Maurilio Pereira Gomes

Samantha Michelle Gateman

Isolda Costa

Oumaïma Gharbi

Kieu Ngo

Jesualdo Luiz Rossi

Mireille Turmine

Dr Vincent Vivier
email: vincent.vivier@sorbonne-universite.fr

Improved Experimental Setup to Reach a Broad Frequency Domain in Local Electrochemical Impedance Spectroscopy Measurements

Keywords: Scanning Electrochemical Probe Microscopy, Electrochemical Impedance Spectroscopy, Low frequency measurements, Electrochemical instrumentation, Microelectrochemistry

A new LEIS setup is presented for performing low frequency measurements -The development of local probes by soft lithography for sensing local current density allows broad-frequency measurements -A comprehensive understanding of the local current densities is provided with the help of a newly developed equipment.

Introduction

The development of local electrochemical techniques such as scanning electrochemical microscopy (SECM) [START_REF] Kai | Scanning electrochemical microscopy at the nanometer level[END_REF][START_REF] Polcari | Scanning Electrochemical Microscopy: A Comprehensive Review of Experimental Parameters from 1989 to 2015[END_REF], scanning vibrating electrode technique (SVET) [START_REF] Bastos | Review-On the Application of the Scanning Vibrating Electrode Technique (SVET) to Corrosion Research[END_REF], and scanning microcell [START_REF] Krawiec | Use of the electrochemical microcell technique and the SVET for monitoring pitting corrosion at MnS inclusions[END_REF] or scanning electrochemical cell microscopy (SECCM) [START_REF] Ebejer | Localized high resolution electrochemistry and multifunctional imaging: scanning electrochemical cell microscopy[END_REF], has enabled local reactivity measurements of various types of interfaces at different length scales. These techniques have been utilized to measure surface heterogeneity of interfaces including the solid electrolyte interphase formation on graphite [START_REF] Martín-Yerga | Scanning Electrochemical Cell Microscopy in a Glovebox: Structure-Activity Correlations in the Early Stages of Solid-Electrolyte Interphase Formation on Graphite[END_REF], electrocatalytic materials [START_REF] Bo | Probing Activities of Individual Catalytic Nanoflakes by Tunneling Mode of Scanning Electrochemical Microscopy[END_REF], corroding metals [START_REF] Gateman | Using macro and micro electrochemical methods to understand the corrosion behavior of stainless steel thermal spray coatings[END_REF], and bio-surfaces and interfaces [START_REF] Zhou | Scanning electrochemical microscopy for biosurface imaging[END_REF].

Additionally, different approaches have been developed to take advantage of frequencyresolved local electrochemical techniques. For instance, the AC-mode of SECM has been devised using single frequency measurements for a fine control of the probe positioning [START_REF] Gabrielli | Scanning electrochemical microscopy imaging by means of high-frequency impedance measurements in feedback mode[END_REF][START_REF] Etienne | High resolution constant-distance mode alternating current scanning electrochemical microscopy (AC-SECM)[END_REF] and for imaging localized corrosion [START_REF] Gabrielli | Concentration mapping around copper microelectrodes studied by scanning electrochemical microscopy[END_REF][START_REF] Eckhard | Alternating current techniques in scanning electrochemical microscopy (AC-SECM)[END_REF]. However, AC-SECM relies on the EIS response of the microelectrode and how it is perturbed by the presence of the substrate, and does not directly measure the substrate's localized EIS response. The local electrochemical impedance spectroscopy (LEIS) technique was devised by Isaacs et al. [START_REF] Lillard | A Novel Method for Generating Quantitative Local Electrochemical Impedance Spectroscopy[END_REF][START_REF] Zou | A high-resolution probe for localized electrochemical impedance spectroscopy measurements[END_REF], taking advantage of local current density measurements using a bi-microelectrode (two stationary microelectrodes) as a local probe. The local potential difference between the two microelectrodes is then expressed as a local current density, , using Ohm's law and the 𝑗 𝑙𝑜𝑐 geometric characteristic of the probe according to Eq 1:

𝑗 𝑙𝑜𝑐 (𝜔) = ∆𝐸 𝑙𝑜𝑐 (𝜔) • 𝜅 𝑑 Eq. 1
where is the potential difference between the two microelectrodes at the frequency ∆𝐸 𝑙𝑜𝑐 (𝜔) , is the bulk electrolyte conductivity, and is the distance between the two 𝑓 = 𝜔/2𝜋 𝜅 𝑑 microelectrodes. Using this local current density measured at different frequencies, it is possible to calculate the local impedance , , in Eq. 2 [START_REF] Gharbi | Local electrochemical impedance spectroscopy: A window into heterogeneous interfaces[END_REF]:

𝑧 𝑙𝑜𝑐 𝑧 𝑙𝑜𝑐 = ∆𝑉 𝑟𝑒𝑓 (𝜔) 𝑗 𝑙𝑜𝑐 (𝜔)
Eq. 2

where is the applied potential perturbation at the substrate of interest with respect to ∆𝑉 𝑟𝑒𝑓 (𝜔) the reference electrode.

An analysis of the various applications of LEIS reported in the literature shows that this technique can still be improved, both for high and low frequencies measurements [START_REF] Gharbi | Local electrochemical impedance spectroscopy: A window into heterogeneous interfaces[END_REF][START_REF] Burczyk | Local electrochemical impedance spectroscopy in dynamic mode of galvanic coupling[END_REF].

LEIS mapping is a technique that is often used to study degradation of protective coatings such as polymers for corrosion resistance [START_REF] Ye | Superior corrosion resistance and self-healable epoxy coating pigmented with silanzied trianilineintercalated graphene[END_REF][START_REF] Jorcin | Delaminated areas beneath organic coating: A local electrochemical impedance approach[END_REF]. The main advantages of this technique for the corrosion and coating fields are that coating delamination can be locally measured (i.e., detachment of the polymeric layer from the metal surface) prior to physical observation of liftoff, and it avoids the need to polarize the substrate far from its steady state. Such measurements are usually performed at a single frequency, most often chosen in the medium or high frequency range (i.e., f > 100 Hz) and in low electrolyte concentration [START_REF] Thi Xuan | Corrosion protection of carbon steel by an epoxy resin containing organically modified clay[END_REF][START_REF] Cheng | Polydopamine modified ultrathin hydroxyapatite nanosheets for anti-corrosion reinforcement in polymeric coatings[END_REF], so that the duration of the experiment is short enough to assume a quasi-steady-state during the mapping and the AC potential measured at the bi-microelectrode is large enough to not be masked by the DC component of the potential.

To improve the spatial resolution of LEIS, both the size of each microelectrode and the intermicroelectrode distance must be reduced, thus resulting in a decrease in the measured AC potential difference. This reduction in AC potential difference poses the issue of the ACpotential contribution being masked by the large DC-current contribution, which stems from the electrochemical reactivity of the electrode material used to fabricate the bi-microelectrodes.

The measurement of an AC-current contribution can be in the nA range or less (i.e., potential differences in the range of the µV down to nV depending on the electrolyte conductivity), whereas the DC-current contribution may result in potential difference as high as few mV.

Thus, the new device must first cancel the DC component before the amplification of the AC response of the system especially for the low frequencies. The solution of working in very dilute electrolytes usually proposed in the literature is however not acceptable because it corresponds to unconventional study environments. Moreover, decreasing the electrode size for improving spatial resolution generally results in a shortening the distance between the current collectors of each probe. This usually leads to a high-frequency stray-capacitance, which is added to the response and singularly complicates the interpretation in the high frequency domain.

