Jean-Baptiste Vaney

Gaëlle Delaizir

Bartlomiej Wiendlocha

Janusz Tobola

Eric Alleno

Andrea Piarristeguy

Antonio P Goncalves

Christine Gendarme

Bernard Malaman

Anne Dauscher

Antonio Pereira Gonçalves

Christophe Candolfi

Bertrand Lenoir

Effect of Isovalent Substitution on the Electronic Structure and Thermoelectric Properties of the Solid Solution

Introduction

Thermoelectric materials are attracting attention due to their ability to convert a temperature gradient into an electrical potential (Seebeck effect) and vice-versa (Peltier effect). These reciprocal effects potentially pave the way to versatile technologies that include waste-heat harvesting devices and cooling set-ups. The thermoelectric performances of a material are evaluated by its dimensionless thermoelectric figure of merit ZT defined as , where α, ρ, κ and T stand for the thermopower (or Seebeck coefficient), the electrical resistivity, the total thermal conductivity, and the absolute temperature, respectively. [START_REF]Thermoelectrics and Its Energy Harvesting[END_REF][START_REF] Goldsmid | Thermoelectric Refrigeration[END_REF] Achieving high ZT values in a broad temperature range is however very challenging due to the subtle balance between the electronic and thermal properties that must be obtained. [START_REF]Thermoelectrics and Its Energy Harvesting[END_REF][START_REF] Goldsmid | Thermoelectric Refrigeration[END_REF] For thermoelectric applications near room temperature, the rhombohedral Bi2Te3 and its derivatives of general chemical formula Pn2Ch3 (Pn = Bi, Sb and Ch = Te, Se, S; space group R3 " m) have been considered as canonical compounds for several decades [START_REF]Thermoelectrics and Its Energy Harvesting[END_REF][START_REF] Goldsmid | Thermoelectric Refrigeration[END_REF] and still remain one of the most studied families of thermoelectric materials nowadays. [START_REF] Poudel | High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys[END_REF][START_REF] Jaworski | Resonant level formed by tin in Bi2Te3 and the enhancement of room-temperature thermoelectric power[END_REF][START_REF] Xie | Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites[END_REF][START_REF] Kim | Dense dislocation arrays embedded in grain boundaries for high-performance bulk thermoelectrics[END_REF] In addition to reaching ZT values around unity near 300 K, either n-type or p-type semiconducting properties can be obtained, both of which being required for the fabrication of thermoelectric devices. [START_REF]Thermoelectrics and Its Energy Harvesting[END_REF][START_REF] Goldsmid | Thermoelectric Refrigeration[END_REF] Despite being another isostructural member of this family, the binary β-As2Te3 has received less attention. [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF][START_REF] Yakushev | New polymorphic modification of arsenic telluride, produced at high pressures[END_REF][START_REF] Toscani | Polymorphism of As2Te3: structural studies and thermal behaviour of rhombohedral β-As2Te3[END_REF] The polymorphic compound As2Te3 exhibits a rich temperaturepressure phase diagram with several crystal structures identified recently. [START_REF] Zhao | Structural phase transitions and metallized phenomena in arsenic telluride under high pressure[END_REF][START_REF] Zhang | Pressure-induced electronic phase transitions of α-As2Te3[END_REF][START_REF] Cuenca-Gotor | vibrational, and electronic study of α-As2Te3 under compression[END_REF][START_REF] Morin | Polymorphism in thermoelectric As2Te3[END_REF] Under ambient pressure, this compound also crystallizes within a monoclinic structure (α-As2Te3) with space group C2/m (Figure 1). [START_REF] Harman | Preparation and some physical properties of Bi2Te3, Sb2Te3 and As2Te3[END_REF][START_REF] Carron | The crystal structure and powder data for arsenic telluride[END_REF][START_REF] Vaney | Thermoelectric properties of the α-As2Te3 crystalline phase[END_REF] Both structures have recently drawn attention for their interesting thermoelectric properties originating from a favorable combination of semiconducting-like ZT = α 2 T / ρκ electronic properties and particularly low lattice thermal conductivities (around 0.5 W m -1 K -1 at 300 K). [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF][START_REF] Vaney | High-temperature thermoelectric properties of Sn-doped β-As2Te3[END_REF] Our investigations on the transport properties of α-and β-As2Te3 have unveiled the important role of charged defects akin to Bi2Te3-based alloys. In α-As2Te3, this defect chemistry yields either n-or p-type samples with carrier concentrations of the order of 10 17 cm -3 depending on the synthesis conditions. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] Optimization of the thermoelectric properties could be realized in both compounds by tuning the electronic properties via substitutions of either Sn or Bi for As. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF][START_REF] Vaney | High-temperature thermoelectric properties of the β-As2-xBixTe3 solid solution[END_REF] These experimental studies have evidenced interesting ZT values of 0.65 at 423 K and 0.85 at 523K in p-type Sn-doped β-As2Te3 and α-As2Te3, respectively. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF][START_REF] Vaney | High-temperature thermoelectric properties of Sn-doped β-As2Te3[END_REF] In the Bi2Te3-xSex solid solution, the Se/Te ratio controls the nature and the concentration of charged defects and thus, offers a control parameter to tune both the carrier concentration and the dominant carrier type. [START_REF] Horák | Point defects in the mixed chalcogenides Bi2Te3-xXx (X= S, Se)[END_REF][START_REF] Champness | Thermoelectric properties of n-type Bi2Te3-Bi2Se3 alloys[END_REF][START_REF] Misra | On the solid solutions of bismuth telluride and bismuth selenide[END_REF][START_REF] Miller | Properties of Bi2Te3-Bi2Se3 alloys[END_REF] In order to determine whether a similar behavior emerges in α-As2Te3, we explore herein the influence of Se on the electronic structure and transport properties in a wide range of temperatures (5 -523 K) of the solid solution α-As2Te3-xSex (0 ≤ x ≤ 1.5). In agreement with first-principles calculations, we show that increasing the Se content leads to an increase in the band gap energy and hence, to higher electrical resistivity values. Although the lattice thermal conductivity of α-As2Te3 is intrinsically very low, the formation of a solid solution results in even lower values that reach 0.35 W m -1 K -1 above 300 K due to enhanced point-defect scattering.

Experimental and computational details

Warning: At high temperatures, the As vapor pressure may be high enough to damage the quartz tube and release toxic As vapor.

Synthesis.

All manipulations of solids and powders were carried out in a dry, argon-filled glove box with O2 and H2O contents of less than 0.1 ppm. Because the α form of the binary As2Se3 is stable only at high pressure (under ambient pressure, As2Se3 crystallizes in the P21/n space group) and due to the high electrical resistivity of the samples with high Se contents, the compositional range probed herein was restricted to 0 ≤ x ≤ 1.5. [START_REF] Kirkinsky | Synthesis of third polymorphic modification of selenide arsenic at high pressures[END_REF][START_REF] Stergiou | The crystal structure of arsenide selenide As2Se3[END_REF] Polycrystalline samples of α-As2Te3-xSex with x = 0.0, 0.1, 0.2, 0.4, 0.7, 1.0 and 1.5 were synthesized by direct reaction of stoichiometric amounts of pure As (Goodfellow, 99.99%), Te (5N+, 99.999%) and Se (5N+, 99.999%) in quartz tubes sealed under secondary vacuum. The sealed tubes were heated in a vertical furnace up to 923 K with a heating rate of approximately 10 K min -1 , dwelt at this temperature for 2 h and eventually furnace-cooled. Contrary to the synthesis of α-As2-xSnxTe3 samples which requires an annealing treatment of the rhombohedral β-phase initially obtained after water quenching, the α phase has been here directly obtained by air quenching. It is worth noting that in the α-As2Te3-xSex system for x ≥ 0.1, water quenching induces the formation of a glassy phase so that a single-phase material cannot be obtained. An additional annealing step at 573 K for 3 days has been further applied to improve the chemical homogeneity of the samples and suppress an eventual glassy phase. After a final quenching, the ingots were ground into micron-sized powders and consolidated by spark plasma sintering (SPS, Dr. Sinter 505 Syntex) between 553 and 593 K (the sintering temperature depending on the composition) under a pressure of 50 MPa for 2 min using a graphite die of 10.4 mm inner diameter. Due to the shrinkage of the sintering window with increasing x, the relative densities, determined by dimensions and weight of the cylindrical pellets, decrease from 98 (x = 0.0) to 93% (x = 1.5).

X-ray and Neutron Powder Diffraction.

Phase purity and crystal structure were verified by X-ray powder diffraction (XRPD) with a Bruker D8 Advance diffractometer (Cu Kα1 radiation) in reflection mode. Room-temperature neutron powder diffraction (NPD) patterns were collected on the x = 0.7 sample at the Institut Laue Langevin (ILL, Grenoble, France) on the high-resolution two-axis diffractometer D1B equipped with a one-dimensional curved multidetector. Rietveld analyses of XRPD and NPD patterns were carried out using the Fullprof software. [START_REF] Rodriguez-Carvajal | Recent advances in magnetic structure determination by neutron powder diffraction[END_REF] Note that the layered crystal structure of these samples results in a slight renormalization of the intensities of the X-ray diffraction peaks, the extent of which varying from sample to sample.

