Jean-Baptiste Barreau

Florent Laroche

Sophie Madeleine

Thomas Pouyet

This document follows up the release of the recommendation of the Consortium 3D for the Humanities available in open access on the HAL platform in 2018. These first recommendations were mostly included into the guide "Guide pour la rédaction d'un cahier des charges de numérisation en 3D" published by the French Ministry of Culture in the context of the National program to digitize and to valorize cultural content.

As part of the activities of Huma-Num's Consortium 3D for the Humanities, many meetings have taken place, bringing together scientists from various fields (historians, archaeologists, computer sciences, architects, 3D engineers, archivists, etc.) with the aim of providing effective solutions for the creation and usage of 3D digital models in the Humanities and Social Sciences (SSH). One of the tasks assigned to the Consortium 3D for the Humanities was to develop and write specifications on how to manage a 3D Cultural Heritage project.

INTRODUCTION

The aim of this document is to ensure seamless potential exchanges between one ordering party who wants to study or valorize a heritage artifact or site using 3D technology and 3D expert service providers. This report is based on the analysis of the requirements to obtain a 3D digital model and defines the different possible purposes according to the recipients (e.g., expert, general public, education, etc.) The organization of this document follows an "acquisition project or 3D restitution project of a heritage site or artifact" type approach. It is based on the document "3D vocabulary: a lexicon for the Human and Social Sciences" and "Long-term preservation of 3D digital models for the Human and Social Sciences" which have to be also consulted when drawing up the specifications to realize a project in 3D for Cultural Heritage.

Six subsections / steps appear:

1. Preparation and project monitoring 2. Data acquisition 3. 3D raw data preprocessing The following recommendations are intended for the ordering party and also for laboratories or companies which request services for acquisition or 3D restitution and their associated processing.

These sub-sections are correlated with different 3D products, corresponding to distinctive requirements and targeting specific audiences. An ordering party wishing to enhance or study a cultural heritage artifact or site through a specific 3D application does not necessarily need all of these steps and they do not necessarily have to be followed in a linear fashion.

Steps 1 and 2 may be sufficient for a study of a building or a pure 3D acquisition in order to preserve an existing state of the heritage site or artifact. Similarly, in the case of the restitution of lost or very damaged heritage objects or site, the direct acquisition of steps 2, 3 and 4 are to be removed. The final stage of prototyping of the object is finally a possibility, but not in any way an obligation.

The aim here is to present all possible deliverables, making a clear distinction between their uses and the audiences they are intended for. The purpose of this document is twofold:

1. To help the ordering party to make the right choice according on their specific problems.

2.

Once the requirements are clearly defined, to provide a guide to best practices to ensure that the project is running well.

For each step, we clearly define:

-The required deliverable;

-The conditions and contexts of intervention;

PREPARATION AND PROJECT MONITORING

The ordering party should, as far as possible, define its present and future requirements. The type of expected deliverable and the target audiences will define the 3D requirements. Do not hesitate to approach experts in the 3D field (e.g., members of Consortium 3D for the Humanities) to support you in your choice of the most suitable solution. This step is essential since it conditions the production process. 3D data required for one kind of requirement are not necessarily compatible with the other development possibilities listed in this section. In case of doubt, at this stage, it may be advisable to ask for a support service, and possibly to add a project monitoring service. Indeed, it is important to have an expert opinion to correctly refine expectations in terms of accuracy, resolution and so forth within a reasonable volume of data.

The ordering party must keep in mind that a 3D production does not simply depend on tools, but also, and most importantly, on human skills and an efficient methodology in using such tools together with a recognized ethic. The key to success is found in the expertise of the service provider at every step, from the production of the raw data to the final deliverable. In this field, more than anywhere else, the service provider must demonstrate its expertise when answering the call for specifications (skills, references of project already carried out, presentation of results in a book, etc.).

When the ordering party examines the offers of service providers, s/he must already think about the archiving of their final product. This must be compliant with OpenScience and OpenData as stipulated by legislation in France and Europe. It is strongly recommended that the formats of the deliverable are compatible with perennial software solutions and also easily convertible in order to extract and convert data in others formats.

Finally, in order for service providers to be fully aware of their responsibilities, it is essential to get them to sign the call for specification in addition to their own proposal.

ACQUISITION OF RAW DATA

Introduction

This step consists of getting a 3D virtual footprint of a heritage artifact or site, most often by lasergrammetry or photogrammetry campaigns (direct acquisition). It can also go with (indirect acquisition) collected iconographic, textual or oral sources, etc.

Deliverable

The raw acquisition files are required for future data processing required by new requirements and by the evolution of tools and software.

Images and videos:

 Photographs in RAW format with all the original metadata (EXIF of images). A copy of these photographs in TIFF, DNG, JPEG or any other format compatible with the long term data preservation (refer to the list of formats recommended by the CINES for data archiving 1 ) as long as all the initial metadata (EXIF) is preserved, while adding those documenting the conversion from RAW format to the new format.

 Provide information of the shooting conditions (light sources positioned and calibrated).

 Add calibration chart images, and generally, the calibration process.

