Virginie Boutueil
email: virginie.boutueil@enpc.fr

Luc Nemett
email: luc.nemett@enpc.fr

Thomas Quillerier
email: thomas.quillerier@enpc.fr

Trends in Competition among Digital Platforms for Shared Mobility: Insights from a Worldwide Census and Prospects for Research

Keywords: Boutueil, Nemett, and Quillerier Shared Mobility, Digital Platforms, Geographic Distribution, Competition, Classification

Mobility systems in metropolitan areas in both the Global North and the Global South have entered an era of rapid change since the early 2010s under the influence of mobile information and communication technologies (ICTs). Mobile ICT-based shared mobility platforms have been filling some of the gaps in transport supply left by historical modes of transport (i.e., private cars, public transit, and for-hire services). Shared mobility digital platforms are a subcategory of mobility applications that give individual customers direct and full access to one or several shared mobility services. Based on a worldwide systematic census, this paper documents the diversity of services provided by such platforms, then analyzes the trends in geographic distribution and competition among platforms across the world's metropolises. It proposes a new classification of shared mobility services. Since innovations in shared mobility are also taking a leading place in the Global South, future research avenues in this field are discussed in an effort to break away from the prior focus of the scientific literature on the Global North.

The census brings out four original findings. First, the rise of shared mobility digital platforms is a worldwide metropolitan phenomenon transcending the traditional distinction between the Global North and the Global South. Second, emerging countries have become clusters for innovation and competition among platforms. Third, three types of shared mobility digital platforms are identified based on geographic reach (local, regional, or global). Fourth, shared mobility digital platforms providing for-hire services are the most widespread in the world.

INTRODUCTION A Boom in Shared Mobility through Digital Platforms

Since the 2000s, shared mobility has been growing steadily in the countries of both the Global North and the Global South, filling the gaps left by historical modes of transport -traditionally divided into private cars (or individual transport), public transit, and for-hire services (i.e., taxi, limousine transport, car rental)-through service diversification [START_REF] Cervero | Paratransit in America: Redefining Mass Transportation[END_REF][START_REF] Enoch | How a rapid modal convergence into a universal automated taxi service could be the future for local passenger transport[END_REF][START_REF] Shaheen | Shared Mobility: a Sustainability & Technologies Workshop[END_REF][START_REF] Behrens | Paratransit in African Cities: Operations, Regulation and Reform[END_REF][START_REF] Boutueil | Urban Mobility and the Smartphone: Transportation, Travel Behavior and Public Policy[END_REF]. From 2007 to 2010 the number of cities with car-sharing services increased from 600 to 1,100 worldwide [START_REF] Shaheen | Growth in Worldwide Carsharing: An International Comparison Transportation Research Record[END_REF][START_REF] Shaheen | Carsharing and Personal Vehicle Services: Worldwide Market Developments and Emerging Trends[END_REF]. ''Shared mobility'' is commonly accepted to refer to the shared use of vehicles (i.e., cars, vans, scooters, bicycles, airplanes, or boats), for the same trip or not, over a short or a medium period of time, on an ''as needed'' basis [START_REF] Shaheen | Shared Mobility: a Sustainability & Technologies Workshop[END_REF][START_REF] Boutueil | Urban Mobility and the Smartphone: Transportation, Travel Behavior and Public Policy[END_REF][START_REF] Shaheen | Mobility and the Sharing Economy: Potential to Overcome First-and Last-Mile Public Transit Connections[END_REF][START_REF] Sae | Taxonomy and Definitions for Terms Related to Shared Mobility and Enabling Technologies[END_REF]. Existing classifications for shared mobility cover different sets of services, and they sometimes use different taxons for the same travel mode (Figure 1). In 2018, the Society of Automotive Engineers (SAE International) released a standardized taxonomy based on a review of all existing classifications at the time [START_REF] Sae | Taxonomy and Definitions for Terms Related to Shared Mobility and Enabling Technologies[END_REF]. Twelve types of shared mobility travel modes were identified and their definitions clarified (Appendix 2): alternative transportation services (ATS), bike-sharing, car-sharing, courier network services (CNS), microtransit, pedicabs, personal vehicle-sharing, ride-sharing, ride-sourcing, scooter-sharing, shuttles, and taxis.

The growth in shared mobility has been fostered by the digital boom in mobile information and communication technologies (ICTs) [START_REF] Boutueil | Urban Mobility and the Smartphone: Transportation, Travel Behavior and Public Policy[END_REF]. As of 2019 there were 5.2 billion unique mobile phone subscribers in the world, meaning that 68% of the world's population used a mobile phone [START_REF]World Population Prospects[END_REF][START_REF]The Mobile Economy[END_REF].

Mobile ICTs have played a role in the restructuring of transport systems through the (re)emergence of shared mobility services better designed to meet the diversity of user needs [START_REF] Boutueil | Urban Mobility and the Smartphone: Transportation, Travel Behavior and Public Policy[END_REF][START_REF]Committee for Review of Innovative Urban Mobility Services[END_REF][START_REF] Eskenazi | L'Asie du Sud-Est, un Terrain d'Innovation par le Numérique pour la Mobilité ? Etudes de Cas à Partir[END_REF][START_REF] Aguiléra | Mobilité Connectée et Changemens dans les Pratiques de Déplacement[END_REF][START_REF]Roundtable Report 175: Regulating App-Based Mobility Services. Summary and Conclusions[END_REF]. Over the past decade in the field of transport and mobility, the rapid diffusion of mobile ICTs has led to the development of new service features (e.g., real-time location or navigation aid using Global Positioning Systems), new mobility services (e.g., free-floating car-sharing), and new business models (e.g., multisided market platforms for user-operator matchmaking) [START_REF]Committee for Review of Innovative Urban Mobility Services[END_REF][START_REF] Aguiléra | Mobilité Connectée et Changemens dans les Pratiques de Déplacement[END_REF][START_REF] Kortum | Free-Floating Carsharing: City-Specific Growth Rates and Success Factors[END_REF]. Shared mobility digital platforms are central to these developments. Shared mobility digital platforms are a subcategory of mobility applications that give individual customers direct and full access to one or several shared mobility services. Digital platforms are market interfaces that 'connect demand and supply' [START_REF] Nurvala | Uberisation' Is the Future of the Digitalised Labour Market[END_REF]. They have been documented to foster growth in many economic sectors by reducing the costs of creation, reproduction and distribution of goods or services through economies of scale, and raising returns on marketing expenditures and unit revenues through better customer knowledge and product personalization [START_REF] Nurvala | Uberisation' Is the Future of the Digitalised Labour Market[END_REF][START_REF] Acquier | Promises and Paradoxes of the Sharing Economy: An Organizing Framework[END_REF][START_REF] Beuscart | Plateformes Numériques[END_REF][START_REF] Levin | NBER Working Paper Series: The Economics of Internet Markets[END_REF][START_REF] Lobel | The Law of the Platform[END_REF]. Their introduction in the field of mobility has been one of the major changes of the past decade both in the Global North and the Global South.

Shared Mobility in the Global South and the Global North: The Challenges of Taxonomy

Post-colonial scientific literature has used the notion of the Global South -defined in the 1980s so as to overcome prior, purely economic classifications that presented some countries as lagging behind othersto put emphasis on the need to build research on, and by, this side of the world, rather than copying theories and analytical frameworks of the Global North onto the Global South [START_REF] Fleury | Pour une Géographie Sociale des Pays Emergents: Introduction du Dossier[END_REF][START_REF] Roy | Worlding the South[END_REF].

Shared mobility takes on specific forms in the Global South. Whenever the scientific literature discusses 'informal transport' [START_REF] Behrens | Paratransit in African Cities: Operations, Regulation and Reform[END_REF][START_REF] Cervero | Informal Transport in the Developing World. UN-Habitat[END_REF], what is at stake is in fact shared mobility, mainly in the form of motorcycle-taxis, minibus-taxis, motorized 3-wheelers, or pedicabs (also known as 'rickshaws'). Having been widely overlooked by the scientific literature on shared mobility, some of these services are not referenced in existing classifications, including the aforementioned SAE classification.

Shared mobility is a rather recent focus of the scientific literature [START_REF] Shaheen | Shared Mobility: a Sustainability & Technologies Workshop[END_REF][START_REF] Boutueil | Urban Mobility and the Smartphone: Transportation, Travel Behavior and Public Policy[END_REF][START_REF]Committee for Review of Innovative Urban Mobility Services[END_REF][START_REF]Roundtable Report 175: Regulating App-Based Mobility Services. Summary and Conclusions[END_REF], and some blind spots remain to be addressed. Indeed, the scientific literature on shared mobility has mainly focused on the Global North, notably the United States, and/or on some specific services, notably ride-sourcing [START_REF] Cervero | Paratransit in America: Redefining Mass Transportation[END_REF][START_REF] Shaheen | Shared Mobility: a Sustainability & Technologies Workshop[END_REF][START_REF] Tcrp/Feigon | TCRP Research Report 196: Private Transit: Existing Services and Emerging Directions[END_REF]. Few scientific studies have taken a closer look at shared mobility in countries or cities of the Global South [START_REF] Behrens | Paratransit in African Cities: Operations, Regulation and Reform[END_REF][START_REF] Cervero | Informal Transport in the Developing World. UN-Habitat[END_REF][START_REF] Shaheen | Bikesharing in Europe, the Americas, and Asia: Past, Present, and Future[END_REF][START_REF] Boutueil | Impacts and Challenges for Developing Countries[END_REF]. The failure to embrace the diversity of shared mobility in the countries and cities of the Global South puts the scientific community at risk of developing biased visions of, and partial taxonomies for, shared mobility worldwide. Besides, little research has endeavored to provide an overview of shared mobility services and even less for shared mobility digital platforms at a global level through systematic comparison across cities or countries, with a few notable exceptions for specific services, e.g., car-sharing (6-7) or bike-sharing [START_REF] Shaheen | Bikesharing in Europe, the Americas, and Asia: Past, Present, and Future[END_REF].

