domain: chim phys

text:
Hiba Saada

Rawa Abdallah

Bruno Fabre

Didier Floner

Stéphanie Fryars

Antoine Vacher

Vincent Dorcet

Cristelle Meriadec

Soraya Ababou-Girard

Gabriel Loget

Boosting the performance of BiVO4 prepared by alkaline electrodeposition with an amorphous Fe co-catalyst

BiVO4 is a very promising n-type semiconductor for watersplitting photoelectrochemical cells. We report here a new method to prepare BiVO4 photoanodes that is based on an alkaline electrodeposition process that avoids chemical etching of Bi. In addition, we present a simple and general method to prepare amorphous coatings of FeOx that behaves as a co-catalyst on our BiVO4 material, improving the water splitting photocurrent.

The conversion of renewable energies into energy-rich fuels that can be stored, transported and used to generate electricity on-site and on-demand is a very attractive way to solve the main problem of renewables, namely their intermittency. [START_REF] Lewis | Proc. Natl. Acad. Sci[END_REF] In this frame, watersplitting photoelectrochemical cells (PECs) are attracting a considerable amount of attention. [START_REF] Rothschild | [END_REF][3][4][5] These devices are made of semiconductor (SC) photoelectrodes that are able to convert solar energy into H2 (an energy-rich fuel) and O2. Upon light absorption, the charge carriers photogenerated in the SC are driven to the solid-liquid interface where they participate to the water splitting half-reactions: hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). [START_REF] Rothschild | [END_REF][3][4][5] In this process, the OER is the most challenging reaction as it requires a considerable energy input [6] and also because most of SCs are subject to photocorrosion, which makes them unstable in photoelectrolysis conditions. [7] Among n-type SCs that have been investigated as photoanodes for OER, BiVO4 stands out for several reasons: [8] , [9] first, it is composed of relatively abundant and non-toxic materials, [10] it has a bandgap narrow enough (2.4 eV) to absorb a significant part of the solar spectrum, [11] a valence band below the O2/H2O standard potential and a theoretical solar-to-hydrogen efficiency of ~9%. [12] However, the water splitting performance of BiVO4 is still limited by its poor charge extraction [13] and its low catalytic activity for OER, which implies to employ additional chemical and surface engineering processes to improve its efficiency. [14] Among these methods, BiVO4 doping [15,16] photocharging [17,18] cathodic polarization, [19] nanostructuration, [20,21] as well as its interfacing with: highly active OER co-catalysts (cocats) [22][23][24][25] another SC [26- 29] and plasmonic materials [30,31] have shown great promise. The synthesis of photoelectrochemically active BiVO4 on a conductive substrate is thus of great importance and can be performed by: i) spray-based, [13,18,29] or ii) hydrothermal [17,19] methods, iii) metalorganic decomposition, [21,28,30] iv) physical vapor deposition [26,32] and v) electrodeposition. [22,[33][34][35][36] The latter approach is very attractive due to its simplicity and its low cost [37,38] and electrodeposited BiVO4 has already led to very important breakthroughs. [22,25] Furthermore, electrodeposition processes are generally easily tunable and can be applied to various types of conductive substrates, regardless their composition and geometry, which is particularly adapted for BiVO4 morphological engineering. [20,21] So far, the great majority of works devoted to electrodeposited BiVO4 employed the electrodeposition processes reported by Choi et al. [22,33,34] and all used organic [34] or acid electrolytes [22,33,35] to ensure the solubility of Bi 3+ . However, acidic media can be detrimental because Bi 0 is soluble at low pH [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF] and acid electrolytes are known to deteriorate the Bisubstrate interaction (Figure S1), [34] in addition, several substrates are incompatible with low pH electrochemical treatments. [START_REF] Armstrong | [END_REF][41][42] In this article, we report the first fabrication process based on alkaline electrodeposition to generate BiVO4 and we introduce a new OER-active Fe-based amorphous cocat to boost considerably its photoelectrochemical performance. Supporting information for this article is given via a link at the end of the document.

Accepted Manuscript

Our strategy (Figure 1a) consisted in first electroplating Bi 0 on fluorine-doped SnO2 (FTO) and then converting it to BiVO4. The first problem for electrodepositing Bi at high pH is to solubilize the Bi source. Indeed; common Bi 3+ salts are only soluble at low pH whereas at high pH they hydrolyze and precipitate as oxides and hydroxides. We thus employed a stable 1:1 Bi 3+ : 2,2bis(hydroxymethyl)-2,2',2''-nitriloethanol (bis-tris) complex that was synthesized by mixing bis-tris with Bi2O3 in strongly basic conditions. Note that bis-tris is a widely available commercial compound, usually employed for the preparation of biological buffers. [43,44] was totally soluble in highly alkaline conditions and was employed as the Bi source in the electrodeposition bath, that also contained 0.1 M NaOH to maintain the high alkalinity (measured pH = 13.2). Electrodeposition was carried out by applying 500 successive 2 s-long galvanostatic pulses of -0.5 mA.cm -2 spaced by a rest time of 1 s in order to resupply the liquid interface with Bi(bis-tris). The resulting coatings were dark grey, and, according to scanning electron microscopy (SEM) images (Figure 1b,c), consisted of ~0.7 µm-thick microcrystalline films that covered all the FTO surface (additional SEM pictures are shown in Figure S3). Energy-dispersive X-ray spectroscopy (EDS), performed on a large area, (blue curve in Figure 2a, see Figures S3 andS4 for more details) confirmed the presence of Bi and Sn (coming from the underlying FTO surface). In addition, all peaks present in the corresponding X-ray diffraction (XRD) pattern (blue curve of Figure 2b) could be attributed to metal Bi (blue lines, ISCD #64703) and FTO (red lines, ISCD #39178). After electrodeposition, the Bi 0 coatings were converted in BiVO4 by a simple two-step process that consisted in drop-casting a solution of vanadyl acetylacetonate (VO(acac)2) and annealing the surface in air at 500 °C for 2 h, as described in previous works. [34] During this treatment, V diffused inside the Bi film which oxidized to generate BiVO4. The excess V2O5 was finally dissolved by soaking the surfaces in 1 M NaOH for 30 min. This treatment converted the Bi coatings to yellow, ~1.1 µm-thick rough and homogeneous films (Figure 1d,e and Figure S6). EDS (green curve in Figure 2a, see Figures S6 andS7 for more details) confirmed the incorporation of V in the coating with a calculated Bi to V atomic ratio of 1.0 (Table S1). Moreover, XRD (green curve in Figure 2b) revealed the total disappearance of the Bi 0 peaks and the apparition of new peaks, which can all be attributed to monoclinic BiVO4 (green lines). These results demonstrate that BiVO4 layers can be prepared via alkaline electrodeposition of Bi. Now, we introduce a general method to immobilize a Fe-based cocat on various substrates that will be applied to our BiVO4 material.

Manuscript

Fe oxides and hydroxides are promising OER cocats for solar fuel systems [6] and Fe has a very low market price, [10] which encouraged us to develop a method to coat Fe oxides on conducting and SC materials. Our process is very simple (Figure 3a) and consists in spin coating a dimethylformamide (DMF) solution containing a soluble commercial Fe-containing polymer, poly(vinylferrocene) (pvf) (shown in Figure S2), and annealing the substrate at a low temperature (300 °C) to generate an OERactive Fe-based cocat layer. SEM did not allow to observe a difference of morphology before and after modification but transmission electron microscopy (TEM) clearly revealed the presence of two distinct phases (Figure 3b). The first one was BiVO4, as indicated by its composition (green curve of Figure 3e, Bi to V ratio of 1) and by the agreement between the selected area electron diffraction (SAED) pattern (Figure 3c) and the structure of this phase (ICSD #100604). The second phase, colored in red in Figure 3b, was amorphous (Figure 3b,d) and contained a high content of Fe (red curve of Figure 3e) resulting from the thermal decomposition of the pvf film on BiVO4 during annealing. As shown in Figure 3b (additional TEM images are shown in Figure S9), this phase was often observed at the edge of the BiVO4 particles, showing that our treatment produced a discontinuous few nm-thick amorphous film over the BiVO4 layer. In addition, X-ray photoelectron spectroscopy (XPS) performed on bare and coated BiVO4 surfaces confirmed the presence of the expected elements (Bi, V, and O), as well as Sn originating from the FTO substrate (Figure S10). After modification, the intensity of the Bi 4f7/2 and 4f5/2 bands (Figure 3g), respectively located at 159.0 and 164.3 eV and the V 2p3/2 and 2p1/2, at 516.4 and 524.0 eV, decreased (note the O 1s satellite peak at 521.1 eV), well in line with the presence of a coating on the outer BiVO4 surface. More interestingly, new bands at 710.6 and 724.2 eV appeared after modification, which fit very well with the Fe 2p3/2 and 2p1/2, of oxidized Fe species. [START_REF] Wagner | Hand Book of X-Ray Photoelectron Spectroscopy[END_REF] In contrast, Fe 2p3/2 values for carbonated compounds such as ferrocene, Fe(CO3) and Fe(CO)5 are commonly found at lower binding energies (707.5 eV for ferrocene, 709.4 eV Fe(CO)5 and 710.2 eV for Fe(CO3)). [START_REF] Wagner | Hand Book of X-Ray Photoelectron Spectroscopy[END_REF][START_REF] Heuer | [END_REF] If residual carbon, originating from pvf decomposition, is expected to be present in the amorphous phase, its presence did not influence the C 1s region (Figure S11). Besides, due to the similitude of XPS spectra of FeO, Fe3O4 and Fe2O3, [START_REF] Wagner | Hand Book of X-Ray Photoelectron Spectroscopy[END_REF] the precise stoichiometry of the formed Fe oxide could not be determined. To conclude, these results demonstrate that the amorphous phase contained Fe that was mainly present in the form of an oxide, thus, for sake of simplicity, we refer to this layer as FeOx (with 1 < x < 1.5). The optical properties of the samples were analyzed by absorbance measurements (Figure 3f). The sample before modification exhibited the typical profile for monoclinic BiVO4 (green curve), [35] with an optical band gap of 2.5 eV (Figure S12a). The sample modified with FeOx (red curve) displayed an enlarged absorption window with a shoulder in the visible range (up to 650 nm), that was attributed to the deposited FeOx, if one refers to the spectrum of a bare FeOx film showing an absorption in this spectral window (brown curve).