1 https://facile.cines.fr/  If possible, save videos in RAW format. Promote a free file format (OGV, MP4, MKV, etc.) for perennial videos.

3D data:

 Output data of 3D scanners (e.g. E57, LAS, PTX, etc.) with all device data, its calibration and the location of the station.

 Raw and preprocessed point clouds (at least with cleaning, registration and georeferencing) if they have been obtained by lasergrammetry (ASCII format or other format readable by any text editor in an open data perspective, and in a format compatible with the archiving instructions of the CINES). The survey must therefore be requested in at least two formats, the first for use according to the requirements of the ordering party, and the second for archiving purposes. This version is called: version V0 of the 3D model.

 The 3D models and manual surveys stating the scale, which will be used for photogrammetry campaigns.

 Topographic surveys, GPS, color calibration chart, scans and photographs (for data archiving purposes).

Unless specified redundancy in requested data should be avoided. For example, it is not necessary to request pictures in PNG and JPEG formats, but it is possible to request them in RAW and DNG formats, because one ensures access to the original data and the other allows long term preservation because it corresponds to a standardized format. It is often more relevant to request a single convertible and perennial format provided that it allows the storage of unprocessed raw data.

Paradata:

 Contextualization of the acquisition phase by photography images or video.

 Calibration data.  Methodological report (field notes).  Software versions and type of hardware.

Condition and context to carry out a direct acquisition

The service provider has a duty to advise the ordering party on technical and legal aspects as follows:

Environmental conditions:

The meteorological conditions during the acquisition by photogrammetry, lasergrammetry, drone and so forth and the influence of brightness, wind, rain, temperature, etc. It may be a good idea to specify the capacity of the service provider to return on site if the conditions are not adequate.



It may be necessary to inform the service provider of the obligation to prepare and clean the site to facilitate access to the remains (devegetation, absence of vehicles, etc.).

Physico-chemical conditions of the object:

 Non-destructive acquisition conditions for the object: heat, light, hygrometry, keeping it in position on a turntable without contact (calibration chart)  Respect for the integrity of the heritage object.

Conditions

for security and administrative intervention:



Ensure the safety of the remains and people.



Authorizations and insurance (management of the people present, UAV flight authorization, etc.).

Working conditions

The signature of the contract is equivalent to receipt of the deliverable (working conditions and inventory of fixtures to be taken) by the service provider.

Particular points of attention that the ordering party and service provider must look at

During a lasergrammetry survey campaign

A sufficient number of stations must be set up to ensure sufficient resolution and avoid areas that are not accessible and therefore not covered.

For future registration

Beforehand, the number of stations required for a complete survey of the studied object must be defined, as well as the methods used for the registration.

The use of spheres (three-dimensional targets) and/or checkerboard targets allows automatic registration based on recognition of geometric entities. A sufficient number of these devices must be placed on the site to ensure three common spheres per pair of scans.

Checkerboard targets captured with a tacheometer along with consolidation will jointly enable the georeferencing of the 3D model in a global coordinate system. The topographic survey of the targets is preferably to be carried out alongside the lasergrammetry survey (also in the case of a photogrammetry survey) considering that the targets are not perennial.

Simultaneous use of spheres and checkerboard targets is recommended. It is also possible to georeference characteristic points for which the homology between two stations is certain (not recommended apart from building archeology surveys).

During a photogrammetric survey

It is necessary to have reference points evidenced on the site and to survey with a tacheometer. The size of the reference points must be adapted to the desired resolution.

It is possible with these reference points to define the scale and spatial orientation of the 3D model and to spatially reposition all surveys carried out in the same coordinate system. This step is called registration.

The redundancy of points between the topographic points and points from the points cloud generated by photogrammetry enable quality control of the 3D model.

Other points of attention for acquisition campaign



The accuracy and spatial resolutions required for acquisition and for all processing requirements to be defined according to purpose o Accuracy of resolution at the level of geometric and/or texture rendering (specify the required scale; including a document for traceability).

In the case of an indirect acquisition, the scientific file completion (texts, inscriptions, iconography, archaeological sources) is the responsibility of the ordering party. The service provider must ensure that the scientific file is complete before drawing up the quotation .

DATA PREPROCESSING Definition

The aim of this step is to define the skills and prerequisites required by the service provider. It provides information on how the data will be processed to be exploited in later steps of analysis and modeling phases.

Typical steps for preprocessing 3D data

The steps below are given for informational purposes only and the order and choice of these steps are to be selected according to the subject of study and the desired aim. Indeed, the choice of algorithms may influence the accuracy, the resolution and thus the final result. As a reminder, all the terms used are defined in the manual "3D vocabulary: a lexicon for the Human and Social Sciences".

Deliverable

It is strongly advised to ask for a deliverable on the treatment methodology followed in order to be able to trace and validate the process. In addition, it should be drawn up prior to this co-construction process with the service provider to ensure that the provider has the required skills.

Recommendations

In the event that modifications are made to the model (hole filling, decimation, etc.), the service provider needs to provide all the intermediate models in order to trace the modifications and possibly be able to judge the loss/gain of information at each step. For example, hole filling or decimation may prove to be contraindicated in the case of archaeological remains or objects for which traces of wear and tear and tool marks contribute to research hypotheses. This step will produce technical data that can be used by the ordering party. This is based on facts and findings from the surveys. An interpretation is given in the next section (Section 6).

