1 year of ageing. On the unaged material (Figure 14-a), an imperfect fibre/matrix cohesion was observed in some very localized areas that exhibited residues of the cortex of the flax stem. This phenomenon was also highlighted for the 0° test samples [START_REF] Cadu | Cyclic hygrothermal ageing of flax fibers' bundles and unidirectional flax/epoxy composite. Are bio-based reinforced composites so sensitive?[END_REF]. After 1 week of ageing (Figure 14-b), fibre/fibre and fibre /matrix debondings appear larger and more numerous than for the unaged material. In addition, cracks initiated at the lumen level appear in some of the fibres. This creation of additional flaws facilitates the initiation of cracks when the material is subjected to tensile forces. As the shear strengths of the interface between two elementary fibres and of the interface between epoxy resin and flax fibres are respectively about 2.9 MPa [START_REF] Beakou | Mechanical properties of interfaces within a flax bundle-Part II: Numerical analysis[END_REF] and 22.5 MPa (Antoine Le Duigou et al., 2014), these debondings may explain the drop in the ultimate tensile strength in the composite, observed after the first week of ageing thanks to the mechanical tests (Figure 2). Debonding can be due to the differential swelling between the fibres and the matrix during hygrothermal ageing cycles [START_REF] Cadu | Cyclic hygrothermal ageing of flax fibers' bundles and unidirectional flax/epoxy composite. Are bio-based reinforced composites so sensitive?[END_REF][START_REF] Li | Hydrothermal ageing mechanisms of unidirectional flax fabric reinforced epoxy composites[END_REF] and the degradation of the covalent bonds created between the epoxy and amine functions of the resin and the hydroxyl functions of the fibres (Antoine Le Duigou et al., 2014). The decrease in the ultimate tensile strength of the composite observed between the first and the ninth week indicates that the debonding phenomenon must be accentuated during these ageing cycles. Finally, after 52 weeks of exposure (Figure 14-c), the cracks initiated at the lumen level in some fibres have spread transversely to their surface.

Therefore, the combination of the physicochemical analyses on the composite and the resin without fibres, the mechanical tests on the constituents and the SEM observations, carried out on the composite sections, indicate that the drop in the ultimate tensile strength of the composite observed during the first ageing cycles (Figure 2) is mainly induced by morphological changes within the composite and in particular the degradation of the fibre/fibre and fibre/matrix interfaces.

Relation between modulus and physicochemical properties

In order to determine the origin of the evolution of the composite transverse modulus observed by the tensile tests (Figure 2) the transverse modulus as a function of the water mass content and the Tg of the composite is presented in figure 15. It appears that the evolution of the composite transverse modulus is proportional to the evolution of the glass transition temperature; it results in a linear relationship (Figure 15). Moreover, the evolution of the composite modulus as a function of the quantity of water is also linear, as shown in Figure 15. The transversal Young modulus of the composite is therefore mainly governed by the matrix and its evolution during hygrothermal ageing cycles is directly and linearly proportional to the Tg of the material. It therefore appears that the modulus reduction is related to the evolution of the physicochemical properties of the resin during these ageing cycles and more particularly to the physical plasticization of the epoxy network induced by the water molecules.

Furthermore, damages induced to the interfaces after the 1 st week (Figure 14-b) have an important effect on the tensile strength (Figure 2) but do not seem to amplify the physical plasticization of the matrix within the composite, even if the fibre/fibre and fibre/matrix debonding facilitates the diffusion of water in the material. This can be explained by the fact that the water diffusion is already faster in the fibres than in the matrix. Thus, from the start, the resin is in contact with more water molecules than it can absorb, and the increase in diffusivity in the composite does not therefore affect the water intake of the resin within the composite.

Figure 16 provides a scenario for the mechanisms involved in the 90° test samples of the unidirectional flax/epoxy composite during cyclic hygrothermal ageing, up to 1 year. The number of icons schematically represents the quantity of elements present in the material and its evolution is only provided as a trend to highlight the qualitative changes that take place in the composite during ageing.

Conclusion

In this study, the influence of a cyclic hygrothermal ageing on the transverse properties of a flax/epoxy composite has been studied. The tensile tests carried out on the unidirectional samples (90°) revealed a drop in the ultimate transverse strength, from the first week of ageing, and a smaller decrease until the ninth week of ageing. Then, between 9 and 52 weeks, the tensile strength seems to stabilize. As for the Young modulus, it decreases according to a hyperbolic profile during the cycles, for the durations of ageing test periods (up to 1 year).

