Yizhe Wang

Béatrice Daille

Nabil Hathout

A study of semantic projection from single word terms to multi-word terms in the environment domain

Keywords: semantic projection, multiwords terms, terminological relations

The semantic projection method is often used in terminology structuring to infer semantic relations between terms. Semantic projection relies upon the assumption of semantic compositionality: the relation that links pairs of simple terms remains valid in pairs of complex terms built from these simple terms. This paper proposes to investigate whether this assumption commonly adopted in natural language processing is actually valid. First, we describe the process of constructing a list of semantically linked multi-word terms (MWTs) related to the environmental field through the extraction of semantic variants. Second, we present our analysis of the semantic projection results. We find that contexts play an essential role in defining the relations between MWTs.

Introduction

Terminology is structured by semantic relations between terms. The relations may be identified by experts, obtained from existing resources or extracted from corpora. They include synonymy, quasi-synonymy, hypernymy, hyponymy, etc. In this study, we focus on the identification of terminological relations between multi-word terms (MWTs) using the semantic projection method. We built a set of French MWT candidates related to the environment domain and containing two lexical words such as réchauffement climatique 'global warming'. Three relations categories (antonymy, quasi-synonym, and hypernymy) between single word terms (SWTs) are extended to these candidates. A subset of these MWT pairs has been validated by three judges to assess the preservation and the validity of the inferred relations between MWTs. The main finding of the evaluation is that the context is crucial for the assessment because they determine the actual meaning of the MWTs. The remaining of the paper is organized as follows. Section 2. presents the related work. Section 3. outlines the projection of the semantic relations on the MWT pairs. Section 4. describes the data and resources used for the generation of semantically linked MWTs (Section 5.). The manual evaluation and an analysis of the projection results are presented in Section 6.. A short conclusion is then given in Section 7..

Related work

Several approaches to semantic relation recognition have been proposed in the literature. They may be classified into three types: lexicon-based approaches [START_REF] Senellart | Automatic discovery of similarwords[END_REF]; pattern-based approaches [START_REF] Wang | Pattern-based synonym and antonym extraction[END_REF][START_REF] Ravichandran | Learning surface text patterns for a question answering system[END_REF]; distributional approaches [START_REF] Rajana | Learning antonyms with paraphrases and a morphology-aware neural network[END_REF][START_REF] Shwartz | Still a pain in the neck: Evaluating text representations on lexical composition[END_REF]. Since MWTs are compositional or at least weakly compositional (L'homme, 2004), the semantic projection method, also known as semantic variant and often referred to as a compositional method, is widely used to generate MWTs and predict relations between them from semantically related SWTs. Synonymy is an important relation in terminology and is addressed in several studies, like [START_REF] Hamon | A step towards the detection of semantic variants of terms in technical documents[END_REF] who identifies synonymous term candidates through inference rules. The authors extract MWT candidates from a corpus on electric power plants and analyze the candidate terms (ligne d'alimentation 'supply line') as being made up of a head (ligne 'line') and an expansion (alimentation 'supply'). They then replace the head or the expansion (or both) by their synonyms obtained from a general dictionary. They assume that the substitution preserves the synonymy relation. In their study, 396 MWT pairs have been validated by an expert; 37% are real synonyms. The same method is used by [START_REF] Hamon | Detection of synonymy links between terms: experiment and results[END_REF] in order to detect synonymous MWTs in specialized corpora on nuclear power plants and coronary diseases. Their results show that general language dictionaries complement specialized hand-built lexical resources for the detection of semantic variants.

In a similar study, [START_REF] Morin | Projecting corpus-based semantic links on a thesaurus[END_REF] uses inference rules to identify hierarchical relations (hypernymy) between MWTs. Instead of using relations from the general dictionary, they take as reference semantically linked SWTs extracted from the AGROVOC terminology. They not only add syntactic and semantic constraints on the reference rules but also use the semantic relations with morphological relations to detect the semantic variants. They then compare the relations generated from AGROVOC with relations generated from a general language dictionary and show that the latter has a significantly lower precision. More recently, [START_REF] Daille | Semi-compositional method for synonym extraction of multi-word terms[END_REF] has generalized the projection method to all types of lexical relations while [START_REF] Hazem | Word embedding approach for synonym extraction of multi-word terms[END_REF] uses it to extract synonymous MWTs with variable lengths.

The main difference between our study and the ones presented above is that we use the context to validate the inferred relations. In our experiment, we consider that the projection is valid if the meaning of two MTWs in two of their contexts is in the relation stated between the two SWTs that yielded them. The above studies do not use the context except [START_REF] Hamon | Detection of synonymy links between terms: experiment and results[END_REF] who checks whether the two MWT candidates can be substituted one for the other in one context. In other words, one contribution of our study is to take into account the possible ambiguity of the MWTs, and the way contexts determine their meanings.

Composition method

Our method is based on the assumption that MWT meaning is compositional. One consequence of this hypothesis is that when two MWTs t 1 and t 2 only differ by one of their components c 1 and c 2 , the semantic relation between c 1 and c 2 is identical to the one between t 1 and t 2 because c 1 and c 2 contribute in the same way to the meanings of t 1 and t 2 . For instance, the relation between the MWTs croissance de la population 'population growth' and diminution de la population 'population decline' is the same as the one between the SWTs croissance 'growth' and diminution 'decline', that is antonymy. Our hypothesis is actually a bit stronger because we consider that this equivalence holds even when t 1 and t 2 do not have the same (syntactic) structure. More formally, let t 1 and t 2 be two MWTs such as

voc(t 1 ) = {u 1 , v 1 } and voc(t 2 ) = {u 2 , v 2 } where voc(x)
is the set of the content words of x. If u 1 and u 2 are SWTs, if v 1 = v 2 and if their is a semantic relation R between u 1 and u 2 , then R also holds between t 1 and t 2 . In other words, if M is a set of MWTs of a domain and S is a set of SWTs, the hypothesis can be stated as follows:

1 ∈ M, ∀t 2 ∈ M such as ∃u 1 , v 1 , u 2 , v 2 / voc(t 1 ) = {u 1 , v 1 } ∧ voc(t 2 ) = {u 2 , v 2 } ∧u 1 ∈ S ∧ u 2 ∈ S, [v 1 = v2 ∧ ∃R, R(u 1 , u 2 ) ⇒ R(t 1 , t 2 )]

Data and resources

Corpus

The corpus used for extracting MWT candidates is a specialized monolingual French corpus in the environment domain (ELRA-W0065) created in the framework of the PANACEA project 1 . The corpus contains 35453 documents (about 50 million words) with different levels of specialization. The corpus has been preprocessed: extraction of the text, normalization of the characters, lemmatization with TreeTagger [START_REF] Schmid | Probabilistic part-of-speech tagging using decision trees[END_REF].

TermSuite

The MWT candidates were extracted from the PANACEA corpus through TermSuit, a terminology extraction tool developed at LS2N 2 [START_REF] Cram | Terminology extraction with term variant detection[END_REF]. TermSuit only extracts noun phrases; the candidates are provided with their part of speech, specificity, and frequency. Table 1 illustrates the extracted candidates. For this study, we only consider the candidates composed of two lexical words (e.g. milieu naturel 'natural environment').

Reference list of linked terms

The semantic relations between MWT candidates are predicted from relations between SWTs. These semantically linked SWTs are taken from a dataset made available by [START_REF] Bernier-Colborne | Evaluation des modeles sémantiques distributionnels: le cas de la dérivation syntaxique[END_REF]. This reference list (RefCD) is extracted from DiCoEnviro (L'Homme and

Generation of semantically-linked MWTs

Raw projection

We extracted all the MWT candidates which contain two content words and formed all the MWTs pairs that share a common word and where the two other words are a pair of SWTs connected in RefCD. We did not impose any other restriction on PoS, the order of the constituents, nor the patterns of the MWT candidates. 18,382 pairs of MWT candidates have been created.

Data filtering

The raw projection yields symmetrical pairs of MWT candidates because some of the SWT pairs in RefCD are not ordered. For instance, the projection produced the couple climat régional : climat local 'regional climate' : 'local climate' and the couple climat local : climat régional. We, therefore, deleted the symmetries of hierarchical relationships. Table 4 shows the number of pairs that remained after the data filtering.

Selection of a validation subset

In order to assess the hypothesis that MWT meaning is compositional and that semantic relations between SWTs are preserved when they are projected on MWTs, we performed a manual validation on a subset of the MWT candidate pairs we have extracted. Since our study focuses on the preservation and the validity of the semantic relations, we do not want the validation also to include the quality of candidates (are they terms of the environmental field?). For instance, a candidate like lutte contre le changement 'fight against the change' is not a term because it is syntactically incomplete, and the actual term is lutte contre le changement climatique 'fight against climate change'. What is more, a candidate like cadre régional 'regional framework' does not belong to the environment domain.

We, therefore, choose to check the term status of the MWT candidates through three online terminological dictionaries, namely TERMIUM Plus3 , Le Grand Dictionnaire4 and IATE5 (Interactive Terminology for Europe). We consider any candidate present in any of these resources as a term of the environmental field since it was extracted from a specialized corpus of this domain. Since many of the extracted terms are very specific, such as conservation des papillons 'butterfly conservation', only a fraction of the pairs have both of their MWT candidates present in one of the resources. As shown in (1) la ventilation est à double flux (l'air vicié intérieur réchauffe l'air frais entrant)

(2) a. il a établi que le changement du climat était « sans équivoque » et que les émissions de gaz à effet de serre provenant des activités humaines étaient responsables (avec 90% de certitude) de l'augmentation des températures depuis cent ans b. à quelle vitesse la réduction des concentrations atmosphériques de GES de courte durée entraînerait un changement du climat

Criteria

The selected pairs have been annotated according to two criteria: the preservation of semantic relations and their validity in the environment domain. Both criteria are based on the expert knowledge of judges on semantic relations and the contexts in which the MWT candidates appear.

1. We consider that a relation is preserved when the relation that holds between two SWTs also holds between two MWT candidates generated from these two SWTs, regardless of its validity as an instance of its category. In other words, the relation is preserved when SWT 1 :SWT 2 ::MWT 1 :MWT 2 form an analogy.

2. We consider that a relation between two MWT candidates is valid in the domain when it actually belongs to the category to which it is assigned.

We assessed the preservation of the relation and its validity separately because we slightly changed the scope of the relation categories. We consider that co-hyponyms are not quasi-synonyms and cannot belong to QSYN. The reason why we Furthermore, we consider the relationship between a pair of contrastive co-hyponym terms as an instance of ANTI.

Preservation

The preservation of the relation only depends on the relations between the two SWTs and the two MWTs. If the relations are identical, the relation is considered as being preserved as in the case of temps froid : temps chaud 'cold weather : 'warm weather (3) with respect to froid : chaud 'cold' : 'warm'.

