Shengli Chen
email: shengli.chen@cea.fr

David Bernard

Laurent Buiron

Study on the self-shielding and temperature influences on the neutron irradiation damage calculations in reactors

Keywords: Self-shielding, DPA, Recoil energy, Doppler effect, ASTRID

Introduction

The neutron irradiation induced embrittlement is one of the major materials challenges of the Reactor Pressure Vessels (RPV) [START_REF] Zinkle | Materials challenges in nuclear energy[END_REF] due to the change of mechanical behaviors by irradiation. The Displacement per Atom (DPA) defines the average number displacements of each atom under irradiation. It is one of the key parameters to measure the irradiated damage. The lifetime of the current water reactors is mainly determined by the accumulated DPA number of the RPV. For fast neutron reactors, the cycle length depends on the DPA. In sodium-cooled fast reactors, the DPA in the fuel cladding is more important than that of the reactor vessel because of the shielding by fertile layer, reflector, and large volume of sodium (and in-vessel neutron shielding in ASTRID [START_REF] Chenaud | Status of the ASTRID core at the end of the pre-conceptual design phase 1[END_REF]) between the inner core and the reactor vessel.

When kinematic particles knock-on an atom in materials, a Frenkel pair (an atomic vacancy combined with an interstitial) is formed. The knocked-on atom is able to induce more crystallographic defects through atomic displacement cascades. Various models have been developed to compute the average DPA number using the Primary Knockon Atom (PKA) energy as a major parameter, including Molecular Dynamics (MD) simulations and the classical DPA formulae. Many works performed with MD simulations show that the DPA depends on temperature (decreases with temperature due to the increase of recombination of displaced atoms with irradiation temperature) [START_REF] Gao | A molecular dynamics study of temperature effects on defect production by displacement cascades in α-iron[END_REF]- [START_REF] Stoller | Primary Radiation Damage Formation[END_REF]. Gao's work shows about 20%-30% decrement of DPA as the irradiation temperature increases from 100 K to 900 K for α -iron [START_REF] Gao | A molecular dynamics study of temperature effects on defect production by displacement cascades in α-iron[END_REF]. However, Phythian concluded the weak dependence of residual defects on temperature for the copper and iron [START_REF] Phythian | A comparison of displacement cascades in copper and iron by molecular dynamics and its application to microstructural evolution[END_REF]. Phythian's conclusion on iron is later verified by Stoller [START_REF] Stoller | The role of cascade energy and temperature in primary defect formation in iron[END_REF]. The present work investigates the temperature effects on DPA by considering the influence of irradiation temperature on recoil energy and Doppler broadening.

For computation of DPA rates in reactors, the typical method is using DPA cross sections and the corresponding spectra of incident particles. Neutron-induced DPA cross sections are calculated with nuclear data by processing codes as NJOY [START_REF] Macfarlane | Methods for Processing ENDF/B-VII with NJOY[END_REF]. The corresponding spectra of incident particles are determined by the transport codes. The two above-mentioned effects of the temperature: (i) the influence on PKA energy due to the thermal vibration of atoms (i.e. exit channel Doppler broadening), and (ii) Doppler broadening of reaction cross sections (i.e. entrance channel Doppler broadening) are considered in the calculation of DPA cross sections. The dependence of spectra on temperature is automatically taken into account in transport codes.

In the compound nucleus theory, the reaction cross section has a peak value when the energy of the compound system is close to one of the excited levels of the compound nucleus. This phenomenon is referred to resonance. Due to the huge cross section in the vicinity of resonance energy, the corresponding neutron spectrum has a local valley at the same energy band. This is the resonance self-shielding, referred simply hereinafter to self-shielding. In deterministic neutron transport codes, due to the finite background cross section at resonance energies, one has to decrease resonant cross sections within the multi-group formalism. This leads to an increase of the multi-group neutron flux at resonant energies to conserve the reaction rate. Many methods have been proposed to treat the self-shielding in the deterministic codes. However, the self-shielding effect is rarely treated in DPA calculations, while DPA is one of the most important characters to measure the properties of materials under irradiation. The present work studies the influence of self-shielding on DPA calculations.

The Stainless Steel (SS) is widely used in the nuclear industry, such as the reflector and the RPV in Light Water Reactors (LWRs), fuel cladding of fast reactors. Recent studies also show that the SS can be a potential fuel cladding material for Accident Tolerant Fuel (ATF) in LWRs [START_REF] Chen | Neutronic Analysis on Potential Accident Tolerant Fuel-Cladding Combination U3Si2-FeCrAl[END_REF], [START_REF] Chen | Radial distributions of power and isotopic concentrations in candidate accident tolerant fuel U3Si2 and UO2/U3Si2 fuel pins with FeCrAl cladding[END_REF]. The abundance of 56 Fe in natural iron is 91.75%, while iron is the main element in SS. Therefore, the numerical results shown in the present work are based on 56 Fe. The neutronic calculations are performed with the deterministic code ERANOS-2.3 [START_REF] Ruggieri | ERANOS 2.1: International Code System for GEN IV Fast Reactor Analysis[END_REF]. The calculations of DPA rates are based on the fuel cladding of the inner core in the Advanced Sodium Technological Reactor for Industrial Demonstration (ASTRID) [START_REF] Chenaud | Status of the ASTRID core at the end of the pre-conceptual design phase 1[END_REF]. All simulations are based on the JEFF-3.1.1 nuclear data library [START_REF] Santamarina | The JEFF-3.1.1 Nuclear Data Library[END_REF]. The DPA cross sections are computed with the modified HEATR module in NJOY-2016.20 [START_REF] Macfarlane | The NJOY Nuclear Data Processing System, Version 2016[END_REF]. The modification in HEATR module for DPA calculations is described in Ref. [START_REF] Chen | Irradiation Damage Calculation with Angular Distribution[END_REF]: the second "stair" in DPA metrics (c.f. Section 2.1: 1 DPA for damage energy between and 2.5 ) is added, while the formula above 2.5 is used by NJOY in this interval.

Methods

DPA metrics

In nuclear reactor applications, the DPA metrics are used to compute the DPA cross sections. Based on elastic scattering among hard spheres, Kinchin and Pease proposed the KP-DPA in 1955 [START_REF] Kinchin | The Displacement of Atoms in Solids by Radiation[END_REF]. The current international standard is the Norgett-Robinson-Torrens (NRT)-DPA model [START_REF] Norgett | A proposed method of calculating displacement dose rates[END_REF]:

= 0, 0 < < 1, < < 2 /0.8 . , 2 /0.8 < < ∞ , (1)
where is the Lindhard's damage energy [START_REF] Lindhard | Integral equations governing radiation effects[END_REF], is the angle-averaged threshold energy of atomic displacement, and the constant coefficient 0.8 is deduced from the Binary Collision Approximation (BCA) calculations [START_REF] Robinson | Computer simulation of atomic-displacement cascades in solids in the binary-collision approximation[END_REF]. The damage energy is computed with the PKA kinetic energy by = × / , where is the partition function that measures the fraction of left in atomic motion (1represents the fraction of energy lost to electronic excitation) [START_REF] Robinson | Energy Dependence of Neutron Radiation Damage in Solids[END_REF]:

= 1/[1 + #$3.4008 '/( + 0.40244 )/* + +, (2)
where # = 0.133745. /) / 0'/ , = / with = 86.931. 3/) (in eV), Z and A are respectively the atomic number and the atomic mass number. The average threshold energy for the iron isotopes is 40 eV [START_REF]Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA), E706[END_REF].

However, the NRT model overestimates the atomic displacement [START_REF] Averback | Ion-irradiation studies of the damage function of copper and silver[END_REF]. Taking the athermal recombination of displaced atoms into account, the Athermal Recombination-Corrected (ARC)-DPA is proposed [START_REF] Nordlund | Improving atomic displacement and replacement calculations with physically realistic damage models[END_REF]:

= 0, 0 < < 1, < < 2 /0.8 . 4 , 2 /0.8 < < ∞ , (3)
where

4 = 1 -5 × 6 . 7 8 + 5, (4)
where b and c are fitting coefficients. Assuming = 40 eV, Ref. [START_REF] Nordlund | Improving atomic displacement and replacement calculations with physically realistic damage models[END_REF] recommends 5 = 0.286 and 9 = -0.568 for iron isotopes according to molecular dynamics simulations.