Multiscale analyses performed on materials allowed to identify the mechanisms responsible of these changes in the mechanical properties. Thus, mass monitoring of the specimens showed a water uptake within the composite over the ageing cycles, that would mainly be stored in the matrix, as pointed out by the empirical relationship of Gordon Taylor. The decrease of the composite resin glass transition temperature during cyclic hygrothermal ageing would therefore be related to a physical plasticization phenomenon of the polymer network.

The tensile tests carried out on the epoxy resin without fibres have shown that the ultimate tensile strength of the matrix is mainly governed by the post-crosslinking and is not much affected by the physical plasticization related to the water absorption. In addition, the mechanical tests carried out on the fibre bundles did not explain the transverse ultimate tensile strength drop of the composite after the first week of ageing. This drop in tensile strength is therefore related to the creation of flaws in the material and more particularly to fibre/fibre and fibre/matrix debondings, as observed by Scanning Electron Microscope. These pictures also highlighted the creation and then the propagation of cracks initiated in the lumen of some fibres.

Finally, this study demonstrated that the evolution of the transverse Young modulus of the composite during hygrothermal ageing is mainly governed by the resin and would mainly depend on the physical plasticization state of the latter.

Figure 1 :

 1 Figure 1: Photo of a unidirectional composite specimen at 90 °

Figure 2 :

 2 Figure 2: Evolution of the transverse mechanical properties of the composite (fibres oriented at 90°) as a function of the ageing time (•) Ultimate tensile strength and (■) Young modulus. (Error bars indicate standard deviation).

Figure 3 :

 3 Figure 3: Evolution of the enthalpy measured on the non-reversible signal of the mDSC measurements: composite (•) and resin without fibres (○), depending on the ageing time (Error bars indicate standard deviation).

Figure 4 :

 4 Figure 4: Rate of crosslinking reaction (α) of the composite (•) and the epoxy resin without fibres (○), as a function of the ageing time.

Figure 5 :

 5 Figure 5: Evolution of the Tg measured by mDSC as a function of the ageing time for the composite (•) and the epoxy resin without fibres (○) (Error bars indicate standard deviation).

Figure 6 :

 6 Figure 6: Evolution of the composite Tg as a function of water intake.

Figure 8 :

 8 Figure 8: Evolution of the Tg composite and Gordon-Taylor relation as a function of the ageing time.

Figure 9 :

 9 Figure 9: Evolution of the Tg as a function of the ageing time before drying for composite (•) and resin without fibres (○) and after 2 months of drying for the composite (▲) and resin without fibres (Δ). (Error bars indicate standard deviation).

Figure 11 :

 11 Figure11: Infrared spectra of the composite: 1) unaged, 2) aged 4 weeks and 3) aged 52 weeks

Figure 12 :

 12 Figure 12: Evolution of the ultimate tensile strength of the epoxy resin without fibres as a function of crosslinking reaction rate (Error bars indicate standard deviation).

Figure 13 :

 13 Figure 13: Evolution of the ultimate tensile strength of fibres bundle as a function of the ageing time. (Error bars indicate standard deviation).

Figure 14 :

 14 Figure 14: SEM observations of 90° composite sections a) unaged, after b) 1 week and c) 52 weeks of ageing. The arrows indicate 1) fibre/fibre debonding inside the fibres bundles, 2) fibres/matrix debonding and 3) cracked fibres.

Figure 15 :

 15 Figure 15: Evolution of the Young modulus as a function of the Tg of the composite (•) and of its water content (Δ). (Error bars indicate standard deviation).

Figure 16 :

 16 Figure 16: Influence of cyclic hygrothermal ageing on the unidirectional flax/epoxy composite (90°).

Acknowledgement

This project is supported by the Bourgogne Franche-Comté region -FRANCE (2015-9201 AAO 04850 3040).

