Virginie Mathivet

Jenny Jouin

Michel Parlier

S Rossignol
email: sylvie.rossignol@unilim.fr

CONTROL OF THE ALUMINO-SILICO-PHOSPHATE GEOPOLYMERS PROPERTIES AND STRUCTURES BY THE PHOSPHORUS CONCENTRATION

Control of the alumino-silico-phosphate geopolymers

properties and structures by the phosphorus concentration

I. Introduction

Over the past decades, numerous researches have been conducted on geopolymer materials. These materials indeed combine interesting mechanical properties, reduced CO2 footprint and high chemical resistance compared to Portland cements, paving the way to new applications ranging from environmentally friendly construction to the encapsulation of toxic waste [1,[START_REF] Irfan Khan | World Sustainability Forum[END_REF]. These materials are synthesized from the dissolution of an aluminosilicate source into an alkaline solution. The resulting oligomers Si(OH)4 and Al(OH)4 -then polycondensate to form amorphous three-dimensional networks. Their working properties have been widely studied, showing that they can be adjusted by the reactivity of the aluminosilicate sources towards alkali activators through their reaction mechanisms [START_REF] Gharzouni | Effect of the reactivity of alkaline solution and metakaolin on geopolymer formation[END_REF]. More recently, a new synthesis process, using an acidic activation solution, has been explored. This path seems promising as the resulting materials present improved mechanical properties [START_REF] Perera | Relative strengths oh phosphoric acid-reacted and alkali-reacted metakaolin materials[END_REF][START_REF] Tchakouté | Mechanical and microstructural properties of metkaolinbased geopolymer cements from sodium waterglass and phosphoric acid solution as hardeners: a comparative study[END_REF]. An acid-based geopolymer formation starts with the dissolution of an aluminosilicate source into an acid (usually orthophosphoric acid) leading to the release of Al 3+ ions, which then polycondense with the phosphorous entities to form three-dimensional hydrated aluminophosphate networks [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF]. The hydrated silica still remaining after the release of those Al 3+ ions can then form some additional silicate networks, that may react with some of the remaining phosphorous entities, thus forming Si-O-P bonds [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF][START_REF] Celerier | Relation between working properties and structural properties from 27 Al, 29 Si and 31 P NMR and XRD of acid-based geopolymers from 25 to 1000°C[END_REF]. As for geopolymers in alkali medium, previous studies were carried out to understand the influence of the aluminosilicate sources, the activation solution and the consolidation temperature on the structure and working properties of acid-based geopolymers [START_REF] Louati | Acid based geopolymerization kinetics: effect of clay particle size[END_REF][START_REF] Celerier | Composition and properties of phosphoric acid-based geopolymers[END_REF]. For example, Thakouté et al. have shown that the addition of gibbsite in a geopolymer negatively affects its properties [START_REF] Tchakouté | The influence of gibbsite in kaolin and the formation of berlinite on the properties of metakaolin-phosphate -based geopolymer cements[END_REF]. The dilution of the concentrated phosphoric acid leads to an improvement of the mechanical properties up to a concentration of 10 M then a decrease was observed simultaneously with the existence of several networks in acid geopolymer [START_REF] Tchakouté | Influence of the molar concentration of phosphoric acid solution on the properties of metakaolin phosphate based geopolymer cements[END_REF] In this study the porosity values did not change with the concentration of hardeners. Another publication has stated that the best mechanical properties, associated with a low porosity of 8 %, are also achieved for [P] equal to 10 M. [START_REF] Dong | Workability and mechanical property of metakaolin phosphate aced bases geopolymer[END_REF] Another work on the effect of the P/Al ratio demonstrated a maximum mechanical resistance for P/Al = 1 [START_REF] Zibri | Mechanical, microstructural and structural investigation of phosphate based geopolymers with respect to P/Al molar ratio[END_REF]. In addition, different phosphorus concentrations have been studied to control the viscosity as well as the setting time. Thus, Dong et al. have demonstrated that the viscosity vary from 3 to 7 MPa.s. [START_REF] Dong | Workability and mechanical property of metakaolin phosphate aced bases geopolymer[END_REF] The viscosity of the acid-based geopolymers' reactive mixture still tends to be high, which is detrimental for industrial applications, such as the production of geopolymer-based composites. Thus, the addition of water in the original reactive mixture can be necessary to improve the rheological properties of the mixture (various Al/P).

The dissolution of the metakaolin in an acidic medium contributes to the overall kinetic control of the geopolymerization reaction [START_REF] Saleh | Dissolution of aluminium from metakaolin with oxalic, citric and lactic acids[END_REF], being dependent on the activation energy, the temperature and the diffusion mechanisms. The difficulty to fully dissolve the metakaolin in the acid may then lead to the leaching of most of the octahedral Al 3+ cations and to the formation of amorphous and highly porous silica-based solids [START_REF] Belver | Porous silica by acid leaching of metakaolin[END_REF], resulting in a high level of inhomogeneity's in the final product. It is thus fundamentally valuable for the production of new materials, that the equilibrium of the system is understood and established in order to control the dissolution of species. Moreover, in order to control the dissolution of metakaolin, it is essential to control both the degree of polymerization of phosphoric acid as well as the chemical mechanism of polycondensation reaction [START_REF] Tchakouté | The influence of gibbsite in kaolin and the formation of berlinite on the properties of metakaolin-phosphate -based geopolymer cements[END_REF][START_REF] Davidovits | Geopolymer chemistry and applications[END_REF]. An example of application for these diluted geopolymers is the production of textile reinforced by phosphate binders, where an investigation is necessary, in particular to understand the water related phases of the process, as it can be absorbed during the various reaction [START_REF] Karsiki | Aluminosilicate phosphate cements a critical review, Advances in applied ceramics[END_REF] This concerns in particular the amount of water involved in the formation mechanisms of geopolymeric materials, including the effect of water addition on the structure and mechanical properties of acid-based geopolymers.

Our study thus addressed the influence of P concentration through water addition on the reactive mixture, the structure and working properties of acid-based geopolymers. First, the effect of the formulation of the reactive mixtures on the working properties (viscosity, consolidation time), and the mechanical properties of the consolidated materials, were characterized in order to be able to adjust the water content to the selected manufacturing process and compared to existing data. The bonding-type of water and its location in the material were then identified by structural analyses. Finally, the evolution of the networks in the material was monitored as a function of the water addition.

II. Experimental part 1. Raw materials and sample preparation

The synthesis of the reference geopolymer was described in a previous study [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF], using a metakaolin produced by Imerys with a Si/Al ratio equal to 1 as the aluminosilicate source, whose characteristics and reactivity have been studied by Gharzouni et al. [START_REF] Gharzouni | Control of polycondensation reaction generated from different metakaolins and alkaline solutions[END_REF], and a 85 wt% pure phosphoric acid produced by VWR. During the synthesis, the phosphoric acid has been first diluted in distilled water to reach the selected water content and mixed with the metakaolin until reaching an Al/P ratio equal to 1, this reactive mixture being then poured in a sealed container and cured at 70°C for 72 h.

In this study, the influence of the water content on the reactive mixture has been studied by synthetizing two series of samples. The first one has been obtained by adding water to the reference composition, originally containing 0.45 mol % of water, and called R [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF], up to a maximum of 0.68 mol %. The notation of those samples has been defined as R-x, x being the ratio of the molar percentage of added water over the reference one. The second series has been synthesized by modifying the Al/P composition of the samples and adjusting the quantity of added water to the metakaolin water demand. Figure 1 shows the ternary diagram regrouping all those compositions. As it can be seen, the compositions of the samples belong to a small range of the diagram, which induce a phosphorus concentration in the range 3.5 -7.23 M.

Characterization techniques

The viscosity of the reactive mixture was characterized with a BROOKFIELD DV2T apparatus and measured up to 2000 Pa.s using a LV-04 mobile. The speed of the spindle was in the range of 10 to 100 rpm, depending on the viscosity of the mixture, which density was determined based on the measurement of the mass of a cubic centimeter.

The Fourier Transform Infrared (FTIR) spectra were recorded and analyzed on a PERKIN-ELMER Frontier apparatus and its software, in transmission mode between 400 and 4000 cm -1 with 4 scans and a 4 cm -1 resolution. Moreover, KBr pellets were elaborated for all the samples. The X-ray diffraction (XRD) patterns have been recorded with a Bruker D8 Advance diffractometer using a CuKα radiation. The acquisitions have been carried out with a 2θ-angle in the range of 5 to 60° with a 0.02° step size and a 50 s equivalent time per step. The decomposition of the contributions from the different amorphous networks has been conducted using the Peakoc software [START_REF] Masson | PEAKOC profile fitting software v1.0[END_REF], and the refinement between 5 and 60° using Voigt functions taking into account the CuKα1 and CuKα2 wavelengths.