In order to evaluate the beneficial effects of the FeOx, nonphotoactive surfaces, such as FTO and carbon paper (Cpap), were first modified with amorphous FeOx and then tested for OER at a moderate pH (K-borate buffer, pH = 9.6). The cyclic voltammetry (CV) results clearly indicate that, in both cases, the presence of FeOx considerably improved OER as it decreased the onset potential (Eonset, here arbitrary set for j = 0.05 mA cm -2 ) from 100 mV for Cpap to 280 mV for FTO and also increased the reaction kinetics, as seen by the higher voltammetric slope after modification (Figure 4a). Next, we applied the method to our BiVO4 photoanodes and tested them for photoelectrochemistry by linear sweep voltammetry (LSV, Figure 4b) under simulated sunlight (AM 1.5G) in the same electrolyte. In the absence of illumination, the measured currents were negligible (dark curves).

In contrast, anodic currents were clearly observed upon illumination. Bare BiVO4 (green curve) was photoelectrochemically active but had a low Eonset of 0.89 V (all potentials are referred vs. Reversible Hydrogen Electrode RHE) and a sluggish activity, as generally observed for unmodified BiVO4 photoanodes. [14] After coating the photoanode, the activity considerably increased (red curve), as demonstrated by the decreased Eonset and the improved fill factor. The performance could be further enhanced by applying a simple cathodic treatment to the photoanode, recently reported by Wang et al., [19] that is expected to create oxygen vacancies on the BiVO4 (see the experimental section for more details). In this case, the photoelectrochemical performance was very close to the benchmark performance obtained for the FeOx-coated BiVO4 in the presence of a hole acceptor (H2O2, dashed red curve). By comparing these two curves, we could estimate a charge transfer efficiency (ηtransfer) of 92% at 1.23 V (vs 65% for the untreated photoanode, see experimental part for more details). [47] Remarkably, all values of Eonset obtained for the FeOx-coated photoanodes were comprised between 0.3 and 0.4 V, close to that of state-of-the-art BiVO4 photoanodes modified with Fe-based catalysts. [22] The benefit of using the FeOx coating was also revealed by the incident photon-to-current efficiency (IPCE) spectra (Figure 4c), which showed a considerable enhancement of the photoconversion efficiency for the coated electrode (note that the IPCE decrease at wavelength <370 nm is likely caused by FTO absorption). [41] Interestingly, it can be observed on plots derived from this data (Figures S11b,c) that the photoelectrochemical band gap was, in both cases, equal to the optical band gap (2.5 eV). In addition, because the band gap energy was the same before and after modification, we can conclude that even if FeOx increased the optical absorbance in the visible spectrum (Figure 3f) it did not dope BiVO4, nor generate electrochemically "active" charge carriers and did not act as a photosensitizer. It rather promoted the extraction of BiVO4 charge carriers and acted as a cocat, improving the reaction kinetics. The so-prepared photoanodes were relatively stable and could operate for 3 h (Figure 4d), without any decrease of their voltammetric behavior (Figure 4e). Further SEM (Figure S13) and EDS (Figure S14) analyses carried out after long-term photoelectrolysis confirmed the stability of the material.

In conclusion, we have reported a new method to fabricate photoelectrochemically-active BiVO4. The process is the first one that is based on an alkaline electrodeposition process, which totally avoids chemical etching of Bi and provides a robust substrate-Bi interaction. This process may allow employing materials that are not stable in acidic conditions as BiVO4 substrates and should be useful to design new structures of photoanode. In addition, we have reported a new, simple and versatile method to coat conducting and SC surfaces with a catalytic amorphous layer of FeOx and we have demonstrated that the resulting FeOx-coated BiVO4 photoanodes show an enhanced photoelectrocatalytic efficiency. Although the performances of these photoanodes are still lower than the best reported (in the range of 5 mA cm -2 ) 22 given the simplicity of the reported methods, they should open new possibilities for the preparation of photoelectrochemical cells for the generation of solar fuels.

Figure 1 .

 1 Figure 1. a) Scheme showing the preparation process. b-e) Colored SEM images showing top views (b,d) and cross-sections (c,e) of Bi (b,c) and BiVO4 (d,e) layers on FTO. In these images, Bi was colorized in blue, BiVO4 in green and FTO in red.

  , Dr. D. Floner, Dr. B. Fabre, S. Fryars, Dr. A. Vacher, Dr. V. Dorcet, Dr. G. Loget Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) UMR6226-ScanMAT, F-35000 Rennes, France. Email: gabriel.loget@univ-rennes1.fr [b] Dr. Rawa Abdallah Lebanese University, EDST, Azm Center for Research in Biotechnology and Its Applications, Laboratory of Applied Biotechnology, LBA3B, El Mitein Street, Tripoli, Lebanon [c] C. Meriadec, Dr. S. Ababou-Girard Univ Rennes, CNRS, IPR (Institut de Physique de Rennes)-UMR6251, F-35000 Rennes, France.

Figure 2 .

 2 Figure 2. a) EDS spectra of a surface after Bi electrodeposition (blue) and after conversion in BiVO4 (green). b) XRD patterns of a surface after Bi electrodeposition (blue, the blue lines indicate the position of the peaks of ISCD #64703), and after conversion in BiVO4 (green, the green lines indicate the peak position of ISCD #100604) the position of FTO peaks (ISCD #39178) are indicated by red lines.

Figure 3 .

 3 Figure 3. a) Scheme showing the modification process on BiVO4. b) Colored HR TEM image showing the BiVO4 (grey)/FeOx (red) interface. Inset: high magnification image showing the spacing of the (101) planes in BiVO4. c,d) Indexed SAED patterns and e) corresponding EDS spectra recorded on a BiVO4 particle [(c) and green curve in (e)] and on a Fe-rich area [(d) and red curve in (e)]. f) Normalized absorbance spectra for BiVO4, FeOx, and BiVO4/FeOx. g) XPS spectra showing the Bi 4f (left), the O 1s and V 2p (middle) and the Fe 2p and Sn 3p (right) areas before (green) and after (red) modification with FeOx, including Fe 2p fits (brown line), Sn 3p fit (blue line), background (black line) and fitting envelope (thin red line).

Figure 4 .

 4 Figure 4. a) CVs showing the anodic behavior of unmodified (thin lines) and FeOx-coated (thick lines) FTO (red) and carbon paper (blue). b) LSVs recorded in the dark (black full line) or under illumination by simulated sunlight for BiVO4 (green full line), FeOx-coated BiVO4 (red full line) and FeOx-coated BiVO4 that was electrochemically treated (blue full line); the LSV of an illuminated FeOxcoated BiVO4 in the presence of H2O2 is also shown (red dashed line). The curves shown in a) and b) were recorded in K-borate buffer (pH = 9.6) at 50 mV s -1 . c) IPCE spectra recorded at 1.3 V with a bare BiVO4 and a FeOx-coated

Acknowledgments

This work was supported by CNRS and Université de Rennes 1. AZM & SAADE Association is fully acknowledged for the financial support. We acknowledge ScanMAT/THEMIS for TEM and F. Gouttefangeas and L. Joanny (ScanMAT/CMEBA) are acknowledged for SEM imaging.

Keywords: bismuth vanadate • iron • electrodeposition • watersplitting • solar fuels


Ali Houssam

El L Husseini
email: ali.elhusseini@ed.univ-lille1.fr

Laurent Ros
email: laurent.ros@gipsa-lab.grenoble-inp.fr

Eric Pierre Simon
email: eric.simon@univ-lille1.fr

Expression for the radius r of an AR(2) process used to model a wireless communication channel

come

Expression for the radius r of an AR(2) process used to model a wireless communication channel

I. INTRODUCTION

This report applies to the context of the Kalman filter (KF) estimation of a flat fading channel with slow fading; i.e., normalized Doppler frequencies less than 10 -2 . Note that this context corresponds to many practical applications, including vehicular applications. The principle of the channel estimation is to track the complex baseband equivalent flat fading coefficient, called the channel complex gain (CG), which will be denoted by α.

The design of the KF requires a linear recursive state-space model to be selected for the parameter to be tracked; i.e., α here. In this report, the selected state-space model is the conventional second order autoregressive model AR [START_REF] Baruah | AR-model of faded MIMO set-up optimized for ITU channels[END_REF] [1]- [START_REF] Lindbom | Tracking of time-varying mobile radio channels. II. A case study[END_REF]. Note that because the true CG does not follow a linear recursive model, the AR(2) model is considered to be an approximation.

The aim of this report is to obtain, in this context, the expression for the pole radius r of an AR(2) as a function of the state noise variance and the resonance frequency of the AR(2).

A. True channel model

We consider the estimation of a flat Rayleigh fading channel. The observation is that1

y (k) = α (k) + w (k) , (1)
where k is the time index, w (k) is a zero-mean additive white circular complex Gaussian noise with variance σ 2 w , and α (k) is a zero-mean correlated circular complex Gaussian channel gain with variance σ 2 α . Note that this report is not limited to the conventional Jakes' Doppler spectrum for α [START_REF] Clarke | A statistical theory of mobile radio reception[END_REF].

B. Approximated channel model

The second order autoregressive AR(2) process α(k) that is used to approximate the true CG α (k) is:

α(k) = a 1 α(k-1) + a 2 α(k-2) + u (k) (2)
where u (k) is a white circular complex Gaussian state noise with variance

σ 2 u = R α[0] -a 1 R α[1] -a 2 R α[2], with R α[p]
the autocorrelation coefficient of α for a lag p. This expression is calculated using Yule-Walker equations [START_REF] Eshel | The yule walker equations for the AR coefficients[END_REF]. It is classically assumed that R α[0] = σ 2 α (i.e., α) has the same power as α. These equations also give R α

[1] = a 1 R α[0] 1 -a 2 and R α[2] = a 1 R α[1] + a 2 R α[0].
Using these expressions, we obtain σ 2 u only as a function of a 1 and a 2 :

σ 2 u = σ 2 α (1 + a 2 )(1 -a 1 -a 2 )(1 + a 1 -a 2 ) (1 -a 2 ) (3)
By passing to the z-transformation of the equation ( 2), the transfer function of the AR(2) model is: This transfer function is also often expressed in the literature with a set of complex conjugate poles in the z-plane at z 1 = r • e -j2πfAR(2)T and z 2 = r • e +j2πfAR(2)T , where r ∈ [0, 1[ is the radius of the poles, and f AR(2) T ∈ [0, 1[ is the normalized resonance frequency of the AR(2) process [START_REF] Lindbom | Simplified Kalman estimation of fading mobile radio channels: high performance at LMS computational load[END_REF]:

H(z) = 1 1 -a 1 z -1 -a 2 z -2 (4) -2 -1 0 1 2 f T ×10 -3
H(z) = 1 (1 -z 1 z -1 )(1 -z 2 z -1 ) = 1 1 -2rcos(2πf AR(2) T )z -1 + r 2 z -2 (5)
By comparing equations ( 4) and ( 5) we have :

a 1 = 2r cos(2πf AR(2) T ) a 2 = -r 2 (6)
In our context of slow fading, f AR(2) T is chosen such that f AR(2) T 1. Let us define δ = 1 -r, which will be used in the following calculations.

