C Inguimbert

Q Gibaru

P Caron

M Angelucci

L Spallino

R Cimino

Modelling the impact on the secondary electron yield of carbon layers of various thicknesses on copper substrate

Keywords: Radiative space environment, Secondary Electron Emission, Copper, Carbon, Surface conditioning, Monte Carlo modelling

This work presents comparisons between numerical simulations and secondary electron emission yield measurements. The impact on the secondary electron emission yield of a growing graphite layer deposited on copper substrates is analyzed. The numerical simulations confirm experimental observations showing that a very thin coating deposit, with a thickness of few nm, can affect significantly the emission yield of an irradiated material. Beyond 5 nm thickness, the surface material alone drives the secondary emission.

Introduction

Secondary electron emission is a physical process that can often appear as a parasitic phenomenon in systems that either use electrons of a few hundred eV, or that can evolve in an environment where low energy electrons are present . In certain cases, the secondary electrons, by an avalanche phenomenon arising when the secondary emission yield of a surface becomes greater than one, can multiply to a level that can disturb the functioning of sensitive equipments (multipactor) [1][START_REF] Cazaux | Secondary electron emission and charging mechanisms in Auger Electron Spectroscopy and related e-beam techniques[END_REF][START_REF] Vaughan | Multipactor[END_REF][START_REF] Gopinath | Multipactor electron discharge physics using an improved secondary emission model[END_REF]. This electron multiplication can also be used to magnify the response of some sensors [START_REF] Wiza | Microchannel Plate Detectors[END_REF][START_REF] Ivanov | Calibration procedure in microchannel amplifiers design[END_REF]. Any electron present in a radio frequency device, can be accelerated by the field of the transmitted wave, and collide the walls of the device, where it can multiply by a resonant phenomenon [START_REF] Vaughan | Multipactor[END_REF][START_REF] Gopinath | Multipactor electron discharge physics using an improved secondary emission model[END_REF] addition to the fact that this phenomenon can be a source of noise, other potentially catastrophic effects, corona discharges can be caused. Beam stability is affected by electron clouds in accelerator facilities [START_REF] Kirby | Secondary electron emission yields from PEP-II accelerator materials[END_REF][START_REF] Yin Vallgren | Amorphous carbon coatings for the mitigation of electron cloud in the CERN Super Proton Synchrotron[END_REF][START_REF] Pinto | Carbon coatings with low secondary electron yield[END_REF][START_REF] Calatroni | Optimization of the secondary electron yield of laserstructured copper surfaces at room and cryogenic temperature[END_REF]. Similarly, the multipactor mechanism strongly impacts the functioning of tokamak facilities [11][12][13][14][START_REF] Lee | Secondary electron emission and the bifurcation of the heat flux to the targets in fusion plasmas[END_REF][START_REF] Fil | Multipactor threshold sensitivity to Total Electron Emission Yield in parallel-plate waveguide and TEEY models accuracy[END_REF]. Multipacting is also an issue for space systems that undergo electrons trapped in the earth radiation belts and that are a source of various damages [START_REF] Prokopenko | High-voltage differential charging of geostationary spacecraft[END_REF][START_REF] Balcon | Secondary Electron Emission on Space Materials: Evaluation of the Total Secondary Electron Yield From Surface Potential Measurements[END_REF][START_REF] Sorolla | New multipactor dynamics in presence of dielectrics[END_REF][START_REF] Inguimbert | Surface Ionizing Dose for Space Applications Estimated With Low Energy Spectra Going Down to Hundreds of Electronvolt[END_REF][START_REF] Sydorenko | Kinetic simulation of secondary electron emission effects in Hall thrusters[END_REF]. The satellite's power chain is particularly sensitive to this physical mechanism. In this context, it is usual to mitigate the risk associated with the electron secondary emission by limiting the transmitted power. But to overcome this strong constraint and allowing gain in competitiveness, satellite's operators usually moderate this effect by limiting the Secondary Electron Emission Yield (SEY) of the guide walls. This is generally achieved by surface treatments [START_REF] Petit | Role of the different chemical components in the conditioning process of air exposed copper surfaces[END_REF][START_REF] Nistor | Multipactor suppression by micro-structured gold/silver coatings for space applications[END_REF][START_REF] Aguilera | CuO nanowires for inhibiting secondary electron emission[END_REF][START_REF] Montero | Secondary electron emission under electron bombardment from graphene nanoplatelets[END_REF][START_REF] Larciprete | Evolution of the secondary electron emission during the graphitization of thin C films[END_REF][START_REF] Xie | 17th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM)[END_REF][START_REF] Wang | Secondary electron emission characteristics of graphene films with copper substrate[END_REF][START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF]. The secondary electron emission is studied in many fields, either to prevent it when the effect is undesirable or to use this phenomenon as a signal amplifier. Different mitigation techniques can be applied to limit the secondary electron emission. The simplest one consists in using the conditioning of the surface induced by the irradiation itself [START_REF] Petit | Role of the different chemical components in the conditioning process of air exposed copper surfaces[END_REF]. The chemical state of the surface is modified by the irradiation in a way that the SEY can be reduced. Etching (laser, chemical) [START_REF] Nistor | Multipactor suppression by micro-structured gold/silver coatings for space applications[END_REF]can be used to enhance the roughness of the surface, that can act as a source of natural traps for the emitted electrons. Another method also consists in depositing a low emissive coating on the material surface [START_REF] Aguilera | CuO nanowires for inhibiting secondary electron emission[END_REF][START_REF] Montero | Secondary electron emission under electron bombardment from graphene nanoplatelets[END_REF][START_REF] Larciprete | Evolution of the secondary electron emission during the graphitization of thin C films[END_REF][START_REF] Xie | 17th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM)[END_REF][START_REF] Wang | Secondary electron emission characteristics of graphene films with copper substrate[END_REF][START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF]. Carbon is known as a low secondary electron emitter [START_REF] Montero | Secondary electron emission under electron bombardment from graphene nanoplatelets[END_REF][START_REF] Larciprete | Evolution of the secondary electron emission during the graphitization of thin C films[END_REF][START_REF] Xie | 17th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM)[END_REF][START_REF] Wang | Secondary electron emission characteristics of graphene films with copper substrate[END_REF][START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF]. The impact of a layer of carbon deposited on a copper substrate has been studied experimentally [START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF]. It is shown that a very thin layer of carbon is surprisingly enough to reduce significantly the SEY of the copper substrate. But, few numerical simulations of such behavior have already been performed [START_REF] Nguyen | Calculations of secondary electron yield of graphene coated copper for vacuum electronic applications[END_REF]. The objective of the work presented here is to study the impact of thin carbon layer deposits of different thicknesses on the SEY performance of a copper substrate. Thicknesses ranging from 0 nm up to 50 nm are investigated. Comparison with experimental SEY [START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF] is shown and discussed for incident electrons in the [20 ~eV, 2 ~keV] energy domain.