Recoil energy of PKA

The recoil energy of PKA is fundamental for DPA calculations. Figure 1 shows the scheme of the collision in the Laboratory (Lab) frame. The incident and emitted kinetic energies are referred to E and E', respectively. ER stands for the recoil energy of the target nucleus. m and v (m' and v') are respectively the mass and velocity of the incident (outgoing) particle. The kinetic energy of the target is set to 1.5kT, which is the average kinetic energy for particles with temperature T. # = 8.617 × 10 0D eV/K is the Boltzmann constant. G denotes the angle of the target due to thermal vibration. The angle between the velocity of Center-of-Mass (CM) and the incident direction is denoted by H . The emission angle is referred to I . The emission angle in the CM frame is noted as I J . (7) At low incident energies, the emission in the CM I J is supposed to be isotropic. At high energies, the angular distribution can be found in Evaluated Nuclear Data Files (ENDF), which often gives the distribution of I J . The angular distribution of I can be determined by that of I J and H because I = I J + H . The conservation of momentum before collision leads to: (

OP + QP R cos G = O + Q P VW cos H, (8)
) 11
The recoil energy depends on the angle of thermal vibration G. However, it is not so important to study the dependence of recoil energy on G because the latter has to be random. The random value of G leads to the isotropic angular distribution. Therefore, the recoil energy averaged over G is investigated. The isotropic angular distribution of G conducts to:

M , K, I J = ' g M , K, I J , G h cos G ' 0' . ( 12
)

DPA calculations in reactors

The DPA rate induced by a particle other than atoms in the material is calculated by:

i / = g ∑ . × k l ,m n m o m p h q , (13)
where the index i reveals the reaction types, such as elastic scattering and inelastic scatterings. n m is the cross section of the reaction i at energy E, p refers to the flux of incident particle, and l ,m is the corresponding damage energy computed by:

l ,m = g , I J 4$ , I J +r , I J hI J s , (14)
where the displacement efficiency 4 = 1 for NRT-DPA and Eq. ( 4) for ARC-DPA, r , I J is the angular distribution for the emission particle. More details can be found in Ref. [START_REF] Chen | Irradiation Damage Calculation with Angular Distribution[END_REF] and [START_REF] Chen | Calculation and Verification of Irradiation Damage Cross Section with Energy-Angular Distribution[END_REF] for discrete reaction channels and continuum reactions, respectively.

In a reactor core, the upper limit of the integral in Eq. ( 13) is 20 MeV. n t ,m = l ,m n m is the DPA cross section (in barn.eV) induced by the reaction type i at incident energy E as shown in Figure 6, which illustrates the total, elastic scattering, total inelastic scattering, and disappearance DPA cross sections (MT444, MT445, MT446, and MT447, respectively) for 56 Fe at 293.15 K. The disappearance DPA cross section is the sum of DPA caused by reactions without neutron emission, i.e. reactions from MT102 to MT120. For 56 Fe in JEFF-3.1.1, only the cross sections from MT102 to MT107 are evaluated. The processing and the reliability of the elastic and discrete inelastic scatterings (continuum inelastic scattering, respectively) with nuclear data are investigated in Ref. [START_REF] Chen | Irradiation Damage Calculation with Angular Distribution[END_REF] (Ref. [START_REF] Chen | Calculation and Verification of Irradiation Damage Cross Section with Energy-Angular Distribution[END_REF], respectively). The disappearance signifies no neutron emission after reaction, such as (n,u), (n,p), and (n,I) reactions. It is noticeable that the DPA rates induced by reactions excluded in MT445-447, e.g. (n,2n) and (n,np), are quite neglectable (values shown in the caption of corresponding figures of DPA rates).

Figure 2 illustrates the different routines of DPA calculations. Eq. ( 13) is the method of DPA calculation without considering the self-shielding correction (green scheme in Figure 2). As mentioned in Section 1, both cross sections and neutron flux are modified in deterministic codes due to the self-shielding treatment. The DPA rate after the correction of self-shielding is calculated by:

i / = g ∑ . × k l ,m n v m o m p w h Wxy , (15)
where n v and p w represent cross sections and neutron flux with the correction of selfshielding. The neutron flux mentioned in the following description is the neutron flux after the correction of self-shielding, p will be thus used rather than p w to simplify the notation. Hence, the DPA rate can be calculated by:

i / = . × g ∑ n t ,m z { | z | m p h Wxy . ( 16
)
Discretizing the integral to the sum of multi-group structure:

i / = . × ∑ ∑ n t ,m,} z { |,z |,m p } • }€' . ( 17
)
where G is the number of groups, n v m,} denotes the self-shielding corrected multi-group reaction cross section. This method corresponds to the red routine illustrated in Figure 2. In order to evaluate the accuracy of self-shielding corrections based on 33-group structure, an additional scheme shown in Figure 2 by blue dashed symbols is used in the present work. Using the multi-group neutron flux p } and self-shielding corrected cross sections n v m,} calculated by transport code in a finer structure (ECCO 1968-group in our studies), we compute 33-group neutron flux by summing neutron flux of which the group j in the finer structure is included in group J of 33-group. The deduced 33group cross sections are obtained by conserving the same reaction rates.

In the following studies, the infinite dilution multi-group cross sections n m,} and n t ,m,} are computed by the GROUPR module in NJOY2016.20 with the weighting function iwt8 (i.e. thermal --1/E --fast reactor --fission & fusion). The self-shielding corrected multi-group cross sections n v m,} are calculated by ECCO, of which the methods of self-shielding calculations are presented in Ref. [START_REF] Rimpault | Validation of new sub-group algorithms for resonance self-shielding in heterogeneous structures[END_REF].

Results and Discussion

Influence of temperature on recoil energy

Figure 3 shows the average recoil energy of 56 Fe for 100 eV, 500 eV, 1 keV, and 5 keV energy neutron elastic scattering with different temperatures. The influence of temperature is more important at lower incident energy. However, due to the threshold energy of atomic displacement, the temperature effect on recoil energy has no influence on DPA computation when the recoil energy is lower than or 2.5 2 /0.8 . For neutron elastic scattering shown in Figure 3, different temperatures of 56 Fe have the same DPA number (0 DPA) for incident energy lower than 500 eV. For 1 keV neutron, the maximum recoil energy is higher than but lower than 2.5 . Therefore, the DPA number does not change with the temperature. For high incident neutron that the recoil energy of 56 Fe can be higher than 2.5 . However, the temperature effect on recoil energy is negligible because of the quite small contribution of the kinetic energy of target (1.5kT = 0.2 eV when T = 1500 K) before collision, as shown in Figure 3 (d). The average recoil energies with different incident energies and different temperatures are given in Table I. Both Figure 3 and Table I shows that the consideration of the thermal vibration of the target has neglectable influence on DPA computations. By consequence, the DPA cross sections computed by NJOY without considering thermal vibration of the target can be directly used. Reaction cross sections depend on the temperature of the material because of the Doppler broadening. Figure 4 shows the total, elastic scattering, inelastic scattering, and capture cross sections (MT1, MT2, MT4, and MT102, respectively) at the reference temperature 293.15 K on the ECCO 1968-group mesh. The ratios of corresponding cross sections at 1500 K to those at 293.15 K (i.e. n m,} 1500 K / n m,} 293.15 K ) for 56 Fe are shown in Figure 5. The ratios higher than unity because the Doppler broadening enlarges the width (> 1 at two wings of resonances), while the lower than unity ratios are due to the decrease of the peak value (< 1 at centers of resonances). No difference is observed at neutron energy E higher than 1 MeV. The Doppler effect has a strong influence on the resonances of capture cross sections in 1 keV < E < 1 MeV, but it influences much less the total cross sections because the elastic scattering is the dominant reaction from 1 keV up to 1 MeV. Only at 1 keV the Doppler effect is important for the total cross section due to the strong resonance of the capture cross section.

The Doppler effect is more important at lower energy due to larger perturbation of relative velocity. However, Figure 5 shows that the Doppler effect does not change the capture cross section at low energy. Although the dependence of elastic scattering cross section on temperature is evident, the variation of elastic scattering cross section at low energy does not influence the DPA cross sections because the corresponding recoil nuclei or atoms have energies lower than the threshold energy of displacement. Figure 7 reveals the ratios of DPA cross sections at 1500 K to those at 293.15 K. Same as nuclear cross sections, the Doppler effect has the most important influence on total DPA cross section at 1 keV, at which the capture reaction dominates. Except for this point, the total DPA changes less than 5%, so the DPA should not be sensitive to the temperature. This can be further verified in Figure 8 with ECCO 33-group mesh that only the DPA cross section MT447 changes -0.02% between 0.1 MeV and 1 MeV when the temperature increases from 293 K to 1500 K. In addition, the contribution of MT447 to total DPA is negligible in this region (see Sections 3.3 and 3.4). Section 3.1 shows that the temperature effect on the recoil energy has neglectable influence on DPA calculations. Only the Doppler effect as illustrated in Figure 7 is considered to show the temperature dependence in ASTRID application. In order to evaluate the influence of Doppler broadening on DPA rate, the example of the 56 Fe in the fuel cladding of the ASTRID inner core is taken. The results are given in Figure 9. As expected, the Doppler broadening is negligible for the calculation of DPA. The Doppler broadening has 0.004% contribution to DPA rate in ASTRID inner core when the temperature changes from 748 K to 1500 K. 748 K and 1500 K are the temperatures of fuel cladding and fuel, respectively. Therefore, the temperature effects are not taken into account in the following studies on DPA rates calculations.