The work presented herein aims to contribute to the LEIS community by providing methods on how to experimentally overcome these problems, that is, measuring LEIS in a broad frequency domain with a small electrode size in highly conductive media. The experimental measurement device developed for this work, namely the potential shifter and the tri-microelectrode LEIS probe, will be first presented and discussed. Then, a theoretical analysis of an electrochemical system will be investigated using finite element modeling. Finally, the proposed experimental solutions will be validated on two different experimental systems: the analysis of the electron transfer on a model redox couple and the characterization of the corrosion of aluminum in acidic medium.

Experimental

The LEIS probes were manufactured by lithography. Briefly, a system of three gold microelectrodes was deposited on a thin glass slide using a standard lift-off process. This microfabrication method was chosen to control the size and the circular shape of each microelectrode, as well as move the wire current collectors away from each other to minimize the capacitive coupling that may exist when the two wires are too close together [START_REF] Abreu | Influence of probe size for local electrochemical impedance measurements[END_REF]. An example of a local probe fabricated for this work is shown in Figure 1a. It consisted of 3 gold micro-disk electrodes, each 50 µm in diameter, with a center-to-center distance of 100 µm. The current collectors are 50 µm wide and are covered with a thin SiO 2 insulating layer. Local probes from 10 to 100 µm have been fabricated using this protocol, but only results with 50 and 100 µm electrodes are presented in this article. The distance between the microelectrodes and the edge of the glass substrate was small in order to bring the device as close as possible to the surface of interest. From the local potential measurements made with these three microelectrodes, the calculation of the normal and radial components of LEIS can be carried out, as illustrated in Figure 1b. As already pointed out by numerous authors measuring local current density, the potential distribution in the electrochemical cell does not result in equipotential surfaces that are parallel to the electrode surface (except for specific electrode configurations). Thus, it is essential to measure these two contributions to accurately describe the local current density [START_REF] Gharbi | Local electrochemical impedance spectroscopy: A window into heterogeneous interfaces[END_REF] since at a given location, the local current density can be calculated as the sum of local normal and local radial current density. All electrochemical experiments were performed using a home-made LEIS setup sketched in Figure 2a and already described elsewhere [START_REF] Gharbi | Local electrochemical impedance spectroscopy: A window into heterogeneous interfaces[END_REF], which consisted of a home-made potentiostat (which was shown to be a good range to allow a fine control of the potential with acceptable value for the common mode rejection ratio), and a potential shifter is added in the measurement circuit to bring this DC potential difference as close as possible to 0 V. This allows small AC potential differences to be measured during impedance measurements using a higher gain since the analysis of the circuit shows an error of less than 1% for a potential difference of 1 mV at 1 Hz and this error increases with the frequency, but in that case, the AC-contribution (quantity of interest for the LEIS measurement) is also larger, making this circuit useful for the whole frequency domain. From an experimental point of view, it is worth noting that this device is also suited to circumvent the problem of measuring LEIS in concentrated electrolytes. As shown in Eq. 1, a high conductivity results in a low local current density measured. The electronic circuit depicted in Figure 2b enables the implementation of electrolytes with a similar conductivity to common electrochemical measurements, as it will be shown in the following with the experiments performed with ferricyanide/ferrocyanide redox couple.

As the local electrochemical impedance spectroscopy relies on the measurement of the local current density in solution arising from the potential gradient [START_REF] Bastos | Review-On the Application of the Scanning Vibrating Electrode Technique (SVET) to Corrosion Research[END_REF], it may be obtained by using local potential probes positioned close to the electrochemical interface. Similarly to the scanning vibrating electrode technique (SVET), two components of the local current density can be readily measured experimentally, namely the normal and the radial local current densities. In this work, the gold-deposited microelectrodes (Figure 1a) were used for measuring the normal local impedance, , as

z 𝑛𝑜𝑟𝑚𝑎𝑙 z 𝑛𝑜𝑟𝑚𝑎𝑙 = ∆𝑉 𝑟𝑒𝑓 j 𝑛𝑜𝑟𝑚𝑎𝑙 = ∆𝑉 𝑟𝑒𝑓 • d 1 (E 1 -E 2 ) • 𝜅 Eq. 3
and the radial local impedance, , as

z 𝑟𝑎𝑑𝑖𝑎𝑙 z 𝑟𝑎𝑑𝑖𝑎𝑙 = ∆𝑉 𝑟𝑒𝑓 j 𝑟𝑎𝑑𝑖𝑎𝑙 = ∆𝑉 𝑟𝑒𝑓 • d 2 (E 1 -E 3 ) • 𝜅 Eq. 4
where is the applied perturbation potential between the reference and the working ∆𝑉 𝑟𝑒𝑓 electrode, the electrolyte conductivity, , and are the local potentials measured with

𝜅 E 1 E 2 E 3
the gold microelectrodes as depicted in Figure 1b, and and are the distances between the d 1 d 2

normal and the radial microelectrodes, respectively.

Numerical simulations

Model description

In this section, we present the main steps for performing the numerical simulations of both global and local LEIS taking into account the geometry of the electrochemical cell and the current and potential distributions in the electrolyte. The detailed description can be found in previous works of different groups [START_REF] Ferrigno | Finite element simulation of electrochemical ac diffusional impedance. Application to recessed microdiscs[END_REF][START_REF] Michel | Numerical computation of the Faradaic impedance of inlaid microdisk electrodes using a finite element method with anisotropic mesh adaptation[END_REF]. For simplicity, we assume that the working electrode consisted in a planar disk-electrode embedded in an insulator. Such an assumption is in agreement with many experiments reported in the literature and allows the use of cylindrical coordinates for deriving the equations of the model. Let us consider a simple redox reaction in Eq 5:

𝑂𝑥 + 𝑛𝑒 -𝑘 0 𝑅𝑒𝑑 Eq. 5
where is the kinetic constant of the electrochemical reaction, and is the number of 𝑘 0 𝑛 exchanged electrons. Assuming that the kinetics of this reaction follows the Butler-Volmer relationship, the total current at the working electrode, , is given by Eq 6:

𝐼 𝐼 = 𝑛ℱ𝑆𝑘 0 ( 𝐶 𝑟𝑒𝑑 (0)exp ( 𝛼𝑛ℱ 𝑅𝑇 (𝐸 -𝐸 0 ) ) -𝐶 𝑜𝑥 (0)exp ( -(1 -𝛼)𝑛ℱ 𝑅𝑇 (𝐸 -𝐸 0 ) )) Eq. 6
where and are the concentrations of redox species at the interface, is the 𝐶 𝑟𝑒𝑑 (0)

𝐶 𝑜𝑥 (0) 𝛼 charge transfer coefficient, is the applied potential, is the formal redox potential, is the 𝐸 𝐸 0 𝑆 electrode surface area, and the other parameters hold their usual meanings. Mass transport of electroactive species to the disk electrode is described by Fick's second law, which expresses for each redox species, in cylindrical coordinate as

𝑘 ∂𝐶 𝑘 ∂𝑡 = 𝐷 𝑘 ( ∂ 2 𝐶 𝑘 ∂𝑟 2 + 1 𝑟 ∂𝐶 𝑘 ∂𝑟 + ∂ 2 𝐶 𝑘 ∂𝑦 2 )
Eq.7

where is the diffusion coefficient of the species , is the radial coordinate measured from 𝐷 𝑘 𝑘 𝑟 the electrode center, and is the normal coordinate to the electrode surface. 𝑦

We thus followed the previous works of Gabrielli et al. [START_REF] Gabrielli | Scanning electrochemical microscopy imaging by means of high-frequency impedance measurements in feedback mode[END_REF] and Michel et al. [START_REF] Michel | Numerical computation of the Faradaic impedance of inlaid microdisk electrodes using a finite element method with anisotropic mesh adaptation[END_REF] to calculate the faradaic contribution to the impedance at an inlaid disk-electrode using the finite difference method. We first assume that the EIS is performed at steady-state, thus the Fick's second law expresses as