Methods and definitions

Monte Carlo SEY simulations

A code performing the transport of electrons in a parallelepipedic volume made of a substrate of copper covered with a thin layer of carbon (< 100 nm) has been developed. The interaction cross sections of the Monte Carlo code are extracted from optical energy loss function obtained from the literature [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF]. In the case of carbon, optical data are representative of graphite but the type of hybridation of the carbon atoms is not known. Three physical quantities are evaluated: first, the energy deposited in the volume as a function of the depth (dose vs. depth curve), second, the amount of electrons escaping from the surface (secondary emission yield), and third the energy spectrum of emitted electrons. The basic geometrical configuration required to calculate secondary emission therefore includes a parallelepiped substrate of copper topped with a carbon sub-volumes. The thickness of the surface layer of carbon can be parameterized and has been varied from 1 nm to 50 nm according to the 9 following values (1nm, 2nm, 3nm, 5nm, 7nm, 10nm, 15nm, 20nm, 50nm).This volume is irradiated with normal incident electrons with energies going from 25 eV up to 3 keV (25eV, 50eV, 100eV, 200eV, 300eV, 400eV, 500eV, 600eV, 700eV, 800eV, 1000eV, 2000eV). All electrons produced during the simulation and re-emitted by the surface are counted using a spherical detector surrounding the irradiated volume. Primary and secondary electrons can be differentiated with the purpose of evaluating secondary emission, and elastically backscattered yields. It is also possible to evaluate the energy spectrum of emitted electrons. The evolution of the secondary emission is estimated for each simulated carbon thickness. The SEY of the electrons is computed with a Monte Carlo simulation toolkit based on the MICROELEC module of the GEANT4 package [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF][START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energy-range validity up to 10 GeV/nucleon[END_REF][START_REF] Pierron | Electron emission yield for low energy electrons: Monte Carlo simulation and experimental comparison for Al, Ag, and Si[END_REF][START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF]. GEANT4 offers a large variety of particle transport models over a wide range of incident energies going from about ten eV and beyond the GeV. We are interested in this work, in the transport of electrons over a range of energies ranging from some ~eV up to a few keV. GEANT4 offers several possibilities to perform this type of calculations. The PENELOPE code, now present in the GEANT4 distribution, addresses the transport of electrons down to an energy of ~50 eV. It proposes a mixed approach which combines a continuous transport (condensed history) and switches to a discrete mode for interactions producing large energy losses. The used interaction cross sections combines data from first-principles simulations, with semi-empirical formulas and evaluated databases. But, the underlying approximations of the model are expected to be valid only for energies larger than about 1 keV, even if PENELOPE can be used down to its energy limit with less accuracy. Other GEANT4 modules allow performing transport for low energy (< keV). For example, the DNA module, specialized in electron transport for radiobiology applications, is based on the exploitation of the complex dielectric function. It is a purely discrete module that follows the particles interactions after interactions. But, the application of this module is restricted to transport in "living materials" (water). On the other hand, the MICROELEC module which follows a similar approach as the DNA module, is dedicated to the transport in other dense materials. This module developed, in partnership with the CEA (French Alternative Energies and Atomic Energy Commission), can be applied to evaluate at small scale, the generation rate of carriers in semiconductor materials (silicon), or to the modeling of Secondary Electronic Emission (SEE). In order to properly deal with the latter issue, a quantum reflection/refraction interaction process at the vacuum/matter or matter/matter interfaces has been implemented [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF][START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energy-range validity up to 10 GeV/nucleon[END_REF][START_REF] Pierron | Electron emission yield for low energy electrons: Monte Carlo simulation and experimental comparison for Al, Ag, and Si[END_REF][START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF]. The height (some eV) of the Work Function (WF), existing at the interface between two materials, and that strongly affect the crossing electrons, is taken into account in our simulations [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF][START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energy-range validity up to 10 GeV/nucleon[END_REF][START_REF] Pierron | Electron emission yield for low energy electrons: Monte Carlo simulation and experimental comparison for Al, Ag, and Si[END_REF][START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF]. At low energy, it is also important to take into account the potential energy of the electrons in the material, which is no longer negligible regarding the incident energy. The binding energy of each atomic shell as well as the potential energy of the weakly bound electrons populating the valence and/or the conduction bands are thus taken into account. The interaction cross sections is evaluated for each inner shell (K,L,…). A random draw is used to select among the different shells the interaction that occurs at a given step. When an energy Q is transferred to an electron having a binding energy I, its remaining kinetic energy is equal to the energy Q reduced from its binding energy I (Q-I) in order to allows the electron to reach the Fermi level with the proper energy. Weakly bound electrons of conduction and valence bands are treated analogously assuming that the excited plasmon is damped systematically by producing a secondary electrons emitted from the band. In this last case, the electrons are assumed to come from an average energy level representing the width of the band. This potential energy is defined regarding the Fermi level. In the case of copper, this energy is taken equal to 1.8 eV. It is the energy of the most important peak in the density of state of the copper. For carbon this energy is taken equal to 2 eV. The last release of the GEANT4/MICROELEC module [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF][START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energy-range validity up to 10 GeV/nucleon[END_REF][START_REF] Pierron | Electron emission yield for low energy electrons: Monte Carlo simulation and experimental comparison for Al, Ag, and Si[END_REF][START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF][START_REF] Asai | The PENELOPE Physics Models and Transport Mechanics[END_REF][START_REF] Gibaru | Geant4 physics processes for microdosimetry and secondary electron emission simulation: Extension of MicroElec to very low energies and 11 materials[END_REF] allows the transportation of electrons in 9 elements (C, Al, Si, Ti, Ni, Cu, Ge, Ag and W). At low energy [eV -keV] electrons trajectories are driven by both elastic scattering with nuclei and inelastic interactions with the electrons of the medium. At these energies the main source of energy loss are the inelastic interactions with weakly bound and plasmon electrons. The dielectric formalism is used to evaluate those typical energy losses. Mermin's dielectric function, is used to derivate the interaction cross section from experimental Optical Energy Loss functions (OELF) [START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF]. The elastic coulombian interaction cross sections are computed with the ELSEPA code using the partial-wave method [START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF][START_REF] Asai | The PENELOPE Physics Models and Transport Mechanics[END_REF][START_REF] Gibaru | Geant4 physics processes for microdosimetry and secondary electron emission simulation: Extension of MicroElec to very low energies and 11 materials[END_REF][START_REF] Allison | Recent developments in Geant4[END_REF]. Readers who want to get a more detailed description of the code are invited to report to references [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF][START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energy-range validity up to 10 GeV/nucleon[END_REF][START_REF] Pierron | Electron emission yield for low energy electrons: Monte Carlo simulation and experimental comparison for Al, Ag, and Si[END_REF][START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF]. The goal of the work is to investigate, with the simulation toolkit of ref. [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF][START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energy-range validity up to 10 GeV/nucleon[END_REF][START_REF] Pierron | Electron emission yield for low energy electrons: Monte Carlo simulation and experimental comparison for Al, Ag, and Si[END_REF][START_REF] Pierron | Ionizing Dose Calculations for Low Energy Electrons in Silicon and Aluminum[END_REF], the impact of a thin carbon layer on the SEY of a copper substrate. In this work, the SEY represents the emission yield of "true" secondary electrons i.e. native electrons from the irradiated material. The amount of backscattered incident electrons is given by the BEY (Backscattered Emission Yield). This corresponds to the amount of the incident electrons escaping from the material. It is different from the BEY(>50eV) that corresponds to the amount of electrons having an energy greater than 50 eV that are emitted by the surface. Since this 50eV criterion is the convention used by experimentalists to discriminate secondary electrons from backscattered electrons, it can also be chosen for the sake of comparison with experimental data. In this case, all electrons having an energy greater than 50 eV are considered to be backscattered electrons. Depending on the case we will use one or the other of these conventions. The corresponding BEY will then be noted BEY or BEY (>50eV).The total amount of electrons emitted by the irradiated surface is referenced as the TEY = SEY+BEY (Total Emission Yield). Throughout the paper simulated SEY are real secondary electrons while experimental SEYs assume obviously a cutoff at 50 eV between backscattered and secondary electrons. The comparison of the experimental and simulated SEYs is therefore not strictly accurate, but the differences remain quite minor. Moreover, only TEY are presented for the measurements made on the copper substrate topped with graphite layers.

