Cédric Parizot

Anne-Laure Amilhat Szary

Gabriel Popescu

Isabelle Arvers

Thomas Cantens

Jean Cristofol

Nicola Mai

Joana Moll

Antoine Vion

Anne Laure

Amilhat Szary

The antiAtlas of Borders, A Manifesto

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

Why an AntiAtlas?

Atlases, as map collections, have instructed populations and delighted book lovers for centuries [START_REF] Cosgrove | Mappings[END_REF], 2008[START_REF] Besse | The Birth of the Modern Atlas[END_REF]. Atlases are valuable objects because they appear to provide a science-based representation of territorial divisions and present a unifying glance at the world as a whole. The powerful aesthetic aspect of their maps and graphics also contributes to their widespread appeal. Spatial sciences such as topography, geometry, geography, have shown constant concern for precise maps, graphs and diagrams at various scales. The modern history of border drawing consists mainly of static and formal outlines of division lines, giving little account of the fluidity of social experience. Setting the world in (right) order through maps is both a social and political process. Maps have always been political objects par excellence, their top-down view establishing a dominating representation of political interactions [START_REF] Farinelli | De la raison cartographique[END_REF]. The process through which current borderlines have come into being is indeed directly related to their mutual recognition in international treaties. However, in the wake of the deep changes that have been affecting borders over the last 20 years there is a need for a radical shift of perspective. At the beginning of the 21 st Century, the functions of State borders have changed. Borders are losing their territorial container aspect, increasingly overflowing spaces, districts and jurisdictions [START_REF] Taylor | Beyond containers: internationality, interstateness, interterritoriality[END_REF][START_REF] Balibar | Qu'est-ce qu'une frontière? La crainte des masses[END_REF][START_REF] Sassen | Territory. Authority, Rights. From medieval to global assemblages[END_REF][START_REF] Balibar | We, the People of Europe?: Reflections on Transnational Citizenship[END_REF]). Borders cannot be reduced anymore to their linear aspects as they are becoming more mobile and diffuse (Amilhat Szary andGiraut 2011, Popescu 2011). Border-making actors have also multiplied substantially. In addition to states, new stakeholders such as international institutions, corporations, and NGOs have emerged as actors of border management [START_REF] Cuttitta | Le monde-frontière. Le contrôle de l immigration dans l espace globalisé[END_REF][START_REF] Brown | Walled States, Waning Sovereignty[END_REF]. The ways in which mobility is controlled are more and more diversified and differentiated (Bigo and Guild 2005[START_REF] Money | Fences and Neighbors: The Political Geography of Immigration Control[END_REF][START_REF] Steinberg | Sovereignty, Territory, and the Mapping of Mobility: A View from the Outside[END_REF]. Crossing borders, people and goods have to pass through multiple networks and complex identification devices. Making sense of these mutations requires sustained in-depth analysis as well as a wide range of modes of inquiry, critical methodologies, and interdisciplinary engagements, that can open the path for creative research [START_REF] Rumford | Does Europe have cosmopolitan borders?[END_REF], Van Houtum et al. 2004, Wastl-Walter 2012, Wilson and Donnan 2012). While atlases express stability, or rather give the illusion of it, the antiAtlas wishes to reintroduce borders dynamic nature and complex manifestations, and to provide a critical approach to border representations. We assert that systematic graphic visualization of space is neither the most acceptable nor the most desirable way of understanding borders. This does not mean that we disqualify the traditional map, as we do not contest the usefulness of maps as knowledge tools. What we claim is that maps systematic compiling does not provide an adequate understanding of the complexity of borders. Maps are not only political but also epistemological devices. They are not simply representations of territories and borders, but they also contribute to their production. Border making is intrinsically linked to map drawing, as maps make the border conceptually as well as practically possible. Maps are models that determine the forms of their production and lay the conditions to produce relations in space.

The study of territorial shape is less essential today than examining borders physical inertia, their contextual materialization and dematerialization, as well as their social construction and highly technological nature. Increasingly, borders appear as evolving devices with electronic and biological characteristics that function as bases for mobile control and surveillance. At the same time, they shape exchanges, generate formal and informal rules, and produce random definitions of what is legitimate and what is not. What is at stake, thus, is to understand the border as a perpetually changing process, using an alternative set of representations that do not reify power positions the way atlases do. In this sense, we prefer the path of multiple investigations to unearth the multifaceted nature of border-making processes. Beyond their topography, borders address sociological, psychological, anthropological and ontological issues. This means that we need to pay attention at the same time to their locations, forms and shapes, as well as to their modes of existence, constitutive processes and imaginaries.

From territorial control to flows and risk management

The transformation of borders is intimately connected to the ways globalization has altered spatial interactions of all kinds, such as production chains, communication and defense systems, work and culture [START_REF] Appadurai | Modernity at Large. Cultural Dimensions of Globalization[END_REF]. Freedom of mobility has been conceived through an economic perspective [START_REF] Peck | Constructions of neoliberal reason Oxford[END_REF][START_REF] Amable | Morals and politics in the ideology of neo-liberalism[END_REF]. Contemporary public policies that are usually qualified as neoliberal have been over-discussed and reinterpreted [START_REF] Hilgers | The historicity of the neoliberal state[END_REF]), but it is widely admitted that they have promoted national reforms that include free trade and labor flexibility [START_REF] Jacoby | Finance and Labor: Perspectives on risk, inequality, and democracy[END_REF][START_REF] Jacoby | Labor and Finance: Some Preliminary Attempts at Quantification 63rd Proceedings of the Labour and Employment Relations Association[END_REF], while promoting altogether on a global scale accounting standards [START_REF] Mattli | Accountability in Accounting? The Politics of Private Rule-Making in the Public Interest[END_REF]Büthe 2005, Richardson and[START_REF] Richardson | Legitimating transnational standardsetting: The case of the international accounting standards board[END_REF], banking prudential norms (Goodhart 2011, Young 2012), and fiscal consolidation [START_REF] Kleinbard | Stateless Income's Challenge to Tax Policy[END_REF][START_REF] Hebous | Cross-border effects of fiscal consolidations: Estimates based on narrative records[END_REF][START_REF] Blanchard | Fiscal consolidation: At what speed?[END_REF]. At the same time, there are new strategies which aim at containing migratory pressures through the selective filtering of human flows [START_REF] Shamir | Without Borders? Notes on Globalization as a Mobility Regime[END_REF]). These transformations have resulted in a contradiction between economic practices that increase unequal global development and the need to implement sustainable and fair global development [START_REF] Sassen | Territory. Authority, Rights. From medieval to global assemblages[END_REF]. There is also a gap between national governments policies, which are limited by their sovereignty, and the need to regulate transnational processes through global governance frameworks (Kramsch andHooper 2004, Ba andHoffmann 2005). To address these contradictions, national governments have assigned state borders the function to guarantee people s security in a world characterized by transnational mobility of people, capital, goods and ideas. In other words, borders are supposed to allow a high level of mobility while protecting against social, economic, political, and public health risks the mobility of people generate. While state borders are clearly more and more represented as legally intangible, it becomes increasingly problematic both for analytical purposes [START_REF] Steinberg | Sovereignty, Territory, and the Mapping of Mobility: A View from the Outside[END_REF][START_REF] Johnson | Interventions on rethinking the border in border studies[END_REF] and in terms of securitization (Brunet-Jailly 2007) to locate the border control within specific and stable places. The lines between domestic and external security have become blurred to such extent that these domains are difficult to separate clearly. Yet, the role of borders does not decline. What is declining is the relative share of controls implemented at borders compared with the forms of control prior and after the border crossing. This share is declining due to the difficulty to distinguish between internal and external origin of migrations, terrorism, economic and financial flows, software piracy and pollution. In this context, border control is conceived and implemented in a selective and individualized manner. Seen in terms of risks, human, commercial and information flows become targets of surveillance, and border control becomes a form of risk management (Beck 1998;Aradau and van Munster 2007). Because these movements overflow the national space, security strategies now have to be conceived on a global scale and are heavily reliant on digital technologies that collect and store vast amounts of data about cross-border flows (Muller 2008;Dillon & Lobo-Guerrero 2008). The main objective of border security policies is not so much to stop these flows as it is to improve the mechanisms to filter and channel them. Consequently, borders are functioning today as firewalls, aiming to facilitate legitimate traffic while containing unwanted people and commodities perceived as security risks (Walters 2006). For example, borders could be very porous to capital, but not to workers with low levels of formal education. The implementation of this new logic of control has led to an unprecedented process of integration of technology-based surveillance systems, such as, biometrics, numeric and satellite networks, RFID, drones, robots, radars, CO2 detectors, and others, used to embed borders into bodies and flows in order to detect, identify and follow their movements. In this way, flows can be monitored continuously along their entire journey [START_REF] Popescu | Bordering and Ordering the Twenty-First Century: Understanding Borders[END_REF]. The main rationale for this convergence is based on the misplaced belief that technological automation will, inevitably, strengthen border control capabilities by reducing enforcement costs and eliminating human error. Following these developments, border security is more concerned with the prediction and the management of the effects of risks rather than with their actual causes. This logic is in accordance with neoliberal thinking that sees addressing the root causes of various issues as more costly than dealing with their effects [START_REF] Agamben | Comment l obsession sécuritaire fait muter la démocratie[END_REF]). In addition, the datafication of human and goods mobility and practices, as well as the emergence of the bigdata paradigm, have further reduced the focus on causes and meanings of processes we observe. Given the amount of data that can be collected and processed by computers, it becomes easier to analyze an event and what is linked to it in order to find out regularities and probabilities, than to understand the factors determining it [START_REF] Cukier | Big Data : A Revolution That Will Transform How We Live, Work, and Think[END_REF]. This shift of focus in border control practices and representations could explain the actual convergence of free trade policies on the one hand, and growing security control apparatus on the other.