An example of the PSDs of the AR(2) process S(f ) = σ 2 u |H(e j2πf T )| 2 is given in Fig. 1 for four different values of δ 1. This figure shows that the AR(2) gives a wide variety of PSD shapes, depending on the value of δ, when assuming δ 1 (i.e., r close to one).

In the next section, analytical expression for r is given in terms of σ u and f AR (2) T .

II. APPROXIMATION OF

because δ 2 δ 1. We have

1 + a 2 2δ (8) 1 -a 2 (1 -δ). (9)

- 3 δ = 10 - 2 δ = 10 - 6 δ = 5 × 10 - 2 Fig. 1 :

 326521 Fig. 1: PSD of the AR(2) model for different values of δ and f d T = 10 -3 .

σ 2 u 2 u, with δ 1 .

 221 AND EXPRESSION FOR r A. Approximation of σ First, let us sum up the assumptions corresponding to our slow fading context : f AR (2) T 1In this section, an approximate expression for σ 2 u is given. Replacing r by 1 -δ in the expression (6) for a 2 yields a 2 = -(1 -δ) 2 = -(1 -2δ + δ 2 ) -(1 -2δ).

Model[START_REF] Husseini | Optimization of the second order autoregressive model AR(2) for Rayleigh-Jakes flat fading channel estimation with Kalman filter[END_REF] assumes that symbols are normalized and known (or decided), in addition to the flat fading assumption. Although this model is admittedly simplistic, it can be applied to different (more involved) contexts, such as pilot-aided multi-carrier systems in frequency-selective wireless channels[START_REF] Shu | Simplified Random-Walk-Model-Based Kalman Filter for Slow to Moderate Fading Channel Estimation in OFDM Systems[END_REF].

By inserting these equations into the expression for σ 2 u defined in (3),

However, cos(2πf

1, so (10) leads to

B. Expression for r

In this section, the expression for r is given in terms of σ 2 u and f AR(2) T . Using the expression for σ 2 u defined in (11):

where ω AR(2) T = 2πf AR(2) T . So r is one solution of the second degree equation

By solving this equation, we found (15)


Maria Ikhennicheu
email: maria.ikhennicheu@ifremer.fr

Benoit Gaurier

Philippe Druault
email: philippe.druault@upmc.fr

Gregory Germain
email: gregory.germain@ifremer.fr

Benoît Gaurier

Grégory Germain

Experimental analysis of the floor inclination effect on the turbulent wake developing behind a wall mounted cube

Keywords: Turbulence, Experimental trials, wall-mounted obstacles, PIV, POD, Quadrant method

Experimental analysis of the floor inclination effect on the turbulent wake developing behind a wall mounted cube

Introduction

The idea of harvesting energy from the sea dates back to antiquity, however it is only recently that industrial projects have started to emerge.

There is a strong tidal potential in France: over 20% of the European potential is located in French water, especially in the Alderney Race (Raz-Blanchard ) that presents currents up to U insitu = 5m/s. Surveys performed in this area give access to the bathymetry (see fig. 1) showing an average depth variation of H insitu = 5m. The Reynolds number in situ, based on H insitu and U insitu and the kinematic viscosity of water ν, is high: R e,insitu = H insitu U insitu /ν = 2.5 × 10 7 . Such variations are causing a high turbulence rate in the water column, where marine current turbines are meant to be installed. Turbulence can have a major impact on the tidal turbines, on their production [START_REF] Medina | Turbulence analysis and multiscale correlations between synchronized flow velocity and marine turbine power production[END_REF] and on the structural fatigue [START_REF] Mycek | Experimental study of the turbulence intensity effects on marine current turbines behaviour. part I: One single turbine[END_REF]. Before trying to reproduce complex structures, we chose to introduce the topic by studying elementary obstacles representatives of real life condition: i.e. with an aspect ratio of the magnitude of the mean bathymetry variations encountered between France and Alderney. The wall-mounted cube is a common obstacle studied in wind tunnels or water tanks. For this obstacle, we count the studies performed by Hearst et al. [START_REF] Hearst | Effect of turbulence on the wake of a wall-mounted cube[END_REF] at R e = 1.8 × 10 6 or Castro & Robins [START_REF] Castro | The flow around a surface-mounted cube in uniform and turbulent streams[END_REF] going up to Re = 10 5 , both in wind tunnels. Hearst at al. [START_REF] Hearst | Effect of turbulence on the wake of a wall-mounted cube[END_REF] studied the impact of turbulence intensity on a wall-mounted cube and found that, when turbulence intensity increases the wake shortens with a stronger dissipation rate although the flow topology remains identical. McArthur et al. [START_REF] Mcarthur | On the near wake of a simplified heavy vehicle[END_REF] studied the flow past Ahmed bodies at R e up to 7.7 × 10 5 in air. However, few studies were achieved at high Reynolds number (R e > 10 5 ). Hussein & Martinuzzi [START_REF] Hussein | Energy balance for turbulent flow around a surface mounted cube placed in a channel[END_REF] and Martinuzzi & Troppea [14] are among the firsts to characterize the flow around a wall-mounted cube and describe its wake. In keeping with their work, Castro & Robins [START_REF] Castro | The flow around a surface-mounted cube in uniform and turbulent streams[END_REF] highlighted the importance of the boundary layer thickness δ. It is fundamental to know where the obstacle intersects the boundary layer to characterize the incoming stress field. The angle of attack is studied by VanOudheusen et al. [START_REF] Van Oudheusen | Phaseresolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence[END_REF] using similar methods as the present study. The cube is studied here as a mean bathymetric variation. In addition, smooth depth variation are observed at the sea bottom (see figure 1). No study on the impact of floor inclination after an obstacle was found in the literature. The closest studies to the present case are those carried out on dunes, such studies are summed up by Best [START_REF] Best | The fluid dynamics of river dunes: A review and some future research directions[END_REF]. However, most cases are for river dunes, hence for lower Reynolds number (R e < 10 3 , [START_REF] Best | The fluid dynamics of river dunes: A review and some future research directions[END_REF]) even if Sarkar & Mazmunder [START_REF] Sarkar | Turbulent flow over the trough region formed by a pair of forward-facing bedform shapes[END_REF] carried out trials on dunes at R e = 1.4 × 10 5 in a small flume tank . Many studies on dunes underline the importance of turbulent events that can rise high in the water column [START_REF] Bennet | Mean flow and turbulence structure over fixed, twodimensional dunes: implications for sediment transport and bedform stability[END_REF][START_REF] Sarkar | Turbulent flow over the trough region formed by a pair of forward-facing bedform shapes[END_REF][START_REF] Best | The fluid dynamics of river dunes: A review and some future research directions[END_REF]. The rise of turbulent structures can have a major impact on turbines used to extract tidal energy [START_REF] Medina | Turbulence analysis and multiscale correlations between synchronized flow velocity and marine turbine power production[END_REF]. So, the knowledge of these high energetic flow structures is of great importance. In this study, experiments are carried out in a large flume tank to investigate the impact of an inclined floor on the wake of a wall-mounted cube. The question of the rise of turbulent events is investigated. For this investigation and following previous works [START_REF] Cai | Study on the characteristics of turbulent drag-reduction channel flow by particle image velocimetry combining with proper orthogonal decomposition analysis[END_REF][START_REF] Saha | Investigation of coherent structure in a turbulent channel with built-in longitudinal vortex generator[END_REF], the Proper Orthogonal Decomposition [START_REF] Lumley | The structure of inhomogeneous turbulent flows[END_REF] coupled with the quadrant analysis [START_REF] Wallace | The wall region in turbulent shear flow[END_REF] is considered. POD application allows first the extraction of energetic flow structures of the turbulent flow. Second, these energetic structures are classified according to the Reynolds-stress values. That permits to detect events called ejection or sweep [START_REF] Wallace | The wall region in turbulent shear flow[END_REF][START_REF] Adrian | Vortex organization in the outer region of the turbulent boundary layer[END_REF]. In the present study, this coupled method is used to detect the influence of the addition of the inclined floor downstream of a wall-mounted cube on the turbulent flow characteristics. Note that to study the turbulent structures developing over dunes, Bennet & Best [START_REF] Bennet | Mean flow and turbulence structure over fixed, twodimensional dunes: implications for sediment transport and bedform stability[END_REF] used the quadrant analysis demonstrating that inclined floor located behind a dune promotes the formation of these events.

After a description of the experimental set-up and a brief explanation of the POD method, experimental results are presented. First, a spatial description is made for the wall-mounted cube in a low turbulence intensity flow. Then, the impact of the addition of an inclined floor is studied through PIV measurements planes analysis and then using a coupled POD-quadrant method.