Experimental Data

The experiment data have been acquired at the Material Science INFN-LNF laboratory of Frascati (RM), with a dedicated experimental apparatus which is described elsewhere [START_REF] Larciprete | Evolution of the secondary electron emission during the graphitization of thin C films[END_REF][40][START_REF] Cimino | Nature of the Decrease of the Secondary-Electron Yield by Electron Bombardment and its Energy Dependence[END_REF][START_REF] Cimino | Can Low-Energy Electrons Affect High-Energy Physics Accelerators?[END_REF][START_REF] Cimino | Detailed investigation of the low energy secondary electron yield of technical Cu and its relevance for the LHC[END_REF]]. The UHV system includes a μ-metal chamber (pressure <1 × 10 -10 mbar) with less than 5 mG residual magnetic field at the sample position, dedicated to XPS and SEY analysis and a second chamber for in situ sample preparation. The SEY is evaluated as Iout/Ip = (Ip -Is)/Ip, where Ip is the current of the primary electron beam hitting the sample and Is is the sample current to ground, as measured by a precision picoammeter (Keithly 6487). A Faraday cup positively biased was used to measure Ip, whereas Is was determined by biasing the sample at -75V. For this study we used an ELG-2 Kimball Physics e-gun with a standard Ta disc cathode. A Polycrystalline, flat 8 × 8 mm 2 Cu sample was used as substrate for C evaporation. The sample was atomically cleaned by cycles of Ar+ sputtering at 1 kV and thermal annealing at temperatures between 800 and 1000 K. Carbon was deposited by means of an electron beam evaporator (Tectra GmbH) from a 99.999% purity C rod at room temperature. During C evaporation, the background pressure was <5 × 10 -10 mbar. C layers, assumed to be reasonably homogeneous, were deposited during increasing time lapses and, after each evaporation, XPS and SEY analyses were performed. As reported in [START_REF] Larciprete | Evolution of the secondary electron emission during the graphitization of thin C films[END_REF], the XPS analysis confirmed that a-C grows with a stable rate and allowed to convert deposition time to carbon coverage in nm.

Results and discussions

SEY and BEY of both pure copper and carbon

Both SEY and BEY have been calculated for pure bulk copper and carbon materials (Fig. 1 (a,b) and Fig. 1 (c,d)). As can be seen in Fig. 1 the Monte Carlo simulations are in satisfactory agreement with the measured data of Bronstein [START_REF] Spallino | On the compatibility of porous surfaces with cryogenic vacuum in future high-energy particle accelerators[END_REF][START_REF]A database on electron-solid interactions -Joy -1995 -Scanning -Wiley Online Library[END_REF] and measurements of [START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF]. The location of the maximum of both SEY and BEY are well reproduced, while the magnitude are predicted with a good accuracy too. This good agreement allows us to analyse the impact of different carbon layer's thicknesses on the SEY of the copper substrate. It can be seen that a very thin layer of 1 or 2 nm is sufficient to reduce significantly the TEY of the copper substrate. Beyond 5 nm of carbon the TEY is mainly driven by the overlayer of carbon. The comparisons of these simulations with experimental data from [START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF] for three overlayers of respectively 2.1 nm, 6.3 nm and 11.5 nm is shown in Fig. 3 nm and 11.5 nm thick carbon layers [START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF]. A very thin layer of carbon of few nanometers is sufficient to change significantly the TEY of the copper substrate.

Monte Carlo simulations: SEY vs. BEY

The calculated SEY and BEY of clean Cu and for C coverage with different thickness layers (1 nm, 3 nm, 7 nm and 15 nm), are reported in Fig. 3 (a) and (b) respectively. Different aspects of BEY behavior can be highlighted. First, the BEY of copper is an increasing function up to 500 eV, meanwhile, that of clean C is a decreasing function over the energy range. This is in good agreement with experimental measurements in the literature [START_REF] Assa'd | Backscattering coefficients for low energy electrons[END_REF]. The second thing to note is the direct impact of the atomic C layers on both the SEY and BEY. From 1 to 7 nm, both yields show significant variation in terms of intensity and shape. For this thickness, the curves are a combination of emission contribution from Cu and C layers. From a thickness of about 7 nanometers both the SEY and the BEY are essentially driven by the C surface layers. However, the BEY presents a minimum at different energies as function of C thickness. This minimum can be understood considering the energy of the incident electrons and their mean free path in solid. At very low energy (<~200 eV) the electron path length in carbon does not exceed few nanometers [START_REF] Assa'd | Backscattering coefficients for low energy electrons[END_REF]. The backscattering phenomenon is entirely governed by the carbon layer. This tendency can be seen on the SEY curve too, which follows the carbon values below 200 eV (Fig. 3 (a)). On the other hand, beyond a few hundred eV and around 1 keV the BEY tends again towards the values of the copper substrate. This shows that the BEY in this case comes from electrons that have crossed the carbon layer and almost all reached the copper substrate. It is thus possible to interpret this behavior according to the penetration distance of the incident electrons. The order of magnitude of the penetration depth of incident electrons is given by what is called the "practical range" [START_REF] Gibaru | Surface ionizing dose deposited by low energy electrons (10 eV-10 keV) in eleven monoatomic materials: Monte Carlo calculations and analytical expressions[END_REF]. It is an average distance travelled by an incident electron in the irradiated material projected on the direction of incidence. The way it is commonly estimated is described in ref. [START_REF] Gibaru | Surface ionizing dose deposited by low energy electrons (10 eV-10 keV) in eleven monoatomic materials: Monte Carlo calculations and analytical expressions[END_REF]. Plotting the practical range [START_REF] Gibaru | Surface ionizing dose deposited by low energy electrons (10 eV-10 keV) in eleven monoatomic materials: Monte Carlo calculations and analytical expressions[END_REF] rmin of the electrons at the energy of the minimum of the BEY, as a function of the thickness of the graphite layer (thC), a clear correlation can be observed (Fig. 4). This clearly shows that the backscattering phenomenon occurs in the very first nanometers. The electron emission phenomenon is thus demonstrated to take place essentially in the first nanometers of the irradiated material. process. Similarly, the peak of the low energy electrons (< 200 eV) remains very close to the carbon case. Here again, we understand that very low energy electrons can only leave the volume if they are produced to the very near surface. This indicates that the carbon layer will be the main contributor to the population of electrons with the lowest energies. Between these two extremes (plateau region), the copper sub-layer impacts the spectrum which presents a stronger amplitude. We just recall at this point, that the distributions are normalized (integral = 1) to be able to analyze the impact of the surface layer on the relative shape of the different energy distributions. Analogous calculations have been performed for a graphite overlayer of 1 nm 6). Similar conclusions as the 5 nm case have been drawn. As can be seen in Fig. 6, the 400 eV incident electrons are able to cross the 1 nm graphite overlayer (projected range ~ 1.5 nm in carbon [START_REF] Gibaru | Surface ionizing dose deposited by low energy electrons (10 eV-10 keV) in eleven monoatomic materials: Monte Carlo calculations and analytical expressions[END_REF]). A similar behavior observed for 1 keV electrons on a 5 nm graphite layer can be seen. In that case, the plateau region is close to that of the pure copper substrate, while the two extreme peaks (400 eV, <100 eV) are comparable to those present on the graphite distributions.