(3) a. par temps froid, cette technique consiste à ne pas laisser tourner son moteur au ralenti plus de 30 secondes b. par temps chaud, le compromis entre confort et pratique est difficile à trouver

On the other hand, diversité is a hypernym biodiversité in RefCD, but the contexts in (4) show that the relation between the MWTs gestion de la diversité 'management of diversity' and gestion de la biodiversité 'management of biodiversity' is different since they are used with the same meaning.

(4) a. les variétés paysannes, issues de millénaires de gestion de la diversité par les agriculteurs sont trop vivantes pour se plier aux critères d'inscription ... b. elle même distincte de l'utilisation (par les agriculteurs) des semences, la gestion de la biodiversité cultivée réunit dans un processus continu ...

Domain validity

Relations that are not preserved are considered as invalid.

However, not all preserved relations are valid in the domain. For instance, agriculture 'agriculture' is a hypernym of élevage 'lifestock farming' in RefCD, and the relation holding between these SWTs is preserved in the MWTs agriculture biologique 'organic agriculture' and élevage biologique 'organic lifestock farming'. However, a context like (5) shows that these MWTs are actually co-hyponyms because hypernyms cannot be coordinated in this way. The reason is that agriculture is polysemous and may also mean cultivation. In this context, agriculture and élevage are cohyponyms, and the inferred relation is not valid because it is not a relation of hypernymy.

(5) ... expérience avec une matrice agricole "sans pesticides ni intrants chimiques" (agriculture ou élevage biologique ou de prairies ...

Analysis of the inferred relations

Three judges have annotated the pairs of the validation subset. Table 6 shows that the inter-annotator agreement measured by Fleiss' kappa is substantial. The cases where the judges disagreed were then resolved.

Conclusion and Future Works

In this study, we have created a dataset of MWT pairs linked by semantic relations. These relations are projected from a reference list of SWTs connected by the same relations. The annotation of a subset of the data highlighted the importance of the contexts because they determine the real meaning of MWTs and subsequently, the semantic relation that holds between them. The following step in this research will be to design a method that automate the annotation on the basis of the semantic relations between SWTs and contextual semantic model like BERT [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF].

Table 2 :

 2 Because we are focusing on the projection of lexicalsemantic relations, we did not use the 259 DRV pairs and excluded them from RefCD. We also excluded the 225 pairs of verbs because TermSuite only extracts noun phrases. The distribution of the three relation categories is imbalanced, as shown in table 2. Number of terms and semantic relations in RefCD

	# type pattern pilot	freq spec
	3 T	N A	parc national	10198 4.17
	3 V[s] N A A parc naturel national	59 1.94
	4 T	A	communautaire	8864 4.11
	13 T	T	biomasse	6239 3.96
	17 T	N A	diversité biologique	5412 3.90
	21 T	N A	milieu naturel	4328 3.80
	21 V[s] N A A milieu naturel aquatique	23 1.54
		Table 1: Excerpt of the TermSuite output
	Lanneville, 2014), a specialized dictionary of the environ-
	ment field which describes the meaning of 1382 entry terms
	of various sub-fields: energy, climate change, transporta-
	tion, etc. RefCD is composed of 1314 term pairs, mainly
	SWTs, connected by four relation categories:
	1. Quasi-synonyms (QSYN): synonyms (diesel 'diesel'

1 http://www.panacea-lr.eu/en/info-for-researchers/datasets/monolingual-corpora 2 https://www.ls2n.fr ↔ gazole 'diesel'); quasi-synonyms (conserver 'preserve' ↔ protéger 'protect'); close meanings (électricité 'electricity' ↔ énergie 'energy'); variants (autopartage 'car sharing' ↔ auto-partage 'car sharing'). 2. Hierarchical relations (HYP): hyponyms (autoroute 'highway' → route 'road'); hypernyms (combustible 'fuel' → pétrole 'oil'). Because HYP mixes hyponyms and hypernyms, the pairs it connects are not ordered. 3. Opposites (ANTI): antonyms (accélérer 'accelerate' ↔ ralentir 'slow down'); contrastives (flore 'flora' ↔ faune 'fona'). 4. Derivatives (DRV): terms with the same meaning but different parts of speech (sensibilité 'sensitivity' ↔ sensible 'sensible').

Table 3 :

 3 Table 3 presents their distribution over the three relation categories. MWTs yielded by the semantic projection

	ANTI	HYP	QSYN	total
	3414 3696 11,272 18,382

Table 4 :

 4 Number of unordered pairs of MWT candidates

Table 5

 5 The meaning of a word strongly depends on the contexts where it is used. In this study, we show that the context also determines the meaning of MWTS and the relations that connect them. The annotation of the MWT pairs is based on the relation between the two SWTs they contain and five contexts (i.e., sentences) extracted from the corpus for each MWT. The validity of the projected relation is decided based on the meanings of the MWT occurrences in the extracted contexts. The relation is valid if it holds between the meanings of at least one occurrence of each of the MWTs. The context may help the judges understand the meaning of a MWT like zone de recharge 'recharge zone' which refers to a free aquifer where water collects. It can be used to disambiguate a term like air frais 'fresh air' which does not mean cool air but air from the outside (1). Contexts may also highlight the polysemy of MWTs like changement du climat 'climate change' which has two meanings: 'global warming' in (2a) and 'climate variability' in (2b).

			, the validation subset is rather
	small.
	ANTI	HYP	QSYN	total
	80	51	100	231
	Table 5: Validation subset

Table 6 :

 6 Fleiss' kappaThe results (Table7) show that most of MWTs have compositional meaning, which confirms the claim of(L'homme, 2004). They also show that the preservation and the validity of the projected relations vary with their category.

	ANTI	HYP	QSYN
	0.77 0.68	0.61

Table 7 :

 7 Results of the validationEven if no restriction on the patterns was used for the generation of the MWT pairs, we observed that in all of the valid pairs, the MWTs have the same patterns and the SWTs that they contain appear in the same positions. 51 out of 231 pairs of MWTs are not preserved. They fall into three groups. (i) The MWTs do not have the same structure like eau de surface 'surface water' and surface de la terre 'Earth's surface'. eau 'water' and terre 'land' are linked by ANTI relation but the MWTs are not because eau and terre do not appear in the same position. (ii) The meaning of the SWTs is not preserved in the MWTs as in route maritime : autoroute maritime 'shipping route' : 'marine highway'. route 'road' is a hypernym of autoroute 'highway', but route maritime and autoroute maritime are synonyms in the contexts extracted for these two MWTs. (iii) The change in meaning may also come from the content word shared by two MWTs as in air libre : eau libre 'outdoor' : 'open water'. The 62 pairs where the relation has been considered invalid are mainly co-hyponyms formed by SWTs linked by a QSYN relation like trafic ferroviaire : trafic routier 'rail traffic' : 'road traffic'.

https://www.btb.termiumplus.gc.ca/tpv2alpha/alphafra.html?lang=fra

4 http://www.granddictionnaire.

com/ 5 https://iate.europa.eu/


Alberto Palazzolo

Cyprien Poucin

Alexy P Freitas

Anthony Ropp

Corinne Bouillet

Ovidiu Ersen

Sophie Carenco
email: sophie.carenco@sorbonne-universite.fr

The Delicate Balance of Phase Speciation in Bimetallic Nickel Cobalt Nanoparticles

Keywords: bimetallic nanoparticles, colloidal synthesis, phase control, cobalt, nickel

Bimetallic nickel-cobalt nanoparticles are highly sought for their potential as catalytic and magnetic nanoparticles. These are typically prepared in organic solvents in the presence of strong stabilizing ligands such as tri-n-octylphosphine (TOP). Due to the variety of cobalt crystallographic phases and to the strong interaction of the ligands with the metallic surfaces, forming fcc nanoparticles rather than phase mixture is a challenging endeavor. Here, using a two-step synthesis strategy that aims at a core-shell nickel-cobalt morphology, we demonstrated that many parameters have to be adjusted: concentration of the metal precursors, stoichiometry of TOP, and heating program from room temperature to 180 °C. We found optimized conditions to form size-controlled fcc NiCo nanoparticles from preformed Ni nanoparticles, and the phase attribution was confirmed with a combination of X-Ray diffraction on powder and X-Ray absorption spectroscopy at Co K edge. We then investigated the early stages of Co nucleation on the nickel using a lower stoichiometry of Co, down to 0.05 equiv. vs. Ni. Using X-ray photoelectron spectroscopy and scanning transmission electron microscopy coupled to energy-dispersive X-Ray spectroscopy and electron energy loss spectroscopy, we showed that cobalt reacts first on the nickel nanoparticles but easily forms cobalt-rich larger aggregates in the further steps of the reaction.