The thermal analyses have been realized on an SDT Q600 apparatus from TA Instrument. The measurements have been performed in platinum crucibles under a flow of dry air (100 mL.min -1 ) with a 5°C.min -1 slope up to 1000 °C.

The measurements of compressive strength have been carried out on a Lloyd EZ20 universal testing machine with a 0.5 mm.min -1 crosshead speed. Seven days after consolidation, five geopolymers with a 15 mm diameter and a 30 mm height have been selected for each composition, ground to obtain plane and parallel surfaces and analyzed. The specific mass has been determined prior to the measurement on the ground samples (/H = 0.5).

Measurements of the volume fraction of porosity have been realized using Archimedes' method [START_REF] Januari | The relationship between Vickers microhardness and compressive strength of functional surface geopolymers[END_REF], thus giving access to the open porosity. The samples have been preliminary vacuum packaged, and then progressively covered with water while kept under vacuum. Weight measurements at dry (mdry), immersed in water (mimm) and saturated of water (msat) stages have been used to determine the porosity, following the equation:

𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦 (%) = 𝑚 𝑠𝑎𝑡 -𝑚 𝑑𝑟𝑦 𝑚 𝑠𝑎𝑡 -𝑚 𝑖𝑚𝑚 . III. Results

Influence of the water addition for Al/P = 1

Reactive mixtures

In order to study the influence of the water addition on the process parameters, the viscosity and setting time of the various compositions R-x have been plotted as a function of the water content in figure 2. The reference sample displays an initial viscosity of 30 Pa.s and needs 46 h to consolidate. The viscosity of the reactive mixtures then decreases with the addition of water, whereas the setting time increases. More precisely, the viscosity drops sharply from 30 to 2 Pa.s between 0.45 and 0.60 mol % of water. At higher water contents, the viscosity decreases slowly down to 0.6 Pa.s at 0.68 mol % of water. This general trend is due to the reduction of the solid/liquid volume fraction of the reactive mixture, diminishing the friction between the particles. The setting time remains constant at around 46 h between 0.45 and 0.55 mol %; however from 0.60 mol % on, a steep increase occurs, leading to a maximum setting time of 69 h for 0.68 mol % of water. This evolution can be explained by the dilution of the reactive species forming for a great part the geopolymer network [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF][START_REF] Dong | Workability and mechanical property of metakaolin phosphate aced bases geopolymer[END_REF], as low phosphorus and aluminum concentrations reduce the encounter probability of those species.

All these data underline that processing and manufacturing parameters, such as the viscosity of the reactive mixture and its setting time, may be adjusted by modifying the water content of the formulations with Al/P =1. However, the influence of the water content on the geopolymer structure has yet to be investigated.

Consolidated materials

In order to evaluate the amount and type of water issued from the polycondensation reaction, thermal analyses of the samples were conducted; as an illustration, figure 3Aa presents the thermogram (20-240 °C) of the sample R-1.2, which is representative of the measurements carried out on similar materials [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF]. Three endothermic phenomena, corresponding to the temperatures ranges T < 110°C, 110 < T < 220°C and T > 220°C and related to weight losses, are identified and labeled I, II and III, respectively. The first weight loss (I) is attributed to the evaporation of physisorbed water. Then, two smaller weight losses (IIa and IIb) are observed between 110 and 240°C, and are associated with the dehydration of hydrated phases [START_REF] Celerier | Composition and properties of phosphoric acid-based geopolymers[END_REF][START_REF] Bwa | Water resistance and thermal behavior of metakaolin based geopolymer cements[END_REF]. Figure 3Ab compares the behavior of three of the samples (R, R-1.2 and R-1.5). As it can be observed, the thermograms present the same general evolution, save for the weight loss during step I, where the physisorbed water evaporates before 100°C. In order to investigate the distribution of physisorbed and chemisorbed water inside the samples, figure 3B displays the weight loss from steps I and II, as well as the total weight loss in the temperature range 25 to 1000°C. This shows that the evolution of the total weight loss occurring after the addition of water is mainly due to the increase of the weight loss from step I. It appears that the excess of water introduced does not participate much to the polycondensation reactions. Thus, the amount of water used for the geopolymer formation (step II) is rather stable and the rest remains as physisorbed water.

Moreover, in order to determine the influence of water on the inner structure of the consolidated geopolymer, FTIR spectroscopy measurements have been carried out and are presented in figure 4A (OH entities) and figure 4B (silicon and aluminophosphate species) for samples R, R-1.2 and R-1.5. The same bands are identified on all the samples, though differing in intensity. More specifically, the bands located at 3680, 3570, 3440, 3350 and 3240 cm -1 are respectively attributed to the following bonds: P-OH, SiOH (asym and sym), OH -AlPO4 and bonded H2O [START_REF] Tchakouté | Influence of the molar concentration of phosphoric acid solution on the properties of metakaolin phosphate based geopolymer cements[END_REF][START_REF] Spspielbauer | [END_REF][START_REF] Hadjiivanov | Chapter Two: Identification and characterization of surface hydroxyl groups by infrared spectroscopy[END_REF]. The contributions around 1640 cm -1 are assigned to the bending of P-OH and water molecules, those at 1220 (w), 1155 (w), 1095 and 920 cm -1 to the stretching of P-O from hydrated aluminophosphates [START_REF] Frost | A vibrational spectroscopic study of the phosphate mineral vantasselite Al4(PO4)3(OH)3; 9 H2O, Spectrochimi[END_REF][START_REF] Boonchom | Study of kinetics and thermodynamics of the dehydration reaction of AlPO4, H2O[END_REF], and the one at 800 cm -1 is related to the bending of Si-O-Si bonds. The bands in the range 1300-500 cm -1 do not evolve significantly with the addition of water and their identification remains complex due to the presence of silicate species in the same region. As it has been outlined by Mathivet et al. [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF], aluminophosphate and Si-OH networks mainly form the geopolymer, which is confirmed here. Their formation takes place regardless of the water content, and in each case consumes the same amount of water. Then, the water in excess, which is not consumed during the geopolymer formation, leads to the presence of hydrated phases or physorbed phases. This last point is in agreement with the increasing amount of physisorbed water observed during the thermal analyses and reported in other works [START_REF] Tchakouté | Mechanical and microstructural properties of metkaolinbased geopolymer cements from sodium waterglass and phosphoric acid solution as hardeners: a comparative study[END_REF][START_REF] Tchakouté | The influence of gibbsite in kaolin and the formation of berlinite on the properties of metakaolin-phosphate -based geopolymer cements[END_REF][START_REF] Dong | Workability and mechanical property of metakaolin phosphate aced bases geopolymer[END_REF][START_REF] Zibri | Mechanical, microstructural and structural investigation of phosphate based geopolymers with respect to P/Al molar ratio[END_REF]. These results outline that an increase in the water content results in the formation of several hydrated compounds or physisorbed water.

The compressive strength and porosity of the consolidated geopolymers are also sensitive to the water content, as shown in figure 5. As a matter of fact, with the addition of water in the reactive mixture, the compressive strength decreases as the porosity increases. The compressive strength values indeed drop from 80 to 11 MPa for a phosphorus concentration of 6.5 to 4.5 M, these values being agreement with the literature [START_REF] Tchakouté | Influence of the molar concentration of phosphoric acid solution on the properties of metakaolin phosphate based geopolymer cements[END_REF]. The decrease of the mechanical properties with water or with the decrease of the phosphorus concentration is associated with the formation of pores in the microstructure as it can observed in figure 5, and in accordance with literature data [START_REF] Tchakouté | Influence of the molar concentration of phosphoric acid solution on the properties of metakaolin phosphate based geopolymer cements[END_REF][START_REF] Saleh | Dissolution of aluminium from metakaolin with oxalic, citric and lactic acids[END_REF]. The addition of water indeed leads to a disordered microstructure and the presence of hydrated networks, weakening the mechanical properties.

Influence of the composition: Al/P ratio

As stated previously, another way to reduce the viscosity of the reactive mixtures lies in a slight modification of their composition. To emphasize this point, several formulations with Al/P ratios ranging from 0.9 to 1.8 have been synthetized at a constant solid to liquid ratio, and compared to the previous samples, belonging to the same range of [P] concentration, the shaping of the samples being highly dependent on the properties of the reactive mixture. After the characterization of their properties, the study focused on the local networks forming the samples.