Impact of the work function

The work function (WF) is a physical quantity that can plays an important role on the emission of low energy electrons.

In the case of copper, the work function employed in our calculations (4.7 eV) has been modified in order to evaluate its impact on the SEY. Indeed, adding a simple layer of coating material can change the work function and impact the SEY. In the following, WF has varies from 4.2 eV up to 5.2 eV using four different values including that of carbon (4.81 eV). The impact on both the SEY and TEY of a target of copper has been studied (Fig. 7

Conclusion

In this work comparisons between numerical simulations and secondary electronic emission yield measurements were presented. The impact of a growing graphite layer on copper substrates has been analyzed. The simulations confirm the experimental observations, which showed surprisingly that a very thin layer of coating was able to greatly modify the emission efficiency of a surface. The calculation confirms that beyond a thickness of 5 nm of a carbon deposit on copper, the yield is essentially driven by the material deposited on the surface. The electron populations most impacted by the change in the nature of the surface are the elastically backscattered and the low energy secondary (< 100 eV) electrons. The first ones are produced essentially at the vacuum/material interface, whereas the low energy secondaries can only leave the material if they are produced at very short distances from the surface. Since these two populations represent an important part of the emitted electrons, a change in the surface state significantly affects the emission yields. In that sense, it is important to remind that in general, but this is true in particular for the calculations presented here, the simulations do not take into account the real state of the material surface. Including in the calculations a contamination layer or a roughness could improve the predictions by the simulations and their comparisons with experimental data.

Acknowledgements

Many thanks to M. Belhaj and A. Andrieux from ONERA/DPHY, for their advice and fruitful discussions we had in the framework of the internal ONERA project COMODHO. This work has been performed with MicroElec GEANT4 module that is developed in partnership with M. Raine and D. Lambert from CEA DAM in the framework of the GEANT4 collaboration. Many thanks to them for their support.

1

Fig. 1 .

 1 Fig. 1. Secondary electron emission yield (SEY) and backscattered emission yield (BEY) are shown for copper respectively in (a) and (b) panels and for graphite in (c) and (d) panels . Comparisons are shown with experimental data of Bronstein [44, 45] and ref. [29].

Fig. 2 .

 2 Fig. 2. (a)Total electron emission yield (TEY) calculated for various carbon thickness layers (0.2 nm, 0.6 nm, 1 nm, 2.1 nm, 3 nm, 6.3 nm, 7 nm, 11.5 nm, 15 nm, 20 nm, 50 nm). (b) Comparisons with measured TEY for a copper substrate covered with 2.1 nm , 6.3 nm and 11.5 nm thick carbon layers[START_REF] Angelucci | Minimum thickness of carbon coating for multipacting suppression[END_REF]. A very thin layer of carbon of few nanometers is sufficient to change significantly the TEY of the copper substrate.

Fig. 3 .

 3 Fig. 3. (a) Secondary electron emission yield (SEY) calculated for various carbon thickness layers (1 nm, 3 nm, 7 nm, and 15 nm,). (b) Backscattered Emission Yield (BEY) calculated for various carbon thickness layers (1 nm, 3 nm, 7 nm, and 15 nm,).

Fig. 4 .

 4 Fig.4. The practical range rmin of the electrons at the energy of the minimum of the BEY, as a function of the thickness of the graphite layer (thC). The BEY is strongly correlated to the thickness of the over-layer material.

Fig. 7 .

 7 Fig. 7. (a) SEY of a copper target as a function of the incident energy. (b) TEY of a copper target as a function of the incident energy. In both cases the work function of the copper target has been varied form 4.2 eV up to 5.2 eV.

The Fig. 5(a) shows the energetic spectra of the secondary electrons emitted by a flat surface irradiated with 300 eV incident electrons. Three cases are shown: a pure copper volume, a pure graphite volume and a substrate of copper topped with a layer of 5 nm of graphite. The shapes of these distributions are very common. At low energy, below ~100 eV one can recognize the peak of "true" secondaries (SEY). The peak of elastically backscattered incident electrons can easily be observed at 300 eV (Fig. 5(a)). In between (plateau region) there is a mix of inelastically backscattered electrons and energetic secondary electrons. It is clearly obvious from the Fig. 5(a) that the energetic distribution of the "Cu+C(5nm)" sample is identical to the one of the pure graphite volume (C). The projected range of the 300 eV incident electrons is in the order of ~1 nm in carbon [START_REF] Gibaru | Surface ionizing dose deposited by low energy electrons (10 eV-10 keV) in eleven monoatomic materials: Monte Carlo calculations and analytical expressions[END_REF], far shorter than the thickness of the overlayer. It is not surprising to see that the secondary electron emission process is driven in that case by the graphite overlayer. However, when the energy of the incident electrons is increased, the electrons begin to penetrate the copper substrate, and the influence of copper layer starts to be felt. At 1 keV (Fig. 5(b)), the electrons have a practical range of ~5 nm [START_REF] Gibaru | Surface ionizing dose deposited by low energy electrons (10 eV-10 keV) in eleven monoatomic materials: Monte Carlo calculations and analytical expressions[END_REF]. In this case we can see several things. First, the peak at 1 keV of the backscattered electrons remains close to that of graphite. This clearly shows that the backscattering phenomenon at the surface of the material is the dominant


Christopher Fletcher

A French Peasants' Revolt

Justine Firnhaber-Baker, The Jacquerie of 1358: A French Peasants' Revolt, Oxford: Oxford University Press, 2021. Pp. xxii+307. $100. ISBN: 978-0-19-885641-2.