Introduction

The combination of two metals in a single nano-object is as interesting as challenging. Indeed, bimetallic nanoparticles have been widely studied during recent years because of the multiple possibilities which can rise from the interaction between the two components. [START_REF] Zhang | Bimetallic Nanostructures: Shape-Controlled Synthesis for Catalysis, Plasmonics, and Sensing Applications[END_REF] Alongside, in the fields of energy harvesting and catalysis, it is of paramount importance to shift from noble metals to first-row transition metals such as Ni, Cu, Co and Fe because of their lower cost and higher availability. [START_REF] Anderson | Chemical Composition of the Mantle[END_REF] In this context, bimetallic nickel cobalt nanoparticles (NiCo NPs) have attracted the attention of the community thanks to the synergic catalytic activity of the combined metals. For example, NiCo NPs were used for the dry reforming of CO 2 , [START_REF] San-José-Alonso | Co and Bimetallic Ni-Co Catalysts for the Dry Reforming of Methane[END_REF][START_REF] Luisetto | Co and Ni Supported on CeO2 as Selective Bimetallic Catalyst for Dry Reforming of Methane[END_REF][START_REF] Alsabban | In-Operando Elucidation of Bimetallic CoNi Nanoparticles during High-Temperature CH4/CO2 Reaction[END_REF] for hydrogen production, [START_REF] Chou | Hydrogen Generation from Catalytic Hydrolysis of Sodium Borohydride Using Bimetallic Ni-Co Nanoparticles on Reduced Graphene Oxide as Catalysts[END_REF] for the depolymerization of lignin, [START_REF] Chen | Highly Stable and Recyclable Graphene Layers Protected Nickel-Cobalt Bimetallic Nanoparticles as Tunable Hydrotreating Catalysts for Phenylpropane Linkages in Lignin[END_REF] for hydrogen production, [START_REF] Mohammad | Recoverable and Recyclable Nickel-Cobalt Magnetic Alloy Nanoparticle Catalyzed Reversible Deactivation Radical Polymerization of Methyl Methacrylate at 25 °C[END_REF] and recently as catalysts for hydrosilylation. [START_REF] Palazzolo | Phosphines Modulating the Catalytic Silane Activation on Nickel-Cobalt Nanoparticles, Tentatively Attributed to Frustrated Lewis Pairs in a Colloidal Solution[END_REF] Interestingly, the ratio of nickel to cobalt greatly affects the catalytic activity and the deactivation rate of the nanoparticles during a dry reforming of methane reaction. [START_REF] Kotel'nikova | Synthesis of Bimetallic Nanoparticles Based on Cobalt and Nickel. Effects of Their Composition and Structure on Catalytic and Magnetic Properties[END_REF] Core-shell NiCo NPs were prepared by depositing cobalt on preformed nickel nanoparticles, and they were tested for the hydrogenation of carbon dioxide into carbon monoxide, methanol and formaldehyde, showing an interesting selectivity for oxygenated products. [START_REF] Carenco | Synthesis and Structural Evolution of Nickel-Cobalt Nanoparticles Under H2 and CO2[END_REF] Such selectivity could not be reached with pure Co or pure Ni nanoparticles. NiCo NPs modified with PPh 3 or PnBu 3 ligands were also active for benzaldehyde reduction by silanes at room temperature. [START_REF] Palazzolo | Phosphines Modulating the Catalytic Silane Activation on Nickel-Cobalt Nanoparticles, Tentatively Attributed to Frustrated Lewis Pairs in a Colloidal Solution[END_REF] Despite the huge interest of NiCo NPs, synthesis of well-defined objects in composition, size and crystallinity is still a challenge. In particular, it is expected that core-shell nanoparticles will exhibit properties that differs from the alloyed ones, especially as several crystalline phase may coexist. While there are many reports of supported NiCo NPs, [START_REF] Alsabban | In-Operando Elucidation of Bimetallic CoNi Nanoparticles during High-Temperature CH4/CO2 Reaction[END_REF][START_REF] Yu | Synthesis of Natural Gas from CO Methanation over SiC Supported Ni-Co Bimetallic Catalysts[END_REF][START_REF] Wang | Quasi-Aligned Nanorod Arrays Composed of Nickel-Cobalt Nanoparticles Anchored on TiO2/C Nanofiber Arrays as Free Standing Electrode for Enzymeless Glucose Sensors[END_REF][START_REF] Hosseini | Superb Catalytic Properties of Nickel Cobalt Bimetallic Nanoparticles Immobilized on 3D Nitrogen-Doped Graphene for Thermal Decomposition of Ammonium Perchlorate[END_REF][START_REF] Ciotonea | Phyllosilicate-derived Nickel-cobalt Bimetallic Nanoparticles for the Catalytic Hydrogenation of Imines, Oximes and N-heteroarenes[END_REF] synthetic path in one pot using colloidal routes seems more difficult to design. These can take advantage of the different reduction potential of Ni and Co, [START_REF] Yamauchi | Nucleation and Growth of Magnetic Ni-Co (Core-Shell) Nanoparticles in a One-Pot Reaction under Microwave Irradiation[END_REF][START_REF] Sciortino | Structural Characterization of Surfactant-Coated Bimetallic Cobalt/Nickel Nanoclusters by XPS, EXAFS, WAXS, and SAXS[END_REF][START_REF] Ung | Growth of Magnetic Nanowires and Nanodumbbells in Liquid Polyol[END_REF][START_REF] Sharma | Synthesis and Self-Assembly of Monodisperse CoxNi100-x (X=50,80) Colloidal Nanoparticles by Homogenous Nucleation[END_REF][START_REF] Usami | Synthesis of Cobalt-Nickel Nanoparticles via a Liquid-Phase Reduction Process[END_REF][START_REF] Almomani | Nickel/Cobalt Nanoparticles for Electrochemical Production of Hydrogen[END_REF][START_REF] Gan | Carbonized Wood Decorated with Cobalt-Nickel Binary Nanoparticles as a Low-Cost and Efficient Electrode for Water Splitting[END_REF][START_REF] Yun | Nitrogen-Rich Porous Carbon-Stabilized Ni-Co Nanoparticles for the Hydrogenation of Quinolines[END_REF][START_REF] Hernández Mejía | Cobalt-Nickel Nanoparticles Supported on Reducible Oxides as Fischer-Tropsch Catalysts[END_REF] of electroless deposition, [START_REF] Dahonog | Electroless Deposition of Nickel-Cobalt Nanoparticles for Hydrogen Evolution Reaction[END_REF] or of laser ablation [START_REF] Zhang | Nickel and Cobalt Nanoparticles Produced by Laser Ablation of Solids in Organic Solution[END_REF] although they may end up being fairly aggregated [START_REF] Garbarino | On the Role of Support in Metallic Heterogeneous Catalysis: A Study of Unsupported Nickel-Cobalt Alloy Nanoparticles in Ethanol Steam Reforming[END_REF] or poorly crystallized, [START_REF] Sharma | Synthesis and Self-Assembly of Monodisperse CoxNi100-x (X=50,80) Colloidal Nanoparticles by Homogenous Nucleation[END_REF] or too crystallized to be attributed to nano-domains. [START_REF] Ahmed | Microemulsion-Mediated Synthesis of Cobalt (Pure Fcc and Hexagonal Phases) and Cobalt-Nickel Alloy Nanoparticles[END_REF] Few reports mention the possibility to form composition-controlled NiCo NPs. [START_REF] Van Schooneveld | Composition Tunable Cobalt-Nickel and Cobalt-Iron Alloy Nanoparticles below 10 Nm Synthesized Using Acetonated Cobalt Carbonyl[END_REF][START_REF] Marusak | Size and Composition Control of CoNi Nanoparticles and Their Conversion into Phosphides[END_REF][START_REF] López-Tinoco | The Preparation and Characterization of Co-Ni Nanoparticles and the Testing of a Heterogenized Co-Ni/Alumina Catalyst for CO Hydrogenation[END_REF] Amongst them, the study by van Schooneveld et al. interestingly proposed a synthetic route in one pot, using a Ni(II) precursor and a Co(0) precursor with ratio that were systematically varied. This provided them with alloy of tunable composition, provided that acetone was used to dissolve the cobalt precursor, thus undergoing an intermediate acetonation reaction. Surprisingly, Co-rich reaction mixture led to even more Co-rich nanoparticles while Co-poor ones led to even more Co-poor nanoparticles. [START_REF] Van Schooneveld | Composition Tunable Cobalt-Nickel and Cobalt-Iron Alloy Nanoparticles below 10 Nm Synthesized Using Acetonated Cobalt Carbonyl[END_REF] In contrast with this study, Marusak et al. used Ni(II) and Co(II) precursors in three molar ratio (1.14, 2.28, 3.42) and they found that, under these conditions, Co was less efficiently introduced in the nanoparticles than Ni. [START_REF] Marusak | Size and Composition Control of CoNi Nanoparticles and Their Conversion into Phosphides[END_REF] This generally raises the question of reaction yield vs. each metal and depending on the precursors and operating conditions.

Phase speciation was studied in few studies, keeping in mind that fcc Ni, Co and NiCo have close lattice parameters and are practically very hard to distinguish as soon as the crystallites are nano-sized. From a polyol route at 170 °C, both pure hcp and mixed hcp+fcc nanocrystalline phase were obtained for NiCo powders with various morphologies. [START_REF] Ung | Growth of Magnetic Nanowires and Nanodumbbells in Liquid Polyol[END_REF] fcc NiCo NPs were obtained at 280 °C for Co/Ni ratio of 0.3 to 0.8, while hcp Ni or  Co were obtained with other ratio. [START_REF] Van Schooneveld | Composition Tunable Cobalt-Nickel and Cobalt-Iron Alloy Nanoparticles below 10 Nm Synthesized Using Acetonated Cobalt Carbonyl[END_REF] The phase affects the nature of the exposed facets, affecting the catalytic performances, as well as the electronic properties of the solid, as was demonstrated for the magnetic properties of Co, for instance. [START_REF] Sun | Synthesis of Monodisperse Cobalt Nanocrystals and Their Assembly into Magnetic Superlattices (Invited)[END_REF] As such, it is quite interesting to describe and control the phase in bimetallic nanoparticles as well.

In order to clarify the phase speciation in NiCo NPs and provide an alternative route to composition-controlled and size-controlled nanoparticles, we investigated the possibility to obtain them from preformed fcc Ni NPs prepared through a robust colloidal reaction. [START_REF] Carenco | Controlled Design of Size-Tunable Monodisperse Nickel Nanoparticles[END_REF][START_REF] Carenco | Revisiting the Molecular Roots of a Ubiquitously Successful Synthesis: Nickel(0) Nanoparticles by Reduction of [Ni(Acetylacetonate) 2[END_REF] We selected Co 2 (CO) 8 as a cobalt source, at the suitable formal oxidation state (0) for avoiding redox reaction at the Ni surface and we investigated several Co/Ni ratio, from 1.0 to 0.05. We investigated a range of operating conditions, varying the dilution, the stoichiometry of the main surface ligand (tri-n-octylphosphine) and the heating program, to finally obtain phasepure fcc NPs. Lastly, we lowered the stoichiometry of the cobalt precursor to get an insight of the first stage of cobalt deposition on the Ni NPs surface. We then discuss the role of each parameter for the production of phase-pure and composition-controlled NPs, while delineating the limits of the proposed synthetic approach. Overall, the present work contributes to the topic of preparing phase-controlled fcc NiCo bimetallic nanoparticles while unveiling the challenge of suppressing the formation of the hcp phase in a robust manner.

Results

Sensitivity of the synthesis to process parameters

The starting point of this study is the protocol reported in a previous study. [START_REF] Carenco | Synthesis and Structural Evolution of Nickel-Cobalt Nanoparticles Under H2 and CO2[END_REF] Briefly, nickel nanoparticles (Ni NPs) are formed in a first step from dry nickel(II) acetylacetonate (acac) in the presence of 3 equiv. of tri-n-octylphosphine (TOP) and 12 equiv. of oleylamine (OAm), which acts both as solvent and reducing agent, at 220 °C for 2 h. In a second step, and without further treatment, the cobalt(0) precursor, Co 2 (CO) 8 (one equiv. of Co vs. Ni), was added at room temperature and the mixture was heated up again. A first temperature step of 120 °C was kept for 20 min, to efficiently solubilize the cobalt precursor. As expected, we observed bubbling in the solution, due to the release of some CO molecules. Then the temperature was increased to 180 °C and kept for 1 h. Small nanoparticles of 12 nm diameter (Figure 1B) were obtained. Powder X-ray diffraction (XRD) was performed on the powder (Figure 1A). Broad peaks were detected corresponding to an average crystallite size of 10 nm according to the Scherrer relation. Interestingly, no cubic metallic phase was observed. Rather, the observed phase was isostructural to Ni 12 P 5 , which indicated that the nanoparticles were more phosphidized than anticipated. In fact, in the study published in 2015, [START_REF] Carenco | Synthesis and Structural Evolution of Nickel-Cobalt Nanoparticles Under H2 and CO2[END_REF] the STEM-EDS mapping of the nanoparticles highlighted the presence of a cobalt-rich shell around a nickel-rich core, but the P K-edge mapping was not inconsistent with phosphorus inside the nanoparticle core. The presence of some phosphorus in the nanoparticle core, as phosphide species, can be explained due to the partial decomposition of the phosphine during the first step of the reaction (the synthesis of the nickel nanoparticles), as showed in a study published in 2017. [START_REF] Carenco | The Birth of Nickel Phosphide Catalysts: Monitoring Phosphorus Insertion into Nickel[END_REF] HRTEM did confirm the presence of nanoparticles with a crystalline core although the observations did not allow excluding the presence of an amorphous shell (Figure S3). This shell is not even in thickness and displays a non-regular TEM contrast: it could be made of cobalt/nickel (possibly oxidized due to air exposure) and/or carbon from the ligands.

