Taeseong Kim
email: tkim@dtu.dk

Anand Natarajan

Anaïs Lovera

Emricka Julan

Christophe Peyrard

Matteo Capaldo

Guillaume Huwart

Pauline Bozonnet

Martin Guiton

An extensive code-to-code comparison of a modified version of IEA15MW-UMaine Floating Wind Turbine for H2020 HIPERWIND project

Keywords: FOWT, aero-servo-hydro-elastic model, benchmark, IEA 15MW, semisubmersible

An extensive code-to-code comparison among DIEGO, DLW and HAWC2 has been performed on a floating wind turbine (modified version of UMaine floater with IEAWIND 15MW wind turbine). In total, 10 cases are compared, and a few key results of this comparison are reported in this paper. The load cases have been defined in the D1.2 and the results are presented in this document. From the comparisons, it is clearly seen that the results predicted by the three codes are in general good agreement despite some differences in specific degrees of freedom like sway and yaw for the extreme wind park case would require additional investigations.

Introduction

The European Commission has set an ambitious target of up to 450 GW of offshore wind by 2050 [START_REF]A Clean Planet for All[END_REF]. With offshore wind power set to form the backbone of green electricity production in Europe, there is an urgent need for cost-effective realization of the reliability of major wind turbine components, especially for floating wind turbines. HIPERWIND H2020 project [2] aims at contributing to this objective by modelling the entire chain from environmental conditions to wind farm design for uncertainty reduction and to increase reliability. As a first step of this project, this paper presents an extensive code-to-code comparison of the model response from three different aero-servo-hydro-elastic numerical tools (DIEGO, DeepLines Wind TM (DLW) and HAWC2). The compared models are a modified version of the IEA15MW /UMaine floating wind turbine [START_REF] Allen | Definition of the UMaine VolturnUS-S Reference Platform Developed for the IEA Wind 15-Megawatt Offshore Reference Wind Turbine[END_REF]. Various design test cases were considered to compare the responses.

Methodology

The methodology employed herein is similar to the OC6 (Offshore Code Comparison Collaboration Continued, with correlation and uncertainty) project of IEA Wind Task30 which also concerns code-tocode comparison [4]. A stepwise comparison procedure is performed. Detailed test cases are summarized in Table 1. The model complexity is increased step-by-step to facilitate the identification of potential modelling discrepancies introduced by different assumptions or model implementations in the various codes. In this study, the floating system used is based on the IEA 15MW turbine defined in [START_REF] Gaertner | Definition of the IEA Wind 15-Megawatt Offshore Reference Wind Turbine[END_REF] and the semisubmersible foundation proposed by University of Maine and detailed in the NREL report [START_REF] Allen | Definition of the UMaine VolturnUS-S Reference Platform Developed for the IEA Wind 15-Megawatt Offshore Reference Wind Turbine[END_REF]. From [START_REF] Allen | Definition of the UMaine VolturnUS-S Reference Platform Developed for the IEA Wind 15-Megawatt Offshore Reference Wind Turbine[END_REF], the first tower natural frequencies are reported to be around 0.48 Hz. However, it was investigated that the first natural frequencies of the tower dropped around 0.39-0.40 Hz when hydrodynamic added mass is considered in the modal analysis. This value is closer to the 3P frequency of the FOWT (about 0.375Hz at the rated rotational speed). This issue has now been mentioned in the FAQ of IEA Wind Task 37 available at [6] and should be fixed in a future design. In this study, to avoid the resonance excitations due to the lowered natural frequency of the tower, a new tower design that provides a safe distance from the 3P frequency (about 15% of 3P frequency) is introduced, whereby the total tower weight was increased from 1263 tons to 1515 tons. Manufacturing constraints are also considered, such as diameter and thickness ratio lower than 200 to avoid local buckling and maximum sectional angle variation of 3 degrees. This led to other modifications on the weight of the nacelle and on the ballast in the floater, in order to have a very small variation in the total mass and to keep the draft of the FOWT unchanged. All the floater geometrical parameters have been kept unchanged and only the ballast has been modified. Furthermore, in this study, the target offshore site is South Brittany (France) with a water depth of 150m different of the original design one at 200m. It thus requires additional modifications for the ballast and the mooring. TM . The hydrodynamic databases are limited to first order in the present benchmark, meaning that the second order wave loads from the diffraction-radiation (QTF) have not been computed and used for the time domain simulations. However, the drag forces coming from the Morison elements are expected to produce a small level of nonlinear loads. These loads could be able to generate second order contribution, depending on the strategies used by the different partners for drag. At the end, this difference in the drag excitation is regarded as negligible in most of cases.

Results

In this paper, some of key results will be presented based on the considered test cases defined in Table 1.

Modal analysis

Initially, the location of the full system (turbine and floater) center of gravity is compared among the three codes. It can be noted that this location does not account for the mooring lines. Table 3 shows coordinates of the complete turbine center of gravity computed by the three codes. It can be concluded that three tools show a good agreement although HAWC2 predicts the center of gravity slightly higher. 4 shows that all modes are well corresponding for all three numerical tools.

Free decay test

Four decay tests in different directions without wind and without waves are performed. These decay tests consist of applying an initial displacement (or rotation) on the floater, set the floater free and then observe the displacement (or rotation) at the keel. Figure 1(a) depicts the time series of the surge motion for the decay test in which initially a displacement of 10m in the surge direction is applied. It can be seen that the three codes are in good agreement, with a decrease of the surge motion very similar among the three time series. Figure 3 shows the electrical power, rotational speed and blade pitch during the wind step case. As expected, the evolution of those quantities is very similar which proves that the floating specific feedback is working properly. The rated power and rotor speed are obtained for a lower wind speed by DLW because of the differences in the model corresponding to the BeamDyn blade version instead of the ElastoDyn one.

(a) The electrical power during the wind steps (b) The rotor rotational speed during the wind steps (c) The blade pitch during the wind steps Figure 3: Floating wind turbine system responses for wind step case

Wave only load cases

In total, three load cases considering regular wave conditions were performed. In this section only the regular wave considering H=2 m and T=6 s is shown. Figures 4 (a

Irregular wave load cases

In total, two load cases considering irregular waves conditions were performed. The irregular wave conditions are given by the following JONSWAP parameters, 1) Hs=2 m, Tp=7 s and ϒ=3 and 2) Hs=13 m, Tp=16 s and ϒ=1. In this section only the irregular wave considering Hs=13 m, Tp=16 s and ϒ=1 is shown. Figure 5 shows the PSD of the wave elevation. Table 5 summarizes the basic statistics of various quantities of interest. Overall, the motion statistics for all DoFs show good agreement between the three codes. DLW produces a higher mean surge due to the stretching model used and a higher amount of roll dynamics, which appears to remain small. Yaw follows the same tendency. HAWC2 produces a lower mean surge because it considers no Morison excitation. The dynamic pitch response is a bit lower than DIEGO and DLW, but this seems to have little effect on the moment at tower bottom which is well aligned with DLW. Mooring tension forces predicted from the three codes are in good agreement for line 2 and 3 but produce significant differences for the line 1 standard deviation, DIEGO being 20% under DLW and HAWC2 40% above DLW. The influence of the mean surge could be part of the reason for this discrepancy but needs further verification. Forces in the tower, Fx, are well aligned for the three codes regarding the standard deviation. where Fx: Tower bottom fore-aft force, My: Tower bottom overturning moment, FT1, FT2, and FT3: mooring #1, #2, and #3 tension force, respectively.

Turbulent wind cases

Two load cases considering turbulent winds were performed considering a mean wind speed at hub height of 1) 8.32 m/s (below rated) for which the wind turbine is rotating at around 5.9 rpm and 2) 15.53 m/s (above rated) for which the wind turbine is rotating at around 7.53 rpm. Accordingly, the excitation frequencies correspond to the rotor frequency (1P), blade passing frequency (3P for threebladed wind turbine) and the corresponding harmonics. The load cases are 700s long, from which the 200s first are regarded as transient and are removed from the analysis.

Figure 6 shows the evolution of the electrical power during both below and above rated turbulent wind load cases. Some differences can be noted between the three codes which may be due to a difference in the pitch servo control.

(a) Electrical power below rated wind speed (b) Electrical power above rated wind speed Figure 6: Electrical power curve comparisons below and above rated wind speed

The PSD of the tower fore-aft bending moment is shown in Figure 7. The rotor frequency, the blade passing frequency as well as the eigen-frequency of the tower are shown on the graph with vertical dashed lines. The agreement between the three codes is very good. The three PSD depict the same peaks at the above-mentioned frequencies. Table 6 shows the statistics of quantities of interest of platform motion under turbulent wind inflow above rated wind speed. It shows a nice agreement between the three codes for the motions, except that DLW produces lower dynamic response in surge/sway/yaw than HAWC2 and DIEGO, as one can see from the standard deviations. The control strategy might be involved in this response. It seems also that the controller used in DIEGO increases a bit the excitation, resulting in slightly higher Fx/My/Pitch responses. where Fx: Tower bottom fore-aft force, My: Tower bottom overturning moment, FT1, FT2, and FT3: mooring #1, #2, and #3 tension force, respectively.

Parked case

This load case consists in considering irregular ocean waves and a turbulent wind inflow at a mean wind speed of 50 m/s. The turbine is parked (i.e., blade pitch at 90° and the rotor is blocked). Figure 8 (a) and (b) show an extract of the time series between 1250 s and 1650 s of the bending moment and force at tower bottom. These figures show that there is a good agreement among the three codes. This good agreement is also confirmed by the basic statistics of various quantities of interest presented in Table 7.

In particular, it can be remarked:

• The surge, heave, roll, and pitch dynamics are well aligned, despite some differences on the mean values. In particular, HAWC2 provides lower mean surge (30% lower than the other solvers) because of low wave drag and mean horizontal force. • Sway and yaw dynamics are not really aligned, and each solver provides a different result. The same behaviour is obtained on mean values, leading to a poor global agreement on these degrees of freedom. The dynamic in roll and yaw is stronger in DIEGO than in DLW and HAWC2.

• The forces at tower bottom present a good agreement between HAWC2 and DLW, but DIEGO produces higher Fx (~30% on the standard deviation) and overturning moment My (~20% on the standard deviation) than HAWC2 and DLW, which are well aligned. Considering the results observed in the "wave only" case, it is probable that aerodynamics could cause this discrepancy. where Fx: Tower bottom fore-aft force, My: Tower bottom overturning moment, FT1, FT2, and FT3: mooring #1, #2, and #3 tension force, respectively.