Experimental set-up

The tests are carried out in the wave and current circulating flume tank of Ifremer in Boulogne-sur-Mer presented in figure 2. The test section has the following dimensions: 18m length × 4m width × 2m height. The incoming flow is assumed to be steady and uniform. By means of grid and honeycomb (that acts as a flow straightener) placed at the inlet of the working section (see fig. 3(a)), a turbulent intensity of I = 1.5% can be achieved. In this study, non dimensional lengths are used: x * = x/H, y * = y/H and z * = z/H, with H the cube height. In this work, we focus on the three instantaneous velocity components denoted (U, V, W ) along the (X, Y, Z) directions respectively (Fig. 3(a)). The Reynolds decomposition is used allowing the decomposition of each instantaneous velocity component into a mean value and a fluctuation part: U = U + u , where an overbar indicates the time average. Turbulence intensity I in the incoming flow is defined as follows:

I = 100 1 3 (u 2 + v 2 + w 2 ) U ∞ 2 + V ∞ 2 + W ∞ 2 (1)
where (U ∞ , V ∞ , W ∞ ) are the uniform velocity components of the incoming flow. In the following, the denoted Reynolds shear stress component corresponds to τ uw = u w and the 2D turbulence kinetic energy is All obstacles considered in this study are chosen to represent the real-life conditions at scale. In the tank, I = 1.5% is the lowest turbulence intensity achievable. Reynolds similitude could not be achieved so the experiments are carried out in a Froude similitude with a Reynolds number as high as achievable to be closer to real conditions, although Castro & Robins [START_REF] Castro | The flow around a surface-mounted cube in uniform and turbulent streams[END_REF] found that for R e > 10 4 , the flow topology achieves a certain Reynolds number independence. Each element represents a key bathymetric element in the area of interest at a 1:20 scale (see table 1). The first set of experiments is carried out on a wall-mounted cube with height: H = 250 mm. The following experimental set-up consists in the same wall-mounted cube with an additional inclined floor downstream of the cube. The floor is a 2m long × 1.2m wide plane with an inclination of 6.5 • representing a smooth variation of the bathymetry that exists at site: it represents an average elevation of 12 meters of the floor over 105 meters. This choice also is a geometry easy to represent both experimentally and numerically for further comparisons [START_REF] Mercier | Towards the modelling of turbulence at tidal stream power sites with the lattice boltzmann method[END_REF][START_REF] Bourgoin | Development of a large-scale eddy simulation approach for tidal currents modelling[END_REF]. Furthermore, the floor inclination do not have much impact on the outer flow nor the surface elevation, only the near wake of the obstacle is impacted. The floor is disposed directly downstream of the cube. In the rest of this study, the flow configuration with the cube alone will be referred to as C 1 test case and the other flow configuration with both cube and inclined floor (6.5 o of inclination) will be referred to as C 1 S 6 test case. PIV (Particle Image Velocimetry) measurements, a Nd-yag Laser Gemini-Like is used with a Camera FlowSens EO-2M 1600pix × 1200pix that makes double images with a time step of 800 µs. A particle is detected on 3 to 5 pixels. PIV acquisitions are made for 150s, hence 2250 double images are taken with a 15H z acquisition frequency. The data are post processed with the software Dynamic Studio. To get rid of noise, the mean image is first subtracted to all images. Then, the displacement of particles is calculated using a Cross-Correlation on a 32pix × 32pix interrogation windows with 50% overlap [START_REF] Meinhart | A parallel digital processor system for particle image velocimetry[END_REF]. Outliers are replaced with the Universal Outlier Detection [START_REF] Westerweel | Universal outlier detection for PIV data[END_REF], depending on the plane, from 1% to 13% of the vectors are substituted. Single-pass method is used as, in our case, multipass adaptive PIV leads to errors generating artefacts rather than improving resolution. Two configurations are used for the PIV measurements:

k uw = 1 2 (u 2 + w 2 ). Scale U ∞ [m/s] Rugosity height H [m] Depth D [m] R e = HU∞ ν F r = U∞ √ gD

Alderney

• for horizontal planes, the laser lightens the (z * = 0.7) plane of the fluid and the camera is placed above the obstacle, perpendicularly to the laser plane and the precision in term of pixel size is 0.21mm for case C 1 and 0.25mm for case C 1 S 6 ,

• for vertical planes, the laser lightens the (y * = 0) plane of the fluid and the camera is positioned beside the obstacle and the precision in term of pixel size is 0.43mm.

Figure 4 illustrates the result of vertical PIV measurement after postprocessing with Dynamic Studio (Cross Correlation and Universal Outlier Detection) applied on the case C 1 S 6 , a mask is applied on the obstacles. PIV horizontal measurement planes carried out for C 1 only. In the following, when regarding the mean flow quantities, an interpolation is done between each consecutive plane allowing a representation of the mean quantities in the whole available domain.

Characterization of the wake behind wall-mounted obstacles

Reference case of the wall-mounted cube

This section focuses on the characterization of the reference case through a spatial and temporal analysis. Reference is chosen for the more canonical of all elements: the wall-mounted cube in a flow (case C 1 ) with high Reynolds number (R e = 2.5 × 10 5 ) and a Froude number of 0.23.

Using PIV measurements, streamlines are plotted in figure 6(a) for the vertical view and in figure 6(b) for the horizontal view. Figure 7 represents U maps in both cases. In these figures, the classical behaviour of the flow past a wall-mounted object can be seen [START_REF] Hearst | Effect of turbulence on the wake of a wall-mounted cube[END_REF][START_REF] Wood | Experimental investigation and large-eddy simulation of the turbulent flow past a smooth and rigid hemisphere[END_REF]: the flow separates at the leading edges of the cube into the outer steady region and the recirculation area downstream of the cube. A shear layer develops in-between and then the flow reattaches. The recirculation lengths are evaluated upstream (l us ), on top (l top ) and downstream (l ds ) of the cube. Results give, for the recirculation lengths, l * us = 0.7, l * top = 0.4 and l * ds = 1.9 and for the stagnation point altitude on the upstream face of the cube: z st * = 0.7. These results are consistent with the conclusions given in [START_REF] Hearst | Effect of turbulence on the wake of a wall-mounted cube[END_REF] for R e = 10 6 and also for lower Reynolds number R e ∼ 10 4 [START_REF] Hussein | Energy balance for turbulent flow around a surface mounted cube placed in a channel[END_REF]. The horizontal view (fig. 6(b)) shows the two counter-rotating vortices. More precisions on the flow topology can be found in [START_REF] Ikhennicheu | An experimental study of influence of bathymetry on turbulence at a tidal stream site[END_REF].

Inclined floor effects

An inclined floor is added downstream of the cube (case C 1 S 6 ). PIV measurements show that the aspect of the wake is strongly influenced by the presence of the floor as can be seen on the streamlines maps (see fig. 8) and the W maps (see fig. 9). W maps clearly show a strong area where W < 0 for case C 1 illustrating the flow going towards the floor on the outline of the recirculation region whereas case C 1 S 6 shows a small area where W < 0 at top of the recirculation region and the rest of the flow shows a reduced area where W > 0. These maps illustrate the fundamental wake In figure 10, τ uw maps give a good visualisation of the shear layer that develops between the outer undisturbed flow and the recirculation zone. The shear layer formation still occurs at the edges of the obstacle where fluid separation takes place. However, downstream, the inclined floor squeezes it. The shear layer is then thinner for case C 1 S 6 . Figure 10 also illustrates the shortening of the shear layer with the inclined floor: at x * = 3.5, the shear is strongly reduced for case C 1 S 6 and still persists for case C 1 . Finally, the impulsion of the floor inclination reorientates the shear layer towards the surface and it reaches higher altitude in case C 1 S 6 . To evaluate the effect of the inclined floor on the flow development, the streamwise growth rate of the shear layer is estimated in the y * = 0 plan for both cases. First, the centre (z 0 ) of the shear layer is determined for each streamwise position. It corresponds to the inflexion point of the mean velocity profile. Second, in each streamwise position x, the vorticity thickness is computed:

δ w (x) = U s (dU s /dz) z=z 0 (2)
where U s = U ∞ -U i (x) with U i (x) the streamwise velocity underneath the shear layer.

In order to find the inflection point, for each streamwise position x, U s (x, z) is fitted by a function f (x, z) = a(x) + b(x)tanh(c(x)z). Results are presented in figure 11 for both cases. The δ w graph shows that the shear layer is thinner for case C 1 S 6 , confirming the squeezing effect mentioned earlier. The vorticity thickness difference between both test cases starts at 0 at the trailing edge of the cube and then increases until x * = 1. Then the difference remains constant at ∆δ w = 0.08. The inclined floor effect is strong where the shear layer originates and then reduced. The streamwise evolution of z * 0 illustrates the rise of the shear layer in case C 1 S 6 contrarily to case C 1 . The shear layer centre evolution follows the inclined plane translation until x * = 2.5. Downstream of that position, the flow becomes more turbulent avoiding any well determination of the U i (x) velocity component. In order to have a more quantitative comparison in the downstream region, two streamwise positions are chosen at: x * = 2.5 and x * = 3.6. These positions are selected to avoid any recovering issues of the different PIV measurement planes. For case C 1 , profiles are measured from z * = 0.2 and for case C 1 S 6 , from the altitude of the floor. The profiles of U , τ uw and k uw are plotted along the Z axis in figure 12 and13. The profiles at x * = 1 are similar for both test cases and are not represented here. However, at x * = 2.5 the floor impact begins to be well pronounced. The shear layer (although thinner) reaches higher positions when impulsed: the τ uw peak at x * = 2.5 is translated ∆z * = 0.23 higher for case C 1 S 6 . It is around the elevation of the inclined floor at this position (z * f loor = 0.28). The peak shows a simple translation of the τ uw profiles. Furthermore at x * = 2.5, the peak intensity is about 10% more intense for case C 1 S 6 indicating a stronger shear. At x * = 3.6, however, the shear peak is as intense for case C 1 as for case C 1 S 6 . This confirms what can be visualized on the maps in figure 10: the shear layer dissipates faster and shortens for case C 1 S 6 . It is expected that, consequently, the wake will be shorter as well. The U profiles show that as long as we are above the shear layer (z * > 0.5 for x * = 2.5 and z * > 1.1 for x * = 3.6), U (C 1 S 6 ) > U (C 1 ). Underneath the shear layer, the impulsion of the floor causes an increase of W (see figure 9) that reduces U . Above the shear layer, for z * > 2.2, for both streamwise positions, τ uw (and U ) profiles meet at τ uw = 0 (U = 1 resp.) and the floor impact is no longer visible. The only difference between cases C 1 and C 1 S 6 at higher altitude appears on the k uw profiles. In figure 13(a), for x * = 3.6, k uw (C 1 S 6 ) > k uw (C 1 ) until the highest location measured (z * = 2.3). This 2D turbulent kinetic energy persists until higher location than the simple translation (z * f loor = 0.4 at x * = 3.6) given by the inclined floor, as can be observed on the τ uw profiles. For a better understanding, the k uw profile for case C 1 is translated of z * f loor = 0.4 in figure 13(b). It shows that, additionally to the translation, k uw is still 50% higher for case C 1 S 6 at z * = 2. 2D turbulent kinetic energy rises substantially with the addition of the inclined floor.