Nanoparticles were smaller than these obtained in ref [START_REF] Carenco | Synthesis and Structural Evolution of Nickel-Cobalt Nanoparticles Under H2 and CO2[END_REF] (26 nm diameter in average).

In order to confirm that this was not due to degradation of the particles after the addition of cobalt, the nanoparticles were isolated and analyzed after the first reaction step, that is, before cobalt was added. This step resulted in nanoparticles with a fairly sharp size distribution and an average diameter of 9 nm (Figure S2A), consistent with the size range expected in more diluted conditions reported in an earlier work. [START_REF] Carenco | Controlled Design of Size-Tunable Monodisperse Nickel Nanoparticles[END_REF] We attribute this difference to the use of a different heating mantle and temperature controller setup, as well as a different TOP source, highlighting the well-known influence of process parameters on the outcome of the synthesis. Moreover, the nickel phosphidized phase could already be observed at this step by XRD (Figure S2B). In more diluted conditions reported in an earlier work, the nanoparticles were mostly amorphous. [START_REF] Carenco | Controlled Design of Size-Tunable Monodisperse Nickel Nanoparticles[END_REF] This indicates that concentrated conditions are prone to favor the interaction of the phosphine with the nickel surface, and more phosphidation of the nanoparticles, in agreement with the interpretation proposed in the litterature. [START_REF] Muthuswamy | Synthetic Levers Enabling Independent Control of Phase, Size, and Morphology in Nickel Phosphide Nanoparticles[END_REF] Besides, the presence of cobalt in the nanoparticles after the second step was confirmed by ensemble analysis: EDS performed at large scale on a SEM provided an average Co/Ni ratio of 0.5. X-Ray fluorescence spectroscopy on a pellet of the power confirmed the Co/Ni ratio of 0.6. EDS performed at the scale of a single nanoparticle using a STEM instrument provided an average Co/Ni ratio of 0.6 (average on 6 locations), confirming the presence of cobalt in each nanoparticle. It appears that about 0.4 equiv. of cobalt did not enter or cover the nanoparticles. Rather, it was eliminated by the washing steps. In the previous study on larger nanoparticles, Co/Ni ratio of 1.0 was obtained, which will be discussed later.

The detection of phosphorus is trickier, because it is present in the remaining ligands in amounts that depend on the washing, and also because of the lower atomic number of this element. SEM-EDS provided a P/Ni ratio of 0.8 and STEM-EDS of 1.0. The difference likely comes from the amount of organics observed in each technique: at low magnification by SEM, an average of the powder is obtained, while STEM is performed on regions of the grids were the nanoparticles are best dispersed, which typically is promoted by a local excess of ligands.

Altogether, the nanoparticles produced here were composed of a nickel-rich phosphide core, likely surrounded by a cobalt-rich shell of poor crystallinity, not detected by XRD. The nanoparticles diameter was smaller than in the previous study, due to the first step of the formation of the nickel nanoparticles. The presence of a phosphorus-rich core was expected.

A phosphide phase was detected, which was not expected but is still consistent with previous observations by STEM-EDS. This could be tamed by increasing the OAm/TOP ratio, based on previous works on nickel phosphides. [START_REF] Muthuswamy | Synthetic Levers Enabling Independent Control of Phase, Size, and Morphology in Nickel Phosphide Nanoparticles[END_REF] The cobalt incorporation at the second step was less efficient than expected, with final Co/Ni ratio lower than the expected value of 1.0, which suggested that some of the cobalt stayed trapped as a molecular species stabilized by TOP in solution. [START_REF] Pregaglia | Catalysis by Phosphine Cobalt Carbonyl Complexes. III. The Synthesis and Catalytic Properties of a New Series of Cobalt(0) Clusters[END_REF] This could be tamed by lowering the TOP stoichiometry, but also by favoring a better nucleation of cobalt as nanoparticle through a gentler heating ramp.

These unexpected results and the seemingly high sensitivity to the operating conditions let us to re-examine in detail the phase speciation in nickel-cobalt nanoparticles prepared by this two-step route. Therefore, we decided to deeper investigate the influence of the synthesis parameters on the phase speciation, with the target of forming fcc NiCo nanoparticles, which is the expected phase at the reaction temperature. [START_REF] Baker | ASM Handbook: Alloy Phase Diagrams[END_REF] We worked on the four actionable parameters mentioned above: (i) the dilution, (ii) the temperature ramp, (iii) the stoichiometry of the phosphine, (iv) the stoichiometry of cobalt.

Influence of dilution

Firstly, in order to hinder the formation of the phosphide phase, we used more diluted conditions. Increasing the amount of oleylamine to 22 equiv. led to the formation of nanoparticles with an average diameter of 12 nm, similar to these obtained above (Figure 2B). STEM-EDS mapping confirmed that each nanoparticle contained nickel and cobalt (Figure S4).

The absence of the crystalline phosphidized phase was confirmed by XRD, as observed on Figure 2A. However, we were puzzled to observe that, upon repetition, XRD measurements were not reproducible leading always to a metallic cubic phase and sometimes to an additional hexagonal phase (Figure 2A). For the cubic phase, the measured lattice parameter of a = 3.526 Å can correspond to either fcc Ni (a = 3.524 Å, JCPDS file 00-004-0850) or fcc NiCo alloy (a = 3.534, JCPDS file 04-004-8490). For this reason and in the sake of clarity, all the following XRD patterns are displayed with the fcc Ni phase as the reference one.

According to the Scherrer formula, the average crystallite size is 8 nm. The second set of broader diffraction peaks is attributable to an hcp cobalt phase (JCPDS file 04-001-3273) and it corresponds to an average crystallite size of 6 nm. XRD sensitivity is limited when the crystallites are small and when the peaks partially overlap, which is the case here. The cubic pattern showed on Figure 2A-(a) may hide some lower amount of hcp phase. Deconvolution of the pattern did not allow detecting such hcp phase (Figure S15).

In order to confirm this, we used X-ray absorption spectroscopy (XAS), which probes the whole volume of the nanoparticle and is also sensitive to the local order. We recorded spectra in transmission mode at both Ni K-edge and Co K-edge for these fcc NiCo NPs and compared them with references compounds of metals and oxides. The X-ray absorption near edge structure (XANES) is presented on Figure 3A and Figure 3B for Ni and Co K-edges, respectively (the whole XAS is showed on Figure S8). We found that the edges of both Ni and Co were close to the metal reference edges indicating that most of their atoms were in a metallic environment and at an oxidation degree of 0. Regarding Ni K-edge (Figure 3A), the spectrum of the fcc NiCo NPs was much more similar to the spectrum of metallic Ni than to the spectrum of NiO. First, the edge position was measured at 8331 eV for the sample, when it was at 8332 eV for metallic Ni and 8343 eV for NiO, confirming the metallic character of the Ni atoms. Second, we noticed on Figure 3A that the oscillations in the extended X-Ray absorption fine structure (EXAFS) region rapidly dampened after the white line. Still, their position matched with these of reference foil of metallic Ni but not with these of the NiO reference. In particular, there are (i) a local maximum at 8381 eV for both the sample and the metal Ni spectra, absent for the NiO spectrum and (ii) a lower absorption between 8394 and 8404 eV for both the sample and the metal Ni spectra, when the NiO spectrum presented a maximum at these energies. EXAFS at Co K-edge is presented on Figure 3C andD. It should be noted that the EXAFS spectra of bulk hexagonal and cubic Co are very similar. [START_REF] Sprouster | Ion Beam Formation and Modification of Cobalt Nanoparticles[END_REF] Significant differences on the EXAFS spectra appear at k > 13.5 Å -1 , a value that cannot be exploited here because of the presence of nickel: Ni K-edge rises at ca. 8300 eV, which corresponds to k = 12.5 Å -1 for cobalt. Here, we were able to collect data up to 10.5 Å -1 . At smaller k-values, two features can be used to discriminate between hcp or fcc phases, as shown Figure 3C on bulk references. [START_REF] Sprouster | Ion Beam Formation and Modification of Cobalt Nanoparticles[END_REF] First, at ca. 6 Å -1 , a shoulder is expected for the hcp phase while the fcc phase presents a peak. Second, between 7.5 and 7.8 Å -1 the observed decrease is twice more pronounced for the fcc phase (ca. 25% of the height of the peak at 8.1 Å -1 ) than for the hcp phase (ca. 10% of the height of the peak at 8.1 Å -1 ). The EXAFS spectrum of the NiCo NPs on Figure 3D (in black) was compared with these of a NiCo NPs powder (in violet) displaying both fcc and hcp phase by XRD. It presents a peak at 6 Å -1 (rather than a shoulder), a strong decrease between 7.5 and 7.8 Å -1 (ca. 30% of the height of the peak at 8 Å -1 ). On the opposite, mixed phase compound has a shoulder at 6 Å -1 and a small decrease between 7.5 and 7. A slight variation of operating conditions might trigger the appearance of the Co hcp phase in some samples. Indeed, the nucleation of the metallic cobalt in the early stages occurs under kinetic control. Some variations come from irreducible process parameters at the lab scale: dissolution rate of the Co precursor grains, elimination rate of the carbonyl gas generated by the precursor decomposition, magnetic stirring efficiency, power surges applied by the heating mantle, etc. Others can be better controlled: ligand stoichiometry and temperature ramp. These two parameters were investigated next, using the diluted conditions, i.e. 22 equiv. of oleylamine.