Conclusions

In this study, an extensive code-to-code comparison has been performed with three different numerical tools (DIEGO, DLW and HAWC2) with a modified version of IEA 15MW and UMaine floater to adapt to an offshore site in South Brittany (France). In total 10 test cases were performed among which 6 test cases were presented and discussed. From the loads and response comparisons, it is clearly seen that the results predicted by the three codes are in general good agreement despite some differences in specific degrees of freedom like sway and yaw. The extreme wind load case would require additional investigations. The resulting models are used in the global workflow of European project HIPERWIND, to reduce aerodynamic and hydrodynamic model uncertainties (WP3) and to provide reliable wind farm designs (WP4). More details can be found in [2].

Figure 1 :

 1 Figure 1: The surge motion during decay test 3.3. Wind step case A wind step simulation has been performed to validate controller behaviours. Figure 2 shows the time series of the wind speed. The initialization duration is marked with a grey rectangle that refers to the first 200 seconds of the simulation. Starting with a wind speed of 4 m/s and ending with a wind speed of 25 m/s. The steps are maintained during 100 s each time and the steps from one wind speed to another are done within 1s.

Figure 2 :

 2 Figure 2: Wind speed at hub height time series considered in the wind steps simulations

  ) and (b) show the PSD of the surge motion and the bending moment at tower bottom. It can be noted that the three codes are in very good agreement for this peak. The y-scale in the PSD plots is logarithmic. (a) PSD of the surge motion (b) PSD of the force at tower bottom Figure 4: The surge motion and tower bottom force during regular wave case (H=2 m and T=6 s)

Figure 5 :

 5 Figure 5: PSD of the wave elevation (Hs=13 m, Tp=16 s and ϒ=1)

Figure 7 :

 7 Figure 7: PSD of the fore aft bending moment at tower bottom (below rated turbulent wind load case)

  (a) Extract of the tower bottom bending moment (b) Extract of the tower bottom force Figure 8: Tower bottom bending moment and force comparison

Table 1 :

 1 List of test cases

	Test case #	Test case description
	1	Free decay test -No wind and wave, Apply and then release an initial displacement and rotation
		in Heave, Surge, Pitch and Yaw directions
	2	Pull out test -No wind and wave, Impose displacement on the floater in Surge direction
	3	Wind step -From 3 to 25 m/s with 1 m/s step at hub height, Wind shear (power law: α=0.2),
		no turbulence.

4 Regular wave test -No wind, Idling condition with 90° blade pitch, 3 different regular waves (H = 2 m and T = 6, 10, and 16 seconds). 5 Irregular wave test -No wind, Idling condition with 90° blade pitch, 2 different JONSWAP spectrum cases with Wheeler stretching model (Hs = 2 m, Tp = 7 s, =3 and Hs = 13 m, Tp = 16 s, =1). 6 Normal shutdown -No wave 7 Shutdown with extreme gust -No wave 8 Turbulent wind without wave -8 m/s and 15 m/s 9 Parked condition without yaw error -Rotor blocked with 90° blade pitch, wind speed at 50 m/s, JONSWAP spectrum with Wheeler stretching model (Hs = 13 m, Tp = 16 s,  = 1). 10 Parked condition with extreme yaw error (±30°) -Rotor blocked with 90° blade pitch, wind speed at 50m/s, JONSWAP spectrum with Wheeler stretching model (Hs = 13 m, Tp = 16 s,  = 1).

Table 3 :

 3 Center of gravity of the entire floating system (except mooring lines)

		X	Y	Z
	DLW	-0.32 m	0.00 m	-2.38 m
	DIEGO	-0.32 m	0.00 m	-2.27 m
	HAWC2	-0.33 m	0.00 m	-2.03 m

Modal analysis, free decay test and regular wave test results are presented. The first modes are compared. The modal analysis in the floating configuration allows comparing floater, tower, and blade modes. Table

Table 4 :

 4 First modes of the entire floating system

		DLW (Hz)	DIEGO (Hz)	HAWC2 (Hz)
	Surge	0.007	0.007	0.007
	Sway	0.007	0.007	0.007
	Heave	0.050	0.050	0.050
	Roll	0.036	0.036	0.036
	Pitch	0.036	0.036	0.036
	Yaw	0.009	0.009	0.009
	1 st tower	0.460	0.427	0.455
	2 nd tower	0.465	0.448	0.465
	Blade	0.524	0.535	0.521

Table 5 :

 5 Basic statistics of quantities of interest for irregular wave simulation (Hs=13 m, Tp=16 s and ϒ=1)

	surge [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	3.44	13.92	-4.25	2.38
	DIEGO	2.04	11.80	-6.36	2.56
	HAWC2	1.12	9.59	-6.07	2.48
	sway [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	-0.01	1.27	-1.66	0.45
	DIEGO	0.0003	0.06	-0.06	0.02
	HAWC2	-0.0007	0.02	-0.02	0.01
	heave [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	-0.02	6.48	-6.63	1.73
	DIEGO	-0.06	6.09	-6.90	1.87
	HAWC2	-0.01	4.50	-4.40	1.46
	roll [°]	Mean	Maximum	Minimum	Standard deviation
	DLW	0.0017	0.72	-0.75	0.24
	DIEGO	-0.0002	0.11	-0.11	0.03
	HAWC2	0.0001	0.01	-0.01	0.003
	pitch [°]	Mean	Maximum	Minimum	Standard deviation
	DLW	-1.49	1.92	-4.86	0.97
	DIEGO	-1.40	1.25	-4.68	0.88
	HAWC2	-1.42	0.41	-3.67	0.59

Table 6 :

 6 Basic statistics of quantities of interest during turbulent wind above rated load case

	surge [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	15.65	18.54	14.02	1.21
	DIEGO	14.91	18.77	10.00	2.10
	HAWC2	13.90	18.62	8.90	2.19
	sway [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	0.60	2.01	-1.16	0.72
	DIEGO	1.15	7.03	-3.65	3.11
	HAWC2	-0.13	5.50	-4.02	2.54
	heave [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	-0.10	-0.06	-0.17	0.02
	DIEGO	-0.08	0.00	-0.15	0.03
	HAWC2	-0.07	0.09	-0.22	0.08
	roll [°]	Mean	Maximum	Minimum	Standard deviation
	DLW	0.56	1.18	-0.27	0.32
	DIEGO	0.55	1.34	-0.30	0.29
	HAWC2	0.16	0.75	-0.65	0.25
	pitch [°]	Mean	Maximum	Minimum	Standard deviation
	DLW	2.69	5.01	1.21	0.76
	DIEGO	2.53	4.80	0.60	0.91
	HAWC2	2.43	4.30	1.14	0.62
	yaw [°]	Mean	Maximum	Minimum	Standard deviation
	DLW	2.08	6.44	-1.84	1.66
	DIEGO	0.79	5.32	-4.20	2.53
	HAWC2	4.10	8.21	-0.31	2.23
	Fx [MN]	Mean	Maximum	Minimum	Standard deviation
	DLW	1.40	2.24	0.82	0.24
	DIEGO	1.31	2.23	0.34	0.32
	HAWC2	1.22	1.93	0.37	0.22
	My [MN.m]	Mean	Maximum	Minimum	Standard deviation
	DLW	219.65	411.96	97.50	54.31
	DIEGO	215.68	387.94	46.40	66.57

Table 7 :

 7 Basic statistics of quantities of interest for the park condition

	surge [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	16.38	27.16	8.98	2.44
	DIEGO	15.65	24.27	8.10	2.64
	HAWC2	10.72	19.27	2.78	2.50
	sway [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	7.71	11.84	3.58	1.47
	DIEGO	-1.26	11.18	-17.15	6.70
	HAWC2	2.91	12.94	-5.90	3.90
	heave [m]	Mean	Maximum	Minimum	Standard deviation
	DLW	0.08	6.64	-6.33	1.71
	DIEGO	0.08	5.71	-5.88	1.66
	HAWC2	0.12	4.71	-4.24	1.43
	roll [°]	Mean	Maximum	Minimum	Standard deviation
	DLW	1.32	2.86	-0.09	0.47
	DIEGO	0.39	2.91	-1.81	0.82

Acknowledgements

This study was part of HIPERWIND project which has received funding from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No. 101006689. The authors are also grateful to NREL and University of Maine for providing the initial design of the model.


This thesis is financed by Agence Nationale de la Recheche (ANR) and is part of a project called "Mistrale" that aims to study alloys in magnesium-ion batteries.

I) Introduction and context

Basics of batteries

A battery is a system that reversibly converts chemical energy into electricity. A battery needs three main components to work: a positive electrode, a negative electrode and an electrolyte.

Additionally, an insulating separator between the two electrodes and current collectors are mandatory to ensure a proper ions and electrons circulation. The role of the electrolyte is to be an electron insulator and to conduct ions from one electrode to another. A high ionic conductivity (0.1 S/cm for aqueous electrolytes) as well as a good stability in potential (high electrochemical window) to avoid parasitic reaction are required. At each electrodes an electrochemical reaction between an oxidant and a reducer occurs:

Reduction:

𝑂 + + 𝑛𝑒 -→ 𝑅 Oxidation: 𝑅 → 𝑂 + + 𝑛𝑒 -
As we can see here, a reduction is a gain in electrons whereas an oxidation is a loss of electrons. Ions created at the anode (or the cathode depending if the battery is charging or discharging) are transported by diffusion/migration/convection through the electrolyte towards the cathode (and vice versa) while electrons are moving from one electrode to another via and external circuit. Primary batteries can only work once as charging is not possible whereas secondary batteries are rechargeable. The potential of an electrode comes from the Gibbs free enthalpy equation:

𝐸 = -𝛥𝐺

𝑛𝐹

Where n is the number of electrons exchanged and F the Faraday constant From here it is possible to deduce the Nernst equation:

𝐸 𝑒𝑙 = 𝐸 0 + 𝑅𝑇 𝑛𝐹 ln ∏ 𝑎 𝑖 𝑣 𝑖

𝑖

Where E 0 is the standard potential of the electrode, R the gas constant, T the absolute temperature, a i the activity of the i th species and ν the stoichiometric coefficient.