The viscosity recorded in table 1 decreases with the addition of water for Al/P = 1, as already seen, and follows the same trend when Al/P increases. This evolution is strongly linked to the amount of water present in the reactive mixture in both cases, as an increase in Al/P is accompanied by an increase in the molar ratio of water. On the other hand, the setting time does not follow the same evolution. It slowly increases with the addition of water for Al/P = 1, and the evolution is inversely proportional to the water content of the reactive mixture, which may be explained by the evolution of the species concentration in the reactive mixture [START_REF] Agassant | Mise en forme des polymères : approche thermomécanique de la plasturgie[END_REF]. For both systems, the viscosity drops due to the electrostatic repulsion [START_REF] Wurger | Thermal non-equilibrium transport in colloids[END_REF] reducing the species' mobility originating from the addition of water and the change of the PO4 entities [START_REF] Davidovits | Geopolymer chemistry and applications[END_REF].

Concerning the consolidation of the samples, for Al/P = 1, the dilution directly limits the polycondensation reactions, which may be the cause of the increased setting time. In the case of a variable Al/P, the growing presence of free reagents in the mixture (especially aluminum) compensates the dilution effect induced by the water, thus leading to a shorter setting time.

Figure 6 shows the mechanical strength as well as some porosity for the different samples.

Whatever the series of samples considered, an increase of the molar number of water introduced leads to a decrease in the compressive strength as shown in figure 6A, linked to the raise of the porosity observed (figure 6B). However, another factor may also influence this degradation, as the reactive species tend to be more diluted with the addition of water, thus reducing the chemical potential. In addition, the reactivity of aluminate species is dependent on their charge and size [START_REF] Weng | Dissolution processes, hydrolysis and condensation reactions during geopolymer synthesis: Part I-Low Si/Al ratio systems[END_REF]. The mechanism of formation of oligomers can thus be modified, giving birth to different local networks based on aluminum phosphate, hydrated silica or other hydrated phases, as it was observed in alkaline medium [29, 30. 31]. These networks can display different values of specific mechanical resistance, leading to a variation of the compressive resistance of the samples depending on their distribution. Finally, some samples were heated at 250°C for 2 hours, heating during which the amount of water lost was measured in order to evaluate its location in the samples (figure 6C). The evolution of the weight loss reveals the existence of poral water and of some chemisorbed water due to hydrated phases [START_REF] Rohee | Composition and properties of phosphoric acid-based geopolymers[END_REF], suggesting that its excess remains physisorbed, which generates a higher porosity. After the thermal treatment (Figure 6D), the porosity still increases with the amount of water introduced, but it is significantly higher than its value before drying the sample. This confirms the presence of water in both open and closed porosity, which fractures the sample during heating, leaving access to a higher fraction of open pores after treatment. Similar results have been established, showing that the phosphorus concentration, water amount and Al/P control the properties of the geopolymers. However, it is also necessary to understand the influence of the availability of reactive aluminous or phosphate species on these materials.

IV. Discussion: modification of the networks

It has been shown that a variable water content introduced into the reactive mixtures modifies the properties of materials, and leads to structural modifications at the local network level as well, including the types of bonds and their distribution. Moreover, many hydrated phases can coexist in this type of material in the temperature range 25-250°C [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF]. To corroborate these hypotheses, the presence of amorphous networks in the geopolymers was studied by XRD; the diagrams measured for various Al/P and Al/P = 1 with different amounts of water are presented in figures 7A and B, respectively. As previously observed [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF], they all display a broad contribution centered at 27°, as well as some peaks attributed to crystalline anatase (JCPDS: 01-071-1166) and quartz (JCPDS: 00-046-1045). These crystalline phases were identified in the metakaolin and are not modified by the geopolymerization process [START_REF] Gharzouni | Recycling of geopolymer waste: influence on geopolymer formation and mechanical properties[END_REF]. Although the main contribution is observed in all the samples, it shows some minor differences in its shape from one sample to another, suggesting the presence of several amorphous networks. They were identified in our previous study [START_REF] Celerier | Relation between working properties and structural properties from 27 Al, 29 Si and 31 P NMR and XRD of acid-based geopolymers from 25 to 1000°C[END_REF] and can be described as follows. The first contribution, thereafter called S, is located at the fixed position of 21.9° and assigned to an amorphous silica network [START_REF] Deshmuk | Determination of silica activity index and XRD, SEM and EDS studies of amorphous SiO2 extracted from rice husk ash[END_REF]. The second one, thereafter called G, is located at an average position of 27.9° and is attributed to the formation of the amorphous geopolymer network, mainly constituted of hydrated aluminophosphates [START_REF] Boonchom | Study of kinetics and thermodynamics of the dehydration reaction of AlPO4, H2O[END_REF]. Furthermore, some diagrams in figures 7A and B show a low intensity dome at low diffraction angles (peak 1), which is assigned to an hydrated silica network [START_REF] Shannon | Structure of the two-dimensional medium-pore high-silica zeolite NU-87[END_REF][START_REF] Guth | Un nouveau type de silice hydratée crystallisée, de formule H2Si3O7[END_REF]. It is then interesting to note that for the samples containing the most water, i.e. R-1.4 and R-1.5 (figure 7B), additional contributions appear at higher angles (peaks 2 and 3). The same phenomenon occurs for variable Al/P samples, but in this case the sole peak 3 was identified. Those two contributions have yet to correlate with a type of amorphous network, as XRD does not give sufficient data for this, but they nonetheless confirm the participation of new amorphous networks in the samples with the highest content of water.

The positions, intensities and broadening of the amorphous contributions identified in the XRD diagrams were thus refined, and the details of those analyses are gathered in the supplementary material. The evolution of the relative intensities IG/IS gives an accurate indication about the level of geopolymerization in the sample, as stated in a previous work [START_REF] Mathivet | Acidbased geoolymers: understanding of the structural evolutions during consolidation and after thermal treatments[END_REF].

In the present work, IG/IS is also clearly related to the water content of the reactive mixture, as presented in figure 8. The samples with a variable Al/P present a two-step evolution. First, for Al/P in the range of 0.9 to 1.1, the diagram shows a relatively small variation, which implies that the geopolymer network is not significantly modified for these compositions. However, with an increasing Al/P ratio, and subsequently an increasing amount of water, IG/IS decreases sharply, indicating that the original geopolymer network is less present in these samples. This occurs in conjunction with the appearance of the signature from a new network (peak 3) and the loss of peak 1, related to hydrated silica. Thus, this new undefined network seems to replace at least partially the original geopolymer's one. When raising the water amount in the sample while keeping Al/P constant, IG/IS decreases more regularly for the R -R-1.3 compositions. This indicates that the geopolymer network prevails less and less, although its intensity is still high. For the highest content of water, i.e. R-1.4 and R-1.5, the signatures of new networks (peaks 2 and 3) appear, and the intensity of G decreases simultaneously, reaching its lowest value. The relative intensity of the geopolymer network is similar for variable Al/P and variable water amount, though modifying the water addition in a sample with Al/P = 1 gives a better control on the intensity of the contribution assigned to the geopolymer network, as there is no threshold effect in this case.

Finally, in order to identify the networks that appear to replace the original Al-O-P-based one, an FTIR study has been carried out to investigate the type of entities present in each formulation. Thus, the evolution of the intensities of some characteristic bands from phosphates, silicate and aluminate networks have been studied, and the full spectra are given in supplementary material. These networks are dependent on the composition of the reactive mixture, which is a combination of the molar P/Al ratio and the amount of available water, which double influence has been expressed in the parameter (nP/nAl) + nH2O. To justify the use of this new parameter, the water content determined by thermal analysis (data are provided in supplementary files) has been plotted as a function of the expression (nP/nAl) + nH2O and is displayed in figure 9. The linear variation observed suggests a strong correlation that outlines the ability of the samples to trap water.