Application of the Proper Orthogonal Decomposition coupled with the quadrant method

In this part, POD is used as a filter in order to select the highest energetic structures and leave aside the non-coherent turbulent part. Then, based on the extracted energetic flow structures, the quadrant method is implemented to try to elucidate the turbulent events present in the flow. After a brief description of the mathematical concept of POD and the quadrant method, the POD analysis of the PIV velocity fields is examined. Then, the results based on the application of the quadrant method to the POD extracted velocity field are discussed.

Brief Mathematical description of POD

First introduced by Lumley [START_REF] Lumley | The structure of inhomogeneous turbulent flows[END_REF], POD is an efficient and optimal mathematical tool to extract energetic coherent structures embedded in a turbulent flow. In this context, a coherent structure is the structure that has the largest mean square projection of the velocity field. Mathematically, it corresponds to the determination of a basis which is optimal in an energetic sense. It consists of searching a function φ(X) which maximizes in a mean square sense the projection of the instantaneous fluctuating velocity field on φ(X). These functions are then the solution of the Fredholm equation:

Nc j=1 R ij (X, X )φ (n) j (X )dX = λ (n) φ (n) i (X) (3)
where R ij (X, X ) = u i (X)u j (X ) is the time-averaged two-point spatial correlation tension, N c is the number of velocity components considered.

u i (X, t) = N P OD n=1 a (n) (t)φ (n) i (X) (4)
Coefficients a (n) (t) are determined through the projection of the velocity field onto φ (n) and are mutually orthogonal and uncorrelated. The previous part describes the classical POD method proposed by Lumley [START_REF] Lumley | The structure of inhomogeneous turbulent flows[END_REF]. The snapshot version of POD [START_REF] Sirovich | Turbulence and the dynamics of coherent structures. part i: Coherent structures[END_REF] is used in the present work.

Details of the implementation of POD technique applied to PIV database can be found in [START_REF] Ph | Use of proper orthogonal decomposition for time interpolation from PIV data. application to the cycle-to-cycle variation analysis of in-cylinder engine flows[END_REF] and [START_REF] Ph | Pod investigation of the unsteady turbulent boudary layer developing over porous moving flexible fishing net structure[END_REF]. Such an application allows the extraction of energetic flow structures embedded in the turbulent flow. A annual review, made by Wallace [START_REF] Wallace | Quadrant analysis in turbulence research: history and evolution[END_REF] explains that quadrant analysis is pertinent preceded by POD. Then following previous works [START_REF] Cai | Study on the characteristics of turbulent drag-reduction channel flow by particle image velocimetry combining with proper orthogonal decomposition analysis[END_REF][START_REF] Saha | Investigation of coherent structure in a turbulent channel with built-in longitudinal vortex generator[END_REF], the resulted POD filtering velocity field is used for the next quadrant analysis to investigate the nature of the extracted organized flow structures.

Brief description of the quadrant method

Quadrant analysis is a way of characterizing energetic event in a turbulent flow not only in turbulent boundary layer flow [START_REF] Adrian | Vortex organization in the outer region of the turbulent boundary layer[END_REF] but also in turbulent flow developing over dunes [START_REF] Bennet | Mean flow and turbulence structure over fixed, twodimensional dunes: implications for sediment transport and bedform stability[END_REF]. It separates each u w event into four categories called quadrants as illustrated in figure 14. Q1 (u > 0, w > 0) represent outward interactions of fluid (outward motion of high-momentum fluid), Q2 (u < 0, w > 0) events are ejections of low-momentum fluid from the shear layer, Q3 (u < 0, w < 0) contain inward interaction of fluid (inward motion of low-momentum fluid) and finally, Q4 (u > 0, w < 0) contain sweep of high-momentum fluid towards the wall. Q2 and Q4 events are associated elements. They correspond to the largest contribution to the Reynolds shear stress [START_REF] Bennet | Mean flow and turbulence structure over fixed, twodimensional dunes: implications for sediment transport and bedform stability[END_REF][START_REF] Wallace | Quadrant analysis in turbulence research: history and evolution[END_REF]. In the present study, a shear layer is formed due to the presence of the cube and turbulent structures are shed from the layer. It is then expected that the application of quadrant method allows the extraction of events that are emitted from the shear layer.

POD analysis of PIV measurement fields

Choice of a common area. Following previous work [START_REF] Bennet | Mean flow and turbulence structure over fixed, twodimensional dunes: implications for sediment transport and bedform stability[END_REF] and to avoid any measurement plane overlap, a common area is retained. The location of this area illustrated in figure 16(a) is defined as follows: x * ∈ [2.2; 3.2] and z * ∈ [1.5; 2.2]. The choice of z * = 1.5 is meant to look above the shear layer, between the shear layer and the outer flow. The spatial area contains (n x × n y ) = (68 × 47) = 3196 measurements points for case C 1 and (n x × n y ) = (59 × 42) = 2478 for case C 1 S 6 .

POD application.

First, the fluctuating part of each instantaneous velocity field is determined thanks to the Reynolds decomposition. Second, in each test case, the vectorial POD is performed from the two available fluctuating velocity components leading to obtain N P OD = N acqu = 2250 modes. Figure 16(b) displays the cumulative energy content for the first 100 modes for both test cases. POD energy repartition differs from both cases. C 1 S 6 reaches higher energy level faster than case C 1 . This shows that more energetic organized flow structures are present in the C 1 S 6 flow configuration. Case C 1 exhibits less organized energetic structures in the common observation window. In each test case, instantaneous velocity vectors are then projected onto the first N i POD modes (with i = C 1 or C 1 S 6 ) as follows:

u P OD (X, t) = N i n=1 a (n) (t)φ (n) u (X) and w P OD (X, t) = N i n=1 a (n) (t)φ (n) w (X)
(5) N i which is function of the flow configuration has to be firstly determined. For such an investigation, the quadrant analysis will be conducted. Beforehand, as the energy level of the u component is higher than the one of w , the resulted φ (n) w (X) POD modes may be questionable. To avoid any ambiguity, a preliminary analysis is done. Two scalar PODs are separately performed on u and w , and results are compared to the vectorial POD results. Spatial shape

√ λ (n) φ (n)
w (X) of the firsts 6 modes is presented for scalar POD (top) on w and vectorial POD (bottom) in figure 15 for case C 1 S 6 on the common plane. In a similar way, comparative analysis of the spatial POD modes

√ λ (n) φ (n)
u (X) was performed and again for both velocity components for C 1 case. For each mode and each component, the order of magnitude and global aspect of the spatial modes are the same. Furthermore, the next following analyses have been done from scalar POD results and similar results are obtained.

A point is randomly chosen in the common plane (X D = (x * D = 3, z * D = 1.6)), where u P OD (X D , t) and w P OD (X D , t) are successively determined with varying N i number. In the graph, N i is the number of POD modes considered for case i (i = C 1 or i = C 1 S 6 ), see equation 5. The study was also carried out for other points and for both cases. Based on these velocity signals, the quadrant method is performed and the study of the impact of the number of POD modes on the quadrant proportion is achieved in figure 17 in X D for both C 1 and C 1 S 6 . It appears that, above N i = 6, the quadrant repartition achieves a certain modes number independence. It would not be necessary to use more modes for this study. Hence 6 modes are chosen for case C 1 S 6 , looking at figure 16(b), it appears that 6 modes represent 45% of energy for case C 1 S 6 . In order to have to same energy content, 9 modes are chosen for case C 1 to reach 45% of energy. Hence, the fluctuating flow field is recomposed using N C 1 = 9 modes and N C 1 S 6 = 6 respectively (see equations 5). The number of modes chosen for the study is higher for case C 1 . Figure 17 also shows that Q2 and Q4 are substantially more present for case C 1 S 6 than for case C 1 at the location D.

Q2/Q4 events predominance for case C 1 S 6 is consistent with the lower number of POD modes N i required that indicates more organized structures.

Quadrant method application.

Each turbulent velocity pair may be investigated either through examination of the entire signal (like [START_REF] Saha | Investigation of coherent structure in a turbulent channel with built-in longitudinal vortex generator[END_REF] and [START_REF] Cai | Study on the characteristics of turbulent drag-reduction channel flow by particle image velocimetry combining with proper orthogonal decomposition analysis[END_REF] and our previous study) or only with u w events that lie above a certain threshold value (H t ) (like [START_REF] Bennet | Mean flow and turbulence structure over fixed, twodimensional dunes: implications for sediment transport and bedform stability[END_REF]) defined in equation 6: The impact of the quadrant proportions versus H t is studied in figure 18 from instantaneous POD filtering velocity field extracted at the point D defined above and point B with X B = (x * B = 3, z * B = 2.1) and for case C 1 S 6 where quadrant differences are the more significant. Of course, the larger the H t value, the lower the quadrants proportion. For point B (figure 18(a)), at H t = 0, Q3 is more present. However, as soon as H t > 0.1, the predominance disappears and results show all quadrants in similar proportions (between 10 and 15%). This shows that what appeared to be a Q3 predominance, when slightly filtered shows an even distribution between quadrants. For point D (figure 18(b)), the study shows that for low filtering (H t < 0.5), Q4 is predominant. However, for higher values (H t > 1), Q2 is more present in point D. It shows that Q2 events dominate the flow, however Q4 events are the most energetic events even if they are in lower proportion. In this study, filtering is achieved with POD. Adding a criteria on H t would add a second filter that is not useful for the comparison here, hence the choice of H t = 0 is retained. However, figure 18 allows to understand the energy repartition between Q2 and Q4 events.

|u P OD w P OD | ≥ H t × |u P OD w P OD | (6)

Results of coupled POD-quadrant analysis

The method described in this section (POD + quadrant, with H t = 0) is now applied on every point of the common window for both cases. Results are presented in figure 19 with the repartition of the quadrant events in the window.

