Vincent Guihard

Frédéric Taillade

Jean-Paul Balayssac

Barthélémy Steck

Julien Sanahuja

Fabrice Deby

Permittivity measurement of cementitious materials with an open-ended coaxial probe

Keywords: Permittivity, coaxial probe, dispersive behavior, cement paste, mortar, concrete, porosity, moisture

This study presents a methodology to investigate the complex permittivity of heterogeneous samples like concrete, mortars and cement pastes by using an open-ended coaxial probe. The probe is associated with portable Vector Network Analyser (VNA) allowing in-situ measurements. Another advantage of the proposed methodology is that the complex permittivity of concrete can be assessed from the measurement of the reflection parameter S11 alone which is innovating in comparison with common devices. This can be achieved by modelling the electrical equivalent circuit of the coaxial probe and the dielectric sample with a capacitive model briefly presented in this paper. A calibration procedure on materials with known permittivity developed to estimate the input parameters of the capacitive model is presented in this paper meanwhile all the details of measurements. Measurements performed on various cementitious materials (cement paste, mortar and concrete) at different degrees of water saturation (from almost dry to fully saturated) show that the probe is able to characterize their dispersive behavior. It is also demonstrated that the probe is able to measure both real and imaginary permittivity of cementitious materials in an extended range of moisture. Relationships are proposed between real or imaginary permittivity and volume water content.

Introduction

Water content of cementitious materials is one of the most important parameters to describe their durability. Water content of cementitious materials can be deduced from permittivity measurement at different frequencies from 30 MHz up to 2 GHz [START_REF] Dérobert | Use of capacitive and GPR techniques for the non-destructive evaluation of cover concrete[END_REF]. The present study is part of a project aiming to predict the water content of aging as well as new concrete buildings, thanks to permittivity measurements made on the bulk material and its constituents. Among all electromagnetic devices available to assess the permittivity of dispersive dielectrics, coaxial line transmission and reflection based instruments are among the most commonly used. Dielectric permittivity can be derived from the analysis of transmission or reflection of electromagnetic waves through a sample inserted into a coaxial structure [START_REF]Microwave Electronics Measurement and Materials Characterization, Chapter 3, Reflection Methods[END_REF]. Coaxial transmission lines have been extensively studied and present numerous benefits, e.g. broad frequency range and capability to measure both reflection and transmission coefficients of a sample. These coefficients enable both the dielectric constant and the magnetic susceptibility to be measured. However, they only allow ex-situ measurement, requiring extraction of samples from the original bulk material. This method is hence not suitable for some applications, including the non-destructive evaluation of civil engineering structures. Methods based on wave reflection do not necessarily require any sample collection. These reflection phenomena are induced by an impedance discontinuity, which, in turn, is caused by the sample located at the end of a coaxial line.

Open-ended coaxial probes are one of the methods reviewed, along with many others, in [START_REF]Microwave Electronics Measurement and Materials Characterization, Chapter 3, Reflection Methods[END_REF] and [START_REF] Stuchly | Coaxial line reflection methods for measuring dielectric properties of biological substances at radio and microwave frequencies -a review[END_REF].

They are simple to implement and have a broad frequency range driven by the network analyzer used to synthesize the RF signal. However, since transmission coefficients are necessary to determine both the magnetic and dielectric properties of materials, reflection probes are essentially reserved for permittivity measurement of non-magnetic materials. The non-destructive and non-invasive characteristics of such tools have enabled investigations of different kinds of media, such as biological tissues and liquids [START_REF] Popovic | Precision open-ended coaxial probes for in vivo and ex vivo dielectric spectroscopy of biological tissues at microwave frequencies[END_REF] [4] [START_REF] Stuchly | Coaxial line reflection methods for measuring dielectric properties of biological substances at radio and microwave frequencies -a review[END_REF] [6] [START_REF] Wagner | Robust low cost open-ended coaxial probe for dielectric spectroscopy in laboratory and in-situ applications[END_REF], agricultural products [START_REF] Sheen | An open-ended coaxial probe for broad-band permittivity measurement of agricultural products[END_REF] [START_REF] You | A small and slim coaxial probe for single rice grain moisture sensing[END_REF], soils [START_REF] Skierucha | A FDR sensor for measuring complex soil dielectric permittivity in the 10-500 MHz frequency range[END_REF] [START_REF] Wagner | Numerical 3d fem and experimental analysis of the open-ended coaxial line technique for microwave dielectric spectroscopy on soil[END_REF] [START_REF] Demontoux | Efficiency of end effect probes for in-situ permittivity measurements in the 0.5-6GHz frequency range and their application for organic soil horizons study[END_REF], and also flat surfaces of solid samples like concrete [START_REF] Filali | Design and calibration of a large open-ended coaxial probe for the measurement of the dielectric properties of concrete[END_REF] [START_REF] Van Damme | Nondestructive determination of the steel fiber content in concrete slabs with an open-ended coaxial probe[END_REF] or, more recently, artificially grown sea ice [START_REF] Komarov | Open-ended coaxial probe technique for dielectric spectroscopy of artificially grown sea ice[END_REF].

The probes exist in different configurations and can be chosen according to the sample position within the system. They are summarized in [START_REF] Stuchly | Coaxial line reflection methods for measuring dielectric properties of biological substances at radio and microwave frequencies -a review[END_REF] and [START_REF] Mbango | Contribution à la caractérisation électrique de matériaux utilisés en microélectronique radiofréquence[END_REF] and have all been studied over recent decades to fully understand wave propagation mechanisms and calculate dielectric properties of materials from the measured signal reflection. Among the different studies dedicated to such systems, numerical simulations of probe operation have been extensively performed using both Finite Element Method (FEM) or Method Of Moment (MOM) calculation processes [START_REF] Sheen | An open-ended coaxial probe for broad-band permittivity measurement of agricultural products[END_REF] [17] [START_REF] Gajda | Numerical analysis of open-ended coaxial lines[END_REF] [19] [START_REF]FEM Analysis of Conical Type Coaxial Open-ended Probe for Dielectric Measurement[END_REF] [21] [START_REF] Ferhat | Broadband dielectric spectroscopy open-ended probe for the characterization of dispersive materials[END_REF].

The approach developed in this study shows that a simple capacitive model describing the behavior of the probe enables the permittivity of flat samples to be calculated. We present a conical probe designed to investigate heterogeneous materials and a new two-dimensional axisymmetric FEM model developed to validate this approach over specific frequency ranges. Measurements were performed on various cementitious materials (cement paste, mortar and concrete) and the results for the real and imaginary parts of the permittivity are presented.

Design of the large, open-ended coaxial probe

The use of a coaxial probe to deduce the permittivity of a dielectric material from the amount of energy reflected on its surface calls upon transmission line theory [START_REF]Microwave Electronics Measurement and Materials Characterization, Chapter 3, Reflection Methods[END_REF]. This concept enables an accurate description of electromagnetic wave propagation through a coaxial cable and is the basis for understanding how the probe operates.

A typical coaxial cable is composed of two concentric cylindrical structures made of a conducting material (a center core and a metallic shield) separated by a dielectric insulator. Parameters a and b will be used in the following to represent the radii of the metallic core and shield, respectively.

In such cables, transverse electromagnetic (TEM) modes are the only propagation modes allowed within the dielectric material. Thus, both the electric and magnetic components of an incident wave are exclusively located in the plane perpendicular to the propagation direction. The same basic structure is used to build open-ended coaxial probes. enables the investigated volume to be expanded in order to perform measurements on heterogeneous samples characterized by large representative elementary volumes (REV). These volumes are defined according to the largest heterogeneity size contained within the material under test. Also, because of the conical shape of the device, values a and b vary along the probe length but the ratio b/a remains constant, thus maintaining the probe characteristic impedance, Z0, equal to 50 Ω and preventing any reflection within the probe.