∂ 2 𝐶 𝑘 ∂𝑟 2 + 1 𝑟 ∂𝐶 𝑘 ∂𝑟 + ∂ 2 𝐶 𝑘 ∂𝑦 2 = 0
Eq. 8

On the surrounding insulator, the flux of electroactive species is zero

∇𝐶 𝑘 • 𝒏 = 0
Eq. 9

where is the concentration gradient with respect to the and coordinates, and is a unit ∇𝐶 𝑘 𝑟 𝑦 𝒏 vector normal to the boundary of the electrochemical system. Far from the electrode surface (i.e., in the bulk solution),

𝐶 𝑘 →𝐶 * 𝑘 as 𝑟 2 + 𝑦 2 →∞ Eq.10
where is the bulk concentration of the redox species . At the electrode surface, the current 𝐶 * 𝑘 𝑘 can be split into a DC component and a harmonic component, where the latter is used to calculate the total impedance of the interface, obtained from the linearization of the Butler-Volmer relation [START_REF] Orazem | Electrochemical Impedance Spectroscopy[END_REF].

Moreover, we also take into account the current and potential distributions due to the polarization and the geometry of the interface [START_REF] Orazem | Electrochemical Impedance Spectroscopy[END_REF]. The potential, in solution is governed by 𝜙,

Laplace's relationship

∂ 2 𝜙 ∂𝑟 2 + 1 𝑟 ∂𝜙 ∂𝑟 + ∂ 2 𝜙 ∂𝑦 2 = 0
Eq. 11

On the surrounding insulator and far from the electrode surface (i.e., on the counter electrode), the boundary conditions for solving the Laplace's law are expressed as

∂𝜙 ∂𝑟 | 𝑦 = 0 = 0
Eq. 12 𝜙→0 as 𝑟 2 + 𝑦 2 →∞ Eq. 13

whereas assuming an ideal capacitor ( ) for describing the double layer at the electrode 𝐶 𝑑𝑙 interface, the current density at the electrode can be expressed as

𝑖 = 𝐶 𝑑𝑙 ∂ (𝐸 -𝐸 0 ) ∂𝑡 + 𝑛ℱ𝑘 0 ( 𝐶 𝑟𝑒𝑑 (0)exp ( 𝛼𝑛ℱ 𝑅𝑇 (𝐸 -𝐸 0 ) ) -𝐶 𝑜𝑥 (0)exp ( -(1 -𝛼)𝑛ℱ 𝑅𝑇 (𝐸 -𝐸 0 ) )) = ∂𝜙 ∂𝑟 | 𝑦 = 0 Eq . 14
This set of equations is then solved in the frequency domain, thus allowing the global impedance response of the electrode to be calculated together with the evaluation of the local impedance measured at various location in the electrolyte, above the surface of the working electrode.

Simulations

In this section, the simulation of the faradaic global and local EIS, taking into account potential distribution at different location above the electrochemical interfaces, are presented with the aim of positioning the problem and identifying the objectives to be achieved to improve the LEIS technique. Figure 3 shows the simulated global and local EIS responses accounting for a ferricyanide / ferrocyanide redox system in a supporting electrolyte. The simulations were performed assuming an electrolyte conductivity of 10 mS cm -1 (corresponding to a 0.5 mol L -1

NaCl solution), and 10 mmol L -1 for each electroactive species. The global impedance response presented in Figure 3a shows the usual features: electrolyte resistance as the high frequency As expected for an ideal behavior for the working electrode, the LEIS response measured at 100 µm above the electrode center results in a similar shape to the global impedance response and the time constants observed remain unchanged as shown in Figure 3b-e. This is consistent with the fact that the processes probed locally are the same as those measured at the global scale. However, some differences exist and need to be discussed. The first point concerns the amplitude of the LEIS response. It depends on several parameters. The larger the distance of the local current measurement probe is, the smaller the potential difference to be measured and the greater the local current density. This results in large values of LEIS measured. The position of the probe above the working electrode is also a parameter to consider. Indeed, when it is close to the center of the working electrode (Figure 3b-c), the main contribution of the current is perpendicular to the surface of the electrode and results in a measured LEIS response obtained from the normal component of the local current density. In this case, the radial component can be neglected. On the other hand, when the probe is positioned above the edge of the working electrode (Figure 3d-e), the radial and normal components are of the same order of magnitude and neither can be neglected for the calculation of the LEIS response. It should be noted that current commercial devices only measure the radial component, thus limiting the possibility of qualitative analysis of the data obtained. It should also be mentioned that the low frequency limit of both local and global electrochemical impedances can significantly vary from one system the other. Actually, some systems may result in low magnitude impedance value in the low frequency limit (e.g., the iron dissolution in the active domain [START_REF] Keddam | Reaction model for iron dissolution studied by electrode impedance. I. Experimental results and reaction model[END_REF] or zinc dissolution [START_REF] Cachet | EIS investigation of zinc dissolution in aerated sulphate medium. Part II: zinc coatings[END_REF]), whereas the impedance measured in the low frequency can be as high as a few M up to a few G (e.g., passive films [START_REF] Abreu | The effect of Ni in the electrochemical properties of oxide layers grown on stainless steels[END_REF] or protective coatings on materials [START_REF] Zomorodian | Corrosion resistance of a composite polymeric coating applied on biodegradable AZ31 magnesium alloy[END_REF][START_REF] Díaz | The corrosion protection afforded by a commercial rust converter doped with graphene oxide[END_REF]). For the latter, the potential difference to be measured in the low frequencies can be very small and requires the use of high gain amplification with a system similar to the one depicted in Figure 2b.

Another significant difference between local and global EIS responses (Figure 3) can be observed in the high frequency domain, which is in the frequency range where the electrolyte resistance is usually determined. The electrolyte resistance value depends on the tip-to-substrate distance; the larger the distance, the larger the uncompensated impedance and may exhibit some inductive and capacitive behavior due to the geometry of the system [START_REF] Frateur | Local electrochemical impedance spectroscopy: Considerations about the cell geometry[END_REF]. It was also shown that this frequency domain can be sensitive to the galvanic current that may exist, for instance, in the case of the corrosion of intermetallic particles embedded in a matrix [START_REF] Lacroix | Simulating the galvanic coupling between S-Al2CuMg phase particles and the matrix of 2024 aerospace aluminium alloy[END_REF][START_REF] Jorcin | Comparison of local electrochemical impedance measurements derived from bi-electrode and microcapillary techniques[END_REF]. However, when small electrodes are used, such a behavior may be hindered by a stray capacitance that distorts the high frequency part of the impedance diagram [START_REF] Abreu | Influence of probe size for local electrochemical impedance measurements[END_REF], thus renders difficulty in conducting a proper analysis of this frequency domain.

Results and discussion

Steady-state measurements

From the seminal work on the measurement of local current density that was later extended to the measurement of LEIS [START_REF] Gharbi | Local electrochemical impedance spectroscopy: A window into heterogeneous interfaces[END_REF], the normal and the radial contributions to the LEIS response can be defined and measured experimentally [START_REF] Ferrari | Influence of normal and radial contributions of local current density on local electrochemical impedance spectroscopy[END_REF]. Figure 4a shows the temporal potential evolution of the three local microelectrodes in a 0.5 M sulfuric acid solution measured against a mercury-mercurous sulfate electrode (MSE) reference. Even if these electrodes are identical, the DC potential measured slightly differs from one electrode to the other due to the different surface states of these microelectrodes. As a result, the potential difference between two microelectrodes is not zero as shown in Figure 4b. This quantity is added to the AC potential that we are interested in measuring. Indeed, if the potential difference that we want to measure is less than µV, the signal has to be amplified by at least a factor of ten thousand, which makes the measurement difficult due to amplification and resulting magnitude of the DC potential contribution measured simultaneously. Conversely, if the measurement is performed following a two-step procedure, this problem is significantly minimized. The calibration step was added where the DC-potential difference is first amplified with a small gain (e.g., 100 in the example presented in Figure 4c) then reduced to a value close to zero with an offset. This enables the measurement of the small AC potential using a high gain without having electronic overload problems. In the impedance measurements presented in the following work, this calibration step was used to measure large impedances and/or use concentrated solutions over a large frequency range.