Figure 10 shows the evolution of the different bands' intensity as a function of the parameter (nP/nAl) + nH2O. As stated previously, at least three types of networks (aluminophosphate, silicophosphate and undissolved silica hydrates) may follow the reaction between the metakaolin and the phosphoric acid. The contributions attributed to the silicates (SiO-H asym and sym) at 3530 -3440 cm -1 and to the bound water at 3240 cm -1 are reported in figure 10A. It reveals that the contribution of silanols increases with a high amount of water. This is related to the availability of water in the reactive mixture, which can react with the metakaolin. Furthermore, for low values of (nP/nAl) + nH2O (corresponding to high Al/P), a higher amount of undissolved metakaolin in the system is associated with its lower hydration and therefore the decrease of the contribution from silanols [START_REF] Gevaudan | PVA an PEG assisted sol-gel synthesis of aluminosilicate precursors for N-A-S-H geopolymer cements[END_REF]. However, the evolution related to the bound water does not follow the exact same trend, as its intensity ratio reaches its highest value for the reference composition. It suggests that increasing the amount of water in the reactive mixture leads to the presence of more physisorbed water, however it does not seem to affect the chemisorbed one. This may be related to the formation of hydrated phases of probably different chemical composition, as suggested from XRD in figure 8, and to the loss of the hydrated silica contribution. Similarly, figure 10B gathers the contributions of the phosphatebased networks at 1220 cm -1 ( Al-O-P), 1095 and 1155 cm -1 (asym and sym  P-O) as a function of (nP/nAl) + nH2O. The intensity of the band at 1220 cm-1 , corresponding to Al-O-P bonds, tends to decrease, especially for the highest amounts of water. This can be explained by a dilution effect that disadvantages the reaction between aluminum and phosphorus species. This was also observed previously by XRD, as the relative intensity of the IG contribution is mostly connected to the presence of Al-O-P networks. Moreover, this dilution effect seems to be expanded to the signature of the P-O bonds. Finally, the evolution of the contributions mainly related to the phosphate lattice, such as hydrated Al-O-P at 3350 cm -1 ,  PO-H at 1640 cm -1 , and  Si-O-P at 1206 cm -1 , are displayed in figure 10C. The bands for hydrated aluminum phosphates and PO-H are almost constant, indicating that these networks are formed regardless of the formulation of the reactive mixture. Concerning the band allocated to the Si-O-P network (1206 cm -1 ), its relative intensity diminishes when (nP/nAl) + nH2O increases. This can be explained by the preferential formation of aluminophosphate entities [START_REF] Derouane | Quantum mechanical calculations on molecular sieves. 2. Model cluster investigation of silicoaluminophosphate[END_REF], when the species are available. Besides, for higher Al/P ratios, the presence of large amounts of unreacted metakaolin and undissolved silica is higher, and the molecular interactions will thus favor the formation of Si-O-P and Si-O-Al bonds [START_REF] Hanada | Properties and network constitution of rfsputtered amorphous films in the system silicon dioxide-aluminum orthophosphate[END_REF].

V. Conclusion

This study focused on the influence of the initial water content on the structure and working properties of phosphoric acid-based geopolymers. The addition of water to the reactive mixtures leads to a sharp decrease of its viscosity, as well as a modification of its setting time, i.e. a longer setting time in the case of a dilution with Al/P = 1 and a shorter one when increasing Al/P. Moreover, the resulting consolidated materials are characterized by a deterioration of their mechanical properties, along with a higher level of porosity, when increasing either Al/P or the water content. On a structural point of view, a combined study by XRD and FTIR showed that: (i)

For Al/P = 1 with different water contents, the network is mainly based on Al-O-P bonds with an hydrated silica network across the different compositions. The contribution of each network can be continuously modified by the addition of water, thus giving a good control over the properties of the resulting geopolymer.

(ii) For variable Al/P, the same networks as in (i) are identified. However, the presence of unreacted metakaolin modifies the control over their distribution, making it more challenging. Moreover, the molecular interactions will favor the formation of Si-O-P and Si-O-Al bonds.

In all the cases, this study showed that both the water amount and the Al/P compositions are parameters that can be used to decrease the viscosity of the initial reactive mixture.

However, their noticeable influence on the structure and properties of the resulting geopolymers is to be carefully monitored.

Figure 1 :

 1 Figure 1: composition of the reactive mixture for samples with () Al/P=1 and a variable water content, () a variable Al/P ratio and () the reference sample.

Figure 2 :Figure 3 :Figure 6 :

 236 Figure 2:() viscosity ( 1%) and () setting time ( 1h) as a function of the percentage of water for the different formulations.

Figure 8 :Figure9: water content determined by thermal analysis as a

 8 Figure 8: IG/IS of () R, () Al/P = 1 and variable water, and () Al/P variable plotted as functions of the water content.

Figure 10 :

 10 Figure 10: evolution of the intensity of characteristic FTIR contributions (identified by their positions in cm -1 ) of (A) silicate hydrated networks ( ) SiO-H (asym 3530 -sym 3440) and ( )H2O 3240 cm -1 , (B) phosphate networks ( ) ν Al-O-P 1220, (,  ) ν P-O asym 1095 -sym 1155 cm -1 , and (C) summary ( ) hydrated Al-O-P at 3350, ( ) PO-H at 1640 and ( ) Si-O-P at 1206 cm-1 . These evolutions are displayed for () R, () Al/P = 1 and variable water addition, and () Al/P variable samples as functions of the parameter 𝒏𝑷 𝒏𝑨𝒍

Table 1 : viscosity and setting time observed for the different samples.

 1

	Samples		[P] (M)	H2O (mol%)	Viscosity (Pa.s)	Setting time (min)
	Al/P = 1	R	6.49	0.45	30.0	46
		R-1.1	5.97	0.50	14.5	46
		R-1.2	5.57	0.55	4.0	48
		R-1.3	5.14	0.60	1.7	63
		R-1.4	4.85	0.63	1.4	56
		R-1.5	4.51	0.68	0.6	69
	Variable Al/P	0.9	7.23	0.39	38.6	68
		1.1	5.82	0.49	19.1	32
		1.2	5.28	0.52	17.2	35
		1.5	4.23	0.58	5.6	17
		1.8	3.50	0.62	2.2	9

2, (e) 1.5, (f) 1.8 and (B) diffraction diagrams of samples with Al/P = 1 and a variable amount of water (a) R, (b) R-1.1, (c) R-1.2, (d) R-1.3, (e) R-1.4, (f) R-1.5. The positions of crystalline anatase (


Adam Jatowt

Ricardo Campos
email: ricardo.campos@ipt.pt

Sourav S Bhowmick

Nina Tahmasebi
email: nina.tahmasebi@svenska.gu.se

Antoine Doucet
email: antoine.doucet@univ-lr.fr

Every Word has its History: Interactive Exploration and Visualization of Word Sense Evolution

Keywords: Word sense change, diachronic word change, historical linguistics

Human language constantly evolves due to the changing world and the need for easier forms of expression and communication. Our knowledge of language evolution is however still fragmentary despite significant interest of both researchers as well as wider public in the evolution of language. In this paper, we present an interactive framework that permits users study the evolution of words and concepts. The system we propose offers a rich online interface allowing arbitrary queries and complex analytics over large scale historical textual data, letting users investigate changes in meaning, context and word relationships across time.

INTRODUCTION

Every word has its own history. In particular, words that have existed for long time are likely to have undergone several changes on a semantic level. As language is our most important communication tool, we believe that properly understanding the nature of changes in the meaning and usage of words -the basic elements of the language -is important for professionals working with historical texts, such as linguists, historians, librarians and social scientists. Many prior approaches relied on manual analysis of old texts. Laborious work was required to trace word occurrences across past texts and to compare their contexts and usage for drawing general inferences. As a result, manual approaches covered a relatively small set of words or time periods. Providing detailed overview of the evolution of any word over an entire timeline has however become currently possible.

Computational approaches applied on large diachronic corpora have significant potential to advance evolutionary linguistic studies and researchers have already started proposing methods for studying word evolution [START_REF] Davies | The Corpus of Contemporary American English as the First Reliable Monitor Corpus of English[END_REF][START_REF] Kim | Temporal Analysis of Language through Neural Language Models[END_REF][START_REF] Jatowt | A Framework for Analyzing Semantic Change of Words across Time[END_REF][START_REF] Hamilton | Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change[END_REF][START_REF] Hilpert | Meaning Change in a Petri Dish: Constructions, Semantic Vector Spaces, and Motion Charts[END_REF][START_REF] Hilpert | Assessing Frequency Changes in Multistage Diachronic Corpora: Applications for Historical Corpus Linguistics and the Study of Language Acquisition[END_REF][START_REF] Rohrdantz | Towards Tracking Semantic Change by Visual Analytics[END_REF]. However, few effective tools to interactively explore word change over time were proposed. Furthermore, they tend to offer simple options such as a term frequency graph and keyword-in-context view [START_REF] Davies | The Corpus of Contemporary American English as the First Reliable Monitor Corpus of English[END_REF], rely on prepared animated scatterplots [START_REF] Hilpert | Meaning Change in a Petri Dish: Constructions, Semantic Vector Spaces, and Motion Charts[END_REF] or apply hierarchical clustering of frequency counts of target word in adjacent time periods [START_REF] Hilpert | Assessing Frequency Changes in Multistage Diachronic Corpora: Applications for Historical Corpus Linguistics and the Study of Language Acquisition[END_REF]. Others like [START_REF] Rohrdantz | Towards Tracking Semantic Change by Visual Analytics[END_REF] focus on relatively short time periods (e.g., 20 years based on news articles from The New York Times Annotated Corpus) by tracking senses over time represented through LDA topics.

Equipped with effective tools, scientists would be able to freely investigate any desired word to see how it evolved over time. Furthermore, such a tool could be useful for non-expert users, as word etymology analysis attracts significant interest of the public. The recent enhancement of automatic definitions generated by the Google search engine for "definition queries" is one example. For an input word, standard word definition is complemented with a brief description of the word's origin as well as its frequency plot over time. Although users can see the count of word over time, they are however left at their own to reason about word meaning change over time.