Figure 1b presents a cross sectional view of the device. The brass core and shield are kept together at the top of the probe by an N connector filled with Teflon and also having a 50 Ω characteristic impedance. The device is directly connected to the vector network analyzer (VNA). The only reflection detected has to come from the sample placed below the probe. If the impedance of the material is not equal to 50 Ω, the system composed of the probe and sample is equivalent to a lossless transmission line terminated by a load impedance ZL, which depends on the electromagnetic properties of the sample. This approximation is restricted to the case of a semi-infinite sample i.e. a sample deep enough to ensure that the amplitude of the electric field E is at least two orders of magnitude lower at the end of the sample than at the interface with the probe [START_REF] Stuchly | Coaxial line reflection methods for measuring dielectric properties of biological substances at radio and microwave frequencies -a review[END_REF]. Komarov et al. [START_REF] Komarov | Open-ended coaxial probe technique for dielectric spectroscopy of artificially grown sea ice[END_REF] recall that wave propagation through the sample can be seen as a distortion of the TEM signal in the vicinity of the probe aperture. This would induce the appearance of a component of the electric field perpendicular to the aperture and a radiation of the wave into the sample. Partial reflection of the energy towards the probe is then observed. Eq.1 can be used to link the S11 parameter, measured with the VNA, and the impedance of a sample, such that = (Eq. 1) with, ZL: Load impedance Z0=50 Ω, characteristic impedance of the probe This reflection coefficient is known to be a function of the electromagnetic properties of the sample under test [START_REF] Filali | Design and calibration of a large open-ended coaxial probe for the measurement of the dielectric properties of concrete[END_REF], [START_REF] Ferhat | Broadband dielectric spectroscopy open-ended probe for the characterization of dispersive materials[END_REF], [START_REF] Filali | Measuring dielectric properties of concrete by a wide coaxial probe with an open end[END_REF], [START_REF] Van Damme | Nondestructive determination of the steel fiber content in concrete slabs with an open-ended coaxial probe[END_REF]. Many models have been developed during recent decades to determine the dielectric constant or the magnetic permeability of semi-infinite materials by measuring a voltage reflection coefficient. For simple system geometry, dielectric permittivity can sometimes be derived from the integral expression of the admittance at the end of the coaxial probe [START_REF] Misra | A quasi-static analysis of open-ended coaxial lines[END_REF]. However, it is acknowledged [START_REF] Filali | Design and calibration of a large open-ended coaxial probe for the measurement of the dielectric properties of concrete[END_REF] that the vast computing resources needed in such cases makes instant measurements impossible. To simplify the expression of impedance at the end of the probe, other approaches have been used: the quasi-static approach, the Taylor-series development approach, or equivalent electrical circuit approaches. The latter assume that the measurement circuit is similar to a classic electrical circuit. Chen et al., [START_REF]Microwave Electronics Measurement and Materials Characterization, Chapter 3, Reflection Methods[END_REF] review the most famous of these models: the capacitive model [START_REF] Stuchly | Coaxial line reflection methods for measuring dielectric properties of biological substances at radio and microwave frequencies -a review[END_REF], the antenna model [START_REF] Brady | Dielectric behavior of selected animal tissues in vitro at frequencies form 2 to 4 GHz[END_REF], the virtual line model [START_REF] Ghannouchi | Measurement of microwave permittivity using six-port reflector with an open-ended coaxial line[END_REF] and the rational function model. Such models offer immediate permittivity calculation but also present drawbacks such as limited frequency range suitability.

Measurement and result processing

Measurement procedure

The vector network analyzer used in this study was an Anritsu MS46121 with a signal frequency range set to [1 MHz; 2 GHz]. Measurement of the S11 parameter over this broad range was performed on materials with known permittivity, such as air and Teflon, and also on materials with unknown electromagnetic properties, such as rock aggregate, cement paste, mortar, and concrete, as presented in Figure 2. A VNA calibration procedure was required before the probe was set up, in order to take external factors influencing the device operation into account, e.g. temperature or hygrometry. This was performed by measuring the reflected signal on three different loads (open circuit, short circuit and 50 Ω load impedance). It is also necessary to recall that the default configuration of the reference plane of the VNA after calibration is defined at the output of the device. S11 parameters should be measured at this exact position. In the present study, this reflection coefficient had to be measured at the interface between the probe and the sample because the phase deployed itself over the additional line length induced by the probe. So a change of reference plane was performed by plugging the probe in and short-circuiting it by placing a conductive material (a copper foil in this case) at its end.

Capacitive model

Estimating the dielectric permittivity of the material under test from the impedance value ZL then required the use of a specific model. Here, the capacitive model [START_REF] Stuchly | Coaxial line reflection methods for measuring dielectric properties of biological substances at radio and microwave frequencies -a review[END_REF] presented in Figure 3 was used.

Figure 3: Electrical equivalent circuit of a coaxial probe and dielectric sample according to the capacitive model

This circuit comprises two capacitors and * = * . connected in parallel. Capacitor * is used to model the electric energy storage capacity of the sample. The complex value of the permittivity Ɛ * allows the dielectric losses within the material to be taken into consideration. The factor is a geometric factor used to take account of the geometry of the probe. The capacitor is often used to interpret the energy storage capacity due to the fringing fields. This capacity is material independent and comes only from the fact that fringing fields exist at the boundaries of every non-infinite planar capacitor [START_REF] Elata | Fringing effect in electrostatic actuators[END_REF]. Parameters and being difficult to estimate, a calibration procedure using wellknown materials is necessary. Using Eq. 1, an expression describing the permittivity of a sample placed at the end of the coaxial probe can be deduced, * = -

(Eq.2)
It is possible to eliminate the two unknown parameters and by measuring the S11 parameter on two materials of known permittivity ( and ). The resulting expression for the dielectric constant of an unknown sample is then given by,

* = + - ! " ! ! (Eq.3)
The two reference materials used in this study were air (Ɛair = 1 + 0j) and a 25x15x10 cm Teflon block (Ɛteflon = 2.1 + 0j).

The use of the capacitive model had been validated in a previous study by using a numerical model and measurements on rock samples [START_REF] Guihard | Modelling the behaviour of an open-ended coaxial probe to assess the permittivity of heterogeneous dielectrics solids[END_REF]. The material, of dimensions 14x7x9 cm, was a homogeneous block of aggregate commonly used as one of the components of concrete. The frequency range chosen was [1 MHz; 2 GHz]. The permittivity deduced from the measurement of the S parameters on the flat surface of the block is presented in Figure 4. The real part lies between 4 and 5 at low frequencies and increases slightly at high frequencies. The imaginary part is almost equal to 0 at low frequencies and also seems to increase at high frequencies. It was observed that the permittivity deviation was probably caused by the measuring system and the capacitive model, and increased with the difference between the permittivity value of the material under test and the permittivity of the dielectric filling the probe (air in this case) [START_REF] Dérobert | EM characterization of hydraulic concretes in the GPR frequency-band using a quadratic experimental design[END_REF].

Effective penetration depth

Many experiments have been performed in order to estimate the effective penetration depth of waves in a sample [START_REF] Meaney | Open-ended coaxial dielectric probe effective penetration depth determination[END_REF] [21] [33] [34]. This effective penetration depth is closely related to the probe diameter [START_REF] Meaney | Open-ended coaxial dielectric probe effective penetration depth determination[END_REF] and is in the same order of magnitude as this diameter [START_REF] Adous | Caractérisation électromagnétique des matériaux traités de génie civil dans la bande de fréquence 50 MHz 13GHz[END_REF]. Meany et al., [START_REF] Meaney | Open-ended coaxial dielectric probe effective penetration depth determination[END_REF] computed the evolution of the penetration depth as a function of probe diameter, frequency and medium permittivity. The probe diameter was found to be the most influential parameter and penetration depth was almost constant with frequency and sample permittivity [START_REF] Meaney | Open-ended coaxial dielectric probe effective penetration depth determination[END_REF]. The effective penetration depth is an important characteristic especially when dealing with heterogeneous samples like concrete. The Representative Elementary Volume (REV) is usually defined as the minimum dimensions of the volume investigated by the probe so that the measurement can be considered representative.

This volume is closely related to the maximum size of the heterogeneities contained in the studied material (around three times the volume of these heterogeneities). Hence, care must be taken when studying materials with quite large heterogeneities like concrete. A probe with a larger diameter might be necessary to study concrete samples comprising aggregates a few centimeters in size. Figure 5 presents the real part of the permittivity resulting from a simulation performed with a heterogeneous sample made of two layers having different permittivities in the aim of estimating the wave penetration depth. The upper layer was made of a material with permittivity 5 + 0j. The lower material was air (ε = 1 + 0j). We computed the effective permittivity following the described procedure for various sample thicknesses, e. Results showed that, for samples with permittivity 5+0j that were thinner than 2 cm, the resulting permittivity was different from 5 + 0j. Effective penetration depth hence lay around 2cm. In the following, the maximum diameter of aggregates for concrete mixes is which should be at least three times the maximum size of the aggregates. To quantify the variability, at least six measurements are performed and averaged to provide a value of permittivity. The coefficient of variation obtained is always less than 11%. tested with different water to cement ratios in order to obtain a significant range of porosity. Different mixes of mortar were designed by using a 0/2 mm sand and changing the sand to cement ratio in order to modify the volume of paste and aggregates. For mortars M1 and M2, the proportion of cement paste was 51% for mortar Mm1 and 43% for Mm2. A concrete with a water to cement ratio of 0.62 and a superplasticizer were also characterized. The cement used was a CEM I 52.5 N from a factory (Italcementi) at Gaurin in France. Alluvial sandlime aggregates were used, a 0/4 mm sand (for mortar and concrete) and a fine, 4/11 mm, gravel (for concrete). The superplasticizer used for concrete was Sikaplast Techno 80 from SIKA.

The porosity was measured by applying the procedure defined in [START_REF] Grandubé | Grandeurs associées à la Durabilité des Bétons[END_REF]. The range of porosity was between 26.5 and 36.0% for cement pastes and between 18.6 and 22.4% for mortars. The porosity of the concrete was 13.9%, so, globally, the mixes covered a range of porosity from 14% to 36%. All the mixes were cured under water for 28 days.

For cement pastes and mortars, two cubes (8 cm*8cm*8cm) per mix were cast. For concrete three cylinders (diameter 11.5 cm and height 23 cm) were cast. After 28 days of curing, the cylinders were cut into 3 slices (6 cm thick). The permittivity measurements were realized on the three slices and averaged for each sample.

To change the saturation degree of the samples, a conditioning procedure was applied. From the fullsaturation state, the samples under test were progressively dried at 60 °C to reach the following saturation degrees:

-90%, 80%, 70%, 60%, 50%, 40%, 30% for cement pastes, -90%, 80%, 60%, 50%, 40%, 30%, 20% for mortars, -90%, 80%, 70%, 60%, 36% for concrete.

