Marc-Olivier Metais
email: marc-olivier.metais@centralesupelec.fr

O Jouini

Yannick Perez

Jaâfar Berrada

Emilia Suomalainen

M.-O Metais

Planning charging infrastructure deployment: A new spatio-temporal model. Extended abstract for the Euro Working Group on Transportation 2021

Keywords: Electric vehicle, Charging infrastructure, Multi-agent simulation

published or not. The documents may come

Introduction

The current climate issue requires a drastic reduction in anthropogenic greenhouse gas emissions. Among the highest emitting sectors, road transport accounts for between 20 and 25% of these emissions in Europe and the US [START_REF]Greenhouse gas emissions from transport in europe[END_REF]. A transition in this sector towards greener mobility is therefore an important lever to reducing global greenhouse gas emissions. The solution currently at work is to transform the fleet of internal combustion vehicles into a fleet of electric vehicles, with much lower emissions [START_REF] Hawkins | Guillaume Majeau-Bettez, and Anders Hammer Strømman. Comparative Environmental Life Cycle Assessment of Conventional and Electric Vehicles[END_REF]. Such a transformation cannot take place without the acceptance of electric vehicles by users. To achieve this user acceptance, electric vehicles must be as convenient as internal combustion vehicles in their daily use, including for those who cannot charge their vehicle at home. An important step required to achieve this goal is the existence of a charging infrastructure adapted to the needs of vehicle users [START_REF]Panorama des politiques publiques en faveur des véhicules à très faibles émissions -Note de synthèse[END_REF]. But due to the high cost of deploying such an infrastructure, it cannot be a prerequisite for the pre-eminence of electric vehicles in the fleet on the road : the infrastructure cannot precede the democratization of electric vehicles, but must accompany it [START_REF] Springel | Network Externality and Subsidy Structure in Two-Sided Markets : Evidence from Electric Vehicle Incentives Resources[END_REF]. However, the existing literature focuses on the final optimality of the charging infrastructure, without taking into account its development according to a temporal pattern consistent with user needs. This risks slowing down the adoption of electric vehicles, and therefore investment in the charging infrastructure, which may never exist in its final version because of this vicious circle [START_REF] Delacrétaz | The chicken or the egg: Technology adoption and network infrastructure in the market for electric vehicles[END_REF].

We propose in this paper an infrastructure deployment model centered on user needs, considering the integration of both spatial (where to place the charging stations) and temporal (in what order to place them) aspects in charging infrastructure deployment. The objective of the analysis of this model is to obtain the charging infrastructure that offers the best possible service to users. Charging vehicles should be as easy as possible for users, who should be able to use their vehicles without having to worry about its autonomy or the time it will take to charge it.

Model description

We employ an iterative approach. First, candidate sites are selected, on which it will be decided whether or not to place a station, and which type of station to place (fast, medium, slow). This pre-selection is not necessary, but limiting the number of potential sites reduces the complexity of the problem, and main locations at which charging events are likely to occur are identifiables [START_REF] Hardman | A review of consumer preferences of and interactions with electric vehicle charging infrastructure[END_REF]. Once these sites are selected, we determine the usefulness of placing one or more stations at each of them according to user preferences and resource allocation efficiency. This usefulness is determined by the charging opportunities offered to users at that site, so that they do not feel the charge as a constraint in the use of their electric vehicle.

We determine the utility of a site according to the following criteria:

• The demand for parking on the site. The more vehicles park at a location, the more useful it will be to put a station there. The number of distinct vehicles is also considered, in order to serve a maximum number of users. • The parking duration on the site. It allows to determine which type of station to put at this location, adapting the necessary charging time to the parking time. For example, if a vehicle is parked for three hours, it is inefficient to install a more expensive station that will charge it in twenty minutes, since the vehicle will unnecessarily occupy the charger for the remaining time. • The state of charge of the vehicles on the site. Except for a few special cases, the less charged the battery of vehicles arriving at the site, the more useful it is for them to be able to recharge. • The area coverage. There must be as few white zones as possible, otherwise users will not have confidence in their electric vehicle, which will remain a second car.

Based on these criteria, a score is calculated for each one of the candidate locations. The principle is then quite intuitive: the first station is placed on the location with the highest score, then the scores of all the sites are recalculated, as these may have changed with the addition of a station on the territory (for example, the state of charge of vehicles may have changed at some locations). The new site with the highest score is then selected, and so on. It is important to note that a site where a station has already been placed is not disqualified for a second station: its score is simply modified, in particular because of the territorial coverage criterion which favours the spreading of stations over the territory.

By doing so, the stations are placed where they are the most useful, following a consistent time pattern. This model also allows for the direct integration of already existing infrastructure, including private facilities, since it is based mainly on criteria related to vehicles.

First results and work in progress

Our first results, obtained by multi agent simulation from MATSim [START_REF] Axhausen | The Multi-Agent Transport Simulation MATSim[END_REF], do not yet include the state of charge of the vehicles. They suggest that the model behaves as expected: it places the stations where the most cars are parked, and selects stations allowing a faster charging when the vehicle parking time is reduced. Moreover, a small change in vehicle behavior does not result in a change in the entire charging infrastructure, which is reassuring for the robustness of the model. Compared to a station placement according to a classical Set Coverage Location Model [START_REF] Wei | Locating road-vehicle refueling stations[END_REF], it seems in most cases to shorten travel times, as charging is integrated during users' other activities.

The next step of the work is to integrate an overall optimum into this model. Indeed, a purely iterative placement of the stations means that the first stations are placed without taking into account the following ones. This gives a necessarily sub-optimal result for the final infrastructure. This optimum will determine the final infrastructure, and the deployment schedule will then be iterative. The complexity of the optimum lies in the integration of the state of charge of the batteries, which depends on the charging stations in place as well as on the users' routes. The optimum will be then compared to the result obtained with the purely incremental method.

Conclusion

We developed a model for the placement of charging stations for electric vehicles that focuses on user behavior, so that the charging of their vehicle is integrated into their daily life. This model allows us to make a spatio-temporal planning of the deployment of a recharging infrastructure, in order to accompany the democratization of electric vehicles. We thereafter want to investigate the effects of this deployment method on the adoption of electric vehicles.


Peer-review under responsibility of the scientific committee of the 23rd EURO Working Group on Transportation Meeting. Planning EV Charging Infrastructures : A Literature Review

Keywords: Electric Vehicle, Charging Infrastructure, Optimization

This paper summarizes the existing work on implementation models of charging stations. It aims to draw up a comparative overview of the approaches that have been used until 2020 to simulate and assess the impacts of location strategies of charging infrastructure. In particular, three categories of approaches are identified. Then, we analysed, for each approach, both technical and economic factors , in order to provide a complete analysis to stakeholders involved in EV charging infrastructure design and planning. Finally, a list of recommendation for future research works are provided in order to develop models that are closer to reality.

Introduction

Electric Vehicles (EVs) have been gaining importance in recent years, and this trend is to be accelerated as EVs are seen as one of the solutions in order to reduce the transport sector's GHG emissions, which represents about 15% of global GHG emissions (IPCC, 2014). However, the adoption of EVs at a large scale is not possible without prior appropriate charging infrastructure (France Strategie, 2019;International Energy Agency, 2019). Due to the high cost of this infrastructure, the deployment must be made with a proper strategy, with the aim to obtain an efficient repartition of the charging stations which allows a large majority to adopt EVs, while avoiding a waste of resources with useless charging stations or grid reinforcement (Cai et al., 2014).

The paper reviews the models developed so far, with the aim to explore their findings and to assess their limitations. The reviewed models fall into three main categories having three distinguished approaches: node based, path-based and tour-based approaches. In the rest of this paper, we describe these three approaches and discuss their strengths, limits. Finally, some directions for further research works are proposed.

Simulation models description and comparison

Three main approaches for locating charging infrastructures are identified:

The most used approach is the node-based approach. It locates charging points in order to satisfy at each instant the overall demand of the territory. It is based on solving a maximum coverage location problem [START_REF] Syvia | Incorporating institutional and spatial factors in the selection of the optimal locations of public electric vehicle charging facilities: A case study of Beijing[END_REF]. This approach is accurate when points of interest are known (for instance, residential zones where EV users need to have a charging station close to their home). Based then mainly on GIS data, node-based approach requires few data. However, it does not always leads to the best coverage with the minimal cost [START_REF] Upchurch | capturing model to optimize the location of fast-charging stations with uncertain electric vehicle flows Xi[END_REF].

The path-based approach, is a flow-capturing model. It aims to locate stations along routes with higher flows (Wu, Sioshansi, 2017). This approach is based on vehicle paths given their origin-destination (OD). Therefore, OD locations are aggregated into larger zones that group OD-trips with nearly the same path, since data required concern the path from origin to destination and not the origin and destination points (Xi, Sioshansi, Marano, 2013). But because the charging stations are placed on paths between those two points, the charging process requires making a stop specifically for charging, which adds the charging time to the trip. As a result, this approach is more adapted for fast-charging stations, the use of which is similar to that of a conventional gas station, but not for slow-charging, which can take several hours (Sun, Gao, Li, Wang, 2018).