Shifting forms of mobility and changing border regimes

Keeping flows under surveillance today means that border controls managed by police, custom services and private companies get partially redeployed away from the formal state borderlines and inside the national territory as well as inside other States territories. Customs may manage extraterritorial operations (Baldaccini 2010). Visa checks are carried out in the country of migrants origin, not only in embassies but also in private offices [START_REF] Infantino | La frontière au guichet. Politiques et pratiques des visas Schengen à l'Ambassade et au Consulat d'Italie au Maroc[END_REF]. Simultaneously, check points are multiplied in order to track people and providers of goods who have managed to circumvent surveillance systems. Lastly, in order to exclude certain categories of flows, special zones such as detention centers, staging areas in airports, or free zones have been created on uncertain juridical basis [START_REF] Marc | Bellecombe-en-Bauges-Paris[END_REF][START_REF] Bigo | Circuler, enfermer, éloigner : zones d attente et centres de rétention des démocraties occidentales[END_REF][START_REF] Mountz | The enforcement archipelago: Detention, haunting, and asylum on islands[END_REF][START_REF] Clochard | Atlas des migrants en Europe (2ème édition)[END_REF][START_REF] Rahola | La forme-camp. Pour une généalogie des lieux de transit et d internement du présent [trad. S. Guimaud[END_REF]). These facilities have proliferated as they generate a highly lucrative business [START_REF] Rodier | Xénophobie Business : à quoi servent les contrôles migratoires ? Paris[END_REF]. Such increasingly selective control implies a diversification of circulatory regimes. Regimes regarding the circulation of goods are increasingly constituted by World Trade Organization agreements on tariffs and trade, whereas the circulation regimes affecting human flows get managed through more or less coercive migratory policies. Border crossing chances are determined by a complex set of factors such as professional status, gender, national origins, ethno-religious stereotypes, economic and linguistic capacities, affiliations, and others. The main outcome is the generalization of negotiated mobility based on contingent arbitration. Creating the conditions for fluidity and interconnections implies increasingly sophisticated overriding clauses that exempt major actors from the formal regulations that should apply. Major transnational corporations, for instance, bargain both accesses and tariffs by providing specialized services to governments such as non-intrusive shipment inspection, trade hubs management, databases and risk management, and certification (of value, quantity or quality), thus establishing themselves as crucial stakeholders in the management of international flows of people and merchandise. In this context, flagrant gaps between hyper-connected spaces or people and disconnected ones have emerged. Mobility of people, goods and ideas is also shaped by the entrepreneurs, and firms that are not directly involved into border control. Yet, motivated by financial gains, transportation, insurance and communication companies, banks, NGOs facilitate international mobility, settlement adaptation, communication and resource transfers of migrants and their families across borders [START_REF] Salt | Migration as a Business: The Case of Trafficking[END_REF]Stein 1997, Hernández-León 2008). While not officially in charge of controlling borders these actors play a more determinant role in structuring international human mobility than it was that it has been acknowledged by migration theory. The impact of non-state actors on mobility is all the more complex as many operate in informal ways. The increasing number of border controls has encouraged the development of clusters of lucrative businesses such as smuggling and other informal activities in borderlands [START_REF] Andreas | Borders Games. Policing the U.S.-Mexico Divide[END_REF] Tightening controls forces people who live near the border or who must cross it regularly to change their habits, activities, journeys and strategies. Due to their limited resources, they are often forced to call for assistance from individuals and groups who specialize in avoiding physical obstacles (i.e. walls and barriers), surveillance systems (i.e. radar, drones, and biometric systems) and state regulations (i.e. visas, travel permits, and work contracts). Hence, traffickers have gained key positions in the system, as they can ease or obstruct entrance according to their own interests. They have become unofficial regulating authorities [START_REF] Roitman | Fiscal disobedience : an anthropology of economic regulation in Central Africa[END_REF]. Formal authorities cannot put an end to their activities and prefer incorporate these informal networks into their own mechanisms of regulation and control [START_REF] Parizot | An Undocumented Economy of Control. Borders, Mobilities and Migrations[END_REF]. The sophistication of entrance regulations leads to an individualization of controls, particularly on the basis of complex sets of data. People who wish to bypass border biometric control systems are obliged to modify their physical aspect, notably by achieving mutilation and erasure of fingerprints. Borders are now likely to be embedded in the person [START_REF] Amoore | Biometric borders: Governing mobilities in the war on terror[END_REF][START_REF] Popescu | Bordering and Ordering the Twenty-First Century: Understanding Borders[END_REF]. Border management is embodied as it detaches from the national territorial limits and embraces alternative forms of spatiality. People increasingly move both to escape the stark inequalities and conflicts and to pursue more individualized and economically rewarding lifestyles, often facing the risk of exploitation and abuse. However, filtering people deserving protection away from those awaiting deportation, on the basis of standardized criteria of absolute, thus almost unattainable, victimhood leads to the onset of a de-politicizing humanitarian rhetoric. The complex experiences of increased vulnerability and self-affirmation through migration are systematically denied, setting the background for the emergence of humanitarian mechanisms of migration control [START_REF] Agier | Humanity as an Identity and Its Political Effects (A Note on Camps and Humanitarian Government)[END_REF]. Since ever more restrictive policies frame global migrations, access to asylum has drawn a humanitarian boundary throughout the world. Depending on how well they fulfill true victim stereotypes [START_REF] Cole | The Cult of True Victimhood. From the war on welfare to the war on terror[END_REF] in which the presentation of a suffering body becomes key to arouse compassion and solidarity [START_REF] Fassin | Compassion and Repression: the moral economy of immigration policies in France[END_REF], migrants are granted, but more often denied, fundamental rights. In the process, the certification of individual suffering and vulnerability has become a border control technology through which migrants can or cannot access social support, legal immigration status and work on the basis of asylum and other humanitarian grounds. The process of certification of the credibility of the suffering of the migrants being both helped and controlled acts as a humanitarian biographical border between deportation and recognition [START_REF] Mai | Between Embodied Cosmopolitism and Sexual Humanitarianism: the Fractal Mobilities and Subjectivities of Migrants Working in the Sex Industry[END_REF]. The ubiquity of these biographical bordering mechanisms is part of the proliferation of mobile borders and of new moral and spatial surveillance mechanisms and technologies of control.