Once the mass corresponding to the saturation degree was reached, the sample was sealed in adhesive aluminum foil and kept at 60 °C for the duration of drying. This process enabled the water content inside the sample to become homogeneous. Then, the sample was tested with the coaxial probe and the procedure was repeated for the next saturation degree.

Measurements

For each saturation degree, permittivity measurements were performed on the six faces of each

sample with the open-ended coaxial probe. Good contact being required between the probe and the sample to avoid measurement bias [START_REF] Guihard | Modelling the behaviour of an open-ended coaxial probe to assess the permittivity of heterogeneous dielectrics solids[END_REF], the probe has to be held tightly on the surface of the material by the operator. The data acquired on all faces was then averaged and could be displayed as a function of frequency. Low standard deviation was observed when six measurements were performed at different positions on a rock sample. As an example, the mean value of the real and the imaginary parts of the permittivity acquired on this rock sample is presented Figure 6 and shows the good reproducibility of the measurement procedure. It can be observed that the variation of the permittivity (real and imaginary) versus the frequency is linked to moisture. The permittivity is frequency-dependent for high moisture content while it does not depend on frequency when the porosity is weakly saturated. This confirms the results already obtained on concrete by Dérobert et al. [START_REF] Dérobert | EM characterization of hydraulic concretes in the GPR frequency-band using a quadratic experimental design[END_REF]. Moreover it can be observed that the real part of the permittivity is almost independent of frequency in the range of [500-1000 MHz] even if the material is fully saturated. On the other hand, the imaginary part increases between 500 and 1000 MHz, especially when the cement pastes are fully saturated. This was already observed on a rock sample and could be attributed to a limit of the capacitive model of the probe [START_REF] Guihard | Modelling the behaviour of an open-ended coaxial probe to assess the permittivity of heterogeneous dielectrics solids[END_REF]. The measurement is also sensitive to the water to cement ratio for 100% saturation. It can be observed in Table 1 that the porosity increases with the water to cement ratio. When the mix is fully saturated, the quantity of water is equal to the porosity, so it increases with the water to cement ratio. It can be noted that both the real and imaginary parts of permittivity increase with the quantity of moisture, which is also in agreement with previous results [START_REF] Dérobert | EM characterization of hydraulic concretes in the GPR frequency-band using a quadratic experimental design[END_REF], [START_REF] Soutsos | Dielectric properties of concrete and their influence on radar testing[END_REF], [START_REF] Haddad | Characterization of portland cement concrete using electromagnetic waves over the microwave frequencies[END_REF]. This effect is not so sensitive for a saturation degree of 30% because the quantity of water inside the porosity is not great enough. The same comparison can be made between the two saturation degrees of a given water to cement ratio. For instance, at 1000 MHz, the real part of the permittivity of mix CP 0.28 changes from 16 to 6.5 for saturation degrees of 100 and 30% respectively.

For the imaginary part, these values are 5.7 and 2.6 respectively.

Figure 8 presents the variation of the real and imaginary parts of the permittivity versus the saturation degree. In this case it was decided to calculate the mean of all the measured values in the range of [500 -1000 MHz] instead of considering only a value for one frequency. Moreover, this frequency range corresponds to the usual GPR frequencies used for the characterization of concrete. The error bars represent the standard deviation calculated from twelve measurements (one per face of the two available cubes). It is clear that the permittivity (real and imaginary) decreases with the saturation degree. It seems, however that the relationship between the two is not proportional throughout the range of saturation. Although the relationship is fairly linear between 30% and 80%, which is in agreement with the literature [START_REF] Dérobert | EM characterization of hydraulic concretes in the GPR frequency-band using a quadratic experimental design[END_REF], [START_REF] Soutsos | Dielectric properties of concrete and their influence on radar testing[END_REF], there is a more marked increase of permittivity between 80% and 100%. This could be due to the effect of macro porosity, which is only filled for the higher moisture content and which could induce a higher increase of the volume water content. An additional measurement at a saturation degree of 95% could confirm this assumption. As for cement pastes, we note that the permittivity is frequency dependent if the saturation degree is high. For the lower saturation degree (30% in this case), neither the real nor the imaginary part of the permittivity depends significantly on the frequency. This dependency observed at high saturation degree is more significant for the imaginary part, as was observed for cement pastes. The effect of moisture is again clearly visible when the values obtained for the fully saturated mortars are compared.

Higher permittivity (real and imaginary parts) is measured on mortar M, which has higher porosity. This difference is not significant for the saturation degree of 30% because the volume of water present in the porosity is too small.

In Figure 10, the variation of the real and the imaginary parts of the permittivity are plotted versus the saturation degree for the two mortars. The error bars represent the standard deviation calculated from twelve measurements (one per face of the two available cubes). In comparison with cement paste results, the variation of permittivity is quite continuous here over the whole range of saturation degrees.

Concrete

The variation of permittivity versus frequency at two saturation degrees (100% and 36%) is plotted in Figure 11. The dispersive behavior is verified again for fully saturated concrete while it seems to vanish for the lower moisture content. This is particularly the case for the real permittivity, whereas the imaginary part of permittivity appears to remain dependent on frequency even for low degrees of saturation. Once again, this variation of permittivity versus frequency is very significant below 500

MHz. For this reason, in the following, as for cement paste and mortar, we will consider the mean of the values measured with the limited frequency range [500-1000 MHz]. The variation of permittivity according to saturation degree is plotted in Figure 12. The error bars represent the standard deviation calculated from 18 measurements (one per face of the 9 available slices). The variation could be fitted by a linear relationship between 36% and 90%. But, as for cement pastes, the values measured for fully saturated samples cannot be predicted by this relationship. Due to the fairly low porosity of concrete, the variation remains between 6 and 10 for the real part of the permittivity and between 0.1 and 1.5 for the imaginary part.

Frequency dependence of permittivity

The variation of real and imaginary permittivity between 100 and 1000 MHz normalized to the mean (normalized variation) is plotted versus the saturation degree for all the mixes in Figure 13. It can be considered that the higher the relative variation is, the higher is the frequency dependence of the mix.

It is clear on the figure that the frequency dependence of real permittivity increases (almost linearly)

with the saturation degree whatever the mix. The maximum variation of real permittivity is about 40%.

Regarding the imaginary part, it can be concluded that there is an increasing trend between the relative variation and the saturation degree, with a maximum significantly higher than for the real part (about 140% obtained for mortar and concrete at 100% saturation). The relative variation is higher for concrete than for mortar or for cement paste. So, a higher frequency dependence of the imaginary permittivity can be expected if the heterogeneity of the mix increases. This effect could be attributed to the presence of the aggregates, which could increase the losses due to interfacial effects. Moreover, the frequency dependence of the real permittivity vanishes for all mixes at the lower saturation degree, as already noted. This can also be observed for the imaginary part of cement paste and mortar but not for concrete, for which results are not available for saturation degree less than 35%.

Measurements at lower moisture content should be performed to check whether the frequency dependence vanishes as for mortars and cement pastes.

Relation between permittivity and moisture content

Works can be found in the literature demonstrating that, in cementitious materials or soils, the best correlation between permittivity and moisture is obtained when volume water content is considered instead of the saturation degree [START_REF] Dérobert | EM characterization of hydraulic concretes in the GPR frequency-band using a quadratic experimental design[END_REF], [START_REF] Klysz | Determination of volumetric water content of concrete using groundpenetrating radar[END_REF], [START_REF] Topp | Electromagnetic Determination of Soil Water Content: Measurements in Coaxial Transmission Lines[END_REF]. The works involving cementitious materials generally focus on concrete, so the range of porosity is limited to 12 to 20%. In the present work, by involving mortars and cement pastes, we extend the range of porosity up to about 35%. Figures 14 and15 present the variation of real and imaginary parts of permittivity versus volume water content for all the mixes. In Figure 14, the 6 points corresponding to fully saturated cement pastes are seen to be outside the tendency. If these points are discarded, a single relationship can be drawn between the real part and volume water content for all the mixes, with an acceptable coefficient of determination.

It is noteworthy that this relation is determined for quite a large range of moisture content, which is not usual in the literature, where the range is limited to the concrete porosity.

Regarding the imaginary part (Figure 15) different tendencies can be observed. For mortar and concrete, a single tendency can be proposed but a specific relationship is required for cement paste.

In this case, the relations are not linear and the best correlation is obtained with an exponential function. Two tendencies can be observed: one for mortar and concrete and the other for cement pastes. In the range [13%-35%] of water content, the imaginary part is higher for mortar than for cement paste. So it can be concluded that the presence of the aggregates increases the dielectric losses for a given water content -possibly due to interfacial phenomena. The results confirm the dispersive behavior of cementitious materials, especially for high saturation degrees. For the real part of permittivity, the dispersive behavior was mainly observed for frequencies below 500 MHz, whatever the material. It was demonstrated that the frequency dependence of the real part, estimated by its coefficient of variation throughout the range of frequency, increased linearly with saturation degree whatever the material (cement paste, mortar or concrete). On the other hand, it was observed that the frequency dependence was significantly higher for the imaginary part of permittivity and was not clearly correlated to the saturation degree. Moreover, the dispersive behavior was globally higher for concrete and lower for cement paste, a characteristic that could be linked to the presence of aggregates.