Verification of self-shielding correction

In order to validate the method of self-shielding treatment during DPA calculation with coarse energy grids, the DPA rates computed with ECCO 1968-group and the deduced 33-group calculation (dashed scheme in Figure 2) are compared. The lattice calculations are performed to compute ECCO 1968-group neutron spectrum and selfshielding corrected cross sections. Figure 10 shows the ECCO 1968-group correction coefficients for the total, elastic scattering, total inelastic scattering, and disappearance cross sections. The corresponding reaction cross sections are shown in the same subfigures to show the resonance self-shielding. The self-shielding corrections on cross sections can be observed in Figure 10 for most resonances. It is noticeable that the small correction coefficients do not mean that the selfshielding is not important at these resonances. In contrast, some of these resonances are so important that the neutron flux is strongly influenced. Because of the strong influence, the self-shielding corrections are directly accounted in the neutron flux. The valley of the neutron spectrum at 28 keV (shown in Figure 11), which is induced by the strong elastic scattering resonance of 56 Fe, is typical for fast reactors. Same phenomena can be found for the two big resonances of elastic scattering at 74 keV and 84 keV. The relative accumulated DPA, accumulated self-shielding corrections of DPA, and self-shielding corrections in each group are shown in Figure 12 for 1968-group calculations. Except the correction at 1.15 keV for the (n,u) reaction, the self-shielding corrections on DPA rates are not found in Figure 12 at incident energies below 50 keV. This is due to the direct corrections on neutron flux, while our calculations with and without self-shielding consideration utilize always the self-shielding corrected neutron spectrum. The self-shielding corrections of cross sections are important for DPA rate at incident energies between 50 keV and 5 MeV.

Figure 13(a) illustrates the DPA rates in the fuel cladding in the ASTRID inner core (lattice calculation) without and with the correction of self-shielding. It is noticeable that the DPA rate induced by reactions other than MT445-447 is only 0.002 DPA/year. Because of the high threshold energies of reactions and the negligible contributions on total DPA, reaction channels excluded in MT445-447 are not treated in self-shielding corrections of PDA rates. The neutron spectrum is the normalized 1968-group spectrum (blue line in Figure 11) multiplied by the total neutron flux of the 33-group spectrum determined in full core calculations (red line in Figure 11). The yellow bars show the negative corrections on DPA rates taking the self-shielding into account. It is noticeable that the DPA computed with total cross sections is less than the sum of three partial values after the self-shielding correction because of the different self-shielding corrections on different cross sections. Therefore, attention should be paid for total DPA rates computed with total DPA cross sections, such as the recent DPA cross sections provided by the Nuclear Energy Agency (NEA) [START_REF]JEFF-3.3/DPA: Atomic displacement (radiation damage) cross sections[END_REF].

As pointed out in Figure 13(a), 2.1% relative elastic scattering induced DPA rate is reduced by taking the self-shielding into account. The relative reduction of inelastic scattering is less important due to the null resonant cross section before the threshold energy of reactions. 2.1% total DPA is reduced due to the self-shielding treatment of cross sections with ECCO 1968-group. In order to evaluate the accuracy of self-shielding corrected DPA rate based on the ECCO 33-group structure, the calculations illustrated by the dashed scheme in Figure 2 are performed. The result based on 33-group computations are given in Figure 13(b). The self-shielding correction on the disappearance DPA rate is less (more respectively) important than the elastic scattering in 1968-group (33-group respectively). The reason is that the self-shielding corrections on disappearance cross section end at 1 MeV in 1968-group calculations (Figure 12), while the corrections continue to the last group in the deduced 33-group calculations. The correction on inelastic scattering is always less important than those on elastic scattering due to the lack of resonant cross sections in JEFF-3.1.1.

In fact, these correction coefficients used Eq. ( 17) are not only due to (i) the selfshielding treatment of cross sections but also (ii) the deviations of multi-group cross sections induced by a general weighting function used in NJOY GROUPR module (orange line in Figure 11). For sufficiently fine mesh such as the ECCO 1968-group, the multi-group cross sections are weighted in a small interval of the resonance, the corrections (ii) of cross sections induced by different weighting function are almost negligible. Due to the fine energy structure, the calculations performed with 1968-group energy structure are considered as standard computations of self-shielding.

Comparing two results shown in Figure 13, it is observed that before the treatment of self-shielding, the DPA rates computed with 33-group are quite different to the reference 1968-group calculations. However, good agreement is shown between the 33group and the 1968-group calculations after the correction of self-shielding. The correspondence of self-shielding corrected DPA rates between 1968-group calculations and 33-group results shows that the self-shielding proposed in Section 2.3 is valid for ECCO 33-group. In addition, the self-shielding should be taken into account for DPA calculations, especially for coarse energy structures, due to the correction (ii) induced by different weighting functions for computing multi-group cross sections.

3.4 DPA rate in the fuel cladding in ASTRID inner core Section 3.3 shows that the 33-group structure is suitable to perform the calculation of DPA rates. The full core calculation of ASTRID is performed to compute the ECCO 33-group neutron spectrum and the self-shielding corrected cross sections. The layout of the ASTRID core is shown in Figure 14. The present work aims to compute the DPA rates for the fuel cladding of ASTRID inner core, which is the yellow region pointed out in Figure 14. The corresponding neutron spectrum is shown in Figure 11 by the red line. Figure 15 illustrates the 33-group correction coefficients for the total, elastic scattering, total inelastic scattering, and disappearance cross sections.

The relative accumulated DPA rates, the accumulated self-shielding corrections of DPA rates, and the self-shielding corrections in each group are shown in Figure 16 for the above-mentioned four reactions. Figure 16 shows that the self-shielding between 25 keV and 6 MeV is most important in DPA calculations. Out of this band, the selfshielding corrections of cross sections and DPA calculations are weak due to few resonances and low neutron flux. The energy band of the self-shielding corrections of cross sections in 1968-group lattice calculations ([50 keV, 5 MeV] shown Figure 12) is included in the correction interval of 33-group full core calculations ([25 keV, 6 MeV] shown Figure 16). For 1968-group, the higher energy of the lower limit of correction is due to the direct correction on neutron flux at low energies at which the resonances are too strong. The lower energy of upper limit of correction is due to fine group mesh while the multigroup cross sections are averaged over a fluctuated flux (see Figure 11) for a coarse mesh such as the ECCO 33-group energy structure.

Figure 17 illustrates the DPA rates in the fuel cladding in the ASTRID inner core without and with the self-shielding corrections of cross sections. The yellow bars point out the negative corrections on DPA calculations taking the corrections of cross sections into account. Same as the results found in Section 3.3, the DPA computed with total cross sections is less than the sum of three partial values after the self-shielding correction because of the different self-shielding corrections on different cross sections. 11% relative elastic scattering induced DPA rate is reduced by taking the self-shielding into account. Because inelastic scattering channels are closed below the minimum threshold energy of 862 keV, the self-shielding corrections in the resonance region below 862 keV have no influence on DPA induced by inelastic scatterings. Therefore, the relative reduction of inelastic scattering is less important than the one of elastic scattering. The self-shielding effect on the disappearance reactions induced DPA is important, but its contribution to total DPA is negligible. 10% total DPA is reduced due to the self-shielding treatment in ECCO 33-group full core calculations. The selfshielding corrected DPA rate is 25 DPA/year, of which 81.9%, 18.0%, and 0.1% are induced by elastic scattering, inelastic scatterings, and disappearance reactions, respectively.

Conclusions

DPA is one of the most important parameters that measure the irradiation damage of materials during and after irradiation. DPA is conventionally computed using the DPA cross sections and neutron spectra in reactors. The temperature influences the DPA cross sections through the PKA energy due to the thermal vibration of atoms and the Doppler broadening of reaction cross sections. The influence of the temperature on PKA energy is important at low incident energy. However, low incident energy leads to low PKA energy. Due to the threshold energy of atomic displacement, the temperature has no effect on DPA calculation for low incident energies. For high incident energy, the temperature effect on PKA energy is negligible because the kinetic energy of PKA before collision (1.5kT) is too small compared with the incident energy. Consequently, the temperature effect on PKA energy does not change the DPA calculations.

The Doppler effect depends on the resonances of the recoil nucleus. For 56 Fe, the Doppler broadening has limited influence on DPA cross sections because of small influence on scattering cross sections above the threshold energies shown in Figure 6. The application in the fuel cladding in the ASTRID inner core shows that the Doppler broadening has less than 0.01% contribution on final DPA computations. Therefore, the temperature dependence of DPA cross sections is negligible for 56 Fe.

The self-shielding effects are studied for DPA calculations with both ECCO 1968group and the deduced 33-group calculations. The reduction of total DPA due to the correction of cross sections is from both (i) the self-shielding treatment of cross sections and (ii) the deviations of multi-group cross sections induced by a general weighting function in NJOY GROUPR calculations. The self-shielding correction (i) is required only for the deterministic methods, while the correction (ii) exists in both deterministic and stochastic methods. The good agreement between corrected DPA rates computed with the two energy structures validates the accuracy of ECCO 33-group based DPA calculations. Large discrepancies are observed between two structures calculations without self-shielding treatment. This points out that Eq. ( 17) should be used to compute DPA rates rather than direct calculations with NJOY processed multi-group DPA cross sections, especially for coarse energy structures, whereas the comparisons between 1968-group and the deduced 33-group calculations show that the correction (ii) is much more important than the correction (i) for the 33-group calculations.