The tour-based approach is more likely to reflect the real charging needs of EV users, by taking into account the whole journeys of EVs. However, this approach requires detailed individual travel data and high computing capacity [START_REF]Modeling and optimization for electric vehicle charging infrastructure[END_REF]. Combined with agent-based modelling of EV users, it could lead to a more accurate location of charging stations, since it enables to simulate the sequence of trips instead of an aggregation of each one as it is the more frequently done in the literature [START_REF] Cavadas | A MIP model for locating slow-charging stations for electric vehicles in urban areas accounting for driver tours Yu[END_REF]. With this method, an efficient charging "at destination" can be made.

Discussion and limits

In all these three approaches, the user behaviour is rarely modelled . In particular, the sensitivity to waiting time for charging, because of queuing at station, the sensitivity to fare, or the sensitivity to access distance are critical to assess the performance and economic relevance of locating a charging station. Hence, introducing a queuing model to consider users behaviour should provide more realistic results. The user's charging choice is also dependent on the type of area (urban, or rural). In urban areas, for instance, public charging could be perceived as a back-up solution for home charging, which is always available, or a solution to make longer distances with EVs. On the other hand, when collective housings are not equipped with private parking slots, home charging is not possible, and developing an infrastructure without taking this in account can be an obstacle to the largescale adoption of EVs in cities.

In addition, most of existing studies focus on only one type of approach, since each one has its specific application domain and is not suitable to all cases. In an urban and semi-urban environment, each zone has its most appropriate method, depending on this zone activities and characteristics which will lead to more accurate results. In order to study large territories where urban, periurban and/ or rural areas are in interaction, it is then required to propose a hybrid model that includes specificities of each zone.

Another limit of existing models concerns the absence of temporal effect to simulate the deployment evolution over time and to assess long-term impacts of such investment in charging infrastructure. In particular, deploying a charging infrastructure is not instantaneous in reality and can take several years. In order to support the fastest possible transition from internal combustion engine vehicles to EVs, the charging infrastructure cannot wait to be fully deployed to be really useful. Otherwise the democratization of the EVs and so the deployment could be slowed down, as soon as the EV and infrastructure markets are twosided markets: users would not buy EVs if there is no convenient infrastructure, and operators would not install charging infrastructure if users do not have EVs (Yu, Li, Tong, 2016).

Finally, the electricity grid capacity is systematically taken as a constraint as soon as the cost of a grid reinforcement is considered to be too expensive. However, the French law about mobility stipulates that the connexion cost is covered up to 75% by the distribution system operator (DSO) (Loi n° 2019-1428). This significantly reduces the cost of such a reinforcement for the charging station operator.

Conclusion

Many works have been undertaken in order to deploy an efficient charging infrastructure, which is a necessary prerequisite to such a democratization, and three main approaches are used: node, flow and tour-based approach . However, we found that those approaches are rarely put together, and a model closer to reality, which includes EV users behavior, territories specificities, temporal effects, and grid constraints as well, should be developed in order to support EVs diffusion and help stakeholders to make strategic decisions.


domain: chim sde shs

text:
Ranya Amer

Tarek Hosny

Eslam Salama

Dina Ihab

Abu Sherif

Harrison El-Magd

Fhumulani Pienaar

Pascal Ramukhwatho

Philippe Breil

Namour

© AfriAlliance Consortium

Aim and

Communication Strategy

•Improve societal awareness by interaction with the local community and NGOs on NBS implementation.

•Assist capacity development by interaction, training and communication of project outputs.

•Dissemination and address policy and decision-makers to adopt projects outputs through.

Prospective design of constructed porous ramps to trap organic matter during low flows and process it during medium to high flow periods.

••

  Local politicians, fishing association, river basin and sewer system managers, and scientists partnership • where and how to implement low cost & nature based solutions,? • improve the highly degraded ecology of intermittent urban rivers. System optimization challenges -algae growth for bio-energy • Assist Mosselbay local municipality to enhance wastewater quality treatment. • Hydrological modeling of Brandwacht WWT plant -• Improve algae growth and resultant algae production for bio-Septic tank of 0.4 m 3 •Input flux of 40 L per days •Biofilter design for 10 days residence time • Assist Naga Diab local farmers, small village in Alexandria, to enhance high salted soil and water quality. • NBS to reuse the domestic wastewater for better water quality and crops.


Bruno Gavazzi
email: bgavazzi@unistra.fr

Rozan Alkhatib-Alkontar

Marc Munschy

Frédéric Colin

Catherine Duvette

On the Use of Fluxgate 3-Axis Magnetometers in Archaeology: Application with a Multi-sensor Device on the Site of Qasr 'Allam in the Western Desert of Egypt

Keywords: Multi-sensors, Magnetic compensation, Magnetometry, 3-axis fluxgate magnetometers, Potential field transformations, Vertical vector fluxgate Magnetometry, 3-axis fluxgate magnetometers, Multi-sensors, Magnetic 33 compensation, Potential field transformations, Vertical vector fluxgate. 34

Situated in the Western Desert of Egypt, the oasis of Bahariya (Figure 1) is inhabited 37 since Prehistory [START_REF] Svoboda | Prehistory of the southern Bahariya Oasis, Western Desert, Egypt. 439 An outline[END_REF]2013). The main phases of the ancient Egyptian 38 civilization can be observed in the area. However, they are not as well documented as in 39 the Nile valley because only a few scholars have studied the Bahariya region. This is 40 mainly due to access difficulties until construction of road infrastructure in the mid-20 th 41 century. The growing number of investigations took place since the end of the nineties. 42

They revealed the archaeological potential of the area for illustration of a locally badly 43 known period, ranging from the Third Intermediate Period to the Roman times, (i.e. 44 from the 9 th century B.C. to the 3 rd century A.D. (Colin, 2013a, pp. 151-152)). This 45 paper focuses on the site of Qasr 'Allam (Figure 1), which integrity is threatened by 46 heavy sedimentary processes and the rapid site destruction by recent increases in 47 agricultural development. Geophysics is used to locate and study the archaeological 48 remains of a historically significant dwelling. 49

The site of Qasr 'Allam 50 Before any archaeological study, the site of Qasr 'Allam was known mostly as a 51 rectangular structure emerging from the sand which was interpreted by the inhabitant as 52 an Arabic fort (Colin and Labrique, 2003, pp. 169-170). More than ten years of 53 excavation then revealed facilities buried within sand and mud to be composed of 54 mudbrick buildings of different natures, such as housings, storerooms and workshops 55 (Figure 2, A-B-C). These structures were interpreted as part of a wide religious 56 estate, the "Domain of Amun" according to stamped potteries found in the domestic 57 dump sites of the dwellings. Two periods of occupation can be identified from 9 th to 7 th 58 centuries B.C. (Colin, 2011, pp. 57-68). A complex network of fossilized irrigation 59 structures can be identified through the traces of wells as well as open and underground 60 channels surrounding the dwelling. In nowadays arid landscape most of these structures 61 are partially or totally covered with sand. Often, only the materials excavated during 62 construction and maintenance are visible on the surface (Figure 2, A-D-E-F). 63

These discoveries might indicate that the site could be a well preserved example of a 64 complete cultic facility with three main components: a cultic core, associated domestic 65 3 buildings and its surrounding agricultural domain, of which most parts are still buried 66 within the ground. The structural organization of the excavated buildings suggests 67 indeed that they were only an annex in the periphery of a much larger and central 68 religious facility (Colin, 2011, pp. 65-66;Colin and Duvette, 2012, pp. 161-162). 69

According to this hypothesis, the direction of the access ramp of a cellular foundation 70 platform (Figure 2, A-B), whose typology is well known in the Nile valley (Spencer, 71 1979a, pp. 116-118;Spencer, 1979b;[START_REF] Traunecker | Les "temples hauts" de Basse époque : un aspect du 445 fonctionnement économique des temples[END_REF]Leclère, 2008, pp. 630-636;72 Malecka-Drozd, 2014), would indicate that the presumed core is located westwards, 73 where lies a sand dune a few metres thick and where no archaeological traces are visible 74 on the surface. 75 However, this hypothesis suffers from two uncertainties: 1-the lack of traces on the 76 surface of the complex core; 2-the lack of information on the spatial and chronological 77 links between the buildings and the irrigation system. 78

Answers to these problems could be gained from a geophysical imaging of the sub-79 surface. The surveying strategy should then take into account strong constraints: the 80 area is highly threatened from the west by the agricultural development, increasing 81 every year. Therewith, the whole dune shows an uneven topography scattered with dried 82 halfa grass and bushes reaching a height up to 0.8 m. Thus, the prospection of the area 83 must be fast and adapted to the roughness of the terrain. 84