With this in mind, we propose a multi-perspective system designed for the analysis of semantic change of words and concepts over time which is derived from our previous work [START_REF] Jatowt | A Framework for Analyzing Semantic Change of Words across Time[END_REF]. Using word representations from distributional semantics, we allow evolutionary word investigation at several levels: word analysis, contrastive word pair analysis, multi-word analysis and temporal context analysis. Altogether these four core modes provide a user with a visual explanation of semantic change for any query word. Their synergy permits storytelling of the word evolution based on visual analytics. We use two datasets as underlying data: COHA and Google Books n-gram dataset. Due to the very large data size of the latter, our methods must be scalable to be able to promptly respond to user queries. We release an online working service that enables anyone to investigate arbitrary words in real time and is accessible at: http://tinyurl.com/WordEvolutionStudy

DATASETS & PREPROCESSING

Large scale data is the basis of effective and reliable analysis. In our approach, we utilize the largest available historical corpus that offers a comprehensive representation of English language in the Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org. . This dataset has been compiled over about 5% of ever published books which were scanned and subject to Optical Character Recognition (OCR). It covers the time frame from before 1600 to 2010. The data is organized as n-gram counts for every year. As an additional corpus, we use the Corpus of Historical American English (COHA) [START_REF] Davies | The Corpus of Contemporary American English as the First Reliable Monitor Corpus of English[END_REF] which has been compiled with a decade level granularity. COHA contains over 400 million words in the form of 4-grams collected from about 107k documents written from 1810 to 2010. An important advantage of COHA is that it is based on a stable rate of diverse document genres for each decade. Comparison of results obtained from these two datasets should allow for more informed judgments. Although COHA contains carefully selected and balanced prose texts based on a stable rate of different genres across decades, it is many orders of magnitude smaller. For efficiency and for facilitating result comparison across both the corpora, we converted the Google 5-gram dataset to the decade granularity by summing 5-grams within each decade. Decade level should be sufficient to reason about word evolution as, typically, diachronic semantic changes materialize over longer time spans. This also provides smoothing effect to decrease the impact of short-term fluctuations. Other preprocessing steps included converting words to lowercase, removing punctuation and discarding rare n-grams.

SYSTEM DESCRIPTION 3.1 Word Representation

We adopt a common approach used in NLP for representing words, the distributional semantics, according to which, a word's meaning is captured by co-occurring words (hereafter called context terms). For a given target word w in a decade d, we collect all n-grams that contain w. We then sum the counts of all context terms. The word representation in d is then given by a vector, whose size is the number of unique words found in the dataset. The weights in this vector are calculated as the normalized counts of context terms co-occurring with the word w in d. Note that neural network based word embeddings have been also used for diachronic sense detection [START_REF] Kim | Temporal Analysis of Language through Neural Language Models[END_REF][START_REF] Hamilton | Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change[END_REF]. We decided to start with simpler and intuitive word representation leaving the addition of other solutions for later stage.

Word Analysis

In the first analysis, word analysis, the user issues a query word and the system evaluates the degree of its context change across time. In particular, the vector representation of the query at a reference decade d r is compared with the one of any other decade. If the similarity between the word's vector at decade d i and the one at reference decade d r is low (i.e. sim(d i [w], d r [w])  0), then a semantic change is likely to have occurred between these two decades. We use the following measures for computing context self-similarity over time: cosine similarity, Pearson Correlation Coefficient and Jaccard Coefficient drawn for the entire time frame 3 . Fig. 1 demonstrates the result obtained for the word mail. The top left-hand side graph shows by the thick blue line the similarity plot between the query's semantics in the reference decade and the ones in each past decade using cosine similarity. It permits understanding when the meaning of the query became similar to the meaning present in the reference decade. The curve with the high and steep increase characterizes a word which acquired the present meaning in a relatively short time period (as in the example of Fig. 1). On the other hand, a flat curve indicates words with stable or slowly changing meaning over time. The right-hand side plot in Fig. 1 (blue line) adds more evidence to the word evolution analysis by outputting similarities between two consecutive decades. It is then possible to examine if the input word underwent other significant changes over time including ones not related to the current meaning. Finally, the bottom graph in Fig. 1 shows both the raw word count and its normalized frequency over time. It offers complementary information about the interplay of word popularity and its semantic change. Additionally, the plot helps to detect periods characterized by low frequencies of query which may poorly reflect query's pattern of semantic change 4 .

Figure 1. Word analysis example (word: mail).

Frequency-based referencing. Reasoning about the sense shift of a word should be always done with proper context. We then draw average similarity curves for all words belonging to different frequency segments (see gray lines in the top-left graph plot of Fig. 1). For example, the shape of mail in Fig. 1 differs greatly from the graph of its corresponding frequency bin (the grayest color curve representing the 0%-19% of the most frequent terms). Note that the curves for less frequent words exhibit on average greater change over time than ones for more frequent words, which confirms the observation made in prior studies [START_REF] Hamilton | Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change[END_REF].

Detailed context exploration. This mode permits fine-grained investigation of query at

Contrastive Word Pair Analysis

Contrastive word pair analysis is another mechanism for quantifying the change in word meaning which works through comparison. Analyzing the similarity of two related words (e.g., synonyms) can shed light on the evolution of each of them.

Figure 3. Contrastive word pair analysis (mouse vs. rat).

For example, it is known that the meanings of nice and pleasant gradually converged. Using the word level analysis, one could then first observe that pleasant was characterized by relatively stable meaning across past decades, while, in contrast, nice assumed variety of meanings in the past including "foolish" or "silly". Then, the comparison of the usage of both words over time becomes helpful for better gauging the changes in their meaning. Fig. 3 shows partial view of the results obtained for comparing example words mouse and rat.

Contrastive exploration of context. While the above-described word-to-word similarity curve quantifies how much the two input words were similar in the past, we also need a way to portray the commonalities and differences of the words at particular time points (similar to the option provided in word analysis described in Sec. 3.2). By clicking on the top plot in Fig. 3 the two side-by-side lists are opened with the top context terms, one for each input query word (see Fig. 4). The lists are color-coded for highlighting the same and different context terms. A user can click on any other decade to analyze variations of the pair's commonalities and differences across different decades.

Multi-word Analysis

Investigating concept evolution is complementary to analyzing the meaning change of a single term. For example, while one may visualize the meaning change of a word car based on the previously discussed word analysis mode, a more complete view of its evolution can be achieved when viewing it "through the lens" of the evolution of the entire concept represented by the set of similar or strongly related words. In the case of the word car, one could then also observe changes of auto, automobile, vehicle or truck to compare the evolution of the word car with the broader concept of an autonomous object driven by a human. Our system allows combining temporal characteristics of words in the word set into a single joint representation. The word analysis and the contrastive word pair analysis described above are then extended here to the multi-word analysis scenario where a word set of up to n terms is tracked over time to reveal the inter-word similarities. Fig. 5 demonstrates the results obtained for the car example. The top left graph in Fig. 5 shows the across-time similarity curves of each word separately by thin lines. Their aggregate is denoted by a thick blue line. The line is computed by combining the context of each individual term from each decade.

Contrasting the plots of individual words with their aggregate allows for understanding if a word's sense followed, or deviated, from the meaning of its corresponding concept over time, offering in this way additional pieces of information for solving "the word's evolution puzzle". The chart on the top right of Fig.

Temporal Context Analysis

Given a query word, a natural question for a careful investigator is how its context terms changed over time. To answer this question, we develop an approach for temporal context analysis by temporal summarization of query context. We use term clouds to represent the context of a query over time. A term cloud is an effective visualization style for quickly grasping contents of large document collections. A standard term cloud is however suited for synchronic text collections. There seems to be no ready solution for effectively showing contents of diachronic collections using standard term clouds. Displaying the cloud of context terms over the entire period in a single view would obviously not allow for a time-focused investigation. One could of course simply display separate clouds for each decade. This would however require sideby-side, sequential comparisons placing cognitive burden on users.

We propose extending the standard word cloud by enhancing it with temporal views of each context term. This helps not only to spot the frequent context terms overall (by comparing their font size) but also to observe how they occurred over time. In particular, we propose two modes for capturing term occurrence patterns over time: time series view and colored matrix view (not shown here due to space limitation). The first one allows for more detailed quantitative analysis while the second is for a quick overview of the data through colored scheme. In both the modes, it is possible to flexibly adjust the amount of terms to be shown and to zoom-in or out the clouds and to switch anytime between the time-focused or standard term cloud ("show/hide details" button). Finally, there is an option of clicking on any context term in the cloud to see the examples of containing it n-grams and the query word, hence, connecting the bird's eye (temporal summary) view with the raw data to allow users detailed investigation or verification of hypotheses.