Research Objectives

This paper pursues five scientific purposes:

• Initiate a documentation of shared mobility digital platforms in the cities of the Global South;

• Document the diversity of shared mobility services listed on digital platforms and complement existing classifications;

• Provide an overview of the presence of shared mobility digital platforms in cities around the world to reduce geographic bias;

• Analyze the trends in competition among shared mobility digital platforms;

• Map out future research avenues in the field of shared mobility. This paper is organized into four sections. The first section introduces the data collection method and the extended shared mobility classification. The second section provides an overview of the census outcome and analyzes the rise in competition among shared mobility digital platforms worldwide. The third section further analyzes the geography of shared mobility digital platforms, and the competition between local, regional and global platforms. A final section highlights key research findings and discusses future directions for research.

METHODS

Data Collection

Platform Census

The authors conducted a worldwide systematic census of shared mobility digital platforms every year in April-May over three consecutive years (2018-2020). An exploratory round of data collection was undertaken in 2018, whereby the authors inventoried the localities where the shared mobility digital platforms with more than 10,000,000 downloads on Google Play had operations. From 2019 onwards, the census was moved to a more extensive approach, whereby all shared mobility digital platforms with more than 100,000 downloads were inventoried together with their networks of localities.

For the purposes of this research, mobility applications available for download from Google Play are considered as shared mobility digital platforms if they give individual customers direct and full access to one or several shared mobility services. Mobility applications that only provide services to, or for, mobility, such as navigation applications (e.g., Waze) or trip-planning applications (e.g., Citymapper), are not included in the scope of shared mobility digital platforms. Besides, mobility applications that only provide integration/brokerage functions for other services (with no original shared mobility services added) were also excluded to avoid double counting of services.

Platforms were identified using Google Play and other internet search engines for a large set of shared mobility keywords -including cab, car-pooling, van-pooling, car-sharing, for-hire, motorbike, ondemand transport, paratransit, ride-hailing, ride-sharing, ride-sourcing, scooter-sharing, taxi, transportation network companies-, as well as their spelling and colloquial variants (e.g., ride-sharing, ride sharing, ridesharing). Those keywords were checked for in English, French, Spanish, German, Swedish and Russian. De facto, not having searched for applications in other languages such as Chinese is a potential gap in the research and a limitation of its findings. Geographic designations like the names of countries, regional or continental areas, were also used in the keyword search to circumvent possible geographic or linguistic biases in the search algorithm. Platforms present on the app distribution service of other mobile operating systems than Android were not integrated for two reasons: either the operating systems were not available in France (e.g., COS in China), or the number of downloads of the shared mobility digital platforms was not indicated (e.g., App Store, Huawei App Gallery). In March 2021, Android had a worldwide market share of 71.8%, compared to 27.4% for IOS and 0.8% for other mobile operating systems (source: https://gs.statcounter.com/os-market-share/mobile/worldwide). Despite the potentially uneven geographic distribution of mobile operating systems, Android's substantial global market share ensures limited bias in data collection.

Following this first step of platform identification, a table was created for each platform to collect further data on: the number of downloads for the application (retrieved from Google Play), the location of the company headquarters (retrieved from the company's official website, the commercial information platform Crunchbase, or LinkedIn), and the localities where the platform operated services. Most platforms release the list of localities where they operate services on their official websites. However, some platforms release incomplete or outdated lists, or no list at all. To complete the lists of localities, the authors e-mailed formal requests to the platforms and/or used press reviews and the platforms' pages on social networks (e.g., Facebook, Twitter, Instagram).

Data Harmonization and Processing

The authors proceeded to harmonize collected data for comparison and aggregation purposes. Indeed, platforms tend to list the localities in which they operate in heterogeneous ways, especially when it comes to large metropolitan areas or yet state-wide areas. Some tend to list cities in an exhaustive way, including for example, several suburban cities of a particular metropolitan area. Others tend to only mention the main city of a metropolitan area even though they operate beyond its administrative and urban borders. It was therefore decided: i) to focus on cities exclusively (and exclude rural localities), ii) to group the cities of a same metropolitan area under the name of the major political city in the area.

For the sake of comparison and aggregation, the authors restricted the analysis to the metropolitan areas of 500,000 inhabitants or more, using the UN database for metropolitan area populations and the census of the Chinese government for Chinese metropolitan areas (as UN database was not exhaustive for China) (sources: https://data.un.org/Data.aspx?d=POP&f=tableCode%3A240; http://www.stats.gov.cn/english/Statisticaldata/CensusData/). The lack of recent updates of demographic censuses by some countries may have led to the exclusion of metropolitan areas that only recently exceeded this threshold. Similar processing was applied to platforms that list vast operating areas (e.g., Uber's "Croatian Coast" operating area), or platforms that only listed countries rather than cities. In such cases, the census only accounts for metropolitan areas of 500,000 inhabitants or more in the operating area, if any.

After processing the lists of cities for aggregation at metropolitan level and filtering by population, individual platform tables were aggregated into a final cross table listing all the metropolitan areas in which a particular platform operates and all the platforms with operations in a particular metropolitan area.

Further processing was needed for the sake of data analysis and visualization. Metropolitan areas were geo-referenced and underwent a cartographic processing on QGIS and Adobe Illustrator with a view to illustrating the geographic footprint of the shared mobility digital platforms.

Classification of Shared Mobility Services

The scientific literature on shared mobility has seen many attempts at classification yet it has not reached a consensus on the exact definition of shared mobility and its related travel modes (1-5, 9, 12, 15, 24-25, 28-29). Figure 1 illustrates how shared mobility services included in each individual classification match with the types listed and defined in the SAE taxonomy [START_REF] Sae | Taxonomy and Definitions for Terms Related to Shared Mobility and Enabling Technologies[END_REF]. Based on all these existing classifications, the authors propose a new classification of shared mobility services (Figure 1). With a view to building broad categories (i.e., groups of service types), three criteria were used, based on the seating capacity of the vehicle, the need for the user to drive the vehicle, and the remuneration of the driver's service.

Following this approach, five main service categories could be established (Figure 1): vehicle-sharing services (e.g., bike-sharing, car-sharing), ride-sharing services (e.g., car-pooling, van-pooling), alternative transportation services (ATS) (e.g., microtransit, shuttles), for-hire services (e.g., ride-sourcing, taxis), and courier network services (CNS).

The following shared mobility services listed in prior classifications found no match in the types listed by SAE: 'jitney', 'dollar vans', 'flexible route-based services', and 'paratransit' (when considered as a service type). Indeed, these modes did not match SAE's definition for microtransit, which is restricted to 'technology-enabled' transit services (Appendix 1). These services were therefore grouped under a special type: 'conventional paratransit services'.

Other shared mobility travel modes identified in the 2019 and 2020 censuses did not match any of the types listed in existing classifications: motorcycle-and minibus-taxis were assimilated to the taxi type, motorcycle-pooling was included in the ride-sharing type, and e-scooter sharing was added as a new type within the vehicle-sharing service category [START_REF] Sae | Behavior of Electric Scooter Operators in Naturalistic Environments[END_REF][START_REF] Shaheen | Shared Micromoblity Policy Toolkit: Docked and Dockless Bike and Scooter Sharing[END_REF].

Figure 1 Proposed Shared Mobility Classification: Bring Existing Classifications into A General Taxonomy

Classification of Shared Mobility Digital Platforms According to Services Provided

Each shared mobility digital platform in the census was then classified along these broad categories according to the services it provided as of May 2020 on the application available for download from Google Play. Services provided by different applications related to the same mother brand were processed separately (e.g., Careem application provides a ride-sourcing service, whereas Careem Now and Careem Bike applications provide respectively a CNS service and a bike-sharing service).

Information on the services provided by each shared mobility digital platform was retrieved from the application, the official website, or through a review of media sources when the information was not available on the website (e.g., social networks of the shared mobility digital platforms; online newspapers, both mainstream and specialized). The classification of services is provided at platform level; it does not document possible differences in the portfolios of services provided by the same platform in different metropolitan areas.

Platforms fall in one of the following two categories:

• If the shared mobility digital platform provides services from a single category (e.g., Karwa Taxi only provides a taxi service, i.e., from the 'for-hire' category only), it is referred to as a specialist platform;

• If the shared mobility digital platform provides services from two or more service categories (e.g., Little provides ride-sourcing, shuttles and CNS services, i.e., from the 'ATS', 'for-hire' and 'CNS' categories), it is referred to as a multi-service platform.

Geographic Classification of Platforms

Platforms were classified according to their geographic reach, whether local, regional or global. A local platform operates in only one country, whereas a regional platform operates in several countries in a given sub-continental area, and a global platform operates in several countries and at least two subcontinental areas (Figure 2).

The metropolitan areas listed in the harmonized cross table were then classified into five categories depending on whether they hosted only local platforms, only regional platforms, only global platforms, a combination of local and regional platforms, or a combination of local/regional platforms and at least one global platform. The rise of platforms also translates into an overall growth in downloads, as illustrated in Table 1 for platforms with more than 5,000,000 downloads on Google Play. The list of platforms with more than 5,000,000 downloads grew from 18 in 2019 to 27 in 2020, with new platforms crossing every download threshold set by Google Play. Most remarkably, Uber Boutueil, Nemett, and Quillerier 10 inaugurated the 500,000,000+ category in 2020 and platforms like Rapido, Snapp! or Ситимобил entered the ranking directly in the 10,000,000+ category.

Out of 27 platforms with more than 5,000,000 downloads on Google Play, 14 are from the Global North (9 from Europe, 4 from the USA and 1 from South Korea), and 13 are from the Global South (5 from South Asia, 3 from Southeast Asia, 3 from the Middle East, 1 from Brazil and 1 from Egypt).