Choice of the geophysical method

85

In such a context, the most appropriate solution would appear to be the magnetic 86 methods. Geomagnetism is a popular and effective method for archaeological purposes 87 [START_REF] Linford | The application of geophysical methods to archaeological prospection[END_REF][START_REF] Gaffney | Detecting Trends in the Prediction of the Buried Past: A Review of 405 Geophysical Techniques in Archaeology[END_REF]. The main advantages are: -1-the anthropic traces show 88 usually a strong contrast of magnetization with their surroundings; -2-the rapidity of 89 measurement and light weight of the sensors to allow mapping of large surfaces with a 90 high density of data. In addition, a first prospection using vector gradiometer (Geoscan 91 FM256) was conducted between the sand dune and the platform in 2006 and 2010 by 92 Tomasz Herbich [START_REF] Herbich | Geophysical surveying in Egypt: periodic report for[END_REF]. It revealed irrigation structures as well as walls and 93 foundation trenches [START_REF]Travaux de l'Institut 362 Français d'Archéologie Orientale en 2005-2006[END_REF][START_REF] Denoix | Travaux de l'Institut 365 Français d'Archéologie Orientale en 2009-2010[END_REF][START_REF] Herbich | Geophysical surveying in Egypt: periodic report for[END_REF], thus giving evidence of 94 a contrast of magnetization strong enough to identify the archaeological remains. 95

However, the study of [START_REF] Herbich | Geophysical surveying in Egypt: periodic report for[END_REF] also revealed some limitations over the sand 96 dune: the topography and vegetation make the implementation of a grid and the 97 preparation of the field. Moreover, one of the properties of the vertical gradient is to 99 enhance short wavelength and to smooth out large wavelength variations of the 100 magnetic field. This makes gradiometers extremely sensitive to shallow objects but of 101 limited capability to identify deeper sources or lower magnetic contrasts as it is the case 102 for Qasr 'Allam (Blakely, 1995, pp. 324-326;Fagaly, 2001, pp. 327-328). This paper 103 proposes to overcome these limitations by adapting the measurement of the total 104 magnetic field with 3-axis vector fluxgate magnetometers, usually used in space 105 research or mining exploration [START_REF] Nabighian | 75th Anniversary: The historical development of the magnetic method 427 in exploration[END_REF], and more recently for the 106 detection of unexploded ordnances [START_REF] Munschy | Magnetic mapping for the 422 detection and characterization of UXO: Use of multi-sensor fluxgate 3-axis 423 magnetometers and methods of interpretation[END_REF] The core of the developed method lies in the measurement of the intensity of the 110 magnetic field with fluxgate magnetometers. Such magnetometers (Figure 3,A) have 111 the advantage of being light (80 g) and consuming low energy (< 1 W). Their three 112 orthogonal sensors allow the measurement of the three components of the magnetic 113 field at rate up to more than 1000 Hz [START_REF] Primdahl | The fluxgate magnetometer[END_REF], from which the total field can 114 easily be calculated. The device developed for this study (Figure 3,C) is built around an 115 in-house developed electronics (Figure 3,B). It powers the rest of the instrument, 116 digitizes and stores the data of 1 to 8 magnetometers as well as 1 to 2 global navigation 117 satellite system (GNSS) antennas. The electronics is mounted on a backpack and 4 118 magnetometers are placed 0.5 m apart from each other in front of the operator, one 119 metre above the ground. A GNSS antenna is placed at the top of the backpack for the 120 navigation. Both navigation and magnetic data are displayed in real time through a head 121 mounted display (HMD). The device weighs less than 15 kg and can be operated by a 122 single person who follows parallel survey lines set every 2 m and displayed in the 123 HMD. Thus, georeferenced magnetic profiles are acquired every 0.5 m centred on each 124 survey line without any preparation on the field. In Qasr 'Allam, 5000 m² to 12000 m² 125 of magnetic data were acquired per hour of measurement. 126 This means that the instrument requires a precise calibration before each session of 129 measurements to correct errors of sensitivity, offset and angle. This problem is well 130 known and various techniques of calibration have been developed. In this study the 131 calibration is done using a process developed initially for space research (Olsen et al., 132 2003). It consists in the rotation of the magnetometers (or the whole device) in all 133 direction around a fixed point where the magnetic field can be considered steady. The 134 registered variations of the magnetic field are therefore only due to the different kinds of 135 errors which can then be minimized using a least squares method. The advantage of the 136 process is that it also compensates the remnant and induced magnetization of the device 137 itself [START_REF] Munschy | Magnetic mapping for the 422 detection and characterization of UXO: Use of multi-sensor fluxgate 3-axis 423 magnetometers and methods of interpretation[END_REF]. This makes the fluxgate the only magnetometer capable of 138 such compensation, allowing compact multi-sensor devices as well as motorized 139 measurements. A typical result of the effect of the calibration and compensation process 140 on a magnetometer is shown in Figure 4, where computed parameters reduce the 141 variations of measurements at a fixed point from around 200 nT to 0.3 nT. 142

Calibration and compensation 127

Time-dependant variations 143

Another issue with the measurement of the total magnetic field is the correction of 144 the time-dependant variations which may be caused by extra-terrestrial sources or 145 anthropic activities. Additionally, fluxgate magnetometers are not absolute and subject 146 to drift with the change of temperature (0.1 to 0.5 nT/°C according to the manufacturer). 147

In an environment affected by homogeneous but not linear temporal variations, as it is 148 often the case in urban areas, corrections can be made by using a magnetometer 149 installed at a fixed point (base station) during the measurements, thus recording only the 150 time dependant part of the signal. Such solution was not possible in Qasr 'Allam due to 151 legal and logistical difficulties to have a base station on the site at the time of the study. 152 However, during the surveying hours (6 to 10 a.m.), time-dependant variations are 153 linear and can therefore be easily corrected. They are the result of a combination of 154 effects from a temperature drift as well as from far external sources of which the linear 155 variation is confirmed by using geomagnetic records of one of the nearest 156

INTERMAGNET observatory (Tamanrasset). 157

Data processing 158 The measurement provides the 3 calibrated components of the total magnetic field, 159 from which the total magnetic intensity is calculated. In archaeology the prime interest 160 is to measure/illustrate subtle spatial variations of the magnetic field. This is achieved 161 by observing the anomalies of the total magnetic field's intensity. The anomaly is 162 defined as the difference between the intensity of the measured magnetic field and the 163 regional field (Blakely, 1995, pp. 178-180). The latest is computed using the 164 International Geomagnetic Reference Field (IGRF) [START_REF] Finlay | International 402 Geomagnetic Reference Field: the eleventh generation[END_REF]. The anomaly 165 of the intensity of the total magnetic field can then be displayed either as profiles or as 166 maps after a gridding computerized operation [START_REF] D'errico | Surface Fitting using gridfit[END_REF]. The node distance of 167 the grid is usually set as half of the distance between each magnetometer, i.e. 0.25 m in 168 this study. After this procedure, the residual errors can lead to the appearance of a 169 levelling effect between profiles [START_REF] Fedi | Decorrugation and removal of directional trends of magnetic 395 fields by the wavelet transform: application to archaeological areas[END_REF]. To solve this problem, the 170 differences at the crossing points between the values on magnetic profiles (in-lines) and 171 traverses (tie-lines) are measured. Then, a constant to apply to each profile is calculated 172 by a linear inversion to minimize the differences at the crossing points. 173

Results

174

The data acquisition over the Qasr 'Allam site took place in April and May 2012. 175

Through 200 km of survey lines, more than 800 km of georeferenced magnetic profiles 176 were recorded over an area about 340,000 m² (Figure 5). 177

Maps of magnetic anomalies 178

Usually, magnetic anomalies are represented using maps with a linear colour scale. 179

Those consist in attributing a colour or grey tone to each node of the grid according to 180 its value using a linear scale, as shown in Figure 6. Unfortunately, such a representation 181 is often not sufficient to show accurately all the anomalies of a site, as they can range 182 from a few to hundreds of nano-Tesla. A common solution to this problem is to display 183 multiple maps with different scales to understand the anomalies from the largest to the 184 smallest. Such a process might be time consuming and is not the most practical, as 185 several maps have to be observed at the same time. To overcome this problem, we 186 introduce another approach, the equi-populated mapping. An equi-populated map 187 consists in attributing a shade (or colour) to each node using a non-linear scale in such a 188 -North-south gradient: the magnetic anomaly field decreases of about 20 nT 206 from north to south. This gradient cannot be explained by the regional magnetic 207 field as the International Geomagnetic Reference Field gives an increase of 3.8 208 nT from north to south. Thus, it is likely that such a gradient is due to a deep 209 local variation of the underlying geology. 210

These anomalies reveal the presence of different kind of magnetic heterogeneities 211 within the ground. Unfortunately, the shape, amplitude and position of an anomaly (as 212 well as the gradient) depend on multiple factor such as the shape, the orientation, the 213 position and magnetization of the source as well as the orientation of the regional 214 magnetic field. To decipher these anomalies, interpretation tools can be found in 215 potential field theory. 216