Scanning Electron Microscopy and Electron Probe Microanalysis. Scanning electron microscopy (SEM) observations were conducted on polished bulk pieces using a Quanta FEG (650F, FEI) to probe the phase purity of the samples. Images of the surface were collected in the backscattering electron mode (BSE). Corresponding elemental X-ray mappings were performed to assess the chemical homogeneity of the samples.

Electron probe microanalysis (EPMA) was performed with a JEOL JXA 8530F equipped with wavelength-dispersive spectrometers. Prior to analyses, bulk pieces of the consolidated samples were carefully polished with alumina powders. Backscattered electrons were used for imaging the surface of the samples and contrast the matrix from possible secondary phases. In order to minimize matrix effects, X-ray intensities of As and Te were compared with those of a calibrated β-As2Te3 standard for quantitative analysis. The calibration of this sample was carried out with the isostructural compound Bi2Te3 as in our previous study on the α-As2-xSnxTe3 samples. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] The chemical compositions of the α-As2Te3-xSex specimens were determined by averaging the results obtained on at least 90 different points for each sample. Because of the good correlation between the actual and nominal Se contents, the latter will be used hereafter to label the samples.

Low-and high-temperature transport properties measurements. The dense cylindrical pellets were cut both parallel and perpendicular to the pressing direction with a diamond-wire saw to probe the anisotropy. Bar-shaped samples (~ 3×2.5×8 mm 3 ) were used to measure simultaneously the thermopower, the electrical resistivity and the thermal conductivity between 5 and 300 K using the thermal transport option (TTO) of a physical property measurement system (PPMS, Quantum Design). For these measurements, four copper leads were brazed onto the surface of the samples with a low-melting-point braze. The same samples were used to determine the Hall resistivity from measurements of the transverse electrical resistivity using the AC transport option of the PPMS. These measurements were realized in a five-probe configuration under magnetic fields ranging between -1 T and + 1 T.

Due to the high electrical resistance of the samples for x ≥ 0.7, the Hall coefficient could be only reliably obtained for x ≤ 0.4. Furthermore, the semiconducting nature of the samples results in a rapid rise in the electrical resistivity upon cooling. For this reason, the transverse resistivity could be measured only in a narrow temperature range below 300 K.

Another set of bar-shaped samples (typical dimensions ~ 1.5×1.5×8 mm 3 ) was cut in the two directions to measure the electrical resistivity and thermopower between 300 and 523 K.

These two transport coefficients were measured simultaneously with a ZEM-3 apparatus (Ulvac-Riko). Thermal conductivity was determined from 300 up to 523 K via thermal diffusivity measurements performed on disk-shaped samples (~ 10 mm in diameter) for the parallel direction and on rectangular prism-shaped (~ 6×6×1 mm 3 ) samples for the perpendicular direction using a laser flash system LFA 467 (Netzsch). Prior to measurements, the samples were spray-coated with a thin layer of graphite to ensure a homogeneous signal absorption and emission on the respective surfaces. The thermal diffusivity a is related to the thermal conductivity by the relation κ = aCpρv where Cp is the specific heat at constant pressure and ρv is the density. Specific heat measurements (DSC 403 F3, Netzsch) were carried out on the binary sample α-As2Te3 in the same temperature range by the continuous scanning method under argon flow, according to the ASTM E 1269 method. This sample was used as a reference sample for the specific heat measurements of the other samples using a LFA 467 Netszch according to the ASTM E 1461-07 method. The combined uncertainty in the determination of the ZT values is estimated to be ~17% above 300 K. [START_REF] Alleno | A round robin test of the uncertainty on the measurement of the thermoelectric dimensionless figure of merit of Co0.97Ni0.03Sb3[END_REF] Optical absorption. Optical absorption spectra were measured on disk-shaped samples at 300 K using a Thermo Scientific Nicolet 6700 FTIR spectrophotometer equipped with an integrated sphere. The electronic band gaps Eg were determined by applying the Kubelka-Munk theory that relates the measured reflectance R to a value proportional to the absorption coefficient

F(R) = (1 -R)²/2R. 28
Electronic Band Structure Calculations. Calculations of the electronic band structure of the series α-As2Te3-xSex (x = 0.5, 1.0 and 1.5) were carried out by the Korringa-Kohn-Rostoker (KKR) method with the coherent potential approximation (CPA) to treat explicitly the chemical disorder that accompanies the substitution of Se for Te. [START_REF] Bansil | Electronic structure and magnetism of Fe3-xVxX (X = Si, Ga, and Al) alloys by the KKR-CPA method[END_REF][START_REF] Stopa | Linear aspects of the Korringa-Kohn-Rostoker formalism[END_REF] The exchangecorrelation effects were taken into account using the Perdew-Wang formula in the local density approximation (LDA). [START_REF] Perdew | Accurate and simple analytic representation of the electron-gas correlation energy[END_REF] Within this formalism, the fully charge self-consistent crystal potentials were constructed in the muffin-tin form. The position of the Fermi level was determined accurately by the generalized Lloyd formula. [START_REF] Kaprzyk | Green's function and a generalized Lloyd formula for the density of states in disordered muffin-tin alloys[END_REF] For all compositions, we used the experimental lattice parameters and atomic coordinates, as determined by Rietveld refinements of the XRPD patterns. For converged crystal potentials and atomic charges (convergence better than 1 mRy and 10 -3 e, respectively), total-, site-and orbital l-decomposed densities of states (DOS) were determined using a tetrahedron method for integration in the reciprocal k-space. [START_REF] Kaprzyk | Green's function and a generalized Lloyd formula for the density of states in disordered muffin-tin alloys[END_REF] Insights into the site preference of Se were obtained by total energy KKR-CPA calculations with Se selectively diluted on the three inequivalent Te sites of the crystal structure of α-As2Te3 (see Figure 1).

Results and Discussion

Electronic band structure calculations. Figure 2 shows the electronic DOS of α-As2Te2.5Se0.5 that illustrates the effect of Se selectively diluted on the three possible Te sites.

As can be expected, the isovalent substitution of Se for Te does not modify significantly the DOS and the energy gap at the Fermi level for all investigated compositions. This gap stems from a strong hybridization of the p-states of As and Te/Se. Inspecting in more details the site-decomposed DOS (Figures 2 to 4), the p-states of Se lie generally at higher energies in the upper part of the valence bands compared to the p-states of substituted Te, regardless on which Te site Se was placed. Remarkably, the overall DOS shape of Se2 is less structured than that of Se1 and Se3, both of which exhibiting more pronounced peaks just below the energy gap. Further, the center of gravity of Se2 DOS is shifted towards lower energies due to the larger DOS hump seen around -3eV below EF with respect to the DOS of Se1 and Se3.

All these features suggest that Se preferentially occupies the Te2 site. This conclusion, based on DOS characteristics, is well supported by the total energy KKR-CPA calculations, which clearly show that the lowest energy is obtained when Se occupies the Te2 site followed by the Te3 site and eventually the Te1 site. Interestingly, the energy difference of about 0.18 eV per atom between the first and the second case is much larger than the corresponding value between the second and third case (0.04 eV per atom, with a numerical accuracy of ~0.1 meV). This large difference further indicates a strong preference for Se to substitute on the Te2 site. Hence, in view of the KKR-CPA results, one can expect that Se should primarily replace Te2 with increasing the Se content up to the entire filling of this site, that is, up to x = 1. Indeed, similar comparison of total energy calculations performed for α-As2Te2Se shows that the energy difference between the case where Se fully substitutes Te either on the Te2 or Te3 site is about 0.5 eV per atom, a value much larger than in the above-mentioned composition (x = 0.5). The electronic reason for such trends can be also seen from DOS features by comparing the KKR-CPA results for x = 1.0 and 1.5 shown in Figures 3 and4.

The DOS peak of Se3 is almost twice larger than that of Se2 in the upper part of the valence states. Once the Te2 site is entirely filled by Se, the simultaneous presence of Se on both the Te1 and Te3 sites represents the most unfavorable situation from an energetic point of view. Thus, for x > 1.0, Se should substitute on the Te3 site rather than Te1. This filling sequence is confirmed by the DOS of the x = 1.5 composition for which the difference in energy between these two cases is about 0.1 eV per atom in favor of Te3.

Another interesting finding derived from these calculations is related to the evolution of the energy gap with x. It should be kept in mind that the KKR-CPA computations were performed in the framework of the LDA approach, which tends to underestimate the energy gap. Thus, only the relative variations in the energy gap are meaningful, not the absolute values. This effect, inherent to the methodology used here, explains the discrepancy between the band gap energy calculated for the pristine compound As2Te3 in the present study (Eg = 0.19 eV) and the value obtained in our prior study (Eg = 0.46 eV). [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] Within these limitations, we find that Eg monotonically increases with x from 0.19 eV for x = 0.0 to 0.23 eV for x = 0.5, to 0.34 eV for x = 1.0 and to 0.40 eV for x = 1.5.