According to this definition, it is now possible to define the potential of the cell:

𝐸 = 𝐸 + -𝐸 -
The energy W (generally expressed in Wh/kg of Wh/L) of a battery is defined by:

𝑊 = 𝐸 * 𝐶

To maximize the energy stored in the battery (which is proportional to its potential) the potential of the positive electrode should be as high as possible and the potential of the negative electrode should be as low as possible.

The quantity of electricity stored inside the battery is called the capacity, C (in Ah) and can be calculated with the followed equation:

𝐶 = ∫ 𝐼(𝑡) ⅆ𝑡 𝑡 0
However, it is more convenient to calculate the capacity of a material by using the Faraday's law and to express it in mAh/g (or mAh/cm 3 ) to compare different battery materials:

𝐶 𝑚 = 𝑧𝐹 𝑀
Here, M molecular weight of active material, z the number of electrons exchanged and F the Faraday constant.

Lithium-metal and Lithium-ion batteries

Lithium is the element that has received the most attention due to its astonishing capacity (3861 mAh/g and 2060 mAh/cm 3 ), lowest standard potential for a metal (-3.04 V vs. SHE), and low molecular weight (6.941 g/mol). However, these attracting parameters require the use of lithium at its metal form which unfortunately has three main hurdles: -Lithium is very reactive so its safety in a commercial battery can be questioned.

-The formation of a Solid-Electrolyte Interphase (SEI) that will appear when lithium and the electrolyte are in contact and will lower the reactivity of the surface by making the diffusion of Li ions harder through it [START_REF] Peled | Review-SEI: Past, Present and Future[END_REF]. -The growth of lithium dendrites that will eventually connect electrically the two electrodes and short-circuit the battery, risking overheating and explosion [START_REF] Wood | Dendrites and Pits: Untangling the Complex Behavior of Lithium Metal Anodes through Operando Video Microscopy[END_REF].

Figure 1 -Dendrite growth on a lithium surface [START_REF] Wood | Dendrites and Pits: Untangling the Complex Behavior of Lithium Metal Anodes through Operando Video Microscopy[END_REF] The first material of interest for rechargeable batteries was TiS 2 and it was studied by Whittingham et al. in the 70's. They reported that Li could intercalate in this structure at 2.5V vs. Li + /Li [START_REF] Whittingham | Electrical Energy Storage and Intercalation Chemistry[END_REF].

In 1981, J.B. Goodenough and his co-workers showed that it was possible to reversibly extract and insert Lithium at 4 V vs. Li + /Li with LiCoO 2 [START_REF] Mizushima | LixCoO2 (0<x<-1): A new cathode material for batteries of high energy density[END_REF] The solution to get rid of dendrite formation is the use of graphite instead of lithium metal eand was found by Yazami and Touzain in 1983, thus considerably increase the safety of lithiumion batteries (LIBs) [START_REF] Yazami | A reversible graphite-lithium negative electrode for electrochemical generators[END_REF]. Goodenough, Whittingham and Yoshino (for his work on using carbonaceous materials and carrying safety tests of the first generation LIBs) were rewarded by the 2019 Nobel prize in chemistry for their discoveries.

The following scheme describes how a LIB is working:

Figure 2 -A scheme Li-ion battery [START_REF] Dunn | Electrical energy storage for the grid: A battery of choices[END_REF] The positive electrode here is LiCoO 2 and the intercalation reaction is the following:

𝐿𝑖𝐶𝑜𝑂 2 ↔ 𝑥𝐿𝑖 + + 𝑥𝑒 -+ 𝐿𝑖 1-𝑥 𝐶𝑜𝑂 2 𝑥 ≤ 0.5
The specific capacity of LiCoO 2 is ~140 mAh/g because only 50% of the lithium can be removed from the crystal lattice [START_REF] Laubach | Changes in the crystal and electronic structure of LiCoO2 and LiNiO2 upon Li intercalation and de-intercalation[END_REF].

The negative electrode is graphite, another layered compound that store Li + between its layers according to the reaction:

𝐶 6 + 𝐿𝑖 + + 𝑒 -𝐶 ↔ 𝐿𝑖𝐶 6
The specific capacity of graphite is 372 mAh/g.

The electrolyte used in commercialized LIBs is a lithium salt (typically LiPF 6 ) in a mixture of carbonated solvents (EC, DMC…) with specific additives. However, LIBs are suffering from different drawbacks:

-The high flammability of the solvent that can cause severe overheating and/or explosion if the battery is exposed to the air. Among the multivalent ions (Ca 2+ , Al 3+ ) Mg is a promising candidate to replace lithium. Its divalent nature allows high capacities (2205 mAh/g 3833 mAh/cm 3 ), as a reminder the one of the lithium is 2062 mAh/cm 3 which is almost 2 times less. Therefore, any application where volume is critical make Mg a choice of high interest. The advantages of Mg are not stopping there : it is the 7 th most abundant element on earth's crust which makes it inexpensive and its components are non-toxic, in fact magnesium is essential for life because it is involved in chlorophyll production in plants [START_REF] Niu | Alloy Anode Materials for Rechargeable Mg Ion Batteries[END_REF]. Moreover, the standard potential of Mg 2+ /Mg is -2.36 V vs. SHE which is only 0.68V higher than Li. This low potential is both an advantage and a disadvantage because on one hand it can allow Mg batteries to have a great energy density but on the other hand this it will reduce salt and solvent at its surface, forming passive films. Hence, one of the main hurdles in magnesium batteries remains the formation of a passive layer that will lower the reactivity of its surface by making the diffusion of Mg 2+ through it more difficult. Mg also suffers from a sluggish diffusion through most intercalation compounds thus no competitive positive electrode material (in terms of mAh/g) exists. Only few working positive materials can be found in the literature and the most promising ones are the Chevrel Phase Mo 6 S 8 [START_REF] Aurbach | Prototype systems for rechargeable magnesium batteries[END_REF], the vanadium oxides α-V 2 O 5 , and sulfur [START_REF] Johnson | The Quest for Functional Oxide Cathodes for[END_REF] [START_REF] Robba | Mechanistic Study of Magnesium-Sulfur Batteries[END_REF].

Interest of magnesium alloys

The most common reaction type used in commercial batteries is called intercalation. Indeed, there are a plethora of intercalation-type materials for LIBs that can reversibly let Li + go in and out of their crystal structure (LiFePO 4 , LiCoO 2 , LiMnO 2 , V 2 O 5 …). Despite the fact that these materials allowed the commercialization of LIBs they suffer from low capacity. Besides LiCoO 2 and its chemical derivatives, there are other types of insertion electrode material (spinel, polyanionic compound, etc.), but other materials also react electrochemically with Li + ions following a conversion reaction or an alloying process i.e. the crystallographic alloying structure is strongly modified during the reaction. Similarly, alloying type materials are also reported in magnesium-ion batteries: [START_REF] Murgia | p-block elements as negative electrode materials for Magnesium-ion batteries : electrochemical mechanism and perfomance[END_REF]).

Element

One has to keep in mind that an Mg alloy will have a lower specific capacity than a pure Mg negative electrode but this loss in capacity is compensated by the fact that Mg alloys show a good compatibility with conventional electrolytes (Mg salt + organic solvent) [START_REF] Niu | Alloy Anode Materials for Rechargeable Mg Ion Batteries[END_REF].

In 2000, Aurbach et al. were the first to make a Mg battery work with outstanding cyclability and capacity retention using a Mg organohaloaluminate salt, Mg(AlCl 3 R) 2 (where R is an alkyl group) dissolved in tetrahydrofuran (THF) [START_REF] Aurbach | Prototype systems for rechargeable magnesium batteries[END_REF]. However, these kind of electrolytes are very toxic and corrosive which make any industrial scale-up impossible (corrosion of the current collector [START_REF] Muldoon | Quest for nonaqueous multivalent secondary batteries: Magnesium and beyond[END_REF] and very exothermic reaction with the air). Organohaloaluminate-based electrolytes will be called "Grignard reagents" in this thesis. The use of a Mg alloy can allow the use of more "friendly" electrolytes, closer to what one can find in commercial batteries. In a battery, the alloy can directly become the negative electrode while the positive can be an intercalation material [START_REF] Niu | Alloy Anode Materials for Rechargeable Mg Ion Batteries[END_REF]. Nevertheless, there is still one main drawback when it comes to alloy and it is the fact that the crystal structure changes a lot during the charge/discharge process (~ 200% of volume expansion between Sn and Mg 2 Sn as an example). This can be seen right after the first cycle where about 60% of the capacity is lost, even though the theoretical capacity was reached in the beginning [START_REF] Singh | A high energy-density tin anode for rechargeable magnesium-ion batteries † ChemComm COMMUNICATION[END_REF].

Figure 6 -Specific capacity vs. cycle number of a full cell where one can observe the loss of capacity due to volume expansion after the first cycle [START_REF] Singh | A high energy-density tin anode for rechargeable magnesium-ion batteries † ChemComm COMMUNICATION[END_REF].

The galvanostatic curve using a Grignard reagent shows less polarization than with the conventional electrolyte which can be attributed by the formation of an ion-blocking SEI in the latter case. After the first charge/discharge, the capacity remains stable for 10 cycles just below 50 mAh/g. Mg alloys can offer good compatibility with "friendly" electrolytes but with poor cyclability whereas Grignard reagents combined with Mg metal are denser in energy but more toxic and corrosive.

1.5.Aims of the thesis

The alloy Mg 2 Sn will be studied in this report and here are the objectives set around its synthesis, characterization and electrochemical behavior have been set: -The phase diagram of Mg 2 Sn predicts one stable phase but a metastable phase was discovered by Suganuma et al. [START_REF] Suganuma | A Metastable Phase in Sn-Mg Alloy Film[END_REF]; the main goal will be to find a protocol to synthesize them separately and then explore their electrochemical behavior.

-Because of the lack of reliable reference electrode in Mg systems [START_REF] Tchitchekova | On the Reliability of Half-Cell Tests for Monovalent (Li + , Na + ) and Divalent (Mg 2+ , Ca 2+ ) Cation Based Batteries[END_REF] the property of Mg 2 Sn as a pseudo reference electrode will be investigated.

II) Mg 2 Sn polymorphs as negative electrode in Mg batteries

Magnesium-Tin alloy

This thesis will focus on Mg/Sn alloy because it seems the most promising element among all the others. Despite the fact that Sn has a lower specific capacity than Si and Ge (see Table 1) the diffusion of Mg 2+ in Sn is easier than Si and Ge (10 -13 cm²/s for Sn, 10 -14 cm²/s for Ge and 10 -17 cm²/s Si). Moreover Si and Ge have a higher overpotential to form the alloy than Sn [START_REF] Li | A review on current anode materials for rechargeable Mg batteries[END_REF].