Both 33-group full core calculation and 1968-group lattice calculation show that the corrections on total cross sections cannot give the same result as the sum of all the corrected partial DPA rates. 2.3% difference is found between the DPA rate computed with total cross sections and the sum of DPA rates calculated with partial cross sections in 33-group full core calculations. Therefore, attention should be paid for DPA rates calculated with total DPA cross sections, such as the DPA cross sections provided by NEA. The recommended method to compute DPA is the calculation of each reaction using Eq. ( 17), especially for coarse energy structures. The full core calculations of 56 Fe show that the relative reductions off DPA rates due to the corrections on multi-group cross sections are respectively 11.3%, 5.9%, and 20.5% for elastic scattering, inelastic scatterings, and disappearance reactions. These lead to 10.4% correction on total DPA rate. The corrected DPA rate in the fuel cladding of ASTRID reactor is about 25 DPA/year using the NRT-DPA metric. The neutron elastic, inelastic scatterings, and the disappearance reactions induced DPA rates contribute respectively 81.9%, 18.0%, and 0.1% on total DPA rate.

Figure 1 .

 1 Figure 1. Scheme of the collision in the Laboratory frame

Figure 2 .

 2 Figure 2. Flowchart of DPA calculations without (green) and with (red) self-shielding corrections. The dashed scheme is only for the verification of ECCO 33-group calculations by using multi-group cross sections and flux computed with transport code with finer energy structure (ECCO 1968-group in this paper).

Figure 3 .

 3 Figure 3. Average PKA energy of 56 Fe for 100 eV, 500 eV, 1 keV, and 5 keV incident neutrons with different temperatures of the target

Figure 4 .

 4 Figure 4. Total, elastic, inelastic, and capture cross sections of 56 Fe at 293.15 K.

Figure 5 .

 5 Figure 5. Ratios of cross sections at 1500 K to those at 293.15 K.

Figure 6

 6 Figure 6 illustrates the total, elastic scattering, total inelastic scattering, and disappearance DPA cross sections at 293.15 K. At neutron energy lower than 500 eV, only the disappearance can induce the displacement of atoms because the target nucleus

Figure 6 .

 6 Figure 6. Total, elastic, inelastic, and disappearance DPA cross sections at 293.15 K.

Figure 7 .

 7 Figure 7. Ratios of DPA cross sections at 1500 K to those at 293.15 K.

Figure 8 .

 8 Figure 8. Ratios of DPA cross sections at 1500 K to those at 293.15 K in ECCO 33group energy structure.

Figure 9 .

 9 Figure 9. DPA rate (DPA/year) of 56 Fe in the ASTRID inner core fuel cladding computed with and without self-shielding treatment and different temperatures. DPA rate induced by reactions other than MT445-447 is 0.002 DPA/year.

Figure 10 .

 10 Figure 10. 1968-group correction coefficients for the total, elastic, total inelastic, and disappearance (sum of MT102 to MT120) cross sections versus incident neutron energy. The grey curves are corresponding relative reaction cross sections.

Figure 11 .

 11 Figure 11. Normalized neutron spectra for NJOY-iwt8, lattice calculation (blue) and full core calculation (red) flux in ASTRID inner core, and the relative elastic scattering cross section of 56 Fe.

Figure 12 .

 12 Figure 12. Self-shielding effects with 1968-group energy structure. DPA stands for the relative DPA rate without self-shielding treatment. i / • refers to the self-shielding corrected DPA rate. i / -i / • represents the reduction of DPA due to selfshielding, normalized by its integration over whole energy.

Figure 13 .

 13 DPA rates (in DPA/year) in the fuel cladding in ASTRID computed with ECCO 1968-group energy structure (a) and the deduced ECCO 33-group calculations (b) illustrated in Figure 2. The absolute neutron spectrum is obtained by multiplying the lattice 1968-group normalized flux and the total flux of full core calculation. The DPA rates of MT447 are multiplied by 100 by the negative corrections are original.

Figure 14 .

 14 Figure 14. Layout of ASTRID core (3-fold rotational symmetry)

Figure 17 .

 17 Figure 17. DPA rates (in DPA/year) in the fuel cladding in ASTRID inner core computed with ECCO 33-group full core calculations. DPA rate induced by reactions other than MT445-447 is 0.0098 DPA/year.

Table I .

 I Average recoil energy (in eV) of56 Fe for 100 eV, 500 eV, 1 keV, 5 keV, and 10 keV incident neutron elastic scattering with different temperature

	E	100 eV	500 eV	1 keV	5 keV	10 keV
	10 K	3.52	17.61	35.22	176.09	352.11
	293 K	3.56	17.65	35.25	176.12	352.15
	1500 K	3.71	17.80	35.41	176.25	352.37


Kevin Vidot
email: kevin.vidot@inra.fr

Marie-Françoise Devaux
email: marie-francoise.devaux@inra.fr

Camille Alvarado
email: camille.alvarado@inra.fr

Sylvain Guyot
email: sylvain.guyot@inra.fr

Frédéric Jamme

Cédric Gaillard
email: cedric.gaillard@inra.fr

René Siret
email: r.siret@groupe-esa.com

Marc Lahaye
email: marc.lahaye@inra.fr

Frederic Jamme
email: frederic.jamme@synchrotron-soleil.fr

Phenolic distribution in apple epidermal and outer cortex tissue by multispectral deep-UV autofluorescence cryo-imaging

Keywords: Malus domestica, phenolic compounds, autofluorescence, multispectral imaging, deep-UV synchrotron light, cryo-microscopy

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

Introduction

Phenolic compounds are common plant secondary metabolites that have been grouped into three classes: flavonoids, phenolic acids and stilbenes [START_REF] Vermerris | Phenolic compound biochemistry[END_REF]. The flavonoids encompass flavanols that are also found as oligomers and polymers (i.e., proanthocyanidins and condensed tannins), anthocyanins and flavonols, while phenolic acids comprise hydroxybenzoic acids and hydroxycinnamic acids (Figure 1). Except for flavanols and hydroxybenzoic acids, which are mainly present in their free form, most phenolic compounds are glycosylated and/or acylated derivatives. Their ultraviolet absorption capacity limits lightinduced damage to tissues while they are part of plant defence mechanisms against external biotic stresses [START_REF] Solovchenko | Optical properties and contribution of cuticle to UV protection in plants: experiments with apple fruit[END_REF][START_REF] Edreva | The importance of non-photosynthetic pigments and cinnamic acid derivatives in photoprotection[END_REF]. In fleshy fruit, phenolic compounds are known for their antioxidant contribution to foods and organoleptic properties, such as colour, astringency or bitterness [START_REF] Williamson | The role of polyphenols in modern nutrition[END_REF][START_REF] Finley | Principles of food chemistry[END_REF][START_REF] Kschonsek | Polyphenolic compounds analysis of old and new apple cultivars and contribution of polyphenolic profile to the in vitro antioxidant capacity[END_REF]. Various studies in apple and grape have shown important differences in phenolic content between varieties according to fruit development and tissue [START_REF] Macheix | Fruit Phenolics[END_REF]. Phenolic compounds are commonly characterized by biochemical techniques on whole fruit, skin, flesh, seed or juice extracts. However, there are few reports on the distribution of specific phenolic compounds at the tissue and sub-cellular scales under in-vivo-like conditions. Flavanols and condensed tannins were determined to be localized in the epidermis, parenchyma and seeds by microscopy of fresh or chemically fixed apple [START_REF] Lees | Localization of condensed tannins in apple fruit peel, pulp, and seeds[END_REF], grape [START_REF] Joutei | Localisation des tanins dans la pellicule de baie de raisin[END_REF][START_REF] Cadot | Evolution of the localisation and composition of phenolics in grape skin between veraison and maturity in relation to water availability and some climatic conditions[END_REF] and other fruits [START_REF] Essig | A Systematic histological study of palm fruits. I. The Ptychosperma Alliance[END_REF][START_REF] Yonemori | Fine structure of tannin cells in fruit and callus tissues of persimmon[END_REF][START_REF] Raymond | Internal breakdown in mango fruit: symptomology and histology of jelly seed, soft nose and stem-end cavity[END_REF][START_REF] Hammouda | Tissue and cellular localization of tannins in tunisian dates (Phoenix dactylifera l.) by light and transmission electron microscopy[END_REF].