Word pair context summary. The time-enhanced views of context terms provide an overview of what context terms co-appeared with the query and what were their occurrence patterns over time. We next extend this analysis to consider also contrastive type analysis of context. This corresponds to the contrastive word pair analysis described in Sec. 3.3. The input is then a pair of words. Recall that in contrastive word pair analysis users could select any decade to compare the context terms of query words at particular decades (as shown in Fig. 4). Now however we wish to contrast the top context terms over the entire time in a single view.

When two words are input, the output cloud contains combined context terms for the two words, each shown in a different color. The shared context terms for both the input query words are aligned one next to another allowing immediate comparison of their saliency. Their temporal plots are also merged to facilitate time-focused comparison. Finally, if the same query is entered twice (e.g., car, car) the system contrasts the summary of context terms occurring before and the ones appearing after the query word. Such a view can help determine similarities and differences between context before and after query.

IMPLEMENTATION

To accommodate the large size of data, we have used MapReduce framework, Apache Spark and PostgreSQL 9.3.9 with default indexing algorithm (B-tree). Scala 2.11.6 was used for data preprocessing and server-side programming together with a Web application framework: Play Framework 2.3.8. TypeScript 1.5 (JavaScript) was applied for client-side programming, while for UI we used the following libraries: D3.js 3.5.6, Bootstrap 3.3.2 and jQuery 2.1.3. We have also pre-computed results for the most common 100k English words. Thanks to these, results are returned relatively fast, typically, within a second.

As mentioned before, the system is available online for arbitrary queries offering then a discovery tool for the audience. Users can also download the results in tsv format for offline analysis. Furthermore, it provides query suggestions computed based on the distinctive shapes of terms' time series plots from Sec. 3.2. For example, it suggests words that retained stable senses over long time or underwent high semantic shift over short time.

2 .

 2 A user can choose either one of them and can compare views based on different measures.

Fig. 1

 1 Fig.1shows the snapshot of the word analysis. The user starts by selecting a particular reference decade (i.e., by default the latest decade) with which the representation of the query in other decades is to be compared. The resulting similarity plot is then

  each decade to let users understand the reasons behind the similarity fluctuations. Users can click on any decade to see the list of the 50 top context terms co-occurring with the query word and their frequencies at that decade. They can then contrast such terms with those in other decades by clicking on any other decade to open up new lists with differing words being automatically colored. Fig 2 shows the joint side-by-side comparison of mail's context over three different decades.

Figure 2 .

 2 Figure 2. The color-coded comparison of top co-occurring terms at three different decades selected by clicking on the view shown in Fig 1 (the lists have been truncated).

Figure 4 .

 4 Figure 4. Visualization of top context terms and their differences for word pair at two decades selected from the view shown in Fig. 3 (the lists have been truncated).

  5 portrays decade-to-decade changes of each word as well as the one of the aggregate curve. Next, the bottom left graph portrays the frequency over time of each word and of the word set, which is Demonstration Paper CIKM'18, October 22-26, 2018, Torino, Italy computed as the sum of the individual term frequencies. Finally, the right bottom graph of Fig. 5 plots word-to-word similarities for each combination of two words in the input word set.

Figure 5 .

 5 Figure 5. Multi-word analysis example (concept: car).

The system allows freely setting the time frame for an optimal view.

To alert users about potential non-representativeness, periods with frequency below a pre-specified threshold are indicated by dashed lines.

ACKNOWLEDGMENTS

This work is partially funded by JSPS kakenhi grants #17H01828, #18K19841, MIC SCOPE (#171507010) and the ERDF through the COMPETE 2020 Programme within project POCI-01-0145-FEDER-006961, and by National Funds through the FCT as part of project UID/EEA/50014/201.


Dr Marcus Fehse
email: marcus.fehse@umontpellier.fr

Dr Dimitrios Bessas

Dr Abdelfattah Mahmoud

Aliou Diatta

Dr Raphael P Hermann

Lorenzo Stievano
email: lorenzo.stievano@umontpellier.fr

Moulay Tahar Sougrati

Stievano, * ,#,@, ¶ Prof Lorenzo

Dr Moulay T Sougrati #

The Fe 4+/3+ redox mechanism in NaFeO 2 : A simultaneous operando Nuclear Resonance and X-ray Scattering study

Keywords: Mössbauer spectroscopy, Chemometrics, MCR-ALS, Na-ion batteries, Nuclear Forward scattering, NaFeO 2

Introduction

Sodium ion batteries (SIB) are ideal for large-scale electrochemical storage which are not subject to weight or volume restrictions. Iron-based cathode materials are particularly interesting, since they fulfil both economical and ecological requirements [1]. In this regard, the layered transition metal oxide NaFeO 2 has received much interest since it was the first electrode material for SIB reversibly cycling on the Fe 3+/4+ redox couple [2]. Moreover, NaFeO 2 has the flattest and highest average working voltage of all single metal O3-type systems [3]. Unfortunately, its electrochemical performance deteriorates rapidly if more than 2 0.5 Na + per formula unit are extracted due to irreversible structural changes which lead to the disturbance of Na pathways caused by the migration of Fe into interslab spaces [4,5].

Substituting Fe partially by other transition metals can suppress structural deterioration and avoid Fe migration hence increasing overall capacity and cycling stability [6,7].

Attempts to elucidate the reaction mechanism based on ex situ Mössbauer spectroscopy suggest that sole Fe 4+ formation cannot explain the overall capacity obtained and that additional charge compensation contribution must be present [8]. As a possible explanation, the contribution of both transition metal and oxygen to the charge compensation has been lately proposed [9]. In their recent in situ XAS study, Susanto et al. highlighted that beyond 0.5 Na + extraction the charge is predominantly provided by oxygen which is irreversibly released when extracting more than 0.6 Na per formula unit [10]. In other studies based on ex situ Mössbauer spectroscopy, it was revealed that Fe 4+ formed during sodium/lithium extraction is unstable and spontaneously reduces back to Fe 3+ upon open circuit storage [11,12], underlining the importance of an in situ or operando based analytical approaches.

These observations demand for a thorough study of the evolution of the physico-chemical properties of the iron centres under realistic cycling conditions in order to closely follow the reaction mechanism and elucidate the working principle of the Fe 4+ /Fe 3+ redox couple.

Such information can be obtained by several techniques such as X-ray absorption and 57 Fe Mössbauer spectroscopy, which provide element-specific core resonance information about the iron centres and can be easily applied under in situ conditions. On the other hand, the high degree of long range order during the phase transition between increasingly desodiated phases makes X-ray diffraction (XRD) a suitable technique to monitor the phase evolution and lattice parameter change upon desodiation reaction.

In this work, we report the application of operando Nuclear Forward Scattering (NFS), a spectroscopic technique based on the Mössbauer effect, to closely monitor the reaction process of NaFeO 2 vs. sodium. NFS, applied here for the first time to the study of battery materials, benefits from the brilliance of 3 rd generation synchrotron radiation sources radiation sources, and therefore has the advantage of providing similar information but with reduced collection times (here 7 minutes per spectrum), thus opening the application of the Mössbauer effect to the study of faster reaction mechanisms than those measured conventionally (several hours per spectrum for samples non-enriched in 57 Fe and large amount of electrode materials). [13] Moreover, NFS allows working on samples with small sizes and is a background free method, thus enabling the collection of data with very high signal-to-noise ratios. Finally, in this experiment NFS could be coupled to operando transmission XRD, which was measured in parallel on the same sample during the same electrochemical processes. In this way, it was possible to measure simultaneously the evolution of both the long-range order of the material and the local physico-chemical properties of the iron centres. To validate the approach, the results of NFS are closely compared to those obtained by conventional lab-scale operando Mössbauer spectroscopy and X-ray diffraction applied on the same system.

Experimental

Material synthesis and electrode formulation

The pristine NaFeO 2 powders used in this work were prepared starting from 260 mg of Na 2 CO 3 and 360 mg of a mixture of α-Fe 2 O 3 and γ-Fe 2 O 3 isotopically enriched in 57 Fe (95 %). The two precursors were finely ground in a mortar for 10 minutes, and then annealed in air at 600 • C for 18 hours with a heating rate of 12 • C h -1 . The phase purity of the pristine material was checked by laboratory X-ray diffraction (Fig. S1 table S1). Due to moisture sensitivity, the NaFeO 2 samples were stored and handled in a glovebox under inert atmosphere.