Hence, Sn has received a lot of attention in the literature [START_REF] Nguyen | Magnesium stannide as a high-capacity anode for magnesium-ion batteries[END_REF]- [START_REF] Yaghoobnejad Asl | In Situ Dealloying of Bulk Mg2Sn in Mg-Ion Half Cell as an Effective Route to Nanostructured Sn for High Performance Mg-Ion Battery Anodes[END_REF]. Tin has two main allotropes: α-tin called "grey tin" which has a cubic face-centered diamond crystal structure and β-tin called "white tin" which has a tetragonal body-centered structure. βtin is the stable phase at room temperature (up to 163°C) and α-tin is only stable below 13.2°C.

When it comes to magnesium, tin can alloy with it and form an intermetallic Mg 2 Sn phase with a 33% -66% at. Mg/Sn ratio: The cubic phase is the stable one but as said above, a metastable one exists [START_REF] Suganuma | A Metastable Phase in Sn-Mg Alloy Film[END_REF]. The author of this paper stated that this phase is orthorhombic (space group Pbnn) however no further investigation on the structure could be found in the literature. It will be called here after the "non-cubic" phase. To synthesize 1g of Mg 2 Sn, 334.1 mg of Mg powder and 709.4 mg of Sn powder were weighted. An excess of 15 wt.% of Mg is added because some of the powder will stick to the SS jar, hence will not react with Sn to form the alloy. Two parameters will be modified in order to obtain one phase or the other: the grain size of the Mg powder and the milling time. The first grain size is micrometric (~ 150 µm) and the second one is nanometric (20-30 nm). The tin grain size is always the same, also ~150 µm.

XRD characterization

X-Ray Diffraction (XRD) will be carried out in this thesis to determine the bulk structure of a crystalline compound. Atoms in a crystal structure can diffract rays because the interatomic distance is the same order of magnitude as their wavelength (between 0.1 and 100 Å).

In 1913, Sir William Bragg found a relation between the wavelength, the interatomic distance and the angle of the incident x-ray and it is illustrated in the following scheme: This law specifies that in order for a wave to be reflected constructively by the crystal lattice it has to have a specific incoming angle which is given by Bragg's law.

𝑛𝜆 = 2ⅆ 𝑠𝑖𝑛𝜃
Every plane separated with a distance d will have a different 𝜃 reflection direction. A diffractometer will measure the signal intensity for every 𝜃 or 2𝜃 and will display a diffraction pattern composed of peaks that represent a specific plane in the crystal lattice. X-rays in a diffractometer are produced in an X-ray tube where a strong potential is applied (around 45 kV in our lab) between two electrodes creating a flux of electrons from the cathode towards the anode. When electrons are crashing into the anode, they will excite its atoms and they will emit X-rays. The most used metal as an anode in this thesis is copper (Kα = 1.5406 Å) but a cobalt (Kα = 1.78901 Å) anode will also be used for operando analysis. The milling parameters were already optimized by F. Murgia [START_REF] Murgia | p-block elements as negative electrode materials for Magnesium-ion batteries : electrochemical mechanism and perfomance[END_REF] to obtain the stable cubic phase but not for the metastable one. The following figure summarizes the results for different parameters tested: It is interesting to observe that the non-cubic phase appears with lower milling time with a nanometric Mg powder than with a micrometric powder. It can be explained by the fact that smaller grain size allows more surface for the powder to react, thus making the metastable phase easier to form. The milling time is proportional to the energy given to the system so it seems that the non-cubic phase is forming at high energy whereas the stable cubic phase needs less energy.

Figure 13 shows the profile matching refinement performed the XRD pattern obtained after 5h milling and a µ-sized Mg powder: This refinement was done according to the orthorhombic space group given by Suganuma [START_REF] Suganuma | A Metastable Phase in Sn-Mg Alloy Film[END_REF] but one has to keep in mind that no further investigation on this metastable phase has been done in the literature (to the best of our knowledge). Therefore, the non-cubic phase might not be orthorhombic and the fact that the fit is somehow correct is because there is a large number of peaks in the pattern thus giving a lot of solutions to the refinement software (see figure 14). The first objective to synthesize both phases separately is done, now their electrochemical performance will be investigated.

Electrode formulation

Self-supported electrodes were prepared from both phase with the following formulation: The different powder materials were mixed in a mortar to obtain a dough, then electrodes were punched into disk of ~8 mm of diameter in an Ar-filled glove-box. The use of different types of carbon (C65 and carbon fiber) is to ensure a good electronic conductivity because Mg 2 Sn is a poor electron conductor (its forbidden energy gap is 0.33 eV at 0 K [START_REF] Lichter | Electrical Properties of Mg[sub 2]Sn Crystals Grown from Nonstoichiometric Melts[END_REF]).

Active material

Electrochemical behavior in half cell

Then, half-cells were made in coin-cell (2032, 316L stainless steel):

Mg 2 Sn || EtMgCl-Et 2 AlCl / THF || Mg
Here the electrolyte is a Grignard-based solution obtained by mixing ethylmagnesium chloride (EtMgCl) and diethylaluminium chloride (Et 2 AlCl) in THF; the final concentration is around 0.35M. EtMgCl and Et 2 AlCl are a a Lewis base and a Lewis acid (respectively) that react together to form a complex that will dissolve the passivation layer on the Mg surface disk, so this electrolyte is specially designed to work with Mg-metal systems. Two Whatman GF/A borosilicate glass fibers were used as separators and wetted with ~100 µL of electrolyte. This configuration needed the use of pure Mg so a Mg foil was scraped with a scalpel in order to remove the passive layer and impurities at its surface. Then disks were punched out of it to make electrodes (~7 mm of diameter). The electrochemical reaction that occurs during the charge/discharge process is:

𝑀𝑔 2 𝑆𝑛 ↔ 𝑆𝑛 + 2 𝑀𝑔 2+ + 4 𝑒 -
The cycling starts in both cases with an activation phenomenon which is represented by a surge in potential at x=2. Then, the de-alloying process occurs at a plateau from 0.25V to 0.3V vs. Mg 2+ /Mg before reaching the cut-off voltage of 0.7V, these values are in agreement with the literature [START_REF] Nguyen | Magnesium stannide as a high-capacity anode for magnesium-ion batteries[END_REF]. It is interesting to see here that it is possible to de-alloy more Mg from the cubic phase than from the non-cubic phase. Actually, almost all of the Mg is removed from cubic-Mg 2 Sn at the end of the first charge. The decrease of polarization afterward may be caused by a phenomenon called electrochemical grinding which is a reduction of the grain size due to a full dealloying/alloying cycle of the materials.

As for the discharge, the alloying process occurs below 0.2V in both polymorphs and it is not possible to recover all the magnesium during this sequence. This will be translated by a capacity fade right after the second cycle in the same way as [START_REF] Singh | A high energy-density tin anode for rechargeable magnesium-ion batteries † ChemComm COMMUNICATION[END_REF] which is well illustrated in the next plot : The theoretical capacity of Mg 2 Sn is almost reached at the first charge and then drops by 2/3 in the next cycle and may be due to the huge volume change between Mg 2 Sn and Sn (the cell volume is going from 309.2(6) Å 3 with Mg 2 Sn to ~100 Å 3 for β-Sn). However, in the work or Nguyen et al. on Mg 2 Sn, one can find another behavior in cycling [22][24]. They obtain for their half cells an increasing specific capacity for the first 10-15 cycles then a decrease to 200/250 mAh/g after 50 cycles. These differences can be explained by different factors:

-The electrode formulation may be more optimized than ours. Also, the binder is different (they used PVdF and we used PTFE). -They made Mg 2 Sn electrode by casting a slurry composed of active material/carbon/binder onto a current collector foil (copper or aluminum) which is a different technique from the self-supported electrode. -They used a different electrolyte: 0.5M PhMgCl in THF. All these parameters combined may affect the cyclability of Mg 2 Sn and one has to keep in that the goal of this thesis is first to compare the two polymorphs not to seek for cell performance. The electrochemical behavior after further cycling is roughly the same for the two polymorphs.

In Situ analysis

Operando measurement was done in a special stainless-steel cell. The two electrodes (Mg 2 Sn vs. Mg) are pressed against each other by a plunger and a beryllium window ensures that the cell is insulated from the air without too much loss in signal intensity. Two different reactions occur at the charge and the discharge: Charge:

𝑀𝑔 2 𝑆𝑛 → 2𝑀𝑔 2+ + 4𝑒 -+ 𝑆𝑛 Discharge:

2𝑀𝑔 2+ + 4𝑒 -+ 𝑆𝑛 → 𝑀𝑔 2 𝑆𝑛
According to the above equations, during the charge, the Mg 2 Sn phase is disappearing while tin is appearing. Indeed, on the operando waterfall graphs (figure 19 a. and c.), one can see the apparition on the two main peaks of β-tin, crystallized in its tetragonal lattice (confirmed by refinement in Figure 19b.) and the fading in intensity of the main peaks of Mg 2 Sn (cubic and non-cubic).

In the following discharge, the cubic phase (figure 19 a. and b.) is appearing again and is still crystalline. However, it is interesting to notice that tin is not disappearing completely thus an electrochemically inactive mass of tin is staying in the system (this phenomenon is observed for both phases). This quantity of tin does not participate anymore in the electrochemical reaction and can explain the loss in capacity after the first cycle (figure 17) in addition with the volume change.

The most surprising point during the discharge in figure 19c. and d. is the apparition of the cubic polymorph. This phase was not present initially and was created only by the electrochemistry. It appears that this phase is favored both electrochemically and by mechanical synthesis because already in ball-milling it needed less energy compared to the non-cubic polymorph to be synthesized.

To conclude this part, Mg 2 Sn is an interesting compound as a negative electrode in Mg batteries for its high capacity (641 mAh/g) but suffer from a poor cyclability as seen in a galvanostatic cycling. Operando analysis helpt understanding the mechanisms that occur during the charge/discharge process of a half-cell and unveiled that a fraction of Sn produced at the charge is not alloyed back during the discharge.

III) Mg 2 Sn/Sn as a pseudo reference electrode

Context

An electrochemical measurement set up is generally composed of three electrodes: the working electrode (WE), the counter electrode (CE) and the reference electrode (RE). The role of the RE is crucial because the potential of the WE is measured compared to it so if the reference potential is subject to variation because of parasitic reaction or instabilities, misinterpretation may be done while analyzing data.