Electrochemical impedance measurements

Impedance diagrams on redox soluble species

Figure 5 shows the global and local EIS diagrams measured simultaneously at the center of the gold electrode and at the edge of the electrode for the ferri/ferrocyanide system in 0.5 mol L -1

KCl electrolyte. These results should be directly compared to the simulations shown in Figure 3. We observe the first time constant in the high frequency domain that corresponds to the charge transfer resistance in parallel with the double layer capacitance. In the medium to low frequency range, the Warburg diffusion is observed as a 45° line. These characteristics are identical to that obtained with local measurements, but with different amplitudes depending on whether the probe is positioned above the edge or the center of the working electrode, or whether the local current density measured corresponds to the radial or normal component. It should be noted that the mHz range can be measured, even for high impedance (greater than 2 10 4  cm 2 ) in a concentrated solution. In the low frequency limit, one can also assume that the diffusion will be controlled by natural convection. In other words, the Warburg impedance describing semiinfinite diffusion may be not the correct way of describing the system, and a finite diffusion layer (i.e., the Nernst diffusion layer) should be used. In that case, the characteristic frequency is the diffusion impedance, given by 𝑓 𝑐 = 2.5 𝐷 2𝜋𝛿 2

𝑁

Eq. 5

where is the diffusion coefficient of the electroactive species, and is the thickness of the 𝐷 𝛿 𝑁 Nernst diffusion layer. Assuming a diffusivity and a diffusion layer 𝐷 = 5 * 10 -6 cm 2 s -1 thickness , a characteristic frequency of ca. is calculated, which is a value 𝛿 𝑁 = 300 µm 2 mHz close to the low frequency limit used for performing experimental EIS and LEIS measurements.

This result shows that the assumption of a semi-infinite Warburg diffusion remains valid in the whole frequency range investigated in this work.

In addition, the design of the probes with current collectors spaced far enough apart to minimize stray capacitance allows for evidence of ohmic impedance on LEIS diagrams at frequencies above 10 kHz as shown in the insets of Figure 5c-f.

Impedance diagrams on a corroding system

In order to show that this new experimental dispersive is suitable for any type of EIS measurement, the case of an aluminum electrode in sulfuric acid medium was studied Figure 6 and Figure 7. Even if the mechanism of dissolution of aluminum in acid medium is still a controversial subject, the objective in this study is not to study this mechanism, but rather to show that the LEIS allows the reactivity of materials to be characterized by several time constants.

Figure 6a shows the global EIS response of a pure Al electrode after one hour immersion in 0.5 mol L -1 sulfuric acid at the corrosion potential. Three time-constants can be clearly observed:

in the high frequency domain, a capacitive loop can be ascribed to the charge transfer at the metal oxide interface in parallel with the capacitance of the thin oxide film [START_REF] Dewit | Electrochemical Impedance Spectroscopy as a tool to obtain mechanistic information on the passive behaviour of aluminium[END_REF][START_REF] Aoki | Ac-impedance and Raman spectroscopy study of the electrochemical behaviour of pure aluminium in citric acid media[END_REF]. In the intermediate frequency domain, an inductive loop is observed, which usually is attributed to the relaxation of adsorbed ions such as oxygen anions that are present at the oxide/electrolyte interface [START_REF] Dewit | Electrochemical Impedance Spectroscopy as a tool to obtain mechanistic information on the passive behaviour of aluminium[END_REF][START_REF] Våland | Reactions at the oxide-electrolyte interface of anodic oxide films on aluminum[END_REF]. In the low frequency domain, the capacitive behavior can be ascribed either to the relaxation of adsorbate intermediates [START_REF] Dewit | Electrochemical Impedance Spectroscopy as a tool to obtain mechanistic information on the passive behaviour of aluminium[END_REF] or to the modulation of the thin oxide film thickness [START_REF] De Wit | Impedance Measurements during Anodization of Aluminum[END_REF]. When LEIS measurements are performed above the working electrode center, the same response was obtained with three time-constants from both the normal (Figure 6b) and the radial (Figure 6c) local current density contributions. Interestingly, the characteristic frequencies remain unchanged and normal contribution is almost similar to the global EIS response. However, the amplitude of the inductive loop measured from the radial current density is larger, showing that this time-constant is sensitive to the position at which the measurements is performed. It is worth noting that despite the fact that the impedance value is very high, it is possible with this new device to measure it. It is also noted that when the measurement is made at the center of the working electrode, the radial component is more than one hundred times higher, which indicates that this contribution is negligible.

Conversely, when the same measurement is performed on the edge of the electrode (Figure 7), the two components of the LEIS response are of the same order of magnitude. These results

show two things: on the one hand it is possible to measure high LEIS at low frequency, and on the other hand, the radial component which is often presented for DC measurements [START_REF] Bastos | Review-On the Application of the Scanning Vibrating Electrode Technique (SVET) to Corrosion Research[END_REF] and often ignored for LEIS measurements, is an important contribution to the measured response, in particular when the probe is positioned near a discontinuity.

Local electrochemical impedance spectroscopy is also widely used for mapping the reactivity of an interface. For LEIS mapping, it is not common to perform measurements in the very low frequency domain since the acquisition of each point requires at least the equivalent time corresponding to one cycle of the applied perturbation. For example, at 10 mHz, the duration of the measurement is 100 s. For a picture of 100 by 100 points, this will require about 280 hours, i.e., more than 11 days. In fact, 1 Hz seems to be the limit for this particular application since it takes about 2.5 hours to acquire the entire image of the same size, assuming little or no change in the electrochemical system during this time.

Conclusions

In

Figure 1 :

 1 Figure 1: (a) Example of a three-electrode local probe for LEIS setup made by lithography -each electrode is 25 µm in radius and current collectors, which are covered by a thin insulating layer, are 50 µm wide -the active surface area for each electrode is delimited by the circle at the end of each strip; (b) definition of local current densities that can be measured with this probe.

Figure 2 :

 2 Figure 2: (a) Diagram of the experimental cell used to measure the local electrochemical impedance; (b) Circuit diagram of the potential shifter used in this work.

  and a data acquisition card (National Instrument) controlled by an in-house developed software for the simultaneous measurement of multiple transfer functions. It provides the unique way of measuring simultaneously global and local EIS responses of the interface. The LEIS probe was positioned above the substrate with a 3-axis positioning system (M-VP-25XA, Newport) driven by a motion encoder (ESP301, Newport) allowing a sub-micrometer spatial resolution in the three directions. Thus, in the present work, the probe dimension governs the attainable spatial resolution, which was in the range of a few micrometers depending on the probe size used and the distance to the substrate to analyze. Compared to the devices previously described in the literature, a specific amplification/offset device has been added to minimize the DC contribution of the potential difference between two microelectrodes Figure2b. It consisted in a potential shifter inserted in the measuring circuit between the probes and the last amplification stage, allowing for the minimization of the DC potential contribution. During a preliminary measurement in the absence of any applied perturbation (i.e., at the open circuit potential of the working electrode, when no impedance measurement is made), the potential difference measured at these microelectrodes is amplified by moderate gain, typically between 10 and 100

  limit of the impedance, a first capacitive time constant ascribed to the charge transfer resistance in parallel with the double layer capacitance, and a diffusion contribution in the low frequency domain corresponding to the Warburg impedance. The set of values used to carry out these simulations correspond to values usually encountered for a mono-electronic transfer involving soluble redox species. The resulting impedance diagram gives impedance values in the range of a few  to a few k, i.e., values that can be easily measured with conventional equipment.