From scientific exploration to artistic experimentation and back

Initially conceived as an exploratory research project, the antiAtlas of borders has become a performance in the artistic meaning of the word. The fact that researchers, professionals of border control, and artists have met for twelve seminars 1 between 2011 and 2013 has of course allowed them to enrich their own approach. Indeed, the first boundary that was crossed was that of our own academic fields of activity as the antiAtlas is a collective whose members are not merely representing their own disciplinary fields. Rather, this companionship has helped them to widen perspectives in order to embrace wider epistemological horizons in a manner that goes beyond traditional inter-disciplinary collectives. The dialogue between art, science, and practice, has generated cognitive gains made of mutual insights, transfers, and examples. At the same time, this dialogue has gone far beyond using one discipline as a vehicle for another. Art, which is not a discipline in the sense of specialization and institutionalization of knowledge, has helped give a transgressive content to this enterprise. Such potential of art-science explorations certainly resides in its call for un-discipline , since the inscription of research within specialized disciplines may invalid or make unthinkable questioning that could precisely come out of the refusal of objects and methods that disciplines acknowledge (Loty 2005 p. 252, quoted by [START_REF] Mekdjian | Figurer les entre-deux migratoires. Une expérience scientifique et artistique d'ateliers de cartographie participative[END_REF]. Neither artists nor practitioners were summoned at the discussion table to illustrate social science analysis. Instead, by recalling the experimental power of contemporary art [START_REF] Thompson | Experimental Geography[END_REF], the collective has made all of its participants be part of an uncommon journey. The evolution of visual arts since their incorporation of fast changing technologies (starting with photography) has led them to abandon the dream of offering faithful representations of our world and to embrace a re-active position. Contemporary artwork aims to challenge the observer position in the world and to trigger affective experiences that can involve the viewer in the interpretation of the artwork. This kind of aesthetic relationship represents a drastic reversal from a time when a frontal meeting between the person who did the art and the one who received it was the norm. The integration of electronic technologies has led artists to deliver not only visual products, such as 2 or 3 D images, but to encode perception itself in a renewed way. In the course of the antiAtlas meetings, artistic works have provided the collective with many explorations and experiences of our ambivalent relation to borders on one hand, what they make of us, of our identity, of our intimacy, and of our body; on the other hand, what we make of them, how we give them material and immaterial visibility or invisibility, how we play with them, either for breaking free of them or for surveying and denouncing our contemporaries. The relations between the rationality of control initiatives and the practices that evade them are perpetually replayed through borders. In addition, the antiAtlas has also led to uncommon productions: the professionals involved in the process have begun to relate to artists as experts; the artists have enjoyed having direct contact with concept making, and the scientists have undergone a change of their epistemic references. This has, most notably, led to the production of hybrid original works, such as an ethno-fiction (Samira), a video game (A Crossing Industry) based on an ethnographic investigation, as well as participative and mobile maps (Crossing Maps), and others2 . Could such an experience have happened in any art-science workshop? Borders have indeed revealed an exceptionally fertile exploratory laboratory. The potential of this type of interactions is such that they can benefit all strains of border studies, from the more quantitative to humanities-based approaches. The antiAtlas challenges both our routines of border experiences and our understanding and analysis of them. By pulling together a complex set of reflections on the reticular structure of borders and on the conditions for a renewed aesthetic relation to borders, this approach has the potential to make people aware that they are a constitutive part of the production of contemporary borders.

Conclusions

Approaching borders in the 21 st century requires us to examine the transformation of spaces, both from space s constitutive elements as well as from our common experiences of it. This makes borders a major element to express how the world we live in can be represented and what is our own position in it. The antiAtlas helps understanding how people cross borders and also how borders modify their experience of space. New technologies of network control settle spaces that look less like areas and more like flows, loops, and intersections. While the nation-state territory has long been associated with areas and boundaries, today we increasingly experience daily life shaped by flows and networks. Understanding contemporary borders raises new questions about the way we conceive space and, consequently, about our new experience of constructing social ties and communities. Communities are now provisional and shifting, they lay upon new forms of participation, and they do not encompass our whole lives any more. Such networked forms of social interaction in space imply a deep reconceptualization of the distinction between the public and the private sphere, the individual and the collective, and the real and the virtual. It is in this context that borders have invaded the spatial imaginaries that artists express as border art (Amilhat Szary 2012) or, to put it differently, art at the border (Cristofol 2012). By sharing the initial findings spanning its three years of existence, the antiAtlas collective wishes to alert the field about the urgent need for transdisciplinarity in order for border studies to bring a more decisive epistemological contribution. We believe that current technologies do not simply consitute one aspect of the border condition, but that the way they decompose and recode our realities are forcing us to reconsider our definition of perception and our ways of expressing it. This is the rationale for a sustained relationship between art and science production at the borders, and for explicitly claiming an experimental status to border studies.

Cédric

  Parizot project coordinator, anthropologist, Institut de Recherche et d Études sur le Monde Arabe et Musulman, CNRS, Aix Marseille Université, Aix en Provence Anne-Laure Amilhat Szary -geographer, Laboratoire Pacte, CNRS, Université J. Fourier, Grenoble Gabriel Popescu Geographer, Indiana University South Bend Isabelle Arvers Curator and producer Thomas Cantens anthropologist, Centre Norbert Elias, EHESS/CNRS, Marseille Jean Cristofol philosopher, École Supérieure d Art d Aix-en-Provence (ESAA) Nicola Mai ethnographer and filmmaker, London Metropolitan University/Laboratoire Méditerranéen de Sociologie, CNRS, Aix-Marseille University, Aix en Provence Joana Moll media artist,Barcelona Antoine Vion sociologist, AMU, Laboratoire d Économie et de Sociologie du Travail, Aix en Provence References

See http://www.antiatlas.net/en/research-seminars/

For further details see www.antiatlas.net/en


V Baijot

L Glavier

J M Ducéré

M Djafari

C Rossi

A Estève

Modeling the pressure generation in aluminum based thermites

Keywords: thermite, pressure generator, Al/CuO, Al/Bi 2 O 3, Al/Sb 2 O 3, Al/MoO 3, Al/WO 3

The paper proposes a new theoretical model based on local thermodynamic equilibrium enabling the prediction of gas generation during the reaction of aluminum-based thermites. We demonstrate that the model has the capability to predict the total pressure and its partial pressure components as a function of the reaction extent and compaction. Al/CuO, Al/Bi2O3, Al/Sb2O3, Al/MoO3 and Al/WO3 thermites are modeled and their capability to generate pressure compared. Simulation results are also validatedthrough dedicated experiments and showgeneral agreement beyond the state of the art. Mechanisms underlying pressure generation are detailed. A two-stage process for the pressure increase in Al/CuO reaction,also observed experimentally,is shown to be driven by oxygen generation as produced byCuO and Cu2O vaporizationthrough different kinetics. Comparison with experiment stresses the issue of the understanding of the complex chemical processes taking place during vaporization and subsequent gas phase reactions and the need to determine their thermodynamicconstants.