The results show that the variation rate of real and imaginary permittivity versus saturation degree is not the same over the whole range of moisture content, especially for cement pastes. Between 80 and 100% saturation, the permittivity increased more significantly than in the range [30%-80%].

On the other hand, a single linear relationship could be determined between real permittivity and volume water content in a range of 3% to 35%. Regarding the imaginary part of permittivity, two tendencies were determined, one for cement pastes and one for mortars and concrete.

The coaxial probe presented in this study can be considered as a promising way to determine the permittivity of cementitious materials, and also their components [START_REF] Guihard | Modelling the behaviour of an open-ended coaxial probe to assess the permittivity of heterogeneous dielectrics solids[END_REF], in a frequency range [100-1000 MHz] and over a large range of porosity. As the device can be easily implemented on real sites, it could be used for the calibration of GPR measurements, for a better assessment of wave velocity, for instance.

Future perspectives will concern the development of probes directly embedded in concrete structures to avoid the effects of an air gap between the sample and the probe. Such a probe could be used for monitoring moisture inside concrete structures.

Figure 1 :

 1 Figure 1: Open-ended coaxial probe

Figure 2 .

 2 Figure 2. Acquisition of the S11 parameter on the surface of a concrete sample.

Figure 4 :

 4 Figure 4: Measurement of the real and imaginary parts of the permittivity of a rock sample.

Figure 5 :

 5 Figure 5: Assessment of the effective penetration depth

Figure 6 :Figure 7

 67 Figure 6: Measurement results obtained at six positions on a rock sample (mean and standard deviation)

Figure 7 :

 7 Figure 7: Real and imaginary parts of the permittivity measured on cement pastes for saturation degrees of 100% and 30%

Figure 8 :Figure 9

 89 Figure 8: Variation of real and imaginary part of permittivity (mean in the range 500-1000 MHz) versus saturation degree (all the cement pastes)

Figure 9 :

 9 Figure 9: Real and imaginary parts of the permittivity measured on mortars for saturation degrees of 100% and 30%

Figure 10 :

 10 Figure 10: Variation of real and imaginary parts of permittivity (mean in the range 500-1000 MHz) versus saturation degree

Figure 11 :

 11 Figure 11: Real and imaginary parts of the permittivity measured on concrete for saturation degrees of 100% and 30%

Figure 12 :

 12 Figure 12: Variation of real and imaginary part of permittivity (mean in the range 500-1000 MHz) versus saturation degree of the concrete

Figure 13 :

 13 Figure 13: Relative variation of real and imaginary permittivity versus saturation degree

Figure 14 :Figure 15 :

 1415 Figure 14: Real part of permittivity versus volume water content for all the mixes

Table 1 : Cement paste properties

 1

	Mix	CP 0.28-1	CP 0.28-2 CP 0.34-1 CP 0.34-2 CP 0.4-1 CP 0.4-2
	W/C	0.28	0.28	0.34	0.34	0.40	0.40
	Porosity (%)	26.7	26.5	31.7	31.8	35.9	36.0

Table 2 : Mortar properties

 2

	Mix	M1	M2	Mm1	Mm2
	S/C	2.1		3
	Cement (kg/m3)	595		500
	W/C	0.53		0.53
	Porosity (%)	22.4	22.4	18.6	19.6

Table 3 : Concrete (C) properties

 3

	Cement (kg/m3)	315
	Sand 0-4 (kg/m3)	819
	Fine Gravel 4-11 (kg/m3)	978
	Water (kg/m3)	194
	Superplasticizer (kg/m3)	2.6
	W/C	0.62
	Density (kg/m3)	2320
	Slump (cm)	15.5
	Porosity (%)	13.9

Acknowledgements

This work has been performed during the PhD thesis of Vincent GUIHARD funded by Electricité de France (EDF). The French National Agency for Research (ANR "Building and Sustainable Cities") is also acknowledged for its financial support during the project CONTINUS. Our thanks are extended to Susan Becker, a native English speaker, commissioned to proofread the final English version of this paper.


CONCEPTUAL THINKING ON MIGRATION STUDIES

Interview with Riva Kastoryano(Sciences Po, Centre de recherches internationales (CERI), CNRS, Paris, France), Ricard Zapata-Barrero & Dirk Jacobs, by Miriam Périer

In : Les Entretiens du CERI, 16 May 2022 URL : https://www.sciencespo.fr/ceri/en/content/conceptual-thinking-migrationstudies-interview-kastoryano-zapata-barrero-jacobs.html Riva Kastoryano, Ricard Zapata-Barrero, and Dirk Jacobs have recently coedited a volume entitled Contested Concepts of Migration Studies (Routledge, 2022). As they claim in the introduction, "The main purpose of this volume is to enhance conceptual thinking on migration studies and clarify the political significance of the fading of old and the advent of new concepts". They have agreed to answer our questions on the genesis of this collective project, on the notion of scientific concepts and their circulation, and on their own contributions to this volume.

What is the genesis of this collective volume?

Ricard Zapata-Barrero: This is a collective effort to articulate a collective concern about the key concepts that shape migration studies today and that have the distinction of fulfilling various overlapping functions, describing, explaining, and also normatively tracing how things should be. These hybrid and "contested concepts", if not clarified, can become a source of misunderstanding and even conflict when they are operationalised. This volume began as a serious invitation to consider the importance of conceptual thinking in migration research and how this task should be done at the different scales and in the different areas where the same concept is applied, not only in the political, policy, and social sphere, but also in the media and everyday use of language, where terms can receive differentiated meanings and outline different problems. We are more than honoured to have attracted so many outstanding colleagues, who are today contributing to frame the agenda of migration research.

Riva Kastoryano: Ricard Zapata-Barrero and I had been exchanging thoughts on the concepts of interculturalism and transnationalism, on the fact that the two concepts overlap, and how they do so. Our debate turned into a confrontation between normative theory (interculturalism) and experiences. Our fruitful exchange inspired me to initiate the project PLURISPACE, a collaborative project where we discuss normative concepts in relation to integration and diversity and social reality as it is experienced in situations such as multiculturalism, interculturalism, and transnationalism. Interestingly enough, Ricard also had the idea of an edited volume on related concepts, obviously "contested". The scope of the political issue of immigration is evident in the verbal war it produces. We therefore brought together our knowledge, energy, and concerns about concepts used in studies on migration.

Dirk Jacobs: While a few decades ago ethnic and migration studies were rather "marginal" topics in the social sciences and migration was already an important but not a main political topic, these days the situation is quite different. In most industrialised countries, the topics of migration and ethnic diversity have risen to the top of political debate and ethnic and migration studies have moved to the core of the social sciences. This evolution has highlighted even more that concepts mobilised in our fields do not exist in a vacuum, but get picked up (and in the process are often altered or criticised) in public debate, in politics, in the media, and sometimes even in everyday language. The movement also goes the other way around: our field of study is impacted by (sometimes heated) political and public debates and our conceptual thinking can be influenced by the political and societal contexts in which we work. All concepts have a history and often their significance and uses evolve. We felt it is important to have a critical reflection on this and to make more explicit what the impact on our use of core concepts is.

You write in the introduction, "one of the objectives of this edited book is to discuss the relation of scientific concepts to the concepts used (and abused) in political and social debates and everyday language, and how these realms interrelate". Would you mind telling us more about this idea, from what sort of ideas do scientific concepts distinguish themselves and how do they circulate and potentially transform through this circulation?

RZB: This has been one of the drivers of this book. It is a claim (a conceptual engagement) on the need for a conceptual clarification in most migration-related debates. The fact is that most of the concepts that are used in migration studies are not technical concepts for just one particular use, but rather ideas that spread through a multidimensional space of uses. This often makes it difficult to communicate arguments and ideas on substantial migration-related issues. You will agree also that many of these concepts provoke emotions, and that these also interfere with a wide web of their meanings. As I myself say in other of my works, interested in deepening qualitative approaches, sometimes the conflicts that are generated in immigration issues are not about real facts but about their interpretations and meanings. This cognitive dimension of the concepts we use is key and is certainly part of the "conceptual thinking" we are claiming is necessary as a preliminary phase to any research, communication, or conversation about migration. This also involves, as we outline in our introduction, to domesticate our critical thinking in the concepts we use not only to argue but also to legitimise our narratives, policies, and practices related to migration.

RK:

We all agree that words and concepts concerning immigration or the presence of immigrants have become controversial, loaded with feeling, sometimes spawning conflicts and sometimes contributing to them. Integration, diversity, communities, minority, ethnicity, are terms and concepts whose meanings shifts in time and space without ends in linguistic reflex in most studies on immigration and become a part of social conflict.

DJ:

The concept of "integration" is a good example. While once only a sociological concept, with a century and a half of history in the social sciences, it has now not only become a very current word in media and political debates but is even used in everyday language. "Are migrants sufficiently integrated?" is a question that makes sense for most people, even in ordinary conversations. When you scratch the surface, you see that the same word can mean a number of things and sometimes these significances or uses are even contradictory. Sometimes one actually means "assimilation"-a concept which needs a definition too by the way-in other cases one thinks more of "inclusion". We could now in fact start discussing how these other concepts we have just introduced are being used and what they mean or could mean. One of the contributions in our volume, written by Adrian Favell, actually criticises the implications of the use of the notion of integration and, among other things, discusses the "organic" use of integration, as if we are talking about cells in a body. Using this kind of metaphorical thinking has a number of implications that we as social researchers should reflect on.