It should be noted that Didi Chuxing (in the 1,000,000+ category) is not listed in Table 1 because the platform does not rely on Google Play as their main downloading platform. The users of Didi Chuxing services appear to access services through social network WeChat, without downloading an extra application (source: https://www.saporedicina.com/english/how-to-use-didi-china/).

Classifying Platforms by Service Category: For-Hire and Vehicle-Sharing Services in the Lead

For-hire and vehicle-sharing services are the service categories most developed among platforms around the world (Table 2). As of May 2020, out of 236 shared mobility digital platforms, 121 provided for-hire services (51% of all shared mobility digital platforms), 111 platforms provided vehicle-sharing services (47%), 24 platforms provided CNS (10%), 18 platforms provided ride-sharing services (8%) and 12 platforms provided ATS (5%). From May 2019 to May 2020, the number of platforms increased for each service category, but the relative shares of each service category remained nearly unchanged.

In the 2020 census, 89% of shared mobility digital platforms were ranked in the 1,000,000+ download category or below, and 58% were ranked in the 500,000+ download category or below.

Platforms with vehicle-sharing services and platforms with for-hire services were overall the most represented in all downloads categories up to 10,000,000+ (Figure 3). De facto, they were the most represented platforms in the world in 2020. Within the 10,000,000+ download category, 14 platforms provided for-hire services, 4 platforms provided vehicle-sharing services, 3 platforms provided CNS and 1 platform provided ATS. Out of 18 platforms providing ride-sharing services, 10 platforms ranked in the 100,000+ download category, suggesting more local customer bases.

The number of metropolitan areas of shared mobility digital platforms also appears to be sensitive to the categories of services provided. As of May 2020, shared mobility digital platforms providing ridesharing services operated in 34 metropolitan areas on average, whereas those providing vehicle-sharing services operated in 14 metropolitan areas on average. Platforms providing for-hire services operated in 18 metropolitan areas on average. Of the 12 platforms providing ATS, 58% were from the Global South (e.g., Grab, Jugnoo) and one third were African platforms (e.g., Little, Swvl). Africa) and one platform provided services from five service categories (Jugnoo). The classification of the 39 multi-service platforms is provided in Appendix 2. Shared mobility digital platforms that provided for-hire services were most likely to be multi-service platforms.

Out of 39 multi-service platforms, 23 had their headquarter and operated in metropolitan areas of the Global South. Thus, countries of the Global South appear to be fertile ground for certain innovations in shared mobility digital platforms, including the diffusion of ATS (which may not be so 'alternative' after all) and the provision of services from multiple categories.

The Drivers of Growth for Shared Mobility Digital Platforms: Geographic Distribution and Service

Diversification

The size of shared mobility digital platforms (analyzed here through the proxy of download counts) appears to be correlated with the extent of their geographic footprint. As illustrated in Figure 4, platforms with more downloads tend to operate in a larger number of metropolitan areas, and vice versa.

Platforms in each of the 100,000+ and 1,000,000+ download categories operated in 6.6 and 18.7 metropolitan areas on average as of 2020, whereas platforms in the 100,000,000+ download category operated in 159 metropolitan areas on average. The size of platforms also appears to be correlated with the diversity of services they provide. As illustrated in Figure 5, platforms with more downloads tend to offer more diverse services and vice versa.

Platforms in the 100,000+ download categories offered 1.3 different services on average as of 2020, whereas platforms in the 100,000,000+ downloads category offer 3.4 different services on average. Geographic distribution and service diversification may be intertwined, as a correlation also exists between the number of metropolitan areas where a platform operates and the number of different services it offers. Two possible interpretations could be that the conquest of new markets brings up the need to adapt to diverse local needs through a diversified portfolio of services, or that large platforms with a wide market foothold and abundant resources operate a diversification of services they provide to users for greater market reach.

A GEOGRAPHY OF SHARED MOBILITY DIGITAL PLATFORMS The Development of Shared Mobility Digital Platforms: A Global Phenomenon Transcending the

North-South Divide

Shared mobility digital platforms have a very broad geographic footprint, covering all sub-continental areas in the world except Central Africa: 814 metropolitan areas from 116 countries (that is 60% of the 193 UN-recognized countries) have at least one platform operating services (Table 3). Despite an uneven distribution around the globe, shared mobility digital platforms now have a global reach (Figure 6) and they have definitely transcended the traditional divide between countries from the Global North and from the Global South. Besides significant clusters in Europe and North America, large emerging countries, like Brazil, China, India or Mexico [START_REF] Fleury | Pour une Géographie Sociale des Pays Emergents: Introduction du Dossier[END_REF], also stand out as fertile ground for shared mobility digital platforms. They could even fight for leadership with Northern countries in the upcoming years, as new local platforms are constantly emerging in those countries, including Grab and Ola which have a number of downloads close to that of Uber (Table 1).

Geographic Footprint of Multi-Service Platforms: The Emergence of Major Players

As already mentioned, service diversification appears to go hand in hand with geographic distribution.

Figure 7 illustrates the geographic footprint of the major multi-service platforms (more than 10,000,000 downloads on Google Play as of May 2020).

Out of these nine platforms, four operated in at least two continents as of 2020. Only Uber had a geographic footprint that covered all continents (354 metropolitan areas with more than 500,000 inhabitants). Russia and China were the only two major economies where Uber did not operate because local competitors Yandex.Taxi and Didi Chuxing enjoyed protectionist market conditions (and commercial agreements were reached among platforms accordingly). The geographic footprint of Taxify-Bolt was more limited, yet with 69 metropolitan areas spread across in Europe, North America, Central Asia, the Middle East and Africa. Both Uber and Taxify-Bolt operated in countries of both the Global North and the Global South. In contrast, inDriver (headquarters in Russia) only operated in countries of the Global South (44 metropolitan areas in South America, Africa and Southeast Asia). Easy Taxi A Cabify App was available in 39 metropolitan areas in South America and Central America, apparently Three types of shared mobility digital platforms can be distinguished based on the extent of their geographic footprint: local, regional and global platforms. Out of the 236 platforms inventoried in the 2020 census, 150 could be classified as local platforms, 50 as regional platforms, and 36 as global platforms. Looking into possible differences among service categories, the authors found that platforms providing ride-sharing services altogether had the most limited coverage of worldwide metropolitan areas, whereas platforms providing for-hire services had the most widespread coverage (18 platforms in 274 metropolitan areas in 27 countries, as compared to 122 platforms in 772 metropolitan areas in 115 countries) (Figures 8 and9).

Platforms with more than 100,000 downloads on Google Play providing ride-sharing services were noticeably absent from the United States of America and Canada, but also from the Middle East (except for Turkey) and from Africa (except for Zimbabwe). Besides, a clear-cut division could be observed among countries where ride-sharing services are operated, with some countries having only one local platform present (Argentina, China, Zimbabwe), other countries having only one regional platform present (countries in Scandinavia and Southeast Asia), and yet others having only one global platform present (most European countries, as well as Turkey, Australia, Mexico, and Brazil). Three countries displayed a more hybrid profile: India, Spain and France.

Shared mobility digital platforms providing for-hire services were present in 115 countries in the world (out of 193 countries), although noticeably absent from 30 of the 54 UN-recognized African countries. The ubiquity of for-hire services mostly resulted from a combination of global and local/regional platforms in most metropolitan areas in the world, from both the Global North (the United States of America, most of Europe) and the Global South (55 countries including emerging countries such as Brazil, India, Indonesia, and countries from all sub-continental areas). Global platforms were the only providers of for-hire services in a limited number of countries, for example, Bolivia, Canada, Finland, Mongolia, South Africa. Few countries relied on regional platforms only for for-hire services, e.g., Benin, Iraq, Kuwait, Myanmar, Pakistan, Togo, Zambia. On top of these, few countries relied on local platforms only for for-hire services, namely China, Iran and Zimbabwe. The exclusive reliance on a local platform in such large markets as China or Iran may point to political or economic protectionism.

The differences in geographic coverage and competition patterns between platforms providing for-hire services and platforms providing ride-sharing services may point to, for example, a stronger influence of local regulation or stronger cultural barriers in ride-sharing services compared with for-hire services. At a global level, the geographic distribution of shared mobility digital platforms highlights the importance of local contexts of the metropolitan areas and countries in which they are embedded (e.g., mobile penetration rate, regulation and public policies, pricing of competing services, platforms users).

In-depth case studies (comparative case studies where necessary) would therefore be useful to achieve a better understanding of the dynamics of competition and complementarity between platform-supported shared mobility services and other, preexisting services.

Through sorting platforms by their geographic reach (local, regional or global), the analysis revealed a diversity of competitive environments for local, regional and global platforms, most probably depending on public policies and strategic options taken by stakeholders. This would be the case if the combined presence of local/regional and global platforms providing the same service in a given area could be interpreted as a sign of open and fair competition (according to WTO standards). Further investigation would still be needed to better understand the competitive dynamics among local and global platforms, both in a given metropolitan area (i.e., agility, adaptation to local regulation and local mobility needs), and at global scale (i.e., economies of scale, learning curves, brand effect).

Shared mobility digital platforms providing for-hire and vehicle-sharing services displayed strongest growth momentum in terms of platform volume and metropolitan areas covered. Other service categories -ride-sharing, ATS and CNS-also grew steadily though at a slower pace, especially in the Global South for ATS. The relative paces of spreading of shared mobility services may result from different combinations of drivers of, and barriers to, digitalization relative to said service categories (including network effects, ownership structure, market concentration, stakeholder interplay).

The strategy of some shared mobility digital platforms to provide users with a growing number of services from different categories hints at the hypothesis that such platforms are on their way to becoming MaaS (Mobility-as-a-Service) platforms. As an illustration, Lyft in the U.S.A. offers for-hire and vehicle-sharing services in addition to allowing users to access public transport schedules on the same application.

The trend towards service diversification appears to be conducive of further platform growth as broader service portfolios allow to address a broader range of user needs.

