Marie-Esther Lacuisse

The Evolution of Conservation Plans in South Arizona Wilderness Areas vs Ranchers' Working Landscapes

INTRODUCTION

Why do environmentalist collaborate with ranchers? How can they build common interests and practices? How do ranchers' participation contribute to change environmental conservation practices?

• Interviews with environmental activists, federal and local administration agents, ranchers

• Content analysis of conservation plans

• A mix approach between sociology and public policy analysis

RESULTS

THE CAUSES OF THE ECOLOGICAL VALUATION OF RANCHING: BETWEEN PRAGMATISM AND KNOWLEDGE

Ecological revaluation of ranching in order to face the environmental risks of urban development and the promotion of "sustainable mining" (T.E. Sheridan).

The involvement of ranchers in conservation plans comes not only from rational reasons (preserving their activity) but also from a collective will to assert a "knowledge of nature" distinct from a standardized "state ecology" (A.Leopold).

Revision of the ecological theory of rangeland areas: ranching may not be the main cause of land erosion and native species disappearance, especially in semi-arid areas. This theorical shift might be a result of experiments in southern Arizona (Santa Rita Experimental Range). WILDERNESS AREA An area where the earth and its community of life are untrammeled by man, where man himself is a visitor who does not remain" (H. Zahniser) "Area of undeveloped Federal land retaining its primeval character and influence, without permanent improvements or human habitation, which is protected and managed so as to preserve its natural conditions" (Wilderness Act) A controversial notion : an obstacle to sustainable development (W. Cronon) Red Rock Canyon is a perennial intermittent stream draining a watershed of 20,000 acres in the Canelo Hills of the Coronado National Forest (CNF).

2001: ranchers become stakeholders of the basin management whereas they were previously entitled to limited allocations.

Grazing bans in some areas have been replaced by a seasonal rotation (continuous grazing in winter and bans during the summer monsoons), while vegetation and land quality have improved.

Ranchers observe that livestock bans, in some rivers supported by environmentalists, are not helping to protect river biodiversity. Since the fences were installed, an endangered fish (the Gila Topminow) has disappeared.

RESEARCH QUESTIONS ON A PARADOXICAL COLLABORATION METHODS

  Cf: N.F. Sayre (2017) The Politics of Scale: A History of Rangeland Science, London et Chicago, The University of Chicago Press. AN ECOLOGICAL PERSPECTIVE Wilderness vs adaptation to local system and « sustainable communities »: towards conservation plan on working landscape (D.M. Waller, N.F. Sayre) (Re) valorization of the perception knowledge (savoir de perception, Leopold) that offers solutions for a preservation of biodiversity more adjusted to environmental constraints than the technical skills of engineers or environmentalists. Next Steps: is the co-production of knowledge with ranchers a real contribution to conservation knowledge? Source: Sonoita Valley Program Partnership (SVPP) Cienegas National Conservation Area Pima County Ranch Land Management Cienega Creek: a specific socio-ecological system a 45.000 acres territory including a corridor of vulnerable vegetation wildlife in wetlands, extended to Mexico, and a space of native grassland declared « National Conservation Area » in 2000 Protection of the lowest and wetter lands from human activity and maintenance of grazing in appropriate areas Empire ranch (cf. western movies): co-production of activities dedicated to the protection of nature the rehabilitation of native species (prairies dogs, etc.) and grazing Actors involved 1995: The Donaldson rancher family signed a contract with the Bureau of Land Management (BLM) for a co-gestion of the Empire ranch 1996: The BLM launched the « Sonoita Valley Program Partnership » to implement a « collaborative planning of the uses of land and of resources in the valley » 2003: Publication of a « Resources Management Plan » dedicated to the restoration of nature with ranchers whose mission is among others to control invasive species (mesquite trees, etc.) Canelo Hills Coalition When ranchers, engineers and scientists work together to manage wetlands Buying back private lands from ranchers and grazing rights on public land Development right: a legally binding agreement that limits uses of land for grazing and conservation easement (real estate and mining prohibited) Payment of ecosystem services (public and private financing from environmentalists organization) South Arizona, a semi-arid area of land use conflicts Mining activities, urban growth, agroindustry, grazing, Ranching, an ecological issue in a historical perspective The Conquest of the « Frontier »: over-grazing, erosion, contamination of rivers (cf. A. Leopold, F.E. Clements) Social and scientific mobilizations against grazing : sectorial and environmental measures Sectorial: Taylor grazing act (1934) defining carrying capacity on public (federal, state) land Environmental: wilderness areas promotion (1964) and the National Environmental Protection Act (1969) Ranch transformation in « wilderness areas (Research Ranch, wildlife centers, etc.) Since the 90's, conservation plans co-produced with ranchers in working landscapes => towards a « rancher ecology » ?


come

Closing the Provence thermal power plant: the stakes of a reconversion in a land of energies

Closing the Provence thermal power plant

The stakes of a reconversion in a land of energies

EDF GazelEnergie

The aim of decarbonising the French energy system implies the transition from a 'thermo-industrial' regime, based on fossil fuels, to a 'post-carbon' regime that values renewable energies (Durand, Pecqueur, Senil, 2015). For the territories of the coal-fired power stations, this energy transition challenge is an opportunity to experiment with new ways of producing energy.

Although focused on the municipalities of Gardanne and Meyreuil, the territorial pact also takes into account the 15 other municipalities of the former Provence Coal Basin. Since the closure of its last mine in 2003, this territory has converted some of its assets -inherited from its industrial and mining past -into innovative energy projects.

With the closure of the thermal power station, the page of coal is definitively turned, and new projects are being studied. Energy then appeared to be a genuine territorial resource with new development possibilities (Gumuchian, Pecqueur, 2007).

1

Diversity of energy end products : heat, biofuels, electricity, hydrogen, gas.

2 The biomass unit (converted in 2012) is at the heart of a new localised energy system.

3

The new projects (dotted lines) complement the projects that have existed for the last twenty years (solid lines).

4 A diversity of implementation scales: local (H2 Gardanne), metropolitan (CANTHEP), regional (Green Gaz, Hynovera).

5

An acceleration in the emergence of energy projects since the signature of the territorial pact in December 2020.

Closing to decarbonise 1.

Closing to territorialise

2.

Closing to diversify 3.

  industrial sites undergoing reconversion serve as laboratories for the energy transition? At the heart of the metropolitan area of Aix-Marseille and the Provence Coal Basin An area undergoing urban, sociological, economic and industrial transformation How do the reconversion projects of the thermal power plant of Provence fit into a dynamic of territorial transition initiated over the last two decades ?

  Sascha Perroux, Aix-Marseille University, CNRS, TELEMMe, Aix-en-Provence, France French Environment and Energy Management Agency 20, avenue du Grésillé-BP 90406 49004 Angers Cedex 01 France. Under the supervision of Sylvie Daviet, Aix-Marseille University, CNRS, TELEMMe, Aix-en-Provence, France The coal fired power plant in Provence Want to know more ? (in French) -DURAND, L., PECQUEUR, B., & SENIL, N. (2015), La transition énergétique par la territorialisation. L'énergie comme ressource territoriale. In Groux, Leducq, Scarwell (Éd.), Réussir la transition énergétique (p. 29-36). -GUMUCHIAN H., PECQUEUR B. (2007). La ressource territoriale, Economica, 252 p.


Quentin Lorente Safran

Eric Villeneuve

Christophe Merlo
email: c.merlo@estia.fr

Guy André Boy
email: g.boy@estia.fr

François Thermy
email: francois.thermy@safrangroup.com

Development of a digital twin for collaborative decisionmaking, based on a multi-agent system: application to prescriptive maintenance

Keywords: Digital twin, decision-support system, maintenance, multi-agent system

The fourth industrial revolution involves more complexity. This research effort focuses on decision-making in helicopter engine maintenance activities. Such a decision-making task is difficult and relies on a variety of experts who only have partial knowledge and incomplete situation awareness, due to the great diversity of everyday operational practices. In this paper, we propose a digital twin multi-agent approach to collaborative decision-making in prescriptive maintenance.

Introduction

The current context of the fourth industrial revolution [START_REF] Maynard | Navigating the fourth industrial revolution[END_REF] is as promising as it is a source of complexity. In complex industrial processes, such as maintenance of helicopter engines, our field of study, each stakeholder owns only a part of necessary information, knowledge, skills and knowhow, which induces only a set of partial views for handling current situations. Consequently, decision-making quality and effectiveness are impacted.

The decision-making process is based on personal expertise, techniques and tools that are easily understood in their immediate environment (i.e., entities such as department or team). Unfortunately, sometimes goals and benchmarks are different within teams and/or departments; therefore, mutual understanding and collaboration can be difficult.

Endsley defines situational awareness (SA) as perception of the elements of an environment in a volume of time and space, understanding of their meaning and projection of their state into the near future [START_REF] Endsley | Toward a Theory of Situation Awareness in Dynamic Systems[END_REF]. SA is recognized as a major issue in such a context. Many techniques are used to support cognitive tasks in companies like knowledge management (KM) [START_REF] Aries | MASK : une méthode d'ingénierie des connaissances pour l'analyse et la structuration des connaissances[END_REF] or machine learning (ML).

Even if techniques currently used locally look satisfactory, their expansion at the level of the entire company requires more systemic socio-cognitive task analyses toward improving collective performance. This is the reason why this study is based on a state of the art and a field study leading to a first proposal for a digital twin model to support decisions by integrating companywide knowledge.

State of the art

Cognitive science

Cognitive science and cognition refer to high-level brain activities such as perception, memory, or abstract reasoning [START_REF] Vignaux | Les sciences cognitives: une introduction[END_REF]. Understanding cognitive issues is crucial in an industrial environment. Transdisciplinary research for cognitive engineering [START_REF] Boy | L'Ingénierie Cognitive: Interaction Homme-Machine et Cognition (The French Handbook of Cognitive Engineering)[END_REF]), or "cognitique" in France (Lespinet-Najib, 2013) intents to adapt technology to the human rather than the opposite, to better assist people, by combining knowledge about humans, technology and the relationships between them.

Three main intellectual fields of cognitive science are currently studied:

• Cognitivism which is based on the hypothesis that cognition is a manipulation of symbols enabling the adaptation of solutions to current situations [START_REF] Pylyshyn | Computation and cognition: Toward a foundation for cognitive science[END_REF]). KM is an example of industrial application of this field. • Connectionism which is based on the assumption that cognition is the emergence of global states (expected responses) of networks of single elements (such as neurons) [START_REF] Hebb | The organization of behavior: A neuropsychological theory[END_REF]. ML is a successful example of connectionism field for tasks such as image or natural language recognition.

The "society of mind" [START_REF] Minsky | The Society of Mind[END_REF] which corresponds to a hybridization of cognitivism and connectionism. Different cognitive functions are performed by various agents (an agent has a function) which know how to solve a type of small-scale problem. For a larger scale problem, several agents linked together will be needed, this group of agents forms an agency. If we look at different levels, each internal agent organization can be seen as an agency itself. Consequently, cognition can be seen as a working society. This type of operation enables to solve more complex and unforeseen problems.

Decision-support and multi-agent system

Minsky's theory of human cognition implementation led to multi-agent systems (MAS) that enable us to model and simulate collective intelligence. Like a colony of ants, a school of fish or a flock of birds, individuals interacting in their environment are autonomous, at least partially. But relatively simple rules these agents individually follow lead to very sophisticated organizations at the collective level.