Electrodes with approximate diameter of 12 mm were prepared as composite self-supported pellets as previously described [14]. In short; electrodes were pasted on an aluminium foil starting from a slurry containing 85 wt.% NaFeO 2 , 10 wt.% super-P carbon, 5 wt.% PVDF (polyvinylideneflouride) dissolved in NMP (1-methyl-2 pyrrolidinone). The electrode used for the operando experiments contained ≈ 2 -4 mg cm -2 of NaFeO 2 .

57 Fe Mössbauer spectroscopy

Operando 57 Fe Mössbauer spectra were measured with a source of 57 Co:Rh using a specially designed electrochemical cell [15] during the first desodiation-sodiation and subsequent desodiation cycle. The measurements were performed with the source and sample at room temperature with a triangular velocity waveform in the classical transmission geometry. A NaI(Tl) scintillation detector was used for the detection of the γ-rays.

Simultaneous Nuclear forward scattering and synchrotron Xray diffraction

The operando NFS measurements were carried out at the nuclear resonance beamline ID18 of the European Synchrotron Radiation Facility. [16] Both the NFS and the XRD data were measured at the nuclear resonance energy (i.e., about 14.412 keV) [17] related to the first excited state of 57 Fe. The NFS measurements utilised the time delayed nuclearly scattered radiation, which was registered with a stack of 4 avalanche photodiode detectors [18]. The time dependence of the NFS signal was detected between 15 and 160 ns after the arrival of an X-ray pulse, which in the 16 bunch operating mode of ESRF arrives every 176 ns. In this study each NFS spectrum was measured for about 7 minutes. Between two consecutive NFS spectra, a transmission X-ray diffraction (XRD) pattern was collected using the prompt electronically scattered 14.412 kev radiation (corresponding to a wavelength of 0.860 Å), which was registered using a MAXIPIX position sensitive detector [19]. Each XRD pattern was measured for about 5 seconds.

Electrochemical cycling

Both Mössbauer spectroscopy and simultaneous NFS-XRD experiments were carried out using a specifically designed in situ cell with two Be windows (with negligible Fe contamination, checked beforehand by conventional Mössbauer spectroscopy) allowing experiments in the transmission mode previously described elsewhere. [15] The cell was assembled in an argon-filled glove-box with a NaFeO 2 positive electrode, a Whatman QM-A quartz fiber separator and a sodium disc counter-electrode, using 1 M NaClO 4 in propylene carbonate (PC) with addition of 5 % fluoroethylene carbonate (FEC) as the electrolyte. Galvanostatic cycling with potential limitation was performed using a Biologic-VSP potentiostat at a C/n rate (expressed as 1 mol of Na reacted in n hours per mole of NaFeO 2 ).

Chemometric data analysis

The complete operando Mössbauer spectroscopy, NFS and XRD datasets were analysed by combining Principal Component Analysis (PCA) and Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) analysis (more details about the application of these methods to operando data are given in ref. [20] and, for this specific case, fig. S2). The MCR-ALS analysis for Mössbauer data set was carried out with the following constraints: non-negativity of the concentration of the components and closure (sum of the components concentrations equal to 100%). For the MCR-ALS analysis of NFS the additional constrains of unimodality, as well as the intensity of components 1, 2, 3, 4 were set to be 100% at spectra #1, 15, 20 and 33, respectively. The reconstructed pure spectral components of both techniques were subsequently fitted in a traditional way.

The components deriving from the analysis of the Mössbauer spectra were fitted with appropriate combinations of Lorentzian lines using the computer program PC-Mos II computer. [START_REF] Grosse | PC-Mos II[END_REF] In this way, hyperfine parameters such as the isomer shift (δ), the electric quadrupole splitting (∆), the full line width at half maximum (Γ) and the relative resonance areas (Area) of the different spectral components were determined. The isomer shift scale is referred to where fitted using the software MOTIF. [START_REF] Shvyd'ko | [END_REF] The same PCA + MCR-ALS procedure was applied to the XRD patterns collected together with NFS using the following constraints: non-negativity of the concentration and of the intensity of the components, and closure (sum of the components concentrations equal to 100%). The cells parameters of the four pure patterns obtained in this way were refined using the Le Bail method (see SI for more information). [23]

Results

The results shown in the following of the article were obtained in two separate operando experiments: a first conventional 57 Fe Mössbauer spectroscopy analysis, and a second synchrotronbased simultaneous NFS and XRD study. The results of these investigations are reported in the following sections and then critically discussed together.

Operando Mössbauer Spectroscopy

The evolution of operando 57 Fe Mössbauer spectra during first desodiation up to 3.5 V, sodiation down to 2.0 V and subsequent desodiation up to 3.8 V of NaFeO 2 and corresponding electrochemical signature are depicted in Fig. 1. PCA applied to the entire operando data set indicates that it can be reproduced by 3 orthogonal vectors (see SI for more details).

The analysis of these data required three spectral components (see SI for more details) thus excluding a biphasic reaction mechanism. Their concentration profile, see Fig. 2, reveals that component 1 is dominant at the pristine state, then completely fades away during electrochemical charge and reemerges at the end of discharge (EOD) to become primary component again. This reflects the high reversibility of the reaction when the voltage cutoff is limited to 3.5 V, as the pristine state is largely recovered after one complete cycle.

Component 3 is the majority component at the end of first and second charge (EOC) reaction The three pure components obtained via MCR-ALS were fitted in the conventional way, the corresponding hyperfine parameters are reported in Tab. 1, and the fits are shown in Fig. 3. Component 1 corresponds to the starting component and can be fitted in straightforward fashion using single species contribution of Fe(III) with a relatively narrow quadrupole splitting ∆ (≈ 0.5 mm s -1 ), well in line with literature values [2,8]. Component 2 corresponds to the phase mix that is formed upon first and subsequent desodiation and consists of two species. Firstly, a majority of Fe(III) contribution with a larger quadrupole splitting (∆) than observed in component 1. According to the bilinear nature of the MCR-ALS approach, this can be interpreted as either the formation of a new phase of Fe(III), or more likely a gradual increase of the ∆ in the Fe(III) phase. Secondly, the apparition of a Fe(IV) minority species at significantly lower isomer shift (δ) is evinced. Component 3, which corresponds to the end of discharge, after completion of one electrochemical cycle can be fitted using same species as for component 2, however, with further increased quadrupole splitting ∆ for both Fe(III) and Fe(IV) species. Such a strong increase in ∆ was previously observed in ex situ Mössbauer studies and has been attributed to the distortion of the FeO 6 octahedra during desodiation [2,11].

The gradual rise of the quadrupole splitting of the Fe(III) species and the simultaneous increase of the average oxidation state upon charge, and its reversion upon discharge are depicted in Fig. 4. It should be noted that quadrupole splitting of Fe(IV) species follows a similar trend as observed for Fe(III).

The evolution of the Mössbauer spectra beyond spectrum #38 is particularly interesting as they reflect the transformation of the cathode material upon oxidation above 3.5 V, surpassing the region of stable cycling x ≤ 0.5. The electrochemical cycling curve reveals an additional plateau at ≈ 3.6 V followed by a steep slope. The chemometric analysis reveals that component 3 which reflects the formation of Fe(IV) is reaching its maximum at spectra #39. Interestingly, no further intensity increase of component 3 upon further forced oxida- tion is noticed. This suggests that the formation of Fe(IV) does not proceed beyond the 0.5 sodiation threshold, which is also reflected by the stagnation (and even a slight decrease) of the average oxidation state in Fig. 4. We can therefore conclude that the capacity obtained beyond 3.5 V is not linked to the Fe +3/+4 redox couple. These results comfort those of Susanto et al., who showed by in situ X-ray absorption spectroscopy that oxygen redox activity is responsible for charge compensation above 3.5 V, when more than 0.5 Na is extracted from the structure. They also suggested the formation of Fe 3 O 4 caused by oxygen release at high voltage. In spite of a slight decrease of the average oxidation state, however, this observation could not be confirmed by our in situ data, since no clear formation of Fe(+II) species was detected.

Simultaneous Nuclear Forward Scattering and X-ray Diffraction

Operando NFS spectra and XRD patterns were simultaneously collected during first charge (desodiation) reaction up to 4.8 V, acquiring a total of 33 pairs of spectra and patterns (Figure 5). The NFS and XRD data sets were analysed via the chemometric approach implying PCA and MCR-ALS; in analogy with the analysis of the Mössbauer dataset (vide supra).

In contrast to Mössbauer spectroscopy, four independent components were identified Table 1: 57 Fe Mössbauer parameters of the components derived from the MCR-ALS analysis. noted that, in contrast to MS, NFS features no reference for the isomer shift and thus only differences in isomer shift between components can be measured, but not the isomer shift itself with reference to, e.g., the source or α-iron). [24].