Deliverables



Orthoimages (graphic scale and spatial resolution of the images (GSD 2 ), georeferencing with clearly identified geographical coordinate system [Lambert 93, WGS 84, etc.], topographic surveys provided with layout , measurement uncertainty -quantified residuals).



Elevations, longitudinal and transverse sections, general and detailed plans with indications of the graphical scale, orientation and legend for building studies (vectorial format, AI, DWG or raster as needed). It also needs to be compatible with the recommendations for archiving at the CINES. Two formats at least can be requested.



Measurement report (spreadsheet table, etc.).



3D Model with a format compatible with the import/exports of the ordering party's software and potentially with the archiving recommendations of the CINES.



Data can be provided with perennial software allowing the visualization, manipulation, measurements, 2D cut, and possible export plans (interoperability).

2 GSD for Ground Sampling Distance -see the «Software and Hardware book from the recommendation of the consortium

RESTITUTION -3D MODELING -VIRTUAL RECONSTRUCTION HYPOTHESIS Definition

The aim of this step is to enable the interpretation of the digital data acquired in the previous steps or to create a 3D restitution of an environment or an object from a pre-established scientific file (ground plans, elevation plans, archaeological sources, textual sources, iconographic sources, etc.). These are versions V1n to V2 of the 3D model. For these purposes, it is possible to validate restitution hypotheses by creating partial or complete virtual environments in order to, for example:

 compute digital simulations for research and for validation of scientific hypotheses  valorize and disseminate works in museology or pedagogy.

It is essential for an interdisciplinary team to be set up to assist the ordering party. Experts in heritage, the analysis of ancient sources, 3D and virtual/augmented/mixed reality should participate in the restitution in order to ensure objectivity about the hypotheses according to their respective fields of expertise.

In the case of the restitution of a lost environment or artifact, a lead scientist who is recognized in the corresponding field (for example an academic or a researcher specializing in the corresponding period) will have to validate the choices of the scientific committee and ensure of the conformity of the 3D model at each step according to the specifications provided by the scientific committee.

Deliverable

 Images  Movie / Video  Photos or 360° panoramas  Immersive and interactive navigation with Virtual Reality  Augmented reality application/model  Website

In addition to the final deliverable, the ordering party is strongly advised to request and store the working data in order to enable the virtual restitution provided to be enriched or changed later.

 Mesh in ASCII format in order to be able to complete the model later.

 Sources of the application defining the digital model of the scene: the complete project must be provided (example: 3DS files, Unity, textures, kinematic models, etc.) on the condition that the exploitation rights have been assigned.

 In addition, a written report is strongly required to define the delivered 3D model. The evolution choices between the different versions have to be justified. The virtual model only makes sense for a given historical date/period and this date/period must be decided before the restitution.  In the case of the creation of a 3D model corresponding to a lost or heavily damaged environment or artifact, in addition to the deliverable related to the 3D model the service provider will give a complete report on the scientific file used for creating the 3D model. All the discussions of the scientific committee and the final choices made by the lead scientist must be clearly shown and justified. The discussions during the creation of the 3D model constitute data to be archived in the same way as the deliverable. The data concerning the final version V2 must also be provided in a format compatible with the archiving recommendations of the CINES.

Supports of deliverable:

 Examples of media: CD, USB keys, external hard disk, cloud storage (preferably institutional: Huma-Num ), etc.

 If the service provider proposes to make the data available via a proprietary system on the Internet, the ordering party must ask that this solution is not only-dependent on the service provider. This is because data would be lost if the service provider is no longer able to monitor the platform.

 In addition, any 3D model developed with public funding must be subject to a transfer of rights assignment and a deposit at the CINES.

Recommendations

Obligations for stakeholders:  Establish a bibliography to justify the hypotheses and to follow the traceability of the studies.



Provide a list of experts defining, among other things, the scientific support that will ensure the final validation (list co-constructed by the stakeholders).



Establish a monitoring schedule.



Define the person who will be in charge of the day-to-day scientific monitoring and who can be called upon on a daily basis by the 3D team during production.



Define the periodicity of the scientific validations during the steps of creation of the restitution.

Points of attention for the virtual model for restitution:

 Specify the date of restitution production (the model is the result of a given state-of-the-art of the research) and the historical period modeled (time T of the history of the concerned object or site).

 Choice of graphical restitution: level of detail (simple volumes, scenery, statuary, tool marks, textures, etc.), environment (topography, vegetation, lighting, etc.), dynamic aspects (kinematics, etc.).

PROTOTYPING / PHYSICAL MOCK-UP Definition

The prototyping of the object on a 1:1 scale or on a reduced scale is carried out by professionals in the field concerned (model maker, carpenter, etc.). It will allow the validation of hypotheses that the virtual model can hardly account for (weight of materials, etc.). This final step is made possible thanks to current technological developments, in particular 3D printing.

Examples:

 Direct cutting on solid materials (stone, metal, moss, etc.).