Flavanols were localized by DMACA staining (4-dimethylaminocinnamaldehyde) [START_REF] Hammouda | Tissue and cellular localization of tannins in tunisian dates (Phoenix dactylifera l.) by light and transmission electron microscopy[END_REF][START_REF] Mayr | Phenolic compounds of apple and their relationship to scab resistance[END_REF][START_REF] Cadot | Flavan-3-ol compositional changes in grape berries (Vitis vinifera L. cv Cabernet Franc) before veraison, using two complementary analytical approaches, HPLC reversed phase and histochemistry[END_REF] while flavonols were highlighted by fluorescence microscopy using the specific dye DPBA (diphenylboric acid-2-aminoethyl ester) [START_REF] Peer | Flavonoid accumulation patterns of transparent testa mutants of Arabidopsis[END_REF][START_REF] Vidot | Cryo-laser scanning confocal microscopy of diffusible plant compounds[END_REF]. However, chemical preparation damage to fleshy fruit tissue integrity affects the cellular localization of diffusible compounds [START_REF] Moore | Combined NanoSIMS and synchrotron X-ray fluorescence reveal distinct cellular and subcellular distribution patterns of trace elements in rice tissues[END_REF], and dyes are limited by their specificities.

To address these issues, mapping phenolic compounds through their autofluorescence characteristics appears to be a good alternative as no specific stain is required.

Hydroxycinnamic acids express a blue fluorescence when excited at the UV wavelength of approximately 350 nm [START_REF] Harris | Detection of bound ferulic acid in cell walls of the Gramineae by ultraviolet fluorescence microscopy[END_REF][START_REF] Rodrıǵuez-Delgado | Separation of phenolic compounds by high-performance liquid chromatography with absorbance and fluorimetric detection[END_REF] while anthocyanins and flavonols are autofluorescent at visible wavelengths [START_REF] Drabent | Fluorescence properties of plant anthocyanin pigments. I. Fluorescence of anthocyanins in Brassica oleracea L. extracts[END_REF]. Monomeric and condensed tannin ((+)catechin, (-)epi-catechin, procyanidins) fluorescence requires deep-UV wavelength excitation at approximately 280 nm [START_REF] Gómez-Alonso | HPLC analysis of diverse grape and wine phenolics using direct injection and multidetection by DAD and fluorescence[END_REF] [START_REF] Airado-Rodríguez | Front-face fluorescence spectroscopy: A new tool for control in the wine industry[END_REF]. The use of different bandpass filters to select specific ranges of fluorescence emissions offers the opportunity to localize different compounds within the same sample through a multispectral approach [START_REF] Corcel | Comparison of UV and visible autofluorescence of wheat grain tissues in macroscopic images of cross-sections and particles[END_REF]. However, data on the fluorescence emission of specific phenolic compounds are scarce due to the high number of entities that constitute this metabolite family and because access to pure reference phenolic compounds is limited.

To avoid artefacts related to small compound diffusion and loss during sample preparation, cryo-fixation, cryo-microtomy and fluorescence cryo-observation of biological samples have seen recent developments. Cryo-confocal observations at high resolutions were introduced with the realization of specific microscope stages and immersion objective lens prototypes [START_REF] Nahmani | High-numerical-aperture cryogenic light microscopy for increased precision of superresolution reconstructions[END_REF][START_REF] Faoro | Aberration-corrected cryoimmersion light microscopy[END_REF]. A simpler and readily accessible setup was developed to observe fleshy fruit tissue by cryo-laser scanning confocal microscopy (LSCM) [START_REF] Vidot | Cryo-laser scanning confocal microscopy of diffusible plant compounds[END_REF]. Among the advantages of cryo-observations is the lower fluorescence bleaching compared to that during room temperature observations and thus the recovery of higher fluorescence intensity [START_REF] Nahmani | High-numerical-aperture cryogenic light microscopy for increased precision of superresolution reconstructions[END_REF][START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF].

Preliminary tests of fresh fruit auto-fluorescence responses after excitation at 375 nm were performed on apple and grape. The latter revealed promising autofluorescence signals, while a lower excitation wavelength was found necessary to assess flavanol localization. The objective of the present work was to map phenolic compounds in cryo-fixed outer tissues of apple. The mapping was performed at a large field of view by multispectral autofluorescence imaging after deep-UV excitation at 275 nm using the setup developed for fleshy fruit cryoobservation. Two cider apple varieties stored in three different conditions were studied to evaluate the genetic and physiological impacts on phenolic compound distribution.

Fluorescence excitation and emission characteristics of reference phenolic compounds were recorded to help identify fruit tissue phenolics.

Materials and methods

Materials

Chemicals

Phenolic compounds used for reference fluorescence spectra were from the laboratory collections of ESA-GRAPPE (Angers, France) and BIA-PRP (Rennes, France). Formic acid was purchased from Sigma-Aldrich (UK) and methanol was purchased from CarloErba (Italy).

Fruits

Apple (Malus domestica, Royal Gala) and grape (Vitis vinifera, Red Italian) for preliminary fluorescence analysis after 375 nm UV excitation were from a local retail store. These fruits were used without further storage. For the fluorescence mapping following excitation at 275 nm, two cider apple varieties, Douce Moën (M. domestica, Douce Moën) and Guillevic (M. domestica, Guillevic), were provided by IFPC (Le Rheu, France). Fruits were harvested on October 2017 in orchards at Surzur (Morbihan, France). Nine fruits of each variety were subjected to three different storage conditions: three were immediately sampled, three were stored at 4 °C for 30 days and three were stored at room temperature for 20 days before sampling.

Methods

Spectrofluorometry

Phenolic references were dissolved at 2 mg mL -1 in 2 mL of H2O:MeOH (1:1 in volume) + 1% formic acid (in volume). Quartz cuvettes (10 x 4 mm, 114F-QS, Suprasil HELLMA Analytics, France) were filled with 500 µL of standard solution and observed by spectrofluorimetry (F-4500, HITACHI, Japan). Emission and excitation spectra for each compound were recorded between 200 nm and 600 nm.

Laser scanning confocal microscopy (LSCM)

Cubes of 5 x 5 x 5 mm 3 were sampled from the epidermal region of equatorial fruit slices of commercial apple and grape. Sections of 100 µm thickness were cut from fresh cubes with a vibrating blade microtome (HM 650V, MICROM, France) and immediately observed or dipped in standard buffer solution pH 10 (HI 70010C, NIST standard, HANNA INSTRUMENTS, Hungary) followed by H2O milliQ wash prior to LSCM observations at room temperature. LSCM (A1 Eclipse Ti inverted microscope, NIKON Inc., Japan) was configured with laser diode excitation at 375 nm. Fluorescence emission was acquired at 20× magnification with a resolution of 0.63 µm pixel -1 and image size of 512 x 512 pixels 2 (16bit). Four bandpass emission filters were used to map fluorescence: 400-450 nm, 500-530 nm, 560-600 nm and 630-700 nm. These form sets of multispectral images of four channels with spectral controlled excitation and emission parameters.

Synchrotron deep-UV wide-field fluorescence microscopy (DUV)

One 5 x 5 x 5 mm 3 cube was randomly sampled from the epidermal region of a cider apple fruit equatorial slice. The cube was frozen in liquid nitrogen-cooled isopentane and stored at -20 °C prior to analysis. Sections (60 µm thick) were cut from frozen cubes using a cryostat microtome (HM 500 OM, MICROM, France) at -20 °C. The section was placed between quartz lamella (R52-5000, ESCO Optics, USA) glued together by frozen water droplets. Synchrotron UV microscopy was performed at the DISCO (Dichroism, Imaging, mass Spectrometry for Chemistry and biOlogy) beamline at the SOLEIL (Source Optimisée de Lumière à Energie Intermédiaire du LURE (Laboratoire à Utilisation du Rayonnement Electromagnétique)) synchrotron radiation facility [START_REF] Giuliani | DISCO: a low-energy multipurpose beamline at synchrotron SOLEIL[END_REF] (Gif-sur-Yvette, Saint-Aubin, France) on the inverted epi-fluorescence TELEMOS microscope [START_REF] Jamme | Deep UV autofluorescence microscopy for cell biology and tissue histology[END_REF]. Observation was realized under cryogenic conditions using a handmade setup composed of a Peltier stage (PE100, LINKAM Scientifics, UK) cooled by dry ice as described in [START_REF] Vidot | Cryo-laser scanning confocal microscopy of diffusible plant compounds[END_REF]. The wide-field microscope TELEMOS modified by the DISCO beamline staff was a Zeiss Axio Observer Z-1 designed to observe samples after deep-UV (DUV) excitation. The microscope was equipped with a motorized sample plate (MS-2000 XY, Applied Scientific Instrument, USA) to move the sample along the X and Y axes. Sample movement along the Z axis was controlled by the inverted microscope. The setup used the 10× magnification Zeiss Ultrafluar lens (N.A 0.2, WD 7.4) and a sharp 300 nm dichroic mirror "DM" (Omega Optical), which reflected the 280 nm excitation and transmitted emission light above 300 nm. Multispectral fluorescence emission was recorded using six different emission bandpass filters: 300-306 nm, 327-353 nm, 352-388 nm, 412-438 nm, 420-480 nm and 600-650 nm (Semrock, Rochester, USA). In the text, filters are referred to by their low wavelength limit. A back-illuminated CCD camera (Pixis BUV, Princeton Instrument, USA) recorded the images (1024 x 1024 pixels; 1 x 1 µm² per pixel; grey level coded in 16 bit). Acquisition times were 12.5 s for the 300 nm filter, 5 s for the 327, 352, 412 and 420 nm filters, and 7.5 s for the 600 nm filter. Acquisition was performed from the sample cuticle to approximately one mm inside the tissue. With three biological repetitions and three different storage modalities, a total of nine images were registered per variety.