Rather surprisingly, this is the first dedicated monograph to be published on the northern French peasant revolt of 1358 known as the Jacquerie since Siméon Luce's École des chartes thesis of 1859. Luce's foundational research in both chronicle and archival material was revisited and expanded in the later twentieth century by Raymond Cazelles and Françoise Autrand, amongst others, but in the form either of articles, or of studies whose focus lead them to be classed as exclusively political history. Douglas Aiton's 2007 thesis remains unpublished. The result has been a slippage in interpretation amongst historians both leftleaning and conservative, who tend to follow the 'anti-explanation' advanced by Jules Flammermont in 1879 in which the revolt is the nihilistic act of 'rude peasants, without education or direction, dazed by poverty and drink'. Thus even Michel Mollat and Philippe Wolff saw the revolt as being as 'incoherent as it was spontaneous', an amorphous outpouring of long-held social animus fundamentally explained by poverty. Historians from Jonathan Sumption to David Green concur. In the light of recent research which stresses the rationality and structure underlying medieval revolts, the time seems ripe to reconsider how Cazelles' emphatically political interpretation, in which the Jacquerie is 'remote-controlled' from Paris by Étienne Marcel and the reformers, might be tweaked to give due prominence to peasant priorities and modes of action.

A monographic approach enables Justine Firnhaber-Baker to show how the political was dominant in this revolt, yet not as something controlled by political professionals in Paris.

Instead the Jacquerie took form through peasant initiatives based on their knowledge of events and the structures of peasant social organisation. Numerous subtle but essential revisions make it possible to fill in this new picture. This is a cumulative process, based on a thorough analysis of lettres de remission (pardons accompanied by narratives that both detail their recipients' crimes and justify them, granted both to rebels and to the nobles who violently suppressed them), Parlement litigation, more miscellaneous sources in provincial archives, and a thorough re-reading of the chronicle material. To start with, Firnhaber-Baker shows that the Jacquerie was not a revolt against lords, but against nobles, the second estate which had so badly failed at Poitiers, and especially those who resisted reform. Ecclesiastical lords, for example, were not attacked, and only two churchmen were victimised, and not because they were clerics. The interpersonal violence which the chronicles put centre-stage was a relatively minor aspect of the revolt next to the destruction of noble castles, fortresses or houses which were often more markers of noble status than military redouts. Only 27 identified individuals were killed by the rebels, 9 of these, including the probable heir of the marshal of Normandy recently murdered by the Parisians, in the incident at Saint-Leu-d'Esserent on 28 May 1358 that marked the beginning of the Jacquerie. Meanwhile, some 32 castles, 2 fortresses, 1 tower and over 27 manor-houses can be identified as destroyed in the documentation, and this is surely the tip of the iceberg. The action at Saint-Leu should be seen as an attempt to stop Charles, duke of Normandy, the king's eldest son, from cutting off Paris' supply lines via the river Oise by garrisoning the castle of Creil, as he had done on the Seine at Montereau and on the Marne at Meaux. So this was a pro-Parisian action, but the initiative was local, and the Parisians were not aware of it in advance. The rebel captains of whom the most famous was Guillaume Calle were home-grown leaders, from the immediate vicinity, although they later joined forces with troops sent from Paris. These were the Jacques Bonhommes mobilised by the summons of the arrière-ban in 1355 and 1356, but whom the king had, fatally, not taken with him against the Black Prince. Moreover, their action was more pre-emptive than reactive. The region north and east of Paris where the Jacquerie broke out had not yet suffered from post-Poitiers military violence, and later activity further east in Champagne seems to have consisted entirely in tentative peasant self-defence initiatives, interpreted by nobles as sedition and violently suppressed as such.

The analysis of the lettres de remission enables Firnhaber-Baker to reject the chroniclerderived clichés which portray the Jacques as impoverished marginals without accepting Cazelles' picture of a revolt of educated officials and well-off artisans. She identifies 498 rebels in the remissions, 27.8% of which include a clause specifying that the pardon will enable the recipient to return to their agricultural occupations, and many of the 15.5% identified as artisans would likely also have pursued agricultural trades. This was thus emphatically a peasants' revolt, although it involved cooperation with towns, both Paris and, more effectively, with locally active towns such as Senlis. Communal mechanisms for information circulation, assembly and mobilisation were its sinews, made effective and legitimate by their frequent use in the cause both of the community and the king. Arguably, however, this ordinariness or normality was also one of the rebels' weaknesses, for the sense it gave of legitimacy was decidedly not shared by the nobles. It seems likely that news circulating from Paris and elsewhere made Charles of Navarre seem a potential ally, convincing Guillaume Calle to parley with him at Mello and Clermont without asking for hostages. Their leader captured, the Jacques were cut down by Navarre's forces, and Calle was murdered soon after. A quarter-century later, Wat Tyler had still not learned the lesson that you can never trust a noble.

Christopher Fletcher

IRHiS (UMR 8529), CNRS/Université de Lille, France


Camille L Grasso
email: grassocamille@gmail.com

Johannes C Ziegler

Jennifer T Coull

Marie Montant

Space-Time Congruency Effects Using Eye Movements During Processing of Past-and Future-Related Words

Keywords: Abstract concepts, lexical decision, embodiment, eye-tracking, space, time

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

Introduction

Time is not associated with any tangible temporal stimulus, there are no sensory receptors for time, and no dedicated "time area" in the brain. So how can embodied theories represent words that refer to time? One possibility is that time-related words are spatially represented and ordered along linear axes known as mental timelines (MTL; [START_REF] Bender | Mapping spatial frames of reference onto time : A review of theoretical accounts and empirical findings[END_REF][START_REF] Bonato | When time is space : Evidence for a mental time line[END_REF][START_REF] Cooperrider | The influence of object-relative visuomotor set on express saccades[END_REF]. Empirical evidence for MTL comes from experiments that manipulated the congruency between the temporal content of verbal stimuli and the spatial location of required responses, resulting in a space-time congruency effect [START_REF] Eikmeier | How strongly linked are mental time and space along the left-right axis?[END_REF][START_REF] Kong | Space-Time Compatibility Effects in the Auditory Modality[END_REF][START_REF] Maienborn | Do we map remembrances to the left/back and expectations to the right/front of a mental timeline? Space-time congruency effects with retrospective and prospective verbs[END_REF][START_REF] Santiago | Time (also) flies from left to right[END_REF][START_REF] Torralbo | Flexible Conceptual Projection of Time Onto Spatial Frames of Reference[END_REF]. On the lateral axis, space-time congruency effects correspond to faster left responses for past-tense stimuli (e.g., I listened) and faster right responses for futuretense stimuli (e.g., I will listen). These effects are typically observed when participants make explicit temporal judgments [START_REF] Aguirre | Do potential past and future events activate the Left-Right Mental Timeline[END_REF][START_REF] Casasanto | Spatial language and abstract concepts[END_REF][START_REF] Kong | Space-Time Compatibility Effects in the Auditory Modality[END_REF], but reduced when participants make non-temporal judgments, such as lexical decisions (e.g., [START_REF] Maienborn | Do we map remembrances to the left/back and expectations to the right/front of a mental timeline? Space-time congruency effects with retrospective and prospective verbs[END_REF]see von Sobbe et al., 2019 for a meta-analysis).