Recommendations

 Define the accuracy and the materials used to make the physical object (example: ABS or PLA for 3D printing, machined to the required dimensions, choice of wood species, etc.).

 Define the patina which must be in accordance with the original color (identification of the pigments and finishes used).

 Conduct interviews with or obtain testimonials from craftsmen / manufacturers to document the prototyping of the object.

GENERAL RECOMMENDATIONS

Project monitoring

All the best practices defined above for the study of heritage sites or artifact must be part of scientific projects. The use of 3D virtual objects or 3D scenes is a way of validating hypotheses.

It is necessary to define:

 A provisional timetable, which will be discussed and finalized with the service provider, in particular by setting the delivery date.

 Some reverse scheduling steps as the project the progress (to control possible delays and setbacks).

Duty of the service provider:

 The provider has to advise the ordering party on requirements (verification of the appropriateness of the requirements with the purpose of the scientific study and the condition of the object of study).

Duty of the ordering party:

 It is strongly recommended that the ordering party relies on a scientific team to carry out the mission that will provide assistance to the project manager. Indeed, a scientist, a team or a research laboratory will be able to help both the ordering party and the service provider in their choices and decisions. This team will assist with the specifications in order to choose the most suitable solution independently of the future service provider. It will also provide assistance in the translation of the digital data which sometimes is described in an abstruse language for the ordering party. Thus, as the scientific support team is not linked to economic profitability concerns, it will guarantee real ethics of use of the 3D digital documentation tools thanks to its expertise.

 The ordering party specifies in the contract clauses that, since the service provider agrees to carry out the mission, s/he fulfills the conditions of execution of the contract considering the state of the site, deadlines, weather conditions and so forth.

 The ordering party should give the service provider access to all documents required for the mission.

 The ordering party defines the confidentiality obligations of the project and for data protection.

 The ordering party checks the authorizations and insurance of the service provider: management of the presence of people in public spaces, required authorizations for the UAV flight (pilot certificate, flight authorization over the site, condition of move in a civil-or defense-controlled space, ground security perimeter, etc.).

Digitized object / 3D digital model

 The expected end-product must be clearly defined and the associated process well known. If necessary, expertise or advice may be asked. o Define the rights of use, reproduction, and modification of 3D content by contract or agreement.

Please note:

Restitution is the result of scientific research and a creation process that may have taken a long time, whereas 3D acquisition is the result of technical knowhow. Providing and transferring a 3D scene for restitution therefore requires more attention to be paid.

At each step of the process, the service provider has to be able to provide an intermediate version (V1n). During the intermediate validations and in particular at the final delivery (V2), a waiting period must be planned to allow the ordering party to evaluate the provided model according on past services, for the purpose to request possible additional work before any closure / payment of the contract.

To ensure traceability, it is essential to name the people who have participated to the project and, to specify the versions of the software and the type of hardware that have been used.

4 .

 4 Data production by acquisition / 3D survey production without interpretation 5. Restitution -Modeling -Virtual reconstruction of hypotheses -Virtual Reality 6. Prototyping / Physical mock-up

Figure 1 :

 1 Figure 1: photogrammetry survey of Cussac Cave (France) -Archeovision Prod.

Figure 2 :

 2 Figure 2: positioning station of the Faro Focus scanner, positioning the spherical targets and the black and white plane target to ensure the 3D survey, the registration and georeferencing -St Honorat, Lerins Monastery (FRANCE) -S. Sorin/CEPAM

o

  Simple object or complex system of objects o Define the extend area to be scanned o Object completeness (hole accepted or not) Type of surface and materials (anticipate scanning difficulties).In order to justify the fidelity of the rendering: o Precision and calibration for colorimetric accuracy (including a document for traceability)

Figure 3 :Figure 4 :

 34 Figure 3: Map view -Lasergrammetry campain with 98 laser stations -Saint Hilaire/Poitier (France) -Archeovision



  Registration for the scan alignment and for their possible merging; automatic or manual mode  Cleaning outliers  Point cloud noise removal  Coloring and/ or mesh texturing of the points.  Point cloud meshing  Point cloud hole filling  Decimation.

Figure 5 :Figure 7 :Figure 6 :

 576 Figure 5: Point cloud hole filling-Nantes project F.Laroche/Epotec LS2N

Figure 8 :Figure 9 :

 89 Figure 8: 3D visualizations of a Cromlech on Île Er Lannic (France) using open source software developed by the consortium 3D -V. Grimaud/LARA

Figure 11 :

 11 Figure 11: Visit of ancient Rome by night in an interactive software -Map of Rome / University of Caen Normandy, CIREVE

Figure 12 :

 12 Figure 12: Restitution of the villa of La Garanne (Bouches-du-Rhône, France) -Study of the definition of volumes, without added textures -V. Mathieu / CNRS, ASM UMR 5140



  3D printing.  Validation or physical simulation of operating modes  Condition state for restoration  Printing of base elements.

Figure 16 :Figure 15 :

 1615 Figure 16: Copy of the Naxian Sphinx from the Museum of Castings in Lyon -Archeovision Production & SNBR, 2005



  Particular attention should be paid to the format of the deliverable o Request non-proprietary formats: OBJ, RTF, DAE (XML), etc.o For a public ordering party, ensure the compatibility of methodologies with the archiving platform of the CINES and / or with standard interoperable formats.o Verify the adequacy between the requested model (deliverable) and the possibilities of use by the ordering party.