The efficiency of cognitive tasks, and more precisely decision is of strategic importance in industry [START_REF] Villeneuve | Decision-support methodology to assess risk in end-of-life management of complex systems[END_REF]. As the company can be seen as a system of systems (Popper et al., 2016), a MAS representation can allow the integration of the company's knowledge [START_REF] Merlo | Modélisation des connaissances en conduite de l'ingénierie: mise en oeuvre d'un environnement d'assistance aux acteurs[END_REF].

Maintenance

The above notions of cognitive science enable us to tend towards a flexible approach necessary in complex contexts [START_REF] Boy | Design for Flexibility: A Human Systems integration Approach[END_REF]. This is intended for application to maintenance of a fleet of helicopter engines, that is to say aimed at maintaining them in operational condition and/or at repairing them.

Our work in progress focuses on the identification of the right levels of maintenance maturity.

Different stages have been identified [START_REF] Nikolaev | Hybrid Data-Driven and Physics-Based Modelling for Prescriptive Maintenance of Gas-Turbine Power Plant[END_REF]. We find in ascending order of maturity:

• Descriptive analysis to understand and describe an event that occurred;

• Diagnostic analysis to identify the cause of the event;

• Predictive analytics to predict future events;

• Prescriptive analysis to obtain recommendations on the best possible choices.

The development of the prescriptive level seems to be the best to improve maintenance efficiency.

The digital twin

We have seen previously that in industry, many cognitive tasks can be supported by different techniques and approaches. Their wide diversity can make difficult gaining an exhaustive view of the actual industrial activity and parameters to be considered in decision-making leading to maximize overall efficiency.

Digital twin (DT) technology is recognized as a tool to manage such a complex system [START_REF] Grieves | Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems[END_REF]. Defined by NASA as "an integrated multi-physics, multi-scale, probabilistic simulation of an as-built vehicle or system that uses the best available structural models, sensors update to mirror the life of its corresponding flying twin" [START_REF] Glaessgen | The digital twin paradigm for future NASA and US Air Force vehicles[END_REF], its definitions evolved in a more generalist way to "a dynamic representation of a physical system using data, models and interconnected processes to enable access to knowledge of past states, present and future to manage action on this system" [START_REF] Camara Dit Pinto | Digital Twin Design Requirements in Downgraded Situations Management[END_REF].

Moreover, different levels of data integration have been identified by Kritzinger (Krintzinger et al., 2018). To achieve a dynamic and real-time DT, data flows should be automatic.

State of the art conclusion

It emerged that DT enables bringing collective intelligence to the maintenance activity at the organizational level.

The cognitivist approach enables us to manage high-level problems but lacks flexibility. Unexpected data or a missing rule lead implementations to fail.

The connectionist approach enables performing a large number of cognitive tasks such as recognizing images, texts or statistical trends but is very specialized. A task that deviates a little from what the program was designed and sized for will defeat it.

These two approaches are effective, each in the specific frameworks for which they have been implemented. It appears that a matrix articulating them would be beneficial. Matrix in the biological sense of the term, that is, the tissue in which more specialized structures are incorporated.

To this end, as already cited, Minsky developed an approach around his "Society of Mind" [START_REF] Minsky | The Society of Mind[END_REF].

More flexible, this approach enables us to understand a complex industry context involving the activity of many actors, humans or machines as an SMA. This is a basis for the design of a DT that reflects them. By modeling them despite their diversity and complexity, we can access predictions according to the known situation and the decisions made, and thus prescribe recommendations. These recommendations would be based on a situational awareness inaccessible to hitherto isolated parties, that is, without the help of a DT that aims to expand into omniscience.

FIELD STUDY

Observations and 21 semi-structured interviews with 15 partners spread over 9 departments were conducted in a helicopter engine maintenance company to see how what has been mentioned in the state of the art applies. A team of engineers in charge of fault diagnostics will look for the origin of a fault reported by a customer and the fastest and least expensive solution for solving the current case. However, the department responsible for fleet and resource management may have relevant information about the consequences of the chosen solution. For example, the longer-term economic cost or the impact on service to a related customer. This is a typical case. Currently, when a department feeds on information from another department, it is made manually or through meetings.

The studied industrial case already deployed several solutions with respect to the following maintenance methods:

• For descriptive maintenance: the collection of flight data in semi-real time following each helicopter flight. This data is collected by on-board sensors and the transfer takes place manually or automatically when the device returns to its base. • For diagnostic maintenance: experts identify the root cause of failures using software based on a Bayesian network. The probability variables are based mainly on past experience. • For predictive maintenance: engine health is monitored, and indicators or alerts based on thresholds are developed through statistical analysis of trends (temperatures, rotation speeds, vibration frequencies…) and artificial intelligence.

Cognitive science applied

Cognitivism: knowledge bases have been identified. Experts are invited to capitalize their knowledge in these bases but they are not integrated directly into the activity and thus their updating is not optimal. However, a Bayesian network (used by diagnostic team) is fed by probabilistic expert estimates of the links between symptoms and causes of engine failures. In this case, it is up-to-date as this system is used on a regular basis.

Connectionism: recent successful applications of deep learning have been observed to sort out large amounts of feedback documents written by customers in natural language to help diagnostics and for the detection of significant statistical trends in flight data in the engine health monitoring team.

Data flows

Some data or information flows tend to be as automated as possible, such as the collection of flight data via on-board sensors. However, some remain entirely manual, such as the transmission of information from the support service, comprising an engine health monitoring team and a diagnostic team, to the management of fleets and stocks of resources through regular meetings. This last flow represents a case of horizontal integration where a DT could help.

PROPOSAL: THE MULTI-AGENT SYSTEM AS A MEANS OF DIGITAL TWIN MODELING AND IMPLEMENTATION

It emerged from the state of the art, reaffirmed by the field study thereafter, that in cognitive science, cognitivism and connectionism have led to efficient industrial solutions such as knowledge management or deep learning respectively. But these solutions correspond to very specialized tasks. The concept of the society of mind, leading to solutions such as MAS, opens up the possibility of modeling systems of significant complexity. In helicopter engine maintenance, operators involved, human or machine, and expertise are very diverse. Each operator can be considered as an agent, and therefore the company as a MAS. Since each agent is itself a system, the helicopter engine maintenance activity can also be seen in other words as a system of systems [START_REF] Boy | Orchestrating Human-Centered Design[END_REF] [START_REF] Boy | FlexTech: From Rigid to Flexible Human-Systems Integration[END_REF].

Figure 1. System of systems [START_REF] Boy | FlexTech: From Rigid to Flexible Human-Systems Integration[END_REF].

The maintenance activity can be represented by a system of systems (Fig 1), corresponding to the physical part of the paired system, whatever the granularity level (part-engine-fleet, individual-teamservice etc.). If the physical twin is a system of systems, so should its digital counterpart. Systems that constitute the human parts of this system of systems have of course cognitive capacities which enable them to carry out their activity, but we can also find non-human cognitive systems like AI.

The DT should generate multi-agent cognition, that involves holistic or holonic decision-making processes (i.e., considering all available system states and information). All agents have a common goal. It is currently impossible for each agent to be aware of what other agents are doing in real time.

A MAS structure is proposed here to represent this multi-agent cognition.

If we combine the system of systems model with the concept of data integration levels previously seen, it gives a digital system of systems representing the physical system of systems. It is like a digital MAS, and its data flows connecting digital agents to physical agents depend on the level of maturity and/or locally-acceptable level of automation. Non-existent or invisible links within the physical twin can be established or highlighted within the DT for exploitation (Fig. 2). Given that:

• The MAS seems to provide flexible solutions adapted to a context which includes many individuals and evolving practices; • The most accomplished form of maintenance seems to be prescriptive maintenance;

• The DT aims to model a physical system and its environment to provide situational awareness;

It appears important to establish as a research objective a digital twin of the helicopter engines and a MAS of the company for prescriptive maintenance and collaborative decision-making at the organizational level.

CONCLUSION AND FUTURE WORK

This work is focused on a MAS as a means of digital twin modeling and implementation for supporting the coordination of maintenance activities and provide better situational awareness. This should lead to better decisions [START_REF] Endsley | Theorical underpinnings of situation awareness: a critical review[END_REF] by improving SA and adding flexibility. It is necessary to create a company-wide DT representing involved and effective actors or agents. DT is intended to prescribe recommendations for each industrial agent or player by specifying possible actions consequences and taking into account collective knowledge and preferences dynamically.

Interfaces that enable each agent to become part of the system will be explored. Finally, we will continue to involve company's stakeholders in the design, in an iterative user-centered design approach.

Figure 2 :

 2 Figure 2: Twin system of systems and data streams inspired by Boy and Krintzinger (Boy, 2019) (Krintzinger et al., 2018).

ACKNOWLEDGMENTS

This paper was produced thanks to the support of Safran Helicopter Engines and ANRT (The French Agency for Research and Technology).

Biography

François Thermy is Head of Services Technical Support at Safran Helicopter Engines, Support and Services division.


Théo Cavignac

Camille Latouche
email: camille.latouche@cnrs-imn.fr

Stéphane Jobic
email: stephane.jobic@cnrs-imn.fr

A theoretical discussion on the stability of (O 2 ) - and (S 2 ) -species in KCl and KBr salts: luminescence spectra and defect energy formation

In the present manuscript we unambiguously demonstrate from first-principles calculations that superoxide (O2) -and supersulfide (S2) -anions play the role of luminescence centers in chalcogen doped potassium halides. Calculations fully account for emissions peaking at about 530 nm in KCl:O, 545 nm in KBr:O, 620 and 492 nm in KCl:S, and 635 and 508 nm in KBr:S and confirm assertions proposed at the very first time in the sixties. Indeed, the experimental emission spectra of KCl:O, KBr:O, KCl:S and KBr:S in the visible range are confidently reproduced via quantum calculations using vibronic coupling and considering isolated (Q2) -(Q= O, S) molecular species in vacuum. Moreover, the stability of single charged O2 and S2 dimers in the KCl host lattice is definitely established from defect formation energy calculations.