Therefore, it has been suggested that the processing of time-related words does not automatically engage spatial networks underlying the MTL [START_REF] Maienborn | Do we map remembrances to the left/back and expectations to the right/front of a mental timeline? Space-time congruency effects with retrospective and prospective verbs[END_REF][START_REF] Von Sobbe | The Space-Time Congruency Effect : A Meta-Analysis[END_REF]. However, [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF] found space-time congruency effects even when temporal processing was implicit (lexical decisions about past/future-conjugated verbs and pseudoverbs) as long as the task involved directional hand movements rather than simple key presses (see also [START_REF] Scheifele | A Replication of ``Processing time shifts affects the execution of motor responses (Sell & Kaschak, 2011; Experiment 1)[END_REF][START_REF] Sell | Processing time shifts affects the execution of motor responses[END_REF]. These results suggest that spatially directed movement (and therefore the motor system) could play a critical role for the emergence of space-time congruency effects. Interestingly, the congruency effect was only observed for real, not pseudo, verbs, reinforcing the hypothesis that the motor system contributes to the lexical processing of past and future related words. If the motor system is a key component for the representation and processing of abstract temporal concepts, what kind of sensorimotor experience might link space and time into a left-to-right MTL? Interestingly, it has been shown that the MTL goes from left-to-right in cultures with a left-to-right writing system, whereas the reverse pattern is observed in cultures with a right-to-left writing system [START_REF] Ouellet | Is the Future the Right Time?[END_REF], which suggests that the lateral MTL results from extensive reading and writing experience [START_REF] Fuhrman | Cross-Cultural Differences in Mental Representations of Time : Evidence From an Implicit Nonlinguistic Task[END_REF].

As concerns language, one prediction is that if the spatial representation of the temporal content of words comes from repeated spatially directed movement executed during reading and writing, then space-time congruency effects in implicit temporal tasks should not be limited to hand movements (used for writing) but should also be observed for eye movements (used for reading). To test this hypothesis, the present study investigated whether space-time congruency effects could also occur when participants gave nontemporal decisions about past/future words using lateral saccades. French verbs and pseudo verbs were presented on a screen in conjugated form (i.e., past or future), and participants had to decide as quickly as possible whether the verb was real or not by producing a saccade towards the left or the right side of the screen. Experimental design and stimuli were taken from [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF]. The grammatical verbal system in French makes it possible to use the same word stem combined with a suffix that indicates either past tense (je marchais [I walked]; je rêvais [I dreamt]) or future tense (je marcherai [I will walk]; je rêverai; [I will dream]). Having the same word stem for different temporal conditions nicely controls for possible orthographic, lexical, and semantic confounds.

Materials and Methods

Participants

The study involved 64 participants from Aix-Marseille University (France). Nine participants were excluded from analyses due to high errors rates or technical data acquisition issues.

The remaining 58 participants (48 women, 54 right-handed, aged 18-42 years, M = 22.2; SD = 4.6) were French native speakers, reported normal or corrected-to-normal vision and no neurological or psychiatric disorder. Participants gave informed consent prior to participation and were informed that data were collected anonymously. The study was approved by the Institutional Review Board of Aix-Marseille University.

Design and Stimuli

Because the main objective of this study was to determine whether previous results obtained with hand movements [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF] could be generalised to eye movements, we used the same design as Experiment 1 of [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF]. This experiment (which included the temporal priming words "yesterday" or "tomorrow") had the strongest effect size (Cohen's d = .74) and control experiments confirmed that the presence or absence of primes did not interact with the congruency effect. Stimuli were taken from [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF] and consisted of 80 French word stimuli (verbs) and 80 pseudoword stimuli (pseudoverbs, see Appendix in [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF]. Each word or pseudoword was presented in past-or future-tense (e.g., je laissais/je laisserai ; je gontrais/je gontrerai, for words and pseudowords respectively) at the centre of the screen (Figure 1). To ensure that participants saw each word or pseudoword only once, we created four counterbalanced lists of 160 stimuli (80 words, 80 pseudowords) using a Latin-Square design. Half of the stimuli in each list were in the past tense, half were in the future tense. All stimuli were preceded by the pronoun je ("I").

Apparatus

Eye movements were recorded with an EyeLink 1000 system (SR Research, Mississauga, ON, Canada) with high spatial resolution (0.01°) and a sampling rate of 1000 Hz.

Viewing was binocular, but only the right eye was monitored. Stimuli were displayed on a 20-inch ViewSonic CRT monitor with a refresh rate of 85Hz and a screen resolution of 1024

x 768 pixels (30 x 40 cm). Stimuli were presented in black 37-point monospaced fonts (droid sans mono) on a grey background. The experiment was created using OpenSesame [START_REF] Mathôt | OpenSesame : An open-source, graphical experiment builder for the social sciences[END_REF]. Participants were instructed to give Yes ("it's a word") or No ("it's not a word") responses in a lexical decision task by moving their eyes towards the left or right of the screen. Left and right correct response areas were spatially delimited by two virtual boundaries at +/-600 pixels from the screen's centre. Participants were seated 86 cm from the monitor, such that every 3 characters equalled approximately 1° of visual angle. We used a chin-rest to minimize head movements.

Procedure

The experiment was run in a quiet testing room. Participants were instructed to decide as rapidly and as accurately as possible whether the stimulus was a real French word or not (i.e., a lexical decision) by moving their eyes towards the left / right side of the screen.

Half of the participants started with "yes" responses towards the left (yes-left) and half with "yes" responses towards the right (yes-right), and all participants switched response sides halfway through the experiment. Participants completed a short training session of 20 trials before each experimental block. Each participant saw a total of 80 words and 80 pseudowords in a pseudo-randomized order across two counterbalanced blocks (yes-right or yes-left). For the yes-right block, future-tense words were congruent with the MTL and past-tense words were incongruent (see Figure 1). In each block, there were 40 words and 40 pseudowords, half of each being conjugated in the past tense and half in the future. In the yes-left block, past-tense words were congruent and future-tense words were incongruent.

At the beginning of the experiment, eye position was calibrated using a 9-point calibration grid. The experiment started once the training session was completed. Each trial started with a drift correction dot presented at the centre of the screen. Participants were instructed to fixate this dot, which triggered the onset of a prime stimulus: hier or demain ("yesterday" or "tomorrow") displayed for 500ms, followed by a 400ms blank screen and then finally by the stimulus (i.e., a word or pseudoword). The stimulus remained on the screen until the participants responded by making a saccade. Saccades that crossed the virtual left or right boundaries were considered as responses, whereas saccades that did not cross the boundaries were considered as refixations or microsaccades (depending on their amplitude). Saccade response side was automatically registered when the eyes crossed the Once participants fixated the central dot, a prime (hier or demain, i.e., "yesterday" or "tomorrow") was displayed, followed by a word or pseudoword (e.g, j'entendrai as a future tense verb or j'entendais as a past tense verb). Participants made their lexical decision by moving their eyes towards the left or right side of the screen (delimited by two virtual boundaries). In this example, the yes-response for the word conjugated in the future tense is congruent with the MTL in Block 1 (rightward eye movement) but incongruent in Block 2 (leftward eye movement). Saccadic responses were automatically detected and recorded as soon as the eyes crossed the left or right virtual boundaries on the screen. We recorded the initiation time (response time) and the amplitude (in degree of visual angle) of the saccades. T1 corresponds to the onset-time of the saccade, T2 corresponds to the boundary-crossing time, and T3 corresponds to the landing time. Therefore, response latencies correspond to the response initiation time, which is the delay between the onset of the stimulus and onset of the saccade response (T1). Saccades that did not reach the left/right boundaries were automatically discarded from the analyses.