Potential field transformations 217

In any kind of magnetometry, the horizontal position of the sources is situated 218 somewhere in between the positive and negative extrema of a skewed anomaly. When 219 the wavelength is shorter than the size of the object, as it is often the case for very 220 shallow objects, this is not a problem. Otherwise, as it is often the case in this study, the 221 error can reach up to a few metres, which is not acceptable to locate properly 222 archaeological trenches. Fortunately, the position of the remains can be obtained by 223 using a potential field transformation known as the double reduction to the pole (DRP). 224

The DRP consists in the calculation of the signal when both the magnetization and 225 regional field are set vertical. Thus the anomalies become symmetrical with their 226 maxima above their sources [START_REF] Baranov | A new method for interpretation of aeromagnetic maps: pseudo-356 gravimetric anomalies[END_REF]. In the spectral domain, the operation is 227 easily done by multiplying the spectrum of the anomaly by 228

݅ ඥ ²ݑ + ²ݒ ݑܽ + ݒܾ + ݅ܿ ඥ ²ݑ + ²ݒ ൩ ݅ ඥ ²ݑ + ²ݒ ݑ′ܽ + ݒ′ܾ + ݅ܿ′ ඥ ²ݑ + ²ݒ ൩ , (1)
where ݑ and ݒ are the wavelengths associated with ݔ and ݕ directions, ݅² = -1, 229 (ܽ, ܾ, ܿ) the components of the unit vector in the direction of the regional magnetic 230 field, and (ܽ ᇱ , ܾ ᇱ , ܿ ᇱ ) the components of the unit vector in the direction of the 231 magnetization [START_REF] Bhattacharyya | Two-dimensional harmonic analysis as a tool for magnetic 358 interpretation[END_REF]. The direction of the regional field is given by the 232 IGRF while the direction of magnetization is either set as the same as the regional field 233 when the ratio remnant/induced magnetization is near zero or obtained through 234 successive iterations until the signal become symmetrical. In Qasr ʿAllam, as the 235 buildings are made in mudbricks, the orientation of magnetization was set equal to that 236 of the regional field. In Figure 8, the anomalies become symmetrical, confirming this 237 induced-only magnetization hypothesis. It must be noted that a simple reduction to the 238 pole (only one vector set vertical) does not give the position of the source (Figure 8). 239

The calculated DRP map gives therefore the position of sources visible or not on the 240 surface (Figure 9). The archaeological interpretation stays difficult due to the presence 241 of a very large wavelength anomaly most probably due to the geology. An easy way to 242 enhance the shortest wavelength while smoothing the largest ones is the use of the 243 vertical derivative. The operation is straightforward in the spectral domain and 244 corresponds to the multiplication of the spectrum of the map by 245

ቀඥݑ ଶ + ݒ ଶ ቁ , (2)

Comparison with gradiometry 250

To assess the quality of the data for archaeological interpretation compared to 251 gradiometry, the area surveyed by [START_REF] Herbich | Geophysical surveying in Egypt: periodic report for[END_REF] with a fluxgate gradiometer (Geoscan 252 FM256) was also covered with the device developed in this study. The comparison of 253 the results (Figure 11) shows that the proposed method reveals at least as many 254 information as a vector gradiometer, even though the magnetometers are more distant 255 from the ground (1 m). The vertical derivative map (Figure 11, A) appears more blurred 256 than the gradiometric map (Figure 11,B) because it corresponds to a more distant 257 acquisition from the sources. 258

Discussion

259

Interpretation of magnetic anomalies 260

The different maps give important information on the sources of the magnetic 261 anomalies. The different linear anomalies can be interpreted as highly probable 262 archaeological remains and are divided into three categories: long wavelengths, straight 263 and non-straight short wavelengths. The non-straight linear elements with short 264 wavelengths follow the same rough orientation pattern and shape as the irrigation 265 structures visible on the ground surface. Some of them directly follow the traces of the 266 irrigation structures observed on the ground surface. They are also mostly connected to 267 an area of visible wells in the south eastern part of the site (Figures 2 and5). This 268 strongly suggests that those anomalies can be interpreted as irrigation structures, present 269 not only under the sand dune, but also within the harder ground in the whole area 270 (Figure 12). A targeted excavation of such a structure within the sand dune (Figure 12, 271 area 15) confirmed open irrigation channels under 1.2 m of sediments (Colin and 272 Duvette 2012, pp. 163-164). The filling sediments of one segment contained artefacts 273 (potteries, terracotta figurines) of a well-attested type, according to the local typology of 274 the 8 th or the 7 th century B.C. (Colin and Duvette, 2012, p. 164). This information 275 validates the hypothesis that at least one part of the irrigation network was 276 The two other types of linear anomalies can be interpreted differently. They are 279 situated in front of the access ramp of the platform, where the rest of a religious facility 280 can be expected. They show angular shapes, and display an orientation similar to the 281 one of the already excavated constructions. It can therefore be stated that they most 282 likely correspond to ancient buildings, thus enlarging the surface of the whole facility 283 from 40 000 m² to 150 000 m² (Figure 12). The variability of wavelengths can be 284 explained as different depths of sources, either due to the variability of the post-285 abandonment sedimentary deposits, to different sizes of structures or to successive 286 archaeological periods. This is verified by two targeted excavations which started in 287 2013 and 2014 and are still in progress (Figure 12, areas 16 and 17). They revealed the 288 presence of cultic buildings corresponding to the magnetic anomalies at different depths 289 from 0.15 to 2.4 metres (Figure 12, area 16 and 17 respectively) which are related to 290 different occupations from at least the 8 th or the 7 th century B.C. to the 2 nd century A.D. 291 and are affected by an environmental change (Colin, 2013b;[START_REF] Colin | Bahariya. 383 Pratiques funéraires et lieux de culte. In: Midant-Reynes B (Ed.). Rapport d'activité 384 2013-2014[END_REF]. The 292 stratigraphy of the tested areas revealed that the sedimentary processes followed two 293 successive patterns. The ruins of the last occupation period (Roman times) are mainly 294 covered by aeolian sand in an arid context, but the remains of the former periods (from 295 Third Intermediate Period until Late Period or later) are filled with alluvial earthen 296 sediments, in a seemingly more humid context. 297

The 3-axis fluxgate magnetometer total field approach 298

In addition to the interpretation results, the study reveals the potential of the use of 3-299 axis fluxgate magnetometers for large scale archaeological surveys. The light weight of 300 the magnetometers and their compensation ability allow the construction of a compact 301 multi-sensors device which can be operated by a single technician. At least four 302 simultaneous georeferenced magnetic data without any preliminary preparation of the 303 site can be acquired. The position of the magnetometers 1 m above the ground surface 304 allow to cover areas with more vegetation or a more uneven topography than with a 305 gradiometer device. Using vertical gradiometry, the lower probe is usually situated 0.2-306 0.3 m above the ground surface. Thus, the proposed approach proved to be capable to 307 survey 5000 to 12000 m² per hour with a 0.5 m spacing and reveal at least as many 308 derivative of the signal (Figure 11). The application of the DRP gives theoretically the 310 exact horizontal position of the sources, unlike a single reduction which leads to a 311 residual skewness. If the difference or even the use of a reduction can be negligible for 312 very shallow sources, it is not the case with deeper sources, as shown in Figure 8 and 313 the comparison between Figure 7 and9. 314

Conclusion 315

The study both validates the application of an innovative approach to magnetic 316 prospections in archaeology and reveals important information on the site of Qasr 317 ʿAllam. 318

The use 3-axis fluxgate magnetometers and associated potential field 319 transformations proved to be efficient to reveal information on both deep and shallow 320 archaeological sources at a large and rapid scale. The results obtained in Qasr ʿAllam 321 offer two prospects for further development: 1-doubling the speed of acquisition by 322 doubling the number of magnetometers; 2-using the compensation ability to develop a 323 smaller device which allows a few centimetres spacing between sensors for high 324 precision small scale surveys. 325

In Qasr ʿAllam, the geophysical survey strengthens the hypothesis of the 326 archaeologists. It locates remains of large scale buildings positioned in the expected 327 area, whose general plan and direction are consistent with the hypothesis of a religious 328 complex which combines a main cultic centre (totally covered by sediments) with 329 economic and domestic facilities (of which parts were previously excavated). The 330 accurate positioning of probable archaeological structures has allowed setting up 331 targeted excavations that led to important results: parts of the irrigation network were 332 already used from the 8 th or 7 th century B.C. in the vicinity of the buildings, the site was 333 used for cultic purposes to at least the 2 nd century B.C. and was impacted by a rapid 334 environmental change from humid to arid in the latest periods of occupation. Without 335 the results provided by the magnetic mapping, the thickness of the sedimentary deposits 336 would have discouraged any attempt to explore the underground by means of the 337 classical archaeological digging methods. A next step would be to investigate further 338 the supposed cultic centre and the associated environmental change to find further 339 chronological and functional data. According to its size and the thickness of sediment, 340 From left to right, map of the magnetic anomaly for a sampled zone of Qasr 'Allam (Figure 7), reduction to the pole of the regional magnetic field and double reduction to the pole. The IGRF-11 was used to obtain the direction to the regional magnetic field and the magnetization direction is set equal to the IGRF direction.