I. INTRODUCTION

Alkali halides crystallize with the well-known rock salt cubic structure and are common case studies to set out and clarify the role of intrinsic point defects in solids. In particular, these ionic compounds are used as model to exemplify the impact of defects on optical properties. Naturally, they contain anionic and cationic vacancies 1 but can also be intentionally doped by transition metals or rare earth elements [START_REF] Bron | Rare-Earth Ions in the Alkali Halides. I. Emission Spectra of Sm 2 + -Vacancy Complex[END_REF] , and more breathtakingly, by poly-sulfide and poly-oxide anionic species [START_REF] Schulman | Luminescent Sulfur Centers in Alkali Halides and Other Inorganic Solids[END_REF][START_REF] Baba | Absorption, Luminescence, and Coloration in Sulfur-Doped KCl and KBr Crystals[END_REF] . Hence, when alkali halides are grown or heated in oxygen or sulfur rich atmospheres, O and S-doped materials are formed [START_REF] Schulman | Luminescent Sulfur Centers in Alkali Halides and Other Inorganic Solids[END_REF][START_REF] Baba | Absorption, Luminescence, and Coloration in Sulfur-Doped KCl and KBr Crystals[END_REF][START_REF] Rolfe | Optical Absorption and Fluorescence of Oxygen in Alkali Halide Crystals[END_REF] . Emission bands are then observed in the 400 nm to 800 nm range, more precisely at 530 nm in KCl:O, 535 nm in KBr:O, 625 and 490 nm in KCl:S, and 631 and 514 nm in KBr:S at 77 K [START_REF] Schulman | Luminescent Sulfur Centers in Alkali Halides and Other Inorganic Solids[END_REF][START_REF] Baba | Absorption, Luminescence, and Coloration in Sulfur-Doped KCl and KBr Crystals[END_REF][START_REF] Rolfe | Optical Absorption and Fluorescence of Oxygen in Alkali Halide Crystals[END_REF] . From the sixties, it is hypothesized that luminescence originates from the presence of (O2) -and (S2) -dimeric entities, even though the chemical intuition might suggest at the very first sight that those were highly unstable and unlikely [START_REF] Schulman | Luminescent Sulfur Centers in Alkali Halides and Other Inorganic Solids[END_REF][START_REF] Baba | Absorption, Luminescence, and Coloration in Sulfur-Doped KCl and KBr Crystals[END_REF] . This assumption was based for Odoped materials first on EPR measurements [START_REF] Känzig | Paramagnetic Resonance of Oxygen in Alkali Halides[END_REF] , second on the structured feature of the emission band with vibronic lines separated by about 1100 cm -1 , and third the absence of this active mode in the infra-red spectra of KCl:O and KBr:O suggesting a centrosymmetric species as luminescent center [START_REF] Rolfe | Optical Absorption and Fluorescence of Oxygen in Alkali Halide Crystals[END_REF] . The occurrence of (S2) -pairs in sulfur doped variants were hypothesized by analogies with O doped potassium halides due to strong similarities of the luminescence spectra [START_REF] Schulman | Luminescent Sulfur Centers in Alkali Halides and Other Inorganic Solids[END_REF] . In this article we bring theoretical confirmation of this hypothesis with the specific study of the KCl and KBr cases. Hence, we evidence the presence of (O2) -and (S2) -species in doped KX (X= Cl, Br) through both the simulation of emission spectra and molecular vibrations with TDDFT and DFT tools, respectively. Moreover, we fully strengthen these hypotheses on the basis of thermodynamics considerations via first principles calculations of the formation energy of intrinsic and extrinsic defects. To the best of our knowledge this report is the first to gather the thermodynamic approach of defect formation enthalpy study with luminescence and vibration simulations. After introducing the theoretical background and the numerical procedure of our approach, we confront the luminescence simulations to measured spectra from literature. We then focus our interest on the defect formation enthalpies of O2 and S2 dimers in KCl taking into account native defects that govern the dopability domain and subsequently the charge of (Q2) dumbbells (Q= O, S).

II. COMPUTATIONAL DETAILS

Luminescence spect ra simulations

To validate the origin of the luminescence spectra in Q doped KCl and KBr, we started an investigation on the emission properties of the (S2) -and (O2) -species isolated molecular species using first principles methods. All the (Q2) dumbbells were relaxed at their ground and excited states and checked to be minima on their potential energy surfaces by diagonalizing their Hessians (frequency calculations). DFT and TDDFT [START_REF] Massuyeau | New Insights To Simulate the Luminescence Properties of Pt(II) Complexes Using Quantum Calculations[END_REF][START_REF] Stoliaroff | Accurate Computations to Simulate the Phosphorescence Spectra of Large Transition Complexes: Simulated Colors Match Experiment[END_REF][START_REF] Schira | TDDFT vs. TDA to Simulate Phosphorescence Spectra of Pt-and Ir-Based Complexes[END_REF] computations were performed with the B3PW91 functional and the very large aug-cc-pvtz basis set, using the Gaussian 16 suite of programs 10 . To simulate the luminescence spectra, the state of the art Adiabatic Hessian (AH) model was used [START_REF] Barone | Fully Integrated Approach to Compute Vibrationally Resolved Optical Spectra: From Small Molecules to Macrosystems[END_REF][START_REF] Barone | Implementation and Validation of a Multi-Purpose Virtual Spectrometer for Large Systems in Complex Environments[END_REF] . It allows the inclusion of the mode-mixing effects upon a decent treatment of the potential energy surfaces of both ground and excited states. The specific choice of an adiabatic model is also based on our previous studies on Ir and Pt based complexes [START_REF] Massuyeau | New Insights To Simulate the Luminescence Properties of Pt(II) Complexes Using Quantum Calculations[END_REF][START_REF] Stoliaroff | Accurate Computations to Simulate the Phosphorescence Spectra of Large Transition Complexes: Simulated Colors Match Experiment[END_REF][START_REF] Schira | TDDFT vs. TDA to Simulate Phosphorescence Spectra of Pt-and Ir-Based Complexes[END_REF] and recently on the solid state study of the scapolite in which we demonstrated the impact of S2 -in an aluminosilicate cage [START_REF] Blumentritt | Unravelling the Origin of the Yellow-Orange Luminescence in Natural and Synthetic Scapolites[END_REF] .

Solid State Computations

First-principles computations on solids are made using the plane wave software VASP (Vienna Ab initio SimulationA Package [START_REF] Kresse | Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF] ) with the meta-GGA SCAN functional [START_REF] Yang | More Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme[END_REF] , using the method of projector augmented wave [START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] and a plane wave basis limited by a cutoff of 500 eV. Host structure study are made on the two atom primitive cell. The first Brillouin zone is paved by a 7x7x7 Monkhorst-Pack grid for the relaxation and a 10x10x10 Γ-centered grid for single point computations using the SCAN functional [START_REF] Sun | Strongly Constrained and Appropriately Normed Semilocal Density Functional[END_REF] . The structure was optimized until atomic forces were under 1 meV/Å and 10 -5 eV on the SCF cycle. Single point computations were converged to 10 -7 eV residual on total energy. The ideal supercell considered for the defects was built with 64 atoms with a 12 Å cell parameter. On this supercell, optimizations containing defects were made with a 2x2x2 Monkhorst-Pack with forces being below 10 meV/Å. Accurate energy computations were performed on a 6x6x6 Γ-centered grid with an energy convergence below 10 -6 eV. In order to correctly reproduce the large band gap, severely underestimated by the SCAN functional, accurate bandgap computations using the GW ansatz were performed on top of the SCAN geometry (formally here the G3W0) [START_REF] Shishkin | Self-Consistent GW Calculations for Semiconductors and Insulators[END_REF][START_REF] Stoliaroff | Accurate Ab Initio Calculations on Various PV-Based Materials: Which Functional to Be Used?[END_REF] . All post processing computations were made with the PyDEF package [START_REF] Stoliaroff | 2.0: An Easy to Use Post-Treatment Software for Publishable Charts Featuring a Graphical User Interface[END_REF][START_REF] Péan | Presentation of the PyDEF Post-Treatment Python Software to Compute Publishable Charts for Defect Energy Formation[END_REF] .

Defect Formation enthalpies (DFE)

In order to approach the defects through a thermodynamics point of view, the defect formation enthalpies (DFE) were computed. For a given defect D at a given charge state q, its DFE is given in function of the chemical potential of electrons with the below equation:

𝛥 𝑓 𝐻 𝐷,𝑞 (𝜇 𝐸 𝐹 ) = 𝐸 𝑡𝑜𝑡 𝐷,𝑞 -𝐸 𝑡𝑜𝑡 ℎ𝑜𝑠𝑡 + ∑ 𝑛 𝑖 𝜇 𝑖 𝑖 + 𝑞(𝐸 𝑉𝐵𝑀 ℎ𝑜𝑠𝑡 + 𝜇 𝐸 𝐹 ) + 𝐸 𝑐𝑜𝑟𝑟 (𝐷, 𝑞)
where 𝛥 𝑓 𝐻 𝐷,𝑞 is the formation enthalpy of a defect 𝐷 in a state of charge 𝑞 . The 𝐸 𝑡𝑜𝑡𝑎𝑙 𝐷,𝑞 -𝐸 𝑡𝑜𝑡𝑎𝑙 ℎ𝑜𝑠𝑡 term is the total energy difference between the faulted structure in the charge state q and the ideal structure. 𝑛 𝑖 is the number of atoms of the 𝑖 th species added (𝑛 𝑖 < 0) or removed (𝑛 𝑖 > 0) from the ideal probed material. 𝜇 𝑖 is the chemical potential of the 𝑖 th species, 𝜇 𝐸 𝐹 is the chemical potential of the electronic reservoir, E VBM host is the energy corresponding to the valence band maximum (VBM) of the host which sets the 𝜇 𝐸 𝐹 reference, and 𝐸 𝑐𝑜𝑟𝑟 corresponds to various corrections of spurious effects. Those corrections include Moss-Burstein band filling correction, Makov-Payne electrostatic correction, band edges corrections using G3W0 reference and potential alignment accounting for charged cells. All of them have been extensively described in a number of reviews.

Charge Transition Level (CTL)

The charge transition level 𝜖(𝑞/𝑞′) between two charge states 𝑞 and 𝑞′ corresponds to the 𝜇 𝐸 𝐹 level at which their respective DFEs are equivalents, i.e., the populations of both 𝑞 and 𝑞′ states are identical within the material for this specific potential. Such thermodynamic quantity is expressed as: 𝜖(𝑞/𝑞′) = 𝛥 𝑓 𝐻 𝐷,𝑞 (𝜇 𝐸 𝐹 = 0) -𝛥 𝑓 𝐻 𝐷,𝑞′ (𝜇 𝐸 𝐹 = 0) 𝑞′ -𝑞 where 𝛥 𝑓 𝐻 𝐷,𝑞 and 𝛥 𝑓 𝐻 𝐷,𝑞′ are the formation enthalpies of a defect 𝐷 in the charged states 𝑞 and 𝑞′, respectively.

III. LUMINESCENCE

Let first discuss the luminescence properties of sulfur doped potassium halides. Baba et al 4 observed in the visible range two luminescence bands for KCl:S and KBr:S centered respectively at ~ 620 nm (16129 cm -1 ) and ~ 492 nm (20325 cm -1 ), and ~ 636 nm (15723 cm -1 ) and ~ 508 nm (19685 cm -1 ). The former are excited at around ~ 350 nm, the latter at ~260 nm. These bands are not vibrationnally resolved and exhibit a Gaussian shape. On the opposite, the luminescence spectra of KCl:S and KBr:S reported by Schulman and Kirk 3 at 77K under excitation at 365 nm display bands at ~ 600 nm (16661 cm -1 ) and ~ 633 nm (15790 cm -1 ) that are well vibrationnally resolved with lines separated by an average value of 588 cm -1 and 582 cm - 1 for the chloride and the bromide variants, respectively. In order to fully assign the observed bands, we started a (TD)DFT study on isolated S2 species. Our simulations on (S2) -entities nicely fit the finely resolved spectrum of KBr:S (Figure 1a), i.e. with a calculated position centered around 15200 cm -1 (659 nm) and a separation of the fine vibronic pattern of about 585 cm -1 comparing well with 15723 cm -1 and 582 cm -1 , respectively. The ~70 meV difference in the positioning of the emission band maximum is in the standard error of TD-DFT calculations. Therefore, we can assign confidently the low energy emission of KBr to the presence of (S2) -. This emission process is issuing from the excitation transition from the π to π* orbitals of the (S2) - entity. By analogy, conclusions related to the KBr emission band can be extrapolated to the band observed at 16129 cm -1 in KCl. Let us notice that the calculated emission of single charged S2 dimers is also in the same region than the one observed for scapolite around 16500 cm -1 . [START_REF] Blumentritt | Unravelling the Origin of the Yellow-Orange Luminescence in Natural and Synthetic Scapolites[END_REF] This suggests that luminescence properties of (S2) -supersulfide anions in solids are almost not perturbed by their coordination sphere (tetraedron, square and octahedron in Na4(Al3Si3O12)Cl, Na4Al3Si9O24Cl and KCl materials, respectively). Consequently, such entity has to be regarded, at least at the first sight, both as a flexible and a rigid entity that accepts different chemical environments but imposes to the solid in which it is embedded its constraints to relax towards its natural ground state with an oscillator frequency of ca. 570-600 cm -1 as commonly assigned to such a dimer. Calculations can also account for the high energy luminescence bands of KCl:S and KBr:S (492 and 508 nm, respectively with an identical gaussian spectral shape).