Phase purity, chemical homogeneity and Se site preference. Figure 5 shows the XRPD pattern of the illustrative sample α-As2Te2.6Se0.4 (XRPD patterns for other compositions are given in the Supporting Information; Figures S1 to S4). In the x = 0.0 and 0.7 samples, weak additional reflections that can be attributed to either the cubic AsTe binary or elemental Te are observed. For the other compositions, all the reflections are indexed to the monoclinic C2/m structure of α-As2Te3, suggesting the absence of secondary phases within the detection limit of XRPD. SEM and EPMA confirmed the XRPD results except for x = 1.0 where some precipitates of elemental Te could be observed, the amount of which being below the detection limit of XRPD. Elemental X-ray maps reveal that all the elements are homogeneously distributed (Figures S5 to S11 in Supporting Information). The average chemical compositions obtained by EPMA (Table 1) indicate a good agreement between the nominal and actual compositions for all samples. The lattice parameters obtained from Rietveld refinements are summarized in Table 1 and the reduced lattice parameters as well as the reduced unit cell volume are shown as a function of the Se content in Figure 6. These analyses indicate a monotonous shrinkage of the unit cell in a quasi-linear manner with increasing x due to the smaller covalent radius of Se with respect to Te. The overall decrease in the unit cell volume is accompanied by a slight variation in the monoclinic distortion associated with the β angle. The NPD pattern collected on the x = 0.7 sample (Figure 7) at 300 K provided further information on the distribution of Se on the three Te crystallographic sites of α-As2Te3. Rietveld refinements against these data were performed by considering three different structural models, where Se occupies one of the Te sites. The best agreement with the data was obtained when Se solely occupies the Te2 site, which is consistent with the predictions of the KKR-CPA calculations (see Tables S1 andS2 in the Supporting Information for the refined crystallographic parameters and main interatomic distances for the x = 0.7 sample).

Optical Band Gap. Figure 8a presents the Tauc-plot of the absorption spectra as a function of the photon energy E, assuming direct transitions for all samples. As shown in our previous study, [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] the optical spectra of α-As2Te3 shows a steep rise above E = 0.43 eV attributed to the optical band gap Eg. This value is in good agreement with first-principles calculations of the electronic band structure of α-As2Te3. [START_REF] Sharma | First principles investigation of electronic, optical and transport properties of α-and β-phase of arsenic telluride[END_REF][START_REF] Vaney | Electronic structure, low-temperature transport and thermodynamic properties of polymorphic β-As2Te3[END_REF] In the α-As2-xSnxTe3 series, all the optical spectra exhibited a shallow rise that was tentatively attributed to either impurity states in the band gap or intra-band scattering. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] Except for the end-member compounds α-As2Te3 and α-As2Te1.5Se1.5, all the spectra display a similar shallow rise. This trend is followed by a steeper rise that likely corresponds to the band gap, the value of which first slightly decreases from 0.43 eV to 0.40 eV for x = 0.1, followed by a monotonous increase with increasing x up to 0.64 eV for x = 1.5 (Figure 8b). The overall increase in Eg with x is qualitatively in agreement with our band structure calculations. The tunability of Eg by substituting Se for Te can be explained by the covalent radii of both atoms. The lower covalent radius of Se with respect to Te leads to a reduced orbital overlap and hence, to a decrease in the dispersion of the bands synonymous with an increase in Eg. The weak influence of isoelectronic Se on Eg from x = 0.0 to x = 0.4 is consistent with a nearly rigid-like evolution of the electronic band structure followed by a non-rigid-like behavior above x = 0.4.

Electronic and galvanomagnetic properties. In the following, only the data measured parallel to the pressing direction are shown for sake of clarity. The data measured perpendicular to the pressing direction are provided in the Supporting Information (Figures S12 to S14). Figure 9a shows the temperature dependence of the electrical resistivity ρ. For all samples, ρ(T) decreases with increasing T indicative of their semiconducting nature. ρ decreases at 523 K from 650 μΩ.m for α-As2Te3 to 430 μΩ.m for α-As2Te2.6Se0.4 before increasing by two orders of magnitude to reach 19000 μΩ.m for x = 1.5. The initial decrease in the ρ values on going from x = 0.0 to x = 0.4 is most likely due to variations in the defect concentration that controls the transport in α-As2Te3. The substitution of Se for Te tends to decrease their concentration and/or changing their nature. The significant increase in ρ observed above x = 0.4 is consistent with the optical absorption measurements and electronic band structure calculations, both of which indicating an increase in the band gap energy with

x. As a result, the electronic band structure no longer evolves in a rigid-like manner above x = 0.4, explaining the lack of clear trend in ρ(T) with x.

Figure 9b shows the thermopower α as a function of temperature for the series α-As2Te3-xSex measured parallel to the pressing direction. As in the Sn-substituted series, 17 α appears isotropic to within experimental uncertainty (Figure S13 in Supporting Information).

All samples show a p-type semiconducting behavior, indicating that the partial substitution of Se for Te does not lead to n-type conduction in the investigated compositional range. This lack of crossover can be attributed to the increase in the band gap values with increasing x.

The situation thus contrasts with Bi2Te3 where alloying with Se has a minimal impact on the band gap and favors the creation of TeBi antisite defects and Te vacancies, both of which being negatively charged. [START_REF] Horák | Point defects in the mixed chalcogenides Bi2Te3-xXx (X= S, Se)[END_REF] α-As2Te3 exhibits a maximum in α of 200 μV K -1 around 200 K, and is rapidly decreasing above this temperature up to around 500 K, where a transition from p-to n-type conduction is observed. This behavior was attributed to the prominent role played by defect chemistry in this compound. [START_REF] Vaney | Thermoelectric properties of the α-As2Te3 crystalline phase[END_REF] Alloying with Se up to x = 0.4 suppresses this dependence and yields a monotonous, non-linear increase in α with temperature. For x ≥ 0.7, the maximum in α reached at high temperatures marks the onset of thermal excitations of minority carriers across the band gap that adversely affect the α values. The large α values that increase with increasing x are consistent with the semiconducting nature of the present samples.

The Hall carrier concentration pH and the Hall mobility μH for the α-As2Te3-xSex samples are listed in Table 2. The results evidence a sudden increase in pH from 3.4×10 18 cm -3 for x = 0.0 to 2.4×10 19 cm -3 for x = 0.1. This increase, similar to that observed in the Sn-substituted samples, [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] is likely tied to variations in defect concentration upon Se alloying. Further increase in x results in a slight decrease in pH down to 2.0×10 19 cm -3 for x = 0.4, a value twice as high as those obtained in Sn-substituted samples. The presence of Se leads to very low hole mobilities, of the order of 1 cm 2 V -1 s -1 as a result of alloy scattering, that is, an additional scattering mechanism introduced by the random distribution of Se atoms on the Te2 sites.

Thermal Transport Properties. Figures 10a and10b show the temperature dependence of the total thermal conductivity κ for all samples. Note that the lower density of the samples with high Se contents has only a moderate influence on the measured values (estimated to at most 10% of the κ values for the x = 1.5 sample when considering the model developed by Landauer (Ref. 35) that takes into account the relative density of the samples). The measurements evidence a moderate anisotropy that tends to decrease with increasing x (Figure S14 in Supporting Information), as already observed in Sn-substituted α-As2Te3. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] The high electrical resistivity of the samples results in negligible electronic contributions to the thermal conductivity. Hence, the measured κ values can be considered to reflect solely the lattice contribution in the temperature range where bipolar conduction is absent. For all samples, κ exhibits a well-defined Umklapp peak around 20 K, characteristic of crystalline solids. Above this temperature, κ decreases with increasing temperature, following roughly a 𝑇 !" law, indicative of thermal transport dominated by Umklapp scattering. Upon Se alloying, κ decreases up to x = 1.5, a behavior consistent with increased point-defect scattering expected in solid solutions. Regardless of the Se content, the room-temperature κ values are below 1 W m -1 K -1 . Except for α-As2Te3 that experiences bipolar conduction above 450 K, κ decreases upon heating to reach ~ 0.35 W m -1 K -1 at 523 K in the x = 1.5 compound. This last value is the lowest achieved so far in both α-and β-As2Te3 compounds (Refs. 16 and 17) and among most of state-of-art thermoelectric selenide compounds. [START_REF] Chen | Thermoelectric properties of p-type polycrystalline SnSe doped with Ag[END_REF][START_REF] Sassi | Assessment of the thermoelectric performance of polycrystalline p-type SnSe[END_REF][START_REF] Wei | Thermoelectric transport properties of pristine and Na-doped SnSe1-xTex polycrystals[END_REF][START_REF] Lee | High-performance tellurium-free thermoelectrics: all-scale hierarchical structuring of p-type PbSe-MSe systems (M = Ca, Sr, Ba)[END_REF] For α-As2Te1.5Se1.5, κ is very close to the amorphous limit estimated to 0.4 W m -1 K -1 in these compounds and approaches the values measured in chalcogenide glasses of similar composition. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF] As shown in Figure 11a, the decrease in κ with increasing disorder in the unit cell, i.e.

with increasing x, follows the expectations of classical models for point-defect scattering of phonons. The lattice thermal conductivity of the alloyed compounds κL,A was calculated by the model developed by Callaway and Klemens using the thermal conductivity of the pure end-member compounds, κL,P, and assuming that both Umklapp and point-defect scattering processes dominate [START_REF] Callaway | Effect of point imperfections on lattice thermal conductivity[END_REF][START_REF] Klemens | Thermal resistance due to point defects at high temperatures[END_REF]

𝜅 #,% 𝜅 #,& = arctan (𝑢) 𝑢 (1)
𝑢 ' = 𝜋. 𝜃 ( . Ω 2. ℎ 𝜐 ' 𝜅 #,& Γ (2)
In Eqs.( 1) and (2), Ω is the average volume per atom, θD is the Debye temperature, h is the Planck constant, υ is the average speed of sound measured on the pure compounds and Γ is the scattering parameter defined as 40,42-44