Figure 3 :

 3 Figure 3: FEM simulation of the impedance response of an electrode immersed in Ox/Red solution (a), LEIS response at the electrode center -normal LEIS (b) and radial LEIS (c), and at the electrode edgenormal LEIS (d) and radial LEIS (e). Simulations were performed with 0.001 cm s -1 , 0.5, E = 𝑘 0 = 𝛼 =

Figure 4 :

 4 Figure 4: (a) Potential of the microelectrodes measured with respect to a MSE reference electrode for one hour in sulfuric acid solution; (b) potential difference between 2 microelectrodes before (b) and after (c)the DC -offset stage (see Figure2b).

Figure 5 :

 5 Figure 5: EIS and LEIS responses of ferri/ferrocyanide redox system at an Au electrode at the standard potential of the system (equimolar concentration of the electroactive species) in a 0.5 M KCl solution.

Figure 6 :

 6 Figure 6: EIS responses of Al in 0.5 mol L -1 sulfuric acid solution at the corrosion potential -measured at the electrode center. (a) Global EIS, (b) normal component of the LEIS (c) radial component of the LEIS.

Figure 7 :

 7 Figure 7: EIS responses of Al in 0.5 mol L -1 sulfuric acid solution at the corrosion potential -measured at the electrode edge. (a) Global EIS, (b) normal component of the LEIS, (c) radial component of the LEIS.

  the present work, we propose an improved measuring device to study the local electrochemical impedance spectroscopy of an interface. The improvement concerns two main points: the measurement device itself with the development of a local probe that allows us to eliminate the stray capacitance due to the coupling of the two gold tracks acting as current collectors to the microelectrodes; and the use of potential shifter to minimize the DC-potential offset between the microelectrodes. The latter is of particular interest since such an enhancement was shown to allow both measuring at low frequency (in the mHz range) and working in concentrated electrolyte, as demonstrated with the experiments performed on the ferri/ferrocyanide redox couple as model system.List of symbolsConcentration of the species -(mol cm -3 ) 𝐶 𝑘 𝑘 𝑘 = 𝑜𝑥 or 𝑟𝑒𝑑 Bulk concentration of the species -(mol cm -3 ) 𝐶 * 𝑘 𝑘 𝑘 = 𝑜𝑥 or 𝑟𝑒𝑑 Double layer capacitance (F cm -2 ) 𝐶 𝑑𝑙 Distance between two microprobes (cm) 𝑑 Diffusion coefficient of the species -(cm 2 s -1 ) 𝐷 𝑘 𝑘 𝑘 = 𝑜𝑥 or 𝑟𝑒𝑑 Corrosion potential (V) 𝐸 corr Standard potential (V) 𝐸 0 Local potential measured with the probe (V) E 𝑖 𝑖 Faraday constant (96485 C mol -1 ) ℱ Frequency (Hz) 𝑓 Characteristic frequency (Hz) 𝑓 𝑐 Current (A) 𝐼 Current density (A cm -2 ) 𝑖 Local current density (A cm -2 ) 𝑗 𝑙𝑜𝑐 Local normal current density (A cm -2 ) j 𝑛𝑜𝑟𝑚𝑎𝑙 Local radial current density (A cm -2 ) j 𝑟𝑎𝑑𝑖𝑎𝑙 Kinetic constant of the electrochemical reaction (cm s -1 ) 𝑘 0 Number of exchanged electrons 𝑛 Molar gas constant (8.314 J K -1 mol -1 ) 𝑅 Radial coordinate measured from the electrode center (cm) 𝑟 Surface area of the working electrode (cm 2 ) 𝑆 Temperature (K) 𝑇 Time (s) 𝑡 Normal coordinate measured from the electrode surface (cm) 𝑦 Global impedance of the sample ( cm 2 ) Z Local impedance ( cm 2 ) 𝑧 𝑙𝑜𝑐 Local normal impedance ( cm 2 ) z 𝑛𝑜𝑟𝑚𝑎𝑙 Local radial impedance ( cm 2 ) z 𝑟𝑎𝑑𝑖𝑎𝑙 Charge transfer coefficient of the electrochemical reaction 𝛼 Potential difference between two microprobes (V) ∆𝐸 𝑙𝑜𝑐 Potential difference between the substrate and the reference electrode (V) ∆𝑉 𝑟𝑒𝑓 Thickness of the Nernst's layer 𝛿 𝑁 Electrolyte conductivity (S cm -1 ) 𝜅 Potential (V) 𝜙 Angular frequency, (rad s -1 ) 𝜔 𝜔 = 2𝜋𝑓

Acknowledgments

The authors acknowledge FAPESP (2013/13235-6) and CAPES-Cofecub (806-14) for the financial support to this research and also for the grant of Maurilio Pereira Gomes (88881.154406/2017-01).


Frédéric Béchet

Elie Antoine

Jeremy Auguste

Géraldine Damnati

Question Generation and Answering for exploring Digital Humanities collections

Keywords: Question Generation, Machine reading Question Answering, Digital Humanities

This paper introduces the question answering paradigm as a way to explore digitized archive collections for Social Science studies. In particular, we are interested in evaluating largely studied question generation and question answering approaches on a new type of documents, as a step forward beyond traditional benchmark evaluations. Question generation can be used as a way to provide enhanced training material for Machine Reading Question Answering algorithms but also has its own purpose in this paradigm, where relevant questions can be used as a way to create explainable links between documents. To this end, generating large amounts of question is not the only motivation, but we need to include qualitative and semantic control to the generation process. In the framework the French ANR project ARCHIVAL, we propose a new approach for question generation, relying on a BART Transformer based generative model, for which input data are enriched by semantic constraints. Question generation and answering are evaluated on several French corpora, and the whole approach is validated on a new corpus of digitized archive collection of a French Social Science journal.

Introduction

Recent advances in representation learning of text have achieved remarkable results on benchmark Natural Language Understanding (NLU) tasks as shown in the recent General Language Understanding Evaluation (GLUE) benchmarks [START_REF] Wang | Glue: A multi-task benchmark and analysis platform for natural language understanding[END_REF], reaching even so-called human performance on several tasks [START_REF] Wang | Superglue: A stickier benchmark for general-purpose language understanding systems[END_REF] such as linguistic acceptability, question answering or semantic similarity. However these impressive results are obtained on corpora specifically prepared for these benchmark evaluations; moreover these understanding tasks, although always related to a linguistic competency, can be considered as rather artificial as they are tailored to fit the need of system benchmark evaluation and can be quite far from a real application. In order to study how the current boost in performance in NLU models on benchmark data translates to reallife settings, the applicative framework considered here is the exploration of digitized collections by professional users that are used to analyze archives in order to perform Social Science research. We chose to focus on the question/answering paradigm, as asking questions and looking for answers is at the same time a natural way for researchers to explore archives and also the task that received the most attention in recent language understanding studies, especially since the release of large training data such as SQuAD [START_REF] Rajpurkar | Squad: 100,000+ questions for machine comprehension of text[END_REF] 1 . In this paper we will present first the self-management corpus, a collection of a French journal ranging over 20 years from 1966 to 1986, which has been chosen as our archival material in the ARCHIVAL project, then we will highlight the differences between bench-1 https://rajpurkar.github.io/SQuAD-explorer/ mark corpora usually based on Wikipedia and digitized archive collections. We will then present the question/answering paradigm, the annotation scheme developed in Archival and point out the differences between the kinds of questions that can be made by professional users and those used in Machine Reading datasets such as SQuAD. We will describe the question generation and question answering models that have been developed to adapt a Machine Reading model trained on Wikipedia to the self-management corpus of the ARCHIVAL project without any supervision. Finally we will present the first results obtained on the selfmanagement dataset with this adapted Machine Reading model.