Formally, the calculated emission band around 20400 cm -1 is in good agreement with the observed ones, i.e. 20325 cm - 1 and 19685 cm -1 and results then from an electronic excitation of the * to the σ* levels of the (S2) -pair. The shoulder observed around 600 nm in Figure 1b is likely due to the emission band depicted in Figure 1a but at low intensity due to a different excitation energy. Let us now discuss the luminescence spectra of KCl:O and KBr:O recorded by Rolfe et al. at 4.2 K that both displays a single band located around 535 nm (18868 cm -1 and 18349 cm -1 , respectively) with vibronic lines spaced by ca. 1065 cm -1 on the high energy side and by ca. 950 on the low energy side probably due to a probable anharmonicity. Our simulation of discrete (O2) -entities satisfactorily reproduces the observed luminescence spectrum of KCl:O (Figure 1c) with a maximum centered at 18500 cm -1 with 1200 cm -1 between each vibrational maximum. To sum up, we confirm for O-doped and S-doped potassium halide the long-time hypotheses that the observed emissions in the visible range are due to the presence of (S2) -and (O2) -. Nevertheless, in order to get some insights on the origin of the stability of superoxide (O2) -and supersulfide (S2) -species, we initiated a thermodynamic investigation on the stability of native and (Q2) x-(Q= O, S; x = 0, 1, 2) dopants in KCl via calculations of defect formation energies to probe both the ability of the KCl host lattice to entrap O2 and S2 pairs.

IV. DEFECT FORMATION ENTHALPY

Study of the bulk structure

Structure and electronic structure

The KCl host crystallizes in the fcc structure type (rock-salt structure, space group Fm-3m, n°225, Figure 2) with a= 6.2952(8) Å [START_REF] Trzesowska | The Structure and Quantum Chemical Study of the Potassium Chloride[END_REF] and K-Cl distances of 3.1476(5) Å to compare with calculated values, 6.2815 Å and 3.1408 Å, respectively. Thus, it can be concluded that the SCAN functional provides accurate geometrical results with respect to experiment. As well known, KCl displays a wide band gap reported between 8.40 and 8.7 eV [START_REF] Trzesowska | The Structure and Quantum Chemical Study of the Potassium Chloride[END_REF][START_REF] Roessler | Electronic Spectra of Crystalline NaCl and KCl[END_REF] . As expected with a meta-GGA functional, the computed bandgap is too small (5.97 eV) compared to experiments. In order to correct this value and accurately position the band edges, a G3W0 calculation was performed on top of the SCAN geometry. The corrected bandgap was 8.26 eV. This mathematical treatment also down and up shifted the band edges of the valence and conduction bands by 0.87 eV and 2.01 eV, respectively.

Doped KCl by ( O2) and (S2) species

In order to fully validate our luminescence band assignments, we started to evaluate the defect formation energies of the doped structure. The KCl:S system is firstly investigated followed by the KCl:O one.

Sulfur impurities in KCl

We focused here our attention only on the S-rich condition for which the insertion of (poly-)sulfide is favorable. We introduced one sulfur in interstitial (Si) and replaced Cl by either S or S2, namely SCl and (S2)Cl. The computed defect formation enthalpies are given in Figure 3. The S-rich atmosphere is detailed in SI and corresponds to a 𝜇 𝑆 = 𝜇 𝑆 ∘ . In the S-rich atmosphere, SCl and (S2)Cl defects are accessible in the dopability domain delimited by the chlorine and potassium vacancies DFEs. In this domain, both neutral and -1 charge states are possible for SCl species, while only neutral charge is expected for (S2)Cl ones. Consequently, our previous band assignments concerning KCl:S stating that (S2) -(q = 0 for (S2)Cl) is responsible for the observed luminescence is fully confirmed. Finally, it must be pointed out that at 𝜇 𝐸 𝐹 ~ 5 eV (the expected position of the Fermi level for KCl:S), four defects exhibit so low formation enthalpies that they are likely to be formed: VK, VCl, SCl and S2Cl. Their estimated computed concentrations for KCl grown at 1000K in S-rich atmosphere and quenched to room temperature are given in Table 1 (details on the computations of concentrations can be found has already been details in several publications [START_REF] Stoliaroff | Point Defects Modeling Explains Multiple Sulfur Species in Sulfur-Doped Na4(Al3Si3O12)Cl Sodalite[END_REF][START_REF] Van De Walle | First-Principles Calculations for Defects and Impurities: Applications to III-Nitrides[END_REF] ). In these conditions, it can be seen that intrinsic vacancies will be the most common types of defects but SCl and (S2)Cl are in significant concentration. The Bader charges of (S2)Cl and its first K+ neighbors are equal to -0.85 and +0.85. It fully confirms that the central entity is (S2) -. The Cl atoms are almost not affected by the presence of the defect.

Oxygen impurities in KCl

As for KCl:S, VCl and VK DFEs determine the dopability domain of KCl:O in O-rich atmosphere (see Figure 4). From the examination of the fH(Ef) diagram, it appears that the striking feature concerns the very low enthalpy formation of (O2)Cl 0 defect, with a DFE of ~ 0.01 eV. This may be related with the existence of KO2 with a rock salt structure [START_REF] Helms | Die Struktur der sogenannten ''Alkalitetroxyde"[END_REF] . On the structural point of view, let us mention here that our simulations conclude that the most stable orientation of (O2) -dimer is the [110] direction in doped KCl while it is [100] in KO2 in full agreement with the observation of Känzig et al. based on EPR mesurments [START_REF] Känzig | Paramagnetic Resonance of Oxygen in Alkali Halides[END_REF] . Against all expectations, this (O2)Cl 0 defect is predominant with respect to all the others. As a matter of fact, the computation of concentrations (see Table 2) shows very high concentration of (O2)Cl defects that would make the material closer to a KCl/KO2 solid solution than a doped KCl material. Indeed, the formulation computed from these concentrations is KCl0.89O0.22 (11% of Cl sites are occupied by O2). This observation is also coherent with the fact that the O-rich atmosphere we picked is adjacent to the stability domain of KO2 (and KO2 is isostructural to KCl). Moreover, structural analysis (see Table S7) shows that (O2) -has only a marginal structural effect on its environment, again emphasizing its compatibility with the site. Nevertheless, we may anticipate that such (O2) - species could also be stabilized in less oxidizing conditions. At the end, based on the examination of Figure 4, (O2) 2- peroxide groups might appear for Ef around 3.20 eV but their formation would be exothermic in oxygen rich conditions and would lead to deterioration of the KCl host lattice. Bader charges were found for (O2)Cl similar to (S2)Cl, confirming the (O2) -entity surround by K + octahedron.

V. CONCLUSION

Through comparison between theoretical and experimental luminescence spectra, we confirmed that (S2) -and (O2) -species can be observed in KCl bulk. Clearly, first principles calculations evidence that these species are thermodynamically stable and give rise to an easy detectable luminescence that can be used as footprint. Definitely, the existence of such exotic species have to be considered as possible anions in a large panel of solid materials (beyond of sodalite, hackmanite, scapolite, etc) against still a too spread preconceived idea. Indeed, their role cannot be limited to superchalcogenide radicals (e.g. (O2 •-) in (photo)catalytic reactions) with a surface chemical (re)activity. The consideration of those stable states could be beneficial in the future to applications of solid state chemistry where reactivity of those supposedly unstable species may have been overlooked before.

VI. SUPPORTING INFORMATION

The Supporting Information is available free of charge at the ACS website. It includes the defect formation energies and their relative concentrations in K-rich(Cl-poor) atmospheres of doped KCl:(S/O) together with the stability domains and their relative chemical potentials. The charge transition levels and the geometrical distortions are also provided.

Figure 1 .

 1 Figure 1. Simulated spectra of the different (S2) -and (O2) - species compared a) to experimental low energy range (dashed) spectra of KCl:S (collected at RT) 4 and KBr:S (collected at liquid nitrogen temperature) 3 , b) to experimental high energy range (dashed) spectra of KCl:S (collected at RT) 4 and c) to experimental luminescence spectra at 4.5 K 5 of KCl:O (collected at liquid nitrogen temperature).

Figure 2 .

 2 Figure 2. 3D representation of the conventional cell for KCl. Green and purple spheres correspond to chlorine and potassium atoms, respectively.

Figure 3 .

 3 Figure 3. Defect formation enthalpies of KCl:S in S-rich atmosphere.

Figure 4 .

 4 Figure 4. Defect formation enthalpies of KCl:O in K-and O-rich atmospheres.

Table 1 . Concentration of main defects in KCl grown in S-rich atmosphere at 1000K.

 1

	Defect	Concentration (cm -3 )
	VCl	1.1 . 10 15
	VK	1.1 . 10 15
	SCl	1.4 . 10 14
	(S2)Cl	5.5 . 10 12

Table 2 . Concentration of main defects in KCl grown in O-rich atmosphere at 1000K. Defect Concentration (cm -3 )

 2

	VCl	1.1 . 10 15
	VK	1.1 . 10 15
	OCl	3.7 . 10 15
	(O2)Cl	1.7 . 10 21

VII. ACKNOWLEDGEMENTS

The authors thank the Region des Pays de Loire and CCIPL. CL and TC thank the ANR for financial support (ANR JCJC MoRDOR: ANR-20-CE08-0013).

TOC Graphic

In the present manuscript we unambiguously demonstrate from first-principles calculations that superoxide (O2) -and supersulfide (S2) -anions play the role of luminescence centers in chalcogen doped potassium halides.


has created an unbearable situation. This divide is accentuated by the involvement of governments at all levels-from town councils to the state-who have made a variety of attempts to address the problem. The expected solutions to these main problems are based on the idea of a Greater Paris, a polysemous concept that is being outlined by a new circle train line. This expensive project intends to develop high-quality underground service in the suburbs by opening several sublines starting in 2020 and attempting to reduce the number of trips along currently congested radial lines.