  0.8 m above the ground highly difficult without an intense 98

  of the fluxgate magnetometers is of being relative devices. 128

-- 202 -

 202 the shades are evenly distributed on the map. Thus, both small and strong 189 magnetic anomalies can be represented on a unique map, as shown in Figure7.190 From both representations (Figure6-7), different kind of anomalies can be observed 191 on the site. Depending on their wavelength and shape, they can be ranked as follows. 192 Dipolar anomalies: the strongest one in the west is due to a metallic pole; the 193 others are due to pieces of metal which are scattered everywhere on the site, 194 showing no particular distribution. 195 Short wavelength lineation (about 1 m and less): they are the most common 196 anomalies and can be sorted in different subgroups. In the southern part, a high 197 concentration of curved lines following roughly N-S and E-W orientations is 198 present. A similar pattern can be seen in the northern part, though in much 199 smaller quantities. In the central part, the lines are straighter and follow an 200 orientation similar to the one of the large wavelength lineation surrounding 201 them. Large wavelength lineation (about 10 m): they approximatively draw two 203 rectangles of 150 x 100 and 125 x 100 m in the central part of the map. Their 204 orientation is of a few degrees east. 205

  and ݒ are the wavelengths associated with ݔ and ݕ directions and ݊ is the order 246 of derivation. Figure10corresponds to the map obtained after computing the vertical 247 gradient of the DRP. It can be observed that the different lines are indeed enhanced and, 248 most importantly, new lineations appear, especially in the central area. 249

  cultic complex and that these farming devices most probably 277 belonged to the religious estate. 278

  remains as a gradiometer through the use of the vertical 309

  need the combination of archaeological excavations and a more 341 detailed geophysical method. In consequence, these conclusions encouraged the 342 Egyptian Supreme Council of Antiquities (SCA) to delimit an area to be protected in 343 2014 to avoid the destruction of remains by the fast progression of agricultural fields. 344 Acknowledgement 345 Some of the results presented in this paper rely on the data collected at Tamanrasset 346 observatory. We thank Centre de Recherche en Astronomie, Astrophysique et 347 Geophysique as well as Institut de Pysique du Globe de Paris, for supporting its 348 operation and INTERMAGNET for promoting high standards of magnetic observatory 349 practice (www.intermagnet.org). The authors would like to thank the Initiatives 350 d'Excellence (IdEx, Programme Investissements d'Avenir) of the University of 351 Strasbourg for their financial support as well as Laurent Ameglio, Daniel Sauter, 352 Nicolas Florsch, Chris Gaffney and the two anonymous reviewers for their advices and of the oasis of Bahariya on a topographic map of Egypt. B-Localization of El Qasr-Bawiti on a topographic map of Bahariya. C-Localization of the site of Qasr 'Allam on a satellite image of El Qasr and Bawiti. Topography from SRTM90 data available at http://srtm.csi.cgiar.org/ (Jarvis et al., 2008). Satellite image from the satellites Quickbird taken in 2003 (DigitalGlobe Incorporated, Eurimage SPA licence). 164x180mm (300 x 300 DPI) of the excavated dwelling (red) and the irrigation structures of the pictures D and E (yellow) on a satellite image of Qasr 'Allam (DigitalGlobe Incorporated, Eurimage SPA licence). B-Architectural plan of the excavated dwelling and orientation of the picture C. Blue and red colours corresponds to buildings of a first and second period of occupation. C-Lateral view of the cellular foundation platform of the second period of occupation. D-Traces of an underground channel. E-Traces of a well. F-Inside of an underground channel similar to the ones of the site and excavated in the oasis of Kharga (Wuttmann et al., 1996axis fluxgate magnetometer (Bartington Inc., Mag-03 MC). B-Custom electronics with 8 magnetometer inputs developed by Institut de Physique du Globe de Strasbourg (IPGS). C-Multi-sensor device developed by IPGS. 90x54mm (300 x 300 DPI) Intensity of the magnetic field measured by one magnetometer during the calibration and compensation process of the device before (blue) and after (red) corrections. Computed error parameters are given in the lower part of the figure. 112x85mm (600 x 600 DPI) Satellite image of Qasr 'Allam (DigitalGlobe Incorporated, Eurimage SPA licence). The area of the geomagnetic prospection is delimited by the white line. The area of the excavated dwelling is delimited by the red line. 126x107mm (300 x 300 DPI) Map of the magnetic anomaly represented with a linear grayscale bar ranging from -25 to 25 nT. 148x147mm (600 x 600 DPI) Map of magnetic anomalies represented with an equi-populated greyscale bar. The area delimited by the white line corresponds to the area displayed in Figure 8. 148x147mm (600 x 600 DPI)

  Map of the magnetic anomaly after double reduction to the pole represented with an equi-populated greyscale bar. 148x147mm (600 x 600 DPI) Map of the vertical derivative of the magnetic anomaly after double reduction to the pole represented with an equi-populated greyscale bar. The enlargement corresponds to the area delimited in red. 125x104mm (600 x 600 DPI) of the vertical gradient computed from the data measured with the device developed by Institut de Physique de Globe de Strasbourg (using a vertical derivative). B-Map of the vertical gradient computed from the data measured by teams directed by Tomasz Herbich with a vector gradiometer Geoscan FM256 during previous surveys[START_REF] Herbich | Geophysical surveying in Egypt: periodic report for[END_REF]Interpretative map of the archaeological remains from the geomagnetic prospection. The hydraulic structures are represented in blue, the buildings in black. The dotted and plain red lines mark the minimal limits of the dwelling known before and after the study. The areas highlighted in green correspond to three excavations numbered[START_REF] Wuttman | Premier rapport préliminaire des travaux sur le site de 'Ayn Manawir (oasis de 449 Kharga)[END_REF] 16 and 17. 133x119mm (300 x 300 DPI)

http://mc.manuscriptcentral.com/arp Archaeological Prospection

The study was sponsored by the Initiatives d'Excellence (IdEx, Programme 15 Investissements d'Avenir) of the University of Strasbourg.


Thibault Broux

Benoit Fleutot

Rénald David

Annelise Brüll

Philippe Veber

François Fauth

Matthieu Courty

Laurence Croguennec

Christian Masquelier
email: christian.masquelier@u-picardie.fr

Benoît Fleutot

Temperature dependence of structural

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

The increasing need for electrochemical energy storage, either for portable electronic devices or for larger-scale applications such as hybrid electric vehicles or static renewable energy storage systems, causes renewed interest in alternatives to Li-ion batteries, in order to overcome drawbacks associated to the availability and prize of lithium resources. [START_REF] Tarascon | Is lithium the new gold?[END_REF] In this context, Na-ion batteries is an emerging field owing to the lower price and very large earth-abundance of sodium. [START_REF] Palomares | Na-ion batteries, recent advances and present challenges to become low cost energy storage systems[END_REF] In terms of energy density, Naion batteries hardly compete with Li-ion ones due to the intrinsic properties of Na: a less negative standard reduction potential (-2.7 V vs SHE for the Na + aq /Na against -3.04 V for the Li + aq /Li one) and a higher molecular weight. Thus the Na-ion technology can be addressed for targeted applications such as domestic energy storage and load-leveling applications for the grid.