https://doi.org/10.1016/j.conbuildmat.2015.09.025


Gianguido Baldinozzi
email: gianguido.baldinozzi@centralesupelec.fr

Luis Casillas-Trujillo

Maulik K Patel

Kurt E Sickafus

Structural complexity of Y 6 BO 12 fluorite-related ternary oxides

Oxides with generic stoichiometry M7O12 occupy, in a generic phase diagram, an intermediate place between fluorite and bixbyite structure types. Their structure is derived from the ideal fluorite structure, and it is characterized by a more or less pronounced ordering of the O vacancies within the average fluorite sublattice. We believe that ternary oxides with this kind of formula provide interesting degrees of flexibility for understanding the structural characteristic of these structures in the context of fission product stabilization in nuclear fuels and in the field of actinide waste forms as well. We would like to discuss the structural characteristics of the chemical bonds in ternary systems consisting of trivalent and hexavalent cations. Eventually, in compounds with generic formula Y6B +6 O12, the B cation can be either a transition metal (W, Mo) or hexavalent uranium. We believe that studying the polyhedron of the sevenfold coordinated Y ion is particularly interesting to understand the flexibility of the chemical bonds: it is often described in the literature as a mono-capped trigonal prism, with bond lengths exhibiting an extremely large dispersion, ranging for instance from 2.19 to 2.70 Å in Y6WO12. We would discuss the implications of this large dispersion of distances on the chemical bond characteristics, compare DFT models with established experimental knowledge on pristine and irradiated specimens.

Introduction

Mixed oxides belonging to the RE2O3-BO2 systems (RE is a are earth element and B is a tetravalent metal element) have been extensively explored because they display a variety of interesting effects, ranging from order-disorder phase transitions [START_REF] Bevan | The role of the coordination defect (CD) in the structures of anion-deficient, fluorite-related compounds[END_REF][START_REF] Andrievskaya | Phase equilibria in the refractory oxide systems of zirconia, hafnia and yttria with rare-earth oxides[END_REF][START_REF] Isupova | A study of the Gd2O3-HfO2 system in the composition range enriched with hafnia[END_REF][START_REF] Subramanian | Oxide pyrochlores : a review[END_REF], to geometrically frustrated magnetism [START_REF] Gardner | Magnetic pyrochlore oxides[END_REF], and ionic conductivity [START_REF] Yamamura | Electrical conductivity anomaly around fluorite-pyrochlore phase boundary[END_REF]. They are encountered in a variety of technological applications, which include solid state electrolytes for fuel cells, thermal barrier coatings, neutron absorbing materials [START_REF] Risovany | Dysprosium hafnate as absorbing material for control rods[END_REF] and nuclear waste storage matrices [START_REF] Ewing | Nuclear waste disposal e pyrochlore (A2B2O7): nuclear waste form for the immobilization of plutonium and "minor" actinides[END_REF][START_REF] Sickafus | Radiation-induced amorphization resistance and radiation tolerance in structurally related oxides[END_REF]. The phase diagrams of these pseudo-binary systems often present a variety of phases related to the fluorite ideal arrangement, but with different structures [START_REF] Shamblin | Probing disorder in isometric pyrochlore and related complex oxides[END_REF][START_REF] O'quinn | Predicting short-range order and correlated phenomena in disordered crystalline materials[END_REF][START_REF] Blanchard | Does local disorder occur in the pyrochlore zirconates?[END_REF][START_REF] Cai | Complex ceramic structures. I. Weberites[END_REF][START_REF] Patel | Divergent short-and long-range behavior in ionirradiated δ-Sc4Hf3O12[END_REF][START_REF] Dl Drey | Disorder in Ho2Ti2-xZrxO7: pyrochlore to defect fluorite solid solution series[END_REF][START_REF] Blanchard | Investigating the local structure of lanthanoid hafnates Ln2Hf2O7 via diffraction and spectroscopy[END_REF][START_REF] Patel | Structural analysis of Gd2Ce2O7[END_REF][START_REF] Stanek | Predicted structure and stability of A4B3O12 d-phase compositions[END_REF] depending on the partial or complete ordering of O vacancies and the metal ions in their respective sublattices. At the extremes of the pseudo-binary diagram, the simple oxides crystallize in the fluorite (BO2) and the bixbyite structures (RE2O3). The fluorite phase is stoichiometric and displays a perfect face centered cubic arrangement of the atoms. The bixbyite phase comes with three flavors (A, B, and C) that have different symmetries: they roughly maintain the metal arrangement of the fluorite structure while the O vacancies order leads to the formation of a different polyhedral connectivity and two environments for the cations. Moving away from the bixbyite towards the middle of the phase diagram, weberite, pyrochlore, and O-rich bixbyite phases can be observed for the 1:1 ratio of the aliovalent cations. Often, the occurrence of a particular structure depends on the synthesis method, and not exclusively on the amounts of the specific initial oxides RE2O3 and BO2. In several cases, kinetic factors as the annealing dwell and the quenching conditions can promote the formation of a specific phase.