Influence of TOP stoichiometry

We analyzed the impact of the phosphine ligand on the outcome of this reaction. Tri-noctylphosphine easily coordinates to Co x (CO) y species and forms various Co x (CO) y (TOP) z complexes which have been observed as intermediates in the synthesis of  Co NPs. [START_REF] De Silva | A New Role for Surfactants in the Formation of Cobalt Nanoparticles[END_REF] These complexes may sequester part of the cobalt as molecular species in solution. Moreover, TOP is directly responsible for the phosphidization of the nanoparticles core. Therefore, we decided to synthetize NiCo NPs using lower amounts of TOP. When 1 equiv. of TOP was used, the nanoparticles were larger with a diameter of 20 nm (Figure S5D), as expected from a previous work. [START_REF] Carenco | Controlled Design of Size-Tunable Monodisperse Nickel Nanoparticles[END_REF] However, the Co hcp cobalt phase still appeared in some samples (Figure S5C). Lowering further the amount of TOP to 0.8 equiv. diminished the signal intensity for the hcp phase in XRD, however the nanoparticles obtained were polydisperse and contained much bigger objects (Figure S6, C and D respectively). This suggested that some cobalt nucleated aside the preformed nickel nanoparticles under these conditions. Therefore, the following reactions were conducted with 1 equiv. of TOP, which means with the lower TOP amounts that still provided a fairly sharp size distribution for the nanoparticles.

Influence of temperature plateaus

Based on the observation made with 0.8 equiv. of TOP, it is possible that the hcp phase could come from isolated cobalt nanoparticles. The heteronucleation of cobalt species on the nickel nanoparticles (providing the desired core-shell structure) should present a lower activation energy than the homonucleation of cobalt in the solution. A too rapid heating ramp could allow both homo-and heteronucleation simultaneously. Rather, a more gentle heating, favoring the cobalt complex decomposition on the nanoparticle surface, may be adequate. Nucleation of cobalt species has been reported to begin at around 175 °C using Co 2 (CO) 8 as organometallic precursor and TOPO as stabilizing agent. [START_REF] Timonen | From Hot-Injection Synthesis to Heating-Up Synthesis of Cobalt Nanoparticles: Observation of Kinetically Controllable Nucleation[END_REF] . Therefore, we reduced the overall heating rate by adding two plateaus to the temperature program, at 140 °C and 160 °C. The resulting process is a ramp of 80 minutes instead of 40 minutes originally (Figure S1B). When these conditions were used along with 1 equiv. of TOP, the hexagonal cobalt phase was not anymore detected by XRD (Figure 4A). An average Co/Ni ratio of 0.95 was detected by ICP-AES as an ensemble measurement (Table S3), very close to the introduced ratio of 1.0, which suggests that the loss of Co as molecular complexes was mostly suppressed under these conditions. The nanoparticles were observed by TEM (Figure 4B). As the major species (95 % to 100 %, depending on the batches), 18 nm nanoparticles were observed. This diameter corresponds to the diameter for a core-shell structure built on 15 nm Ni nanoparticles (see Figure S7 and the geometrical model used for calculation in ESI section 11). We also noticed that these optimized conditions sometimes led to the presence of small quantities (less than 5 % in number) of larger 40 nm nanoparticles. To analyze the composition of the larger nanoparticles, STEM-EDS measurements were performed (Figure 5). On the color-coded maps, the pixel intensity is linear vs. the photon counts, meaning that the lower concentrations of Co or Ni do not appear well when another region of the picture is highly concentrated in the same metal. The larger nanoparticles were rich in cobalt, with an average Co/Ni ratio between 10 and 35, depending on the particles. This result suggests that the temperature plateaus were not able to suppress the homonucleation of cobalt nanoparticle. However, no hcp phase was observed by XRD, suggesting that under these conditions the Co crystallized as a fcc phase (of pure Co or NiCo alloy) even in the few larger nanoparticles present in the sample. The introduced Co/Ni ratio of 1:1 failed to provide solely the expected fcc core-shell nanoparticles. Thick shells seem to be difficult to form under these conditions. As a consequence, we performed reactions with lower amounts of cobalt in the hope to decrease the occurrence of larger cobalt-rich nanoparticles. Moreover, performing reactions with a low cobalt stoichiometry was an opportunity to better understand which were the preferential reaction sites for cobalt species.

Influence of cobalt stoichiometry and consequence on the surface

Using the long temperature program (80 min.) and 1 equiv. of TOP, the Co/Ni ratio was varied from 0.5 to 0.05. In none of this case was the hcp phase detected by XRD (Figure S10).

Only the fcc phase was detected. Moreover, XANES at Co K-edge and Ni K-edge were very similar for the whole series of samples (Figure S9). ICP-MS and ICP-AES confirmed that the ratio Co/Ni in the products follows the expected ratio (Figure 6B, blue circles and green squares, Table S3). This means that the reactions can be considered as quantitative vs. Ni and vs. Co under these reaction conditions. TEM revealed again the presence of two populations of nanoparticles: the expected smaller ones (diameter between 10 and 25 nm), and larger ones (Figure S11 and Table S2, Figure S12). The occurrence of larger nanoparticles was only 3% with the lower Co/Ni ratio of 0.05. Two average diameters were calculated to describe this situation (Table S2): the regular average diameter taking into accounts all the nanoparticles and the average diameter of the small nanoparticles population. The first was poorly informative, as it came from a bimodal population. The second value allowed commenting on a more significant trend: as expected, larger average diameters were obtained with a larger amount of cobalt added at the second step: from 14.4 ± 2 nm (for 0.05 equiv. of Co) to 17.5 ± 3 nm (for 0.5 equiv. of Co) (Table S2).

We decided to evaluate the Co/Ni surface ratio by X-Ray photoelectron spectroscopy (XPS) (Figure 6A), keeping in mind that the few larger nanoparticles had a comparatively low contribution to this value. All spectra highlighted the presence of cobalt, cobalt oxide, nickel and nickel oxide (see fitting parameters in Table S1). The presence of surface oxides was expected considering the lack of stability of Ni(0) and Co(0) in air. The most appropriate region to calculate this ratio is the NiCo 3p region were Ni and Co are observed with very close binding energies, thus with the same inelastic mean free path of ca 2 nm. [START_REF] Tanuma | Calculation of Electron Inelastic Mean Free Paths (IMFPs) VII. Reliability of the TPP-2M IMFP Predictive Equation[END_REF] Considering that the cross sections are also very close for Ni and Co, the surface fraction for cobalt was calculated directly from the spectra as the fraction of the total area under Co 3p and Ni 3p: we thus plotted the Co/Ni surface ratio, as measured (Figure 6B, red dots). For samples with 0.05, 0.1 and 0.2 equiv. of Co vs. Ni, the experimental fractions of Co follow the introduced ones, consistent with the idea that most of the cobalt was deposited onto the preformed nickel nanoparticles. Above 0.5 equiv. of Co vs. Ni, the surface ratio was lower than expected, by comparison with the measurements by ICP (Figure 6B, green diamonds and blue triangles), suggesting that cobalt above 0.5 equiv. was not anymore covering the nickel. Rather, this was consistent with more and more cobalt being sequestered in large nanoparticles. EDS is a low-yield process, and as a result, STEM-EDS maps require fairly long exposure time. In order to confirm the core-shell structure of the nanoparticles and the absence of beam damage, electron energy loss spectroscopy (EELS) was employed (Figure 7E-H). It allows first, to collect the map in a faster way, and second, to avoid broadening effect of the probe in the material. As a result, a cartography with a resolution of 0.5 nm was obtained, for example on the Co/Ni = 0.1 sample (Figure 7E). Both the filtered images and the cross-section (Figure 7H) confirm the core-shell structure of the nanoparticle, that is, a cobalt-rich outer region on top of a nickel-rich region. Due to the mobility of Co and Ni atoms in this binary compound, [START_REF] Bonifacio | Thermal Stability of Core-Shell Nanoparticles: A Combined in Situ Study by XPS and TEM[END_REF] there may be the presence of few Ni atoms in the shell region and few Co atoms in the core region.

Discussion

In the results showed above, we identified several key points in the synthesis of bimetallic nanoparticles. First, the reaction performed under concentrated conditions (12 equiv. of OAm vs. Ni, Table 1 entry 1) and with a fairly large amount of TOP (3 equiv.) was found to yield a significant phosphidation of the nickel core, and this, already at the first step of the reaction, prior to the addition of cobalt. The crystalline structure of the core was unchanged as a result of the second step (addition of 1 equiv. of Co), although partial substitution of Ni by Co in Ni 12 P 5 would give a similar signature in XRD and cannot be excluded a priori.

The results of the first step stands in contrast with reactions forming fcc nickel nanoparticles reported at higher dilution and/or with lower amounts of phosphine. [START_REF] Carenco | Controlled Design of Size-Tunable Monodisperse Nickel Nanoparticles[END_REF] It thus appears that the phosphine concentration (and not only the stoichiometry) is a key parameter to anticipate the nickel core phosphidation, which may start at temperatures as low as 150 °C during the reaction. [START_REF] Carenco | The Birth of Nickel Phosphide Catalysts: Monitoring Phosphorus Insertion into Nickel[END_REF][START_REF] García-Muelas | Initial Stages in the Formation of Nickel Phosphides[END_REF] This seems in agreement with idea proposed in the literature that TOP and OAm compete as surface ligands: [START_REF] Muthuswamy | Synthetic Levers Enabling Independent Control of Phase, Size, and Morphology in Nickel Phosphide Nanoparticles[END_REF] TOP needs to stay coordinated long enough to the nickel surface for the P-C bond to be broken. However, the actual mixture composition during and after the first step is more complex than a binary one. Indeed, we showed in a previous mechanistic work that the sole reaction of Ni(acac) 2 and OAm produces a range of species including water, keto-ene-amine and acetamide derived from OAm and acetylacetone secondary reactions, as depicted on Figure 8. [START_REF] Carenco | Revisiting the Molecular Roots of a Ubiquitously Successful Synthesis: Nickel(0) Nanoparticles by Reduction of [Ni(Acetylacetonate) 2[END_REF] Thus, it is worth discussing in details all the experimental parameters that may affect the reaction outcome due to their variability. From a previous study on copper nanoparticles, we know that water forms in variable amounts from one synthesis to another and may further react with oxophilic metals. [START_REF] Pesesse | Influence of the Copper Precursor on the Catalytic Transformation of Oleylamine during Cu Nanoparticle Synthesis[END_REF] Here, small amounts of water may affect the precise nature of reactions intermediates from Co 2 (CO) 8 to metallic cobalt.

Moreover, water and some of the other byproducts are able to react with TOP upon heating, forming TOPO. This potentially lowers the available amount of TOP to stabilize intermediate cobalt complexes in the second step, but also provides an additional surface ligand that may play a role in selecting the cobalt phase obtained at the end of the second heating step. TOPO was used for forming both hcp and  Co nanoparticles, starting from Co 2 (CO) 8 as the cobalt precursor. 42,47 However, the  Co phase was stabilized only for nanoparticles below a few nanometers, [START_REF] Puntes | Self-Assembly, and Magnetic Behavior of a Two-Dimensional Superlattice of Single-Crystal ε-Co Nanoparticles[END_REF][START_REF] Dassenoy | Experimental Evidence of Structural Evolution in Ultrafine Cobalt Particles Stabilized in Different Polymers-From a Polytetrahedral Arrangement to the Hexagonal Structure[END_REF] which explains why it was not encountered in the present study. Here, the amount of TOPO formed in situ would depend from the kinetics of side-reactions, thus on the heating ramp but also on the dead volume of the flask and other operating parameters such as the stirring speed.