Among several polyanionic-based electrode materials, [START_REF] Jian | Superior Electrochemical Performance and Storage Mechanism of Na 3 V 2 (PO 4 ) 3 Cathode for Room-Temperature Sodium-Ion Batteries[END_REF][START_REF] Sauvage | Crystal structure and electrochemical properties vs. Na+ of the sodium fluorophosphate Na 1.5 VOPO 4 F 0.5[END_REF][START_REF] Shakoor | A combined first principles and experimental study on Na 3 V 2 (PO 4 ) 2 F 3 for rechargeable Na batteries[END_REF][START_REF] Liu | Preparation of NaV 1-x Al x PO 4 F cathode materials for application of sodium-ion battery[END_REF][START_REF] Chihara | Cathode properties of Na 3 M 2 (PO 4 ) 2 F 3 [M= Ti, Fe, V] for sodium-ion batteries[END_REF][START_REF] Kim | Na 2 FeP 2 O 7 as a Promising Iron-Based Pyrophosphate Cathode for Sodium Rechargeable Batteries: A Combined Experimental and Theoretical Study[END_REF][START_REF] Masquelier | Polyanionic (phosphates, silicates, sulfates) frameworks as electrode materials for rechargeable Li (or Na) batteries[END_REF] one of the most promising family of compounds turns out to be the sodium-vanadium fluorinated oxy-phosphate Na 3 V 2 (PO 4 ) 2 F 3-y O y where y can vary from 0 to 2. [START_REF] Serras | High voltage cathode materials for Na-ion batteries of general formula Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF][START_REF] Serras | Electrochemical performance of mixed valence Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x /C as cathode for sodium-ion batteries[END_REF][START_REF] Park | A new high-energy cathode for a Na-ion battery with ultrahigh stability[END_REF][START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na 3 (VO 1-x PO 4 ) 2 F 1+2x (0 ≤ x ≤ 1): Combined First-Principles and Experimental Study[END_REF][START_REF] Bianchini | Comprehensive Investigation of the Na 3 V 2 (PO 4 ) 2 F 3 -NaV 2 (PO 4 ) 2 F 3 System by Operando High Resolution Synchrotron X-ray Diffraction[END_REF][START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF][START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF][START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na 3 V 2 (PO 4 ) 2 F 3[END_REF][START_REF] Song | Multifunctional dual Na 3 V 2 (PO 4 ) 2 F 3 cathode for both lithium-ion and sodium-ion batteries[END_REF][START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] This whole range of compositions from V III -rich (y = 0) to V IV -rich (y = 2) can be oxidized to an average oxidation state of V IV to V V respectively, by the deintercalation of two sodium ions. For instance in Na 3 V 2 (PO 4 ) 2 F 3 (y = 0) the extraction of 2 Na + ions was experimentally demonstrated with two main voltage-composition plateaus at around 3.7 and 4.2 V vs. Na + /Na for a theoretical energy density of 507 Wh/kg [START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na 3 V 2 (PO 4 ) 2 F 3[END_REF][START_REF] Barker | Hybrid-ion a lithium-ion cell based on a sodium insertion material[END_REF][START_REF] Barker | Li 4∕3 Ti 5∕3 O 4 ‖ Na 3 V 2 (PO 4 ) 2 F 3 : An Example of a Hybrid-Ion Cell Using a Non-graphitic Anode[END_REF] (128 Ah/kg at an average potential of 3.95 V), competitive with that delivered by LiFePO 4 in Li-ion batteries. As recently depicted, a small amount of oxygen in the initial material (i.e. slightly oxidized) induces significant differences on the electrochemical properties although they are isostructural in the range 0 ≤ y ≤ 0.5. [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] In this range of compositions, Na 3 V 2 (PO 4 ) 2 F 3-y O y crystalizes in the Amam space group at room temperature where the structure consists of a tridimensional framework of V 2 O 8+y F 3-y bi-octahedra which are connected by PO 4 tetrahedra. This framework provides large tunnels where Na + ions are mobile upon extraction/insertion reactions. Regardless the oxidation state of the initial material, the system Na 3 V 2 (PO 4 ) 2 F 3-y O y is reported to undergo an order-disorder transition at 122 °C for the V III -rich (y = 0) composition [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] and at 230 °C for the V IV -rich (y = 2) composition. [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] On the other hand, from the electrochemical point of view, the amount of oxygen in the pristine material induces significant modifications of the electrochemical behaviour, as previously reported. [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] The main drawback of V IV defects is the decrease of the average potential vs. Na upon Na + extraction. Nevertheless, higher capacity as well as lower polarization are observed for the y = 0.5 composition that may reveal better ionic and/or electronic conductivity. In order to obtain a deeper understanding of the transport properties of Na 3 V 2 (PO 4 ) 2 F 3 and oxidized related phase, two samples Na 3 V 2 (PO 4 ) 2 F 3 and Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 have been prepared and studied as a function of temperature via in situ synchrotron X-ray powder diffraction (SXRPD) and thermogravimetric analysis combined with differential scanning calorimetry (TGA-DSC). These results are confronted with temperaturecontrolled electrochemical impedance spectroscopy, on sintered pellets and single crystals, to evaluate the contributions of ionic and electronic conduction.

Experimental

The two Na 3 V 2 (PO 4 ) 2 F 3 and Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 powder samples were synthetized according to the method already described in details elsewhere. [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] NaF, Na 2 CO 3 , V III PO 4 and V V OPO 4 precursors were mixed in stoichiometric proportions by ball milling and the resulting mixtures were heated at 750°C under Argon for 2 hours. The O content in our materials was extrapolated from XRD, XAS, and NMR data, as described in details in [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] . As expected, the y = 0 compound Na 3 V 2 (PO 4 ) 2 F 3 has similar cell parameters to those already reported by Bianchini et al. [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] (a = 9.0285(1) Å, b = 9.0444(1) Å, and c = 10.7467(1) Å), and once again the orthorhombic distortion with a b/a ratio of 1.002 is confirmed.

Here the oxidized composition y = 0.5 is near to be tetragonal as the b/a ratio is as low as 1.0003 (a = 9.0323(1) Å, b = 9.0352(1)Å, c = 10.6847(1) Å) in line with the values reported in [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] .

Electrochemical tests were performed in CR2032-type coin cells. The positive electrodes were prepared from a slurry made of 80 wt% Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≤ y ≤ 0.5), 10 wt% carbon black, and 10 wt% polyvinylidene fluoride (PVDF) dispersed in N-methyl-2-pyrrolidone (NMP), casted on an Al foil and dried at 80 °C overnight. The loading of the active material on the electrodes was around 2.5 mg/cm². The negative electrode was sodium metal, whereas the electrolyte was home-made from a 1 M solution of NaPF 6 (Strem Chemical; 99%) in ethylene carbonate and dimethyl carbonate (EC:DMC = 1:1) with 3 wt% of fluoroethylene carbonate (FEC) as additive. The electrochemical cells were charged and discharged in galvanostatic mode, at a C/20 between 2.5 and 4.3 V vs Na + /Na corresponding to the exchange of 0.1 mol of sodium ions/electrons per hour. Galvanostatic intermittent titration technique (GITT) measurements have been performed at the beginning of the charge (i.e. near the as prepared compositions) and such as 10 minutes of C/25 galvanostatic charge were followed by a relaxation up to 1 mV/h. High angular resolution SXRPD data as a function of temperature from room temperature (RT) to 180 °C were collected using the MSPD diffractometer at ALBA (Barcelona, Spain). The powders were placed in a 0.5 mm diameter capillary and data recorded in Debye-Scherrer geometry with a wavelength of 0.9530 Å in the 2θ angular range of 1 -52 ° with a 0.006 ° step and an accumulation time of 5 minutes. As already reported by Bianchini et al. [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] for the structural determination of Na 3 V III 2 (PO 4 ) 2 F 3 (y=0), the use of very high angular resolution techniques is essential as a very small orthorhombic distortion exists. Their detection is important to reveal significant changes in the distribution of sodium ions within the 3D framework and thus in the interpretation of electrochemical processes.

TGA-DSC has been performed in inert atmosphere with heating/cooling ramps of 10 °C/min under argon. A first heating/cooling cycle between RT and 150 °C has been carried out to remove possible adsorbed water that might influence TGA-DSC curves then a cycle from RT to 500 °C is performed to highlight temperature dependent structural transitions. No significant weight loss or gain was detected by TGA (<0.5%) that I hence not shown.

The growth of Na 3 V 2 (PO 4 ) 2 F 3 single crystals was performed by the flux method from a Na 3 V 2 (PO 4 ) 2 F 3 solute and a NaF solvent acting as a self-flux. As previously reported, [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] the pristine powder of Na 3 V 2 (PO 4 ) 2 F 3 was obtained by planetary milling between NaF and VPO 4 . Here, an excess of NaF was added in order to obtain a 75 %mol of Na 3 V 2 (PO 4 ) 2 F 3 and 25 %mol of NaF mixture for the pellet which was sintered at 800 °C during 1 hour under 95%/5% Ar/H 2 . This sintered pellet was placed into a platinum assembly sealed under primary vacuum [START_REF] Albino | Growth and Characterization of Centimeter-Sized Ba 2 LaFeNb 4 O 15 Crystals from High-Temperature Solution under a Controlled Atmosphere[END_REF] . The platinum assembly was first heated for 24 h at 1050 °C in a vertical resistive furnace, then cooled down to 950 °C at 0.5 °C.h -1 within a longitudinal thermal gradient about 0.5 °C.cm -1 and finally cooled down to room temperature at 120 °C.h -1 . The as-grown piece was cut into a single crystal (2.4 x 3.1 x 1.4 mm 3 ) oriented along 3 crystallographic directions [100], [010] and [001] checked by Laue X-rays backscattering.

For electrochemical impedance spectroscopy of Na 3 V 2 (PO 4 ) 2 F 3 and Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 , the powders were pressed into pellets of 10 mm diameter by means of a uniaxial press (700 MPa). The pellets were sintered at 650 °C for 1 hour under argon (to reach 82 % compactness), polished and then metalized on each face by gold sputtering used as ion-blocking electrodes. After being dried at 120 °C under vacuum during one night, the pellets were transferred into a dry glove-box to be introduced into an air tight high temperature sample holder (HTSH) to perform AC impedance measurements under argon.