Introduction

Alumino-thermite materials represent an interesting class of energetic substancesnotably because of their high energy densities, adiabatic flame temperature, and when nanosized, high reaction rates. Aluminothermite is an oxydo-reduction reaction involvinga metal (fuel) and a metallic oxide (or possibly a nonmetallic oxide) to form a stable product after reaction.

Thermites materials have been actively investigated for a wide range of potential applications including railroad welding, materials processing to form refractory materials, additives in propellants, explosives and pyrotechnics [START_REF] Stamatis | Aluminum Burn Rate Modifiers Based on Reactive Nanocomposite Powders[END_REF][START_REF] Reese | Preparation and Characterization of Energetic Crystals with Nanoparticle Inclusions[END_REF][START_REF] Wang | Electrospray Formation of Gelled Nano-Aluminum Microspheres with Superior Reactivity[END_REF] and more recently also for micro initiation [START_REF] Churaman | Initiation and reaction tuning of nanoporous energetic silicon[END_REF][START_REF] Zhang | In-situ Preparation of a Porous Copper Based Nano-Energetic Composite and Its Electrical Ignition Properties[END_REF][START_REF] Wang | An investigation into the fabrication and combustion performance of porous silicon nanoenergetic array chips[END_REF][START_REF] Zhang | A nano initiator realized by integrating Al/CuO-based nanoenergetic materials with a Au/Pt/Cr microheater[END_REF][START_REF] Morris | Rapid initiation of reactions in Al/Ni multilayers with nanoscale layering[END_REF][START_REF] Zhou | Influence of Al/CuO reactive multilayer films additives on exploding foil initiator[END_REF][START_REF] Zhu | Energetic igniters realized by integrating Al/CuO reactive multilayer films with Cr films[END_REF][START_REF] Morris | Streak spectrograph temperature analysis from electrically exploded Ni/Al nanolaminates[END_REF][START_REF] Staley | Silicon-based bridge wire micro-chip initiators for bismuth oxide-aluminum nanothermite[END_REF][START_REF] Qiu | A micro initiator realized by reactive Ni/Al nanolaminates[END_REF][START_REF] Yang | Fabrication and performance characterization of Al/Ni multilayer energetic films[END_REF][START_REF] Morris | Streak spectroscopy and velocimetry of electrically exploded Ni/Al laminates[END_REF][START_REF] Taton | Micro-chip initiator realized by integrating Al/CuO multilayer nanothermite on polymeric membrane[END_REF][START_REF] Zhu | Characterization of Al/CuO nanoenergetic multilayer films integrated with semiconductor bridge for initiator applications[END_REF][START_REF] Lee | Crystallization of amorphous silicon thin films using nanoenergetic intermolecular materials with buffer layers[END_REF][START_REF] Bae | Crystallization of amorphous Si thin films by the reaction of MoO3/Al nanoengineered thermite[END_REF][START_REF] Hossain | Crystallization of amorphous silicon by selfpropagation of nanoengineered thermites[END_REF], environmentally clean primers, in situ welding [START_REF] Rossi | Nanoenergetic materials for MEMS: A review[END_REF].

Among numerous possible exothermic metal/oxide couples listed in [START_REF] Fischer | Theoretical energy release of thermites, intermetallics, combustible metals[END_REF], the most investigated ones mix Al with MoO 3 , CuO, Bi 2 O 3 , Fe 2 O 3 , MnO 2 , WO 3 , I 2 O 5 . For the last two decades most of the research efforts aimed at reducing metal and oxide components size, improving their intimacy, to increase the reaction rate and decrease the ignition delay while improving safety.

More recently, thermite materials were also considered to produce gas species or pressure bursts opening new potential fields of applications as pressure mediated molecular delivery [START_REF] Rodriguez | A microactuator based on the decomposition of an energetic material for disposable lab-onchip applications: fabrication and test[END_REF][START_REF] Korampally | Transient pressure mediated intranuclear delivery of FITC-Dextran into chicken cardiomyocytes by MEMS-based nanothermite reaction actuator[END_REF], biological agent inactivation [START_REF] Sullivan | Synthesis and reactivity of nano-Ag2O as an oxidizer for energetic systems yielding antimicrobial products[END_REF][START_REF] Grinshpun | Inactivation of Aerosolized Bacillus atrophaeus (BG) Endospores and MS2 Viruses by Combustion of Reactive Materials[END_REF][START_REF] Clark | The aluminium and iodine pentoxide reaction for the destruction of spore forming bacteria[END_REF], hydrogen production [START_REF] Fan | Studies on hydrogen generation characteristics of hydrolysis of the ball milling Al-based materials in pure water[END_REF][START_REF] Dupiano | Hydrogen production by reacting water with mechanically milled composite aluminummetal oxide powders[END_REF] or propulsion systems [START_REF] Zhang | A nano initiator realized by integrating Al/CuO-based nanoenergetic materials with a Au/Pt/Cr microheater[END_REF][START_REF] Morris | Rapid initiation of reactions in Al/Ni multilayers with nanoscale layering[END_REF][START_REF] Zhou | Influence of Al/CuO reactive multilayer films additives on exploding foil initiator[END_REF] .

A few teams demonstrated experimentally that Al/Bi 2 O 3 and, to a lesser extent, Al/I 2 O 5 mixtures generate the highest pressure pulses [START_REF] Clark | The aluminium and iodine pentoxide reaction for the destruction of spore forming bacteria[END_REF][START_REF] Martirosyan | Synthesis and performance of bismuth trioxide nanoparticles for high energy gas generator use[END_REF][START_REF] Martirosyan | Novel nanoenergetic system based on iodine pentoxide[END_REF]in comparison with other thermite couples. Martirosyan [START_REF] Martirosyan | Novel nanoenergetic system based on iodine pentoxide[END_REF]considered that the reaction product (bismuth or iodine) boils at a temperature of 1560°C and 184°C, respectively, that is lower than the maximum reaction temperature, causing bismuth or iodine evaporation with subsequent increase of the released gas pressure. For some thermites as Al/CuO, experiments using time-resolved mass spectrometry have measured significant O 2 release, undergo rapid heating [START_REF] Chowdhury | Diffusive vs Explosive Reaction at the Nanoscale[END_REF][START_REF] Zhou | Time-Resolved Mass Spectrometry of the Exothermic Reaction between Nanoaluminum and Metal Oxides: The Role of Oxygen Release[END_REF].The formation of gaseous intermediates and their contribution to the pressurization may suggest why a system such as Al/MoO 3 , which is thermodynamically predicted to produce approximately only the percent of the gas that Al/CuO or Al/Bi 2 O 3 does, can still react rapidly and exhibit pressures as the other thermites.