Data analyses

We recorded and analyzed saccade latency (in milliseconds), and saccade amplitude (in degrees of visual angle). Saccadic eye movements are stereotyped ballistic movements that cannot be modified once initiated [START_REF] Gilchrist | Saccades[END_REF], and can be described by their latency and their angular rotation [START_REF] Findlay | Visual attention : The active vision perspective[END_REF][START_REF] Findlay | Active vision : The psychology of looking and seeing[END_REF]. Saccade latency corresponds to the time needed to process the visual stimulus, to make a decision, and to program the motor response [START_REF] Gilchrist | Saccades[END_REF]. Saccade amplitude corresponds to the spatial distance between starting and landing positions of the eyes. Although this feature of the saccade may appear to be stereotyped (Edelman et al., 2007), it has been shown that linguistic factors (e.g., unusual orthographic patterns) influence saccade amplitude [START_REF] Beauvillain | The 'center of gravity' of words : Evidence for an effect of the word-initial letters[END_REF]. Given that the accuracy of goal-directed movements, including saccades, "depends on the quality of the encoding of spatial information by the central nervous system and the frame of reference" (Ghafouri & Lestienne, 2006, p.25), we predicted that saccade programming as measured by saccade amplitude should be sensitive to the space-time congruency effect. Obtaining such an effect would imply that motor planning networks are involved in the representation of words referring to time.

Both saccade latency and amplitude were analyzed using linear Mixed Effect Models (LMEs) with participants and items as crossed random effects [START_REF] Baayen | Analyzing linguistic data : A practical introduction to statistics using R[END_REF][START_REF] Barr | Random effects structure for testing interactions in linear mixed-effects models[END_REF]. Note that the space-time congruency effect is indexed by the interaction between response side and verb tense. That is, when the side of response for a past-tense word switches from left to right from one block to the other, the word stops being congruent and, instead, becomes incongruent. Similarly, when the side of the response for a future-tense word switches from left to right, the word stops being incongruent and becomes congruent (see Figure 1). Data were fitted with lmer functions from the lme4 package [START_REF] Bates | Fitting Linear Mixed-Effects Models using lme4[END_REF] in the R statistical computing environment (Version 3.5.2; R Core Team, 2020). We report unstandardized regression coefficients, standard errors (SEs), and t values. Fixed effects were deemed reliable if |t| was greater than 1.96 [START_REF] Baayen | Analyzing linguistic data : A practical introduction to statistics using R[END_REF]. In a forward stepwise model selection procedure, fixed and random effects of the models were selected according to the Akaike Information Criterion (AIC; [START_REF] Akaike | Maximum likelihood identification of Gaussian autoregressive moving average models[END_REF], the Bayesian Information Criterion (BIC; [START_REF] Schwarz | Estimating the Dimension of a Model[END_REF] using the anova() function of the package lmerTest package [START_REF] Kuznetsova | lmerTest Package : Tests in Linear Mixed Effects Models[END_REF] for model comparison. Therefore, fixed effects and random slopes were only included if they significantly improved the model parsimony (as assessed by the AIC/BIC).

We built our models using the following procedure: we started with an empty model containing no fixed effect but a random intercept for participant and a random intercept for item. In a second step, fixed effects were selected using the forward stepwise selection procedure. Finally, we included a random slope for each of the selected fixed effects if it improved the model parsimony (as assessed by the AIC/BIC). Model assumptions were checked for each model using the check_model() function from the performance [START_REF] Lenth | performance : An R Package for Assessment, Comparison and Testing of Statistical Models[END_REF] package. Following the procedure described by [START_REF] Brysbaert | Power Analysis and Effect Size in Mixed Effects Models : A Tutorial[END_REF], we conducted power analysis based on 200 simulations with powerSim functions from the simR package [START_REF] Green | SIMR: an R package for power analysis of generalized linear mixed models by simulation[END_REF]. We used the Satterwaithe method as implemented by the afex package [START_REF] Singmann | afex : Analysis of Factorial Experiments[END_REF] for computing p-values. To create figures, we used the emmeans package [START_REF] Lenth | performance : An R Package for Assessment, Comparison and Testing of Statistical Models[END_REF] and computed estimated marginals means (EMMs) for the interaction between response side and verb tense for each model (see Figure 2).

Results

Saccade latency and saccade amplitude were analysed for the 58 participants. We removed trials containing blinks (2.91%), trials with no-response (2.21%), trials with negative fixation duration (2.41%), trials with a total fixation duration below 100ms (anticipatory responses, 1.63%), and trials in which the initial position of the response saccade on the x-axis was outside the left-or-right boundaries (0.72%)1 . Trials with latencies greater than the possible trial duration (i.e., above 2500ms) or less than 300ms (0.06%), and trials with saccade amplitude greater than 30 degrees and less than 2 degrees (0.20%) were also discarded. Finally, after removing incorrect response trials (3.91%) latency outliers were removed following the classic ± 2.5 standard deviations from the participants' mean response time (2.66%). Statistical analyses were conducted separately for words and pseudowords.

Words

For the analysis of saccade latencies, the final model included Time (past vs future), Side (left vs right) and their interaction as fixed effects, as well as word length (in pixels) and number of word refixations (i.e., the number of fixations that were made on the word before providing the response) as covariates. The model also included by-participant and by-item random intercepts, and a random slope for Time, Side and number of refixations byparticipants and a random slope for time by-items.

Overall, participants were significantly faster to initiate a response saccade to the right side of the screen than to the left side (b = 20.63, SE = 10.14, t = 2.03, p= .044) but there was no significant difference for past versus future tense words (b = 11.86, SE = 8.62, t = 1.37, p= .171). Saccade latencies increased significantly with word length (b = 1.10, SE = 0.27, t = 4.30, p< .0001) and number of refixations (b = 84.97, SE = 5.83, t = 14.57, p< .0001).

Importantly, the congruency effect, which is the interaction between Time and Side, was highly significant (b = -26.49, SE = 9.90, t = 2.68, p= .007). That is, saccade latencies to pasttense stimuli were slower when the correct ("yes") response was on the right rather than the left, and saccade latencies for future-tense verbs were slower when the correct response was on the left versus the right (see Figure 2). The power of this model (i.e., congruency and time) in 200 simulated studies was .81, CI95= [74,86]. No other effect or interaction was significant.

The final model for the analysis of saccade amplitude included Time, Side and their interaction as fixed effects, as well as number of refixations as a covariate. The model also included by-participant and by-item random intercepts, and a random slope for Side byparticipant. Results showed a marginal effect of the number of word refixations (b = -0.05, SE = 0.02, t = 1.89, p= .060). More importantly, the interaction between Time and Side was significant (b = -0.20, SE = 0.08, t = 2.28, p = .023) reflecting the space-time congruency effect (see Figure 2). The power of this model (i.e., congruency and time) in 1000 simulated studies was .66, CI95= [59,73]. No other effect or interaction was significant.