In this edited volume, you explore fifteen core concepts and, necessarily, their related (sub)concepts. How did you select these concepts and why did you choose to organise this edited volume according to these? RK: It was important to choose concepts that have been largely debated and/or that have created controversies, where theoretical approaches and normative vision and empirical studies were confronted and have not led to a consensus, such as "multiculturalism". It was also important to choose concepts that travel over time and space, terms and concepts whose meanings shift without regard for "the marks of their ancestral memory", as Michel Foucault put it, such as "cohesion", "integration", "diversity", "identity", "discrimination", and "tolerance". Besides, as Ricard put it, it was also important to take into consideration the subconcepts to show the complexity of the use of concepts in the social sciences.

RZB:

This has been one of the most difficult, but also exciting and fruitful discussions we have had, as editors first, but also with all the contributors. We realised that any concept we select is trapped in a web of other concepts (a conceptual system), and since concepts are interconnected, many arguments and ideas that underlie many debates began to emerge. In the end we opted, as often happens in complex situations, for commonsense and simplicity. We were also guided by the criteria of an idea's topicality and cross-interest in the media, public opinion, and academia. What we can say is that although some substantial ones are still missing (perhaps to be addressed in a second volume), those that were selected are substantial, and that is what ultimately matters to us.

DJ:

We thought these were the most useful ideas to critically reflect upon, but that's obviously open to debate. In one of the first book reviews, published in the journal Ethnic and Racial Studies, which praised the edited volume for its informative and compelling nature, Erdem Dikici said we should have also included "anti-racism", "Islamophobia", and "solidarity". We could have long discussions on that. For instance, I could counterargue that "solidarity" falls outside the scope of the book because it is more often used in other types of debates than in those on migration or in ethnic studies. It's fine to discuss Islamophobia, but then we also need to take anti-Semitism on board. It's true that anti-racism is not discussed head on in the volume, but, in my opinion, it is indirectly covered in the chapter on discrimination. I am not saying colleague Dikici does not have a point here, I totally understand it and think it's a very legitimate remark. However, there were pragmatic constraints and for this reason we also did not keep "intersectionality", even though it was initially on my list of important concepts to cover… Choosing is losing.

Question to Riva Kastoryano: In your chapter, you explore the concept of transnationalism as part of the process of globalisation. Why did you choose this concept? Can transnationalism be defined as an autonomous and non-territorial nationalism? RK: I have been exploring this concept for a long time from different perspectives. My first research was on the solidarity networks of migrant populations in Europe and community formation across borders. Transnationalism portrays the bonds of solidarity based on an identity-national, religious, linguistic, or regional-across national borders. The concept takes into account the context of globalisation and economic uncertainty that facilitates the construction of worldwide networks. It is in large part the result of the development of means of communication, the appearance of large regional groups, and the increased importance of supranational institutions which either originate there or facilitate such groups' administration. Intensified by the magnitude of international migration, transnational networks not only favour cultural, social, political, or ideological transfer but also both guide the activities and generate their mobilisation.

Many questions with regard to membership, allegiances, and affiliations arise from these developments: what becomes of the relationship between citizenship and identity; between territory and the nationstate; between rights and identities, culture and politics, states and nations? A new transnational community that is imagined either out of a religion or an ethnicity, which encapsulates linguistic and national differences, seeks self-affirmation across national borders and without geographic limits, as a deterritorialised nation in search of an inclusive (and exclusive) centre around a constructed identity or experienceimmigration, dispersion, minority. Increasing mobility and the development of communication technologies have intensified such transborder relations, leading to social and political mobilisations beyond boundaries. The rhetoric of mobilisation recentralises, in a nonterritorial way, the multiplicity of identities-national, religious, ethnic, or linguistic-that are fragmented yet represented in such a structure. Together they point to the existence of a new type of nationalism that is transnational, that is a nationalism that is expressed and developed beyond and outside the borders of the state and its territory, and creates new expressions of belonging and a political engagement that reflects the nationalisation of communitarian sentiments guided by an "imagined geography", leading to a non-territorial nationalism that I called transnational nationalism.

Question to Ricard Zapata-Barero and Dirk Jacobs: Your chapters explore the concepts of cohesion and diversity, respectively. Would you mind presenting us these two concepts and how they articulate with others? RZB: I must confess that I took the concept of cohesion because it was one that continuously interfered in my research on diversity and interculturalism. It was a real need to clarify this important concept for myself. Of course, the main premise was the concern regarding how far cohesion is related to diversity in conflictive terms, and I worked according to the argument that we need to bridge cohesion and diversity since there is a false understanding that cohesion is only possible in "imagined" homogeneous societies. The chapter argues that nowadays there is an assumed view that diversity erodes cohesion and that we need to go beyond this "threatening hypothesis". I immerse myself in the multistranded concept of cohesion and its relation to the liberal nationalistic tradition that tends to assume that cohesion is only possible in homogeneous societies. After digging into its conceptual agenda, I jump into the policy domain of cohesion, and particularly the three normative frames that share the effort of bridging cohesion and diversity: multiculturalism, civic nationalism, and interculturalism. At the end, I leave open the question of the benefits of considering cohesion and diversity as friends rather than foes.

DJ:

The main point of my chapter on diversity is that it is not just a descriptive or technical concept which is being mobilised to capture the different possible forms of heterogeneity (as opposed to homogeneity). Let me first say that as a technical concept it's tougher to deal with than you might initially think. Consider the following question: Is there more diversity when you have a lot of small ethnic minority groups (next to one dominant ethnic majority group) or when there are a few large groups with all of them being of the same size (including the sociological ethnic majority group)? The main message of my chapter is that, even when seemingly used in a "neutral" way, the notion of diversity always unavoidably has a political dimension. "What groups do you distinguish?" is a very power-laden question. It seems to be a very clear and easy concept, easily measurable, but it is not. Indeed, the significance of "diversity" changes with the context (and who has the power of definition). In the two scenarios that I just gave as an example, the challenges and recipes for assuring social cohesion will most probably be quite different.

Interview by Miriam Périer, CERI.


UNDERSTANDING MINISTRIES OF FOREIGN AFFAIRS IN THE WORLD

Interview with Christian Lequesne (Sciences Po, Centre de recherches internationales (CERI), CNRS, Paris, France), by Miriam Périer

In : Les Entretiens du CERI, 20 April 2022 URL : https://www.sciencespo.fr/ceri/en/content/understanding-ministriesforeign-affairs-world-interview-christian-lequesne.html

The study of foreign ministries has generally focused on one state, one nation, possibly a group of countries such as the European Union. But can we compare the foreign ministries of states that are very different in terms of their regime-democratic, autocratic, etc.-and what can a comparative study of these ministries and the diplomats who run them teach us today? These are among the issues addressed in Christian Lequesne's book, Ministries of Foreign Affairs in the World. Actors of State Diplomacy (Brill, 2022). Interview with the editor. What was missing in the literature was a book that sought to bring together different national cases, including work on MFAs in authoritarian countries, and conceptualizes the role of MFAs in International Relations. Guillaume Beaud's chapter on Iran in the current book is very innovative from this point of view. This new book will become a reference work in the literature that replaces tools dating from the late 1990s. If international relations researchers have done little work on foreign ministries, it is because they considered that the object was outdated compared to others such as NGOs, multilateral agencies, etc. This is where there is a flaw: although foreign ministries have existed for several centuries, they have undergone dramatic changes in practices and resources over the last twenty years that are far from having been studied. I would like to add that working on this subject is not easy in terms of access. Diplomatic administrations are still rather reluctant to be observed and "objectified" by the researcher. In this sense, Iver Neumann's ethnographic work and mine were the manifestation of an evolution among diplomatic practitioners realising that scholarly observation was not an unnecessary intrusion.

Ministries of Foreign

Your book offers a comparative study of MFAs, but is it possible to compare MFAs in democratic regimes and those in non-democratic or authoritarian regimes? Are there criteria that allow for such comparisons?

You are absolutely right to ask this question. And I might add that, even within regimes that we would call liberal democracies, there are significant differences in the way MFAs operate. If you look at the literature on diplomatic studies, you will see that a lot of empirical work on MFAs focuses on northern European countries or Canada: in short, contexts where the transparency of the public administration is governed by law. These are countries where a scholar can work on MFAs without having to pledge allegiance to the object of study, because there is an understanding of what independence of scientific work is. It is obviously much more difficult to work on foreign administrations of authoritarian regimes. But there are ways to get around the obstacles by doing detailed analyses of the online output of such ministries and by managing to interview diplomats or former diplomats, especially abroad. Again, Guillaume Beaud's chapter on Iran is remarkable from this point of view. More fundamentally, it isn't possible to understand the work of an MFA without a broader analysis of the political system, or what we can call politics, within which it functions. This brings us to the recent findings of foreign policy analysis; I am thinking of the work of Juliet Kaarbo on the domestic determinants of international relations. I would add that a scholar can also behave foolishly towards diplomats by considering that contact with them is synonymous with compromising. This reminds me of a review of my book on the Quai d'Orsay in the leading French political science journal, where the author announced proudly that if I had probably written this book, it was because I wanted to become a diplomat. In this suspicious way of thinking, penetrating an MFA necessarily means that you aspire to power within it. This false critical thinking masks in fact a refusal to confront other worlds than yours. It is so comfortable to be a critical armchair academic! Does this volume contribute to a historical perspective on the field of the professionals of international diplomacy?