The self-management corpus

Origin of the collection

The "self-management" notion falls within the large spectrum of social sciences. It concerns daily social environment, economic life, as well as political life, education, ecology, culture, architecture, . . . . It addresses populations structure, the relationship of populations with resources, the political, legal and administrative framework of society and the authority relations between individuals and groups. Since the 1960's, the FMSH2 foundation's library has gathered a pluridisciplinary multilingual mixed collection (archives and documents) about self-management (autogestion in French). It gathers around 25000 pieces: books, journals, reports, leaflets, correspondences.

Corpus description

For this study, we are particularly interested in the Autogestion journal3 which is distributed in its digitized form by the French Persée organization. We are using a version of the corpus that has been OCRized with Tesseract without manual corrections. Hence data are not free of OCR errors but the structure of the journal (mono-column, few figures) implies that the OCR quality is good (further studies could imply precise evaluation of OCR quality and impact of OCR errors on downstream NLP tasks but for this study, OCR output are taken as is). The resulting corpus is composed of 46 issues ranging over 20 years, for an overall amount of 6298 pages and 1.98M tokens.

Specificities of texts from an NLP point of view

Most studies in Information Extraction or Question Answering are carried out on Wikipedia pages. Wikipedia documents are particularly well suited for theses tasks as they intrinsically dedicated to convey factual information. Another characteristic of Wikipedia is that articles are supposed to follow a Neutral Point of View policy4 . Recent work [START_REF] Bertsch | Detection of puffery on the english wikipedia[END_REF] aims at detecting so-called puffery (i.e sentences that do not respect that policy, which are tagged by editors as "peacock phrases") but this phenomenon remains very rare.

On the contrary, texts that are relevant for Digital Humanities and studies related to Social Science are not only factual and neutral documents but also essays or articles that reflect the writer's point of view. Description of events are not only depicted by facts but with deeper analysis of the previous notions or influences that yielded this event as well as their consequences and how they influenced the thinking of other actors.

The following figures provide a few insights of the differences between language in Wikipedia pages and language in the "Autogestion" journal. Of course a more comprehensive study would be necessary to characterize precisely "Autogestion" journal texts, but we propose these figures as we believe they can be relevant for our tasks of Information Extraction and Question Answering. Distributions from Wikipedia were extracted from two portals (Archeology and First World War) as gathered in the public French corpus CALOR [START_REF] Marzinotto | Semantic frame parsing for information extraction : the calor corpus[END_REF] designed for Semantic Frame analysis and Machine Reading Question Answering [START_REF] Béchet | Calorquest: generating a training corpus for machine reading comprehension models from shallow semantic annotations[END_REF]. Figure 1 and figure 2 respectively show the distribution of Part of Speech tags and morphological features, as obtained by the Spacy tokenizer and syntactic parser. The main differences in terms of POS distribution is that the Autogestion corpus contains less Proper Nouns (PROPN) and less prepositions (ADP). These two observations suggest that sentences are less descriptive.

On the other hand it contains more pronouns (PRON) suggesting longer sentences with more anaphoras and more adverbs (ADV) and adjectives (ADJ). The higher proportion of symbols (SYM) however is probably an artefact of OCR errors. The morphological features distributions reveal a higher proportion of plural and feminin forms and a higher proportion of present tense and less past tense.

The question answering paradigm

With recent advances in Machine Reading Comprehension (or MRQA for Machine Reading Question Answering) and Knowledge-Base Question Answering (KBQA) along with a very active community participating to competitions and challenges on several public QA benchmark corpora, it is now accessible to use such models in realistic use-cases. In our vision, questioning documents can be a voluntary process performed by users who express a given question on purpose or can be an implicit process that helps creating links between documents, transforming a collection of documents into a graph of documents. The former is already implementable through efficient Question Answering Search platforms such as Haystack5 but the latter is more original and implies that the system can automatically infer relevant questions on documents.

The Question Answering Paradigm can be summarized as follows:

• Questions to a general (or specifically designed) Knowledge Base: Q&A as an assistant for the user to improve its prior knowledge or to facilitate its comprehension of the mentioned notions

• Questions as an advanced search engine, beyond keyword search for the user: finding all documents that might contain an answer to a specific question with the candidate answer highlighted (Text Retriever + Machine Reading Question Answering)

• Questions as an implicit yet explainable generator of links towards related documents: if two documents raise the same questions, or if a document contains the answer to a question raised in another document, there is a link between these documents (these links can be explained by an ananlysis of the questions used to create them).

In the framework of the French ANR project ARCHIVAL6 we will focus on the last two tasks of this paradigm, therefore we need models that can retrieve answers from users questions and which can generate questions from a text or a segment of text. These models are described in the following section, we will see

Question generation and answering models

Question generation and question answering are two classical NLP tasks which have been completely rethought with the development of large pre-trained language models. Thanks to generation models such as BART [START_REF] Lewis | BART: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension[END_REF] or classification models such as BERT [START_REF] Devlin | Bert: Pre-training of deep bidirectional transformers for language understanding[END_REF], these two tasks which were traditionally handled through complex linguistic pipelines in the pre-deep-neural-network era have been replaced with straightforward end-to-end approaches with a large boost in performance. In these approaches, the pre-trained models are fine-tuned on the final task thanks to an end-to-end process where the adaptation to the task is done through the choice of the format and the content of the input and output sequences of sym-bols which will encode the data.

As presented in [START_REF] Du | Learning to ask: Neural question generation for reading comprehension[END_REF], the question generation task can be modeled as a neural generation task where a sequence-to-sequence model is trained to translate a sequence of words representing a sentence or a passage into another sequence of words representing a question on the input. The task is then to generate a question given a (passage, answer) pair. Large sequence-to-sequence generation models such as BART in conjunction with large databases of question/answer/context triplets such as SQUAD can be used to directly train a passage-to-question translation model. Training such generation models with generalization capacities beyond existing available reference corpora remains challenging though. [START_REF] Lyu | Improving unsupervised question answering via summarization-informed question generation[END_REF] propose an unsupervised way of generating synthetic training material for question generation, by using simplified summaries of documents along with simple heuristics to generate domain related training exam-ples of questions that are used to adapt the generation models.

Several approaches have been proposed to make use of synthetic question/answer/context triplets to train Machine Reading models in a data augmentation perspective or in few-shot or zero-shot settings. In [START_REF] Béchet | CALOR-Frame : un corpus de textes encyclopédiques annoté en cadres sémantiques[END_REF], we proposed to use Semantic Frame parsing along with generic patterns in order to generate questions, whose answers would be selected from Frame Elements. [START_REF] Puri | Training question answering models from synthetic data[END_REF] introduced generative approaches with pre-trained language models by selecting candidate answers with a BERT detection model and generating the corresponding question with a GPT-2 generation model. In a more systematic approach, [START_REF] Shakeri | Endto-end synthetic data generation for domain adaptation of question answering systems[END_REF] extended their approach, predicting (question, answer) pairs from a passage by systematically considering any token as a potential answer. A filtering process based on predictions likelihood is used to select the most relevant questions.