Γ = Γ )*++ + Γ +,-*./ 1.234 = 𝑥(1 -𝑥) ;< 56 6 !"# = ' + 𝜀 < 57 7 !"# = ' ? 𝐶 (3)
where x is the relative concentration of the impurity atom, Mavg and δavg are the average molar mass and atomic radius, respectively, ΔM and Δδ are the molar mass and atomic radius differences, respectively, between those of the substituting and substituted atoms. For a compound of chemical formula AmBn(1-x)Snx where B is substituted by the atoms S, the parameter C is defined as follows [START_REF] Slack | Thermal conductivity of MgO, Al2O3, MgAl2O4, and Fe3O4 crystals from 3° to 300[END_REF][START_REF] Meisner | Structure and lattice thermal conductivity of fractionally filled skutterudites: solid solutions of fully filled and unfilled end members[END_REF] In Eq.( 4), Mtot is the total molar mass as described in Ref. 43. Γmass corresponds to the scattering related to atomic mass contrast while Γstrain field describes the scattering due to the network distortion. In this model, ε is a phenomenological fitting parameter that can be related to the Grüneisen parameter characterizing the anharmonicity of the lattice vibrations. [START_REF] Klemens | Thermal resistance due to point defects at high temperatures[END_REF] Typical values of ε fall within the range 10 -100 for various thermoelectric materials. [START_REF] Klemens | Thermal resistance due to point defects at high temperatures[END_REF] Taking the covalent radii of the atoms for the parameter δ, this model was used to calculate the blue curve shown in Figure 11a yielding a fit ε value of 12, that is, in the above-mentioned range. The good agreement achieved with the experimental results indicates that the decrease in κ with increasing the Se content can be attributed to enhanced point-defect scattering.

Figure 11b shows the ratio between Γmass and Γstrain field as a function of the Se content.

While Γ increases with x, the ratio Γstrain field / Γmass linearly decreases with increasing the Se content. At low substitution levels, phonon scattering due to mass fluctuations is the dominant term, while at higher Se contents up to x = 1.5, the relative influence of both effects balances.

𝐶 = 𝑛 𝑚 + 𝑛 𝑀 *89 𝑀 ,:, (4)
However, the variations in strain field fluctuations relative to mass fluctuations is not straightforward, as not only does it depend on the atom mass differences with respect to the atomic radii differences, but also on the bonding character and crystallographic site environment. [START_REF] Yang | Strain field fluctuation effects on lattice thermal conductivity of ZrNiSn-based thermoelectric compounds[END_REF] In particular, the site preference of Se leads to an inhomogeneous distribution of Se atoms within the unit cell, the variation of which with x implying an evolution in strain field fluctuations.

Dimensionless thermoelectric figure of merit ZT. The temperature dependence of the ZT

values is shown in Figure 12. The mixed electrical conduction of the binary compound above 200 K leads to very low ZT values. The ZT values increase with x up to x = 0.4 due to the concomitant decrease in ρ and increase in α to reach maximum of 0.17 at 523 K. Above x = 0.4, this trend reverses and the ZT values decrease with increasing x due to the large electrical resistivity values. Hence, Se alloying has an overall detrimental effect on the electrical properties and does not enable achieving higher thermoelectric performances compared to substitutions of Sn and Bi for As. [START_REF] Vaney | High thermoelectric performance in Sn-substituted α-As2Te3[END_REF][START_REF] Vaney | High-temperature thermoelectric properties of the β-As2-xBixTe3 solid solution[END_REF]

Summary and conclusion

The solid solution α-As2Te3-xSex (0 ≤ x ≤ 1.5) has been successfully synthesized by a combination of powder metallurgy and spark plasma sintering. The monoclinic crystal structure of α-As2Te3 is preserved across the Se concentration range studied. As suggested by room-temperature NPD data and KKR-CPA calculations, Se preferentially occupies the Te2 site due to the weaker modifications of the electronic band structure induced by this substitution. Calculations further indicate a rigid-like behavior at low Se contents, a prediction in agreement with the nearly constant optical band gap measured between x = 0.0 and x = 0.4 and band gap opening at higher substitution levels. Unlike the solid solution Bi2Te3-xSex, where substituting Se for Te leads to a n-type behavior, this substitution leaves unchanged the p-type electrical conduction of α-As2Te3. The samples show semiconducting-like properties with large electrical resistivity and thermopower values that increase with increasing x.

Despite the very low lattice thermal conductivity values measured in α-As2Te3 (0.5 W m -1 K -1 above 300 K), Se substitution further lowers the lattice contribution that reaches an extremely low value of 0.35 W m -1 K -1 above 300 K in α-As2Te1.5Se1.5. This reduction is due to increased disorder in the unit cell upon alloying with Se, the influence of which on the lattice thermal conductivity is well described by classical models for alloy scattering of phonons.

Associated Content

The Supporting Information is available free of charge on the ACS Publications website.

Rietveld refinements of the XRPD patterns of the x = 0.0, 0.1, 0.2 and 0.7 samples; Backscattered electron images and elemental X-ray mappings of the α-As2Te3-xSex samples; Tables S1 andS2; Temperature dependence of the electrical resistivity, thermopower and total thermal conductivity measured perpendicular to the pressing direction. (PDF)

Tables Table 1. Nominal and actual compositions obtained by EPMA and lattice parameters determined by Rietveld refinements against the XRPD data of the series α-As2Te3-xSex. All the compositions were normalized to five atoms per chemical formula. correspond to the values of the unsubstituted compound α-As2Te3 (see Table 1). E -E F (eV)

Nominal

Figures captionsFigure 1 .

 1 Figures captions

Figure 2 .

 2 Figure 2. Energy dependence of the total and site-decomposed density of states (DOS) of α-

Figure 3 .

 3 Figure 3. Energy dependence of the total and site-decomposed density of states (DOS) of α-

Figure 4 .

 4 Figure 4. Energy dependence of the total and site-decomposed density of states (DOS) of α-

Figure 5 .

 5 Figure 5. Experimental XRPD pattern (black curve) and calculated profile (red curve) for the

Figure 6 .

 6 Figure 6. Reduced lattice parameters a/a0, b/b0, c/c0 and reduced unit cell volume V/V0 as a

Figure 7 .

 7 Figure 7. Rietveld analysis of the experimental neutron powder diffraction pattern for α-

Figure 8 .

 8 Figure 8. (a) Optical absorption spectra of α-As2Te3-xSex for x = 0.0, 0.1, 0.2, 0.4, 0.7, 1.0 and

Figure 9 .Figure 10 .

 910 Figure 9. (a) Temperature dependence of the electrical resistivity ρ and (b) thermopower α for

Figure 11 .

 11 Figure 11. (a) Thermal conductivity averaged on all direction at 300 K as a function of the Se

Figure 12 .

 12 Figure 12. Temperature dependence of the dimensionless thermoelectric figure of merit ZT

Figure 2

 2 Figure 2

Figure 6 36

 6 Figure 6

Figure 7 Figure 8

 78 Figure 7

Figure 9

 9 Figure 9

Figure 12

 12 Figure 12

Table 2 .

 2 Electrical resistivity ρ, hole concentration pH and Hall mobility μH at 300 K of α-

	composition	EPMA	a (Å)	b (Å)	c (Å)	b (°)
	As2Te3	As1.985Te3.015	14.3392(4)	4.0146(1)	9.8859(3)	95.046(1)
	As2Te2.9Se0.1 As1.993Te2.919Se0.087 14.3302(7)	4.0074(2)	9.8740(5)	95.029(2)
	As2Te2.8Se0.2 As2.001Te2.812Se0.187 14.3184(7)	3.9955(2)	9.8511(5)	94.940(2)
	As2Te2.6Se0.4 As2.010Te2.635Se0.355 14.3010(7)	3.9812(2)	9.8253(4)	94.860(2)
	As2Te2.4Se0.7 As2.052Te2.277Se0.671 14.2745(6)	3.9515(1)	9.7564(4)	94.651(1)
	As2Te2Se1 As2.026Te1.879Se1.096 14.2073(2)	3.9171(4)	9.6785(1)	94.595(5)
	As2Te1.5Se1.5 As2.097Te1.436Se1.467 14.126(2)	3.8825(4)	9.6161(2)	94.561(5)
	As2Te3-xSex for x = 0.0, 0.1, 0.2 and 0.4. Because the binary α-As2Te3 features a mixed
	electrical conduction above 250 K, the Hall carrier concentration inferred at 300 K should be
	taken as an upper limit to the actual value while the Hall mobility should be considered as a
	lower limit.
	Nominal	ρ (μΩ m)	pH (cm -3 )	μH (cm 2 V -1 s -1 )
	composition
	As2Te3	5500		3.4×10 18		3.3
	As2Te2.9Se0.1	2000		2.4×10 19		1.3
	As2Te2.8Se0.2	1500		2.3×10 19		1.8
	As2Te2.6Se0.4	1700		2.0×10 19		1.8

Acknowledgments

The authors would like to thank financial support from the French National Agency (ANR) in the frame of its programme "PROGELEC" (Verre Thermo-Générateur "VTG"). B.W. and J.T. were partly supported by the National Science Center (Poland) (Project No. DEC-2011/02/A/ST3/00124). J.-B. V. and B. L. thank P. Boulet for his help in the measurement of the XRPD pattern of P21/n As2Se3. The authors thank the Institut Laue Langevin (ILL) for granting access to the D1B neutron scattering instrument.