Pseudowords

The final model for the analysis of saccade latencies to pseudowords was exactly the same as that for saccade latencies to words. Saccade latencies increased significantly as a function of pseudoword length (b = 0.81, SE = 0.26, t = 3.19, p= .002) and the number of refixations (b = 83.60,SE = 5.41,t = 15.45,p< .001). The interaction between Time and Side was not significant (b = 3.17, SE = 9.74, t = 0.33, p= .744) No other effect or interaction was significant.

The final model for the analysis of saccade amplitude included Time, Side, number of pseudoword refixations and their interaction as fixed effects, and by-participant and byitem random intercepts. Results showed a significant effect of Side (b = 0.00, SE = 0.00, t = 3.05, p= .002), number of pseudoword refixations (b = 0.00, SE = 0.00, t = 4.35, p< .001) and a signification interaction between them (b = 0.00, SE = 0.00, t = 5.92, p<. 001), that is, participants made more refixations before responding to the left than to the right. No other effect or interaction was significant.

Discussion

Results replicate space-time congruency effects in a lexical decision task in which temporal processing was implicit and responses were provided by lateralized eye movements. Both saccade latency and saccade amplitude were affected. Leftward saccades were initiated more quickly and were smaller in amplitude for past-tense words whereas rightward saccades were quicker and smaller for future-tense words. Given that saccade latency corresponds to the time needed to visually process the stimulus, make the lexical decision, and execute the motor response [START_REF] Gilchrist | Saccades[END_REF], the space-time congruency effect observed for saccade latencies can be considered analogous to the congruency effect obtained previously for manual lexical decision times [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF]. In contrast, the space-time congruency effect for saccade amplitude is more likely driven by lexical interference operating on metrical adjustment and motor programming of the saccadic response. As parameters of the saccade cannot be modified once it is initiated (e.g., Edelman et al., 2007;[START_REF] Gilchrist | Saccades[END_REF], this suggests that the calculation of the ballistic movement itself is affected by space-time congruency. Different amplitudes between congruent and incongruent trials show that the processing of the temporal content of words interferes with saccade programming.

As in our previous study [START_REF] Grasso | As time goes by : Space-time compatibility effects in word recognition[END_REF], these effects were not found for pseudowords, suggesting that they tap lexical access or lexical representations. These results further replicate our previous findings by confirming that the space-time congruency effect can be obtained even when the processing of the words' temporal information is not explicitly required to perform the task, suggesting that the key factor for obtaining this effect might be spatially directed movement per se.

Finally, the significant interaction between the temporal content of words and the direction of eye movements suggests that the lexical representation of words that refer to time contains spatially oriented information (see also ;[START_REF] Hartmann | Eye movements during mental time travel follow a diagonal line[END_REF][START_REF] Stocker | Eye Movements Reveal Mental Looking Through Time[END_REF]. Interference arises because, in the incongruent conditions, leftward or rightward movements engage spatially oriented motor networks that are incompatible with the leftright oriented spatio-temporal information associated with the lexical representation of the word. These results are consistent with the idea that the spatial representation of the temporal content of words derives from culture-dependent directional movements that are habitually produced during writing and reading (e.g., [START_REF] Boroditsky | Remembrances of Times East : Absolute Spatial Representations of Time in an Australian Aboriginal Community[END_REF][START_REF] Fuhrman | Cross-Cultural Differences in Mental Representations of Time : Evidence From an Implicit Nonlinguistic Task[END_REF][START_REF] Oliveri | Representation of time intervals in the right posterior parietal cortex : Implications for a mental time line[END_REF]. In the future, it would be informative to investigate to what extent reading development or reading expertise determines the emergence of the space-time congruency effect.

Interestingly, the replication of the space-time congruency effect with eye movements also suggests that the spatial frame of reference used to distinguish between the left and the right space is centred on the median axis of the whole-body. To test further this hypothesis of a body-centered frame of reference engaged in the coding the spatio-temporal representation of words, one could replicate the experiment with another effector that is not involved in reading or writing, such as the foot.

To conclude, our results fit nicely with an embodied conception of language and time, by showing that directional movements of body parts through space are involved in the coding of past-and future-tense verbs.

Declarations

  left or right boundary. Responses time corresponded to saccade latency (latency between the onset of the stimulus and onset of the saccade). To assess the kinematic features of the saccade, we measured saccade amplitude expressed in degrees of visual angle. After each response, participants were instructed to fixate the central black dot in order to start the next trial. The time interval between the onset of the stimulus and the new fixation dot was 2500ms. A break was offered to participants every 20 trials. Half-way through the experiment (80 trials) participants were instructed to switch sides for yes/no responses. Each testing session lasted approximately 1 hour.

Figure 1 .

 1 Figure 1. Task design.Once participants fixated the central dot, a prime (hier or demain, i.e., "yesterday" or "tomorrow") was displayed, followed by a word or pseudoword (e.g, j'entendrai as a future tense verb or j'entendais as a past tense verb). Participants made their lexical decision by moving their eyes towards the left or right side of the screen (delimited by two virtual boundaries). In this example, the yes-response for the word conjugated in the future tense is congruent with the MTL in Block 1 (rightward eye movement) but incongruent in Block 2 (leftward eye movement). Saccadic responses were automatically detected and recorded as soon as the eyes crossed the left or right virtual boundaries on the screen. We recorded the initiation time (response time) and the amplitude (in degree of visual angle) of the saccades. T1 corresponds to the onset-time of the saccade, T2 corresponds to the boundary-crossing time, and T3 corresponds to the landing time. Therefore, response latencies correspond to the response initiation time, which is the delay between the onset of the stimulus and onset of the saccade response (T1). Saccades that did not reach the left/right boundaries were automatically discarded from the analyses.

Figure 2 .

 2 Figure 2. Estimated marginal means from the mixed models (EMMs) for saccade latencies (A) and for saccade amplitude in Degrees of Visual Angle (B) showing the interaction between Time (past vs future) and Side (left vs right) for words but not pseudowords. Error bars represent within subjects' standard errors.

A saccade response was detected as soon as the eyes crossed the virtual left and right boundaries on the screen. Thus, if the initial position of the eye on the x-axis at the beginning of a trial is not at the center of the screen but outside these boundaries, the trial is considered impossible and discarded.

Acknowledgments

We thank Jonathan Mirault, Françoise Vitu and Boris Quetard for tremendously helpful comments and suggestions.

Funding

Camille Grasso was supported by a doctoral fellowship of the French Ministry of Higher Education, Research, and Innovation. This study benefited from support of the Institute of Convergence ILCB (ANR-16-CONV-0002) and the Excellence Initiative of Aix-Marseille University (A*MIDEX).

Availability of data, code, and materials

According to the open science practices all data and script are available at https://osf.io/5ehnc/

Conflicts of interest

We have no known conflict of interest to disclose.