Moving beyond the 1:1 ratio, closer to the fluorite phase, oxides with generic stoichiometry M7O12 are often observed [START_REF] Bevan | Structural Principles for Anion-Deficient, Fluorite-Related Superstructures in the Zirconia-Scandia System[END_REF]. They possess a trigonal structure derived from the ideal fluorite structure, that displays a pronounced ordering of the O vacancies within the average fluorite sublattice. Depending on the respective charges of the two atoms, their generic formula can be RE4B +4 3O12 or RE6B +6 O12. While both systems display highly ordered vacancies, the first system does not display significant cation ordering or site selectivity, while the second systems are perfectly ordered. The ordered compounds undergoing ion irradiation see their structure transforming from ordered rhombohedral to amorphous. In the ordered compounds (Y6MoO12, Y6WO12, …) a competitive oxygen deficient cubic fluorite phase can be observed at high temperature. This observation suggests the irradiation behavior (amorphization) is not following the path of the thermally driven polymorphism. The disordered compounds (as for instance Sc4Hf3O12) do not become amorphous but they transform into an oxygen deficient long-range fluorite structure. Recently [START_REF] Patel | Divergent short-and long-range behavior in ionirradiated δ-Sc4Hf3O12[END_REF], we discovered the local structure rearranges according to an O excess bixbyite structure, suggesting a not random configuration of the O vacancies. In both systems, the change of crystal symmetry between the ordered rhombohedral and the irradiated phase is expected to involve a drastic change of the connectivity and coordination of the atom polyhedra, involving a possible semi-reconstructive character. It is therefore interesting to analyse the strength and the characteristics of the chemical bonds occurring in these polyhedra. We believe that ternary oxides with this generic formula (RE1-xBx)7O12 can display an excellent structural flexibility to incorporate fission products and minor actinides, and eventually be interesting for the design of advanced nuclear fuels. This paper addresses the specificity of the chemical bonds of a particular subset of fully ordered compounds of chemical composition Y6B +6 O12 that can explain the reasons of the chemical and structural flexibility of these ordered and disorder members.

Materials and Methods

To examine the characteristics of the chemical bonds in a quantitative way, atoms-in-molecule (AIM) Bader's analysis method was used to model the electron density. The AIM-Bader analyses using AIM-UC software [START_REF] Vega | AIM-UC: an application for QTAIM analysis[END_REF] provided estimates for the Bader charges of the individual atoms, as well as the locations of the bond critical points (BCPs) between bonding atoms, the charge densities at these BCPs, and the local curvature of the charge density. The analysis for each compound was performed according to the procedures described in [START_REF] Casillas-Trujillo | Comparison of bonding and charge density in δ-UO3 , γ-UO3, and La6UO12[END_REF]. DFT calculations were performed to obtain the electron charge densities for three compounds of interest in this paper: Y6MoO12, Y6WO12, and Y6UO12. For these calculations, we used the generalized gradient approximation Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation[END_REF] exchange-correlation functional. The yttrium 4s4p5s4d, molybdenum 4p5s4d, tungsten 5p6s5d, uranium 6s6p5f6d7s, and oxygen 2s2p electrons were treated as valence electrons. The electron-ion interaction was described by the projector augmented wave method, and the plane-wave basis energy cutoff was set to 520 eV. The Vienna ab initio package VASP [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF] was employed to perform the GGA calculations. GGA+U functionals within the simplified rotationally invariant approach introduced by Dudarev [START_REF] Dudarev | Electron-energyloss spectra and the structural stability of nickel oxide: An LSDA+U study[END_REF] were required to take into account the strongly correlated nature of the f states of uranium. An effective Hubbard parameter equal to 4eV was employed. A uniform 4x4x4 k-point mesh for the Brillouin zone sampling of the primitive trigonal rhombohedral cell was adopted based on the Monkhorst-Pack scheme. That choice was found to be sufficient to achieve well converged energies. Electronic self-consistency was considered achieved when the total energy change between electronic steps was less than ≤ 10μeV. The lattice metric was relaxed for all crystal symmetries and the internal structural parameters were relaxed until all Hellmann-Feynman forces on each ion were ≤ 3 meV/Å. Real space sampling of the charge density was performed on a regular 635x635x635 grid. The different characteristic of the charge density distribution for the two polyhedral can be displayed drawing same value isosurfaces of the charge density. The amount of charge density along the bonds of the BO6 octahedron (for the three compounds) is much larger than the one observed in the YO7 polyhedron (Fig. 2).