The book itself does not go into the history of ministries of foreign affairs. There are good works on the history of diplomacy, including the classics by Harold Nicolson as Diplomacy Then and Now (1961). In locating the analyses it provides firmly in the post-Cold War period, the book is intended to reflect a very contemporary moment of change within MFAs. This is evidenced by the presence of several chapters on diplomacy and social networks, or Pierre-Bruno Ruffini's chapter on scientific diplomacy. The historical perspective is also present in Karla Gobo's chapter on the recruitment of Brazilian diplomats, in this case to show permanence rather than change. But even if this book does not include many historians, I am convinced that history teaches us a lot about the functioning of MFAs. History even prevents the sociologist or the political scientist from reinventing the wheel. Take the so-called practices of public diplomacy; a whole literature in diplomatic studies tells us that it is an invention of the contemporary emergence of societies in international relations. Frankly, this has never convinced me. As early as the nineteenth century, societies were not neglected in the work of influence made by diplomats. A historian would have to delve one day into the Quai d'Orsay's archives to show how diplomats under the Third Republic for instance had practices to influence French and foreign press correspondents. This book (with a few exceptions) is written by academics and not by practitioners or former practitioners of diplomacy, as is often the case when dealing with MFAs. I therefore felt it was necessary to ask a colleague like Iver Neumann to tell us what it means to make an ethnography of an MFA. His chapter is particularly useful for students and researchers. Similarly, practice theorists are increasingly working on the relationship between power and materiality (buildings, space). We see in diplomatic studies the revival of the postmodern concept of assemblage, as Jason Dittmer shows very well in this book. We must continue to work on these subjects and theorise them. Behind diplomatic compounds, for example, as they exist in Lomé or Islamabad, with embassies next to each other, but also golf clubs and restaurants, you have a wonderful illustration of the role that networks play in diplomatic practice. Of course, a more difficult question for the scholar is to identify to what extent the networked exchanges influence diplomatic decisions. But these subjects are fascinating and can really be dealt with if we think about a form of theorisation of diplomatic practices.

Interview by Miriam Périer, CERI.

  France's MFA. Other interesting monographic works have been published, notably at CERI. I am thinking of Alice Ekman's doctoral thesis, supervised by Françoise Mengin , on the Chinese MFA, and Melissa Levaillant's doctoral thesis on the Indian Foreign Service, supervised by Guillaume Devin.

Finally

  , in the introduction of this edited volume you write "scholarly research must address the question of how to better connect the study of MFAs to new theoretical and methodological debates on diplomacy and, largely, International Relations." Would you mind commenting?

  Affairs (MFAs) no longer hold the monopoly on state diplomacy but are part of a wider community of actors of different types. You state that there is a lack of scholarly work devoted to the comparative study of these administrations. Why has there been what you call a renewed interest to study MFAs? As usual, things are not simple. Since the 2000s, there has been a revival of diplomatic studies with a practice theory approach largely inspired by French empirical sociology and the English School of International Relations. My colleague Iver Neumann played a fundamental role in this revival by publishing articles on his anthropological work in the Norwegian Ministry of Foreign Affairs and then his book with Cornell University Press in 2012. It was in the vein of Iver Neumann's work that I began my own research, which resulted in the publication of Ethnographie du Quai d'Orsay in 2017. But both books are monographic. One is about Norway's MFA and the other about


Laurianne Wendling

Xavier Henning

François Roulland

Marc Lenertz

Giles Versini

Laurent Schlur

U-Chan Chung

Aziz Dinia

Silviu Colis

Mircea V Rastei

Structural properties and polarization switching of epitaxial Bi2FeCrO6 thin films grown on La2/3Sr1/3MnO3/SrTiO3 (111) substrates

Keywords: Ferroelectricity, Bias Field, Strain, Switching Field, Polarization, Bismuth iron chromium oxide

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

Introduction

The asymmetric distribution of charges in the unit cell of ferroelectric (FE) materials induces a directional spontaneous polarization that can be switched by applying an external electric field. This process is essential for different type of applications such as sensors [START_REF] Damjanovic | Ferroelectric sensors[END_REF][START_REF] Muralt | Ferroelectric thin films for micro-sensors and actuators: a review[END_REF], actuators [START_REF] Muralt | Ferroelectric thin films for micro-sensors and actuators: a review[END_REF], memories [START_REF] Cho | Realization of 10Tbit∕in.2 memory density and subnanosecond domain switching time in ferroelectric data storage[END_REF], spintronic devices [START_REF] Bea | Integration of Multiferroic BiFeO$_3$ Thin Films into Heterostructures for Spintronics[END_REF][START_REF] Ramesh | A new spin on spintronics[END_REF], capacitors [START_REF] Ma | Enhanced energystorage performance with excellent stability under low electric fields in BNT-ST relaxor ferroelectric ceramics[END_REF][START_REF] Veerapandiyan | Strategies to Improve the Energy Storage Properties of Perovskite Lead-Free Relaxor Ferroelectrics: A Review[END_REF] or solar cells [START_REF] Yang | Above-bandgap voltages from ferroelectric photovoltaic devices[END_REF][START_REF] Grinberg | Perovskite oxides for visible-light-absorbing ferroelectric and photovoltaic materials[END_REF] , where FE materials are mostly used in the form of thin films. In the case of solar cells, photon absorbers made of ferroelectrics can be particularly interesting because of the intrinsic internal field brought by the polarization of the material. Such internal fields are very efficient for exciton splitting as needed in photovoltaic devices. Specifically, the polarization of FE materials can induce a large open-circuit voltage that can be several orders of magnitude larger than the bandgap of the absorber leading to large conversion efficiencies. One of the most well-known FE materials is BiFeO 3 (BFO) that has attracted a lot of attention due to its large electric and magnetic transition temperatures of T c ~ 1100 K and T N ~ 640 K, respectively. Because of its antiferromagnetic character, the applications in magnetism are to date rather limited. However, several studies suggested the use of BFO materials in photovoltaic cells. The relatively large bandgap of BFO (between 2.4 and 3 eV) has nevertheless limited the current flowing through the cell. As a consequence, despite a large open circuit voltage that could reach 15 V, the efficiency of BFO-based cells remained until recently below 1 %. [START_REF] Yang | Above-bandgap voltages from ferroelectric photovoltaic devices[END_REF] Ab initio calculations performed by Baettig et al. revealed that by replacing half of the Fe atoms by Cr, the band gap could be reduced to 1.5 eV. The resulting BiFeCrO 6 (BFCO) double perovskite exhibit a polarization of about 80 µC/cm², large enough to split the electron-hole pairs, as well as a ferrimagnetic character with a magnetization of about 160 emu/cm 3 (i.e. 2 µ B per formula unit) [START_REF] Baettig | Ab initio prediction of a multiferroic with large polarization and magnetization[END_REF]. It was reported that the films exhibited ferroelectricity due to 6 s 2 lone pairs on the Bi 3+ and ferrimagnetism due to the super-exchange coupling between Fe 3+ and Cr 3+ [START_REF] Nechache | Bandgap tuning of multiferroic oxide solar cells[END_REF][START_REF] Nechache | EFFECT OF EPITAXIAL STRAIN ON THE STRUCTURAL AND FERROELECTRIC PROPERTIES OF Bi 2 FeCrO 6 THIN FILMS[END_REF]. In such conditions, Nechache et al. managed to grow high-quality epitaxial BFCO thin films on SrTiO 3 (001) substrates using the pulsed laser deposition (PLD) method [START_REF] Nechache | Growth, structure, and properties of epitaxial thin films of first-principles predicted multiferroic Bi2FeCrO6[END_REF]. Moreover, by controlling the Fe-Cr order through the laser-modulation frequency during the deposition, a controlled variation of the gap was found possible. Thus, by stacking BFCO layers with different bandgaps a multijunction-like solar cell with a power conversion efficiency to 8.1 % under AM 1.5 G irradiation could be obtained [START_REF] Nechache | Bandgap tuning of multiferroic oxide solar cells[END_REF]. In the case of single BFCO absorption layer, the cell efficiency was about 3.1 %, larger than the 1.25 % record efficiency obtained previously on a Pb(Zr,Ti)O 3 -based FE cell. [START_REF] Zheng | Above 1% efficiency of a ferroelectric solar cell based on the Pb(Zr,Ti)O 3 film[END_REF] Since then, Tiwari et al succeed to fabricate a solution processed BFO-based solar cell showing an efficiency of about 4%. The band gap of BFO was reduced to 2.2 eV and the thickness of the absorber layer was about 1.5 µm [START_REF] Tiwari | Solution Processed Bismuth Ferrite Thin Films for All-Oxide Solar Photovoltaics[END_REF]. Although these results are encouraging many structural and ferroelectric details still need to be understood.