Recent efforts to achieve a robust classification of shared mobility services have found an extension in this research, as new types of services have been documented -namely motorcycle taxis, motorcycle-pooling and e-scooter sharing-that call for the addition of new services to prior classifications, including SAE's [START_REF] Sae | Taxonomy and Definitions for Terms Related to Shared Mobility and Enabling Technologies[END_REF]. Interestingly, two of the suggested additions stem from shared mobility services that first emerged in the Global South. Explicit inclusion of these services in taxonomies can help foster dedicated research on their development and position in mobility systems. As far as taxonomy is concerned, the authors also want to bring forth their view that the concept of 'intermediate transport modes' may be preferable to that of 'shared mobility', as it is more explicit as to the expected role (and conditions for sustainability) of these modes relative to public transit and private car use (and other individual transport means).

"'Alternative transportation services' is a broad category that includes multi-occupant modes such as shuttles, vans, and small busses, as well as paratransit and microtransit services. Alternative transportation services are differentiated from public transit services by the lower volume of individuals moved on average per trip. In some contexts, alternative transportation services may also be referred to as 'demand responsive transport'"

Bikesharing

"Bikesharing provides users with on-demand access to bicycles at a variety of pick-up and drop-off locations for one-way (point-to-point) or roundtrip travel.

Bikesharing fleets are commonly deployed in a network within a metropolitan region, city, neighborhood, employment center, and/or university campus."

Carsharing

"Carsharing offers members access to vehicles by joining an organization that provides and maintains a fleet of cars and/or light trucks. These vehicles may be located within neighborhoods, public transit stations, employment centers, universities, etc. The carsharing organization typically provides insurance, gasoline, parking, and maintenance. Members who join a carsharing organization typically pay a fee each time they use a vehicle."

Courier Network Services (CNS)

"CNS provide for-hire delivery services for monetary compensation using an online application or platform (such as a website or smartphone app) to connect couriers using their personal vehicles, bicycles, or scooters with freight (e.g., packages, food, etc.). CNS are also referred to as flexible goods delivery."

Microtransit

"Microtransit is defined as a privately or publicly operated, technology-enabled transit service that typically uses multi-passenger/pooled shuttles or vans to provide on-demand or fixed-schedule services with either dynamic or fixed routing."

Pedicabs

"Pedicabs are for-hire services in which a cyclist (or "pedaler") transports users on a cycle containing three or more wheels and a passenger compartment."

Personal Vehicle Sharing

"Personal vehicle sharing is defined as the sharing of privately owned vehicles, where companies broker transactions between vehicle hosts and guests by providing the organizational resources needed to make the exchange possible (e.g., technology, customer support, driver and motor vehicle safety certification, auto insurance, etc.). This model also includes P2P carsharing, P2P marketplace, hybrid B2C and P2P models, and fractional ownership."

Ridesharing "Ridesharing (also known as carpooling and vanpooling) is defined as the formal or informal sharing of rides between drivers and passengers with similar origin-destination pairings. Ridesharing includes vanpooling, which consists of 7 to 15 passengers who share the cost of a van and operating expenses, and may share driving responsibility."

Ridesourcing

"Ridesourcing services are prearranged and on-demand transportation services for compensation in which drivers and passengers connect via digital applications. Digital applications are typically used for booking, electronic payment, and ratings."

Scooter Sharing

"Scooter sharing allows individuals access to scooters by joining an organization that maintains a fleet of scooters at various locations. Scooter sharing models can include a variety of motorized and non-motorized scooter types. The scooter service provider typically provides gasoline or charge (in the case of motorized scooters), maintenance, and may include parking as part of the service. Users typically pay a fee each time they use a scooter. Trips can be roundtrip or one way."

Shuttles

"Shuttles are shared vehicles (typically vans or buses) that connect passengers from a common origin or destination to public transit, retail, hospitality, or employment centers. Shuttles are typically operated by professional drivers, and many provide complimentary services to the passengers."

Taxis

"Taxi services provide prearranged and on-demand transportation services for compensation through a negotiated price, zone pricing, or taximeter (either traditional or GPS-based). Passengers can schedule trips in advance (booked through a phone dispatch, website, or smartphone app), street hail (by raising a hand on the street, standing at a taxi stand, or specified loading zone), or e-Hail (by dispatching a driver ondemand using a smartphone app).

Figure 2

 2 Figure 2 The Geographic Classification of Platforms Illustrated according to their Geographic Distribution THE RISE OF SHARED MOBILITY DIGITAL PLATFORMS: A SNAPSHOT The Rise of Shared Mobility Digital Platforms: An Overview of Trends in Downloads Shared mobility digital platforms are growing fast. The number of platforms with more than 100,000 downloads on Google Play grew from 146 in May 2019 to 236 in May 2020. As of May 2020, 141 platforms had their headquarters in countries of the Global North and 94 platforms in countries of the Global South.

Figure 3

 3 Figure 3 Distribution of Shared Mobility Digital Platforms by Number of Downloads and Service Categories as of May 2020 (Source: Authors, 2020 census of shared mobility digital platforms) Shared mobility digital platforms can, in some cases, diversify their offer through providing services from multiple service categories. As of May 2020, 197 platforms provided services from only one service category, 32 platforms provided from two different service categories (e.g., Go-Jek, Uber, Snapp!), four platforms provided services from three different service categories (13Cabs, Didi Chuxing, Little and OHI CABS), two platforms provided services from four service categories (Grab and Vaya

Figure 4

 4 Figure 4 Distribution of Platforms with more than 100,000 Downloads on Google Play by Number of Metropolitan Areas with more than 500,000 Inhabitants and Number of Downloads as of May 2020 (Source: Authors, 2020 census of shared mobility digital platforms)

Figure 5

 5 Figure 5 Distribution of Platforms with more than 100,000 Downloads on Google Play by Number of Services Provided and Number of Downloads as of May 2020 (Source: Authors, 2020 census of shared mobility digital platforms)

Figure 6 Worldwide

 6 Figure 6 Worldwide Distribution of Platforms in Metropolitan Areas with more than 500,000 Inhabitants as of May 2020 (Source: Authors, 2020 census of shared mobility digital platforms)

  following a classical pattern of linguistic and cultural influence rooted in the Spanish and Portuguese colonization. The same footprint was observed for Beat being available in 17 metropolitan areas across Central America and South America. Finally, Grab, Kakao Taxi, Lyft and Snapp! were concentrated in specific geographic areas: Grab in Southeast Asia (with 42 metropolitan areas), Kakao Taxi in South Korea and Vietnam (13 metropolitan areas), Lyft in the United States of America (89 metropolitan areas), and Snapp! in Iran (17 metropolitan areas).

Figure 7 Worldwide

 7 Figure 7 Worldwide Presence of Major Multi-Service Platforms in Metropolitan Areas with more than 500,000 Inhabitants as of May 2020 (Source: Authors, 2020 census of shared mobility digital platforms) Emergence and Strengthening of Local, Regional and Global Platforms

Figure 8 WorldwideFigure 9

 89 Figure 8 Worldwide Presence of Local, Regional, Global Ride-sharing Platforms in Metropolitan Areas with more than 500,000 Inhabitants as of May 2020 (Source: Authors, 2020 census of shared mobility digital platforms)

2020) Cervero (1997) Vuchic (2007) Shaheen et al. (2015) Enoch (2015) Committee for Review of Innovative Urban Mobility Services (2016) R. Behrens et al. (2016) TCRP (2018) ITF (2019) Aguiléra and Boutueil (2019)

	Proposed Categories		Vehicle-sharing					Ride-sharing			ATS			For-hire services
	Proposed Service Types	Bike-sharing	Car-sharing	Personal vehicle-sharing	P2P carsharing	Scooter (moped)-sharing	E-Scooter (standing)-	sharing	(SAE, 2019)	Car-pooling	Van-pooling	Motorcycle-pooling	Microtransit	DRT*	Conventional paratransit	services	Shuttles	Pedicabs	Ride-sourcing	Taxis hail	Taxis e-hail	Taxis in advance	Limousines	Motorcycle-taxi	Shared-taxis	Minibus-taxis	CNS
	Proposed Criteria	High-capacity vehicle? User driver?			No Yes						No Yes / No	Yes	No No	Yes		No No								Yes / No No	Not included
		Driver paid?			No							No				Yes			Yes								Yes
	SAE (2018)		Bikesharing	Carsharing	Personal vehicle sharing P2P* carsharing	Scooter sharing		-		Carpooling Vanpooling	Microtransit Shuttles	ATS Demand responsive transport Shuttles Microtransit Paratransit	Shuttles	Pedicabs	Ridesourcing		Taxis hail Taxis e-hail Pedicabs Limousines Taxis in advance		CNS
											Carpool Vanpools	Dial-a-Ride & DRT Hybrid Services	Jitney	Commuter vans Shuttles Buspool					Taxis			Intercity buses
				Carsharing							Carpool Vanpools	Dial-a-Ride & Hybrid Services	Jitney	Subscription bus					Taxis
																				Ridesourcing
			Bikesharing	Carsharing			Scooter sharing				Ridesharing Carpool Vanpools	Microtransit	Paratransit Jitney	Shuttles		TNCs* ride services On-demand		E-hail services On-demand ride		CNS
																				Ridesplitting
																												Bus
				Standard car club	P2P* car club Rental car Lease car					Vanpools Casual liftsharing Organised liftsharing	DRT*	Jitney	Shuttles		TNCs Private-hire vehicle	Taxis Shared-ride taxi Private-hire vehicle	Private car Voluntary car schemes Community
																												transport
			Bikesharing											Microtransit			Employee Bus		TNCs			E-hail
														DRT
														Microtransit Prearranged route-or zone-based services	Jitney Dollar vans Flexible route-based services	Employer-based commuter services Property-based services		TNCs On-demand pooled services	Shared taxis On-demand pooled services
			Bikeshare								Ridesharing	Microtransit DRT					Ridesourcing			Taxis
			Bike-sharing Car-sharing							Traditional ride-sharing	Microtransit			Employee Bus		TNCs			E-hail
														On-demand
	C2 Smart (													microtransit			Shuttles		TNCs
														DRT
	*Alternative Transportation Service (ATS), Courier network services (CNS), Demand Responsive Transport (DRT), peer-to-peer (P2P), Transportation Network Companies (TNCs)