Results

BO6 (Mo, W, U) YO7

Fig. 2 Contour maps showing the charge density distributions for the two polyhedra in the ordered d-phase structures of Y6MoO12, Y6WO12, and Y6UO12.

The results of the Bader analysis of the charge density are reported in Table 1. The 6 identical bonds of the MO6 octahedra are the shortest and the strongest in the three compounds. The 7 bonds of the yttrium environment are arranged according to their decreasing bond length and increasing strength. The 6 shorter bonds are medium to strong, but the extreme weakness of the longest bond is remarkable. This confers a quite interesting picture of a YO7 polyhedron where one of the bonds with the atoms O atoms can be easily modified. This bond is increasingly weaker going from the Mo to the W, and finally to the U compound. The experimental Y-O distances in these three compounds display an excellent agreement with our DFT results. The Y-O bond lengths range from 2.19(1) to 2.70(1) Å for Y6WO12 [START_REF] Diot | X-ray powder diffraction data and Rietveld refinement for Ln6WO12 (Ln=Y, Ho)[END_REF]. In Y6UO12, Y-O bond lengths range from 2.17(4) to 2.78(3) Å [START_REF] Bartram | Crystal Structure of the Rhombohedral MO3:3R2O3 Compounds (M = U, W, or Mo) and Their Relation to Ordered R7O12 Phases[END_REF]. The delta phase polymorph of Y6MoO12 [START_REF] Schildhammer | Cubic Bixbyite-Structured Phases of Yb6MoO12 and Y6MoO12 Prepared by the Solution Combustion Method at Low Temperatures[END_REF] only occurs above 1670K, therefore a direct comparison with the experimental bond lengths of this phase is not straightforward because of the significant thermal expansion, but the compound retains the same structural features of the prototype Y6WO12 compound. 1. Bader analysis of the charge density at the bond critical points for the three compounds.

Y6MoO12 bcp density curvature laplacian dist

The charge density of the seven Y-O bonds in the three compounds behaves according to a same master exponential curve (fig. 3), providing a direct correlation between bond strength (charge at the bcp) and bond length for this polyhedron. The analysis of the curvature (and the Laplacian) of the charge density along the bond direction confirms this conclusion.

Figure 1 Fig. 1

 11 Figure 1 reports the relaxed structural parameters of Y6WO12 in the trigonal rhombohedral primitive lattice. A schematic representation of the structure is provided in the same figure, showing the particular connectivity of the 7-fold coordinated Y atoms.

Fig. 3

 3 Fig. 3 Green squares represent the charge at the bcp of a given bond formed by Y atoms and oxygen in Y6UO12. Red dots are for Y6MoO12. Blue diamonds for Y6WO12. The dotted line is the simple exponential fit of the three sets of data.

Discussion

Bader analysis of the charge density of three ordered d-phases allows to single out the particular weakness of one of the bonds formed by Y and O. This weak bond systematically concerns one of the O atoms that is also simultaneously bonded to the hexavalent metal. The effect is stronger (i.e. the bond is the weakest) in the uranium compound. We believe that the polymorphism observed at high temperature can be related of a polyhedron reshaping that is favored by this anisotropic characteristic of the bonds. This polyhedron reshaping is related to the modification of the ordered distribution of O vacancies on the anionic sub-network. Indeed, the perfect oxygen/vacancies ordering characteristic of the delta phase no longer occurs when the delta-phase structure is perturbed. This effect seems also likely to be transferable to the problem of the changes observed under irradiation in Sc4Hf3O12 [START_REF] Patel | Divergent short-and long-range behavior in ionirradiated δ-Sc4Hf3O12[END_REF], where a large bond spread exists in the pristine samples and a drastic change of these bond lengths is observed after irradiation leading to a O vacancy arrangement similar to the one observed in bixbyite compounds. In the Y6MoO12 compound, a competition between bixbyite and delta phase structures as a function of T, aliovalent doping, and sintering conditions is also observed [START_REF] Sobota | Fabrication of Y6MoO12 molybdate ceramics: from synthesis of cubic nano-powder to sintering[END_REF], leading to a similar modification of the O vacancy distributions, involving the modification of the longer Y-O bond of the YO7 polyhedron. This weakness of the sevenfold coordinated polyhedra can be an interesting parameter for designing materials that must withstand intense irradiation, where the flexible environment can reconstruct, can help healing the radiation damage, and thus increase the radiation tolerance of these system.

The authors declare no competing interests. The datasets generated during and analysed during the current study are available from the corresponding author on reasonable request.