Despite these experimental research investigations, the effects of thermite composition, packing densitytogether with its environmental conditions on the gas production (type and repartition of produced species and rate of gas release) need to be studied and understood in greater details.On the theoretical side, a first attempt to simulate thermite pressure release was published by K. Martirosyanet al. [START_REF] Martirosyan | Modeling and simulation of pressure waves generated by nano-thermite reactions[END_REF]. They proposed to solve numerically the equations of gas dynamics.Apreliminary study by the authors showed systematic overestimation of the calculated generated pressures [START_REF] Glavier | NanoEnergetics as pressure generator for nontoxic impact primers: comparison of Al/Bi2O3, Al/CuO, Al/MoO3 nanothermites and Al/PTFE[END_REF]. Our goal is to bring the simulation closer to the actual chemical processes that may occur during reaction including gas phase interactions, vaporization and condensation processes.

The aim of the present work is to propose a new generic model, based on thermodynamic considerations, able to predict the maximum reaction pressure, temperature and reaction end products (gas and solid formed species) as a function of the overall extent of reaction and packing density. This theoretical tool makes it possible to establishquantitatively a hierarchy of alumino-thermite couples in relation to applicative requirements, specifically concerning pressure and gas delivery.

The paper is organized as the following. Section 2 is dedicated to the model description.Simulation results are reported in section 3 starting with a case study on Al/CuO followed by a comparison with other materials, namely Al/MoO 3 , Al/Bi 2 O 3 , Al/WO 3 and Al/Sb 2 O 3 . For all of them, the maximum pressure, temperature and reaction products are given as a function of the extent of reaction and the percentageof Theoretical Maximum Density (TMD). In section4, theoretical results are compared with experimental data allowing the validation and discussion of the theoretical approach before concluding and giving some perspectives in section5.

Model description

For Al based thermites, the reaction can be written as:

2.b 3 Al + M a O b → b 3 Al 2 O 3 + a M
(1) whereM a O b is the metal oxide corresponding to the metal M with valency 2b/a. Equation ( 1) is only a schematic representation of mechanisms occurring during thermite reaction. Indeed, in most practical cases, various intermediates and end products, such as oxides, sub-oxides and alloys, may be encountered during the reaction process. All possible phases are not well known and characterized experimentally. A theoretical approach would require a thorough investigation, using quantum chemical methods, of all possible intermediates and end products, including metastable phases and metallic aggregates. This is not the purpose of this paper where only the most documented compounds are considered.

A combustion process is basically an out of equilibrium process. But, an accurate kinetic model should necessarily include the various kinetic constants associated with various phase transitions that are not available today. On the other hand, the high temperatures reached during the reaction enhance the reactions towards the thermodynamic equilibrium. For this reason, and in the absence of available thermodynamic data on possible intermediates and end products, we will confine our model to the thermodynamic equilibrium. However, in order to get insight into the temporal evolution of the reaction process, we introduce the extent of reaction parameter ξ ranging from 0 to 1. The extent of reaction is not proportional to the time, since the reaction rates increase with the temperature. But, at least, the extent of reaction is a monotonically increasing function of time.

In our model, we consider stoichiometric mixture (no excess of Al) and assume that the thermodynamic equilibrium is temporarily reached for each value of the extent of reaction, although the global equilibrium is only reached at the end of the reaction. This is equivalent to the usual assumption of local thermodynamic equilibrium in the treatment of irreversible processes. The schematic reaction represented in Eq. ( 1) can now be reformulated as:

2.b 3 Al + M a O b → bξ 3 Al 2 O 3 + a. ξ M + 1 -ξ . 2.b 3 Al + 1 -ξ M a O b (2)
whereξrepresents the fraction of thermite converted, while the remaining 1 -ξ fraction is still in its initial form. At this stage, additional phases are introduced into equation ( 2), depending on the nature of the oxide, the actual temperature and the different vapor partial pressures in the reaction chamber.

These phases result from:

-the melting and boiling of all species, -the decomposition of alloys and oxides, -the condensation in alloy or oxide forms.

All thermodynamicsconstants, including formation energies, concerning these phases are taken from the literatureand the main ones are reported in Tables1.a and 1.b. The free energies are preferred to enthalpies since all of the experiments to validate the model are performed in a constant volume pressurized chamber. In most cases, both the boiling points and the partial vapor pressures reported in the literature correspond to atmospheric pressures or less. In order to obtain boiling points at high pressures such as the ones reached in confined thermite reactions, we have extrapolated these values to higher pressures using the following expression:

𝑃 𝑖 (𝑇) = 𝐾 𝑖 × 𝑇 3/2 × exp (- Δ U 𝑖 𝑘 𝐵 𝑇 ) (3)
where𝑃 𝑖 (𝑇)is the partial pressure of the gas specie 𝑖 at the temperature 𝑇 and ΔU 𝑖 its vaporization energy. 𝑘 𝐵 is the Boltzmann constant. Equation (3) can either be deduced from the kinetic theory of gases or by equating the chemical potentials of species in the gas phase and in the condensed phase. In equation ( 3), the entropic part of the free energy, resulting from the thermal motion of atoms and molecules, is contained in the pre-exponential factor 𝐾 𝑖 and the internal energy appears in the exponent. Both theoretical approaches lead to the constant 𝐾 𝑖 :

𝐾 𝑖 = 2𝜋𝑚 𝑖 𝑘 𝐵 3 𝑠 𝑖 ℎ ( 4
)
where𝑚 𝑖 is the molecular mass of the speciei. s i the area of its surface unit cell (in the condensed phase), and ℎis the Plank constant. However, in our model, we have considered the constants 𝐾 𝑖 as adjustable parameters and have fitted them to experimental boiling points at atmospheric pressure. The vaporization energies ΔU 𝑖 correspond to the formation of elemental metallic atoms and O 2 molecules in the gas phase, except for MoO 3 which evaporates in its molecular form. The perfect gas law is adopted for all species in the gas phase.

The simulation procedure follows closely the experiments performed for the validation of the model. In these experiments, the reaction chamber is filled with a given amount of thermite, i.e. a given TMD percentage. We should notice that the chamber can never be completely filled such that the maximum experimental %TMD is 50%. For a given thermite Al/M a O b and %TMD, we first choose a value of the extent of reaction ξ and scan the temperature from ambient to 4000°C. The partial pressures of various species are then calculated at each temperature using equation ( 4) and the number of molecules determined from the perfect gas law. The composition of the condensed phase is then deduced by subtraction. We remind that, in these experiments, the volume of the condensed phase is not small compared to the total volume of the reaction chamber. It is therefore necessary to take it into account when applying the perfect gas law.