The samples were thus maintained out of contact with oxygen and/or moisture during the AC impedance measurements which were performed, at various stabilized temperatures ranging from RT to 250 °C (upon heating and cooling in steps of 15 °C), outside the glove-box, by means of a MTZ-35 frequency response analyser and the specific high temperature furnace HTF-1100 developed by BioLogic. A frequency range of 30 MHz to 10 mHz (20 points per decade and 10 measures per points) and an excitation voltage of 0.1 V were applied during the measurements. From the Nyquist and Phase-Bode plots of the complex impedance, the total grains and grain boundaries conductivities (ionic and electronic) were obtained as well as the activation energy. The Hebb-Wagner method was used to extract the grain electronic conductivities by DC measurement at different potentials: 0.1, 0.2, 0.3, 0.4, 0.5 V with 7 h of current stabilisation wait for each potential. The same types of experiments were performed on the Na 3 V 2 (PO 4 ) 2 F 3.0 single crystal along the [001] Amam direction: gold contacts were sputtered on opposite faces along this direction and the single crystal was placed in the air tight high temperature sample holder (HTSH) to perform AC/DC measurements in temperature with the same method that described previously for Na 3 V 2 (PO 4 ) 2 F 3 and Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 pellets.

Results and discussion a. Electrochemical Properties

As previously reported [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] the amount of oxygen in the pristine material Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≤ y ≤ 0.5) induces significant changes in the electrochemical performances. Figure 1 shows the voltage composition data obtained for Na 3 V 2 (PO 4 ) 2 F 3-y O y (y = 0 or 0.5) during their second cycle in Na batteries at the rate of C/20. These electrochemical data are similar to each other with two main voltage domains at around 3.65 and 4.15 V versus Na + /Na and a voltage jump around x = 2. In fact, in agreement with our previous study, [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] the average potential of the cell decreases as y increases : from 3.89 V for y = 0 to 3.83 V for y = 0.5. This effect was ascribed to the formation of highly covalent vanadyl-type bonds (V=O) 2+ at the apex of the bi-octahedra V 2 O 8 F 3-y O y that "continuously" replace the more ionic V-F bonds as y increases. A more covalent environment around the transition metal ion raises the energy of its antibonding levels closer to the Fermi energy of sodium and thus induces a decrease in voltage for the involved redox couple versus Na + /Na. Thus the electrochemical voltagecomposition data differs significantly in their shape depending on the oxygen content: the more oxidized the compound, the "smoother" their cycling profiles. A small change in the initial oxygen content composition of the material and thus in their vanadium average oxidation states has a major impact on the phase diagram stabilized upon cycling. It evolves from a complex series of biphasic domains and solid solutions for y = 0, as determined for Na 3 V 2 (PO 4 ) 2 F 3 by Bianchini et al. [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] to an "extended solid solution" for y = 0.5.

In addition, another noteworthy feature of the electrochemical performances is the decrease of the hysteresis between charge and discharge as y increases. To verify this, galvanostatic intermittent titration technic (GITT) was used to observe the evolution of the ohmic drop as a function of oxygen amount in the pristine material at the beginning of the charge (i.e. near the as prepared compositions).

As presented in Figure 1, the lower polarization resistance for the oxidized compound is also confirmed by a lower iR drop in similar conditions. Besides, the lower relaxation time for the oxygenrich composition reveals a faster return to equilibrium. At a first glance the smaller relaxation time for the y = 0.5 composition might be ascribed to better transport properties (ionic and/or electronic conductivity) which also may be responsible for higher capacity and lower polarization. Thus the amount of oxygen in the pristine material that induces a mixed valence V III /V IV improves electrochemical properties despite the lower voltage. [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF]

b. Temperature dependence of the crystal structure

The DSC data collected on Na 3 V 2 (PO 4 ) 2 F 3 and Na 3 V 2 (PO 4 ) 2 F 2.5 O .5 when heated under argon are presented in Figure 2. They clearly show endothermic peaks for both compositions without any mass change which corresponds to a temperature dependent structural transition around 130 °C. More precisely, the transition temperature varies from 125 °C to 135 °C for Na 3 V 2 (PO 4 ) 2 F 3 to Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 respectively. Previous works on the y = 0 [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] and y = 2 [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] compositions reported transition temperatures of 122 °C and 230 °C respectively which is in good agreement with our observations, i.e. an increase of the transition temperature with the oxygen content.

Concerning Na 3 V 2 (PO 4 ) 2 F 3 , the thermal effect observed by DSC can be attributed to the order-disorder transition from the RT Amam orthorhombic space group to the high temperature I4/mmm tetragonal space group already mentioned by Bianchini et al. [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] Na 3 V 2 (PO 4 ) 2 F 3-y O y 0 ≤ y ≤ 0.5 compositions are isostructural at RT and crystallize in the orthorhombic space group Amam with the distribution of the Na + ions among a larger number of crystallographic sites, suggesting also an increased ionic mobility within the tunnels of the three-dimensional structure.

Figure 3 displays the temperature-controlled SXRPD data for Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 , from 40 °C to above the transition temperature (137 °C). A progressive decrease of several peak intensities is observed. The (011), ( 211) and ( 031) reflections (among others not displayed here) satisfying the condition k + l = 2n allowed in a A-centered symmetry progressively vanish to account for the transition from the Amam to the I4/mmm space group, similarly to Na 3 V 2 (PO 4 ) 2 F 3 but at higher temperature, in accordance with the DSC data described previously.

As expected, the present y = 0 compound Na 3 V 2 (PO 4 ) 2 F 3 has similar cell parameters to those already reported by Bianchini et al. [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] . In both cases, as shown in Figure 4, a and b cell parameters are progressively merging as the temperature is increased. Furthermore the smaller orthorhombic distortion and the higher disordered sodium distribution observed for the oxygen-rich composition may explain the lower enthalpy of the order-disorder phase transition as displayed in Figure 2. On the other hand the temperature dependence of the c parameter is straightforward as it linearly increases with temperature (thermal expansion).

As presented in Figure 5, the structure of Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≤ y ≤ 0.5) consists of a tridimensional framework of V 2 O 8 F 3-y O y bi-octahedra, which are connected by PO 4 tetrahedra. For y > 0, the substitution of oxygen for fluorine occurs at the apex of the V 2 O 8 F 3-y O y bi-octahedra, which induces the formation of shorter covalent vanadyl-type bonds as terminal bonds and thus the contraction of the bi-octahedra. Regardless the F/O ratio, the framework of Na 3 V 2 (PO 4 ) 2 F 3-y O y is characterized by large tunnels where the Na + ions are mobile upon the intercalation and deintercalation reactions. Compared to Na 3 V 2 (PO 4 ) 2 F 3 , an additional sodium site Na( 4) is necessary to describe the structure of Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 . [START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≦ y ≦ 0.5) on its structural and electrochemical properties[END_REF] At room temperature, Na( 1) is localized at the center of a pyramid with an occupancy around 85% (figs. 5 and6) whereas the remaining Na + ions reside in pyramidal (Na(2) and Na( 4)) or capped prismatic (Na(3)) sites, but not at their center. Because of their vicinity, and to minimize the electrostatic repulsions, neighboring Na(2), Na(3), and Na(4) positions cannot be occupied simultaneously. For the same reason, the more distant a Na site is from its equivalent position, the more occupied appears this site. In fact, the sodium ions are located within the whole torus provided by the polyanionic framework similarly to what has been reported before for the high temperature structure of Na 3 V 2 (PO 4 ) 2 F 3 . [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] Rietveld refinements of temperature-controlled SXRPD of Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 give new insights on how the transition proceeds. First the framework do not undergoes major structural modifications. As highlighted in Figure 6, from RT to 40 °C, no major change is observed in Na site occupancies. From 40 °C to the transition temperature (137 °C) the Na(4) site occupancy increases concomitantly with the decrease of the Na(1) site. This progressive smooth phase transition involving no major structural rearrangement is of the second-order (orderdisorder) type.

c. Temperature dependence of electronic and ionic transport properties

The characteristic complex impedance spectra obtained at various temperatures for Na 3 V 2 (PO 4 ) 2 F 3 are given in Figure 7a in Nyquist coordinates. An asymmetric semicircle is observed classically at high frequencies, ascribed to the Na 3 V 2 (PO 4 ) 2 F 3 ceramic resistance. At low frequencies, a straight line with an angle of 45° vs. the horizontal real axis is observed, as a clear signature of a mixed ionic/electronic conductor [START_REF] Delaizir | The stone age revisited : building a monolithic inorganic lithium-ion battery[END_REF] . A fast reduction of the asymmetric semicircle diameter upon heating reveals the enhancement of the total conductivity as the temperature increases. This asymmetric semicircle indicates the presence of two separated phenomena. Hence, the spectra were fitted by an equivalent circuit (Figure 7b) composed by an initial resistor R 0 (for the device and current collectors resistance), in series with i) a system constituted by one resistor R 1 in parallel with a constant phase element CPE1 for the non-ideal capacitance, ii) a second R 2 / CPE2 system (attribution will be discussed later) and iii) a Warburgh element for the diffusion. An example of fit of the data with this equivalent circuit is presented in Figure 7b. The value of the n factor for the pseudo-capacitor CPE1 is around 0.9 for all temperatures. The final capacitance extracted value for the corresponding capacitor is temperature independent and around 2.5 10 -10 F.cm -2 . The first semicircle at higher frequency is thus attributed to the bulk conductivity of Na 3 V 2 (PO 4 ) 2 F 3 . The n factor of the second CPE in parallel with the third resistor R 2 is around 0.7 with a CPE value around 5 10 -9 F.s n-1 , characteristic of material grain boundaries.