Author Information

+ Present Address: National Institute for Materials Science (NIMS), 1 Chome-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Corresponding Author * E-mail: bertrand.lenoir@univ-lorraine.fr

Notes

The authors declare no competing financial interest.

For Table of Contents Only

The solid solution α-As2Te3-xSex (0 ≤ x ≤ 1.5) has been synthesized and its structural and transport properties determined. Se substitution results in increased electrical resistivity and thermopower due to larger energy band gap and lowered lattice thermal conductivity due to enhanced point defect scattering.


A-L Nivesse

N Baglan

Gilles F Montavon

G Granger

O Péron

Cellulose, proteins, starch and simple carbohydrates molecules control the hydrogen exchange capacity of bio-indicators and foodstuffs

Keywords: Organically bound tritium, hydrogen exchangeability, isotopic exchange, buried tritium. Highlights

Introduction

At the present time, tritium is one of the main radionuclides released into the environment at nuclear installations. According to current forecasts, these release rates are expected to rise due to the planned development of nuclear power plants and their fuel management methods, as well as to new tritium emitting facilities, such as the International Thermonuclear Experimental Reactor (ITER) and the Evolutionary Power Reactor (EPR). Understanding the behavior of tritium in the environment is therefore an ongoing societal issue, in recognizing this behavior to be directly related to the chemical forms of tritium, i.e. tritium speciation (ASN, 2010;IRSN, 2017). In environmental matrices, tritium is found in the form of Tissue-Free Water Tritium (TFWT) and Organically Bound Tritium (OBT) after the integration of tritiated water (HTO) during photosynthesis and metabolic processes [START_REF] Diabaté | Organically bound tritium[END_REF][START_REF] Pointurier | Determination of organically bound tritium background level in biological samples from a wide area in the southwest of France[END_REF]. Over the last decade, a focus on monitoring OBT has become a major concern in many countries for both public and regulatory assurance [START_REF] Kim | Current understanding of organically bound tritium (OBT) in the environment[END_REF][START_REF] Péron | Anthropogenic tritium in the Loire River estuary, France[END_REF][START_REF] Baglan | Feedback of the third interlaboratory exercise organised on wheat in the framework of the OBT working group[END_REF]. OBT is typically differentiated into two pools: the exchangeable pool (E-OBT), which equilibrates with the surrounding atmosphere; and the non-exchangeable pool (NE-OBT), which is experimentally inert and remains in organic matter until its degradation [START_REF] Sepall | Hydrogen exchange between cellulose and water: II. Interconversion of accessible and inaccessible regions[END_REF][START_REF] Kim | Current understanding of organically bound tritium (OBT) in the environment[END_REF]. The latter is directly representative of the amount of tritium released into the environment during growth of the biological organism; the interest of its study lies in the ability to conduct retrospective studies of tritium release into the environment.

From an analytical standpoint, it is widely assumed that the E-OBT fraction corresponds to the tritium bound to heteroatoms, while the NE-OBT fraction corresponds to the tritium covalently bound to carbon [START_REF] Mann | Deuteration and titriation[END_REF][START_REF] Kim | Current understanding of organically bound tritium (OBT) in the environment[END_REF]. Based on the molecular model, it is then possible to assign to each organic molecule a theoretical exchangeable parameter

(
) from the hydrogen bound to the heteroatom pool versus total hydrogen atoms.

However, this description has been challenged since previous studies highlighted major limitations of E-OBT accessibility in environmental matrices [START_REF] Sepall | Hydrogen exchange between cellulose and water: II. Interconversion of accessible and inaccessible regions[END_REF][START_REF] Baumgartner | Non-exchangeable organically bound tritium (OBT): its real nature[END_REF][START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF] when comparing the theoretical ( ) parameter to an experimentally determined ( ) parameter [START_REF] Feng | Determination of D/H ratios of nonexchangeable hydrogen in cellulose: a method based on the cellulose-water exchange reaction[END_REF][START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF]. Molecular conformation is thus supposedly responsible for the loss of exchange capacities from a part of the theoretically exchangeable hydrogen positions, hence the designation buried tritium (BT) [START_REF] Baumgartner | Non-exchangeable organically bound tritium (OBT): its real nature[END_REF]. The IAEA (International Atomic Energy Agency) has therefore suggested in its EMRAS program [START_REF] Emras | EMRAS (Environmental Modelling of Radiological Safety) Program, Modelling the Environmental Transfer of Tritium and Carbon-14 to Biota and Man[END_REF] that the NE-OBT fraction must be defined as both covalently carbon bound tritium atoms and buried tritium atoms [START_REF] Kim | Experimental investigation of buried tritium in plant and animal tissues[END_REF][START_REF] Kim | Current understanding of organically bound tritium (OBT) in the environment[END_REF]. This issue is still undergoing heated debate and requires further investigation.

The present work is therefore aimed at providing insight into tritium speciation and distribution on environmental matrices by means of evaluating the impact of molecular composition and arrangement on OBT behavior. To this end, it is being proposed herein to: (i) compare ( ) and ( ) parameters and, through reliance on the knowledge of molecular structures, grasp the origin of the buried tritium form, (ii) define the exchangeable capacity of environmental matrices compared to their main constituent, and (iii) assess the NE-OBT distribution with respect to both structural and exchangeable aspects.

Starch, cellulose, proteins and simple carbohydrates are among the most widespread biomolecules of the biomass on earth and may be found under diverse molecular structures in environmental matrices [START_REF] Sun | Hydrolysis of lignocellulosic materials for ethanol production: a review[END_REF][START_REF] Hopkins | Rapport Actualisation des connaissances Tritium Environnement[END_REF][START_REF] Sakintuna | Hydrolysis of freshly prepared wheat starch fractions and commercial wheat starch using a-amylase[END_REF]. Two food chain matrices, i.e. wheat grains and apples, plus a bio-indicator, water-milfoil, presenting initial anthropogenic OBT activities, have been selected while their main constituents were effectively extracted in order to represent the corresponding biomolecule types and undergo exchangeability assessments.

To access the exchangeable ( ) parameter, an original methodology based on isotopic exchange under a soft path regime has been previously developed [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF] and subsequently validated for exchange capacity investigations in carbohydrate molecules.

Knowledge of this parameter thus yields insight into the true nature of the exchangeable hydrogen pool within a studied environmental matrix and serves to improve our understanding of OBT speciation [START_REF] Nivesse | An overlooked pool of hydrogen stored in humic matter revealed by isotopic exchange: implication for radioactive 3H contamination[END_REF].

Materials and methods

Reagents and chemicals

Tritium solutions were prepared at the Subatech Laboratory using a certified and calibrated source and a low-level tritium water source "Eau des Abatilles" (whose HTO activity lies significantly below 0.2 Bq.L -1 [START_REF] Fourré | Reference waters" in French laboratories involved in tritium monitoring: how tritium-free are they?[END_REF]).

All reagents were purchased from Fisher Scientific International and met at least ACS reagent grade (i.e. match or exceed the specifications established by the American Chemical Society).

Ultrapure water (18.2 MΩ•cm resistivity at 25° and < 5 μg.L -1 TOC) obtained from a Milli-Q Advantage A10® system (Merck Millipore, France) was used. The tritium contaminations from reagents were considered to be negligible since the initial tritium activities of the studied matrices were significantly higher, thus suggesting only tritium depletion could be observed.

Sample preparation

The tritium contents of environmental matrices and extracted constituents were adjusted to the same reference date of July 1, 2020 by only considering the tritium radioactive decay impact.

The initial contents in organically bound tritium (OBT) within environmental matrices and extracted constituents are recorded in Table 1 (insert Table 1 here).

Wheat grains and starch

Wheat grains (Matrix A-1) from the Organically Bound Tritium (OBT) working group were previously studied as part of the work presented in [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF].

Starch (Matrix A-2) is the main component of wheat grains (Matrix A-1) and was extracted according to a procedure adapted from [START_REF] Verwimp | Isolation and characterisation of rye starch[END_REF]), Xie et al. (2008) and [START_REF] Liu | Isolation and characterization of wheat bran starch and endosperm starch of selected soft wheats grown in Michigan and comparison of their physicochemical properties[END_REF]. Briefly summarized, wheat flour was obtained from ground and sieved wheat grains passing through a 74-μm size sieve. Wheat flour (4 g) was suspended in 28 mL of 0.25% (v/v) NaOH, followed by 1 h of stirring prior to 10 min of centrifugation at 3900 x g.

The sediment was then washed three times with deionized water by stirring for 30, 15 and 10 min respectively until final neutralization with 1 M HCl prior to 10 min of centrifugation at 3900 x g for each step. The brown fraction was removed and the white fraction was first suspended in 15 mL of deionized water then passed through a 75-μm nylon screen; approx. 20 mL of deionized water was used to wash the overs. The white extracted starch filtrate was freeze-dried for 1 week and stored under vacuum prior to further use.

Water-milfoil and the cellulosic wall

Water-milfoil (Matrix B-1) samples were taken from the Loire River (47°45'18.7"N, 2°28'25.3"E) 2 km downstream of the Dampierre Nuclear Power Plant (NPP) (France). The fresh samples were immediately transferred into sealed plastic bags and stored frozen. After 48 h of freezing, the samples were dehydrated by oven drying at 90°C for 2 weeks. Freezedrying was performed for 48 h to ensure complete removal of the free water fraction, and lastly the samples were stored under vacuum.