The equation of conservation of energy is applied to determine the actual temperatures as a function of extent of reactionξ. The heat released by the reaction is equal to ξ. τ. Q , with τ being the %TMD and Q the specific heat of reaction (see Table 1.a). This heat is used to increase the temperature of the system and to supply the latent heats required for the phase transitions. The overall heat quantity 𝑞 𝑇 required to heat the system to the desired temperature 𝑇 can be formulated as:

𝑞 𝑇 = 𝐶 𝑣 𝑇 + ℎ 𝑇 . 𝑑𝑇 𝑇 𝑇 0 (5)
Where 𝑇 0 is the initial temperature, taken here as the ambient temperature (25°C). 𝐶 𝑣 𝑇 is the temperature dependent heat capacity of the whole system and ℎ 𝑇 the latent heat. The function ℎ 𝑇 is composed of a series of Dirac delta functions, at appropriate temperatures, for all phase transitions, except the vaporization considered as a continuous process, in relation with partial vapor pressures. The temperature dependent heat capacities, for all species, are taken from the literature [START_REF] Lide | Handbook of Chemistry and Physics[END_REF][START_REF] Boissière | Équation d'état des métaux prenant en compte les changements d'état entre 300 et 200 000 K pour toute compression. Application au cas du cuivre et de l'aluminium[END_REF][START_REF] Zhang | The melting-point, latent-heat of solidification, and enthalpy for both solid and liquid alpha-Al2O3 in the range 550-2400 K[END_REF], and interpolated before integration. In the temperature ranges where the data are not available, particularly at high temperatures, we use 3𝑘 𝐵 𝑇 for each atom in the solid phase or MoO 3 molecule in the gas phase, In these equations, the subscripts (s), (l) and (g) stand for solid, liquid and gas phases respectively. Among these nine reactions, four are phase transitions between condensed phases, represented by direct reactions. A transition temperature is systematically assigned to each of them. The five remaining reactions are reversible (as indicated by the reverse arrows), with the presence of a gas phase. The driving force balancing the direct or reverse reaction is the partial vapor pressure in the gas phase.

As described in section 2, the equilibrium temperature is calculated for each value of ξ. The calculated temperatures are independent of TMD percentage since both the released reaction heat and the heat necessary to increase the temperature are proportional to %TMD. As a consequence, temperature splitting as a function of %TMD, may appear as a result of heat losses that are neglected at this point. The Al/CuOequilibrium temperatures as a function of ξ are reported in Fig. 1. We observe that, for Al/CuO, the equilibrium temperature increases up to 3400°C with a slight plateau at 2072°C corresponding toAl 2 O 3 melting. Fig. 1 shows the maximum pressures for three different TMD percentages(10%, 30% and 50%). Themaximum pressure depends on the temperature, but also on the volume available for the expansion of the gas. Increasing the %TMD leads to a decrease of the free volume and an increase of the total pressure. For all three %TMD values, the pressure rise starts at ξ = 0.3, corresponding to a temperature around 1000°C (see Fig. 1), corresponding to the Al/CuO reaction onset. We can further observe that the pressure rise is not monotonic such that the maximum pressure is reached when the reaction is still incomplete. This result is against the general belief that the pressure drop is only a consequence of reaction stop and subsequent cooling of the system through heat losses. Moreover, for low compaction (%TMD=30), the pressure evolution shows clearly an oscillating behavior. This trend can also be observed for higher compaction rate, although the first maximum is less pronounced and rather replaced by a shoulder.

To explain this behavior, we have plotted in Fig. 2, Al, Cu and O 2 partial pressures in the gas phase, together with the total pressure and the temperature, as a function of ξ and for a TMD percentage of 30%. Fig. 2 shows clearly that all partial pressures do not rise simultaneously. This results from the variety of their specific vapor pressures dependence against the temperature.

Fig. 2: Theoretical partial pressures together with the total pressure and the temperature, as a function of extent of reaction and for TMD percentage of 30%.

As observed in experiments [START_REF] Zhou | Time-Resolved Mass Spectrometry of the Exothermic Reaction between Nanoaluminum and Metal Oxides: The Role of Oxygen Release[END_REF], wesee in Fig. 2 that the total pressure is mainly driven by the oxygen gas phase which shows a first pressure peak at ξ = 0.6 and a gentle pressure shoulder at ξ = 0.8, resulting from the decomposition of CuO and Cu 2 O, respectively. Aluminum and, to a much lesser extent, copper gas phases only impact the end of the reaction process.

The Cu vapor comes from the evaporation of liquid Cu, while Al vapor comes from the decomposition of Al 2 O 3 . The latter process explains the increase of the total pressure observed from ξ = 0.9 to ξ = 1 (see Fig. 2). This results from the vaporization of Al 2 O 3 due to the high final temperature (3330°C) that is superior to the decomposition temperature of the alumina (2977°C).

When the reaction is near completion, the total pressure behavior is almost entirely governed by the aluminum partial pressure. The oxygen partial pressure stabilizes due to compensation between vaporization of the liquid alumina providing oxygen molecules and oxidation reaction with aluminum.

Fig. 3: Experimental Al/CuO pressure versus time at 30 %TMD [START_REF] Glavier | NanoEnergetics as pressure generator for nontoxic impact primers: comparison of Al/Bi2O3, Al/CuO, Al/MoO3 nanothermites and Al/PTFE[END_REF].

Similar pressure evolution tendency, i.e. a peak and a shoulder, has also been found experimentally (see Fig. 3). But, the positions of the peak and the shoulder are reversed. The reason is the relative intensities of the two oxygen peaks. Calculated oxygen partial pressure coming from the decomposition of CuO is too high because of its lower latent heat of vaporization (see Table 1 b.This first peak replaces therefore the experimental shoulder, but hides, in turn, the real experimental peak.

To summarize, for 10 %TMD, the pressure saturation is reached at the end of the reaction (ξ=1) giving rise to a pressure saturation plateau around18 MPa. For 30 and 50 %TMD, maximum pressures of 49 and 118 MPa are obtained at an extent of reactionξ =0.6. From these maximum pressure values, the pressure decreases up to ξ =0.9 where the high temperature reached by the system causes the alumina to decompose and in consequence, the pressure to increase again, up to a value of71 MPa.

3.2Applications to other thermites

In this sectionfour other thermitecouples among the most widely studied (Al/Sb 2 O 3 , Al/Bi 2 O 3 , Al/MoO 3 and Al/WO 3 ) areanalyzedand their capability to generate gases and pressure compared. As previously indicated, a number of phase transitions are considered for the species involved ineach thermite reaction as summarized in Table 2. The general pressure curve shapes are similar for all thermites: a succession of peaks corresponding to the evaporation or decomposition onsets of various species, depending on the nature of the thermite and its associated chemistry. The origin of the peaks corresponds to the generation of gaseous species during thermite reaction,according tophase transitions ((l)(g) as well as (s)(g)) at equilibrium, as described in the section 2.

Considering Al/Bi 2 O 3 (see Fig. 5.a), we observe first a decomposition of the bismuthoxide into molecular oxygen (O 2 ) and liquid bismuth occurring at ξ =0.6 and around 2041 °C. The Bi 2 O 3 decomposition produces a pressure peak ranging from 32 MPa to 280 MPa,depending on TMD percentage. Thispressure peak is followed by the evaporation of Bi at ξ = 0.8, which corresponds to the gentle pressure shoulder especially visible at 50 %TMD. For Al/MoO 3 (see Fig. 5.b), we observe first the vaporization of condensed MoO 3 into molecular MoO 3(g) at ξ =0.5 leading to an important increase of the pressure: principal pressure peak of 221 MPa at 50% TMD. At the same time, the temperature rises rapidly leading to the decomposition of alumina (at ~2977°C) into Al (g) + O 2 occurring at ξ =0.8. At this temperature, Mo is still in a liquid phase. Moreover, only a small fraction of liquid alumina is decomposed at this stage. As a result, the final theoretical pressure is very low and only of0.5 MPa.This results from the low final temperature reached at complete reaction. One would expect a higher final temperature since Al/MoO 3 is more energetic than Al/Bi 2 O 3 where decomposition of alumina is observed. The lowering of the temperature in the case of Al/MoO 3 is due to the higher heat capacity of Mo compared to Bi making it absorbing more energy.