Alice Berthier
email: alice.berthier@utt.fr

Hicham Chehade

Alice Yalaoui

Christian Bouillot

Lionel Amodeo

Farouk Yalaoui

Case study of supply chain in textile industry: a dynamic product allocation decision problem

Keywords: Supply chain, production allocation, optimization, mathematical model

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

INTRODUCTION

In any industry, the supply chain is one of the most important part of organization. The supply chain decisions have a great influence on the rest of the system. The related costs are not negligible and are composed by inventory, production, and transportation costs. Depending on strategic decisions, the time to market can vary, or the service level can be significantly impacted. The Industry 4.0 revolution is accelerating the pace of supply chain transformations. This increases the necessity of agility and flexibility which can adapt to the constant changes in the market. Transportation must be reduced to the minimum to save time and money depending on the production and inventory locations. This is also motivated by a desire and need to move towards a more sustainable and ecological supply chain.

The case study in this paper is inspired from an industrial real case in textile industry. There are three main production stages (Figure 1):

• The first one is the creation of a knitting roll from the cotton yarn.

• The second step provides color properties and resistance to the fabric.

• The final one is the garment making. The knitting roll is cut into different pieces and these pieces are assembled. The first stage of this textile process was analyzed in [START_REF] Berthier | Machines group and load balancing: an industrial case[END_REF]. The authors focused on a dynamic layout of the workshop. The main subject is about the creation of groups of machines to balance the workload between all the operators and to propose a new implementation method of the machines. Nevertheless, the scope of the work of [START_REF] Berthier | Machines group and load balancing: an industrial case[END_REF] was only at the tactical level and one component of the supply chain. Strategic work on the whole supply chain can conduct to better results if optimization is also conducted across the whole elements of the supply chain.

For each stage, several production locations can be used, each with different production costs. Currently, in the industrial case considered, two different locations for knitting and dyeing operations are available and four different locations for assembling operation. Transport is therefore necessary if the product changes from a location to an other between two production stages. The impact will be felt at stor- On the case study analyzed in this paper, the large diversity of products are grouped into four families.

At each stage of the process excepting for the assembling, the available locations are qualified to make all the products. The dyeing operation has a production cost that varies according to the product family. Meanwhile, the costs do not present a large variation in the knitting operation. Therefore, the families are classified depending only on the dyeing operation:

• Bleaching: an unbleached fabric is transformed into a white fabric.

• Printing: a plain fabric is printed with a pattern using a printing process.

• Washing: the fabric is knitted directly with dyed yarns. The dyeing process only consists of a washing cycle.

• Dyeing: an unbleached fabric is transformed into a plain fabric. The darker the colour, the longer and more complex the process.

On each assembling location, the proportion of each family is known in advance and is determined by the production process. This paper seeks to answer the question of where to produce fabrics at each stage of the manufacturing process to supply finished product assembly locations with the lowest possible costs on the whole chain. This represents a strategic choice assignment which is performed every six months. A dynamic decision model would be very useful for the company. Nowadays, a whole team is dedicated to decide where each product is manufactured at each stage. They only have standard calculation tools without any decision support. The study of this paper searches to provide them a dynamic decision support tool. The problem decision is to determine the quantity x kij of product The rest of the paper is organized as follows. Section 2 gives a literature review of similar problems. Section 3 presents the resolution method and the mathematical model proposed using graph theory. Section 4 provides preliminary results of the model on a real case instance. A conclusion and future research directions end up the paper in section 5.

STATE OF THE ART

In this section, a review of supply chain related problem and production allocation is conducted.

Supply chain is a set which includes all the related activities with commodities stream from raw materials to final product [START_REF] Parsanejad | An applied intelligent fuzzy assignment approach for supply chain facilities[END_REF]). By the stream side, there are two other streams known as information stream as well as financial and credit resources stream [START_REF] Giannoccaro | Inventory management in supply chains: a reinforcement learning approach[END_REF]). The supply chain management is a collection of some methods that is used to integrate effectively the suppliers, producers, warehouses and stores. The supply chain includes all the direct and indirect steps which are involved in the completion of the customers orders. The supply chain is not just related to manufacturers and suppliers but it is also applicable to transportation, warehouses, retailers and even the customers.

In today's rapidly changing economic and political conditions, operations managers and planners need to address accurately questions such as which plants to operated on which product mix per plant (Tsiakis and Papageorgiou ( 2008)). There are several papers related to the production allocation and distribution. Mixed integer programming models have been developed to allocate customer order to forest product company with various plants located in different countries to reduce production and transportation costs [START_REF] Aydinel | Optimization of production allocation and transportation of customer orders for a leading forest products company[END_REF]). The necessity to develop strategic and tactical planning models in the supply chain have been recognized by the industry. Particularly, by using quantitative approaches rather than the qualitative ones [START_REF] Shapiro | Challenges of strategic supply chain planning and modeling[END_REF]). This has created many challenges both for researchers and practitioners who wish to successfully implement supply chain support systems.