In order to have reliable measure a RE should have the following requirements:

-Non-polarizable (the potential does not change with current input <50pA) -Stable potential over time -Lowest impedance possible Often in battery chemistry, the metal CE is also the RE and this configuration is useful because it allows the use of standardized coin cell. However, if a reaction is happening at the reference electrode (passivation, dissolution ...) the above criteria are not fulfilled anymore and the measure may be incorrect. In fact, they are not strictly achieved and for this reason, the RE is called a pseudo-reference electrode (pseudo RE) or sometimes. While it is not that much of an issue in lithium chemistry, Ponrouch et al. [20][31] showed that Mg electrodes are far from being a reliable pseudo RE and can even lead to incorrect interpretations. In carbonated solvent like EC, PC, he and his co-workers highlighted the high instability and polarization of Mg as a pseudo RE: In figure 20 a., Mg cell shows significant oscillations around OCV (~ 40mV) whereas lithium cell is way more stable over time, hence the reliability of Mg as a pseudo RE is being questioned.

Regarding the impedance on figure 20 b., Mg cell is a very resistive system and the values of resistance are around 10 6 Ohm whereas with lithium, the resistance is only a few hundred [START_REF] Tchitchekova | On the Reliability of Half-Cell Tests for Monovalent (Li + , Na + ) and Divalent (Mg 2+ , Ca 2+ ) Cation Based Batteries[END_REF].

To the best of our knowledge, the only attempt of pseudo-RE with divalent cations is the use of Ag/Ag 2 S wire in Ca batteries and Mg/S batteries [31][32]. The purpose of this part is to investigate the use of Mg 2 Sn as a pseudo RE because Mg alloys show great potential stability in most electrolytes [START_REF] Niu | Alloy Anode Materials for Rechargeable Mg Ion Batteries[END_REF].

Methodology of the study

First, a polarization test in symmetrical cell has been done. It is a routine experiment in battery science to have information on cyclability, polarization and stability of a compound. Here, the purpose of this technique is to compare Mg 2 Sn versus Mg-metal in EtMgCl-Et 2 AlCl dissolved in THF and in a more conventional and friendly-to-use Mg salt magnesium bis(trifluoromethanesulfonyl)imide salt (Mg(TFSI) 2 ) dissolved in DME. For the preparation of this electrolyte the salt was dried at 250°C in a vacuum flask, while DME was dried by a first argon bubbling, then in a 4 Å molecular sieves for 3 days. Polarization test is done in symmetrical cells (the same electrode at the cathode and the anode) encapsulated in coin cells and tested by galvanostatic cycling with potential limitation (GCPL). A constant current of 0.1 mA/cm² was applied for 30 min then the opposite current for 30 min. These two sequences are repeated over the course of 150h. Then, the same electrolyte than [START_REF] Tchitchekova | On the Reliability of Half-Cell Tests for Monovalent (Li + , Na + ) and Divalent (Mg 2+ , Ca 2+ ) Cation Based Batteries[END_REF] was made for further testing, a 0.1M Mg(TFSI) 2 in EC:PC. The authors used a 50:50 wt.% ratio for the solvent so 2.37mL of PC (which is a liquid) are taken and 3.3g of EC (which is a solid) are weighted. The solution was stirred for 48h and then dried for another 48h in 4Å molecular sieves. Symmetrical cells with Mg and Mg 2 Sn were assembled to measure the OCV for 50h in the two above electrolytes. This simple test allows to see potential variation with time without any current input. Electrochemical Impedance spectroscopy (EIS) was carried out to measure the resistivity of every system. It is a powerful tool to characterize electrode/electrolyte interfaces and understand chemical processes. Finally, to investigate Mg 2 Sn as a pseudo RE in real Mg-ion batteries, full cells were assembled in 3-electodes Swagelok type cells (all cells configuration are in figure 21). The 3 electrodes configuration separates the contribution of the counter electrode from the reference. Mo 6 S 8 is one of the few functional positive electrode material and is a reference material for full cell testing [START_REF] Aurbach | Prototype systems for rechargeable magnesium batteries[END_REF], hence it will be the working electrode for all cell configuration. The selfsupported electrode formulation is: 3.3. Results

Polarization test in symmetrical cell

The following figure demonstrates the efficiency of the Grignard reagent on a bare Mg disk in the polarization test. In addition, the behavior of Mg 2 Sn in Mg(TFSI) 2 / DME was tested with composite self-supported electrodes of Sn/Mg 2 Sn which were prepared by ball-milling. A 1:1 molar ratio between Mg and Sn powder was used (15% of Mg excess) with 5 h of milling time.

The purpose of this composite material is to contain Sn at both electrodes of the cell. This way, the alloying reaction between Mg and Sn can occurs normally. Moreover, being on a biphasic alloying plateau (see figure 16) means that a small change in the composition of the alloy may not change its potential too much. This way, only the plating and stripping phenomenon is observed in the following curves. The polarization keeps increasing slowly and eventually reaches 0.2V after 350h of cycling but stays stable during this time.

Open Circuit Voltage

Figure 24 summarizes the results of symmetric cells left at OCV for 50h: The behavior of Mg in Mg(TFSI) 2 /EC:PC is similar to the results of Tchitchekova et al. [START_REF] Tchitchekova | On the Reliability of Half-Cell Tests for Monovalent (Li + , Na + ) and Divalent (Mg 2+ , Ca 2+ ) Cation Based Batteries[END_REF] and highlights the poor compatibility of Mg in carbonated solvent. The authors used a mixture of EC and PC because they wanted to have an electrolyte close to what can be found in commercial LIBs. In figure 24, Mg seems to be working fine in Mg(TFSI) 2 /DME systems with a stable potential that stays under 10mV and surprisingly, Mg 2 Sn in Mg(TFSI) 2 /DME shows a really stable and low potential compared to the others configuration (the potential shift doesn't exceed 0.2mV during 50h). The potential of Mg 2 Sn in Mg(TFSI) 2 /EC:PC stabilize over time and eventually reaches 0V after 50h.

Electrochemical Impedance Spectroscopy

The next figure summarizes the EIS results obtained with different cell configuration and electrolytes: On all systems, "t0" takes in account the 10 minutes time between the addition of the electrolyte and the start of the measure. Figure 25 b. shows a similar behavior than [START_REF] Tchitchekova | On the Reliability of Half-Cell Tests for Monovalent (Li + , Na + ) and Divalent (Mg 2+ , Ca 2+ ) Cation Based Batteries[END_REF] and is in agreement with the OCV test: Mg in carbonated solvent is a highly resistive system (the order of magnitude of resistance is 10 6 Ω and much higher than other systems). As expected, Mg in Mg(TFSI) 2 /DME (figure 25d.) is less resistive than Mg(TFSI) 2 /EC:PC but it is interesting to notice that the impedance increases with time. It might be related to the ionic diffusion through the SEI that is forming between the electrolyte and the metal and becoming thicker with time.

The behavior of Mg 2 Sn is similar than Mg in the two solvent: resistance values are higher in Mg(TFSI) 2 /EC:PC than Mg(TFSI) 2 /DME but the order of magnitude of the latter is way less: a few thousands of Ohms. Here, it is possible to observer more phenomenon: the inset in figure 25c. displays a semi-circle in the middle frequencies which is characteristic of charge transfer at the electrode/electrolyte interface. At lower frequencies, the behavior of Mg 2 Sn in Mg(TFSI) 2 /EC:PC stays the same with time and the impedance does not increase with time and act as a pure blocking capacitance. It is possible to see two phenomena in figure 27a.: the ionic transfer represented by the tiny half-circle and the limited diffusion (zoom in figure 26). The shape of the spectra at low frequencies seems to be a quarter of Lemniscate and can be interpreted by the diffusion of Mg 2+ ions in the finite thickness of a forming SEI. The fact that the impedance of this spectra increases strongly reinforces this hypothesis. Figure 27 a. is the standard Mg prototype with Mg at the RE, the potential of the CE stays close to zero and the polarization (i.e. the difference of potential between the charge and the discharge around 1V at equilibrium) is really low. However, with the same cell configuration but using the 0.5M Mg(TFSI) 2 in DME (figure 27 b.), one can see a totally different behavior. Here the CE-RE curve is not centered around zero even though it is the same RE and CE material. This potential difference between the charge curve and the discharge curve of ~0.6V can be attributed to the formation of a passive layer that is forming at the Mg CE in contact with the electrolyte. This polarization is reported on the black curve so by differentiating the contribution of the CE and the WE with a RE in a 3 electrodes cell, it is possible to conclude that the poor behavior of this system is due to the incompatibility between Mg and ether-based electrolytes. Figure 27c. CE-RE curve shows a small offset of 0.2V which is the phase potential between Mg and Mg 2 Sn. This curve stays stable both at the charge and the discharge its polarization seems a bit lower that in figure 27a. Besides this feature, the cycling remains the same as figure 27a., Sn/Mg 2 Sn as a RE in a full cell with AEC electrolyte works well. Finally, no improvement is seen by using the composite material in a DME-based electrolyte. One can notice that the discharge capacity is higher in figure 27d. than figure 27b. but cannot be explained by the change of reference electrode, it is rather due to the fact a lot of parameters are changing between experiment like the homogeneity of the electrode, the storage temperature of the materials, the sealing of the battery may not be perfect every time and the pressure (exercised manually) between the electrodes may change from one experiment to another. To conclude this part, this preliminary work seems to show that the composite material Sn/Mg 2 Sn could suit as a pseudo-RE. In ether-based solvent its impedance sufficient (a few kΩ), has a stable potential over time and a low polarization (way lower than bare Mg). Further investigations could be done like a polarization test coupled with EIS to see the behavior in cycling of the different materials in carbonate solvents. Moreover, to better understand the electrode/electrolyte interface, in situ IR spectroscopy coupled with EIS can be done.

Conclusion

In this thesis, the alloy Mg 2 Sn has been studied as an anode and pseudo reference electrode. Its synthesis was done by mechanical ball milling and two polymorphs can be obtained by slightly changing some synthesis parameters. Their electrochemical behavior was determined by assembling coin cells and while there are little differences between the two phases in cycling, more magnesium can be extracted from the cubic polymorph during the first charge. A rapid fade of specific capacity was observed and may be explained by the volume change between Mg 2 Sn and Sn.