For Al/Sb 2 O 3 (see Fig. 5 c), the decomposition of Sb 2 O 3 and the vaporization of Sb are respectively at 1425 °C and 1314°C (see Table 2). Not only the two peaks are very closeand collapse, but also Sb vaporization precedes Sb 2 O 3 decomposition such that almost all Sb produced should immediately evaporate. The result is that only one peak is clearly visible in Fig. 5 c.At the final stage of reaction, no alumina can be decomposed since the final temperature of 2411°C is well below alumina vaporization temperature. But, all Sb metal is vaporized leading to a pressure of 37MPa (at 50 %TMD).

For Al/WO 3 (see Fig. 5 d), the phase transformation leading to pressure generation are the decomposition of WO 3 into WO 2 and O 2 at 1625°C and then into W (l) and O 2 at 1730°C(see Table 2). After this point, the pressure decreases and falls to0.06 MPa At the final temperature of 2870°C, neither W (l) nor Al 2 O 3(l) can be vaporized.

To conclude this section we can state that the best alumino-thermite material to generate pressure is not necessarily the most energetic thermite, here Al/CuO, but the one with the oxide whose metal evaporates easily and where temperature allows for alumina decomposition: here Al/Bi 2 O 3 .

Experimental validationand discussion

Theoretical results were compared to experimental data in order to evaluate their validity. For that purpose, stoichiometric Al/oxide thermites were prepared by ultrasonic mixing. The maximum pressure generated by the exothermic reaction was measured for each couple.

Materials

The Al nanoparticles, with a diameter of 80 nm, are supplied by Novacentrix.They exhibited spherical shapes and the purity has been measured at 68 % leading to an alumina shell thickness of 4 nm. Bi 2 O 3 , CuO, MoO 3 , WO 3 and Sb 2 O 3 oxide nanopowders are supplied by SigmaAldrichwith characteristics summarized in Table 3.

Random shape

The Al and oxidizer nanopowderswere mixed in stoichiometric ratios, taking the fractional alumina content into account. The Al/oxide ratios in the mixture are of 35.5 wt. %, 15 wt. %, 24.6 wt. % and 21.4 wt. % for Al/MoO 3 , Al/Bi 2 O 3 , Al/CuO and Al/Sb 2 O 3 mixtures, respectively. First, Al and oxidizer nanopowders were weighted, suspended in hexane and then mixed with an ultrasonic rod style transducer for a total of 4.5 min with a 1 s delay after every 2 s of sonication to avoid heating the solution that could lead to undesired ignition of mixture. The mixture suspension was then dried at 70°C under 2.10 4 Pa and collected for pressure characterization.

Characterization set-up

The pressure released by the reaction was measured in a stainless steel, high pressure resistant (up to 100 MPa) cylindrical reactor. The reactor has 4 mm inner diameter and is 0.7 mm long (total volume of ~ 9 mm 3 ). A pressure up to 100 MPa can be measured by a highfrequency pressure transducer (Kistler 601H) on the back of the reactor and connected to a Kistler charge amplifier (5018 type). A schematic is shown in Fig. 6. Densities were calculated based on the reactor volume and the mass of powder loaded inside. For each sample, 10, 30 and 50 %TMD were systematically investigated. For ignition, we used a multilayer nanothermite Al/CuO on a chip [START_REF] Taton | Micro-chip initiator realized by integrating Al/CuO multilayer nanothermite on polymeric membrane[END_REF]. The best fit between modeling and simulation is obtained for Al/CuO with a model/experimental results agreement within a factor of 3, while in [START_REF] Glavier | NanoEnergetics as pressure generator for nontoxic impact primers: comparison of Al/Bi2O3, Al/CuO, Al/MoO3 nanothermites and Al/PTFE[END_REF], the pressures were overestimated by one order of magnitude. The main reason for this improvement is that the chemical processes occurring Al/CuO combustion are well known and documented.

Discussion

Experimentally, the highest pressure is obtained at 50%TMD for Al/CuO followed by Al/Bi 2 O 3 , Al/Sb 2 O 3 and Al/MoO 3 : 29 MPa, 15 MPa and 12 MPa respectively.

At 10 %TMD(see Fig. 7), our calculations show that Al/Sb 2 O 3 produces more pressure than Al/CuO. But, its low pressure increase with TMD leads to lower pressures for 30 and 50 %TMD, compared to Al/CuO. We observe the same trend experimentally: at 10 TMD percentage, the Al/Sb 2 O 3 experimental pressure reaches 4.4 MPa, very close even if still lower than Al/CuO thermite 5.1 MPa.Increasing the TMD percentage, the experimental pressure increases slowly to reach 15 MPa for Al/Sb 2 O 3 , well below Al/CuO pressure that stabilizes at 42 MPa.

The overestimation of pressure for Al/Bi 2 O 3 and Al/Sb 2 O 3 thermites is due to the easy evaporation of Bi and Sb atoms in the respective thermites. The assumption of the gas phase containing metals in atomic form, adopted in our model, is probably not accurate. The metal should aggregate thus decreasing the calculated pressures. In contrast to all other cases, the pressures calculated for Al/MoO 3 thermite are well below experimental ones: at 50 %TMD the calculation gives 0.5MPa instead of 12 MPa measured. As stated in section 3, the highest temperatures of Mo vaporization and alumina decomposition are not reached during combustion so that all the end products are found in condensed form, leaving a residual pressure of 0.5 MPa at the end of the reaction.

The discrepancy between experimental and theoretical pressures may be attributed to three effects: (1) the expected composition of the final gas phase, (2) the chemical processes in condensed phase and (3) the real kinetic effects. First, the complexity of the gas phase is difficult to grasp. In the present paper, we consider that vaporization processes lead only to the formation of gas phases constituted of individual metallic atoms or O 2 molecules, except for MoO 3 where the existence of molecular gas is well known. Obviously, this assumption that completely neglects the potential formation of metallic aggregates in the gas phase, and the associated condensation properties, will lead to an overestimation of pressures. For example, it is probable that Bi will preferentially form Bi 2 molecules. For what concerns Sb 2 O 3 decomposition, it is suggested that liquid Sb 2 O 3 will evaporateas Sb 4 O 6 molecules [START_REF] Asryan | p-T-x phase diagram of the Sb-O system[END_REF]. All these reactions are not sufficiently documented to allow a precise treatment in our modeling procedure.

Second, the chemical processes are not limited to the gas phase, but may also occur in the condensed phase. Apart from the trivial melting of solids, already taken into account in our present model, one can observe solid-to-solid phase transitions, stoichiometry variations, alloying in solid phase and mixing in liquid phase. An example is the formation of AlCu alloy during Al/CuO thermite combustion. AlCu alloy is actually found in combustion residues, but no more detail upon its formation is presently available. Given the range of temperatures scanned, such processes may happen very frequently. An accurate representation of these processes needs also a thorough study using quantum chemical calculations.

Our intention in the present paper is not to speculate on the chemistry of phase transitions, but rather to demonstrate the possibility of establishing a generic model predicting the maximal pressure and temperature for combustion of thermite depending on the available thermodynamic data. Further insights on the phase transitions chemistries, in condensed or gas phase can be unraveled and quantified properly from first principles quantum chemistry calculations.