Previous attempts to improve the performance of supply chain networks have mainly focused on the logistic aspects rather that the business decisions associated. In an early attempt [START_REF] Arntzen | Global supply chain management at digital equipment corporation[END_REF] developed a mixed integer linear programming "global supply chain model" aiming to determine: the number and location of distribution centres, customerdistribution centre assignment, number of echelons and the product-plant assignment. The objective of the model is to minimise a weighted combination of total cost and activity days as a bill of material problem. [START_REF] Guinet | Multi-site planning: A transshipment problem[END_REF] has examined the economics of multisite production systems using a two-level approach to allocate production to sites and address the workshop scheduling problem. [START_REF] Kaihara | Multi-agent based supply chain modelling with dynamic environment[END_REF] has used an agent based approach to manage supply chains in terms of product allocation and resource distribution. To the best of our knowledge, no previous papers have handled a supply chain management problem in the particular case of textile industry with production possible in different locations. This is an assignment problem of product on production locations.

RESOLUTION METHOD

In order to solve this problem, the supply chain flow is represented as a graph. A mathematical model based on this representation allows to solve this specific problem arising from the industry. Figure 2 can be translated into a graph as it is shown in figure 3. On this representation 30 nodes are necessary. On each arc, a cost value c kij is assigned and a decision variable x kij can be associated for each product category k between nodes i and j. To solve the most generic problem with a fixed cost f ij , a binary decision variable b ij is used too.

The quantity assigned to arcs of the first part of the graph (from the first node) are known (supplier procurement). The quantities purchased to each supplier are known beforehand. Similarly, the arcs of the last part (to the last node) are also pre-determined (figure 1). The proportion of each product category on each assembling locations are known on this study. They are considered as customers of the supply chain. On all the other arcs, a decision variable x kij is available to determine the optimal quantity of category k between locations i and j. As it is explained in Introduction section, the number of product category is 16 according to the distribution of the products by family and assembly locations.

c kij ∈ R: Cost per unit of product k (k ∈ K ) between nodes i and j (i, j ∈ N ) f ij ∈ R: Fixed cost between nodes i and j (i, j ∈ N ) d k ∈ N: Last assignment node of product k (k ∈ K ) (location of assembly operation) q k ∈ N: Quantity of product k (k ∈ K ) capa ij ∈ N:
Maximum capacity between nodes i and j (i, j ∈ N )

Decision variable

x kij ∈ N: Quantity of product category k (k ∈ K ) assigned between nodes i and j (i, j ∈ N ) b ij ∈ {0, 1}: equal to 1 if quantities are assigned on the arc i,j (i, j ∈ N ), 0 otherwise

The decision variables determine over every arc the quantity to transit for each category of products. This ensures the full representation of product movement across the distinct stages considering the constraints in section 3.4.

Objective function

M inimize

k∈K i∈N j∈N ,i =j

x kij c kij + i∈N j∈N ,i =j b ij f ij (1)
The objective function (1) minimizes the supply chain total cost. The cost c ijk takes the production, transportation and inventory cost per unit.

Constraints

j∈N x k1j = q k , ∀k ∈ K (2) j∈N x kN j = 0, ∀k ∈ K (3) i∈N x ki1 = 0, ∀k ∈ K (4) j∈N x kij = j∈N x kji , ∀k ∈ K , i = 2...N -1 (5) i∈N x kij ≤ q k , ∀k ∈ K (6) x kd k N = q k , ∀k ∈ K (7) k∈K x kij ≤ capa ij , ∀i, j ∈ N (8) k∈K x kij ≤ k∈K q k * b ij , ∀i, j ∈ N (9)
Constraint (2) initializes the first node with the total quantity of each product k. Constraint (3) ends the flow at node N . Constraint (4) starts the flow at the first node. Constraint (5) ensures the flow conservation between the input and output of each node. Constraint (6) guarantees that there is no return flow. Constraint (7) ensures that the product flow ends at the node d k provided in data for the last production step. The constraint (8) ensures that capacity is respected between the different nodes. The final constraint (9) determines the value of b ij on each arc.

PRELIMINARY RESULTS

In a first time, the model has been tested on the first problem instance from [START_REF] Panicker | Ant colony optimisation algorithm for distributionallocation problem in a two-stage supply chain with a fixed transportation charge[END_REF]. The instance is a two stages supply chain composed of 9

MOSIM'20 -November 12-14, 2020 -Agadir -Morocco 2013) as decision variable are not decomposed by stages to be more generic. On this instance, the same objective function value, 112 600 is reached with the same product assignement per location.

In a second time, the model has been tested on real data set. This one does not consider the fixed cost. This part is deleted from the objective function and the variable b ij is not useful in this case as well as the constraint 9. In the industrial data, there are 16 category products:

• 4 flow families: bleaching, printing, washing and dyeing

• 4 assembling locations Two hypothesis have been made. The volumes of fabrics consumed by manufacturing locations remain the same. Material losses are not considered including between knitting and dyeing operations. The volumes of yarn supplied by each supplier are known per category of products.