The total, grains and grain boundaries conductivities were calculated from where d is the pellet thickness, A the pellet surface area and R x the respective resistances deduced from the Nyquist and Phase Bode plots. The evolution of these different conductivities as a function of temperature is

shown in Figure 8. The bulk (grains) conductivity (electronic and ionic) is very close to the value of the total conductivity. The grain boundaries appear thus not detrimental to these measurements. The determination of the electronic conductivity of our bulk material, on the same pellet, allowed the extraction of the ionic conductivity, from the difference between grains conductivity and grains electronic conductivity.

The Hebb-Wagner method was used to determine the bulk electronic conductivity of our material. As shown in Figure 9a, a DC electric potential was applied across the sample sandwiched between two blocking electrodes (gold electrodes in the present study) and the current was monitored as a function of time. During the first instants of polarization at fixed potential, the peak current obtained initially decreased rapidly with time. For each potential polarization, the current reached a constant value after a certain time (~ 7 hours), as the signature of a partial electronic conductivity and in line with the straight line observed in the Nyquist diagrams (Figure 7a). The ohmic-law was verified through varying potentials (in our case 0.1, 0.2, 0.3, 0.4 and 0.5 V) and temperatures. The stabilized currents are plotted as a function of polarization potential and temperature in Figure 9b. As expected, a linear relationship between stabilized current and applied potential is obtained for each temperature. The ohmic-law was confirmed and for each temperature the electronic resistance was extracted.

The conductivities (total grains from AC impedance and electronic from DC measurements) follow a linear Arrhenius behavior when log(.T) is plotted as a function of 1/T as represented in Figure 10a for Na 3 V 2 (PO 4 )F 3 . From the slopes of the linear fittings, the values of the activation energies are 1.05 eV before 125 °C and 0.77 eV after for the total grains conductivity, whereas they are 0.79 eV and 0.68 eV respectively for the electronic part. A break of slope is observed for total grains and electronic conductivities at around 125 °C, which corresponds exactly to the temperature of the disappearance of along the [001] direction, which is expected from the structure itself, made of isolated vanadium bioctahedra connected through PO 4 groups. As a consequence, the ionic conductivity is essentially 2D, perpendicular to [001]. The increasing content in oxygen in Na 3 V 2 (PO 4 ) 2 F 3-y O y induces an increase of the structural order-disorder transition temperature combined with an increase of the electronic conduction with a lower activation energy, that latter being not affected by the structural transition which is essentially linked with the ionic mobility.

Conclusion

Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≤ y ≤ 0.5) compositions are isostructural and crystallize in the orthorhombic space group Amam, with an increasing disorder in the Na + ions distribution and a continuous oxidation of vanadium resulting in the formation of vanadyl-type bonds. The electrochemical signature obtained for the sodium cells Na//Na 3 V 2 (PO 4 ) 2 F 3-y O y evolves from a complex phase diagram with two voltage plateaus for y = 0, to solid solution type reactions with a "S-shape" for the two voltage domains for y = 0.5. The influence of the oxygen substitution for fluorine on the structural and transport properties of Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≤ y ≤ 0.5) has been investigated as a function of temperature. Changes in the crystal structure have been identified using high resolution Synchrotron powder X-ray diffraction, whereas the electronic and ionic conductivities have been determined for powders and single crystals and separated using Electrochemical Impedance Spectroscopy in AC-DC configuration. The orderdisorder transition occurs at 125°C for Na 3 V 2 (PO 4 ) 2 F 3 , with the formation of a more symmetrical tetragonal structure (space group I4/mmm) and a full disorder on the Na + sites. The temperature of this transition increases slightly with the content in oxygen. This transition affects only the ionic transport properties, with a significant decrease of the activation energy associated with a break of slope in the evolution of a and b cell parameters with the temperature. The oxygen substitution allows improving the electronic transport properties (higher electronic conductivity and smaller activation energy), which can explain the better electrochemical performances of the mixed valence Na 3 V 2 (PO 4 ) 2 F 3-y O y materials (with y > 0).

  (a = 9.0285(1) Å, b = 9.0444(1) Å, and c = 10.7467(1) Å), and once again the orthorhombic distortion with a b/a ratio of 1.002 is confirmed. Here the oxidized composition y = 0.5 is near to be tetragonal as the b/a ratio is as low as 1.0003 (a = 9.0323(1) Å, b = 9.0352(1) Å, c = 10.6847(1) Å) in line with the values reported in

Acknowledgments

The authors thank Matteo Bianchini (ILL/LRCS/ICMCB) for his technical assistance and fruitful discussions, and MSPD beamline at ALBA for Synchrotron X-ray diffraction. The authors also acknowledge the RS2E and Alistore-ERI networks for the funding of TB's postdoctoral fellowship.

This project has received funding from Région

Nouvelle Aquitaine, the French National Research Agency (STORE-EX Labex Project ANR-10-LABX-76-01 and SODIUM Descartes project ANR-13-RESC-0001-02), and the European Union's Horizon 2020 research and innovation program under grant agreement No 646433-NAIADES.

the orthorhombic form of Na 3 V 2 (PO 4 )F 3 . [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: a high-resolution diffraction study[END_REF] The ionic and electronic conductivity values obtained at various temperatures, as well as the corresponding activation energies, are summarized in Table 1. Na 3 V 2 (PO 4 ) 2 F 3 is a mixed-conductor electrode material with the same order of electronic (1.2.10 -10 S.cm -1 at 95°C) and ionic (5.10 -10 S.cm -1 at 95°C) conductivities below the order-disorder transition.

Above this order-disorder transition a difference of around one decade is observed in favor of the ionic conductivity (2.2.10 -7 S.cm -1 compared to 1.4.10 -8 S.cm -1 for the electronic conductivity at 200 °C). In parallel, the activation energy decreases more drastically for the ionic part (from 1.10 eV to 0.79 eV) than for the electronic one (0.79 eV to 0.68 eV) before and after the order-disorder transition respectively. This may be correlated with the strong anisotropic variation of a and b lattice parameters with T, as ionic motion essentially occurs in (001) planes. The lower variation of electronic transport properties from below to above the transition temperature could be correlated with the weaker variation of the c cell parameter as a function of temperature. Same types of measurements were performed for Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 : the obtained conductivity values are gathered in Figure 10b and in Table 1. Contrary to Na 3 V 2 (PO 4 ) 2 F 3 , the activation energy of electron transport within Na 3 V 2 (PO 4 ) 2 F 2.5 O 0.5 is not affected by the order-disorder structural transition, with a constant activation energy value around 0.58 eV. This can be related by the linear evolution of the c cell parameter presented in Figure 4, contrary to that of Na 3 V 2 (PO 4 ) 2 F 3 . It worth noticing that this activation energy (0.58 eV) is lower than those of Na 3 V 2 (PO 4 ) 2 F 3 . The electronic conductivity is higher (3.8 10 -10 S.cm -1 compared to 1.2 10 -10 S.cm -1 at 95°C) when NVPF is partially oxidized, which is attributed to the mixed valence V III /V IV in Na 3 V 2 (PO 4 ) 2 F 3-y O y with y > 0. Indeed, it induces the contraction of the c cell parameter along the bi-octahedra V 2 O 8+y F 3-y O y and could promote electron conduction. However, a break of slope is observed in the Arrhenius plot of total grains conductivities at around 135 °C. This temperature corresponds to the structural transition temperature highlighted by DSC and XRD. The activation energy for the ionic conductivity evolves from 0.97 eV to 0.72 eV below and above the order-disorder transition. This variation is lower than that of Na 3 V 2 (PO 4 ) 2 F 3 as is the variation of a and b lattice parameters. The slightly higher ionic conductivity in Na 3 V 2 (PO 4 ) 2 F 2.0 O 0.5 compared to that of Na 3 V 2 (PO 4 ) 2 F 3 is to be related with the smaller degree of orthorhombicity (hence higher disorder) at a given T.

To link the ionic and electronic conduction properties with the crystallographic directions of NVPF, same types of measurements were performed on a single crystal of Na 3 V 2 (PO 4 ) 2 F 3 , along the [001] direction with coupled studies in AC and DC (Figure 11). Due to the shape of the single crystal, we were able to obtain data only above 185 °C. The overall data overlapped those obtained for Na 3 V 2 (PO 4 ) 2 F 3 pellets by DC measurements showing thus that the electronic conduction occurs only