Finally, the explicit time dependence of the reactions is a major source of discrepancies. The experimental rising times of the pressure in the combustion chamber are always less than 1 ms. The approximation of local thermodynamic equilibrium, leading to the concept of extent of reaction, is only a rough approximation. A kinetic approach, substituting the real time variable to the extent of reaction, is under development. This approach would enable us to consider transient metastable species, which may appear, more or less briefly, in the combustion chamber. These species may not of long lifetimes, but will have a significant importance on the pressure evolution. For example, aggregates of various sizes shall momentarily decrease the pressure, and disappear rapidly, forming new species. If the thermodynamic of these aggregates is well documented, through quantum calculations or experiments, they can be easily incorporated in our kinetic approach.

Conclusion

A local thermodynamics equilibrium model describing the pressure generation through reaction of various aluminum-based thermites is established in this paper. The model includes the determination of partial pressures as a function of condensation temperatures. It allows determining the partial pressures of gas phase reactants as well as the total pressure reached during and up to the complete reaction process (i.e. as a function of the extent of reaction). It also makes it possible to study the pressure delivered as a function of the compaction rate (%TMD). We applied our model to some commonly used thermite compositions, namely Al/CuO, Al/MoO 3 , Al/WO 3 , Al/Bi 2 O 3 and Al/Sb 2 O 3 . We observe that the highest final pressure is obtained for Al/CuO and Al/Bi 2 O 3 couples, mainly due to the partial decomposition of liquid alumina since the heat of reaction permits to reach high final reaction temperature, 3330°C and 3327 °C for Al/CuO and Al/Bi 2 O 3 , respectively. Simulations are compared to experiment for validation purpose. The final pressures predicted by the model are in fair agreement with experimental values. However, details on the mechanisms of gas generation are obtained such as the two-stage growth regime of the total pressure generated during reaction of Al/CuO, which has been observed experimentally. We should emphasize that all the parameters in the model are taken from thermodynamic data in the literature. No adjustable parameter, to be fitted to validation experiments, is used in the model. In order to improve our model quantitatively, without introducing adjustable parameters, future work is required, specifically by investigating the chemistry of the reactants in both the condensed and gas phases.

Fig. 1 :

 1 Fig. 1: Theoretical pressures, for different %TMD, and the equilibrium temperature, as a function of extent of reaction, during Al/CuO combustion.

Fig. 4 :

 4 Fig. 4givesthetemperatureevolutionas a functionoftheextentofreactionandfor all

Fig. 5 :

 5 Fig. 5: Theoretical pressure, for different %TMD, and the temperature as a function of extent of reaction,for Al/Bi 2 O 3 (a), Al/MoO 3 (b), Al/Sb 2 O 3 (c) and Al/WO 3 (d).

Fig. 6 :

 6 Fig. 6: Schematic view of the experimental pressure measurement set up.

Fig. 7

 7 Fig. 7 gives a comparison of simulated and experimental pressures at completed reaction for Al/Bi 2 O 3 , Al/MoO 3 ,Al/Sb 2 O 3 and Al/CuO respectively and for the three different TMD percentages: 10, 30 and 50 %TMD. As in the simulations, experimental measurements indicate that all thermites produce pressure. At 30 and 50 %TMD, thermites can be divided into two groups. Al/CuO and Al/Bi 2 O 3 exhibit the highest pressures, from 20 to 40 MPa, while as expected Al/Sb 2 O 3 and Al/MoO 3 generate less gas with pressures ranging from 7 to 15 MPa. For Al/CuO, Al/Sb 2 O 3 and Al/Bi 2 O 3 theoretical results overestimate the pressure with respect to experiments.The best fit between modeling and simulation is obtained for Al/CuO with a model/experimental results agreement within a factor of 3, while in[START_REF] Glavier | NanoEnergetics as pressure generator for nontoxic impact primers: comparison of Al/Bi2O3, Al/CuO, Al/MoO3 nanothermites and Al/PTFE[END_REF], the pressures were overestimated by one order of magnitude. The main reason for this improvement is that the chemical processes occurring Al/CuO combustion are well known and documented.

Fig. 7 :

 7 Fig. 7: Comparison of simulated and experimental pressures at completed reaction for Al/MoO 3 ,Al/CuO, Al/Bi 2 O 3 and Al/Sb 2 O 3 for three %TMD: 10%, 20% and 50%.

Table 1

 1

	.a:Specific heat of thermite reaction.
	Thermite couple	Specific heat of reaction (kJ/cm 3 )
	Al/CuO	20.6
	Al/WO3	15.6
	Al/MoO3	18.0
	Al/Bi2O3	15.0
	Al/Sb2O3	10.6
	Table 1.b: Latentheatsof vaporization/decomposition at
	atmospheric pressure.
	Boiling species	Latent heat of
		vaporization (kJ/mol)
	Al Vaporization	294
	Al2O3Decomposition	1402
	Cu Vaporization

Table 2 :

 2 Phase transitions considered in the model for Al/Bi 2 O 3 , Al/MoO 3 ,Al/Sb 2 O 3 and Al/WO 3 thermites (note that CuO phase transitions are detailed in the previous section 3.1).

	Materials T (°C)	Phase	Species
			transition
	Al 2 O 3	2042	Melting	Al 2 O 3(s) , Al 2 O 3(l)
	Al 2 O 3 Decomposition Al Sb 2 O 3 2977 655 Melting Sb 2 O 3(s) ,
				Sb 2 O 3(l)
	Sb 2 O 3	1425	Decomposition Sb 2 O 3(l) , Sb (g) ,
				O 2(g)
	WO 3	1200	Melting	WO 3(s) , WO 3(l)
	WO 3	1627	Decomposition WO 3(l) ,
				WO 2(l) ,O 2(g)
	WO 2	1730	Decomposition WO 2(l) , W (s) ,
				O 2(g)
	MoO 3	802	Melting	MoO 3(s) ,
				MoO 3(l)
	MoO 3	1155	Vaporization	MoO 3(l) ,
				MoO 3(g)
	Bi 2 O 3	279	Melting	Bi 2 O 3(s) ,
				Bi 2 O 3(l)
	Bi 2 O 3	1344	Decomposition Bi

2 O 3(l) , Al (g) , O 2(g) Bi 272 Melting Bi (s) , Bi (l) Bi 1564 Vaporization Bi (l) , Bi (g) Sb 357 Melting Sb (s) , Sb (l) Sb 1314 Vaporization Sb (l) , Sb (g) Mo 2623 Melting Mo (s) , Mo (l) Mo 4639 Vaporization Mo (l) , Mo (g) W 3422 Melting W (s) , W (l) W 5663 Vaporization W (l) , W (g) Al 660 Melting Al (s) , Al (l) Al 2519 Vaporization Al (l) , Al (g) 2 O 3(l) ,Bi (l) O 2(g)

Table 3 :

 3 Summary of powders used in the nanothermites mixture.

	Element Manufacturer	Measured size	Shape
	Al	Novacentrix	-150 nm	Spherical
	Bi2O3	SigmaAldrich	100 -500 nm	Ovoid
	MoO3	SigmaAldrich	90 -6000 nm	Random shape
	CuO	SigmaAldrich	240 nm +/-50 nm	Random shape
	Sb2O3	SigmaAldrich	120 -4200 nm

ACKNOWLEDGEMENTS

This work has been supported by CNRS with the contribution of DGA. The authors wish to thanks the DGA (French general delegation of armament) for their support.