For confidentiality reasons, results will not be detailed precisely. The mathematical model has been solved using the CPLEX-ILOG solver with an Intel Core i5 processor.

The total cost has been reduced by 3% on the entire supply chain. But the transportation cost was reduced by 37% which is the most significant reduc- tion on this study. The total cost does not decrease significantly because production level has to be maintained on the different locations. So the production cost is relatively identical. The main improvement is the streamlining of travel. Right from the start of the process, products are manufactured as close as possible to their assembly location. The evolution is shown by comparing figure 4 The final transportation is the most expensive. To go from location B to location D, products have to pass through A. Table 2 shows the comparison be-tween initial transportation flow and flow determined by the the MILP model between dyeing and assembling stages. The flows between locations B and D are reduced by 88% in preference (+33%) to transportation between locations A end D closer.

These results can be used by the company as a dynamic decision tool to manage the affectation process of new product made at every collection launch. This represents a strategic choice assignment which is performed every six months, and can lead to keep the total supply chain costs as low as possible under the current configuration.

CONCLUSION

In this paper, a real case of textile industry problem has been studied. A production allocation problem in supply chain context is a very strategic decision problem for any company. The is explained in this paper. The production process is composed of three different operations and for each stage, multifactories are available in different locations. The decision consists on determining which quantity of each product category will be manufactured at each location. The pursued of objective is to minimize the supply chain costs. The latter are composed by inventory, production and transportation costs.

Preliminary results are presented. The model proposed is first tested on an instance from [START_REF] Panicker | Ant colony optimisation algorithm for distributionallocation problem in a two-stage supply chain with a fixed transportation charge[END_REF]. The same objective value and product assignment are found. In a second time, the model is used to solve the problem from an industrial company. However, due to confidential obligation, details can not be provided. Despite this, an important reduction on the transportation costs can be achieved by using the proposed mathematical model. The improvement in the transportation costs is of 37% when compared to the current product allocation. This study offers to the company a new dynamic decision support tool that can help them to take supply chain strategic product allocation decisions every six months (at every collection launch).

For future research, a profit model should be considerate. In this way, a variable selling price can be proposed depending on the production channel used.

For instance, products 100% Made In France can be sold at a higher price. On the other hand, the number of sales and therefore of production can also vary according to the places of production of the different stages. The Made In France can be more attractive to customers.

Figure 1 -

 1 Figure 1 -The three fabrication stages in textile industry

Figure 2 -

 2 Figure 2 -The supply chain flow representation of the industrial case

Figure 3 -

 3 Figure 3 -The supply chain graph representation

  [START_REF] Panicker | Ant colony optimisation algorithm for distributionallocation problem in a two-stage supply chain with a fixed transportation charge[END_REF] has solved a fixed charge transportation problem. Each route is associated with a fixed charge (or a fixed cost) and a transportation cost per unit transported. This author has used an algorithm based on ant colony optimisation to solve the distribution-allocation problem in a two-stage supply chain. The first problem instance used by this author is used in this paper to validate the proposed model.For a more detailed state of the art on supply chain allocation problem, readers may refer to the recent review made by Di[START_REF] Di Pasquale | Order allocation in purchasing management: a review of state-of-the-art studies from a supply chain perspective[END_REF]. The authors have conducted a systematic literature review specifically regarding order allocation methods. The research aimed to evaluate how often and when the issue has been defined with an individual focus, independently of the supplier selection problem.

3. 1

 1 Notations N : Set of nodes N ∈ N: Number of graph nodes i, j = 1...N : Nodes indexes K : Set of category products K ∈ N: Number of category products k = 1...K: Products indexes

Figure 4 -

 4 Figure 4 -Initial supply chain proportion between the different locations

  and figure 5. On these figures, larger lines represent bigger associated quantities. The first figure shows the proportion of production on each location with the transportation flows generated, before the implementation of the model. The second figure shows the same data when the MILP model is used to determine the flows. Clearly, the presence of cross-flows is less important in the second figure. The transportation costs are thus reduced.

  Table1presents the distribution of families of product on the different assembling locations. Each location makes a specific type of product. For instance, location C is specialized on underwear whereas location D is specialized on adult clothing. This two categories can use similar product families (fabrics) but do not use the same manufacturing processes to obtained different finished products.

		A	B	C	D
	Bleaching 3% 13% 15% 70%
	Printing	1% 24% 25% 50%
	Washing 3% 28% 27% 42%
	Dyeing	1% 22% 25% 52%
	Table 1 -Finished product per location distribution
	for each product families
	Each product family are divided into four, one for
	each assembly locations. So finally, we have 16 prod-
	uct categories as products are grouped by product
	family and assembling location. The assembling lo-
	cation d

k is the last assignment location for product category k.

Acknowledgment

This research was supported by ANRT (Association National Recherche Technologie). These acknowl-edgements also go to our industrial partner. Their participation allows us to work on research topics applied to the current industrial context.