The circle line and other political fixes are aimed at addressing the problems caused by Paris's poorly functioning mobility system, problems that are increasingly growing in importance within Parisian politics and in the local press. At the same time, however, historians, geographers, and town planners have been encouraging broader reflection on the dysfunctions of the city's transport systems since the early 2000s. Xavier Desjardins, Nicolas Douay, and Vincent Gagnière have written an interesting long-term analysis of the history of transport planning in the Paris area. Their work resonates importantly with the regional planning document that was published in 2013. 4 Cooperation between geographers and historians has also shed light on the relationships between rail and territory and on the cultural differences visible in how the British and French view these topics. 5 In the frame of mobility studies, researchers in urban and social geography, notably Lionel Rougé, have worked to better understand suburban areas, contributing to making them a focus of transport planning that can be addressed by public policies .6 On the topic of Greater Paris, scholars have published books for a general audience that have allowed them to join in the debate alongside citizens and politicians. 7 Historians have also broadened their point of view, investigating the whole agglomeration and not just inner Paris. This trend is not restricted to the historians of transport and mobility. Indeed, it is pervasive across disciplines. Greater Paris and its history, punctuated by two major moments of reform-the 1860s and the 1960s-has become its own field of research. 8 The relationship between Paris and its suburbs was first studied through an institutional point of view. Florence Bourillon, Annie Fourcaut, and Nathalie Montel have published new research on the expansion of the capital in 1860, which was the first step in the increasing tensions between Paris and the communes of the département de la Seine. 9

Increasingly, the suburban territory of the twentieth century has also been widely addressed by scholars. For instance, Pierre Chabard and Virginie Picon-Lefebvre edited a comprehensive dictionary on the iconic La Défense. 10 Emmanuel Bellanger and Julia Moro have recently proposed a historical perspective on a more common area, the Val-de-Marne département. 11 Along the same lines, the opening of archives from the 1970s has allowed new works to be written on the important moment of the Pompidou era, which for years had been hidden by the shadow of the de Gaulle/Delouvrier moment that preceded it. 12 Transport, given its variety, is crucial to understanding that the actors of that time already conceived the metropolis on a regional scale.

Today, as in earlier periods, the history of transport systems in the Paris area is still concerned more with projects and planning than the experience of traveling. And no amount of daily reports on the difficulties of transport produced by the press and discussed by politicians have changed that focus. The origin of this arrangement may be traced to the relationship between historians of transport and mobility of Paris and geographers, political scientists, architects, and engineers, who traditionally focused on technical, economic, and 8 Among the different works on this theme, the annual conferences organized by historians Florence Bourillon and Emmanuel Bellanger must be mentioned, with colleagues from schools of architecture (the most recent one was "Inventer le Grand Paris," in December 2014). project (1960s-1970s) still awaits scholars who could write a history based on oral archives at the scale of the metropolis. Historians have not really addressed walking and cycling in Paris, mainly because of source problems. But here imaginative efforts on the part of scholars could help collect historical materials on these practices, such as pictures of streets, unstructured archives of associations, and more.

Whereas other technical networks (water, energy supply, etc.) have been studied, particularly by Emmanuel Bellanger, Sabine Barles, and Isabelle Backouche, the history of transport in the suburbs is still to be written. 25 Monographs on railway lines exist, often written by nonscholars, as well as academic works on the suburban territory, often without real consideration of the history of transport systems. 26 Here, one can only regret the lack of historical works on the history of suburban mobility, beyond the already written transport history of the inner Paris territory, inscribed in the périphérique motorway and equipped with the Métro network.

Because mobility and planning are also a matter of words, scholars could shed light on the history of how many came to see Paris as a world city because of transport networks.

From

  the History of Transport in Paris to the History of Mobility in Greater Paris? Arnaud Passalacqua, Paris Diderot University (ICT-LIED) Historians are scholars of their times. This sentence is well illustrated by recent work done by academics on the history of mobility in Paris. While current trends in transport planning and politics have been addressed by historians of mobility, this article will discuss whether historians have tackled all the most important developments around transport in the Paris area. It will first consider the latest focus of the research in this field in connection with recent evolutions of transport policies. Then the article will try to highlight the valuable topics not yet addressed by existing academic work. The election of Mayor Bertrand Delanoë in 2001 marked the beginning of a shift in Parisian attitudes toward transport that have since unfurled during the first decade of the twenty-first century. Under Delanoë and his deputy mayor for transport, Denis Baupin, the role and legitimacy of every mobility system was publicly analyzed. These discussions led to a general reorganization of public space away from cars, in favor of public transport, bikes, and pedestrians. At the same time, historians were studying similar debates in the longue durée, considering especially the example of the automobile and conflicts between mobility systems. The relationships between Paris and the newly contested car became a historical theme illustrated by Mathieu Flonneau. 1 Simultaneously, the development of new transport systems in the street-dedicated bus lanes and tramways-induced a historical reflection by Arnaud Passalacqua on the cohabitation between systems in a constrained and common space. 2 In 2006 a new tramline opened and marked the reemergence of that system in Paris, yet few scholars have embraced this specific mode or its historiography, which remains dominated by Jean Robert. 3 This new tram, an exclusively Parisian project, can be understood as the last milestone of a period of relative cold war between Paris and its suburbs around the subject of transport. Since the end of the 2000s, both public policies and academic studies have increasingly converged on new configurations of actors and mobility. Both worlds have addressed new stakes, at a new level: the (old) difficulties of mobility and governance in the suburbs have become a new priority for politicians and academics alike. The unbalanced concentration of jobs in the western part of the agglomeration and housing in the eastern part 1 Mathieu Flonneau, Paris et l'automobile: Un siècle de passions (Paris: Hachette Littératures, 2005); Mathieu Flonneau, "City Infrastructures and City Dwellers: Accommodating the Automobile in Twentieth-Century Paris," The Journal of Transport History 27, no. 1 (2006): 93-114. 2 See Arnaud Passalacqua, L'Autobus et Paris: Histoire de mobilités (Paris: Economica, 2011). 3 The reference is old but useful: Jean Robert, Les Tramways parisiens (Neuilly-sur-Seine: Jean Robert, 1992). More recent works also exist: Peter Soppelsa, "Reworking Appropriation: The Language of Paris Railways, 1870-1914," Transfers 4, no. 2 (2014): 104-123; Arnaud Passalacqua, "Resident Alien: France's Ambivalent Relationship to the Tramway Before 1914," in Mobility in History: Themes in Transport (T 2 M Yearbook 2011), ed. Georgine Clarsen et al. (Neuchâtel: Alphil, 2011), 71-86. On the new wave of tramways, in France and not only in Paris, I underline the importance and the success of the seminar "Réinventer le tramway? Quarante années de TCSP, tramways et transports guidés en France: controverses et réalisations," organized by Rails et histoire and the UMR AUSser (2013-15).

4

  Xavier Desjardins, Nicolas Douay, and Vincent Gagnière, "Évolution des schémas, permanence des tracés: La planification de la région parisienne au prisme des réseaux ferroviaires," Géocarrefour 87 (2012): 69-84. 5 See Town Planning Review 85, no. 2 (2014), special issue, "Linking Rail and Urban Development: French and British Experiences." 6 See, for instance, Claire Aragau, Martine Berger, and Lionel Rougé, "Vers une maturité des territoires périurbains?," EchoGéo 27 (2014), http://echogeo.revues.org/13683 [accessed June, 26 2015]. 7 The most discussed work is Jean-Pierre Orfeuil and Marc Wiel, Grand Paris. Sortir des illusions, approfondir les ambitions (Paris: Scrineo, 2012).

9

  figure of the horse, which is at the center of the transport system of this first industrial century, deserves new research to update the works done by Ghislaine Bouchet, 22 on the pattern of what has been published on the seventeenth and eighteenth centuries by Daniel Roche. 23 Historical works seem to have also underexamined the recent decades. No overview study on the last thirty years of the history of transport in the Paris area has been written. The last complete book, by Dominique Larroque, Michel Margairaz, and Pierre Zembri, does not go beyond the 1980s. 24 More precisely, the recently finished mayoralty of Delanoë, which was explicitly based on mobility (r)evolutions, could provide a very stimulating topic for a historical perspective. The older and probably more classic Réseau Express Régional (RER) 16

20

  Stéphanie Sauget, À la recherche des pas perdus: Une histoire des gares parisiennes au XIXe siècle (Paris: Tallandier, 2009). 21 Carlos López Galviz, "Metropolitan Railways: Urban Form and the Public Benefit in London and Paris c. 1850-1880," The London Journal 38, no. 3 (2013): 184-202. 22 Ghislaine Bouchet, Le Cheval à Paris de 1850 à 1914 (Geneva and Paris: Librairie Droz, 1993).23Daniel Roche, La Culture équestre de l'Occident, XVIe-XIXe siècle, L'ombre du cheval(Paris: Fayard, vol. 1, 2008; vol. 2, 2011). 24 Dominique Larroque, Michel Margairaz, and Pierre Zembri, Paris et ses transports, XIXe-XXe siècles: Deux siècles de décisions pour la ville et sa région (Paris: Éditions Recherches/AHICF, 2002). For instance, the contemporary Greater Paris project focuses on Paris's main airport (Paris-Charles-de-Gaulle) as a key component of the city's international reputation and as a site in dire need of improved transportation connections. This trend hides local stakes, such as problems with unequal transportation provision across the metropolitan area because of unbalanced network configurations and high fares. Such local issues have yet to be fully investigated by historians. Another way to develop this question is to study the history of Paris not only as the urban (anti)model in the French frame, as developed by Bernard Marchand, but also as the mobile one. 27 Convergences between mobility history and the now established field of environmental studies are also likely to happen. Whereas the history of freight is nearly nonexistent, studies based on the environmental impact of the functioning of a great metropolis such as Paris may open the way to a new interest in historical studies of freight 25 See, for instance, on electrical networks, Emmanuel Bellanger and François-Mathieu Poupeau, Lumières sur la banlieue: Histoire du Syndicat intercommunal de la périphérie de Paris pour l'électricité et les réseaux de communication (Paris: Éditions de l'atelier, 2013). On water, see Sabine Barles, "The Seine and Parisian Metabolism: Growth of Capital Dependencies in the 19th and 20th Centuries," in Urban Waters: Rivers, Cities and the Production of Space in Europe and North America, ed. Stéphane Castonguay and Matthew D. Evenden (Pittsburgh: Pittsburgh University Press, 2012), 94-112; Isabelle Backouche, La Trace du fleuve, La Seine et Paris (1750-1850) (Paris: Éditions de l'École des hautes études en sciences sociales, 2000). 26 See, for instance, the classic book by Annie Fourcaut, La Banlieue en morceaux: La Crise des lotissements défectueux en France dans l'entre-deux-guerres (Grane: Créaphis, 2000). 27 Bernard Marchand, Les Ennemis de Paris: La haine de la grande ville des Lumières à nos jours (Rennes: Presses universitaires de Rennes, 2009). systems. But the quantitative approach of some environmental studies does not necessarily match well the paradigm of the mobility turn. 28 Continued methodological exchanges could open a useful dialogue between the fields. This could be built from the existing works of historians like Geneviève Massard-Guilbaud on pollution 29 or Jeffrey Jackson on the 1910 flood of Paris. 30 As a last point, one can only regret the current state of Paris's mobility heritage. While the French capital was one of the most important birthplaces of the car and an industrial center of that sector during the twentieth century, the memory of the automobile in the city is poorly commemorated by Parisians. The agglomeration does not provide any historical museum worthy of the name on this transport system. The history of public transport is hardly treated better. Since the closing of the Museum of Saint-Mandé in 2001, attempts to build a new museum, first in Colombes, then Chelles, have been threatened by divergences between the AMTUIR-a public transport enthusiasts' association that owns a unique collection-and museum professionals, who have the know-how but no collection. The lack of physical monuments to mobility history is all the more damaging given the popular enthusiasm for historical perspectives on transport. A recent exhibition on the Métro 31 and the success of a nonscholarly book by Grégoire Thonnat on the history of the Métro ticket 32 have confirmed that a real interest in transport heritage exists. This enthusiasm 28 See, for instance, Sabine Barles et al., "Grain, Meat and Vegetables to Feed Paris: Where Did and Do They Come From? Localising Paris Food Supply Areas from the Eighteenth to the Twenty-First Century," Regional Environmental Change 12, no. 2 Guilbaud, "Pour une histoire environnementale de l'urbain," Histoire urbaine 18 (2007): 5-21. 30 Jeffrey Jackson, Paris Under Water: How the City of Light Survived the Great Flood of 1910 (London: Palgrave, 2010). should be the impetus for the development of the mobility history museum that Paris deserves. Here lies a tension: whereas historians of mobility of the Paris area follow the contemporary debates and focuses, they lack the necessary support from contemporary institutions to develop a richer relationship with a public audience. Arnaud Passalacqua is an assistant professor of contemporary history at the Paris Diderot University. He works on the history of mobility in different European cities as well as on railways. He recently coedited Les Transports de la démocratie: Approche historique des enjeux politiques de la mobilité (Rennes: PUR, 2014). Notes 31 Métro . . . Ticket pour une expo, exhibition, Musée des arts et métiers, 2011-12. 32 Grégoire Thonnat, Petite histoire du ticket de métro parisien (Paris: Télémaque, 2010).