The cellulosic wall (Matrix B-2) of water-milfoil (Matrix B-1) was recovered by extraction and elimination of the cytoplasmic fraction following a procedure adapted from [START_REF] Sun | Comparative Study of Crude and Purified Cellulose from Wheat Straw[END_REF] and [START_REF] Mochochoko | Green synthesis of silver nanoparticles using cellulose extracted from an aquatic weed; water hyacinth[END_REF]. Briefly summarized, freeze-dried water-milfoil were ground to pass a 1-mm size sieve, and the resultant powder (100 g) was dewaxed with toluene-ethanol (2:1 v/v) in a Soxhlet apparatus at 80°C for 6 h, followed by filtration at 63 μm and washing with ethanol (96% v/v) for 24 h. Extra washing steps with water and ethanol (96% v/v) were carried out to ensure a high degree of purification. The gradual loss of green coloration was due to chloroplast leak and representative of the effective removal of the cytoplasmic fraction. The purified powder was then allowed to dry in an oven at 90°C for 48 h, freeze-dried for 48 h and stored under vacuum.

Apples and simple carbohydrates

Apples (Matrix C-1) were sampled at a distance 2 km from the Cernavodă Nuclear Power Plant (NPP) (Romania, 44°20'10.0"N 28°02'13.9"E). Fresh samples were roughly cut and stored frozen for 48 h, then freeze-dried for 2 weeks, ground to pass a 1-mm size sieve and stored under vacuum.

Simple carbohydrates (Matrix C-2) were extracted from the apples (Matrix C-1) according to the procedure described in [START_REF] Besle | Extraction et purification des glucides: application à divers aliments dérivés du soja[END_REF]. Briefly summarized, apples were cut into thin strips, and the resultant sample (20g) was extracted with 1 L ethanol (85% v/v) under reflux and stirring at 80°C for 1 h. After successive filtrations at 63, 20 and 0.45 μm with manufactured filters, the extracted solution was reduced using Rotavapor concentration and then freeze-dried for 1 week, homogenized under dried atmosphere (RH < 10%) and stored under vacuum.

Sample characterization

The samples were characterized on each studied matrix, and the composition in % by weight was recorded. A broad range of common components was investigated, with certain components being examined more closely by virtue of representing the specific constituents of selected matrices. The common components tested were: starch, cellulose, sucrose, proteins, and fat contents. For starch-type matrices, i.e. A-1 and A-2, the main essential amino acids of the former were described in [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF], while the maltose and glucose contents were determined in the latter by applying the AACC 76-13.01 Standard method with the Total StarchKit Assay (Megazyme International Ireland Ltd. Co., Wicklow, Ireland). For cellulose-type matrices, i.e. B-1 and B-2, the proportions in parietal constituents of cellulose, hemicellulose and lignin were analyzed using NDF (neutral detergent fiber), ADF (acid detergent fiber) and ADL (acid detergent lignin) analyses, as stated in [START_REF] Van Soest | Use of detergents in the analysis of fibrous feeds. 2. A rapid method for the determination of fiber and lignin[END_REF]. For simple carbohydrate-type matrices, i.e. C-1 and C-2, the fructose and glucose contents were also recorded.

For each previously analyzed component, a theoretical exchangeable parameter ( ) was calculated from their respective literature-based and well-known molecular formula according to the analytical definition of E-OBT, i.e. hydrogen bound heteroatoms are exchangeable hydrogen. On this basis, a theoretical exchangeable parameter ( ) could then be calculated for each matrix according to its composition in % by weight in each component and its assigned unitary ( ). The contribution of the mineral fraction was considered to be negligible due to the low hydrogen content found in the mineral fractions of living organic matrices.

Isotopic exchange procedure

The gas-solid isotopic exchange process, as described in [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF], is based on the isotopic steady state between a bath of KCl-saturated solution (

! " , = ! " , = ! " , = ! " , (1)
As part of this description, a vapor phase has been produced from a bath containing saturated KCl solutions with controlled tritium activities, for the purpose of equilibration with the atmosphere contained in a glove box (RH = 85.11 ± 0.89% at T = 20°C, Plas-Labs 890-THC) (see [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF] for further details).

Isotopic exchanges were separately conducted on each studied matrix following both one tritium-depletion experiment with a low-level tritium bath (HTO < 0.2 Bq.L -1 ) and three tritium-enrichment experiments with tritium-rich baths (HTO = 120, 300 and 500 Bq.L -1 ).

Three aliquots were extracted from each bath during the isotopic exchange step to quantify the exact HTO activity. Samples were recovered from the confined glove box at days 2, 3 and 4 to ensure that steady state had been reached. After liquid nitrogen immersion and freezedrying, the samples were heat-treated in a tubular furnace (Eraly, France), where the organic matter was transformed into carbon dioxide and combustion water [START_REF] Cossonnet | Experience acquired on environmental sample combustion for organically bound tritium measurement[END_REF][START_REF] Cetama | Analyse des radionucléides dans l'environnement -Analyse du tritium dans les matrices[END_REF][START_REF] Péron | Anthropogenic tritium in the Loire River estuary, France[END_REF]. Bath aliquots and combustion water from the samples were distilled and neutralized for pH correction, if needed, while tritium activities were measured by means of liquid scintillation counting (PerkinElmer Tri-carb 3170 TR/SL) using an Ultima Gold LLT cocktail. The detection limit was estimated at 3 Bq.L -1 for a counting time of 180 minutes and a blank value of 2 counts per minute. The relative uncertainty was calculated based on a calibration step, according to the quench curve and systematic uncertainties; this relative uncertainty typically reached 10%.

At each steady state, a mean value of the combustion water from each matrix sample

Results

Molecular model-based theoretical exchangeable parameter ($ %&'() )

For each studied matrix, a theoretical exchangeable parameter ( ) was calculated from the molecular model of its main components and respective experimentally determined composition in % by weight. The main essential components analyzed along with their associated ( ) and distributions in % by weight in the A-1, A-2, B-1, B-2, C-1 and C-2 matrices are listed in Table 2 (insert Table 2 here). The distribution in % by weight of starch (A-2) in wheat grains (A-1) was directly measured at 75.3 ± 3.7% of organic matter. Towards the cellulosic wall (B-2) in water-milfoil, this distribution was estimated at 56 ± 27% of organic matter by assuming that the entire cellulose, hemicellulose and lignin parts were recovered (40.6 ± 7.3% in water-milfoil) and moreover that the protein fraction found in the cellulosic wall was correlated with the structural proteins part without the cytoplasmic proteins part (calculated at 15.2 ± 6.8% and 22.1 ± 9.6% in water-milfoil, respectively). For simple carbohydrates (C-2), their distribution in % by weight of organic matter was calculated at 88.2 ± 5.9% in apple (C-2) due to the addition of its respective content in glucose, sucrose and fructose. The resultant calculated ( ) parameters on each studied matrix are given in Table 3.

Starch and cellulose are two of the most abundant bio-macromolecules of terrestrial ecosystems. They are carbohydrate molecules of glucose monomer ((C6H10O5)n) with 3/10 hydrogen atoms bound to hydroxyl groups, hence an assigned ( ) equal to 30% was adopted for these polysaccharides. Glucose and fructose are simple carbohydrate monomer molecules (C6H12O6) with 5/12 hydrogen atoms bound to hydroxyl groups, explaining the assigned ( ) value of 41.7%. Maltose, composed of two glucose molecules, and sucrose, comprising one molecule of glucose and one of fructose, are simple carbohydrates with an assigned ( ) value of 36.4%.

Lignin is a macromolecule composed of variable polyphenolic polymer biomolecules, whose structure and organization depend on the environmental physicochemical conditions of formation. Lignin is mainly found with an association of proportional coumaryl, coniferyl and sinapyl alcohols [START_REF] Kratzl | Reactions of lignin and lignin model compounds with ozone[END_REF] with ( ) equal to 20, 18.2 and 15.4%, respectively.

Considering that the loss in hydrogen atoms bound to carbon and those bound to hydrogen compensates for each unit bond, as identified in several theoretical molecular structures and conformations of this biomolecule [START_REF] Hopkins | Rapport Actualisation des connaissances Tritium Environnement[END_REF], the ( ) value assigned to lignin was estimated at 17%.

Hemicellulose is a cellulose-like macromolecule predominantly represented in the dual form of xyloglucan (( ) = 29.2%) and arabinoxylan (( ) = 25%) [START_REF] Hopkins | Rapport Actualisation des connaissances Tritium Environnement[END_REF] in primary and secondary plant cell walls. In order to maintain the representativeness of these two biomolecules, the ( ) value assigned to hemicellulose was estimated at 27.1% for our study.

Protein content was determined by means of total nitrogenous content quantification. Proteins are made up of amino acids whose ( ) values lie within a range of 23 to 58%. The essential amino acids were therefore analyzed in each matrix separately. For matrix A-1, the composition in % by weight is available in [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF] and the ( ) for proteins was calculated at 37%. For matrices B-1 and B-2, the amino acid composition was determined by data available in the literature [START_REF] Muztar | The chemical composition of aquatic macrophytes. II. Amino acid composition of the protein and non-protein fractions[END_REF] and an assigned ( ) for proteins of 42% was estimated. For the A-2, C-1 and C-2 matrices, the protein content was considered to be negligible.