TABLE 1 Shared Mobility Digital Platforms with more than 5,000,000 Downloads in 2019 and 2020

 1

	Download category	2019	2020
	500,000,000+	-	Uber
	100,000,000+	Grab Uber	Grab Ola
			99
	50,000,000+	Go-Jek Ola	Go-Jek Blablacar
			Yandex.Taxi
			Beat
			Bolt
			Cabify
		99	Careem
		Blablacar	Easy ACabify App
		Bolt	FreeNow
		Cabify	Gett
	10,000,000+	Careem Gett	inDriver Lime
		Lyft	Lyft
		Yandex.Taxi	maxim
		카카오 T	Rapido Snapp!
			Ситимобил
			카카오 T
		Beat	GoViet
		Didi	Jugnoo
	5,000,000+	maxim	Pathao
		mytaxi	Swvl
		Zoomcar	Zoomcar
	*Bold characters point to shared mobility digital platforms that have exceeded
	a threshold in downloads from 2019 to 2020 on Google Play.
	Source: Authors, 2019 and 2020 censuses of shared mobility digital platforms
	(open dataset to be released soon).

TABLE 2 Distribution of Shared Mobility Digital Platforms by Service Categories* Vehicle-sharing Ride-sharing ATS For-hire CNS Total 2019

 2

		Platforms -Unit	72	11	6	75	16	146
		Platforms -%	49	7	4	51	11	100
		Average (median)
		number of
		metropolitan	20 (8)	51 (13)	18 (6)	22 (6)	9 (4)	19 (7)
		areas* per
		platform
		Platforms -Unit	111	18	12	121	24	236
		Platforms -%	47	8	5	51	10	100
	2020	Average (median) number of
		metropolitan
		areas** per
		platform

*Multi-service platforms are counted once in each column for which they offer the corresponding service category, but only once in the "total" column. **Metropolitan areas with more than 500,000 inhabitants. Source: Authors, 2019 and 2020 censuses of shared mobility digital platforms.

TABLE 3 Geographic Footprint of Shared Mobility Digital Platforms with more than 100,000 Downloads on Google Play as of May 2020, by Sub-Continental Area*

 3

		Countries**	Metropolitan Areas**
	Africa	21	61
	• Central	0	0
	• East	7	11

*According to the UN geographic classification. **Number of countries and metropolitan areas where at least one shared mobility digital platform operates services. Source: Authors, 2020 census of shared mobility digital platforms.

At a global level, 530 metropolitan areas of more than 500,000 inhabitants in the Global South have at least one platform operating services, as compared to 284 metropolitan areas in the Global North.

Platforms operate more extensively in some areas. Europe (161 metropolitan areas covered), East Asia (160), North America (124) and South Asia (112) are extensively covered. Other areas, including the Middle East and Africa, may appear to lag behind, but platforms have very strong momentum there. Africa, for instance, went from 22 metropolitan areas with at least one platform operating services in 2019 to 61 in 2020, following significant development in West Africa.

[START_REF] Behrens | Paratransit in African Cities: Operations, Regulation and Reform[END_REF] 34[START_REF]World Population Prospects[END_REF] 26 (6) 18 (4) 8 (4)

Snellen, D., and G. de Hollander. ICTs Change Transport and Mobility: Mind the Policy Gap! Transportation Research Procedia, 2017. 26:3-12. https://doi.org/10.1016/j.trpro.2017.07.003.

ACKNOWLEDGMENTS

This research was funded by the Sustainable Mobility Institute Renault-ParisTech (IMD), as part of the NexMob research project undertaken by LVMT (City Mobility Transport Lab) on car-based mobility in the service era.

AUTHOR CONTRIBUTIONS

The authors confirm contribution to the paper as follows: study conception and design V. Boutueil


Clément Pechberty

Antoine Klein

Bernard Fraisse

Lorenzo Stievano

Dr Romain Berthelot
email: romain.berthelot@umontpellier.fr

Mechanisms of electrochemical magnesium (de)alloying of Mg-Sn and Mg-Pb polymorphs

Keywords: Alloy electrode, mechanochemistry, operando measurements, X-ray diffraction, Magnesium battery

Introduction

Magnesium batteries are currently investigated as a possible alternative to the well-established lithium-ion technology. 1,2 Driven by the growing market of electric vehicles, the increasing demand for batteries could indeed face some sustainability issues regarding specific raw materials, such as cobalt, nickel or lithium. It is thus important to investigate other types of batteries employing more abundant elements such as magnesium. The story of rechargeable magnesium batteries really started with the prototype systems of Aurbach, with the Chevrel phase Mo 6 S 8 at the positive electrode, a magnesium metal negative electrode and Grignard-based electrolytes. [START_REF] Aurbach | Prototype Systems for Rechargeable Magnesium Batteries[END_REF] This pioneering work already underlined the two major challenges of the Mg-batteries: the easy surface passivation of the magnesium in contact with conventional electrolytes classically used for battery and the lack of positive electrode materials due to the sluggish ionic diffusion of Mg 2+ into classical host electrodes. [START_REF] Pei | Recent Progress and Challenges in the Optimization of Electrode Materials for Rechargeable Magnesium Batteries[END_REF][START_REF] Rashad | Recent Advances in Electrolytes and Cathode Materials for Magnesium and Hybrid-Ion Batteries[END_REF] Tremendous efforts have been made to identify new generations of electrolytes suitable for a magnesium electrode, and more practical than the Grignard-based ones (simpler, less corrosive and with a wider electrochemical stability window). At the positive electrode, sulfur-based composites seem to focus nowadays most of the attention. [START_REF] Zhao-Karger | Magnesium-Sulfur Battery: Its Beginning and Recent Progress[END_REF] Indeed, the conversion process leading to magnesium sulfide MgS is reversible and induces high capacities. The theoretical combination of magnesium and sulfur in a same battery would offer high energy density above 3200 Wh/L, while being sustainable and affordable. However, such a promising system would also come along with the well-known drawbacks of metal/sulfur systems (insulating nature of sulfur implying limited loading in the electrode, polysulfide shuttle effect, etc.). [START_REF] Zhao-Karger | Magnesium-Sulfur Battery: Its Beginning and Recent Progress[END_REF] Recently, the spotlight has been focused on alloy-type electrodes for magnesium-ion systems, thanks to the relatively high theoretical capacity and the low alloying potentials of elements from groups IIIA, IVA and VA. Bismuth, antimony were the first alloy-type electrodes investigated in magnesium-ion batteries, followed by reports on silicon, germanium, tin, indium and more recently gallium. [START_REF] Niu | Alloy Anode Materials for Rechargeable Mg Ion Batteries[END_REF] Obviously, most of the studies evaluated these elements in half-cell configuration with magnesium counter electrode and Grignard-based electrolytes.

However, the compatibility with more conventional and practical electrolytes has been rapidly underlined and stands now as the main advantage of these alloy-type electrodes.

Consequently, the use of magnesium alloy Mg x M has been proposed to investigated Mg-free positive electrode materials, like the Chevrel phase standard Mo 6 S 8 , but also vanadium oxide V 2 O 5 or carbon/sulfur composites, in simple electrolyte generally made from Mg(TFSI) 2 salt dissolved in acetonitrile, tetrahydrofuran or dimethoxyethane. [START_REF] Murgia | Insight into the Electrochemical Behavior of Micrometric Bi and Mg3Bi2 as High Performance Negative Electrodes for Mg Batteries[END_REF][START_REF] Tan | High Voltage Magnesium-Ion Battery Enabled by Nanocluster Mg3Bi2 Alloy Anode in Noncorrosive Electrolyte[END_REF][10] Among the different Mg x M alloy systems, promising results can be predicted for Sn-and Pbbased alloys based on the behavior of these metals as alloy-type negative electrodes.

Concerning tin, during the first investigation of its electrochemical behavior in magnesium batteries, Singh et al. observed at C/200 an alloying plateau around 0.15 V ending with a high discharge capacity of 900 mAh/g Sn , i.e., close to the theoretical value corresponding to the formation of Mg 2 Sn. However, they also showed that magnesiated electrodes further deliver a fraction of this initial capacity (~300 mAh/g Sn ). 11 Irreversible pulverization and amorphization upon cycling could explain this limited capacity. The electrochemical behavior of bulk Mg 2 Sn prepared by ball-milling was then investigated by Nguyen and coworkers. After initial capacity below 200 mAh/g Mg2Sn a maximum of 270 mAh/g Mg2Sn was reached upon cycling.

Galvanostatic intermittent titration technique, or optimized electrode formulation, enabled reaching higher values. 12,13 In the case of lead, its electrochemical behavior was investigated in 2015 by the group of Obrovac, starting from electrodes either prepared by sputtering or made from micrometric Pb powder. 14 At 60°C and current rates of C/40 or C/50, reversible capacities of 450 and 275 mAh/g Pb were obtained, respectively, with Grignard-based electrodes. The alloying process occurs at 125 mV vs. Mg. Only indium-based electrodes exhibit a lower alloying potential. To bypass an initial catalytic reaction on the electrode surface, the application of a current pulse prior to the discharge was proposed. To the best of our knowledge, no investigation of the electrochemical behavior of Mg 2 Pb has been performed until now.

In this current work, the electrochemical behavior of intermetallic compounds around the Mg 2 Sn and Mg 2 Pb compositions prepared by mechanical alloying is investigated. In particular, operando X-ray diffraction is used to follow the corresponding electrochemical processes. Lastly, compatibility with conventional electrolyte is also demonstrated by assembling full cells with a Chevrel phase positive electrode.