Khang Hoang
email: khang.hoang@ndsu.edu

Camille Latouche

Stéphane Jobic

Why is it so difficult to realize Dy 4+ in as-synthesized BaZrO 3 ?

Rare-earth doped barium zirconate (BaZrO3) ceramics are of interest as proton-conducting and luminescent materials. Here, we report a study of dysprosium (Dy) and other relevant point defects in BaZrO3 using hybrid density-functional defect calculations. The tetravalent Dy 4+ is found to be structurally and electronically stable at the Zr lattice site (i.e., as Dy 0 Zr ), but most often energetically less favorable than the trivalent Dy 3+ (i.e., Dy - Zr ) in as-synthesized BaZrO3, due to the formation of low-energy, positively charged oxygen vacancies and the mixed-site occupancy of Dy in the host lattice. The Dy 4+ /Dy 3+ ratio can, in principle, be increased by preparing the material under highly oxidizing and Ba-rich conditions and co-doping with acceptor-like impurities; however, postsynthesis treatment may still be needed to realize a non-negligible Dy 4+ concentration. We also find that certain unoccupied Dy 4f states and the O 2p states are strongly hybridized, a feature not often seen in rare-earth-containing materials, and that the isolated DyZr defect might be the source of a broad blue emission in band-to-defect ("charge-transfer") luminescence.

I. INTRODUCTION

Dysprosium (Dy) is very stable as the trivalent Dy 3+ in solid compounds, yet the divalent Dy 2+ has also been observed in some fluorides [START_REF] Mcclure | Survey of the spectra of the divalent rare-earth ions in cubic crystals[END_REF][START_REF] Kiss | Energy levels of Dy 2+ in the cubic hosts of CaF2, SrF2, and BaF2[END_REF] and suspected to be photogenerated under irradiation in persistent luminescent phosphors [START_REF] Joos | Identification of Dy 3+ /Dy 2+ as electron trap in persistent phosphors[END_REF]. The tetravalent Dy 4+ was almost unknown up to very recently [START_REF] Han | Tetravalent dysprosium in a perovskite-type oxide[END_REF][START_REF] Ricote | Conductivity behavior of BaZr0.9Dy0.1O 3-δ[END_REF][START_REF] Ricote | Non stoichiometry and lattice expansion of BaZr0.9Dy0.1O 3-δ in oxidizing atmospheres[END_REF]. Han et al. [START_REF] Han | Tetravalent dysprosium in a perovskite-type oxide[END_REF] was the first to claim experimental evidence of Dy 4+ in BaZrO 3 , a perovskite structure type host lattice commonly investigated for its proton conductivity ability [START_REF] Regalado | A mini-review on proton conduction of BaZrO3-based perovskite electrolytes[END_REF]. Subsequent reports provided further evidence for the presence of the tetravalent state in samples prepared in oxidizing atmospheres [START_REF] Ricote | Conductivity behavior of BaZr0.9Dy0.1O 3-δ[END_REF][START_REF] Ricote | Non stoichiometry and lattice expansion of BaZr0.9Dy0.1O 3-δ in oxidizing atmospheres[END_REF] and the mixed-site occupancy of Dy in the host lattice [START_REF] Han | Dopant occupancy and chemical expansion in rare earth-doped barium zirconate[END_REF], and discussed the possible role of Dy 4+ as a charge-compensating defect in the oxidation reaction [START_REF] Ricote | Conductivity behavior of BaZr0.9Dy0.1O 3-δ[END_REF][START_REF] Ricote | Non stoichiometry and lattice expansion of BaZr0.9Dy0.1O 3-δ in oxidizing atmospheres[END_REF]. The stability of Dy 4+ is thus of interest because of not just the exotic valence state but also the implication it has for defect-related processes in the material.

On the theory side, the interaction between the Dy dopant and BaZrO 3 , including native point defects and other impurities that may be present in the host material, has not been investigated, and thus a theoretical foundation for understanding the experimental observations is still lacking. First-principles defect calculations [START_REF] Freysoldt | First-principles calculations for point defects in solids[END_REF] based on a hybrid density-functional theory (DFT)/Hartree-Fock approach [START_REF] Heyd | Hybrid functionals based on a screened Coulomb potential[END_REF] can provide a detailed understanding of the atomic and electronic structure (including the oxidation state), energetics, and optical properties of rareearth (RE) dopants in solid compounds [START_REF] Hoang | Hybrid density functional study of optically active Er 3+ centers in GaN[END_REF][START_REF] Hoang | Tuning the valence and concentration of europium and luminescence centers in GaN through co-doping and defect association[END_REF].

Here, we present an investigation of Dy and other relevant defects in BaZrO 3 using hybrid density-functional defect calculations. Explicit calculations are carried out for native point defects and substitutional Dy and yttrium (Y) impurities. Based on the results, we discuss the stability of Dy 3+ and Dy 4+ and the tuning of the Dy 4+ /Dy 3+ ratio and the lattice site preference via tailoring the synthesis conditions and co-doping, or via postsynthesis treatment. Possible band-to-defect and defectto-band (also known as "charge-transfer") optical transitions involving the isolated Dy Zr defect are also explored.

II. METHODOLOGY

Defects in BaZrO 3 are modeled using a supercell approach in which a defect is included in a periodically repeated finite volume of the host material. Here, the term "defect" is referred generally to either native point defects or impurities, i.e., extrinsic defects, intentionally added (i.e., dopants) or unintentionally present in the material. A defect is characterized by its formation energy. Defects with a lower formation energy will be more likely to form and occur with a higher concentration.

The formation energy of a defect X in effective charge state q (with respect to the host lattice) is defined as [

9] E f (X q ) = E tot (X q ) -E tot (bulk) - i n i µ i (1)
+ q(E v + µ e ) + ∆ q , where E tot (X q ) and E tot (bulk) are the total energies of the defect-containing and bulk (i.e., perfect and undoped) supercells; n i is the number of atoms of species i that have been added (n i > 0) or removed (n i < 0) to form the defect; µ i is the atomic chemical potential, representing the energy of the reservoir with which atoms are being exchanged. µ e is the electronic chemical potential, i.e., the Fermi level, representing the energy of the electron reservoir, referenced to the valence-band maximum (VBM) in the bulk (E v ). Finally, ∆ q is the correction term to align the electrostatic potentials of the bulk and defect supercells and to account for finite-size effects on the total energy of charged defects [START_REF] Freysoldt | Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations[END_REF][START_REF] Freysoldt | Electrostatic interactions between charged defects in supercells[END_REF].

From the defect formation energy, one can determine the thermodynamic transition level between charge states q and q ′ of a defect, ǫ(q/q ′ ) (q > q ′ ), defined as the Fermilevel position at which the formation energy of the defect in charge state q is equal to that in state q ′ . This level [also referred to as the (q/q ′ ) level], corresponding to a defect level, would be observed in experiments where the defect in the final charge state q ′ fully relaxes to its equilibrium configuration after the transition. The optical transition level E q/q ′ opt , on the other hand, is defined similarly but with the total energy of the final state q ′ (q) calculated using the lattice configuration of the initial state q (q ′ ) for the absorption (emission) process [START_REF] Freysoldt | First-principles calculations for point defects in solids[END_REF].

The total-energy electronic structure calculations are based on DFT with the Heyd-Scuseria-Ernzerhof (HSE) functional [START_REF] Heyd | Hybrid functionals based on a screened Coulomb potential[END_REF], the projector augmented wave method [START_REF] Blöchl | Projector augmented-wave method[END_REF], and a plane-wave basis set, as implemented in the Vienna Ab Initio Simulation Package (vasp) [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF]. The Hartree-Fock mixing parameter and the screening length are set to the default values of 0.25 and 10 Å, respectively. We use the PAW potentials in the vasp database which treat Ba 5s 2 5p 6 6s 2 , Zr 4s 2 4p 6 5s 2 4d 2 , O 2s 2 2p 4 , Dy 5s 2 5p 6 4f 10 6s 2 , and Y 4s 2 4p 6 5s 2 4d 1 explicitly as valence electrons and the rest as core electrons. Defects are simulated using a cubic 40-atom supercell and a 2×2×2 Monkhorst-Pack k-point mesh for the integrations over the Brillouin zone. In the defect calculations, the lattice parameters are fixed to the calculated bulk values but all the internal coordinates are relaxed. In all the calculations, the energy cutoff is set to 500 eV and spin polarization is included; structural relaxations are performed with HSE and the force threshold is chosen to be 0.01 eV/ Å. The DFT+U method [START_REF] Dudarev | Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study[END_REF], with U eff = 6.0 eV applied on the Dy 4f states, is also employed to calculate the electronic structure of Dy-doped BaZrO 3 , and the result is compared with that from the HSE calculations (see Sec. III B). For a detailed discussion of the suitability of the hybrid DFT/Hartree-Fock approach to the study of defect physics in RE-doped materials, in comparison with other methods such as DFT and DFT+U , see Ref. [START_REF] Hoang | Tuning the valence and concentration of europium and luminescence centers in GaN through co-doping and defect association[END_REF].

The chemical potentials of Ba, Zr, Dy, Y, and O are referenced to the total energy per atom of bulk Ba, Zr, Dy, Y, and O 2 at 0 K, respectively. µ Ba , µ Zr , and µ O vary over a range determined by the formation enthalpy of BaZrO 3 such that µ Ba + µ Zr + 3µ O = ∆H(BaZrO 3 ) (calculated to be -17.29 eV at 0 K). We examine defect landscape in BaZrO 3 in two limits: (i) the (Ba,O)-rich condition where the host material is assumed to be in thermodynamic equilibrium with BaO (∆H = -5.09 eV) and O 2 gas at 1 atm, and (ii) the (Zr,O)-rich condition where equilibrium with ZrO 2 (∆H = -10.99 eV) and O 2 gas at 1 atm is assumed. The temperature range from 1000 • C to 1600 • C is often used in the preparation of Dy-doped BaZrO 3 samples [START_REF] Han | Tetravalent dysprosium in a perovskite-type oxide[END_REF][START_REF] Ricote | Conductivity behavior of BaZr0.9Dy0.1O 3-δ[END_REF][START_REF] Ricote | Non stoichiometry and lattice expansion of BaZr0.9Dy0.1O 3-δ in oxidizing atmospheres[END_REF][START_REF] Han | Dopant occupancy and chemical expansion in rare earth-doped barium zirconate[END_REF]. Under the mentioned condi-tions, µ O is -1.45 eV (at 1000 • C) or -2.56 eV (1600 • C) [START_REF] Stull | JANAF Thermochemical Tables[END_REF]. The specific value of µ Dy and µ Y is obtained by assuming equilibrium with Dy 2 O 3 (∆H = -18.53 eV) and Y 2 O 3 (∆H = -19.00 eV), respectively.