Independently from the question of side-reactions, another parameter decreasing the reproducibility of the reactions is the presence of impurities in TOP batches: they vary in amount, from technical TOP to high-purity TOP, but also in nature from one manufacturer to the other. Actually, some works even used mixtures of technical and higher-purity TOP as a way to optimize the growth of cobalt nanoparticles. [START_REF] Puntes | Self-Assembly, and Magnetic Behavior of a Two-Dimensional Superlattice of Single-Crystal ε-Co Nanoparticles[END_REF] We also know from our experience that TOP with purity higher than 90% but from different providers produces nickel nanoparticles with various diameters due to the presence of different impurities. [START_REF] Carenco | A New Versatile Route to Metal Phosphide Nanoparticules Using White Phosphorus : Applications in Catalysis and for Lithium Batteries[END_REF] Here, because TOP is involved both in the stabilization of intermediate Co complexes, or even clusters such as [Co(CO) 2 (TOP) 3 ] 3 , [START_REF] Pregaglia | Catalysis by Phosphine Cobalt Carbonyl Complexes. III. The Synthesis and Catalytic Properties of a New Series of Cobalt(0) Clusters[END_REF] and in the final size control of the nanoparticles, any variation on TOP nature and amount (affected by the possible formation of TOPO) may impact the outcome of the synthesis. For example, when only 0.8 equiv. of TOP was used (section 2.3, Table 1 entry 4), the stabilization of such species, which requires 3 TOP per Co, would have been disfavored. Lower TOP amounts resulted in the appearance of a number of large cobalt-rich nanoparticles that may have come from a secondary nucleation path directly from the solution rather than at the surface of existing nanoparticles. Moreover, the amount of available TOP is expected to directly affect the phase of the final nanoparticles: a study by de Silva et al. showed the role of intermediate clusters involving TOP, oleic acid and TOPO in explaining mixture of fcc and hcp vs. the selective production of fcc, hcp or even  phases. [START_REF] De Silva | A New Role for Surfactants in the Formation of Cobalt Nanoparticles[END_REF] Overall, the complexity of the reaction mixture, in terms of the nature of the species present at each step and their relative amounts, is one key parameter explaining the sensitivity of the phase control in our reaction.

Figure 8

Simplified reaction mechanism proposed for entries 2-9 of Table 1. The stoichiometries were omitted for clarity. Species in grey are not fully defined in amount or nature. In this scheme,  indicates a small quantity of the species.

We also need to discuss the question of temperature control and heat power applied during the second heating step, after the addition of cobalt. Devices for temperature control vary from one laboratory to the other, as do the operating conditions (flask volume, heating mantle maximum power, parameters of the temperature control feedback, etc.). Even after a careful calibration, heating mantle and temperature control devices are never strictly equivalent. In most cases, this has no consequences on the reaction outcome: for example, in the first step, the nucleation of Ni(0) is a sharp process happening only above 212 °C. [START_REF] Carenco | Revisiting the Molecular Roots of a Ubiquitously Successful Synthesis: Nickel(0) Nanoparticles by Reduction of [Ni(Acetylacetonate) 2[END_REF] In the case of cobalt, the reaction is more delicate as it is strongly endothermic, and significantly affects the temperature of the mixture. [START_REF] Timonen | From Hot-Injection Synthesis to Heating-Up Synthesis of Cobalt Nanoparticles: Observation of Kinetically Controllable Nucleation[END_REF] When the ramp was too fast, as in section 2.2 (Table 1 entries 2, 3 and4), molecular processes of precursor decomposition, generation of reactive Co(0) species and crystallization may overlap, explaining a lack of repeatability. In contrast with this, introducing more temperature plateaus provides an empirical mean to better separate these processes.

We also should discuss the phase crystallization. In macroscopic compounds, hcp cobalt is expected to be a stable phase below 425 °C while fcc cobalt is the stable structure above this temperature. [START_REF] Sun | Synthesis of Monodisperse Cobalt Nanocrystals and Their Assembly into Magnetic Superlattices (Invited)[END_REF] For nanocrystals, these temperatures may have to be revised due to the low spatial extension of the crystals and the higher energetic contribution of the surface.

In the present work, we may consider as a first approximation that hcp Co is the kinetic product while fcc Co is the thermodynamic one. This would explain in a satisfactory manner why the introduction of the several heating plateaus (section 2.4, Table 1 entry So far, we have only discussed the reactions conducted with 1 equiv. of Co vs. Ni. This corresponds to a very large excess of cobalt species vs. available surface nickel sites, a situation that may favor the nucleation of cobalt inorganic compounds aside the existing nanoparticles. In other words, thick shells of cobalt are difficult to obtain when adding the whole amount of the highly reactive cobalt precursor at the same time. The use of a lower cobalt stoichiometry, down to 0.05, provides an opportunity to propose a reaction mechanism regarding how cobalt may cover the nickel nanoparticles (section 2.5, Table 1 entries 6 to 9). Two points should be mentioned at this stage. First, Ni and Co are miscible in our reaction conditions, [START_REF] Baker | ASM Handbook: Alloy Phase Diagrams[END_REF][START_REF] Guisbiers | Thermal and Martensitic Phase Transitions in Ni-Co Nanoparticles[END_REF] meaning that the formation of cobalt-nickel gradient into the NPs top layers cannot be excluded. Second, a previous study by in situ annealing in STEM-EDS revealed that Ni and Co alloying starts above 440 °C, a temperature well above the reaction temperature. [START_REF] Bonifacio | Thermal Stability of Core-Shell Nanoparticles: A Combined in Situ Study by XPS and TEM[END_REF] From these two facts, we retained a core-shell model for the NiCo NPs produced in section 2.5, while assuming that there could be a slight gradient at the interface of the Ni and Co. This proposition is consistent with STEM-EDS mapping of the nanoparticles (Figure 7). Regarding the phase, only the fcc one was obtained, regardless of the Co/Ni ratio, which is in contrast with another report using a higher reaction temperature (280 °C) and a different protocol. [START_REF] Van Schooneveld | Composition Tunable Cobalt-Nickel and Cobalt-Iron Alloy Nanoparticles below 10 Nm Synthesized Using Acetonated Cobalt Carbonyl[END_REF] Regarding the morphology, at the lower Co/Ni ratio of 0.05, we expected from our geometrical model (ESI section 10) that a full monolayer of Co cannot already be formed, as depicted on Figure 9. When increasing the stoichiometry of Co, it appeared that Co would start forming islands on the NiCo NPs while also nucleating as larger nanoparticles in the solution. The shell produced under these reaction conditions is thus not conformal to the starting nanoparticles, which is in agreement with previous observations using slightly different synthetic parameters. [START_REF] Carenco | Synthesis and Structural Evolution of Nickel-Cobalt Nanoparticles Under H2 and CO2[END_REF] The quantity of larger nanoparticles increased sensibly when increasing the cobalt stoichiometry, suggesting that the growth rate increases with the nanoparticles diameter and that the 'over growth' process is intrinsically hard to avoid in this synthetic design.

Besides, we propose that the larger nanoparticles form due to either a too high concentration of cobalt in the reaction medium when using the higher stoichiometries, and also possibly due to Ostwald ripening in the later stages of the temperature program. Indeed, for Co/Ni = 0.5, the cobalt would have to form at least 3 conformal monolayers if it was homogeneously deposited (Figure S7). Regarding this point, it may be useful to remove amines from the medium, as it may promote cobalt dissolution upon prolongated reaction times, [START_REF] Van Schooneveld | Composition Tunable Cobalt-Nickel and Cobalt-Iron Alloy Nanoparticles below 10 Nm Synthesized Using Acetonated Cobalt Carbonyl[END_REF] but this would mean a change in strategy for the first step of the reaction (the synthesis of the Ni NPs). As another perspective, further optimization of the protocol could include a step-wise addition of Co (inspired from the SILAR method for the growth of quantum dots) [START_REF] Narayanaswamy | The Effect of Temperature and Dot Size on the Spectral Properties of Colloidal InP/ZnS Core-Shell Quantum Dots[END_REF] or using continuous flow microreactors [START_REF] Baek | Investigation of Indium Phosphide Nanocrystal Synthesis Using a High-Temperature and High-Pressure Continuous Flow Microreactor[END_REF] in order to obtain conformal coreshell nanoparticles with a single size-distribution. However, this will still represent a challenge, in particular regarding the very high sensitivity of the cobalt precursor, which decomposes rapidly at room temperature even under strict inert atmosphere, and the lack of colloidal stability of the NPs.

Conclusion

This work aimed to a better comprehension of the phenomena leading to the formation of fcc nickel cobalt nanoparticles. The apparently random presence of a Co hcp phase in the XRD of these nanoparticles raised the question of the high sensitivity of the protocol to small operating conditions. We tried to rationalize such observation by studying the effect of different parameters such as the amount of ligand or the heating program for the formation of the cobalt shell. The amount of TOP ligand utilized in this synthesis did not affect the crystallinity of the final nanoparticles while it affected greatly their shape and dimension. On the other hand, the use of a longer heating program for the deposition of the cobalt shell allowed the production of phase-pure fcc NiCo NPs.

Our experiments demonstrated that, when several temperature plateaus were used along with few equiv. of Co, the first cobalt layer was effectively deposited onto the Ni Nps. However, at higher Co/Ni ratio, thicker cobalt layer tended to grow on top of existing cobalt layer, and the formation of a second population of larger nanoparticles was observed as a byproduct. The sole criterion of phase purity was therefore not a good indicator of the final structure of the nanoparticles. Finally, we rationalized these observations in relation with the complexity of the reaction in terms of molecular species appearing both at the first and second step of the reaction, and we proposed a schematic growth mechanism for the cobalt domains.

There is no doubt that a full understanding of this seemingly simple protocol has yet to be reached by varying further operating conditions, such as the temperature of addition of the cobalt precursor, the absolute influence of cobalt concentration and possibly the use of alternative cobalt precursors. Preliminary attempts concerning the first point revealed that every degree counts when dealing with such highly reactive precursor. On a more general note, we call for a more systematic report of nanoparticles syntheses that are highly sensitive to operating conditions, because robustness is a key issue of nanotechnology developments. 54- 56 Although these may have been so far flying under the radar, being sometimes considered as "negative results", this will be enlightening to the community as an effort to strengthen our protocols, and this will also be key to successful implementation of automated methods and analysis in NPs synthetic design, eg. using AI technologies. Moreover, our work suggests the relevance of more comprehensive studies of phase control for metallic core-shell nanoparticles that may adopt several combination of phases, in order to further exploit the catalytic and magnetic [START_REF] Guisbiers | Thermal and Martensitic Phase Transitions in Ni-Co Nanoparticles[END_REF] properties of these objects.