In this work, we report on the structural and ferroelectric properties of BFCO thin films grown by PLD on SrTiO 3 (STO) (111) substrates covered with a La 2/3 Sr 1/3 MnO 3 (LSMO) buffer layer. A particular emphasis is given to the polarization switching mechanism which is particularly important in applications such as ferroelectric-based storage devices where the electric resistance of the material is correlated with the local polarization orientation of the film and where the polarization reversal has to be perfectly controlled. The X-ray diffraction measurements reveal an epitaxial growth without spurious phases. The double perovskite superstructure diffraction peaks indicate an Fe-Cr cationic ordering along the growth axis. Atomic force microscopy images show a coalesced grained structure with an average in-plane grain size of about 200 nm. Local measurements realized by piezoresponse force microscopy (PFM) show open polarization hysteresis loops, which display an asymmetric polarization switching with respect to the external bias voltage. After poling the BFCO film in opposite directions, PFM imaging reveals stable domains with clear up and down orientations. In addition, the upward poled areas reveal the same contrast as the as-grown regions, indicating a strong preferential polarization orientation in the "up" direction. Statistical PFM measurements performed on different grains show the existence of an internal bias field of relevance for the polarization switching of BFCO. This is observed by asymmetric hysteresis loops with respect to zero applied voltage and found important for the stability of the ferroelectric domain structure.

Experimental details

Sixty nm thick Bi 2 FeCrO 6 films were grown by PLD on STO (111) substrates covered by a 20 nm thick LSMO layer. LSMO was used as conductive bottom electrode in all PFM experiments. The choice of the (111) orientation for the STO substrate was motivated by the fact that the film polarization can easily align with the growth axis. This axis is also the one along which the FeO and CrO atomic planes are stacked leading to the periodicity expected in the pseudo-cubic double-perovskite BFCO structure. Besides its good conductive properties LSMO was chosen because of its small lattice mismatch with the respect to the STO substrate. LSMO was grown at 700 °C, in an O 2 atmosphere corresponding to a working pressure of 10 Pa. The laser energy was kept at 30 mJ (fluence of 1.5 J/cm 2 ) and the frequency at 5 Hz. For the BFCO deposition, the temperature was 790 °C, the pressure 1 Pa of O 2 , the laser energy 46 mJ (fluence of 2.3 J/cm 2 ) and the laser frequency 5 Hz. Other details on the deposition conditions can be found in previous works [START_REF] Nechache | Bandgap tuning of multiferroic oxide solar cells[END_REF][START_REF] Quattropani | Band-Gap Tuning in Ferroelectric Bi 2 FeCrO 6 Double Perovskite Thin Films[END_REF][START_REF] Rastei | Thickness Dependence and Strain Effects in Ferroelectric Bi 2 FeCrO 6 Thin Films[END_REF].

The crystalline structure was investigated by X-ray diffraction (XRD) using a SmartLab Rigaku diffractometer equipped with a Cu source and a Ge (220 × 2) crystal delivering the monochromatic CuKα 1 radiation (0.154056 nm). The high angle measurements (θ-2θ and  scans) allowed identifying the crystalline structure, checking the phase purity, the Fe-Cr ordering and and epitaxial quality of the films. Piezo-response Force Microscopy (PFM) measurements with a vertical polarization sensitivity were performed using a Bruker Icon microscope equipped with a Nanoscope V controller. The microscope was operated out-of-resonance at 40 kHz. The PFM hysteresis loops were acquired by applying V AC of 1 V to the LSMO electrode, while recording the phase and amplitude signals as a function of an additional external DC voltage applied to the tip. Probes presenting spring constants of about 80 N/m and tips covered with doped diamond were used all along this study.

Results and discussion

SrTiO 3 and La 2/3 Sr 1/3 MnO 3 present cubic (Pm-3m; JCPDS card 00-035-0734) and rhombohedral (R-3c; JCPDS card 00-051-0409) structures, respectively. Nevertheless, the LSMO structure is often approximated to a cubic one with a lattice parameter of 3.89 Å (JCPDS card 04-013-6950) [START_REF] Lyonnet | Heterostructures of La0.67Sr0.33MnO3/SrTiO3/La0.67Sr0.33MnO3 grown by pulsed laser deposition on (001) SrTiO3[END_REF]. As a consequence, the close symmetry and the small lattice mismatch with respect to STO (bulk lattice parameter of 3.906 Å) allows a layer by layer growth of LSMO on STO [START_REF] Liao | Controlled lateral anisotropy in correlated manganite heterostructures by interface-engineered oxygen octahedral coupling[END_REF][START_REF] Moubah | Growth and Magnetic Properties of La 2/3 Sr 1/3 MnO 3 /Ca 3 Co 2 O 6 Bilayers[END_REF]. As for BFCO, its rhombohedral structure (R3 symmetry) with lattice parameters of a=b= 5.477 Å, c= 13.390 Å and α= 60.09° (JCPDS card 04-011-8839) can be also well approximated with a pseudo-cubic one with lattice parameters of a=b=c= 3.93 Å [START_REF] Quattropani | Band-Gap Tuning in Ferroelectric Bi 2 FeCrO 6 Double Perovskite Thin Films[END_REF].

Figure 1(a) shows an X-ray diffraction pattern obtained on a BFCO/LSMO/STO(111) sample. As expected, only peaks corresponding to the (111) plane families of STO, LSMO pc and BFCO pc are observed, indicating a textured growth of LSMO and BFCO on the STO substrate. For a better visibility, a zoom of the X-ray diffractogram around the 111 peak of the substrate is shown in Fig. 1(b). The epitaxial quality of the films was fully confirmed by the ϕ-scans shown in Fig. 1(c). Upon rotation by 360° around the growth axis, a clear 120°-periodicity is observed for the out of plane peaks indicating an in-plane structural relation between the STO, LSMO and BFCO lattices. On the basis of the θ-2θ diffractogram presented in Fig. 1 (a) the lattice parameters along the growth axis can be calculated for the substrate as well as for both films. As expected, the lattice parameter of the substrate is of 3.90 Å equal to the one reported in the bulk. For LSMO the lattice parameter is slightly smaller (3.88(1) Å) than in the bulk and with respect to that of STO [LSMO(222) pc peak observed at larger angles [START_REF] Guo | Orientation Control of Interfacial Magnetism at La 0.67 Sr 0.33 MnO 3 /SrTiO 3 Interfaces[END_REF][START_REF] Zhou | Magnetic anisotropy of epitaxial La 2/3 Sr 1/3 MnO 3 thin films on SrTiO 3 with different orientations[END_REF]]. For BFCO instead, the lattice parameter of the thin film is slightly larger than that of STO, as the BFCO(222) pc peak is shifted to the left with respect to STO(222) suggesting an in plane compressive strain of BFCO of about 1.2% with respect to the substrate. Interestingly, the BFCO peak seems constituted of two component lines observed at 85.02° (L1) and 85.48° (L2). Such observation was already made on BFCO (100)-oriented films [START_REF] Rastei | Thickness Dependence and Strain Effects in Ferroelectric Bi 2 FeCrO 6 Thin Films[END_REF][START_REF] Nechache | Photovoltaic properties of Bi 2 FeCrO 6 films epitaxially grown on (100)-oriented silicon substrates[END_REF] and attributed to Fe-Cr cationic ordered (low angle peak) and disordered (high angle peak) phases. This is a first indication that our films are ordered, at least partly. The Fe-Cr cationic order is also evidenced from the presence of the superstructure (½ ½ ½)BFCO and (3/2, 3/2, 3/2)BFCO diffraction peaks observed at [START_REF] Liao | Controlled lateral anisotropy in correlated manganite heterostructures by interface-engineered oxygen octahedral coupling[END_REF].5° and about 60°, respectively. This well-defined cationic ordering along the growth direction is observed despite the similar (3+) valences of Fe and Cr as well by their similar ionic radii [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. Note finally that no spurious phases could be evidenced within the detection limit of the XRD technique.

In order analyse the strains of the LSMO and BFCO films on the STO substrate, a reciprocal space map recorded around the 332 peaks of STO, LSMO and BFCO is shown in fig. 1d. As can be observed both the LSMO and BFCO films are perfectly strained on the substrate. This result can be easily understood if we keep in mind the small lattice mismatch between the different layers that do not exceed 1.2% and the small thickness of the layers (20 nm and 60 nm for LSMO and BFCO, respectively).

The surface morphology of the sample was investigated by atomic force microscopy (AFM) at different scales. An example of AFM image is shown in Fig. 2. The film presents a granular structure consisting in coalesced grains with different sizes and shapes. An estimate of the average grain size results in a mean lateral extension of about 200 nm. The height of the grains ranges between approximately 20 and 80 nm. Such a granular morphology can be the result of the interfacial mismatch and the strain effects, in agreement with other film morphologies reported in literature [START_REF] Nechache | Epitaxial Patterning of Bi2FeCrO6 Double Perovskite Nanostructures: Multiferroic at Room Temperature[END_REF][START_REF] Nechache | Recent progress in nanostructured multiferroic Bi2FeCrO6 thin films[END_REF].