In the above, we explicitly take into account the temperature and pressure dependence when considering gasphase species, specifically when calculating the oxygen chemical potential (which is related to the Gibbs free energy of O 2 gas at temperatures and oxygen partial pressures under consideration) [START_REF] Reuter | Composition, structure, and stability of RuO2(110) as a function of oxygen pressure[END_REF]. Temperature and pressure effects are usually small for solid phases and thus can be ignored; besides, significant cancellation occurs between different terms in the defect formation energy and when comparing different defects [START_REF] Freysoldt | First-principles calculations for point defects in solids[END_REF]. Also note that the defect transition levels, ǫ(q/q ′ ) and E q/q ′ opt , are independent of the choice of the atomic chemical potentials.

It should be realized that the sets of the chemical potentials determined from the above assumptions are relevant to the system during synthesis, when all the constituent elements of the host compound are in exchange with their respective reservoirs. The experimental conditions during, e.g., post-synthesis treatment, measurement, or use are often very different, according to which only certain element(s) of the host may be exchanged with the environment. These conditions, if known, can be translated into other sets of the chemical potentials. For further discussion with examples of defect landscape in different experimental situations in other classes of materials and physical phenomena, see Refs. 20 and 21.

III. RESULTS AND DISCUSSION

A. Bulk properties and native defects

In bulk (cubic) BaZrO 3 , the calculated lattice constant is 4.200 Å, compared to 4.192 Å in experiments [START_REF] Yamanaka | Thermochemical and thermophysical properties of alkaline-earth perovskites[END_REF]. The calculated band gap is 4.68 eV, an indirect gap with the VBM at the R ( 1 2 , 1 2 , 1 2 ) point in the reciprocal space and the conduction-band minimum (CBM) at the Γ (0,0,0) point. For comparison, the reported experimental band gap varies in the range from 4.0 eV to 5.3 eV [START_REF] Borja-Urby | Blue and red emission in wide band gap BaZrO3:Yb 3+ ,Tm 3+[END_REF][START_REF] Yuan | Synthesis and photocatalytic characterization of a new photocatalyst BaZrO3[END_REF][START_REF] Robertson | Band offsets of wide-band-gap oxides and implications for future electronic devices[END_REF]. The electronic contribution to the static dielectric constant is found to be 3.98 in our HSE calculations, based on the real part of the dielectric function ǫ 1 (ω) for ω → 0. The ionic contribution is calculated using density-functional perturbation theory [START_REF] Gajdoš | Linear optical properties in the projector-augmented wave methodology[END_REF], within the generalized-gradient approximation [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. The total dielectric constant is 51.75, in good agreement with the reported experimental value of ∼47 at 0 K (or ∼52 if taking into account the porosity of the sample [START_REF] Akbarzadeh | Combined theoretical and experimental study of the low-temperature properties of BaZrO3[END_REF]). In a simple ionic model, BaZrO 3 can be regarded as consisting of Ba 2+ , Zr 4+ , and O 2-.

Figure 1 shows the formation energy of selected native point defects in BaZrO 3 . The dominant defects are positively charged oxygen vacancy, V 2+ O (or, equivalently, the removal of an O 2-ion from the host material), and negatively charged barium vacancy, V 2- Ba (the removal of a Ba 2+ from the host). In the absence of impurities, in- tentionally incorporated or unintentionally present, the Fermi level is "pinned" at the position where V 2+ O and V 2- Ba have equal formation energies and hence charge neutrality is maintained. Other defects, such as the oxygen interstitial (O i ), have a higher formation energy. In O i , the extra O combines with one of the O atoms of the host to form an O-O dumbbell that is perpendicular to the line connecting the two Ba atoms in the original Ba-O-Ba chain. Our results for the native defects are in agreement with those reported by Rowberg et al. [START_REF] Rowberg | Optimizing proton conductivity in zirconates through defect engineering[END_REF], except that we find a lower-energy configuration for O 0 i .

B. Doping with dysprosium

Figure 2 shows the formation energy of the substitutional Dy impurity either at the Ba site (Dy Ba ) or the Zr site (Dy Zr ). We find that Dy Ba is stable only as Dy + Ba (i.e., the trivalent Dy 3+ at the Ba site, with spin S = 5/2), irrespective of the chosen set of chemical potentials (which represents synthesis conditions). In the Dy + Ba configuration, the Dy 3+ ion moves off-center by 0.69 Å and comes closer to six of its twelve neighboring O atoms, with the Dy-O bond length being 2.277-2.512 Å. Dy Zr is, on the other hand, structurally and electronically stable as Dy - Zr (i.e., the trivalent Dy 3+ at the Zr site, S = 5/2) and Dy 0 Zr (i.e., the tetravalent Dy 4+ at the Zr site, S = 3). The thermodynamic transition level (0/-) of Dy Zr is at 1.61 eV above the VBM; i.e., above (below) this level, Dy 3+ (Dy 4+ ) is energetically more stable (see further discussion later). In the Dy 0 Zr (Dy - Zr ) configuration, the Dy-O bond is 2.131-2.134 Å (2.188 Å), consistent with the fact that the ionic radius of Dy 4+ (0.78 Å) [START_REF] Knop | Revision of the Shannon and Prewitt effective ionic radii of tetravalent elements[END_REF] is smaller than that of Dy 3+ (0.912 Å) [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF].

To understand the electronic stability of Dy 3+ and Dy 4+ , we show in Fig. 3 the total and Dy 4f -projected electronic density of states (DOS) of Dy-doped BaZrO 3 . In the DOS calculations, one Zr atom in the 40-atom BaZrO 3 supercell is substituted with Dy; i.e., the chemical composition is Ba 8 DyZr 7 O 24 , which corresponds to the Dy 0 Zr defect configuration discussed earlier. Highquality DOS is achieved by using a Γ-centered 4×4×4 k-point mesh. The ground state of Dy 4+ is 4f 8 . In the calculated DOS, we find that Dy introduces seven spin-up occupied 4f states at about -9 eV, one spin-down occupied 4f state at about -0.7 eV (not clearly seen in Fig. 3 due to the energy resolution of the calculation but is confirmed by electron counting and by an examination of the wave functions), and six spin-down unoccupied 4f states in the host band gap (at about +2.5 eV and +3.2 eV). In going from Dy 0 Zr to Dy - Zr , the lowest unoccupied Dy 4f state captures an electron and Dy 4+ becomes Dy 3+ (4f 9 ). Note that our DFT+U calculations produce an electronic structure that is qualitatively similar to that reported in Fig. 3. However, since the Hubbard U term is only applied on the Dy 4f states and all other orbitals in the compound are left uncorrected, the host DFT+U band gap is significantly underestimated. As a result, the position of the Dy 4f states with respect to the band edges are different from that obtained with HSE.

Although the RE 4f orbitals are often regarded as being well shielded by the outer 5s 2 and 5p 6 electron shells and thus contribute very weakly to chemical bonding, we find a strong hybridization between certain unoccupied Dy 4f orbitals and the O 2p states. This can be observed in the relatively broad peak at about +2.5 eV in the calculated DOS shown in Fig. 3 where there are contributions from the O 2p states and the structure of the O 2p-derived DOS peak resembles that of the Dy 4f -derived one. Figure 4 shows the lattice geometry of Dy 0

Zr and the charge density of the associated electron hole (with respect to Dy - Zr ). The charge density, again, shows a strong Dy 4f -O 2p hybridization. Note that the mixing of the RE 4f states and the O states has also been reported in the case of Gd 3 Ga 5 O 12 [START_REF] Juhin | Measurement of f orbital hybridization in rare earths through electric dipole-octupole interference in x-ray absorption spectroscopy[END_REF].

It should be noted that the Dy-derived peaks in the DOS (Fig. 3) are not defect levels associated with Dy Zr . Indeed, those Kohn-Sham levels cannot directly be identified with any levels that can be observed in experiments [START_REF] Freysoldt | First-principles calculations for point defects in solids[END_REF]. The (0/-) level of Dy Zr , for example, must be calculated using the total energies of the Dy 0 Zr and Dy - Zr configurations as described earlier and reported in Fig. 2.

Considering only the Dy-related defects, we find that, under the (Zr,O)-rich condition, Dy 3+ (in the form of Dy + Ba and/or Dy - Zr ) is energetically more favorable than Dy 4+ (in the form of Dy 0 Zr ) in the entire range of Fermilevel values; see Figs. That Dy 4+ -favorable range, however, may not even be accessible if one takes into consideration the native defects. Under the (Ba,O)-rich condition at 1600 • C, for example, the Fermi level is at 1.90 eV, determined predominantly by V 2+ O and Dy - Zr , at which the formation energy of Dy 0 Zr is higher than that of Dy - Zr by 0.30 eV; see Fig. 2(c). Only at lower temperatures, e.g., 1000 • C, Dy 0 Zr has a lower energy than Dy - Zr (by 0.11 eV, where the Fermi level is at 1.50 eV); see Fig. 2(a). Note, however, that an energy difference of ∼0.1 eV is within the error bar of our calculations. Yet what is clear here is that lowenergy, positively charged defects, e.g., V 2+ O and Dy + Ba , reduce the Dy 4+ -favorable range or make it inaccessible. The effect of Y co-doping will be discussed later.

Overall, our results indicate that higher Dy 4+ concentrations might be achieved with higher oxygen (µ O ) and barium (µ Ba ) chemical potential values [and hence lower zirconium (µ Zr ) chemical potential values]. Higher µ O values represent more oxidizing environments, which are usually associated with oxygen gas at lower temperatures and higher oxygen partial pressures [START_REF] Reuter | Composition, structure, and stability of RuO2(110) as a function of oxygen pressure[END_REF], and lead to a reduced oxygen vacancy concentration (particularly, that of V 2+ O ) due to an increase in the defect's formation energy. Similarly, higher µ Ba values, which can be achieved by preparing the material under Ba-rich conditions, result in a reduction or suppression of the Ba-site occupancy (the formation of Dy + Ba ). Lower µ Zr values result in a lower formation energy (and hence a higher concentration) of Dy at the Zr site. Note that our argumentation assumes that the material is prepared under (or close to) thermodynamic equilibrium conditions. It is, however, not clear at this point if the defect landscape reported in Fig. 2(a) or others that are close to it can be realized under actual synthesis conditions such that the Dy 4+ concentration is significant, or if post-synthesis treatment is needed to realize Dy 4+ (see more below).

The above results showing Dy + Ba can have a low formation energy are consistent with experimental reports of the mixed-site occupancy in which Dy is incorporated at both the Ba and Zr sites [START_REF] Han | Dopant occupancy and chemical expansion in rare earth-doped barium zirconate[END_REF]. The synthesis conditions in Han et al. [START_REF] Han | Dopant occupancy and chemical expansion in rare earth-doped barium zirconate[END_REF] should be somewhere between the (Ba,O)-rich and (Zr,O)-rich limits discussed in this work.