Experimental

Magnesium, tin and lead powders (Sigma-Aldrich, 99%, 325 mesh, Alfa Aesar, 99.5%, 100 mesh and 98%, 20-230 mesh, respectively) were used as received and mixed in a 3D Spex mill (Spex SamplePrep 8000 M) in argon atmosphere with stainless steel jar and balls. For typically 1 g of powders mixture, 4 grinding balls of 10 mm diameter are used. The nominal powders proportions varied around the stoichiometric 2:1 ratio.

The resulting materials were then characterized by X-ray powder diffraction (XRPD) with a Panalytical X'Pert Pro diffractometer operating with Cu Kα radiation, under a protective airtight polymeric film to limit moisture reaction. Powder morphology was also observed by scanning electron microscopy (SEM) with a Hitachi S-4800 microscope.

Self-supported electrodes were prepared in a mortar by mixing 70 wt.% of active powder (Mg 2 Pb or Mg 2 Sn), 10 wt.% of carbon (C65, Timcal), 10wt% of vapor grown carbon fibers (VGCF-H, Showa Denko K.K.) and 10 wt.% of polytetrafluoroethylene (PTFE, Sigma-Aldrich, >40µm). The paste obtained was punch into disc to form 8mm diameter electrodes with an average mass loading of 30 mg/cm². All these operations were made in an argon-filled glove box (MBraun LABSTAR) with an oxygen level <0.5 ppm.

Chevrel phase Mo 6 S 8 was synthetized by adapting widely accepted 2-step protocol. 15 Firstly, the ternary Cu 2.5 Mo 6 S 8 Chevrel phase was obtained by heating a stoichiometric mixture of Cu (Sigma-Aldrich, 99.9%, 325 mesh), Mo (Alfa-Aesar, 99.95%, APS 3.7µm) and MoS 2 (Sigma-Aldrich, 99%, <2µm) during 24 hours at 1000 °C under constant argon flow. Secondly, Cu was removed by acidic leaching with HCl aqueuous solution (6 M) under bubbling O 2 .

Finally, the solid was filtered, washed with distilled water and ethanol and lastly dried at 60 °C. The final product was characterized by XRPD to check the purity of the obtained Chevrel phase. Mo 6 S 8 electrodes film were formulated by mixing 80 wt.% of Mo 6 S 8 , 5 wt.% of C65, 5 wt.% of VGCF-H, 10% of polyvinylidene fluoride (PVDF, SOLEF 21216/1001) and NMP as the solvent. The slurry was then tape-casted on 10 µm carbon-coated aluminum foil and dried following the above-mentioned procedure, leading to electrodes with an average mass loading around 1.5 mg/cm². All-ethyl-complex magnesium electrolyte (AEC) was obtained by mixing ethylmagnesium chloride (EtMgCl, 2M in THF, Sigma -Aldrich) and diethylaluminium chloride (Et 2 AlCl, 97% Sigma-Aldrich) in THF. The final concentration of the EtMgCl-Et 2 AlCl-THF electrolyte is around 0.35 M. Conventional magnesium electrolyte was prepared by dissolving magnesium bis(trifluoromethanesulfonyl)imide salt (Mg(TFSI) 2 , 99.5%, Solvionic) in dimethoxethane (DME, Sigma-Aldrich purity > 99 %)) with a 0.5 M concentration. Prior to use, Mg(TFSI) 2 was dried at 250°C in a vacuum flask, while DME was dried first by argon bubbling, then by addition of 4 Å molecular sieves for 3 days, next refluxed with K/Na (3/1 wt.%) for 1 day and finally distilled.

2-electrode coin-cells (2032, 316L stainless steel) were assembled in an argon-filled glovebox, with Mg disks (Goodfellow, 99.9%, 250 µm) as both the negative and reference electrode. Two Whatman GF/A borosilicate glass fibers were used as separator and wetted with 100 µL of electrolyte. All Galvanostatic tests was perform on an MPG potentiostats (Biologic).

Operando XRD measurements were carried out on an electrochemical cell with a specific Be window to probe the structural evolution of the electrode material. 16 Mg disc and Mg 2 Pb selfsupported electrode were used as negative/reference and positive electrode, respectively. The current rate was C/25 during the charge and the start of the discharge, then a constant potential was applied to force the discharge to continue.

Results and Discussion

The XRPD patterns obtained after mechanical alloying of Mg-Sn and Mg-Pb mixtures with various stoichiometries around Mg 2 M and milling times are gathered in Figure 1. In 5 hours and with a molar magnesium excess of 10 %, the cubic phases Mg 2 Sn and Mg 2 Pb are obtained. The patterns exhibits well-defined diffraction patterns that can be indexed with the cubic space group Fm-3m. The corresponding refined cell parameters are in good agreement with the literature (a = 6.762(2) Å for Mg 2 Sn, a =6.820(1) Å for Mg 2 Pb, Figure S1). For longer milling times, and/or with lower amounts of magnesium, the patterns significantly change and early-stage phase searching did not provide a unique solution (Fig. 1b and1d).

Consequently, it is important to detail the equilibrium phase diagrams of the Mg-Sn and Mg-Pb systems. If cubic Mg 2 Sn and Mg 2 Pb, crystallizing in the antifluorite-type structure, 17,18 are reported as the thermodynamically stable allotropes at ambient conditions, other polymorphs are known in a narrow region around Mg 2 Sn and Mg 2 Pb compositions.

For the Mg-Sn system, an hexagonal phase was reported firstly at high-pressure and hightemperature, [START_REF] Cannon | Magnesium Compounds: New Dense Phases[END_REF][START_REF] Dyuzheva | Crystal Growth of the High-Pressure Phase of Mg2Sn[END_REF] but then also through long-time mechanical alloying. [START_REF] Urretavizcaya | Metastable Hexagonal Mg2Sn Obtained by Mechanical Alloying[END_REF] A slight Mg-deficient composition, Mg 9 Sn 5 , was later proposed for this dense form with the hexagonal cell parameters a = 13.222 Å and c = 13.15 Å. [START_REF] Range | Studies on AB2-Type Intermetallic Compounds. Part V1. The Crystal Structure of Mg9Sn5, a Supposed High-Pressure Modification of Mg2Sn[END_REF] Also through ball-milling, a metastable phase with an orthorhombic structure was detected by Clark et al. with cell parameters a = 15.23 Å, b = 8.90 Å and c = 13.10 Å, [START_REF] Clark | Synthesis of Mg2X (X = Si, Ge, or Sn) Intermetallics by Mechanical Alloying[END_REF] on the basis of a first example on thin film obtained by metal evaporation. [START_REF] Suganuma | A Metastable Phase in Sn-Mg Alloy Film[END_REF] Profile matching was attempted with both the orthorhombic and the hexagonal models. Owing to the quite broad diffraction peaks (usually obtained with mechanochemical alloying), however, the refinements were not satisfactory enough to clearly discriminate between the two models. Consequently, this polymorph will be hereafter named "non-cubic Mg 2 Sn". Nayeb-Hashemi and Clark, which is now widely spread and used in reference books. 18 More recently, additional studies specially focused on the composition region around Mg 2 Pb reinstated the existence of the β' phase. [START_REF] Siviour | Mg-Pb Phase Diagram and Phase Transformations in the Intermetallic Compounds Mg2Pb and β[END_REF][START_REF] Stankus | Density and Phase Diagram of the Magnesium-Lead System in the Region of Mg2Pb Intermetallic Compound[END_REF] However, the crystallographic structure of the latter has not yet been determined with certainty. An orthorhombic PbCl 2 -type structure (space group Pnma, a = 7.50 Å, b = 4.45 Å and c = 8.82 Å) was proposed initially, but has not been confirmed afterwards. [START_REF] Eldrige | Magnesium-Lead Phase Diagram and Activity of Magnesium of Liquid Magnesium-Lead Alloys[END_REF] More recently, ab initio evolutionary methods were performed and concluded on tetragonal symmetry (space group P4/nmm, a = 4.5396 Å, b = 7.5278 Å). [START_REF] Li | Identification and Properties of the Non-Cubic Phases of Mg2Pb[END_REF] It is interesting to note strong similarities between the XRPD patterns of the non-cubic Mg 2 Sn and of this Mg 2 Pb polymorph. Therefore, a profile matching refinement with an hexagonal space group was also tried in parallel with the previously mentioned models. However, as in the case of the Mg-Sn system, it was not possible to obtain a clear unique solution, and therefore this compound will be hereafter named "non-cubic Mg 2 Pb".

The particle morphology of these intermetallics is shown in insets in Figure 1. Unsurprisingly, the ball-milled powders consists on large aggregates of sub-micrometric particles, as already reported for alloys prepared in similar conditions. [START_REF] Murgia | Insight into the Electrochemical Behavior of Micrometric Bi and Mg3Bi2 as High Performance Negative Electrodes for Mg Batteries[END_REF][START_REF] Murgia | First Investigation of Indium-Based Electrode in Mg Battery[END_REF] The electrochemical behavior of cubic and non-cubic Mg 2 Sn and Mg 2 Pb is evaluated in halfcell at a significantly higher current rate of C/30. The two first cycles of the four compounds are compared in Figure 2. In both cases, the de-alloying process starts with a stable plateau slightly increasing from 0.25 to 0.3 V before a progressive increase to reach the cut-off value of 0.7 V. With the cubic polymorph of both Mg 2 Sn and Mg 2 Pb, almost all the magnesium seems to be extracted during the initial charge. After that, the alloying occurs at a low voltage (below 0.2V for Mg 2 Sn, below 0.1 V or Mg 2 Pb), with a rather limited capacity in both cases that continues upon cycling. Regarding the non-cubic Mg 2 Sn and Mg 2 Pb polymorphs, the initial electrochemical charge starts similarly to the cubic polymorph with the same plateau potentials. However, in both case the cut-off value is reached more rapidly and induces a capacity reduced by 50 %. The existing literature on alloy-type materials for Mg-ion batteries clearly underlines that electrodes made from Bi or Mg 3 Bi 2 exhibit the best behavior, with especially a limited capacity decay upon cycling with optimized electrode formulation, [START_REF] Niu | Alloy Anode Materials for Rechargeable Mg Ion Batteries[END_REF] whereas the cycling performance when starting with Mg 2 Sn or Mg 2 Pb active materials is somewhat expected to be worse,. The fundamental interest thus lies more on the comparison of the behavior between polymorphs. It is interesting to note that in both case, an almost full electrochemical charge is possible with the cubic polymorphs.