Fat molecules primarily consist of carbon and hydrogen atoms with a highly negligible amount of hydrogen atoms bound to the heteroatom representation [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF]. The ( ) assigned to fat molecules is thus less than 0.1% but must still be considered when performing calculations.

Isotopic exchange-based exchangeable parameter ($ *+& )

Isotopic exchanges were conducted on each studied matrix with various T/H ratios in order to evaluate the isotopic exchangeable parameter ( ), as described in [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF].

For each steady state achieved, the mean value of the combustion water from each matrix sample , was plotted versus the mean value of each saline solution , , as presented for each matrix in Figure 1 (insert Figure 1 here). The slope of the linear regression obtained was therefore considered as ( ) and calculated according to Eq. ( 2):

= , ! , , ! , (2)
From this set-up, a wide range of isotopic exchangeable parameters ( ) was obtained on the studied environmental matrices, i.e. from 16.1 ± 0.6% to 39.6 ± 1.3%, and compared to the ( ) listed in Table 3 (insert Table 3 here). The standard uncertainties on ( ) parameters were calculated using the least squares method with a coverage factor k equal to 2.

Determination of the non-exchangeable organically bound tritium (NE-OBT)

Following the isotopic depletion exchange experiment, which was conducted separately on each studied matrix with a low-level tritium bath (HTO < 0.2 Bq.L -1 ), the samples were devoid of exchangeable organically bound tritium (E-OBT) atoms. The remaining tritium fraction at steady state thus relates to the non-exchangeable organically bound fraction (NE-OBT). After an adequate post-treatment, as previously described, the activities measured in the combustion waters of the three solid sample replicates were averaged to obtain a mean NE-OBT value in each analyzed matrix.

Furthermore, supplementary information provided by the gas-solid isotopic exchange process served to calculate , -by using Eq. ( 3) [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF] obtained below:

! " , - = . ! , - × ! , 1 (1 - ) (3)
The results produced, expressed in Bq.L -1 of combustion water (NE-OBT (Bq.L -1 )), were converted into Bq.kg -1 of dry matter (NE-OBT (Bq.kg -1 )) using the content in % by weight of hydrogen in each matrix (%! ) as well as that in water (%! 4 ) by applying Eq. ( 4) below:

NE -OBT (Bq. kg > ) = NE -OBT (Bq. L > ) × %! @ABCDE %! FAGEH (4)
The measured and calculated values of NE-OBT for each studied matrix are presented in Table 4 (insert Table 4 here). The uncertainties associated with the results obtained were determined by calculating the average uncertainty and the propagation of uncertainties squared using a coverage factor k equal to 2. For each matrix, these two values were similar and displayed consistent assigned values of relative uncertainties. Accordingly, only the measured values will be mentioned in the Discussion section.

matrix is mainly composed of starch, proteins and cellulosic compounds (cellulose, hemicellulose and lignin), but only the last two are capable of presenting complex 3D molecular structures. Let's start out discussion with cellulose since it contains a long linear unbranched chain of D-glucose units linked through β(1→4)-glycosidic bonds with monomer arrangements oriented at 180°, thus promoting the formation of both intra and intermolecular hydrogen bonds and allowing for the distinction of amorphous and crystalline regions (Zugenmaier, 2001;[START_REF] Klemm | Cellulose: Fascinating Biopolymer and Sustainable Raw Material[END_REF]Wuestenberg, 2014). This specific structural stabilization corresponds to a three-dimensional network [START_REF] Nishiyama | Crystal structure and hydrogen bonding system in cellulose II-alpha from synchrotron X-ray and neutron fiber diffraction[END_REF][START_REF] Nishiyama | Crystal structure and hydrogen-bonding system in cellulose II-beta from synchrotron X-ray and neutron fiber diffraction[END_REF][START_REF] Jarvis | Chemistry: cellulose stacks up[END_REF], whose involvement in decreasing hydrogen exchangeability has already been discussed in [START_REF] Péron | Towards speciation of organically bound tritium and deuterium: Quantification of non-exchangeable forms in carbohydrate molecules[END_REF]. In this 2018 investigative work, isotopic exchangeable parameters ( ) were observed at 13.0 ±1.0% and 21.0 ±1.0% in commercial celluloses with various crystalline ratios (with respect to ( ) = 30%). The hydrogen bond phenomenon present in the crystalline regions of celluloses therefore justifies that a portion of hydrogen atoms in the theoretical exchangeable position could behave as if they were placed in non-exchangeable positions.

Such a phenomenon can also be expected with proteins possessing a three-dimensional structure. Proteins are in fact polypeptides of amino acids linked by peptide bonds occurring between a carboxyl group and an amine function [START_REF] Richardson | The anatomy and taxonomy of protein structure[END_REF][START_REF] Makhatadze | Energetics of protein structure[END_REF][START_REF] Kim | Experimental investigation of buried tritium in plant and animal tissues[END_REF]. Each peptide bond formation thus leads to the elimination of two theoretically exchangeable hydrogen atoms from the initial molecule of two amino acid units. The three-dimensional protein structures are then defined by a pattern of hydrogen bonds between these primary chain peptide groups, with a regular geometry of mostly α-helix and β-sheet saturating all the hydrogen bond donors and acceptors in the peptide backbone [START_REF] Richards | Areas, volumes, packing, and protein structure[END_REF][START_REF] Branden | Introduction to protein structure[END_REF][START_REF] Shulz | Principles of protein structure[END_REF]. These aspects of the protein structure are then more likely to induce a drastic impact on the exchangeable parameter of the entire protein chain, depending on the sequence length and nature of the amino acid units involved.

As such, the cellulosic wall (Matrix B-2) containing all the resultant cellulosic compounds along with a portion of the proteins (the structural proteins part) were recovered from the water-milfoil. After the compositional analyses and isotopic exchange process, a considerable gap was observed between this cellulosic wall theoretical exchangeable parameter (( ) = 29.0%) and its corresponding isotopic exchangeable parameter (( ) = 16.1 ± 0.6%). These elements therefore enable corroborating the hypothesis of a massive impact of the cellulose and protein compounds found in environmental matrix structures on hydrogen exchangeability, i.e. the presence of crystalline parts and then three-dimensional local structures yields buried tritium.

The apples (Matrix C-1) also presented an isotopic exchangeable parameter (( ) = 28.0 ± 1.7%) significantly below the corresponding calculated theoretical exchangeable parameter (( ) = 38.7%). This matrix is basically composed of simple carbohydrates displaying a very high theoretical exchangeability rate, with an assigned ( ) value of up to 41.7%

(see Table 2). However, simple carbohydrates are known to partially adopt a specific conformation in complex environmental matrices and form compact aggregates with crystal or ramified arrangements [START_REF] Beevers | The crystal structure of sucrose[END_REF][START_REF] Kanters | The crystal and molecular structure of β-d-fructose, with emphasis on anomeric effect and hydrogen-bond interactions[END_REF]. As previously noted for water-milfoil (Matrix B-1), these crystalline regions, which are typically characterized by a hydrogen bond, may supposedly be responsible for the observed decrease of hydrogen exchangeability in apples. Ramified arrangements of sugars in environmental matrices are also assumed to contain a hydrogen bond and favor a structure hindering phenomenon that could explain the loss in hydrogen exchangeability as well.

To confirm this hypothesis, simple carbohydrates (Matrix C-2) were extracted from apples and underwent partial destruction of their initial complex 3D structure due to solubilization during the extraction process. The polar nature of simple carbohydrate molecules does indeed provide them with both a property of very high solubility in water; moreover, access to a substantial amount of water during the extraction process was assumed to allow for their entire solubilization and dissociation from other simple carbohydrate associations [START_REF] Lee | Investigation of the Heating Rate Dependency Associated with the Loss of Crystalline Structure in Sucrose, Glucose, and Fructose Using a Thermal Analysis Approach[END_REF]. It is important to note that, as opposed to other previously extracted component matrices (i.e. A-2 and B-2 from A-1 and B-1) with a preserved initial structure, the simple carbohydrate matrix (C-2) extraction process from Matrix C-1 was intended to trigger destruction of the initial sugar structure arrangements due to solubilization. After compositional analyses and the isotopic exchange process, the extracted matrix (C-2) presented theoretical and experimental values closely bunched together as compared to the raw (C-1) matrix, i.e. (( ) = 40.4%) versus (( ) = 39.6 ± 1.3%). These results have shown that the molecular conformation destruction of sugars leads to the opening of their initial ramified structure, thus allowing the entire pool of theoretically exchangeable hydrogen atoms to be accessible for isotopic exchange with the surrounding atmosphere. As such, it can be assumed that the initial complex 3D structure of simple carbohydrates (Matrix C-2) in apples (Matrix C-1) is responsible for the hindering phenomenon and hence for the inaccessibility of a portion of the theoretically exchangeable hydrogen atoms in sugar-like environmental matrices.

Whenever environmental matrices are composed of various compounds with an array of complex 3D molecular conformations, such as a crystalline structure or ramified arrangement, it then becomes possible to ensure that the analytical point of view (i.e. based on chemical bond type) is insufficient to describe OBT speciation and behavior. In contrast, the molecules displaying a simple molecular conformation and arrangement like starch do not appear to cause buried tritium forms in wheat grains, which allows confirming that the analytical point of view is indeed sufficient to describe the NE-OBT and E-OBT forms on starch-like environmental matrices. The inferiority or equality observed between the isotopic exchangeable parameter ( ) and the theoretical parameter ( ) have therefore highlighted the relatively substantial presence or total absence of the buried tritium (BT) form depending on the molecular structure specificities and complexity of the studied environmental matrices and their main component.