The use of such synthetic question/answer/context triplets have shown to yield improvements in MRQA benchmarks or in adaptation configurations. However the quality of the generated questions remains a drawback. In this work were are not only interested in improving our MRQA model on our Social Science journal corpus, but we are also interested in generating questions that can be used in our question answering paradigm to explore these archival collections.

For instance, if we are to propose a link between two passages based on a question they would both provide an answer to, we want this question to be relevant, sounded and correct from a semantic and syntactic point of view. Furthermore we want to be able to explain why this question has been chosen. In this perspective, we will present in this section how we propose to encode the question generation and answering tasks in order to fit this end-to-end paradigm with pretrained models based on Transformer Language Model architectures, while conciliating both qualitative and quantitative objectives for synthetic question generation.

Question generation model

In our study, following previous work done on the CALOR-QUEST corpus, a semantic representation is added to the sentence as input to the generation model. The goal of this semantic representation is to guide the question generation by explicitly modeling the semantic link between the answers and the arguments of the questions. Two kinds of semantic representation have been tested in this study: a Berkeley FrameNet representation [START_REF] Baker | The berkeley framenet project[END_REF], following previous work done on question generation on the CALOR-QUEST corpus [START_REF] Béchet | Calorquest: generating a training corpus for machine reading comprehension models from shallow semantic annotations[END_REF], and Semantic Role Labelling (SRL) following the PropBank formalism as it was proposed to control question generation with BART in [START_REF] Pyatkin | Asking it all: Gener-ating contextualized questions for any semantic role[END_REF].

Training the question generation model from BART on a corpus of question/answer/context triplets such as SQUAD is done with the following steps in our study:

1. Annotate with FrameNet and SRL labels the text corpus 2. For each question/answer/context:

(a) Find the semantic role that corresponds to the answer of a given question thanks to the annotation performed. To do so, we align gold answer spans and semantic role spans and chose the one with the maximal overlap.

(b) Generate a training example with an input sequence containing the selected answer, the context and eventually additional semantic information derived from the semantic role analysis. The question is the output sequence.

3. Fine-tune the pre-trained generation model on the corpus collected.

At inference time, generating questions on a given sentence consists in first performing semantic analysis on the sentence, then generating an input sequence for each semantic role detected. The fine-tuned seq-to-seq model then generates a question for each of them.

In this study we compare 4 different representations for the input format of the question-generation seq-to-seq model:

1. basic-Frame-ctx : the answer is extracted thanks to the alignment process with the Frame Elements as described in step 2.(a) above. The context is simply given as the original sentence with no additional semantic information;

2. basic-SRL-ctx : the answer is extracted thanks to the alignment process with the Semantic Roles as described in step 2.(a) above. The context is simply given as the original sentence with no additional semantic information;

3. full-Frame-ctx: the answer is extracted thanks to the alignment process with the Frame Elements as described in step 2.(a) above and is further enriched with the FrameNet Frame Element label. The context is also explicitly enriched with an extraction of the other Frame Elements and the label of the trigger (Lexical Unit); in this representation we use the Frame Elements labels of the FrameNet lexicon instead of generic roles to characterize the answer and the context.

4. full-SRL-ctx: the answer is extracted thanks to the alignment process with the Semantic Roles as described in step 2.(a) above and is further enriched with the PropBank Semantic Role label. The context is also explicitly enriched with an extraction of the other Semantic Roles and the label of the trigger (Lexical Unit);

The following example7 illustrates these 4 representations. In this case, Frame and SRL provided the same span for the answer extraction and the two first configurations are identical.

Context:

Paleolithic tools with teeth and mammoth bones found at [Flins-sur-Seine]answer

Question:

Where were found paleolithic tools?

basic-Frame-ctx:

Question Answering model

The question answering task on text (Machine Reading Question Answering) consists in detecting the answer to a given question in a text. State-of-the-art approaches consists in fine-tuning a large pre-trained language model such as BERT into the task of predicting the start and end offsets of an answer in a paragraph. The paragraph and the question are given as input features.

To this purpose we used a Machine Reading Comprehension model based on a large language model for French called CamemBERT [START_REF] Martin | CamemBERT: a tasty French language model[END_REF], fine-tuned on the question/answering task on different dataset as it will be presented in the experiment section. The question generation model will be used to produce, in an unsupervised way, the training corpus necessary to fine-tune the model to the MRQA task.

Corpus annotation

We performed two annotation processes on the selfmanagement corpus. The first one was conducted by professional readers, researchers in social science, that were asked to perform a text analysis on several articles of the Autogestion journal. We asked annotators to select areas in the text that they consider as areas of interest and put comments that would explain why these areas would be selected. These comments could be key-words, concept or topics related to their analysis or they could be questions that were raised by the selected areas. The second annotation process was conducted by asking annotators specialized in linguistic annotation for NLP projects to collect a question/answer corpus on the same documents. Annotators selected areas in the documents corresponding to answers, and they were asked to write a question for each text area selected. This process is rather similar to the one used through crowdsourcing to build the SQuAD corpus. One significant difference is that we asked annotator to give a difficulty rating to each question, 1 being easy, very litteral questions (similar to SQuAD), 2 being difficult questions were lexical choices were different between the question and the context of the answer, and 3 being very difficult questions requiring some abstraction between the text, the question and the segment of text corresponding to the answer. On the overall, 1102 questions were produced but for this study we focused on direct questions and discarded multi-hop questions, resulting in 842 questions. Our motivation in this double annotation process was that the questions collected through the professional readers are the realistic questions and the ultimate goal of a language understanding system, and on the opposite the SQuAD-like collected questions are those that could be handled by current machine reading systems, but that might be too simple or artificial for being of any utility in a real deployed application. By studying the differences between these 2 sets of questions and by measuring how current question/answering systems are affected by changes in lexical choices or abstraction, we hope to open the path to the design of more realistic settings for evaluating language understanding systems.

Annotation

Experiments

All the experiments reported in this study have been made on three corpora:

• FQUAD (d'Hoffschmidt et al., 2020) is a dataset built with the same methodology as the SQUAD corpus [START_REF] Rajpurkar | Squad: 100,000+ questions for machine comprehension of text[END_REF]. The 1.0 version used in this study contains 145 articles randomly sampled from a dataset of 1,769 highquality French Wikipedia articles. A set of 26,108 question/answer pairs have been collected through crowdsourcing. As for SQUAD , this corpus contains mostly easy questions with similar lexical choices for the questions and the answers.

• CALOR-QUEST [START_REF] Béchet | Calorquest: generating a training corpus for machine reading comprehension models from shallow semantic annotations[END_REF]) is a question/answer corpus built on top of the CALOR-FRAME [START_REF] Marzinotto | Semantic frame parsing for information extraction : the calor corpus[END_REF] corpus which contains French encyclopaedic documents (Wikipedia, Vikidia, ClioTexte) semantically annotated following a manual FrameNet semantic analysis of the documents. The test partition of CALOR has been annotated with natural questions with the constraint that the answer matches a Frame Element. This constraint allows us to evaluate MRQA in a semantically controled experimental framework. The test corpus contains 2069 (paragraph, question, answer) triplets manually written by several expert annotators.

• ARCHIVAL is the self-management corpus presented in the previous section.

In these experiments FQUAD represent the large generic corpus that is used to train question generation and question answering models for French. It contains relatively easy data (high-quality Wikipedia pages and literal questions) but has the main advantage of being manually labeled and rather large. CALOR-QUEST is the upper-bound of what we could obtain in terms of MRQA performance with our unsupervised question answering model adaptation process because we use gold semantic annotations to generate triplets (paragraph, question, answer) on which a MRQA model can be trained. ARCHIVAL is the target corpus with challenging data (OCR noise, difficult subjects, automatic semantic annotation) and more realistic questions.