Results show a clear increase of Q4 events for case C 1 S 6 . Furthermore, the rise of these events is all the more intense when they are impulsed. This analysis justifies the assumption made that, with the presence of an inclined plane, turbulent structures are emitted higher and with a stronger intensity away from the shear layer. It is worth noting that at x * = 2.2, the inclined floor is at z * = 0.25 and for x * = 3.2, at z * = 0.36. It is clear that Q4 events rise higher than the simple impulsion given by the inclined floor. As mentioned in previous section, Q2 events do not appear in figure 19 because they are less present as Q4 but they exist in lower proportion and with a high intensity. Case C 1 S 6 also shows a light increase of Q3 events for z * > 2. As explained in previous paragraph, looking at point B that lies in this area, when increasing H t > 0.1, all events are in similar proportions (see figure 18(a)). For a more quantified comparison, profiles are plotted against the alti-tude at x * = 3 in figure 20. For case C 1 and z * < 1.6, Q4 is the more present event. However, higher in the water column, all the events are in even proportions (between 20 and 30%). For case C 1 S 6 , as observed earlier, strong predominance of Q4 event is seen for z * < 2. Higher in the flow, events are in similar proportion (between 18 and 35%). It is assumed that, higher in the water column (z * > 2.2), even quadrant repartition is achieved. Even quadrant proportion indicates that no energetic structures (sweep or ejections) is detected hence the equipartition of all events. It is the outer flow where the obstacle no longer have influence. Results are schematically represented in figure 21. Using figure 19 and profiles in figure 20, the Q4 area of predominance is determined in the chosen observation window. The rise of the cube influence due to the inclined floor presence is represented.

To summarize, we use a POD filter and look at the different Reynoldsshear stress events with the quadrant method. With a proper choice of POD modes number, quadrants proportion can be evaluated on a map for both cases. Q2 and Q4 events are known to be the main contributors to Reynolds shear stress. It is shown in this study that these events are stronger and rise higher in the water column for case C 1 S 6 compared to case C 1 .

Conclusion & Perspectives

In this study, the flow past elements representative of the seabed is described. The rise of turbulent structures and the behaviour of the shear layer are studied. First set of experiments on the wall-mounted cube in a low turbulence intensity flow show similar results to those found in the literature for lower Reynolds number with regards to the flow topology (like the recirculation length, l * ds = 1.9).

In order to understand the impact of the floor inclination on the obstacle wake, an inclined floor is added downstream of the cube. Consequently, to have a flow rate conservation, the average streamwise velocity increases with the addition of the floor. The recirculation zone reduces from l * ds = 1.9 to l * ds = 1.7 and a stagnation point S appears. The shear layer becomes shorter and thinner. However, the Reynolds shear stress, at its maximal value is more intense: 10% stronger at x * = 2.5. It is assumed that due to the squeezing effect, the shear is stronger indicating a better mixing. Then, the greater the mixing, the faster the wake dissipation. Hence the wake shortens. It is also observed that, above z * = 2.2, in spite of the inclined floor translation, the 2D turbulent kinetic energy is stronger for the case with inclined floor. This indicates stronger fluctuating velocities. It is assumed that the presence of a stagnation point above the floor increases the emission of turbulent structures that reach high altitudes in the water column. A POD analysis is carried out and instantaneous velocity vectors are projected onto the first six (for C 1 S 6 ) and nine (for C 1 ) energetic modes to reach 45% of energy level. The resulted POD filtered velocity fields are used as input data for a quadrant analysis. Results show a more intense presence of Q4 events for case C 1 S 6 on a chosen observation window. Q2 events are also present in a lower proportion but with a higher energetic level. This study showed the strong impact of an inclined floor downstream of a wall-mounted cube in a high-Reynolds number incoming flow. The inclined floor, does not only translated the obstacle wake, it is the source of a stronger emission of sweep and ejection events that are highly energetic. The major conclusion is that these event are stronger for case C 1 S 6 and they are expected to rise substantially higher in the water column, more than the simple impulsion given by the floor altitude variations. The results of this study are meant to explain real-life phenomenon observed at sea, the goal being to understand the turbulence generated at the sea bottom in the Alderney Race. The cube is representative of the mean bathymetric variation of this area and the inclined floor of a smooth depth variation. When choosing an area for marine current turbines, one must consider the presence of seabed elevation or not (i.e. presence of an inclined floor or not). Shear layer presence and energetic events may have an impact on the turbine and blade fatigue, hence floor elevation need to be considered and a specific study on the seabed topology might be required.

In this study, the measurements are limited to the near wake of the obstacle in order to properly study the impact of the obstacle on the flow. Measurements in the far wake are then required and PIV measurements seem to be appropriate for that purpose even if the obstacles considered here remain simple cases that are too canonical to reproduce real life turbulent structures. After studying each individually, a combination of several cubes, wide cylinder and the inclined floor will be investigated. Then, the effect of this kind of turbulent structures on the behaviour of a tidal turbine will be investigated. A turbulence intensity closer to real-life conditions (I = 15%) is achievable in the tank, the impact of the incoming turbulence intensity on obstacles wake is another possible development. Upstream turbulence intensity impact on the wake of a cube is already studied in the literature and the present study offers the understanding of the effect of the addition of an inclined floor on the wake. Combining both could also be investigated.

the reference ANR-10-IEED-0006-11. The authors also acknowledge the financial support of Ifremer and the Hauts de France Regional Council for this PhD study. We are most grateful to Thomas Bacchetti and Jean-Valery Facq for their assistance and precious advices. Highlights for paper entitled: Experimental analysis of the floor inclination effect on the turbulent wake developing behind a wall mounted cube:

Nomenclature

-Tests are carried out on a wall-mounted cube with and without an inclined floor representative of seabed elements, in Froude similitude with high Reynolds number, -PIV measurements are perfomed in horizontal and vertical measurement planes and spatial analyses are performed, -POD filter and quadrant analyses show the rise of coherent energetic structures.

Figure 1 :

 1 Figure 1: Bathymetry of the English Channel with a zoom of the Alderney Race area, SHOM [21]

Figure 2 :

 2 Figure 2: Ifremer Flume tank in Boulogne-sur-Mer

Figure 3 :

 3 Figure 3: Schematic view and picture of the cube in the wave and current circulating tank of Ifremer

Figure 4 :

 4 Figure 4: Instantaneous velocity field in a vertical PIV measurement plane, after postprecessing with DynamicStudio for case C1S6, a mask is applied on the obstacles

Figure 5 (

 5 Figure 5 (a) and (b) show the 10 and 6 PIV vertical measurement planes related to C 1 and C 1 S 6 test cases respectively and figure 5(c) shows the 6 PIV horizontal measurement planes carried out for C 1 only. In the following, when regarding the mean flow quantities, an interpolation is done between each consecutive plane allowing a representation of the mean quantities in the whole available domain.

Figure 5 :

 5 Figure 5: Representation of vertical measurement planes with a resolution of 1600pix × 1200pix and a precision in term of pixel size for vertical planes of 0.43mm and for horizontal planes of 0.21mm for case C1 and 0.25mm for case C1S6

Figure 6 :Figure 7 :

 67 Figure 6: Streamlines for case C1. Left hand side: vertical PIV measurements, at the median plane y * = 0. Right hand side: horizontal PIV measurements, at an altitude of z * = 0.7. White parts indicate areas where measurements were no measures are performed or where the laser light was not sufficient. l * us = 0.7, l * top = 0.4, l * ds = 1.9 and zst * = 0.7.

Figure 8 :Figure 9 :

 89 Figure 8: Streamlines using PIV vertical measurements at median plane (y * = 0). Left hand side: case C1. Right hand side: case C1S6. C the recirculation zone centre and S the stagnation point.

Figure 10 :

 10 Figure 10: τuw/U 2 ∞ (with U∞ = 1 m/s) maps using PIV vertical measurements (y * = 0). Left hand side: case C1. Right hand side: case C1S6.

Figure 11 :

 11 Figure 11: Left hand side: streamiwse evolution of the vorticity thickness δw. Right hand side: streamwise evolution of the z0 shear layer centre; for case C1 (•) and C1S6 (*)

Figure 12 :

 12 Figure 12: U /U∞ and kuw/U 2 ∞ profiles comparison cases C1 (-) and C1S6 (--) at x * = 2.5 and x * = 3.6, y * = 0 and along the Z axis.

Figure 13 :

 13 Figure 13: Left hand side: kuw/U 2 ∞ profiles at x * = 2.5 and x * = 3.6. Right hand side: kuw profiles at x * = 3.6. Case C1 is translated from ∆z * = 0.4 (altitude of the 6.5 • inclined floor at x * = 3.6). Profiles comparison cases C1 (-) and C1S6 (--) at y * = 0 and along the Z axis.

Figure 14 :

 14 Figure 14: Schematic representation of quadrant decomposition

Figure 15 :

 15 Figure 15: Spatial modes √ λ (n) φ (n) w (X) of w with n ∈ [1; 6] the mode number using scalar POD (top) and vectorial POD (bottom) for case C1S6, plane 4. Colormaps are different for modes 1,2,3 and modes 4,5,6.

Figure 16 :Figure 17 :

 1617 Figure 16: POD applied on a common plane for cases C1 and C1S6

Figure 18 :

 18 Figure 18: Quadrants proportion (%) versus Ht in XB = (x * B = 3, z * B = 2.1) (Left hand side) and XD = (x * D = 3, z * D = 1.6) (Right hand side). Case C1S6, NC 1 S 6 = 6.

Figure 19 :

 19 Figure 19: Top: case C1, NC 1 = 9. Bottom: case C1S6, NC 1 S 6 = 6. Quadrants proportion (%) in the whole common plane for both cases.

Figure 20 :

 20 Figure 20: Left hand side: case C1, NC 1 = 9. Right hand side: case C1S6, NC 1 S 6 = 6. Quadrants proportion (%) at x * = 3 against altitude z * .