To grasp further details of the electrochemical processes, an operando XRD follow-up of the first galvanostatic cycles was carried out for the four polymorphs (Figure 3). Previous ex situ XRD patterns collected after magnesiation of tin-based or lead-based electrodes confirmed the formation of the cubic Mg 2 Sn and Mg 2 Pb, respectively. 11, [START_REF] Periyapperuma | The Reversible Magnesiation of Pb[END_REF] No details, however, were reported about possible intermediates formed along the electrochemical discharge. The dealloying sequences of the intermetallic compounds are characterized by the disappearance of the peak of each polymorph, while the peaks of tin (β) on one side, or lead on the other side, regularly increase in intensity. This logical observation is in line with the steady-flat voltage plateau characterizing a biphasic alloying reaction.

In case of Mg 2 Sn cubic pristine electrode, without any surprise, the subsequent discharge shows the reformation of the cubic Mg 2 Sn, the latter exhibiting better crystallinity (narrower diffraction peak at 26.5 ° in Figure 3a). The magnesiation appears more complex in case of the non-cubic pristine electrode: indeed, the beginning of the discharge shows an increase of the diffraction peaks of non-cubic form of Mg 2 Sn, followed by a regular increase of the cubic form of Mg 2 Sn (Figure 3b). For lead-based electrodes, the early stages of the electrochemical magnesiation are characterized by the appearance of weak reflections that can be assigned to the non-cubic form of Mg 2 Pb, whatever the pristine polymorph. As the alloying process continues, these peaks slowly disappear in favor of the cubic form of Mg 2 Pb. This unexpected mechanism is better pictured in a top-view plot of the XRPD patterns (Figures S2 to S5). A more detailed analysis of these operando XRD studies using a chemometric approach, provided in the supplementary information, globally confirmed the above-mentioned observations, and also provided complementary information on the evolution of the crystallinity between the pristine and electrochemically formed phases (Figures S6 to S16).

For non-cubic Mg 2 Pb pristine electrode there is no memory effect that could induce the formation of the non-cubic phase The formation of metastable intermetallic forms during discharge was already observed during the electrochemical alloying of p-block elements, such as antimony, with alkali ions. [START_REF] Darwiche | Better Cycling Performances of Bulk Sb in Na-Ion Batteries Compared to Li-Ion Systems: An Unexpected Electrochemical Mechanism[END_REF][START_REF] Allan | Tracking Sodium-Antimonide Phase Transformations in Sodium-Ion Anodes: Insights from Operando Pair Distribution Function Analysis and Solid-State NMR Spectroscopy[END_REF] In addition, it is reasonable to assume that the early moments of the electrochemical magnesiation of lead, i.e., when the amount of magnesium is limited, could see the formation of the non-cubic form of Mg 2 Pb which is reported to be slightly deficient in magnesium. [START_REF] Eldrige | Magnesium-Lead Phase Diagram and Activity of Magnesium of Liquid Magnesium-Lead Alloys[END_REF]

Figure 3: Operando XRPD investigation of the electrochemical behavior of Mg 2 Sn cubic (a= and non-cubic (b) and Mg 2 Pb (cubic) and non-cubic (d). For each case, peaks indexation or at least Bragg peaks are provided when possible. To enhance the magnesiation process during discharge, a floating was applied once the cell reaches 0 V. Symbols (*) and (#) stand for the beryllium window and unidentified inactive impurities on its surface.

Finally, the compatibility of these intermetallic compounds with Mg(TFSI) 2 /DME electrolyte in full cells needs to be evaluated. As we previously demonstrated that the cubic forms of The initial discharge shows a sloppy plateau occurring between 0.8 and 0.5 V for Mg 2 Sn, but slightly higher from 0.9 to 0.5 V for Mg 2 Pb due to the lower potential of Mg 2 Pb below that of Mg 2 Sn (respective calculated values of 121 and 197 mV vs. Mg 2+ /Mg) [START_REF] Gerstein | Thermal Study of Groups II-IV Semiconductors. Lattice Heat Capacities and Free Energies of Formation. Heat Capacity of Mg2Si from 15°-300[END_REF] . During the corresponding charge, both Mg 2 Sn and Mg 2 Pb show two plateaus at 1 and 1.4 V that can be attributed to the sequential insertion of Mg 2+ in the two insertion sites of Mo 6 S 8 . [START_REF] Mei | Chevrel Phase Mo6T8 (T = S, Se) as Electrodes for Advanced Energy Storage[END_REF] The differentiation between the two plateaus is not observed on the discharge due to intrinsic kinetic limitations. In both cases, there is a progressive but limited capacity decay upon cycling. The initial capacity loss of 20 mAh/g can be attributed to the partial irreversible magnesium trapping in Mo 6 S 8 . [START_REF] Ling | Thermodynamic Origin of Irreversible Magnesium Trapping in Chevrel Phase Mo6S8: Importance of Magnesium and Vacancy Ordering[END_REF] After that, the progressive loss of capacity may have different origins: first, the degradation of the electrolyte in contact with Mg at low potential can progressively form a blocking layer on the negative electrode. [START_REF] Kopač Lautar | Electrolyte Reactivity in the Double Layer in Mg Batteries: An Interface Potential-Dependent DFT Study[END_REF] Another possible reason could be the dissolution of the alloying element in the electrolyte and its migration to the positive side that have been observe for Mg 3 Bi 2 /S batteries. 10 This shuttle phenomenon, which

is not yet well understood and could have a negative effect on the cycle life, will be the object of further detailed investigations. Finally, the Mg that is non-reversibly alloy can possibly plate on the negative electrode/electrolyte interface at low potential resulting in the formation of passive Mg and loss of active material.

Conclusions

Different Mg 2 Sn and Mg 2 Pb allotropes can be prepared by mechanochemical synthesis: besides the cubic forms thermodynamically stable at ambient conditions, this synthetic method allows also obtaining metastable allotropes of these compositions by slightly tuning the milling conditions. The electrochemical evaluation of these phases shows that the first demagnesiation is almost complete with cubic Mg 2 Sn and Mg 2 Pb, but only partial with the other polymorphs. Operando XRD reveals that, during the following magnesiation, the cubic polymorphs are obtained independent of the pristine polymorph, even though a transient metastable phase is formed at the very beginning of the process in the case of Pb. The compatibility of these phases with Mg(TFSI) 2 /DME electrolyte when used as negative

Chemometric analysis of the X-ray diffraction (XRD) patterns

A common chemometric approach based on Principal Component Analysis (PCA) was applied to determine the minimum number of components expressing the variance included in the whole set of operando XRD data. The analysis was carried out separately for the four operando datasets. PCA is a factor analysis tool typically used to structure and simplify complex data sets by narrowing the multitude of variables with the least number of independent components. [1] In this specific case, this corresponds to the number of different XRD patterns necessary to express, by appropriate linear combinations, each dataset collected during a full electrochemical demagnesiation-magnesiation cycle.

The number of principal components determined in this way can be used as the basis for Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) analysis. This algorithm allows the stepwise reconstruction of the "pure" components that are necessary for interpreting the whole operando multiset. The whole procedure is described in detail in ref. [2]. The MCR-ALS analysis was performed with the following constraints: (i) non-negativity of the intensity and of the concentration of the components, (ii) no unimodality and (iii) closure (sum of the components always equal to 100 % of the intensity). In this way, the different patterns which are necessary reproduce by the linear combination the whole dataset are obtained. The results of the application of this process is detailed below for the four operando XRD datasets collected during a full electrochemical demagnesiation-magnesiation cycle of cubic and non-cubic Mg 2 Pb and Mg 2 Sn. In order to help this analysis to converge to reasonable values, a linear background was subtracted to all patterns in order to bring the baseline at 0 before applying PCA and MCR-ALS.

Cubic Mg 2 Pb

The results of the PCA analysis of the operando XRD data measured for Mg 2 Pb are collected in Figure S6. By inspection of the variance plot and of the shape sand evolution of the different components, four to five independent components are necessary to express the whole dataset. The application of MCR-ALS provides sufficiently good results using four independent components, as shown in Figure S7. In this case, components 1 and 4 Correspond to the same phase, i.e., cubic Mg 2 Pb, but are differentiated by a strong modification of the line shape and width: component 4 has a much narrower shape, corresponding to the reversible formation of sensibly smaller crystallites at the end of a full electrochemical cycle. Component 2 corresponds to pure Pb metal, whereas component 3 has contributions from both cubic Mg 2 Pb and Pb metal, but contains also additional reflections corresponding to the pattern of non-cubic Mg 2 Pb. In this last component, all linewidths are very narrow, corresponding to well-crystallised phases. By looking at the evolution of their concentration, one can thus quite straightforwardly understand the reaction mechanisms occurring along the demagnesiation and the following magnesiation. The first process is the biphasic transformation of non-cubic Mg 2 Pb into Pb. At the beginning of the following discharge, both noncubic and cubic well-crystallised Mg 2 Pb appear at the beginning, at the expenses of the smaller crystallites of Mg 2 Pb. Non-cubic Mg 2 Pb reaches a maximum in the course of the discharge and then disappears completely, leaving the place to the cubic form, which is the only phase detected at the end of the magnesiation.