Experiments on question generation

The first experiments consists in training a question generation model as presented in section 4.1 on the FQUAD corpus. To this purpose this corpus has been automatically semantically annotated with FrameNet and ProbBank annotations, then 3 different question generation training corpora have been produced: basicctx, Frame-ctx and SRL-ctx as described in section 4.1.

A seq2seq question generation model based on the BARTHEZ [START_REF] Eddine | Barthez: a skilled pretrained french sequence-to-sequence model[END_REF] pretrained model is then trained on each corpus. Table 3 presents the results obtained on the test partition of the CALOR-QUEST corpus in terms of BLEU and BERTScore [START_REF] Zhang | Bertscore: Evaluating text generation with bert[END_REF] scores between the questions generated by the BARTHEZ model and those manually written on the CALOR-QUEST cor- [START_REF] Post | A call for clarity in reporting BLEU scores[END_REF]) that correspond to BLEU-4 and the configuration of BERTScore9 with a baseline rescaling in all our experiments. As we can see, adding semantic annotation during the generation process seems to improve both the BLEU and BERTScore scores. However BLEU focuses only on the surface forms of the questions and does not reflect their semantics and although BERTScore uses contextual embeddings, it is still based on a single reference question in our case. Human evaluations will be needed in the future to confirm these tendancy on subjective evaluations. The evaluation in terms of MRQA performance of models trained on the generated questions can also give some insights on the relevance of these generation methods. To this purpose we applied this question generation process to the ARCHIVAL corpus in order to generate a large corpus of context/question/answer triplets on which an MRQA model can be learned. The manual inspection of the questions produced shows that their linguistic quality is very high. However some semantic incoherence can occur, probably when the automatic semantic annotation failed, as we can see in table 4 for example 7.

Experiments on Machine Reading Comprehension

We carried out experiments on the CALOR-QUEST and ARCHIVAL corpora with MRQA models trained on the question/answering annotations automatically generated as described in section 4.2. 6 presents MRQA performance on the challenging ARCHIVAL test partitions according to the training corpus used for the question answering model. Here, contrarily to the previous table, the semantic analysis used to extract potential answers and to guide the generation process are produced with an automatic semantic parser. As expected, MRQA performances degrade as the level of difficulty of questions increases. We can also see that relying only on generated questions (ARCHIVAL ) is much worse that using a large off-theshelf generic corpus such as FQUAD . But using both improves the Exact Match metric, suggesting that the model generates more consistent answer spans.

Conclusion

We propose a new approach for question generation, relying on a BART Transformer based generative model, for which input data are enriched by semantic constraints. Question generation and answering are evalu-ated on several French corpora, and the whole approach is validated on a new corpus of digitized archive collection of a French Social Science journal. In particular we presented the question generation and question answering models that have been developed to adapt a Machine Reading model trained on Wikipedia to the self-management corpus of the ARCHIVAL project without any supervision.

Figure 1 :

 1 Figure 1: Comparison of Wikipedia and Self-Management (FMSH) corpora according to POS distributions

  [ANS] Flins-sur-Seine [CTX] Paleolithic tools with teeth and mammoth bones found at Flins-sur-Seine basic-SRL-ctx: [ANS] Flins-sur-Seine [CTX] Paleolithic tools with teeth and mammoth bones found at Flins-sur-Seine full-Frame-ctx: [ANS:Location] Flins-sur-Seine [LU:Locating] found [Sought-entity] Paleolithic tools [CTX] Paleolithic tools with teeth and mammoth bones found at Flins-sur-Seine full-SRL-ctx: [ANS:ARGM-LOC] Flins-sur-Seine [LU] found [ARG1] paleolithic tools [CTX] Paleolithic tools with teeth and mammoth bones found at Flins-sur-Seine

Table 3 :

 3 Question generation evaluation with the BLEU and BERTScore metrics on the test partition of the CALOR-QUEST corpus pus. We used the default values of sacreBLEU's 8

		BLEU	P	BERTScore R F1
	basic-Frame-ctx	20.4	52.2 49.4 50.6
	basic-SRL-ctx	21.5	52.4 49.3 50.6
	full-Frame-ctx	22.0	54.2 51.6 52.7
	full-SRL-ctx	22.3	54.2 51.0 52.4

Table 5

 5 When did the first Russian soviets take shape? 2 What event took place in Brussels? 3 Under which government were the first workers' councils formed? 4 Who is the founder of the Russian trade unions? 5 What is the essential characteristic of revolutionary syndicalism?

	presents MRQA results on the CALOR-
	QUEST test partition with models trained on gener-
	ated questions with 3 different models representing 3
	different input sequence format. As we can see, un-
	like BLEU scores, adding semantic annotations during
	the question generation process doesn't seem to im-
	prove MRQA performances. On the overall the ap-
	proach, with a model entirely trained on automatically
	generated questions, yields good performances. Even
	if for CALOR-QUEST the semantic analysis is per-
	formed manually, this validates the question generation

Table 4 :

 4 Examples of generated questions on the ARCHIVAL corpus (translated from French to English)

	input-seq.	Exact Match	F1
	basic-Frame-ctx	67.6 (±0.9)	78.1 (±1.5)
	basic-SRL-ctx	68.9 (±0.4)	79.2 (±0.6)
	full-Frame-ctx	68.5 (±0.4)	78.4 (±0.4)
	full-SRL-ctx	66.3 (±1.3)	77.3 (±0.8)

Table 5 :

 5 Question answering results on the CALOR-QUEST test partition with MRQA models trained on the automatic question generated in 4 different conditions (basic-Frame-ctx, basic-SRL-ctx, Full-Framectx, full-SRL-ctx) approach as a useful tool to provide MRQA training corpora.

	Train	easy (1)	difficult (2)	very difficult (3)
	metrics	EM	F1	EM	F1	EM	F1
	FQUAD	37.5 (±0.7) (±1.0) (±0.3) (±0.5) (±0.6 62.9 25.0 54.8 18.0	48.2 (±3.7)
	ARCHIVAL	21.0 (±0.8) (±0.2) (±0.3) (±1.9) (±1.1) (±1.7) 39.9 9.7 27.7 1.3 20.7
	both	40.6 (±0.9) (±0.4) (±1.6) (±0.7) (±0.6) (±1.7) 63.4 27.4 53.8 19.4 44.3

Table 6 :

 6 Question answering results on the ARCHIVAL test corpus according to the level of difficulty of the questions, trained on FQUAD only, generated questions only (ARCHIVAL ), or a combination of both Table

Fondation Maison des Sciences de l'Homme, https://www.fmsh.fr/

https://www.persee.fr/collection/autog

en.wikipedia.org/w/index.php?title= Wikipedia:Neutral point of view

https://haystack.deepset.ai

https://anr.fr/Project-ANR-19-CE38-0011

from CALOR-QUEST , translation into English of the French sentence extracted from an illustration caption "Outils du Paléolithique, avec dents et ossements de mammouth, trouvés à Flins-sur-Seine"

sacreBLEU's hash signature of our experiments : "nrefs:1|case:mixed|eff:no|tok:13a|smooth:exp|version:2.0.0"

BERTScore's hash signature : "bert-base-multilingualcased L9 no-idf version=0.3.11(hug trans=4.5.0)-rescaled"

Acknowledgements

This work has been partially funded by the Agence Nationale pour la Recherche (ANR) through the following program: ANR-19-CE38-0011 (ARCHIVAL).

This work was performed using HPC/AI resources from GENCI-IDRIS (Grant 2021-AD011012688).

The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille -A*MIDEX (Archimedes Institute AMX-19-IET-009), a French "Investissements d'Avenir" Programme.