Figure 21 :

 21 Figure 21: Left hand side: case C1. Right hand side: case C1S6. Schematic representation of the extend of the obstacle influence using POD analysis and selecting Q4 predominance area

Table 1 :

 1 in situ and experimental conditions (1:20 scale)

  Non dimensional quantities: (Quantities stated with a * are length reduced by H, for instance: x * = x/H) Modes number selected for analysis for case C1 NC 1 S 6 Modes number selected for analysis for case C1S6 nx Spatial sample in the horizontal direction ny Spatial sample in the vertical direction

	Dimensional quantities:
	D	Depth	m
	δw	Shear layer thickness	m
	fe	Sampling frequency	Hz
	H	Cube height	m
	l ds	Downstream recirculation length	m
	ltop	Top of the cube recirculation length	m
	lus	Upstream recirculation length	m
	U	Average streamwise velocity	m/s
	u	Fluctuating streamwise velocity	m/s
	u POD	POD filtered, fluctuating streamwise velocity m/s
	V	Average spanwise velocity	m/s
	v	Fluctuating spanwise velocity	m/s
	v POD	POD filtered, fluctuating spanwise velocity	m/s
	W	Average vertical velocity	m/s
	w	Fluctuating vertical velocity	m/s
	w POD POD filtered, fluctuating vertical velocity	m/s
	z0	Shear layer centre altitude	m
	zst	Stagnation point altitude	m
	Ht	Threshold value for quadrant method
	kuw	2D turbulence kinetic energy
	Nacqu	Number of temporal sample
	NP OD Total modes number for snapshot POD
	NC 1
	Re	Reynolds number
	Fr	Froude number
	I	Turbulence intensity
	St	Strouhal number
	τuw	Averaged Reynolds shear stress

Acknowledgement

This work benefits from a French State grant managed by the National Research Agency under the Investments for the Future program bearing


Professor Pierre Lucas

Bo Fan

Bai Xue
email: baixue@szu.edu.cn

Zhongkuanluo

Xianghuazhang
email: xiang-hua.zhang@univ-rennes1.fr

Hongli Ma

Laurent Calvez

Pressure dependence of interfacial resistance in pellets made from GeS 2 -Ga 2 S 3 -Li 2 S-LiI glass powder

Keywords: chalcogenide glass, lithium ionic conductivity, solid electrolyte, interfacial resistance

The interfacial resistance and capacitance in pellets made from GeS 2 -Ga 2 S 3 -Li 2 S-LiI glass powder are studied under uniaxial compression. By varying the pressure, remarkable change of the geometric dimension of the interfacial resistance and capacitance is observed. Assuming that the interfacial resistance and capacitance arise from the contact region between the powder particles, a quantitative model is established that well describes the

Accepted Article

. geometric dimension change of the interfacial resistance and capacitance. This work emphasizes that ameliorating the contact between the particles is one of the most important methods to reduce the interfacial resistance in the powder-type ionic-conduction devices made from highly-conductive sulfide solid electrolyte powders.

1.Introduction

Sulfide solid electrolytesshow excellent ionic conductivity [START_REF] Liu | Recent progress in sulfide-based solid electrolytes for Li-ion batteries[END_REF][START_REF] Bachman | Inorganic solid-state electrolytes for lithium batteries: mechanisms and properties governing ion conduction[END_REF] and are of great potential for applying in solid-state batteries [START_REF] Han | High-performance all-solid-state lithium-sulfur battery enabled by a mixed-conductive Li 2 S nanocomposite[END_REF][START_REF] Yamada | All solid-state lithium-sulfur battery using a glass-type P 2 S 5 -Li 2 S electrolyte: benefits on anode kinetics[END_REF][START_REF] Lin | Lithium polysulfidophosphates: a family of lithium-conducting sulfur-rich compounds for lithium-sulfur batteries[END_REF] . Different from its oxide counterpart, the influence interfacial/grain boundary resistance on the total conductivity in sulfide solid electrolytes is normally considered to be negligible [START_REF] Tatsumisago | Recent development of sulfide solid electrolytes and interfacial modification for all-solid-state rechargeable lithium batteries[END_REF] . However, recent researches confirm that once the conductivity of the sulfide electrolyte reaches 10 -3 S/cm or more, the interfacial/grain boundary resistance turns out to be a crucial factor for the ionic conductivity [START_REF] Xu | Preparation of Li 7 P 3 S 11 glass-ceramic electrolyte by dissolution-evaporation method for all-solid-state lithium ion batteries[END_REF][START_REF] Wei | Influence of annealing on ionic transfer and storage stability of Li 2 S-P 2 S 5 solid electrolyte[END_REF] .

To be applied in solid-state batteries, sulfide solid electrolytes are typically used in the form of powder. For example, mixtures of active material powders, solid electrolyte powders and carbon are widely used as composite cathodes [START_REF] Ohtomo | All-solid-state lithium secondary batteries using the 75Li 2 S•25P 2 S 5 glass and the 70Li 2 S•30P 2 S 5 glass-ceramic as solid electrolytes[END_REF][START_REF] Nagata | All-solid-state lithium-sulfur battery with high energy and power densities at the cell level[END_REF][START_REF] Xu | Construction of all-solid-state batteries based on a sulfur-graphene composite and Li 9.54 Si 1.74 P 1.44 S 11.7 Cl 0.3 solid electrolyte[END_REF] . Additionally, pellets cold-pressed

Accepted Article

. from the solid electrolyte powders are used as the ion-transport layers which separate the anode and the cathode [START_REF] Nagao | Sulfur-carbon composite electrode for all-solid-state Li/S battery with Li 2 S-P 2 S 5 solid electrolyte[END_REF] . In such powder-type solid-state batteries, there exists a large amount of interface. Despite the importance of interfacial resistance to the application, deep discussions about the origin of interfacial resistance in sulfide solid electrolyte are rarely reported in the literatures. GeS 2 -based glasses are of good chemical and thermal stability [START_REF] Cozic | GeS 2 -Ga 2 S 3 -LiCl glass system: electrical conductivity and structural considerations[END_REF][START_REF] Xu | Broadband near-IR emission in Tm/Er-codoped GeS 2 -In 2 S 3based chalcohalide glasses[END_REF] . By the addition of lithium, the ionic conductivity of this glass system can reach 10 -4 S/cm, and can be further improved to 10 -3 S/cm by the addition of LiI [START_REF] Saienga | Preparation and characterization of glasses in the LiI+Li 2 S+GeS 2 +Ga 2 S 3 system[END_REF][START_REF] Saienga | The comparative structure, properties, and ionic conductivity of LiI + Li 2 S + GeS 2 glasses doped with Ga 2 S 3 and La 2 S 3[END_REF] . In this paper, the interfacial resistance in the pellets made from ionic-conductive GeS 2 -Ga 2 S 3 -Li 2 S-LiI glass powder is studied under varying uniaxial compression. This study helps us to understand the origin of the interfacial resistance in this sulfide solid electrolyte. A simple model is proposed to describe the observed pressure dependence of the interfacial resistance.

Experimental procedures

32GeS 2 -8Ga 2 S 3 -40Li 2 S-20LiI (in mol%) glass powders were prepared by ball milling.

Starting materials, Ge (99,99%, Alfa Aesar), Ga (99.99%, Alfa Aesar), S (99%, Alfa Aesar) , and Li 2 S (99.9%, Alfa Aesar) were weighed according to the glass composition. Then 8 g starting materials were put into a tungsten carbonide jar with ten tungsten carbonide grinding balls (φ=10mm). The filling rate is about 1/3. The ball milling was conducted at 600 rpm using a planetary ball mill apparatus (Pulverisette 7, Fritsch GmbH, Germany). The duration of ball milling was 62 h. All the operations were conducted in an Ar-filled glove box.

Accepted Article

. X-ray diffraction (D8 Advance, Bruker AXS GmbH, Germany) were used to monitor the amorphization degree of the ball-milling product. Raman spectra were recorded by a Raman spectrometer (inVia, Renishaw Inc., UK) with a 532 nm DPSS laser as the source. The as-prepared glass powders were cold-pressed into pellets under 330 MPa (~15 mm diameter and ~1.4 mm thickness) in anAr-filled glove box. The pellets were then sealed in silica tubes which were pumped to high vacuum (8×10 -4 Pa). The pellets were sintered under vacuum at 240 °C for 10 h to improve the density. Finally, the pellets were coated by Au films on top and bottom surfaces for conductivity measurement. The coating was carried out with a low vacuum coater (EM ACE200, Leica Microsystems, Germany) which was installed inside an Ar-filled grove box. The morphology of the sintered pellets was recordedby a scanning electron microscope (Zeiss supra 55, Carl Zeiss GmbH, Germany).The sample preparation was carefully conducted to avoid direct air exposure. Only a transient air contactoccurredduring the sample installation of SEM characterization, which might have slight influence on the recorded sample morphology images.

The ionic conductivity was measured using an AC impedance method in an argon filled glove box, using a frequency response analyzer (Solartron 1260A, SolartronAnalytical Inc., UK). A tablet press machine is modified to be used as the sample holder so that varying uniaxial compression can be applied onto the samples during the conductivity measurement.

Accepted Article

.

Results and discussions

The XRD pattern of the 62 h ball-milling product is shown in Figure 1(a). No diffraction peaks are detected in the sample, indicating that the sample is thoroughly amorphized. Figure 1(a) also shows the XRD pattern of the pellet sintered at 240°C for 10 h. The absence of diffraction peaks of this sintered pellet confirms that the crystallization is negligible during the sintering process.

Figure1(b) shows the Raman spectra of the as-milled 32GeS 2 -8Ga 2 S 3 -40Li 2 S-20LiI glassy powder and the pellet sintered at 240 °C for 10 h. Two spectra have similar features. The broad Raman signal is principally composed of two peaks: the peak around 350 cm -1 , which is attributed to the vibration of [GeS 4/2 ] tetrahedrons, and the peak around 407 cm -1 , which is attributed to the vibration of [GeS 2/2 S 2

2-

] tetrahedrons [START_REF] Liu | Recent progress in sulfide-based solid electrolytes for Li-ion batteries[END_REF] . This is a typical Raman signal for GeS 2 -based glasses.Raman spectra indicate that no significant structural evolution takes place during the sintering, that is accordant with the XRD results.

By applying different uniaxial compression, the impedance spectra of one sample pellet were measured and are presented in Figure2. All the spectra consist of a high-frequency arc and a low-frequency tail, manifesting ionic conductive behaviour. The arc is attributed to the parallel of the interfacial capacitance C if and the interfacial resistance R if , while the tail, a typical signal of a Warburg element W el , is attributed to the diffusion of ions near the electrolyte/electrode interface [START_REF] Barsoukov | Impedance Spectroscopy: Theory, experiment, and applications[END_REF] . The intragrain resistance R ig can be obtained at the high frequency end of the arc, and the sum of R ig and R if can be obtained at the low frequency end of the arc. Evidently Figure2 shows that the dimension of the arc decreases with the increasing applied pressure, which indicates a remarkable decrease of R if under compression.

Accepted Article

.

To precisely characterize the parameters R ig , R if and C if , the impedance spectra are fitted with a typical equivalent circuit for solid electrolytes, as shown in the insert of Figure2. The fitting results are listed in Table 1. When the applied pressure increases from 0 to 330 MPa, the intragrain resistance R ig decreases slightly. Quite differently, the pressure dependence of the interfacial resistance R if and the interfacial capacitance C if is evident.