Exchangeable capacity of environmental matrices and impact of NE-OBT distribution

The isotopic exchange results on extracted matrices A-2, B-2 and C-2 revealed that the structure of their constituents has exerted an influence on the global behavior of hydrogen in environmental matrices A-1, B-1 and C-1. Considering the distribution of starch (A-2) in % by weight in wheat grains (A-1) (i.e. 75.3 ± 3.7%) and the distribution of the cellulosic wall (B-2) in % by weight in water-milfoil (B-1) (i.e. 56 ± 27%), as provided in Table 4, it then appears that the isotopic exchangeable parameters ( ) of the extracted matrices directly predetermine that of the environmental matrices being studied (Table 3). The result obtained on the B-2 matrix ( ) = 16.1 ± 0.6% and the ( ) of the other constituents associated with their weight distribution in B-1 would actually lead to results calculated on the exchangeability parameter I JKLJMLKNOP Q for the B-1 matrix very close to the results obtained by isotopic exchange (approx. 24.2 ± 14.9% vs. an actual of 26.4 ± 0.5%). From this finding, a slight relative difference ( R deviation) of 8 ± 5% was recorded from this calculated exchangeability parameter I JKLJMLKNOP Q compared to the experimental ( ) parameter on the B-1 matrix. In the case of matrices A-1 and A-2, both ( ) results were also basically equal, which exhibits the exchangeability rate control from the extracted main components. The relative difference of ( ) vs. a calculated exchangeability parameter I JKLJMLKNOP Q (approx. 31.1 ± 0.8%) was then determined to equal 0.4 ± 0.1%. Regarding the apple (C-1) and simple carbohydrate (C-2) matrices, the significant difference ( From the results with starch (A-2) and cellulosic wall (B-2) as the major and determinant constituents for hydrogen exchangeability in wheat grains (A-1) and water-milfoil (B-1)

respectively, an exchangeable capacity model of hydrogen in environmental matrices can then be expressed by the following formula:

JKLJMLKNOP S = T H U VWPON × ( ) U VWPON + H U V × ( ) U V (7)
where:

I JKLJMLKNOP Q = the calculated isotopic exchangeable parameter of environmental matrix "X", H U VWPON = the distribution in % by weight of the determinant constituent "Y " of the matrix, ( ) U VWPON = its isotopic exchangeable parameter, H U V = the distribution in % by weight of every other "x" constituent of matrix "X", ( ) U V = the isotopic exchangeable parameter of every other "x" constituent of matrix "X".

The deviations between calculated I R Q parameters and experimental ( ) parameters for each of the studied environmental matrices are reported in Table 3. The determinant constituent Y of an environmental matrix is then designated not only as one of the main constituents but also with specific structural arrangements in the particular environmental matrix.

Furthermore, the calculated distributions of the initial NE-OBT matrix on the determinant extracted matrix in our present study (Table 4) would seem to display a relative trend proportional to the mass distribution of the given compounds while also undergoing influence from their isotopic exchangeable parameter ( ).

A NE-OBT recovery rate on the cellulosic wall (B-2) from water-milfoil (B-1) of 44 ± 22%

was thus observed with a slight downward trend for its own mass distribution in the initial matrix, i.e. 56 ± 27%, thus suggesting the hypothesis that a smaller portion of the nonexchangeable organically bound tritium (NE-OBT) might be located in this area rather than other compounds. In displaying the lowest ( ) parameter value due to crystalline and local three-dimensional structures of cellulose and proteins, the cellulosic wall (B-2) is potentially subjected to a slight tritium distribution deprivation during molecular synthesis and sample growth as a result of the 3D molecular complexity of these compounds. On the other hand, the NE-OBT recovery rate on A-2 from A-1 of 71.0 ± 8.7% appears to conform to the mass distribution of the constituent (75.3 ±3.7%), demonstrating that the exchangeability rate concordance of these two matrices leads to a proportional mass distribution of the NE-OBT on the raw matrix (A-1). Concerning apples (C-1) and their simple carbohydrates (C-2), the structural modification of sugars during the extraction step was assumed to be responsible for opening the ramified structure, hence leading to the accessibility of a pool of theoretically hindered exchangeable hydrogen atoms, as translated by a higher value obtained for the It is therefore possible to affirm that the hydrogen exchangeability behavior of an environmental matrix is controlled and established by one of its determinant constituents, which implies a proven influence on the OBT distribution on environmental matrices.

Conclusion

The impact of molecular structure and conformation on tritium behavior has been highlighted and evaluated in both food chain and bio-indicator matrices, as well as in widespread biomolecules contained in the Earth's biomass. Theoretical ( ) parameters were compared to experimentally determined ( ) parameters to understand OBT speciation of studied matrices in respect to their molecular constituent. Complex 3D molecular structures of cellulose, proteins and simple carbohydrates have been identified as responsible for the hydrogen exchangeability decrease in the water-milfoil and apple matrices. The presence of the buried tritium form was thus detected for environmental matrices containing main constituents with crystalline structures or ramified molecular arrangements, while its nonappearance was concluded in wheat grains and correlated with the simpler structure of the starch molecule. It has thus been shown that determinant constituents with specific molecular conformation have total control over the hydrogen transfer mechanisms in environmental matrices and directly establish their associated exchangeable hydrogen capacity. OBT speciation in a matrix was then found to be entirely correlated to OBT speciation in its determinant constituent. A significant influence of these structural aspects was observed on the NE-OBT distribution in environmental matrix constituents, hence providing access to critical information on remnant tritium in organic matter and tritium transfer in the environment.

,

  was obtained by averaging the sample values forming the plateau. A mean value of each saline solution , was also derived by averaging the three bath aliquot values once steady state had been reached.

R

  deviation) of 26 ± 7% between the two parameters was directly explained by the inherent partial degradation and modification of the initial structure of simple carbohydrates during the extraction process. The extracted simple carbohydrate (C-2) molecular structure was indeed no longer representative of the initial structure inside the apple (C-1) matrix, thus preventing any establishment of a direct link between the two matrices and their respective exchangeability parameters.

(

  ) parameter. This phenomenon has been confirmed by the extremely low NE-OBT recovery rate onto C-2 from C-1 (i.e. 47 ± 11% of recovery rate vs. a weight distribution of 88.2 ± 5.9%), since part of the measured NE-OBT on apple (C-1) was actually buried tritium (hindered tritium form) and freed during the molecular structure modification of simple carbohydrates (C-2). Consequently, this freed buried tritium recovered its exchangeability capacities and behaved like E-OBT, thus ultimately leading to a lower value of NE-OBT measured after isotopic exchange depletion in simple carbohydrates (C-2) compared to their mass distribution in C-1.

Acknowledgments

This work was financed by the CEA Research Center, Subatech Laboratory, France's Loire Valley Regional Council (under the POLLUSOLS OSUNA Project) and the EDF utility company. The authors would also like to thank the members of the Environmental Laboratory

Discussion

The impact of molecular structure on hydrogen exchangeability

Among all the matrices studied, only wheat grains (Matrix A-1) and their extracted starch (Matrix A-2) presented both isotopic exchangeable parameter results (( ) = 31.0 ± 1.0%

and ( ) = 31.1 ± 1.0%, respectively) similar to their calculated theoretical exchangeable parameters (( ) = 30.0% and ( ) = 31.6%, respectively). Wheat grains are mainly composed of starch, a macromolecule comprising 25% amylose (α(1→4) bound glucose molecules) and 75% amylopectin (α(1→4) bound glucose molecules branched with α(1→6) bound glucose molecules) [START_REF] Sakintuna | Hydrolysis of freshly prepared wheat starch fractions and commercial wheat starch using a-amylase[END_REF]. These glucose polymers exhibit wellknown linear and helical molecular structures with a predominantly weak crystalline area and only a few intermolecular hydrogen bonds [START_REF] Tester | Starch composition, fine structure and architecture[END_REF]. It can then be assumed that the analytical point of view (i.e. based on chemical bond type) is well suited and adequate to describe OBT speciation and behavior for this specific type of environmental matrix molecular structure.

In contrast, results obtained on the other matrices studied (B-1 and C-1) showed disparities between the calculated exchangeable parameter ( ) and the isotopic exchangeable parameter ( ) obtained from the vapor phase (T/H) isotopic exchange experiment.

According to the state-of-the-art, the first hypothesis implies that this difference is correlated with the presence of buried tritium due to the explanation of the exchangeability phenomenon inertia derived from the local 3D structure. For this reason, such compounds are particularly prized.

Water-milfoil (Matrix B-1) yielded an isotopic exchangeable parameter (( 42% --37.3 (±2.7) 25.1 (±2.7) --Fat < 0.1% 3.0 (±0.9) -3.2 (±1.3) 0.2 (±0.9) 0.9 (±0.9) -

Table 2:

The main essential components analyzed along with their associated theoretical ( ), and measured/analyzed distribution in % by weight in wheat grains (A-1), starch (A-2), water-milfoil (B-1), cellulosic wall (B-2), apples (C-1) and simple carbohydrates (C-2) matrices. (i) and (ii) are representative of wheat grains and water-milfoil protein types, respectively.

( 33.1 (±3.6) (i) 33.1 (±2.6) (i) 19.7 (±1.6) -