The beamline intensity, which was focused at the centre of the observation field, led to raw images that required corrections to homogenize illumination. In addition, the camera provided a non-null background without illumination. Both inhomogeneous illumination and background corrections were realized according to the following formula:

= - ℎ -
where Ic is the corrected image; I is the raw image; Dark is the background and White is the flat field For this purpose, nine different "dark" images were recorded without sample and without any illumination, one for each of the six emission filters. The "White" images were acquired using a frame (1.0 x 1.0 cm 2 , AB-0576, Gene Frame, THERMOSCIENTIFIC, UK) displaying a homogeneous autofluorescent signal. Thresholding was also required to define the sample image from the camera noise. Image pretreatments were performed using MATLAB® 2017b.

The corrected images were cropped to 300 x 400 µm² size to fit within a pertinent sample image area. To take into account out-of-plane sample sections, several acquisitions were recorded for the same sample area with a maximum of six focal planes. As this method was not confocal imaging, a clear image was reconstructed by combining the different focal plane views with the extended focus software HeliconFocus6® (version 6.8.0) using the pyramidal method.

Multispectral analysis of DUV fluorescence images

DUV fluorescence emission was valued based on the grey scale intensity of pixels in cropped images. Principal component analysis was applied separately on each multispectral image, and fluorescence profiles were extracted from selected emission filters.

Image Analysis

Individual emission images were unfolded to form one vector [START_REF] Grahn | Multivariate and hyperspectral image analysis[END_REF]. The image vectors were combined into one table per sample containing six columns corresponding to the six filters and n rows corresponding to the n pixels of the image. Principal component analysis (PCA) was applied to the resulting data table, and correlation circles were drawn from the PCA loadings. Principal component images were obtained by refolding scores [START_REF] Grahn | Multivariate and hyperspectral image analysis[END_REF].

Component images were filtered to keep 99% of pixels closer to the median value and to remove eventual aberrant pixel values prior to normalization of grey levels between 0 and 255. PCA reconstructed colour images were created from components 1, 2 and 3 identified in the blue, red and green channels, respectively.

Localization of phenolic compounds in samples was also analysed by computing fluorescence intensity profiles from the cuticle to the inner tissue. This "image distance" analysis was realized using FIJI/ImageJ® software [START_REF] Schneider | NIH Image to ImageJ: 25 years of Image Analysis[END_REF] and the mathematical morphology plugin process/erode (3D) [START_REF] Neves | Exploiting the potential of free software to evaluate root canal biomechanical preparation outcomes through micro-CT images[END_REF]. Thresholding was first applied to create a binary mask of the sample.

Distance from the cuticle was obtained by the following procedure: one-pixel erosion (pixel size = 1 x 1 µm 2 ) was applied to the sample mask and the resulting binary image was subtracted from the initial sample binary image. This step was iteratively applied until the last image column was reached. The mean profile was smoothed to reduce intensity variations due to the presence of cell lumens with low fluorescence and cell walls with high fluorescence.

This was realized by applying local regression (LOESS) with a degree of smoothing of 0.4.

Normalization between 0 and 1 was realized on the maximum smoothed mean value to allow profiles comparison between samples. Examples of raw and smoothed profiles are shown for Douce Moën at harvest in Supplementary Figures 1 and2. The smoothed profiles from the three biological replicates per storage modality were averaged and the mean profile per modality was plotted with its 95% confident interval (Supplementary Figure 3).

Statistical analyses

The effect of storage was evaluated by Student's t-tests of the smoothed mean pixel values of three biological replicates per pixel distance. As no significant differences were found between storage modalities, Student's t-test for variety effect was performed on the nine replicates.

Principal component analysis, LOESS smoothing and Student's t-tests were performed in R [START_REF] Core | R: A language and environment for statistical computing[END_REF].

Results

Fluorescence properties of reference phenolic compound

Excitation and emission fluorescence spectra were registered from standard phenolic compounds (Supplementary figure 4) and the maximum wavelength responses recorded (Table 1). If associating specific compounds with peculiar emission wavelengths is difficult due to the width of spectra with large overlaps, distinguishing families of compounds, such as flavanols (including condensed tannins), phenolic acids, anthocyanins and flavonols remains possible. For example, phenolic acids, such as p-coumaric acid, ferulic acid and caffeic acid have a maximum emission at approximately 420 nm, while flavanols such as (+) catechin, (-) epi-catechin and procyanidin share maximum emission at approximately 320 nm. In fact, due to their large excitation spectra, most phenolic compounds will fluoresce under excitation at 275 nm. Among the tested reference compounds, only phloridzin, rutin and arbutin will not fluoresce after deep-UV excitation.

Preliminary analysis of autofluorescence observed after excitation at 375 nm

In a preliminary study, autofluorescence observations of fleshy fruit were realized with a laboratory confocal laser scanning microscope using a UV diode laser at 375 nm. This test was performed to check the pertinence of autofluorescence analysis on two types of fleshy fruits: Royal Gala apple and Italian Red grape. In all cases, the cuticle presented bright and intense fluorescence as previously observed [START_REF] Considine | Development and histochemistry of the cells, cell-walls, and cuticle of the dermal system of fruit of the grape, Vitis-vinifera L[END_REF]. Red spots were observed within the cells of both fruit but particularly in grape, while light yellow fluorescence was observed in vacuolelike compartments only in apple. Red fluorescence could correspond to chlorophyll residues while yellow emission could be related to compounds of the flavonol class, such as quercetin derivatives [36] [37]. A weak blue emission was also observed in the cell wall at native pH and was found to increase at pH 10, as reported for ferulic or coumaric acids [START_REF] Harris | Detection of bound ferulic acid in cell walls of the Gramineae by ultraviolet fluorescence microscopy[END_REF]. These emission variations after UV excitation at 375 nm provided support for the mapping of phenolic compounds using multispectral autofluorescence imaging. However, a lower excitation wavelength was sought to access compounds in the flavanol family.

Autofluorescence after excitation at 275 nm

The autofluorescence of flavanols in fleshy fruit tissue requires excitation at a low UV wavelength, which is yet inaccessible with a common microscopy laser beam. The synchrotron beamline at DISCO allows for exciting samples in the 200-350 nm range. To limit the diffusion of phenolic compounds, apple tissue was first cryo-fixed prior to cryoobservation of multispectral fluorescence from 300 nm to 650 nm (Figure 3). Outer-cortex parenchyma fluorescence was distinguished from that of epidermal tissue, which encompasses cuticle and sub-cuticular cell layers (Figure 3). Between 327 and 388 nm, subcuticular cell layer fluorescence was more intense and disappeared at higher bandpass wavelength filters except, for the 600 nm filter. Intense fluorescent spots were observed inside the cell mainly with 300 and 327 nm filters, but in all cases, cells walls showed a more intense signal than cells.

To better distinguish differences in sample fluorescence, principal component analysis was applied to the collection of images obtained with the different bandpass filters. All principal component analyses performed on the three modalities presented similar loadings.

For example, the loading and component images are shown in Figure 4 for representative samples of Douce Moën and Guillevic apple varieties at harvest. Fluorescence through 300, 327, 352, 412, 420 and 600 nm filters contributed mainly to components 1 and 2 and fluorescence at 300, 327 and 600 nm contributed more weakly to components 3 and 4. Most filters contributed to component 1, which corresponded to the general variations of fluorescence intensity and explained 65.8% and 61.7% of the total variance for Douce Moën and Guillevic, respectively. The component images showed that the highest overall fluorescence intensity was mainly localized in the walls of outer-cortical cells. The second component, expressing the contribution of the 300 and 327 nm filters (positive side) in opposition to the emission filters 412 and 420 nm (negative side), contrasted the sub-cuticular cell layers. Filters 352 and 600 nm were inversely related to this second component for the two varieties. The third component pointed out the cuticle region with a relatively higher fluorescence measured using the 327 nm emission filter (in red) compared to the 300 and 600 nm filters (in blue), showing the rest of the sample. The fourth component showed a higher level of noise and a relatively higher fluorescence level associated with the 300 nm filter (in blue) in the epidermal region as well as in the cell walls of sub-cuticular cells and outer cortical cells. Thus, fluorescence distinguished three areas: the cuticle region with a relatively higher fluorescence emission using the 327 nm filter, the sub-cuticular cell layers with the 300 nm and 600 nm filters, and the walls of outer-cortical cells with the 352, 412 and 420 nm filters. The three first component images of the representative samples were combined in an RGB image to better visualize the tissue regions according to fluorescence (Figure 4). To objectivize differences observed in fluorescence distribution, normalized intensity profiles for all images of the two varieties at the different storage conditions were measured.