Table of Content Entry

Figure 1 (

 1 Figure 1 (A) XRD pattern of the nanoparticles powder, the reference phase in red corresponds to Ni 12 P 5 (PDF 03-065-4018, dotted lines are a guide to the eye). (B) TEM of the nanoparticles and size distribution in the inset.

Figure 2 (

 2 Figure 2 (A) XRD pattern of two samples (a, b) prepared in diluted conditions, the reference phase in green corresponds to fcc Ni (JCPDS file 00-004-0850) and the reference phase in red corresponds to hcp cobalt (JCPDS file 04-001-3273). (B) Representative TEM of the nanoparticles and size distribution in the inset.

  8 Å -1 . Based on the interpretation extracted from the reference compounds of fcc Co and hcp Co, experimental observation of the two NiCo powders strengthens the trend observed by XRD, namely, the absence of the hcp phase in the black spectrum.

Figure 3 (

 3 Figure 3 (A) XANES of the fcc NiCo NPs at Ni K-edge, (a) NiO ref, (b) Ni(0) foil ref, (c) NiCo NPs. (B) XANES of the fcc NiCo NPs at Co K-edge, (d) Co 3 O 4 ref, (e) CoO ref, (f) Co(0) hcp ref, (g) Co(0) fcc ref 40 and (h) NiCo NPs. (C, D) EXAFS at Co K-edge of (blue) Co hcp, (orange) Co fcc, (black) fcc NiCo NPs and (violet) fcc+hcp NiCo NPs. The red circles are a guide to the eye to point the features used to discriminate between Co hcp and fcc phases.

Figure 4 (

 4 Figure 4 (A) XRD pattern (the reference phase in green corresponds to fcc Ni, JCPDS file 00-004-0850, and the reference phase in red corresponds to hcp cobalt, JCPDS file 04-001-3273). (B) TEM, size distribution in the inset (average diameter in red is for the smaller nanoparticles (10-25 nm) and average diameter in yellow is for the whole population).

Figure 5 (

 5 Figure 5 (A) STEM bright field, (B) STEM-HAADF and (C) STEM-EDS mapping of NiCo NPs synthetized using 1 equiv. of TOP and temperature steps (red for cobalt and green for nickel).

Figure 6 (

 6 Figure 6 (A) XPS NiCo 3p region of the NiCo NPs with decreasing stoichiometry of introduced cobalt (from 1 to 0.05 equiv. vs. Ni). Color code: Ni(0) in dark green, nickel oxide in light green, Co(0) in red, cobalt oxide in deep pink. (B) Ratio Co/Ni, as measured: at the surface from XPS peak areas (red dots), by ICP-MS (blue triangles), by ICP-AES (green diamonds).

Figure 7 (

 7 Figure 7 (A-D) STEM-EDS overlay maps of NiCo with a variable Co vs. Ni ratio: (A) 0.05, (B) 0.1, (C) 0.2, (D) 0.5. (E-G) STEM-EELS measurement of a nanoparticle from the sample with Co/Ni = 0.1. (E) overlay, (F) Co L-edge signal, (G) Ni L-edge signal, (H) crosssection along the dotted line in (E).

  5), providing more time for the intermediate to evolve, effectively suppressed the formation of the hcp phase.

Figure 9

 9 Figure 9 Proposed mechanism for the cobalt reaction with the nickel nanonoparticles at selected stages. The bottom table recalls selected Co/Ni ratio. The top values recall the average diameters of the smaller NP population as well as the amount of larger NPs.

Table 1 :

 1 Summary of the operating conditions, phase and morphology observed through the study. Co, OAm and TOP are given in equiv. vs. Ni. Heating programs refer to these described in FigureS1.

	Entry Section Co	OAm TOP	Heating program	Phase (XRD)	Morphology
	1	2.1	1	12	3.0	short	Ni 12 P 5	single population, 12.4±1.2 nm
	2	2.2	1	22	3.0	short	fcc or fcc+hcp	single population, 12.0±1.2 nm
	3	2.3	1	22	1.0	short	fcc or fcc+hcp	single population, 20.3±2.2 nm
	4	2.3	1	22	0.8	short	fcc or fcc+few hcp two populations
	5	2.4	1	22	1.0	long	fcc	major population (93%): 18.1±2.7 nm
	6	2.5	0.5	22	1.0	long	fcc	major population (93%): 17.5±3 nm
	7	2.5	0.2	22	1.0	long	fcc	major population (91%): 16.3±2.4 nm
	8	2.5	0.1	22	1.0	long	fcc	major population (95%): 16.2±3 nm
	9	2.5	0.05	22	1.0	long	fcc	major population (97%): 14.4±2 nm

Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 758480). Sorbonne Université, Collège de France and CNRS are acknowledged for support. Antoine Miche (Sorbonne Université, CNRS, Fédération de Chimie et Matériaux de Paris-Centre, LRS) is acknowledged for the XPS measurements. Elodie Barruet-Collard (NIMBE, CEA and CNRS) is acknowledged for ICP-MS and ICP-AES measurements. Sandra Casale (Sorbonne Université, CNRS, Fédération de Chimie et Matériaux de Paris-Centre) is acknowledged for HRTEM and EDS measurements. We acknowledge SOLEIL synchrotron for beamtime allocation on the SAMBA beamline under project 20191697, and we acknowledge Andrea Zitolo for help with the measurements on the beamline. The authors are grateful to the French METSA network (FR3507) for the financial support of the scanning transmission electron microscope experiments. Mounib Bahri (from IPCMS) is acknowledged for help with the preliminary measurements on the samples. We acknowledge Prof. D. Sprouster (Stony Brook University) for providing us with the data at Co K-edge of the Co fcc reference.


Keywords: end-of-life systems, dismantling, decision, Bayesian network, warranty management, recertification I

In this paper, a new approach to determine optimal disassembly plan of an end-of-life system by using Bayesian network is introduced. The best solution is called the optimal trajectory. A trajectory model is proposed which allows handling the different key factors and also makes it possible to manage uncertainties specific to system deconstruction. After having presented the disassembly planning issue, Bayesian networks instantiated to dismantling problem are introduced together with the influence diagram which allow the decision maker to proceed to the economic assessment of the different possible strategies. Among the various cost factors is the cost related to warranty of the recycled products. A warranty program management is described. Eventually, the global trajectory model, including the implementation of the warranty cost has a decision variable, is presented.

INTRODUCTION

For many years now, the end-of-life stage of systems has come the subject of more and more studies. This is due, on one hand, to legislative pressures in terms of environmental protection and, on the other hand, to possible economical profits that may be gained by implementing product recycling solutions. It is a designer responsibility to integrate recycling constraints by proposing disassembly processes for their systems at the design stage. Increasing value strategies must respond to all decisional problems raised during the retirement step. Mainly valuable products must be selected according to technical, economical, and environmental criteria and disassembly systems enabling the products to be obtained have to be defined and optimized.

Within this framework three types of decision are considered. The first relates to the determination disassembly level i.e. the best option of valorization and, for the subsets, the choice between disassembling or recycling. The second relates to operation sequencing which aims at fixing how to obtain the products and the logical sequence of the operations to obtain them. Finally the quantities of products and their obtaining date on a given horizon have to be determined. The decision support in disassembly must make it possible to handle these three types of decision and to establish the link between them to keep a total control of the strategy. A disassembly trajectory leads to the identification of valuable products of an end-of-life system, of their value increasing channels and of the way to obtain them.

Modelling of disassembly trajectories requires taking into account the whole influencing factors. Among them is the warranty which is usually defined as the written guarantee of the integrity of a product and of the maker's responsibility for the repair and replacement of defective parts. This notion is interesting to be considered in order to provide the decision maker with a full integrated tool.

Based on this framework, this paper is divided into four parts. After a brief introduction on disassembly planning issues, bayesian networks applied to deconstruction problems are presented. Warranty aspects are then introduced before being implemented onto a global trajectory model.

DISASSEMBLY PLANNING PROBLEM A. Problem modelling framework

In a deterministic context, there are many works that address these problems in the literature. We present a way of linking these different approaches.

Generally, the modelling of the disassembly planning problem requires three main steps. The first step concerns the structure modelling of the end-of-life system. The goal of these models is to represent the valuable parts and subassemblies and the connections between them [START_REF] Moore | Disassembly Petri net generation in the presence of XOR precedence relationships[END_REF].

The second step of the disassembly planning problem concerns the modelling of the disassembly process. The obtained model represents the different operations that can be made on the system to obtain the valuable part and subassembly.

The third step concerns the search of the optimal sequence among those identified in the process model. The purpose is to jointly determine the disassembly level and sequence.

The model must take into account the preferences of the different stakeholders involved in the end-of-life phase of the system. Classic approaches model the decision problem as a linear program and solve it by existing algorithms [START_REF] Lambert | Linear Programming in Disassembly/Clustering Sequence Generation[END_REF].

B. Variables of the disassembly process

Solving disassembly planning problem involves different models and algorithms. Most of the works on this subject we encounter in the literature propose their own method and modelling language. In most cases, the considered approaches do not facilitate the integration of uncertainties.

Integration of Warranty as a Decision Variable in The Process of Recertification of Parts Resulting from End-Of-Life System Dismantling

Our goal is not to propose one more approach to solve this problem but to integrate the uncertainties of the disassembly process on the basis of existing models in order to determine an optimal and robust solution. To achieve this objective, we will use concepts and entities utilized by different approaches and then add uncertainties using a modelling language that cope with uncertainties.

The main entities involved in the resolution of the disassembly planning problem are the following:

(i) components: they represent the composition of the end-of-life system and can correspond to parts, subassembly and/or intermediate disassembly states;

(ii) connections: in relation with the component, they complete the structural point of view by representing the joints and/or contact connections as well as relationships between components and subassemblies;

(iii) end-of-life variables: linked with each component, they describe the different recovery actions which can be recycling actions or disassembly operations;

(iv) contextual variables: attached to component and endof-life variables, they model the recycling actors and other constraints on the recovery actions;

(v) decision variables: related to component and end-oflife variables, they represent the different actions of the decision-maker and give a framework to the decision process;

(vi) performance parameters: attached to end-of-life variables, they describe the consequences of the decision-maker actions.

On the basis of these entities, we propose in Figure 1 the generic framework of the modelling of disassembly planning problem (UML class diagram). At this stage, we have underlined the steps in solving disassembly planning problem and the different variables that decision-makers have to manage. We will introduce now Bayesian network to cope with uncertainties on some of these variables.