Component Species ∆ [mm s -1 ] δ * [mm s -1 ] Γ [mm s -1 ] Area [%] MCR#
Analogous to Mössbauer spectroscopy results, a continuous increase in quadrupole splitting of both species upon desodiation reaction is observed. The reported absolute value of difference in isomer shift (∆(δ)) of ≈ 0.4 mm s -1 for component 2 and of 0.33 mm s -1

for component 4 are in good agreement with the differences in isomer shift of the spectral contributions of Fe(III) and Fe(IV) observed in the conventional Mössbauer spectra for the intermediate and the EOC components, which confirms the formation of Fe(IV) upon desodiation. The concentration profile shows a flat plateau for the intensity of component 4 (Figure 6) beyond spectrum #25, which coincides with a voltage above 3.5 V. This indicates that no significant changes occur to the iron doublets beyond this point. This observation is well in line with the findings of Mössbauer spectroscopy (vide supra) for the second charge reaction surpassing 3.5 V corresponding to spectrum ≥ #35.

For the linewidth (Γ) of pristine material (Component 1) a value of 0.35 is found which The first two components could be refined using the R 3m space group (O3-type), whereas the last two had to be refined within the monoclinic C2/m space group, designated as the O 3 phase and typical of the partially desodiated Na 0.5 FeO 2 . [2] The electrochemical process seems to occur though a sequence of a monophasic-biphasic-monophasic regions. The first two components, in fact, can be linearly combined to represent the first solid solution O3

domain, the first one representing pristine Na 0.5 FeO 2 and the second one of the same structure but with a decrease. The O3 → O 3 transition is observed at about halfway through the charge process, and is followed by a second solid solution O 3 domain which can be obtained through the combination of components #3 and #4.

Discussion

The reversible extraction and insertion of Na from the NaFeO Analogously, the two techniques reflect that the electrochemical charge transfer above 3.5 V, revealed by their corresponding cycling curve, is not linked to the Fe +3/+4 redox couple.

Whether these irreversible oxidation reactions are linked to electrolyte degradation or anodic charge contribution, as recently proposed [10], cannot be answered with certainty based on our findings. Nevertheless, the formation of iron species with higher oxidation states can most certainly be excluded, in line with the findings of previous works. The increasing distortion upon oxidation is also reflected by the operando XRD pattern measured simultaneously with the NFS spectra. In this case, the process consists of a first solid solution domain, implying a slight decrease of the cell volume, followed by a biphasic O3 → O 3 transition which occurs at about halfway through the extraction of the first 0.5 Na, i.e., at a composition around Na 0.75 FeO 2 . This transition is followed by a further solid solution domain which ends with the extraction of 0.5 Na.

Interestingly, the application of chemometric tools to the two spectroscopic datasets leads to different number of principal components for describing the same oxidation process. The reason for this could be the more favourable signal-to-noise ratio of NFS technique compared to conventional lab-scale Mössbauer spectroscopy. Indeed, NFS data are intrinsically noise-free and do not suffer from the broadening of the experimental linewidth, which in conventional MS is the convolution of the linewidths of the source and of the absorber: in fact, the linewidth measured in NFS is that of the sample alone.

Consequently, to describe the gradual transformation of Fe(III) to Fe(IV) and their steady increase in quadrupole splitting an additional component is needed for NFS data set. Therefore, NFS allows an improved discrimination of unresolved superimposed quadrupole doublets compared to conventional MS under similar experimental conditions.

Moreover, NFS allows for faster data collection and is particularly valuable when the concentration of Mössbauer active nuclei is low, when the size of the sample is particularly small (down to fractions of mm) or thin, and when the acquisition time is limited by the experimental framework as it is usually the case for operando measurements [25]. The collection of spectra in very short times permits capturing different instants of the reaction, while Mössbauer spectroscopy, collected over longer times, produces less spectra averaged over longer process fractions, and thus a lower resolution of the whole mechanism. The same is true for XRD, which thanks to the intensity of the synchrotron source provides a very good description of the redox process in relatively short measurement times.

In this regard the findings are well in line with our previous study on iron-based electrode materials in which the use of synchrotron source allowed a noticeably reduced acquisition time thanks to strongly reduced background noise compared to lab based source. [26]

Conclusion

In this paper, we show that Mössbauer spectroscopy and NFS are both suitable techniques to follow closely the redox reaction at the iron centres during desodiation and sodiation of NaFeO 2 . By applying a chemometric approach for data analysis, combining PCA with MCR-ALS, it was shown that the oxidation reaction going along with the gradual extraction of sodium from the host structure involves only Fe(III) and Fe(IV) species up to the extraction of half of the sodium. After this point, the oxidation processes occurring at voltage above 3.5 V are not linked to the Fe 3+/4+ redox couple, in line with previous works suggesting the presence of anionic redox activity during the second part of the process. Ancillary XRD analyses, measured simultaneously with NFS, show that the redox reaction implies at least three redox processes, i.e., solid solution, biphasic and again solid solution. By comparing conventional Mössbauer spectroscopy and synchrotron-based NFS results, it is demonstrated here that the latter has greater accuracy for identifying characteristics of iron doublets.

Figure 1 :

 1 Figure 1: Evolution of operando 57 Fe Mössbauer spectra overlain with corresponding electrochemical cycling curve. First desodiation up to 3.5 V, sodiation and second desodiation reaction up to 3.8 V of NaFeO 2 vs. sodium.

Figure 2 :

 2 Figure 2: Concentration profile of MCR-ALS components during first 1.5 cycle of NaFeO 2 vs. Na. Dotted lines indicate end of charge (EOC) at #15, begin of discharge (sodiation) at #18 and end of discharge (EOD) at #25 followed by second charge (desodiation) up to 3.8 V.

Figure 3 :

 3 Figure 3: Mössbauer fits of pure components obtained via MCR-ALS for component 1 (pristine), component 2 (intermediate), and component 3 (EOC) in the top, centre, bottom, respectively.

Figure 4 :

 4 Figure 4: Evolution of Fe(III) quadrupole splitting (∆) and Fe mean oxidation state during first 1.5 cycle of NaFeO 2 vs. Na. Dashed lines mark the end of first charge and the begin of first discharge at spectra # 15 and # 18 respectively. The dotted line at spectra # 25 indicates end of one complete electrochemical cycle.

Figure 5 :

 5 Figure 5: Evolution of (a) NFS spectra and (b) XRD pattern during first charge (desodiation) of NaFeO 2 up to 4.8 V vs. Na + /Na. The NFS scattering intensity is plotted in logarithmic scale, the wavelength of angular scale is 0.86 Å. Graph (c) shows the corresponding operando electrochemical signature with markers for consecutively numbered data acquisition points.

Figure 6 :

 6 Figure 6: Concentration profile of (a) NFS and (b) XRD MCR-ALS components during first charge (desodiation) of NaFeO 2 vs. Na.

Figure 7 :

 7 Figure 7: Fitted NFS MCR-ALS pure components during desodiation reaction of NaFeO 2 . Black points and red lines are the pure components and the fitted data respectively.

2

 2 was thoroughly monitored by operando Mössbauer spectroscopy and for the first charge by combined operando NFS-XRD. All these techniques go hand in hand, revealing the progressive oxidation of Fe(III) to Fe(IV) upon first charge. Moreover, the trend of increasing quadrupole splitting for the two iron species is mutually reflected by MS and NFS. This observation suggests an increasing distortion of the local iron environment upon extraction of sodium from the host structure.

Table 2 :

 2 Iron NFS fitting parameters of the MCR-ALS components. Values without errors were fixed during the fit.

	%]

Component Species ∆ [mm s

-1

] ∆(δ) [mm s -1 ]) * Γ [mm s

-1

] Angle [ • ] ** Area [* Absolute value of difference in isomer shifts between two species. ** Angle refers to preferential orientation indicating texture effect. *** (MS) attributed to Fe(III), see Table 1. The other three NFS MCR components could be fitted only assuming the presence of two species with different isomer shifts. It must be

* Isomer shift values are given relative to α-Fe at RT. ** Values without errors were fixed during the fit.

Acknowledgements

Alistore-European Research Institute is gratefully acknowledged for financial support through the postdoc grant to M. Fehse. ESRF is acknowledged for providing beamtime at beamline ID18. Spanish Ministerio de Ciencia e Innovación is acknowledged for its support through the project ION-SELF (ref. PID2019-106519RB-I00). RS2E network is acknowledged for funding A. Diatta. Work by R.P.H. at Oak Ridge National Laboratory, managed by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE), was sponsored by the Energy Efficiency and Renewable Energy (EERE), Vehicle Technologies Office (VTO). The technical assistance provision by Mr. J.-P. Celse is acknowledged during the beamtime at ID18.

Supporting Information Available

Characterisation of pristine NaFeO 2 ; Principal Component Analysis of the operando Mössbauer spectroscopy, NFS and XRD data; Operando XRD data analysis.