The relatively large lateral sizes of the grains allowed acquiring PFM hysteresis loops at specific locations with respect to the grains. In particular, in this study we chose to locate the tip apex in contact with the centre of well identified grains. This procedure strongly reduces the grain boundary effects and the variability between the hysteresis loops, since the size of the tip apex is smaller than the grain lateral size. The exact values can be found from the curves recorded while changing the bias voltage from low to high values (black) and from high to low values (red). The fact that the switching fields are at the same voltage values in phase and amplitude hysteresis loops is expected for a FE material. However, as shown in Fig. 3, there are variabilities between the grains, as the shift on the voltage axis (labelled as V bias ) and opening of the loops depend on the grain. As a consequence, although a majority of grains exhibits an asymmetric hysteresis loop, the centre of the loops, i.e. V bias value, varies from grain to grain asking for a statistical analysis. Such a statistical study resulting from 32 different grains is shown in Fig. 4. An average shift of the loops of V bias  = + 1.0 V and a large variability is observed. Such a shift of the hysteresis loops, is reminiscent of an imprint effect [START_REF] Kim | An analysis of imprinted hysteresis loops for a ferroelectric Pb(Zr,Ti)O3 thin film capacitor using the switching transient current measurements[END_REF][START_REF] Mahendiran | Size and shape effects on polarization reversal of nanoscale BaTiO 3[END_REF], which may have different origins, such as strong strain effects generating uniaxial gradient field variation across the film thickness, surface electrostatic effects induced by surface charges, or interfacial built-in electric fields. However, in this system strong strain gradients are not expected since the lattice mismatch between the BFCO and the LSMO/STO substrate is small and the BFCO film is fully strained on the substrate. Biasing effects due to surface charges can also be excluded since there are no changes after multiple scans of the surface with a grounded tip. The interfacial built-in voltage is therefore of particular interest in the present system, as discussed later.

The average voltage value corresponding to the centre of the loops V bias  can be considered as a measurement of the impact of the built-in potential on the polarization switching. However, the variations of the measured V bias cannot be lined to variations of the interface properties which are expected to mainly depend on the nature and structure of the two materials in contact. In fact, the barrier at the BFCO/LSMO interface must be more or less constant, generating a rather constant electric field, regardless of the lateral position. Nevertheless, the impact of such a constant electric field on the polarization switching of an individual grain must depend on the grain characteristics and its environment. This impact, quantified by the V bias , represents the only experimentally accessible measure of the effect of the interface field. Considering, the large distribution in the size, shape and likely internal defects of the grains, it is therefore not surprising to have a large variation of the measured V bias among the grains.

From Fig. 4, it can be deduced that V bias ranges from -4.2 V to + 0.7 V, with the mean value V bias  = 1.0 V. Indeed, such variations can be assigned to the heterogeneities present in the film and the exact location probed by the tip with respect to the grain boundaries. This may also include other local factors, such as the polarization state of the nearby grains, the surface state of the grain, the local interfacial state with the buffer layer, and the size and morphology of the grain [START_REF] Liu | Coercive field dependence of the grain size of ferroelectric films[END_REF]. The built-in interfacial field manifests therefore as an intrinsic preferential polarization direction of the BFCO film, locally acting as a bias field applied to the film, contributing to an upward preferential polarization direction of the film. To further describe the polarization reversal behaviour, one can consider that a measured grain is embedded in an upward polarized medium constituted by the neighbouring grains. During the application of the external continuous (DC) voltage, the surrounding medium, which is not in contact with the tip apex, experiences far less electric field because of the field localization at the tip apex. Consequently, regardless of the external voltage, the polarization of the surrounding medium can be considered as polarized in the upward direction, which is a consequence of the intrinsic upward polarization direction.

In order to confirm the stability of the polarization state, we show in Fig. 5 a PFM phase image (8 × 8 µm²) after locally poling the film. The area was poled down in the centre (6 × 6 µm²) by a DC voltage of + 8 V applied to the tip, and then poled up in the middle by applying -8 V to the tip (bright square of 3 × 3 µm²). The phase signal distribution across the whole image is shown in Fig. 5 . Thus, as expected, the phase difference between the down and up poled areas is 180°. The as-grown (AG) polarization state resulting from the periphery of the image in Fig. 5 (a), is also expected to be comprised in the signal given by D + AG peak as the polarization is up. The small peak that can be observed at about 150 ° corresponds to the phase signal given by the grain boundaries.

The results presented above can therefore be understood by considering an interfacial built-in field arising at the BFCO/LSMO interface. The formation of a Schottky barrier is expected at this interface, as it occurs between the BFCO and the SRO or ITO for example [START_REF] Nechache | Bandgap tuning of multiferroic oxide solar cells[END_REF]. The LSMO film is thin enough to allow a space charge region across its thickness. In fact, previous studies conducted on other epitaxial FE systems have demonstrated that the polarization switching in ferroelectric films can be controlled by interface built-in fields [START_REF] Glinchuk | Influence of Built-In Internal Electric Field on Ferroelectric Film Properties and Phase Diagram[END_REF][START_REF] Yang | Room temperature ferroelectricity in fluoroperovskite thin films[END_REF][START_REF] Stengel | Enhancement of ferroelectricity at metal-oxide interfaces[END_REF][START_REF] Lichtensteiger | Built-in voltage in thin ferroelectric PbTiO 3 films: the effect of electrostatic boundary conditions[END_REF]. The reversed process where the polarization influences the band bending at the interface was also observed [START_REF] Huang | Direct observation of ferroelectric polarization-modulated band bending at oxide interfaces[END_REF]. In the case of the BFCO/LSMO sample studied here, this upward preferential polarisation direction agrees with the PFM image of the asgrown region (Fig 5 ), showing a majority of white grains as compared with the dark grains. The presence of some dark grains, downward polarised, can also be understood as only about 10 % of the analysed loops in the statistical study reveal a downward polarised state.

Conclusion

Ferroelectric BFCO films were grown by PLD on thin conductive LSMO films deposited on STO(111) substrates. The X-ray diffraction measurements have shown that the BFCO layer is epitaxial, free of spurious phases and showing a correct Fe-Cr cation ordering. AFM and PFM investigations reveal a granular morphology and a preferential upward polarization direction, as well as an asymmetric local hysteresis loop of the polarization, in agreement with the presence of a built-in interfacial field. The impact of the built-in field on the the film was estimated by analysing 32 different grains and found to be about V bias = 1 V. The exact reason why this value varies from grain to grain still remains to be investigated. Nevertheless, the as-grown state is found to be composed of a majority of up-polarized grains which is consistent with the preferential upward polarization direction. Only about 10 % from the grains are found intrinsically down-polarized. The results also indicate a mutual influence between the polarization and the interface bias field.

Fig. 1 :

 1 Fig.1: (a) X-ray diffraction pattern of a BFCO film (60 nm) deposited on LSMO (20 nm)/STO (111) substrate. The narrow peak at 20° is due to the used monochromator. (b) Zoom on the 111 peak of STO substrate. The BFCO peaks are constituted of two lines, L1 and L2, attributed to Fe-Cr ordered and disordered BFCO phases, respectively. (c) ϕ-scans recorded on the (221)STO peak in grey, (332)LSMO peak in red and (3/2 3/2 1/2) pseudo-cubic BFCO in blue showing a 120° periodicity. (d) Reciprocal space map recorded around the (332) peaks of STO, LSMO and BFCO.

Fig. 2 :

 2 Fig. 2: (a) AFM topographic image (4 x 4 µm²) of BFCO grown atop the LSMO/STO (111) substrate. (b) Scan profile along the solid line from (a), revealing the lateral extension and height of the grains. Examples of phase-voltage PFM hysteresis loops acquired on different grains are shown in Fig. 3 (a). The corresponding amplitude loops are presented in Fig. 3 (b). Both phase and amplitude signals show open hysteresis and asymmetric shapes with respect to zero voltage. This asymmetry can be quantified by the shift of the centre of the loops which in a large majority is towards positive voltage values. The voltage values corresponding to the left and right switching fields are identical in phase and amplitude signals.The exact values can be found from the curves recorded while changing the bias voltage from low to high values (black) and from high to low values (red). The fact that the switching fields are at the same voltage values in phase and amplitude hysteresis loops is expected for a FE material. However, as shown in Fig.3, there are variabilities between the grains, as the shift on the voltage axis (labelled as V bias ) and opening of the loops depend on the grain.

Fig. 3 :

 3 Fig. 3: (a) PFM phase vs voltage hysteresis loops acquired above three different grains. Red and black arrows show the sweeping direction of the voltage. (b) Corresponding PFM amplitude vs voltage hysteresis loops.

  (b). The possibility to fully reverse the polarization is therefore demonstrated in the central area. The PFM image [Fig. 5 (b)] shows a stable downward polarization direction (dark contrast in the image) with an average PFM phase around 40° [D peak in Fig. 5 (b)]. The bright signal in the centre corresponds to the area which was poled up. It shows a phase signal of about 220° [U +AG peak in Fig. 5 (b)]

Fig. 4 :

 4 Fig.4: Statistical analysis of the centre of the phase loops (i.e. -V bias ) value obtained by analysing 32 different grains with the same tip and under equivalent measurement conditions. All grains were measured with the same tip and in the same conditions and that loops exhibiting a reproducibility over 3 consecutive acquisitions were used.

Fig. 5 :

 5 Fig.5: (a) PFM phase image (8 x 8 µm²) of the BFCO film grown on LSMO/STO after poling down an area of 6 x 6 µm² at V t = +8 V (larger square), and then a smaller one of 3 x 3 µm² in the up-direction V t = -8V (inner square). (b) Phase diagram of the area imaged in (a), revealing the distribution of phase signal, and the 180° phase difference between the up and down polarized zones. The small peak at about 150 ° corresponds to an intermediate phase signal resulting from grain boundaries.

Acknowledgment

This work was supported by the French National Research Agency (ANR) through the Programme d'Investissement d'Avenir under contract ANR-11-LABX-0058 -NIE and ANR-17-EURE-0024 within the Investissement d'Avenir program ANR-10-IDEX-0002-02