Operando XRD has been carried out to have a better look on phase change during cycling and two remarkable results could be seen. First, a portion of Sn formed during the charge is not alloyed back at the discharge and can explain (in addition with volume change) the poor cyclability. Second, even by starting with the non-cubic phase it is the cubic Mg 2 Sn that is forming during the alloying process (discharge). This study is included in a broader investigation on Mg alloy-based electrode and will be submitted for publication. The main issue in magnesium battery chemistry is the creation of an ion-blocking passivation layer at the surface of magnesium in contact with most electrolytes. Evidence of this phenomenon were shown by polarization test where a large potential(around 4V) was needed to plate and strip Mg in conventional electrolyte. Doing the same test with Mg 2 Sn demonstrated the good compatibility of the alloy versus Mg(TFSI) 2 in DME. Mg 2 Sn may not be a suitable negative electrode in magnesium batteries but its stability in conventional electrolytes could make it a reference electrode (RE). Indeed, there is a lack of a reliable reference electrode in Mg systems and this alloy could fulfill the requirement of a RE (or pseudo RE). Different experiments were carried out to determine its potential stability, polarization and behavior in a real electrochemical setup with three electrodes. An OCV test showed little potential variations of the material and EIS reinforces the idea that Mg 2 Sn works well in ether solvents (like DME) but displays high resistance values in carbonated ones (EC, PC …). Finally, the full cell testing allowed to separate the contribution of the working electrode (a self-supported electrode of Mo 6 S 8 ) from the counter electrode (a Mg disk) and confirmed that Sn/Mg 2 Sn can be used as a reference under real conditions. A second article is also in preparation with these primary data. All in all, the different objectives of this thesis were achieved but the story of Mg batteries is not stopping here as several paths can be explored in this domain of battery science. Coating a bare Mg disk could be a solution to get rid of the passive layer. Indeed, most element form the block p can deposit on its surface either by soaking the disk into a solution or by dropping the solution directly on the disk. Metals with a low fusion point (Mercury, Gallium or eutectic mixture) can also be an interesting way the protect the Mg. The idea of forming a protective layer can be also done by adding additives in the electrolyte to form an artificial SEI, thus allowing a fast ion transfer at the interface.

Diagramme de Gantt :

1. Optimisation de la synthèse des polymorphes de Mg2Sn

2.

3.

4.

5.

6.

7.

8.

  @grenoble-inp.fr III ) Mg 2 Sn/Sn as a pseudo reference electrode 3.1. Context......................................................................................................................................24 3.2. Methodology of the study..........................................................................................................25 3.3. Results 3.3.1. Polarization test in symmetrical cell......................................................27 3.3.2. Open Circuit Potential...........................................................................28 3.3.3. Electrochemical Impedance Spectroscopy............................................29 3.3.4. 3-electrodes full cells.............................................................................31 Conclusion...........................................................................................................................33 References......................................................................................................................

Figure 3 -

 3 Figure 3 -A LIB pierced by a nail (screenshot from [8])

Figure 4 -

 4 Figure 4 -Comparison between lithium and divalent cations (adapted from [11])

Figure 5 -

 5 Figure 5 -A schematic representation of the different reaction mechanisms observed in electrode materials for lithium batteries. Black circles: voids in the crystal structure, blue circles: metal, yellow circles: lithium. [16]

Figure 7 -Figure 8 -

 78 Figure 7 -Phase diagram of Mg/Sn[START_REF] Mostafa | Essential Magnesium Alloys Binary Phase Diagrams and Their Thermochemical Data 12 PUBLICATIONS 24 CITATIONS SEE PROFILE Essential Magnesium Alloys Binary Phase Diagrams and Their Thermochemical Data[END_REF]

2. 2 .

 2 Figure 9 -The ball-milling device and the SS jar that has been used for the synthesis

Figure 10 -

 10 Figure 10 -Bragg's law illustrated by a scheme[START_REF] Ramachandran | Handbook of Analytical Techniques in Concrete Science and Technology[END_REF]

Figure 11 -

 11 Figure 11 -XRD sample holder, polymer film in yellow

Figure 12 -

 12 Figure 12 -diffractograms obtained with different parameters

Figure 13 -Figure 14 -

 1314 Figure 13 -Refined diffraction pattern of cubic Mg 2 Sn

Figure 15 -

 15 Figure 15 -Left: Schematic representation of a coin cell[START_REF] Talaie | Methods and Protocols for Electrochemical Energy Storage Materials Research[END_REF] Right: A Mg foil with a scraped part in its top left corner

Figure 16 -

 16 Figure 16 -Galvanostatic first two cycles of Mg 2 Sn vs. Mg at C/30 with EtMgCl-Et 2 AlCl / THF 0.35M electrolyte: a) cubic b) non-cubic

Figure 17 -

 17 Figure 17 -Capacity fade (charge) of 30 cycles, Mg 2 Sn vs. Mg at C/30 with 0.35M EtMgCl-Et 2 AlCl / THF

Figure 18 Figure 19 -

 1819 Figure 18 -An In Situ cell

Figure 20 -

 20 Figure 20 -a) OCV of Li, Na, Ca and Mg symmetric cells, b) Impedance spectroscopy measurement in two-electrode configuration. In both graphs, the electrolyte for Mg cells was a 0.1M Mg(TFSI) 2 in EC:PC (50:50 wt.%), the electrolyte for element A is 0.1M A(TFSI) n in EC:PC (n=1 for Li, Na and n=2 for Mg, Ca) [20]

3 -Figure 21 -

 321 Figure 21 -Summary of the different Swagelok-type cell configuration used. "AEC" stands for All-Ethyl-Complex electrolyte and is the 0.35M EtMgCl-Et 2 AlCl in THF.

Figure 22 -

 22 Figure 22 -Polarization test of, Left: a bare Mg disk versus different electrolytes: Blue: EtMgCl-Et 2 AlCl in THF at 0.35M, Red: 0.5M Mg(TFSI) 2 in DME Right: Mg 2 Sn in 0.5M Mg(TFSI) 2 / DME

Figure 23 -

 23 Figure 23 -Polarization test of a symmetrical cell of Sn/Mg 2 Sn in 0.5M Mg(TFSI) 2 in DME with the shape of the cycles on the right

Figure 24 -

 24 Figure 24 -Open circuit voltage of symmetric cells, comparison between Mg and Mg 2 Sn in two electrolytes

Figure 25 -

 25 Figure 25 -EIS at room temperature of symmetric cells under OCV at different times. a) Mg 2 Sn in 0.5M Mg(TFSI) 2 / DME b) Mg in 0.1M Mg(TFSI) 2 / EC:PC c) Mg 2 Sn in 0.1M Mg(TFSI) 2 / EC:PC, inset : zoom on high frequencies d) Mg in 0.5M Mg(TFSI) 2 / DMEThe frequency range is 20 kHz -10mHz with a 10mV amplitude signal.

Figure 26 -

 26 Figure 26 -EIS at t0 of a Mg 2 Sn symmetric cell in a 0.5M Mg(TFSI) 2 in DME electrolyte.

Figure 27 -

 27 Figure 27 -First galvanostatic charge/discharge of Mo 6 S 8 working electrode in different electrolyte and reference electrode.

  The Institute Charles Gerhardt Montpellier (ICGM), Institute for Molecular Chemistry and Material Sciences, is a Joint Research Unit (UMR 5253) created in January 2007 and supported by the Centre National de la Recherche Scientifique (CNRS), Université de Montpellier (UM) and Ecole Nationale Supérieure de Chimie de Montpellier (ENSCM).The ICGM is a multidisciplinary laboratory working in the fields of Energy, Environment and Health. Organized in three scientific departments, it represents 240 permanent staff and over 200 non-permanent staff (including doctoral students, post-doctoral students, and visiting/guest researchers). (https://www.icgm.fr/en/accueil/presentation-en) I am part of a team lead by Laure Monconduit and Lorenzo Stievano that is working both on next-generation battery technology like Potassium batteries, Magnesium batteries or Calcium batteries and also improving Lithium technology with recycling or different treatment procedures.

	Glossary Institut Charles Gerhardt de Montpellier (ICGM)
	XRD: X-Ray Diffraction
	GCPL: Galvanostatic Cycling with Potential Limitation
	DME: 1,2-Dimethoxyethane, Diglyme C 4 H 10 O 2
	THF: Tetrahydrofuran C 4 H 8 O
	EC: Ethylene Carbonate C 3 H 4 O 3
	PC: Propylene Carbonate C 4 H 6 O 3
	DMC: Dimethyl Carbonate C 3 H 3 O 3
	Mg (TFSI) 2 : Magnesium Bis(trifluoromethanesulfonic)imide, Mg[N(SO 2 CF 3 ) 2 ] 2
	LIB: Lithium-Ion Battery
	PTFE: Polytetrafluoroethylene (C 2 F 4 ) n
	SHE: Standard Hydrogen Electrode
	SEI: Solid Electrolyte Interphase
	VGCF: Vapor Grown Carbon Fibers
	OCV: Open Circuit Voltage
	EIS: Electrochemical Impedance Spectroscopy
	RE: Reference Electrode
	CE: Counter Electrode
	WE: Working Electrode

.....

34

Table 1 -

 1

		Theoretical Specific	Alloy	Magnesiation
		Capacity (mAh/g)		voltage (V)
	Si	3817	Mg 2 Si	0.151 (theor.)
	Ge	1476	Mg 2 Ge	0.241 (theor.)
	Sn	903	Mg 2 Sn	0.15
	Sb	660	Mg 3 Sb 2	0.32
	Pb	518	Mg 2 Pb	0.11
	In	467	MgIn	0.06
	Bi	382	Mg 3 Bi 2	0.25

Different characteristics of p-block elements in Mg-ion batteries (reproduced from

Table 2 -

 2 Electrode formulation

		Carbon	Binder
	70 wt%	10 wt% C65	10 % PTFE
	(Mg 2 Sn)	+ 10 wt% VGCF

  Figure27shows the results of the different full cell configuration. The theoretical capacity of Mo 6 S 8 is 128 mAh/g and a charge / discharge capacity of around 120/110 mAh/g was achieved at the first cycle. Like said before, Mo 6 S 8 is one of the few positive electrode materials in which Mg 2+ ions can intercalate with good kinetics so it has a good cyclability and capacity retention. It is possible to observe 2 plateaus at the charge and they are characteristic of the different sites where Mg 2+ ions intercalate. Indeed, there are 2 occupation sites for Mg between the channels of Mo 6 S 8 cubes[START_REF] Aurbach | Prototype systems for rechargeable magnesium batteries[END_REF] .