C. (Co-)doping with yttrium

To understand the effects of doping or co-doping with Y, calculations are also carried out for the substitutional Y impurity. Figure 2 shows that Y Ba is most stable as Y + Ba (i.e., Y 3+ at the Ba site, S = 0), in a very small range of Fermi-level values near the VBM (0 to 0.15 eV) where it is stable as Y 2+ Ba that is, in fact, a complex of Y + Ba and a localized hole at an O site (i.e., O -); the Y 3+ ion in the Y Ba defects is significantly off-center (by 0.73 Å in the case of Y + Ba ), similar to Yb Ba . Y Zr introduces a defect level, (0/-), at 0.18 eV above the VBM; and the extra electron in Y 0 Ba is localized over several neighboring O sites. Like Dy, Y can thus be incorporated at the Zr site and/or the Ba site, depending on the Fermi-level position, which is consistent with the mixed-site occupancy observed in experiments [START_REF] Azad | Structural origins of the differing grain conductivity values in BaZr0.9Y0.1O2.95 and indication of novel approach to counter defect association[END_REF][START_REF] Yamazaki | Cation non-stoichiometry in yttrium-doped barium zirconate: phase behavior, microstructure, and proton conductivity[END_REF][START_REF] Han | A comprehensive understanding of structure and site occupancy of Y in Y-doped BaZrO3[END_REF]. Our results for Y are similar those reported by Rowberg et al. [START_REF] Rowberg | Optimizing proton conductivity in zirconates through defect engineering[END_REF].

When Y is incorporated at the Zr lattice site (thus forming the Y - Zr defect) with a concentration higher (i.e., a formation energy lower) than that of Dy - Zr , as it is the case shown in Fig. 2, the Fermi level will be shifted toward the VBM as the system reestablishes charge neutrality. Under the (Ba,O)-rich condition, for example, the Fermi level is now determined predominantly by V 2+ O and Y - Zr ; see Figs. 2(a) and 2(c). As the Fermi level is shifted leftward, the formation energy of Dy - Zr increases (and hence its concentration decreases) whereas that of Dy 0 Zr remains constant, thus increasing the Dy 4+ /Dy 3+ ratio. Any acceptor-like defect that shifts the Fermi level would lead to a similar effect. For instance, Rb Ba and Sc Zr , stable as Rb - Ba and Sc - Zr , respectively, as reported in Ref. [START_REF] Rowberg | Optimizing proton conductivity in zirconates through defect engineering[END_REF], would be effective if incorporated with a concentration higher than that of Dy - Zr ; for an illustration of the Fermilevel shifting effect, see, e.g., Fig. 11(a) of Ref. [START_REF] Hoang | Defect physics in complex energy materials[END_REF]. Note that, even with co-doping, one still need to suppress the formation of oxygen vacancies and the Ba-site occupancy (see above), otherwise V 2+ O and/or Dy + Ba will counteract the effect of co-doping. Also note that, a Fermi-level shift alone (i.e., without decreasing the formation energy of Dy 0 Zr ) does not increase the Dy 4+ concentration as Dy 0 Zr is a neutral defect and its formation energy is independent of the Fermi-level position; i.e., it only changes the Dy 3+ concentration and thus the Dy 4+ /Dy 3+ ratio.

D. Post-synthesis treatment

Given the above results and discussion, one may expect that Dy exists entirely or predominantly as the trivalent Dy 3+ (i.e., Dy - Zr ) in BaZrO 3 under normal synthesis conditions, and Dy - Zr is charge-compensated predominantly by V 2+ O and/or Dy + Ba . The native defects and RE-related defects, once formed or incorporated during the synthesis reaction, are expected to remain trapped in the material after the synthesis and act as athermal, prexisting defects in subsequent experiments [START_REF] Hoang | Defect physics in complex energy materials[END_REF]. We refer to the BaZrO 3 material at this stage as being as-synthesized.

Upon heat treating as-synthesized BaZrO 3 in oxidizing atmospheres, the following reaction is expected:

1 2 O 2 + V 2+ O + 2Dy - Zr → O 0 O + 2Dy 0 Zr , (2)
in which oxygen from the environment fills the oxygen vacancies and, to maintain charge neutrality, Dy 3+ (i.e., Dy - Zr ) is oxidized to Dy 4+ (i.e., Dy 0 Zr ). Here, we assume that the system exchanges only oxygen with the environment. It should be emphasized here that reaction (2) is possible because Dy 4+ (and Dy 3+ ) can be stabilized in BaZrO 3 , even when Dy 4+ is not already present in as-synthesized samples. Also note that, in principle, the right-hand side of Eq. ( 2) can include Dy - Zr and an electron hole localized at an O site ("O -") or a free hole (h + ) which acts as a charge-compensating defect; however, we find that neither O -nor h + can be stabilized when an electron hole is added to the supercell containing Dy - Zr . The above oxidation reaction may explain the presence of the tetravalent Dy 4+ reported in BaZrO 3 -based materials prepared in highly oxidizing atmospheres [START_REF] Han | Tetravalent dysprosium in a perovskite-type oxide[END_REF][START_REF] Ricote | Conductivity behavior of BaZr0.9Dy0.1O 3-δ[END_REF][START_REF] Ricote | Non stoichiometry and lattice expansion of BaZr0.9Dy0.1O 3-δ in oxidizing atmospheres[END_REF]. It would be useful if the Dy 4+ /Dy 3+ ratio and the Fermi-level position of those samples can be determined.

As reported by Han et al. [START_REF] Han | Tetravalent dysprosium in a perovskite-type oxide[END_REF], Dy 4+ can be converted into Dy 3+ again in subsequent heat treatment in highly reducing atmospheres (e.g., H 2 ). Using our defect notation, the reaction can be written as

O 0 O + H 2 + 2Dy 0 Zr → H 2 O + V 2+ O + 2Dy - Zr . (3)
Again, this reaction, like reaction (2), is possible because both Dy 3+ and Dy 4+ can be stabilized in BaZrO 3 .

E. Band-to-defect luminescence

Finally, we examine optical transitions involving the isolated Dy Zr defect in BaZrO 3 . Given the presence of the (0/-) level in the host band gap, Dy Zr may act as a carrier trap for band-to-defect and defect-to-band optical transitions. Figure 5 illustrates Dy Zr -related optical absorption and emission processes. Under illumination, for example, the Dy - defect configuration can absorb a photon and become Dy 0 Zr with the removed electron being excited into the conduction band. The peak absorption energy related to the optical transition level E -/0 opt (the formation energy difference between Dy - Zr and the Dy 0 Zr configuration in the lattice geometry of Dy - Zr ) is 3.55 eV, with a relaxation energy (i.e., the Franck-Condo shift) of 0.48 eV. Dy 0 Zr can then capture an electron from the CBM, e.g., previously excited from Dy - Zr (or the valence band) to the conduction band, and emits a photon. The peak emission energy related to the optical transition level E 0/opt (the formation energy difference between Dy 0

Zr and the Dy - Zr configuration in the lattice geometry of Dy 0 Zr ) is 2.64 eV, with a relaxation energy of 0.43 eV. This indicates that Dy Zr can potentially be the source of a broad blue emission associated with the Dy 4+ + Zr 3+ → Dy 3+ + Zr 4+ transition. Further experimental studies are needed to characterize these possible "chargetransfer" transitions (as well as Dy 4f -4f transitions, not considered in this work) in Dy-doped BaZrO 3 .

IV. CONCLUSIONS

We have carried out a study of Dy and other relevant defects in BaZrO 3 using hybrid density-functional calculations. We find that Dy has mixed-site occupancy and is stable predominantly as the trivalent Dy 3+ in the bulk material. The tetravalent Dy 4+ is found to be structurally and electronically stable at the Zr lattice site, but most often energetically less favorable than the trivalent Dy 3+ . This is due to the presence of low-energy, positively charged oxygen vacancies and the mixed-site occupancy of Dy in as-synthesized BaZrO 3 . The Dy 4+ /Dy 3+ ratio can, in principle, be increased by preparing the material under highly oxidizing and Ba-rich conditions and co-doping with acceptor-like impurities; however, postsynthesis treatment in oxidizing atmospheres may be needed to realize a non-negligible Dy 4+ concentration. The lattice site preference of Dy (and Y) can also be tuned by tuning the synthesis conditions. Interestingly, we find a strong hybridization between the Dy 4f states and the O 2p states and that the isolated substitutional Dy Zr defect can be the source of a broad blue emission in band-to-defect luminescence. Our work thus provides a theoretical foundation for understanding experimental observations as well as guidelines for further studies. It also serves as a methodological template for investigating impurities with suspected exotic valence states.

FIG. 1 .

 1 FIG. 1. Formation energies of selected native defects in BaZrO3 as a function of the Fermi level from the VBM (at 0 eV) to the CBM (4.68 eV), under the (Ba,O)-rich or (Zr,O)rich condition at 1000 • C or 1600 • C. Only segments of the energy line corresponding to the lowest-energy charge states are shown. The slope of these segments indicates the charge state (q): positively (negatively) charged defect configurations have positive (negative) slopes; horizontal segments correspond to neutral configurations. Large solid dots connecting two segments with different slopes mark the defect levels.

FIG. 2 .

 2 FIG. 2. Formation energies of Dy-and Y-related defects as a function of the Fermi level from the VBM to the CBM, under the (Ba,O)-rich or (Zr,O)-rich conditions. Large solid dots mark the defect levels. The results for VO under the (Ba,O)-rich condition are repeated here for easy comparison.

FIG. 3 .

 3 FIG. 3. Total and projected densities of states (DOS) of Dydoped BaZrO3, specifically Dy 0Zr , obtained in HSE calculations. The spin-majority spectrum is on the +y axis, and the spin-minority spectrum is on the -y axis. The number of 4f electrons at the Dy 4f -projected DOS peaks is indicated. The zero of energy is set to the highest occupied state.

  2(b) and 2(d). Under the (Ba,O)rich condition, Dy 4+ is energetically more favorable than Dy 3+ in a small range of Fermi-level values, and this range is greater at lower temperatures; see Figs. 2(a) and 2(c). This is because the lower temperature leads to higher formation energies of V 2+ O and Dy + Ba and lower formation energies of Dy 0 Zr (as well as Dy - Zr ), thus increasing the range of Fermi-level values in which Dy 0 Zr is energetically more favorable; the formation energy of Dy 0 Zr is 0.78 eV at 1000 • C, compared to 1.19 eV at 1600 • C.

FIG. 5 .

 5 FIG. 5. Configuration-coordinate diagram illustrating optical emission (down arrow) and absorption (up arrow) processes involving DyZr in BaZrO3. The thermal energy [also called the zero-phonon line (ZPL), the dash-dotted line] is the thermodynamic transition level ǫ(0/-) relative to CBM. The values sandwiched between two dotted lines are the relaxation energies (the Franck-Condon shifts). Axes are not to scale. For a detailed discussion of the configuration-coordinate diagram representation, see, e.g., Alkauskas et al. [36].

ACKNOWLEDGMENTS K.H. is grateful to Université de Nantes for supporting his visit to Institut des Matériaux Jean Rouxel (IMN) during which this work was initiated. This work used resources of the Center for Computationally Assisted Science and Technology (CCAST) at North Dakota State University, which were made possible in part by NSF MRI Award No. 2019077, and of Centre de Calcul Intensif des Pays de Loire (CCIPL), France.