Intensity profiles from the cuticular to the outer cortical tissue were obtained for the four bandpass filters discriminating the most apple tissues: 300, 327, 420 and 600 nm. As cell lumen and cell walls showed marked differences in fluorescence intensities, smoothing of variety at harvest in Supplementary Figures 1 and2. Considering close fruit calibres within varieties, Student's t-test at each distance point per filter showed that storage modalities had no effect on fluorescence profiles (p-value > 0.05; Supplementary Figure 3). Thus, all biological replicates (n= 9) were used to evaluate the effect of apple varieties on fluorescence intensity profiles. Significant differences were particularly noted with the 327 nm and 420 nm filters (Figure 5). For the 327 filter, an inverse gradient was observed between the two varieties with a rupture point at approximately 100 µm from the cuticle. Douce Moën showed higher fluorescence intensity than Guillevic, particularly in the first 10 µm under the cuticle but was lower than that of Guillevic 60 µm away from the cuticle. The 420 nm filter also presented two significantly different areas, first in the epidermis where the Guillevic signal was higher than that of Douce Moën and opposite to the 327 nm filter profile and second in the outer cortex (300 to the 400 µm limit of the images) where Guillevic fluorescence was lower. A maximum was observed at approximately 100 µm for Guillevic, while for Douce Moën, it was at approximately 330 µm from the cuticle. Weak significant differences were observed between Guillevic and Douce Moën in the sub-cuticular cell layers for the 300 nm filter and in the outer cortex for the 600 nm filter. These two profiles also showed similar ruptures at approximately 75-100 µm from the cuticle. The mean smoothed plot profiles (Figure 6) showed good agreement with the fluorescence distribution observed in the representative PCA reconstructed images (Figure 4). The three regions observed may be approximately delimited from these results (Figure 6) for Douce Moën to range from approximately 0 to 50 µm, 50 to 200 µm and 200 µm to 400 µm while for Guillevic, to range from approximately 0 to 60 µm, 60 to 150 µm and 150 to 400 µm. These regions may correspond to the cuticle and the sub-cuticle forming the epidermis and the outer cortex as depicted in Figure 3.

The fluorescence emission of reference phenolic compounds allowed us to propose the possible nature of chemicals in the different tissues (Table 1). Fluorescence observed with the 300 nm filter was more likely due to proteins as this range of emission is related to the aminoacids tyrosine and phenylalanine [START_REF] Teale | Ultraviolet fluorescence of the aromatic amino acids[END_REF]. Fluorescence through the 327 nm filter may have corresponded to the tryptophan and most likely to catechins that are predominant in apple fruit tissue. Since these compounds are flavanol monomers and oligomers, by extension such fluorescence would also reveal condensed tannins. Likewise, fluorescence at 420 nm would represent the phenolic acid family, such as hydroxycinnamic acids, while the fluorescence at 600 nm would be pigments, such as anthocyanin or chlorophyll. According to these propositions, pigments would be particularly localized in the sub-cuticular cell layers of both varieties, while flavanols including condensed tannins would be present in the epidermis and outer cortex of both varieties, though with higher intensity in the sub-cuticular cell layers of Guillevic. The distribution of phenolic acids differed markedly between the two varieties. In Douce Moën, they were present mainly in the outer cortex, while in Guillevic they were also present in the sub-cuticular cell layers. Storage conditions did not appear to affect these distributions.

Discussion

The results showed that multispectral observation of auto-fluorescence provides a convenient alternative for localizing phenolic compound families in fleshy fruit tissue with limited sample preparation and artefact introduction compared to classical resin embedding and staining methods. Adaptation of the cryogenic procedures developed for cryo-LSCM [START_REF] Vidot | Cryo-laser scanning confocal microscopy of diffusible plant compounds[END_REF] to the wide-field TELEMOS microscope of the DISCO beamline at the SOLEIL synchrotron facility allowed observation of fluorescence from 275 nm, which excited flavanols and condensed tannins together with other phenolic compounds in well-preserved apple tissue with limited metabolite diffusion. The obtained images confirmed the efficiency of the cryogenic process as intracellular content appeared filled, though of lower fluorescence intensity compared to cell walls. Cryo-observation also improved fluorescence intensity [START_REF] Nahmani | High-numerical-aperture cryogenic light microscopy for increased precision of superresolution reconstructions[END_REF],

likely by reducing fluorescent bleaching due to the temperature dependency of quencher diffusion [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF]. This phenomenon was particularly helpful in establishing the qualitative distribution of fluorescent compounds in fruit tissue.

Fluorescence tended to indicate phenolic compounds within cell walls. However, most phenolics are localized within cell organelles, vacuoles or the cytoplasm [START_REF] Moskowitz | Vacuolar contents of fruit subepidermal cells from Vitis species[END_REF][START_REF] Kitamura | Transport of flavonoids: from cytosolic synthesis to vacuolar accumulation[END_REF] with fewer in cell walls. In apple, phenolic compounds have not been described as part of the cell wall polysaccharide composition [41] [42]. Some authors [START_REF] Gagné | Composition and cellular localization of tannins in cabernet sauvignon skins during growth[END_REF] suggested that tannin accumulation takes place in the vacuole, but their polymerization appeared near the cell walls.

As apple fruit cells are highly hydrated, ice crystals formed during cryo-fixation of the waterfilled vacuoles [START_REF] Chassagne-Berces | Changes in texture, cellular structure and cell wall composition in apple tissue as a result of freezing[END_REF] may have pushed fluorescent organelles and cytoplasmic materials close to the cell walls. As a consequence, part of the cell wall fluorescence observed with the 10× magnification lens (resolution: 1.24 µm / pixel) may have resulted from nearby intracellular fluorescent compounds/organelles. However, the blue emission observed by LSCM in the cell wall of fresh apple and grape tissue and its increased fluorescence at basic pH supported the presence of hydroxycinnamic acids in cell walls. This observation was realized at higher magnification (20×, resolution of 0.63 µm / pixel) than that of the TELEMOS setup and excluded the potential of ice crystal effects on cell wall fluorescence. Hydroxycinnamic acids have already been reported in apple fruit mostly in vacuoles due to their characterization in the juice [45] [46, 47], but they are also known to be present in plant cell walls [START_REF] Albersheim | Plant cell walls[END_REF]. Their low concentration in apple cell walls likely prevented their detection by classic analytical techniques. However, further work is needed to assess the nature of these compounds and whether they are esters of cell wall polysaccharides, as reported for other plants [20] [49, 50].

The cuticle was the most fluorescent zone of apple and grape fruit tissues observed by LSCM (Figure 2). The observation of cuticle autofluorescence was already reported in several fruits, including apples and grapes and may be related to high concentrations of proteins and phenolic acids [35] [51]. Though anthocyanins, flavonols, flavanols (including condensed tannins), hydroxycinnamic acids and proteins were essentially reported in the epidermis region [START_REF] Awad | Flavonoid and chlorogenic acid changes in skin of Elstar and Jonagold apples during development and ripening[END_REF][START_REF] Khanizadeh | Polyphenol composition and total antioxidant capacity of selected apple genotypes for processing[END_REF][START_REF] Di Lecce | Phenolic profiling of the skin, pulp and seeds of Albariño grapes using hybrid quadrupole time-of-flight and triple-quadrupole mass spectrometry[END_REF], they were more rarely localized in sub-cuticular cell layers [START_REF] Lees | Localization of condensed tannins in apple fruit peel, pulp, and seeds[END_REF][START_REF] Cadot | Evolution of the localisation and composition of phenolics in grape skin between veraison and maturity in relation to water availability and some climatic conditions[END_REF][START_REF] Hammouda | Tissue and cellular localization of tannins in tunisian dates (Phoenix dactylifera l.) by light and transmission electron microscopy[END_REF]. The high concentration of phenolic compounds in the sub-cuticular cell layers is probably related to defence against pathogens [START_REF] Bostock | Suppression of Monilinia fructicola cutinase production by peach fruit surface phenolic acids[END_REF] or light damage to tissues. The firmer mechanical resistance of grape and apple skins compared to their flesh [START_REF] Grotte | Mechanical properties of the skin and the flesh of apples[END_REF][START_REF] Bargel | No. 3: Structure-function relationships of the plant cuticle and cuticular waxes -a smart material?[END_REF] may also be associated to the important presence of phenolic compounds in the skin. Indeed, phenolic compounds and, in particular, flavonoids were proposed to increase the rigidity of the cutin matrix in the cuticle of ripe tomato [START_REF] Khanal | Mechanical properties of cuticles and their primary determinants[END_REF]. Comparatively, excitation with DUV at 275 nm revealed a lower cuticle autofluorescence. Although flavonoids and phenolic acids, the main cuticle phenolic compounds, have large excitation and emission spectra (Supplementary Figure 4), 275 nm excitation was not optimal to yield high autofluorescence intensities. Though such a wavelength was beneficial for exciting flavanols and proteins fluorescence, it appears that flavanols are in low concentration -if any-within the cuticle but are present in the first cell layers underneath (Figure 3).