	3.3.4.	3-electrode full cells

  2. Caractérisations électrochimiques de Mg2Sn 3. DRX "operando" 4. Préparation et caractérisation des électrodes revêtus par trempe 5. Caractérisation des électrodes revêtus par pulvérisation cathodique 6. Mg2Sn en tant que "pseudo-référence" 7. Rédaction du rapport 8. Rédaction d'un article sur Mg2Sn en pseudo-référence

	M1	M2	M3	M4	M5	M6
	1.

Abstract

Energy storage is one of the major challenges of our century because it would promote technologies for a sustainable development (electric vehicles, renewable energies…). Lithiumion batteries are well established in our life but are still limited by their price, theoretical capacity and the available quantity of some resources for their fabrication. Magnesium-based rechargeable batteries are an interesting alternative to lithium because of their high volumetric capacity and their low price due to the natural abundance of magnesium. However, this technology is strongly limited by the formation of a blocking passive layer to Mg 2+ in contact with conventional electrolytes. The purpose of this internship is to study the alloy Mg 2 Sn in order to use it in Mg-ion batteries and see if it can mitigate this passivation issue. To do so, its behavior in half cell configuration was investigated and operando XRD was done to better understand phase change in cycling. Furthermore, polarization test coupled with electrochemical impedance spectroscopy was carried out to test if Mg 2 Sn could be a reference electrode in Mg systems. Then, the alloy was used in a three-electrode full cell assembly to observe its electrochemical behavior.

Résumé

Le stockage de l'énergie est un des défis majeurs de notre époque car il permettrait l'essor de technologies aidant à un développement durable de l'humanité (véhicules électriques, énergies renouvelables…). Les batteries Li-ions assurent ce rôle mais sont aujourd'hui limitées par leur prix, capacité théoriques et la rareté de certaines ressources nécessaires à leur fabrication. Les accumulateurs à base de magnésium sont une alternative intéressante au lithium de par leur capacité volumique élevée et leur prix très bas grâce à l'abondance naturelle du magnésium. Cependant, cette technologie est fortement limitée par la formation d'une couche passive imperméable aux ions Mg 2+ à la surface du magnésium au contact d'électrolytes conventionnels. Le but de ce stage est d'étudier l'alliage de magnésium et d'étain Mg 2 Sn dans le but de l'intégrer dans les batteries Mg-ion et espérer combattre le problème de passivation. Pour ce faire, son comportement en demi-pile a été étudié et de la DRX operando a été réalisée afin de mieux comprendre les changements de phase en cyclage. De plus, des tests de polarisation couplés à de la spectroscopie d'impédance électrochimique ont été réalisés pour étudier Mg 2 Sn en tant qu'électrode de référence. Enfin, l'alliage a été utilisé en pile complète pour observer son comportement électrochimique.


Omar Sakka
email: omar.sakka@insa-lyon.fr

Valérie Botta-Genoulaz

A model of Factors Influencing the Supply Chain Performance

Keywords: supply chain, performance, practices, collaboration, information exchange

Improvement of industrial performance such as cost, lead-time, adaptability, variety and traceability is the major finality of companies. Thus, they need to collaborate and to strengthen their coordination mechanisms. Information exchange, supply chain practices and inter-organizational collaboration becomes then strategic issues: what is the nature of the information that can be shared with customers and suppliers? Which impact on the performance of a company is expectable? What is about the performance of the whole supply chain? It is essential for a company to identify the information whose exchange contributes to its performance, to control its information flows and to redefine its relationships with its partners. This study aims to release from the literature the main tendencies of collaboration practices and information exchanges leading to the performance and to propose a model of their relations.

INTRODUCTION

To face the strong pressures of the world competition, companies are constantly in search of new ways to improve the performance of their supply chain in order to reduce costs, to improve quality and to increase productivity. To go from an activity centred on the product to an activity, which must permanently meet the needs for the other members of the, chain is not an easy change. The borders of a company are then exceeded so that the other partners are regarded as members of a wide structure. However to exchange/share information, competences with other actors of the chain is not easy. To meet this organizational change, it is necessity for the companies to strengthen significantly their mechanisms of coordination and collaboration. Then, information sharing and collaborative practices become strategic questions. In this study, we are interesting in identifying, at first, the main factors and practices of information exchange and collaboration which can contribute to the supply chain performance in general and the supply chain actors performance individually, and in the second time, to build a generic model which is based on these various factors. We realized a bibliographical study relating to information exchange and collaboration practices, which lead to the performance, in order to identify checked or unchecked relations of cause and effect. From this study, we propose a model of factors influencing supply chain performance. The following section is devoted to the bibliographical study where we analyze the main recent research works dealing with the subject. A synthesis and a classification of the factors contributing to the performance of supply chains are proposed in section 3. In section 4, we present the generic model gathering all factors that contribute to the performance, such as information exchanges and collaboration practices. In section 5, we highlight some strong points of the study and offer suggestions for future research.

LITERATURE REVIEW

Companies try to improve their industrial performance in terms of cost, delays, adaptability, variety and traceability. Collaboration and information exchange between partners becomes essential within any supply chain. Many works seek how to improve the performance of the supply chains. We based our study on the main recent research works in order to emphasize factors contributing to supply chains performance. Authors try through their models and hypothesis to reinforce collaboration and cooperation devices that contribute to company or supply chain performance. We find various strategies and contributions based on information technologies, information exchange, information sharing, supply chain practices, inter-organizational communication and collaboration. Paulraj et al. [START_REF] Paulraj | Inter-organizational communication as a relational competency: Antecedents and performance outcomes in collaborative buyer-supplier relationships[END_REF] consider inter-organizational communication as a critical factor for strategic collaboration between companies. They define the inter-organizational communication as a relational competence, which can provide a strategic advantage for the partners of the chain and thus improve their performance. Focused on the collaboration and the use of the information technology, Chen et al. [START_REF] Chen | Evaluating the supply chain performance of IT-based inter-enterprise collaboration[END_REF] use the CPFR (Collaborative Planning Forecasting and Replenishment), a collection of practices which aims to radically reduce stocks and expenses and also tries to increase the customer service, to simulate four scenarios of collaboration between a retailer and a supplier. The authors show that the use of the IT cannot alone ensure that partners can gain. Mutual trust plays an essential role in achieving this goal. Always based on the use of information technologies and with the aim to improve other types of performance -the performance of the market and the financial performance -Seggie et al. [START_REF] Seggie | Do supply chain IT alignment and supply chain interfirm system integration impact upon brand equity and firm performance[END_REF] explore IT alignment and inter-firm system integration between supply chain partners as supply chain specific IT facilitators of brand equity. However, there could be more supply chain facilitators of brand equity including inter-firm coordination, inter-firm information exchange, partner flexibility and inter-firm integration of supply chain activities. The improvement of brand equity influences positively on market and financial performance. More generally and while always seeking to improve the performance of the company, Sander [START_REF] Sanders | An empirical study of the impact of e-business technologies on organizational collaboration and performance[END_REF] aims to extend knowledge on how the use of e-business technologies impacts organizational collaboration, and organizational performance. The author proposes a model of the relationship between organizational use of e-business technologies, organizational collaboration, and organizational performance. Indeed, the growth of Information Technology and especially the Internet and the Web may have had the most profound impact on business integration and collaboration. This study confirmed that e-business technology use have a significant direct impact on both intra and inter-organizational collaboration. Another important finding is the significant impact of intra-organizational collaboration on performance. Hence, companies should invest in strategies that promote cooperation and integration across the functions of the organization. New concepts appeared with Yang et al. [START_REF] Yang | Relational stability and alliance performance in supply chain[END_REF]. The authors test the links between relational capital, relational commitment, relational stability, and alliance performance. The cooperation in the form of alliance enables firms to share financial risk, improve service quality, increase productivity, and reduce cost. This study shed light on the importance of managing relationships in supply chain alliances in terms of ensuring relational commitment, trust of suppliers, and relational stability to lead the performance. Other types of performance are considered in the literature such as delivery performance, supplier performance, customer performance, etc. Zhou et Benton [START_REF] Zhou | Supply chain practice and information sharing[END_REF] investigate the integration of information sharing and supply chain practice in supply chain management. This study focuses on three aspects of information sharing -information sharing support technology, information content, and information quality -and considers three categories of supply chain practice: supply chain planning, just in time (JIT) production, and delivery practice. On the other hand, this research takes an interest in the delivery performance defining by on-time delivery, perfect order fulfilment rate, and delivery reliability/dependability. The result of this study shows that both effective information sharing and effective supply chain practices are necessary to achieve improvement in supply chain performance, and have significant influence on delivery performance. Other works are interested in testing the influence of other types of practices on the supply chain performance. Li et al. [START_REF] Li | The impact of supplychain management practices on competitive advantage and organizational performance[END_REF] define supply chain management practices as the set of activities undertaken by an organization to promote effective management of its supply chain, and propose five dimensions of supply chain management practices: strategic supplier partnership, customer relationship, level of information sharing, quality of information sharing, and postponement. These practices influence positively the financial performance, the market performance and create a competitive advantage for the company in terms of price, quality, reliability, product innovation and time to market. Chowa et al. [START_REF] Chowa | Supply chain management in the US and Taiwan: An empirical study[END_REF] add others practices like communication, integration and customer service management, supply chain concerns, information sharing and specify that even if these practices are different geographically, they influence always positively the total performance of the chain. Among all the practices studied in the literature, the information exchange and the information sharing remain the most involved practices. Many authors such as [START_REF] Gaonkar | Collaboration and information sharing in global contract manufacturing network[END_REF], [START_REF] Laux | Impact of information sharing on inventory replenishment in divergent supply chains[END_REF], [START_REF] Liu | Leveraging information sharing to increase supply chain configurability[END_REF], [START_REF] Sahin | Information sharing and coordination in make to order supply chain[END_REF], [START_REF] Shore | Information sharing in global supply chain systems[END_REF], [START_REF] Llerena | Evaluer les impacts du partage d'information: objectif, méthodologie, résultats[END_REF], [START_REF] Gruat-La-Forme | Référentiel d'évaluation de la performance d'une chaîne logistique: Application à une entreprise de l'ameublement[END_REF] and [START_REF] Botta-Genoulaz | Questionnaire d'enquête sur les pratiques de partage d'informations par une entreprise participant à une chaîne logistique établie[END_REF] have sought to identify information that may be shared and to evaluate the impact and the profit of these exchanges. We can so release six kinds of information to be exchanged in the supply chain: products, resources, stocks, delays, demands and planning information. In practice, to improve supply chain performance, executives often choose to implement either effective information sharing or effective supply chain practices because limited resources usually prevent firms from pursuing both simultaneously. As a solution, Zhou and Benton [START_REF] Zhou | Supply chain practice and information sharing[END_REF] propose the standardization of supply chain processes. The standardization of supply chain processes tends to help companies to take better advantage of the information shared among supply chain partners. Information sharing is a means to capture the supply chain dynamics and thus reduce uncertainty in external and internal environments. When coupled with the standardization inherent in effective supply chain practices, this uncertainty reduction allows performance improvement. Klein [START_REF] Klein | Customization and real time information access in integrated eBusiness supply chain relationships[END_REF] examines supply chain management relationships between service providers and clients, and focuses on the impacts of the provider's information exchange behaviour and both parties' level of trust. Trust has been established as core component of persistent business partnerships and strategic alliances [START_REF] Ganesan | Determinants of long-tem orientation in buyer seller relationships[END_REF][START_REF] Gulati | Does familiarity breed trust? the implications of repeated ties for contractual choice alliances[END_REF]. Trust influences cooperation and teamwork within organizations characterized as mutually beneficial initiatives. The relationship between service providers and clients is also based on the level of client customization of integrated supply chain functions through outsource service providers' e-business applications and solutions. Fynes et al. [START_REF] Fynes | The impact of supply chain relationship quality on quality performance[END_REF] study the nature of supply chain relationships with the aim of improving customer satisfaction. The authors define the supply chain relationship quality as the degree to which both parties in a relationship are engaged in an active, long-term working relationship, and using indicators of communication, trust, adaptation, commitment, interdependence, and co-operation. The mutual interest of the works presented above is that they try to improve the supply chain performance while following several strategies or models. The use of information technologies, information exchange, and sharing, inter-organizational communication, trust, cooperation and intra-and inter-organizational collaboration form essential factors of supply chain performance. However a company must be able to clearly define its requirements in performance in order to identify which are the best practices meeting these needs. In the following section, we are going to present more precisely and exhaustively all the factors collected from the literature which we could gather and which lead the performance of the supply chain.