Non-cubic Mg 2 Pb

The results of the PCA analysis of the operando XRD data measured for non-cubic Mg 2 Pb are collected in Figure S8. By inspection of the variance plot and of the shape sand evolution of the different components, four to five independent components are necessary to express the whole dataset. The application of MCR-ALS provides good results using four independent components, as shown in Figure S9. In this case, components 1 and 4 can be easily indexed as non-cubic and cubic Mg 2 Pb, respectively, while both intermediate components 2 and 3 correspond to Pb metal, with however different profile shapes: component 2 has a larger linewidth, corresponding to smaller crystallites. By looking at the evolution of their concentration, one can then easily describe the sequence of processes occurring along the demagnesiation and the following magnesiation. The first process is the biphasic transformation of non-cubic Mg 2 Pb into small particles of Pb, which grow towards the end of the charge, corresponding to pattern #11. During the following discharge, both non-cubic and cubic Mg 2 Pb appear at the beginning, but the former, metastable, reaches a maximum after transforming back to the cubic form, which is the only phase detected at the end of the magnesiation.

Cubic Mg 2 Sn

The results of the PCA analysis of the operando XRD data measured for cubic Mg 2 Sn are collected in Figure S10. By inspection of the variance plot and of the shape sand evolution of the different components, three independent components are necessary to express the whole dataset. The application of MCR-ALS provides good results using three independent components, as shown in Figure S11. In this case, components 1 and 3 can be both indexed as cubic Mg 2 Sn, respectively, components 2 corresponds to -Sn metal. Components 1 and 3 are differentiated by a different profile shape: component 1 has a larger linewidth, corresponding to smaller crystallites. These three components describe a sequence of two simple biphasic mechanisms, with cubic Mg 2 Sn transforming into Sn during the charge, and then transforming back to cubic Mg 2 Sn with higher crystallinity during the following discharge. This transformation is not completed at the end of the latter process, where only half of the tin is transformed back into Mg 2 Sn

Figure 1 :

 1 Figure 1: XRPD patterns and SEM pictures of Mg 2 Sn cubic (a) and non-cubic (b) and Mg 2 Pb

Figure 2 :

 2 Figure 2: Galvanostatic behavior of Mg/Mg 2 Sn and Mg/Mg 2 Pb half-cells at C/30 current rate

Mg 2

 2 Sn and Mg 2 Pb (i) exhibit the best first capacity during de-alloying process and (ii) are mainly formed during electrochemical alloying of both tin and lead forms, only those polymorphs were considered in full Mg-ion cell with Chevrel phase Mo 6 S 8 positive electrode materials (Figure4).

Figure 4 :

 4 Figure 4: Galvanostatic cycling of full cells Mg 2 Sn-cubic/Mo 6 S 8 (a) and Mg 2 Pb-cubic/Mo 6 S 8

  Alloys to Replace Mg Anodes in Efficient and Practical Mg-Ion/Sulfur Batteries. ACS Energy Lett. 2019, 4 (9), 2040-2044. https://doi.org/10.1021/acsenergylett.9b01389. (11) Singh, N.; Arthur, T. S.; Ling, C.; Matsui, M.; Mizuno, F. A High Energy-Density Tin Anode for Rechargeable Magnesium-Ion Batteries. Chem. Commun. 2013, 49 (2), 149-151. (12) Nguyen, D.; Song, S. Magnesium Stannide as a High-Capacity Anode for Magnesium-Ion Batteries. J. Power Sources 2017, 368, 11-17. https://doi.org/10.1016/j.jpowsour.2017.09.054.(13) Nguyen, G. T. H.; Nguyen, D.-T.; Song, S.-W. Unveiling the Roles of Formation Process in Improving Cycling Performance of Magnesium Stannide Composite Anode for Magnesium-Ion Batteries. Adv. Mater. Interfaces 2018, 5 (22), 1801039. https://doi.org/https://doi.org/10.1002/admi.201801039. (14) Periyapperuma, K.; Tran, T. T.; Purcell, M. I.; Obrovac, M. N. The Reversible Magnesiation of Pb. Electrochim. Acta 2015, 165 (0), 162-165. (15) Chusid, O.; Gofer, Y.; Gizbar, H.; Vestfrid, Y.; Levi, E.; Aurbach, D.; Riech, I. Solid-State Rechargeable Magnesium Batteries. Adv. Mater. 2003, 15 (7-8), 627-630. (16) Morcrette, M.; Chabre, Y.; Vaughan, G. B. M.; Amatucci, G. G.; Leriche, J.-B.; Patoux, S.; Masquelier, C.; Tarascon, J.-M. In Situ X-Ray Diffraction Techniques as a Powerful Tool to Study Battery Electrode Materials. Electrochim. Acta 2002, 47 (19), 3137-3149. https://doi.org/10.1016/S0013-4686(02)00233-5. (17) Nayeb-Hashemi, A. A.; Clark, J. B. The Mg-Sn (Magnesium-Tin) System. Bull. Alloy Ph. Diag. 1984, 5 (6), 466-476. https://doi.org/10.1007/BF02868320. (18) Nayeb-Hashemi, A. A.; Clark, J. B. The Mg-Pb (Magnesium-Lead) System. Bull. Alloy

Figure S2 :

 S2 Figure S2: Top view of the operando XRD patterns measured during a full demagnesiationmagnesiation cycle of cubic Mg 2 Pb and corresponding electrochemical signature.

Figure S3 :

 S3 Figure S3: Top view of the operando XRD patterns measured during a full demagnesiationmagnesiation cycle of non-cubic Mg 2 Pb and corresponding electrochemical signature.

Figure S4 :

 S4 Figure S4: Top view of the operando XRD patterns measured during a full demagnesiationmagnesiation cycle of cubic Mg 2 Sn and corresponding electrochemical signature.

Figure S5 :

 S5 Figure S5: Top view of the operando XRD patterns measured during a full demagnesiationmagnesiation cycle of non-cubic Mg 2 Sn and corresponding electrochemical signature.

Figure S6 :

 S6 Figure S6: Variance plot (a), principal components (b) and the evolution of their contribution (c) along the full demagnesiation-magnesiation cycle of cubic Mg 2 Pb.

Figure S7 :

 S7 Figure S7: Pure components (a) and evolution of their concentration (c) along the full demagnesiation-magnesiation cycle of cubic Mg 2 Pb.

Figure S8 :

 S8 Figure S8: Variance plot (a), principal components (b) and the evolution of their contribution (c) along the full demagnesiation-magnesiation cycle of non-cubic Mg 2 Pb.

Figure

  Figure S9: MCR-ALS pure components (a) and the evolution of their concentration (c) along the full demagnesiation-magnesiation cycle of non-cubic Mg 2 Pb.

Figure S10 :

 S10 Figure S10: Variance plot (a), principal components (b) and the evolution of their contribution (c) along the full demagnesiation-magnesiation cycle of cubic Mg 2 Sn.

Figure

  Figure S11: MCR-ALS pure components (a) and the evolution of their concentration (c) along the full demagnesiation-magnesiation cycle of cubic Mg 2 Sn.

Figure S13 :

 S13 Figure S13: MCR-ALS pure components (a) and the evolution of their concentration (c) along the full demagnesiation-magnesiation cycle of cubic Mg 2 Sn.

Acknowledgements

The authors gratefully acknowledge financial support from the French National Research Agency (project MISTRALE, ANR-19-CE05-0013, and Labex STORE-EX, ANR-10-LABX-76-01). Access to the Analysis and Characterization platform of "Pôle Chimie Balard" (PAC-Balard) is gratefully acknowledged. Calypso Baril (MEA platform, Univ Montpellier) is acknowledged for the SEM pictures. CIDETEC is acknowledged for providing the C-coated Al foil, with the support of E-Magic FET-PROACTIVE and VIDICAT FET-OPEN projects in the frame of Horizon 2020 Program (Grant agreement 824066 and 829145, respectively).

electrode materials in Mg-ion batteries was confirmed in Mg 2 Sn/Mo 6 S 8 and Mg 2 Pb/Mo 6 S 8 systems. The observed cycle life shows that the behavior of Mg 2 Sn and Mg 2 Pb as negative electrodes in Mg-ion batteries with a simple Mg(TFSI) 2 /DME electrolyte are promising regarding the previous studies, [START_REF] Niu | Alloy Anode Materials for Rechargeable Mg Ion Batteries[END_REF] and a benchmark in the same electrochemical conditions appears thus necessary to clearly determine the most relevant alloy to be used in magnesiumbattery research.

Supporting Information for:

Electrochemical behavior of

Non-cubic Mg 2 Sn

The results of the PCA analysis of the operando XRD data measured for non-cubic Mg 2 Sn are collected in Figure S12. By inspection of the variance plot and of the shape sand evolution of the different components, three independent components are necessary to express the whole dataset.

Figure S12: Variance plot (a), principal components (b) and the evolution of their contribution (c) along the full demagnesiation-magnesiation cycle of non-cubic Mg 2 Sn.

The application of MCR-ALS with three independent components provides a good reconstruction of the pure components, as shown in Figure S13. In this case, components 1 can be indexed as the pristine non-cubic Mg 2 Sn, while component 2 corresponds to -Sn metal. A direct and complete transformation of the first component into the second one is obtained along the first charge, corresponding to the full demagnesiation of non-cubic Mg 2 Sn. During the charge, the formation of components 3 occurs: this component is rather interesting, since it contains at the same time the contributions of non-cubic Mg 2 Sn and cubic Mg 2 Sn, the former better crystallised than the pristine material represented by component 1. The fact that both phases are contained in the same component suggest that both phases are formed at the same rate during the discharge, and that, differently from the case of non-cubic Mg 2 Pb shown above, the non-cubic Mg 2 Sn reformed during magnesiation does not transform into the cubic form. The charge, however, is not complete, and a majority of tin metal is still present at the end of the process.