The red-skinned Douce Moën and the yellow-skinned Guillevic cider apples were used as model fruits to help distinguish phenolic compound locations by their autofluorescence. Douce Moën is known to be richer in hydroxycinnamic acids and in monomeric tannins, such as (+) catechin, (-) epicatechin and procyanidin with lower tannin degrees of polymerization compared to Guillevic [START_REF] Sanoner | Polyphenol profiles of french cider apple varieties (Malus domestica sp.)[END_REF]. Anthocyanins were not characterized in the two varieties, but the more colourful Douce Moën skin evidenced higher anthocyanin and/or pigment contents than that of Guillevic. Based on distinct fluorescent emissions of reference compounds after 275 nm excitation, autofluorescence in Douce Moën and Guillevic cryo-sections allowed the detection of pigments in the sub-cuticular cell layers in agreement with the known flavanols, anthocyanins and chlorophyll concentrations in apple skin [START_REF] Veraverbeke | Non destructive analysis of the wax layer of apple (Malus domestica Borkh.) by means of confocal laser scanning microscopy[END_REF][START_REF] Bae | Anatomical observations of anthocyanin rich cells in apple skins[END_REF].

The main distribution of tannins in the sub-cuticular area together with that of phenolic acids in the outer cortex parenchyma may be related to the ratio reported for procyanidin (PC) and hydroxycinnamic acid (HC) concentrations in the fresh peel (HC/PC: 0.68) and parenchyma (HC/PC: 1.29) [START_REF] Guyot | Reversed-Phase HPLC following thiolysis for quantitative estimation and characterization of the four main classes of phenolic compounds in different tissue zones of a french cider apple variety (Malus domestica Var. Kermerrien)[END_REF]. This different distribution was not reported in the literature for grape in which flavanols were mainly localized in the epidermis and in the seeds although hydroxycinnamic acid content was higher in skin than in pulp [START_REF] Cadot | Flavan-3-ol compositional changes in grape berries (Vitis vinifera L. cv Cabernet Franc) before veraison, using two complementary analytical approaches, HPLC reversed phase and histochemistry[END_REF][START_REF] Di Lecce | Phenolic profiling of the skin, pulp and seeds of Albariño grapes using hybrid quadrupole time-of-flight and triple-quadrupole mass spectrometry[END_REF][START_REF] Cadot | Anatomical, histological, and histochemical changes in grape seeds from Vitis vinifera L. cv cabernet franc during fruit development[END_REF].

Changes in phenolic compounds distribution were not observed with storage modalities that were aimed at impacting apple ripening. This result is at odds with studies showing phenolic compound variations during ripening of fruit [START_REF] Macheix | Fruit Phenolics[END_REF], such as apple [START_REF] Awad | Flavonoid and chlorogenic acid changes in skin of Elstar and Jonagold apples during development and ripening[END_REF][START_REF] Murata | Relationship between apple ripening and browning: changes in polyphenol content and polyphenol oxidase[END_REF] and grape [START_REF] Cadot | Evolution of the localisation and composition of phenolics in grape skin between veraison and maturity in relation to water availability and some climatic conditions[END_REF][START_REF] Delgado | Changes in the phenolic composition of grape berries during ripening in relation to vineyard nitrogen and potassium fertilisation rates[END_REF]. The lack of autofluorescence discrimination between ripening stages may be related to the small tissue area observed. Instead, the present study evidenced a variation in phenolic distribution between apple varieties. This may be related to different tissue thicknesses as for both varieties, different rupture points in phenolic distributions were observed along distance profiles from the cuticle. These ruptures could correspond to different cell layers in the epidermis and the outer cortex. In particular, a rupture was discernible in fluorescence profiles at an approximately 100 µm depth from the skin samples.

Apple histology studies have shown changes from smaller cells in the epidermis to larger cells in the outer cortex parenchyma tissue at an approximately 100-µm depth from the surface of mature fruit [START_REF] Bell | The protective layers of the apple[END_REF][START_REF] Tukey | Gross morphology and histology of developing fruit of the apple[END_REF][START_REF] Khanal | Mechanical properties of apple skin are determined by epidermis and hypodermis[END_REF]. Thus, differences in phenolic compound distribution between the two varieties could reveal genetically distinct thicknesses of epidermal cell layers as well as different secondary metabolism in these tissues.

Conclusion

The cryo-method used here could benefit from further developments in sample preparation and means of cryo-multispectral fluorescence observations. Applying microwaves during cryo-fixation [START_REF] Xanthakis | Development of an innovative microwave assisted food freezing process[END_REF] to avoid ice crystal growth combined with the use of confocal microscope stages and lenses for high-resolution cryo-observations [START_REF] Nahmani | High-numerical-aperture cryogenic light microscopy for increased precision of superresolution reconstructions[END_REF][START_REF] Faoro | Aberration-corrected cryoimmersion light microscopy[END_REF]

  each profile was realized by local regression (LOESS) at the expense of fine structures contributing to fluorescence (cells, cell walls, sub-cellular structures). The smoothed and normalized curves allowed comparison of trends in fluorescence variations along the first 400 µm under the cuticle. Examples of raw and smoothed profiles are shown for the Douce Moën

Figure 1 :

 1 Figure 1: Generic phenolic compound structures. -R may correspond to -H, -OH or -OCH3 and -X may correspond to -H in monomeric form or other flavanol units in polymeric form (Vermerris and Nicholson 2006).

Figure 2 :

 2 Figure 2: Local retail store fresh apple and grape autofluorescence at natural pH and at pH=10.1 after excitation at 375 nm. The fluorescence emissions recorded are 400-450 nm (blue), 500-530 nm (green), 560-600 nm (yellow), and 630-700 nm (red). C: cuticle, CW: cell wall, Chl: chlorophyll residues, Flv: flavonols. Scale bar: 20 µm.

Figure 3 :

 3 Figure 3: Frozen apple autofluorescence for one replicate of Douce Moën and Guillevic at harvest after excitation at 275 nm. Tissue regions are drawn on the right image resulting from a combination of whole Guillevic filter emission images. C: cuticle, CW: cell wall, Scale bar: 40 µm.

Figure 4 :

 4 Figure 4: Principal component analysis on the six emission filter images for one replicate of Douce Moën (blue character and arrows) and Guillevic (black character and arrows) at harvest and the PCA images of the four components. On the component images, blue and red pixels represent negative and positive contributions of the emission filters to the component. RGB reconstructed images from PCA components were built from dimension 1 (blue), dimension 2 (red) and dimension 3 (green). C: cuticle, CW: cell wall

Figure 5 :

 5 Figure 5: Smoothed (LOESS method: α = 0.4) and normalized average plot profiles of DouceMoën (DM) and Guillevic (GU) signal acquisition for emission filters 300 nm, 327 nm, 420 nm and 600 nm after excitation at 275 nm. The dotted lines represent the 95% confidence interval. The coloured areas correspond to significant differences between DM and GU with a p-value < 0.01 by Student's test (n = 9).

Figure 6 :

 6 Figure 6: Superposed smoothed (LOESS method: α = 0.4) and normalized average plot profiles of Douce Moën and Guillevic signal acquisition for emission filters 300 nm (grey

Table 1 :

 1 Fluorescence excitation/emission maxima of phenolic compounds registered by 459 spectrofluorometry: regular case: literature, bold case: this study.

	460
	Compounds	λ max excitation (nm)	λ max emission (nm)	Compounds	λ max excitation (nm)	λ max emission (nm)
	Emission range (<350 nm)		Emission range (400-500nm)
	Protein group		Phenolic acids group
	Phenylalanin[70]	258	285	Ferulic acid	310/370	420
	Tyrosin [70]	276	302	p-Coumaric acid	350	420
	Emission range (300-400 nm)		Caffeic acid	270/360	440
	Flavanols group		Chlorogenic acid	360	460
	(-) Epicatechin	290	320	Others compounds
	(+) Catechin	290	320	Kaempferol[21]	268	422
	Procyanidin B1	285	320	Rutin	300	460
	Procyanidin B2	295	320	Emission range (500-600nm)
	Epigallocatechin	275	320	Flavonols group
	Others compounds		Anthocyanins[22]	300/410	360/420/530
	Tryptophan [22]	280	357	Cyanidin hydrate	278	550
	2,5-Dihydroxybenzaldehyde[21]	278	360	Quercetin-3-O-glucoside	260/410	510
	Syringic acid	310	360	Quercetin	420	520
	Vanillic acid[21]	278	360	Quercetin galactoside	295	600
	Gallic acid	320	370	Others compounds
	Myricetin[21]	268	370	Arbutin	420	530
	Resveratrol	310/360	390	Phloridzin	250/330	540
				Chlorophyll/chloroplast[37]	360	680
	461
	462

Acknowledgements

Part of this work was realized and supported under the proposal number 20170043 at synchrotron SOLEIL. This work was also supported in part by the Food for Tomorrow programme from the Region Pays de la Loire.

Appendix A: Supplementary data

Supplementary data associated with this article can be found, in the online version.