CLASSIFICATION OF FACTORS INFLUENCING THE PERFORMANCE

According to our literature review, we realize that each study aims to identify the influences of some collaborative or technical practices on one or two types of performance, by testing several hypothesis. The goal of this section is to gather and classify every practice identified in the literature leading to the improvement of the performance. We could extracted fifty seven hypotheses from the studied research [START_REF] Sakka | Pratiques d'échanges d'information et pratiques collaboratives pour la performance des chaînes logistiques[END_REF], which have been tested by experts of the domain through companies surveys.

To classify these hypotheses, we initially sought to characterize the nature of each of them. That led us to express the hypotheses in the form of "A has a positive effect on B" where A is a characteristic known as "factor" and B is a characteristic known as "impact/result", by respecting the original idea of the authors. Example: "The use of information technologies has a positive effect on an inter-organizational communication". In this example, "the use of the information technology" is the factor and "the inter-organizational communication" is the impact/result. We found some hypotheses, which were verified and others, which the experiments of the authors did not allow the verification. We state that a hypothesis is verified if the characteristic "A" can generate or improve the characteristic "B". If the characteristic "A" does not generate or does not improve the characteristic "B", we say that the hypothesis is not verified (not to confuse with a false hypothesis). We then gathered the identified characteristics in four main categories: performance characteristics, technical technological characteristics, relational and contextual characteristics and characteristics of the supply chain practices.

Performance characteristics

This class gathers ten characteristics, which represent the various forms of performance quoted in studied work: customer performance, supplier performance, financial performance, market performance, delivery performance, performance of service providers, alliance performance, and organizational performance. The goal is generally to improve these performances. Thus, it happens very often that these characteristics of performance are the "impact / result" characteristics of a tested hypothesis. The global performance of the supply chain is a combination of these various performances.

Relational and contextual characteristics

These characteristics form the big class (seventeen characteristics) because they present the various relationships, which can exist between the actors of the supply chain, and characterize the context, in which evolves the company. These characteristics describe the behaviour, the vision, the type of relationships and interactions between a company and its partners (suppliers or / and customers). Among these characteristics, we quote trust towards the supplier/customer, long-term relationship orientation, inter-and intra-organizational communication, collaboration… Some characteristics can be gathered in subclasses because they concern the same concept: as example the quality of supply chain relationship, the trust, the capacity…

Technical and technological characteristics

This class of eight characteristics is based on the use of information technologies. It gathers the techniques and the technological choices made by a company such as information sharing support technology, inter-firm system integration mode, e-business technologies…

Characteristics of supply chain practices

This class gathers nine characteristics dealing with supply chain practices. These practices have been defined as a set of activities undertaken in an organization to promote effective management of the supply chain [START_REF] Li | The impact of supplychain management practices on competitive advantage and organizational performance[END_REF]. Therefore, we find in this class the practices of information sharing, production, planning, etc. Table 1 presents the four classes of characteristics and refers to the studied bibliographical sources. Each research work was interested in one or more characteristics. On each line, figures represent for every research work the number of hypotheses in which a characteristic appears, either as factor (F) or as result (R).

This table highlights certain interpretations:

• The common goal of all these works is to improve one or several kinds of performance. • All the authors were more interested in the relational and contextual characteristics. • The technical and technological characteristics and the characteristics of supply chain practices are rather factors characteristics. • Almost every author (except one) has studied the relational and contextual characteristics that are rather factors than results.

Table 1. Bibliographical reference synthesis

Ref.

Characteristics

Technical and technological

SC practices

Relational and contextual

Performance

F R F R F R F R [1] 2 6 6 2 [4] 3 2 3 2 [5] 4 3 1 [17] 5 3 4 2 4 [3] 5 5 4 2 1 3 [22] 1 4 4 1 [6] 1 7 2 2 1 7 [7] 5 5 5 2

FACTORS MODEL INFLUENCING THE PERFORMANCE

The identification of the hypotheses studied in the literature and the classification of the characteristics led us to build a detailed model of the factors influencing the performance. We have considered only verified hypotheses. This model (figure 1) is a directed graph including four types of vertex (a type of vertex for each type of characteristic). A vertex can have one of the following forms: rectangle, round rectangle, hexagon and octagon to present respectively characteristics of supply chain practices, technical and technological characteristics, relational and contextual characteristics and performance characteristics. Each class gathers characteristics, which can be at the same time "factors" (origin of an arrow), and/or "results" (destination of an arrow). The various relations between these elements model the hypotheses: a directed arc between two characteristics, in the same class or not, models a hypothesis. Moreover, one class of characteristics can gather one or more subclasses of characteristics. These subclasses are the semantic grouping of some characteristics. We can represent the model in an aggregate form (Figure 2) according to the number of arrows connecting a class to another. This global model gathers obviously the four classes of characteristics. Full arrows present the interactions between these various classes, the thickness of the arrow being proportional to the number of hypotheses checked between these classes. As first interpretation, we can notice that the class of characteristics of performance is the "target" class. The class of the relational and contextual characteristics represents the "core" of the model since it interacts with all the other classes. Moreover, it has the greatest influence on the class of performance. Thus, for a company, it is interesting to concentrate on this type of characteristic and to define its relations and its strategies with its partners. So important, the class of the technical and technological characteristics has a rather strong influence on the characteristics of performance. This class also interacts with the class of relational and contextual characteristics but not with the one of supply chain practices. Finally, the class of supply chain practices characteristics has a medium influence on the class of performance and has no relation with the technical and technological characteristics. On the other hand it appears to be rather influenced by the class of relational and contextual characteristics. The contribution of these two models is double. On one hand for the researchers, these models aggregate various factors of performance (through several types of characteristics: technical, relational…), what is almost absent in the scientific literature. We find generally one or two types of characteristics studied in every research work. In other words, they propose a general sight of the factors contributing to performance and of their weights. On the other hand, these models allow a company to situate itself regarding its collaborative practices and relationships that it keeps with its supply chain partners. These models offer companies knowledge on causal relations between technical / technological, relational / contextual, supply chain practices and performance characteristics. A company may better understand in which direction focusing its efforts: partners' relationship reengineering, information and communication technologies investments… and the limits of some practices for the improvement of its supply chain performance. Moreover, our model reveals many hypotheses, i.e. causal relations, which have not been tested yet.

CONCLUSION

To remain competitive, any company tries to build a strategy allowing remaining in the best conditions in front of present competitive strengths within its sector. The performance of a company, in terms of cost, quality and delays, depends more and more strongly on its capacity to optimize its relationships with its partners and on its ability to collaborate and to exchange the good information. Based on a review of recent literature, we have identified the main factors, which can contribute to the performance. This performance concerns either each actor of the chain as such, or all the supply chain. We have distinguished the performance of the company, of the supplier, of the customer, as well as the indispensable elements to reach these performances such as the use of information and communication technologies, intra and inter-organizational collaboration, inter-organizational communication, production practices… Each one of the authors was interested in one aspect of the performance. The proposed model, which gathers 48 hypotheses on 44 characteristics, represents a reference model of factors contributing to the performance of the supply chains for researchers and companies. This model could be of course completed and enhanced by a more complete analysis of the literature. Indeed, one can wonder about the role of the other supply chain practices as VMI or CPFR on the performance, and their place in the model. In terms of perspectives, it would be interesting to test new hypotheses and to study the correspondence between the configuration of a company -such as its global strategy, the characteristics of its products lines -and the collaborative practices, which it puts in place (or wishes to implement) to assure the required coordination between actors for the improvement of their performance. It would be also interesting to test the transitivity of the relations between the various characteristics; for example, if "A has a positive effect on B" and "B has a positive effect on C", could we say, "A has a positive effect on C"? This could give more choices to decision makers and possibly reduce the number of characteristics. Finally, the notion of hypotheses could be widened to conditional hypotheses. Certain unchecked "simple" hypotheses may be verified under certain conditions: if "A has no positive effect on B", it may be that, by adding factor "C", "A, under the condition C, has a positive effect on B".

Figure 1 .

 1 Figure 1. Detailed model of factors influencing the performance