The pressure dependence of the ionic conduction was also reported in other ionic conductors, as summarized in Table 2. It was observed that in high purity Y 2 O 3 -stabilized tetragonal zirconia ceramics (YTZ), by applying a 270 MPa pressure, both intragrain and interfacial resistances changed about 8% [START_REF] Peko | Ionic transport in polycrystalline zirconia and Frenkel's space-charge layer postulation[END_REF] .In this case, the interfacial resistance is principally ascribed to the space-charge layers at the grain boundary, according to the Frenkel's model [START_REF] Barsoukov | Impedance Spectroscopy: Theory, experiment, and applications[END_REF] . It is proposed that under pressure the deformation of YTZ reduces the interionic space, limits the ion mobility and consequently changes the resistance [START_REF] Peko | In situ characterization of the grain and grain-boundary electrical responses of zirconia ceramics under uniaxial compressive stresses[END_REF] . Since the mechanical deformation is small, the pressure dependence of the ionic conduction is not evident. Additionally, based on the space-charge layer postulation, bulk and grain boundary form a unique mechanical entity, so that intragrain and interfacial resistances show identical behavior under pressure.

It is worth noting that in our case, the interfacial ionic conduction change is as high as 1666%, far more pronounced than the intragrain. Therefore, the interfacial resistance of the glass powder in this study cannot be simply ascribed to the space-charge layers or a secondary interfacial phase. Actually, the space-charge layers are typically built with charged lattice defects, whichare usually absent in glass materials. A similar phenomenon was observed in Li 2 S-P 2 S 5 glass, where the ionic conductance increased more than 420% after

Accepted Article

. applying 360 MPa pressure [START_REF] Sakuda | Sulfide solid electrolyte with favorable mechanical property for all-solid-statelithium battery[END_REF] . Such an evident increment can be attributed to the densification of the sample pellets by cold-pressing. Therefore, we propose that the highly pressure-dependent interfacial resistance of our sulfide glass pellets is intimately associated with a geometrical factor, the pore distribution in the pellets.

As well known, the resistance and the capacitance are determined by both the material parameters such as resistivity ρand permittivity ε r , and the geometric parameters such as area and thickness. Since the maximal applied pressure is 330 MPa that is too low to evidently change ρ orε r (as demonstrated in Ref. 18),the significant decrease of R if and the increase of C if indicate that the pressure evidently changes the geometric dimension of the two elements.

Viewing the significant geometric dimension change of the interfacial resistance and capacitance under compression and considering the influence of pore distribution onthe interfacial resistance, a model is proposed for the interfacial resistance in pellets made from GeS 2 -Ga 2 S 3 -Li 2 S-LiI glass powder,which is schemed in Figure3. For simplification of the modeling, it is assumed that the powder particles are spheres with identical size, and are close-packed so that they are in a hexagonal arrangement (Figure3(b)). Due to the presence of compression or sintering, the contact region between the powder particles deforms.

Geometrically, such deformation is described by the overlap of the powder spheres.

Consequently, a porous morphology appears (Figure 3(b)). The porous morphology as described by the model is coincident well with the real morphology of the sample pellets, which is illustrated by the SEM image in Figure3(a).

Accepted Article

.

Here we focus on the contact region between two particles (Figure3(c)). Because of the imperfect contact between the particles, the ion transport path shrinks in the contact region.

We propose such a shrinkage is the major origin of the interfacial resistance. Therefore, the interfacial resistance has the same resistivity ρ i as the intragrain resistance. As for the geometric dimension, the area A of the interfacial resistance is roughly the area enveloped by the intersection of the two powder spheres, and its thickness is the thickness of the contact region 2w. The geometric dimension of the interfacial resistance is colored by red in Figure3(c). Thus, the resistance of a single interfacial can be expressed as follow:

A w R i 2 s if    (1)]
A and wis geometrically related by the following equation:

] ) 2 3 ( [ 2 2 w r r A     (2)
where r is the radius of the powder sphere.

The interfacial capacitance is proposed to be contributed from both the intergranular contact region (red in Figure3(c)) and the air in the voids (bluein Figure3(c)). The area of interfacial capacitance is fixed as A', while the thickness 2w varies with different applied pressure. The ratio between w and r, defined as the reduced interfacial width w * , can be calculated from the intragrain capacitance C ig and the interfacial capacitance C if , by the following equation:

t C S C C r w w if 0 if ig if if ig *         (3)

Accepted Article

. where 0  is the vacuum dielectric constant, if  is the average permittivity of interface, ig  is the permittivity of particle, S and t are respectively the area and thickness of the sample pellet. The reduced interfacial width under different pressure is calculated and listed in Table 1. It decreases with the applied pressure (the overlap between the powder spheres becomes more evident), reflecting the densification of the pellet under uniaxial compression.

According to the SEM image in Figure3(a), the interfacial width 2w, which is associated with the pore size, is about 40 nm, and the average powder (cluster) size 2r is 500 nm. The reduced interfacial width w * in the pressure-free sample could be estimated to be 0.08, and results in an interfacial capacitance of about 10 -10 F. The value coincides well with the experimental data listed in Table 1. A typical interfacial capacitance in polycrystalline solid electrolytes with similar sample size is about 10 -9 F, higher than the one observed in our samples. It is because that the interfacial layers caused by space-charge layer or secondary phase is typically thinner than the ones caused by poor particle-contact as discussed above.

Since the geometric parameters A and w of the interfacial resistance are all associated with the reduced interfacial width w * , rearranging Equation ( 1) - (2) gives the relationship between the interfacial conductance G if and the reduced interfacial width w * :

* 2 * if if ) 2 / 3 ( 1 1 w w R G     (4)
Figure4 shows the normalized interfacial conductance G if versus reduced interface width w* in two pellet samples. The relationship described by Expression (4) is also plotted in Figure4. It can be seen that the modeling curve well predicts the trend of the experimental data. Thus, the model proposed above can well explain the pressure dependence of the

Accepted Article

. interfacial resistance and capacitance: On one hand, under high pressure, the width of the contact region between the particles decreases evidently. As a result, the thickness of the interfacial capacitance decreases so that the capacitance increases; On the other hand, high pressure improves the contact area between the particles, so that the ion transport path across the interface is enlarged. Consequently, the area of the interfacial resistance increases and lower resistance can be observed. The predicted curve somehow deviates from the experimental data under high pressure with low w*. It might be caused by the simplicity of our geometric assumption that is inaccurate when large deformation of the particles occurs under high pressure.

The modeling curve in Figure4 also predicts that by further reducing the interfacial width, the interfacial conductance can be rapidly improved. However, further reduction of w * by the increase of applied pressure seems to be difficult and ineffective. Sintering techniques such as hot-pressing or SPS are expected to be a more effective way to improve the interfacial conductance. This conclusion is coincident with the experimental study on Li 7 P 3 S 11 , whose ionic conductivity can be raised one order of magnitude by an optimized heat treatment in comparison with the cold-pressed samples [START_REF] Seino | A sulphide lithium super ion conductor is[END_REF] .

Conclusions

In summary, this work demonstrates that in the pellets made from GeS 2 -Ga

Accepted Article

.

Figure1.( a )

 a Figure1.(a) XRD patterns and (b) Raman spectra of the as-milled glass powder and the pellet sintered

Figure2.

  Figure2. Impedance spectra of one sample pellet measured under varying uniaxial compression. The

Figure3.

  Figure3. Morphology of the pellets made from GeS 2 -Ga 2 S 3 -Li 2 S-LiI glass powder and schematic

Figure4.

  Figure4. Normalized interfacial conductance G if versus reduced interface width w*. The solid line is

  2 S 3 -Li 2 S -LiI glass powder,the geometric dimension of the interfacial resistance and capacitance can change remarkably under compression. To explain such a phenomenon, it is proposed that the interfacial resistance arises from the boundary region where good intergranular contact is the interfacial capacitance is contributed from both the intergranular contact region and the air in the voids. Since the contact region deforms under compression, its thickness is reduced and the contact area is enlarged. That's the reason for the geometric dimension change of the interfacial resistance and capacitance. Moreover, a quantitative model is successfully established to describe this geometric dimension change. This work indicates that ameliorating the contact between the particles is essential to reduce the interfacial resistance in the powder-type ionic-conduction devices made from highly-conductive sulfide solid electrolytes. Sintering techniques such as hot-pressing or SPS may be necessary to achieve this goal.

	established, and
	Accepted Article
	.

superior to liquid ion conductors for use in rechargeable batteries. Energy Environ Sci. 2014; 7: 627-31.

Table and Figure Captions Table 1 .

 andCaptions1 Intragrain resistance R ig , interfacial resistance R if, interfacial capacitance C if, and reduced interface width w* of one pellet under different pressure. All the parameters are deduced from the impedance spectra in Figure 2.

Table 2 .

 2 Pressure dependence of ionic conductivity in the studied pellet sample and in other ionic conductive glasses and ceramics.

Table 1 .

 1 Intragrain resistance R ig , interfacial resistance R if , interfacial capacitance C if , and reduced interface width w* of one pellet under different pressure. All the parameters are deduced from the impedance spectra in

	Figure 2.
	Pressure	R ig	R if	C if	w*
	(MPa)	(ohm)	(ohm)	(pF)
	0	866	3072	164	0.0679
	55	848	1105	329	0.0340
	110	871	313	655	0.0171
	165	805	276	672	0.0166
	220	738	214	874	0.0128
	275	671	174	1060	0.0105
	330	624	152	1215	0.0092

Table 2 .

 2 Pressure dependence of ionic conductivity in the studied pellet sample and in other ionic conductive glasses and ceramics.

	Material	Applied Pressure	|(σ-σ 0 )/σ 0 |		Reference
		(MPa)	intragrain	interface
	GeS 2 -Ga 2 S 3 -Li 2 S-LiI glass 275	29%	1666%	This work
	YTZ	270	8%	8%	[18]
	Li 2 S-P 2 S 5 glass	360	--	>420% *	[20]

* The relative conductivity change induced by pressure in Li 2 S-P 2 S 5 glass is calculated with the total conductivity measured under 40 MPa and 360 MPa. The total conductivity is mainly determined by interfacial conductivity in this material[START_REF] Sakuda | Sulfide solid electrolyte with favorable mechanical property for all-solid-statelithium battery[END_REF] .

Acknowledgement

This work is the financially supported by the National Natural Science Foundation of China (No. 61504085/51702216), the Natural Science Foundation of Guangdong Province (No. 2017A030313325), and the Natural Science Foundation of Shenzhen University (No. 827-000037/201520).

Accepted Article

.