II. BAYESIAN NETWORKS FOR DISASSEMBLY PLANNING

A. Bayesian networks and influence diagram

We propose to use Bayesian networks as the modelling mathematical tool to solve the following decision problem: for a given end-of-life system, determine the disassembly levels and sequences on the basis of the process model while taking into account the uncertainties of the disassembly process.

We use the Bayesian network and their extension to influence diagrams because the problems we want to solve have the following features [START_REF] Godichaud | Outils d'aide la décision pour la sélection des filières de valorisation des produits de la déconstruction des systèmes en fin de vie : application au domaine aéronautique[END_REF]:

(i) they can be represented graphically, (ii) there is necessity to integrate and manage uncertainties, (iii) there is necessity to solve an optimal uncertain problem.

The first reason is important in a multi-actors context as in the case of the problem considered here. Indeed, the Bayesian networks and the influence diagrams facilitate the understanding of the problem by all the actors by means of a simple and natural graphical representation.

Furthermore, they enable the interaction between these actors and the sharing of knowledge in a unique representation. Indeed, a Bayesian network is a graph model in which knowledge is modelled as variables and each variable correspond to a node in the graph. The directed arcs represent dependence relationship between the variables. The first step in developing a Bayesian network model consists in the elicitation of the interesting variables.

The second point corresponds to the purpose of our problem approach. The Bayesian networks enable inference that consists in the determination of probabilities for hidden variables of the problem given evidence. When decision-makers think there are uncertainties on some variables, they can evaluate them by probability formulation. Given the knowledge of the stakeholders, these probabilities can be conditional (they depend on some others variables) or marginal.

Once the uncertainties of the disassembly process have been evaluated, decision-makers have to determine the optimal solution according to several criteria. Decision and utility nodes are then added into the Bayesian network that becomes an influence diagram. It models the selection problem of end-of-life options for each component including the utility of these options. In [START_REF] Jensen | Bayesian network and decision graph[END_REF], the authors propose inference algorithms that determine the optimal solution.

B. Modelling disassembly decision problem using influence diagram

In this work, we propose to use influence diagrams (ID) as a decision tool to model disassembly problem and we suppose that a process model is given. Disassembly Petri Nets (DPN) are used to model this disassembly process. DPN clearly describe the precedence constraints between operations in the disassembly process. The places represent system, components and subassemblies and the transitions represent joints and disassembly actions. The purpose is to represent all the possible sequences of operations. The decision problem is to determine the best sequence according to one or more criteria.

Once the DPN behaviour mechanisms has been translated into an influence diagram the states (retrieved components, subassemblies, joint states …) of the disassembly process have to be determined according to different decision's configurations [START_REF] Godichaud | Disassembly Process Planning Using Bayesian Networks[END_REF].

Disassembly solutions are evaluated by means of utility nodes in the ID. They model the economic performance of the different recovery actions and disassembly operations. ID models enable the integration of utility in table forms. There are three types of nodes:

(i) disassembly cost nodes: linked to disassembly operation node, their value is function of disassembly operation realization, (ii) recycling cost nodes: they evaluate each recycling action realization mode of recycling node to which they are linked, (iii) recycling revenue nodes: they model economical flow that is generated when a recycling option is validated.

These different utility nodes allow the optimization of a criterion for selecting a disassembly plan. This criterion is decomposed at each product in order to select the option or operation for each of them. To achieve this goal, decision node of each product indicates the evaluation of each option. The decision rule consists in selecting the option that maximises the expected utility of the product and it is called end-of-life policy.

The set of all polities forms the strategy. It gives the products that have to be generated from the end-of-life system, the recycling options for these products and the disassembly operations that are needed to generate them. The purpose of optimization method is to determine the strategy for a given end-of-life system.

III. STRATEGIC WARRANTY MANAGEMENT

Among the different sources of costs and incomes, the determination of the disassembly strategy has to consider the ones associated with the warranty program proposed with the functional recycling of a system, subsystem or component. Determining an economic evaluation of a warranty program necesitates first assessing the risk associated with the different actions likely to be implemented and second, identifying the cost of the logistic support required to carry out the corrective tasks

A. Risk assessment

The warranty risk management is the systematic process of identifying, analysing, and responding to risk appeared during a program of warranty assistances. It includes maximizing the probability and consequences of positive events and minimizing the probability and consequences of adverse events to warranty objectives. Related to this point of view are for instance reference [START_REF] Ghodrati | Spare parts estimation and risk assessment conducted at Choghart Iron Ore Mine: A case study[END_REF], which deals with issues regarding risk and spare parts estimation.

Warranty risk is understood as an uncertain event or condition that, if it occurs, has a positive or negative effect on the program objective. It includes both threats (negative effects) and opportunities (positive effects) to improve those objectives. Known risks are those that have been identified and analysed and may be possible to plan for their occurrence and mitigation.

In the case of the recertification of parts resulting from system deconstruction, the risk assessment is made easier since the decision maker has at its disposal the data corresponding to the history of the system being considered for possible second-hand life.

Risks that are threats to the warranty program may be accepted if they are in balance with the reward that may be gained by taking the risk. The Figure 2 illustrates the risk management process, divided in different steps.

In order to approach the risk management activities to a warranty program, a planning for such processes can help to ensure that the level, type and visibility of this management are proportional with both the risk and importance of the warranty assistance to the whole organization. Once the planning is done, the risk identification is the following step to follow. This is the process of determining which risks can affect to the warranty program and to document the characteristics of each one.

A qualitative analysis of risks must then be performed which is the process of assessing the impact of the identified risks in the warranty assistances [START_REF] Marquez | A Structured Approach for the Assessment of System Availability and Reliability Using Continuous Time Monte Carlo Simulation[END_REF]. It prioritizes risks according to their potential effect on the program objectives, determining the importance of addressing specific risks and guiding risk responses.

Following, a quantitative analysis of the possible risks during the application of the warranty assistance has to be carried out. This is a process which measures the probability and consequences of risks, estimating their implications for program objectives. It helps to analyse numerically the probability of each risk and its consequence during the warranty service.

The following step on the risk management of a warranty program is the response planning, which is the process of developing options and determining actions to enhance opportunities, reducing threats to the program's objectives.

Finally, the last step is to monitor and control risks which is the process of keeping track of the identified risks, monitoring residual risks and identifying new risks, ensuring the execution of risk plans, and evaluating their effectiveness in reducing risks.

B. Logistic support specification

Once the risks have been identified and assessed and in order to launch a product to the market with a proper assigned warranty program, it is necessary during the very early stages of the product life cycle to identify and characterize the logistic support for such product. Some references and standards deal with this matter (e.g. [START_REF] Murthy | Product Warranty logistics: Issues and challenges[END_REF]).

The logistic support analysis is an iterative process which can be very helpful for the business management board to organize the after-sales department, the qualification of the staff, the required materials etc. in order to provide to the customer the adequate technical assistance during the warranty period [START_REF] Jones | Integrated Logistic Support Handbook[END_REF].

The identification and assessment of a new system or product involves to analyse the types and quantities of spare parts, the requirements of technical and skill levels, the tools and technical documentation to use... and many others, all focused to the application of a warranty program to a specific product positioned in the market. Therefore, in order to get as an output from the logistic support analysis the identification and justification of those types and quantities of spare parts, skill level requirements etc., it will be necessary a data base which compiles sources of logistical support such as the identification and procurement of logistic support elements.

IV. INTEGRATING WARRANTY IN A DECONSTRUCTION MODEL

We present in this section the trajectory model that is the model allowing the decision maker to define the level of disassembly optimizing the economic profit. The model used is a bayesian network. It has been first implemented in [WCEAM]. The originality comes here from the consideration of warranty costs likely to modify the decision in terms of disassembly level.

The disassembly trajectory problem is represented by Bayesian networks (BN). Indeed, they enable all the elements of this decision problem to be represented. Generally speaking, system disassembly modelling with Bayesian networks is described by the following items: (i) "product" nodes representing end-of-life system components that have one or more recycling option (ii) "activity" nodes representing disassembly operations or recycling action on each product, (iii) arcs characterizing precedence and exclusion relationships between activities, (iv) node parameters that make it possible to characterize disassembly process progress.

Decision variables are attached to each product. They indicate the direction of the disassembly trajectory towards one option (disassembling or recycling). Constraints are specified by the arcs. Economical parameters are associated with "activity" nodes by means of utility nodes. They represent costs and incomes potentially generated by the realization of an activity. They enable the economic profit of the various trajectories to be evaluated.

The set of nodes of the Bayesian networks disassembly model is noted . The following subsets of nodes characterize the model structure: • representing recycling action on ,

• an element of , (iii)
is the set of utility nodes. They are associated with each activity and ! is the utility node associated with the activity modelled by node .

The model represents the whole deconstruction trajectory that the decision maker has identified. The objective is to find an optimal trajectory that for each product, given its state, allows the best activity (further disassembly, functional recycling or material recycling) to be selected. In this network, Succ(A) represents the set of product node successors of a disassembly activity A. A disassembly policy model is drawn from the global model to evaluate each product separately. It enables the required defining recursive equation to be obtained to determine the optimal disassembly trajectory.

Disassembly policies are modelled by decision nodes associated with each product. These nodes are integrated in the model as presented in Figure 3(node " ). The considered product is modelled by node and modalities of node " characterize all the possible options likely to be selected on the product. Utilities ! # # $ %&'' $ (i.e. # is a component of ) represent the evaluation of product components generated by each disassembly operation. A policy model being associated with each product, these utilities correspond to the optimisation result of the product component policies.

Warranty parameters are introduced through utility nodes related to the option of functional recycling, precising for each disassembly level, the cost of the resulting warranty program as well as the probability (that is the reliability of the considered system, subsystem or component) characterizing the chance of implementing the corresponding actions.

V. CONCLUSION

We have presented in this paper a model for the determination of the dismantling optimal trajectories i.e. the optimal level of disassembly applied to the deconstruction of end-of-life systems. Disassembly solutions are evaluated by means of utility nodes in Influence Diagrams which are an extension of Bayesian networks. They enable the modeling of the economic performance of the different recovery actions and disassembly operations. Warranty parameters are integrated in the model in order to evaluate the real costs of the products in the case of a second-hand life.

In the proposed work, warranty parameters are considered as a known input. The perspectives of future works deal with the use of Bayesian network to determine the risks associated with the warranty. Through a bottom up approach (whereas the work presented here is a top down methodology), it should allow the decision maker to define the reliability of the different subsystems according to the decomposition level by associating the failure rate of the components with respect with their mode of association.

Figure 1 .

 1 Figure 1. Structure of disassembly variables

Figure 2 :

 2 Figure 2: Risk management workflow

Figure 3 :

 3 Figure 3: Disassembly policy model

Laboratoire Génie de Production ENIT -INPT Université de Toulouse, France

Industrial Management School of Engineering, University of Seville, Spain