Dr Franck Bourdelle
email: franck.bourdelle@univ-lille.fr

Emily Lloret

Cyril Durand

Laura Airaghi

Evaluation of scanning transmission X-ray microscopy at the Mn L2,3-edges as a potential probe for manganese redox state in natural silicates

Keywords: manganese valence, STXM, XANES spectroscopy, L2,3-edges, redox mapping, silicates

Determining the Mn valence variation at the nanometer scale will be an important advance in the study of heterogeneous natural silicates. Here, the potential of the scanning transmission X-ray microscopy at the Mn L2,3-edges (640 -655 eV) as a probe for manganese redox state is evaluated. For this purpose, several natural Mn-silicates (rhodonite, ardennite, piemontite, Mn 4+ -silicate, jacobsite), covering several Mn valence, were analysed to identify the spectral parameters most sensitive to the Mn valence, regardless of the coordination environment, the crystal field strength, the nature and the length of the metal-ligand bonds, and the intraatomic Coulomb and spin-orbit interactions. Two suitable spectral empirical calibrations are thus proposed, linking the Mn valence to two peak intensity ratios: one ratio of intensities from two energy points of the L2 peak (at 651.7 and 655.2 eV), and one ratio of intensities from one energy point of the L2 peak (at 655.2 eV) and one of the L3 peak (at 641.6 eV).

Thank to them, the first quantitative Mn valence maps are constructed, with a high spatial resolution (< 40 nm pixel size), opening the way to exhaustive crystallochemical studies of silicates containing Mn with different valences.

Introduction

Constraining redox conditions during sediment deposition, rock formation or mineralogical transformation is of primary importance to understand the P-T-X history (pressure-temperature-composition) of geological systems. Redox conditions are usually assessed by the analysis of minerals since they partly influence their chemical composition.

The evaluation of redox conditions is often based on the iron redox state, i.e. by the quantification of the Fe 3+ /Fe 2+ ratio in mineralsmainly silicates, major constituents of crusts when they can contain both divalent and trivalent cations (i.e. [START_REF] Inoue | Application of chlorite thermometry to estimation of formation temperature and redox conditions[END_REF]). More rarely, the redox state of other metals is investigated, as manganese. However, Mnwhich can be present as Mn 2+ , Mn 3+ and sometimes-but-rarely Mn 4+could be a good indicator of paleo-conditions of rock formation [START_REF] Loomer | Manganese valence imaging in Mn minerals at the nanoscale using STEM-EELS[END_REF], even if Mn-silicates, specially P-T-X sensitive silicate solid solution such as phyllosilicates, are infrequent, at the very least not ubiquitous in sedimentary and metamorphic rocks, and that the Mn content of these silicates is low. In this way, [START_REF] Sussenberger | MnO vertical bar SiO2, Al2O3, FeO, MgO] balanced log-ratio in chlorites: a tool for chemo-stratigraphic mapping and proxy for the depositional environment. 16th International Clay Conference (ICC) Location: Granada[END_REF] suggest that Mn content in chlorite could be a proxy for chemo-stratigraphic conditions in depositional environment. For their part, [START_REF] Bobos | Fe-, Fe,Mn-and Fe,Mg-chlorite: a genetic linkage to W, (Cu, Mo) mineralization in the magmatic-hydrothermal system at Borralha, northern Portugal[END_REF] establish a link between Mn-chlorite and Wolframite, the Mn content in chlorite becoming an indicator of W-Mo mineralisation.

Unfortunately, authors could not determine the Mn 3+ /Mn 2+ ratio which would have noticeably modified the chlorite structural formula calculation, and potentially the subsequent interpretations. In the past, different techniques have been envisaged for this purpose, including electron microprobe analysis (EMPA, e.g. [START_REF] Albee | Semiquantitaive electron microscope determination of Fe2+/Fe3+ and Mn2+/Mn3+ in oxides and silicates and its application to petrologic problems[END_REF], X-ray photoelectron spectroscopy (XPS, e.g., Ilton et al. 2016) or X-ray absorption near edge structure (XANES) spectroscopy at the K-edge (e.g. [START_REF] Manceau | Nanometer-sized divalent manganese-hydrous silicate domains in geothermal brine precipitates[END_REF][START_REF] Manceau | Determination of Mn valence states in mixedvalent manganates by XANES spectroscopy[END_REF]. However, none of these methods provides a nanometer-scale spatial resolution, which could be particularly useful to identify chemical and redox zonation patterns in lowtemperature crystals (e.g. [START_REF] Bourdelle | Nanoscale chemical zoning of chlorite and implications for low-temperature thermometry: Application to the Glarus Alps (Switzerland)[END_REF]. On the other hand, several studies (e.g., Garvie and Craven 1994;van Aken and Liebscher 2002) have shown that electron energy-loss spectroscopy (EELS) carried out in a transmission electron microscope (TEM) is a powerful method for determining the redox state of transition metals at a submicrometric resolution, including Mn in silicates, but sometimes induces severe beam damage effects, such as electron beam-induced reduction of manganese [START_REF] Lauterbach | Mossbauer and ELNES spectroscopy of (Mg, Fe)(Si,Al)O3 perovskite: a highly oxidised component of the lower mantle[END_REF][START_REF] De Groot | Insitu scanning transmission X-ray microscopy of catalytic solids and related nanomaterials[END_REF][START_REF] Livi | Electron Energy-Loss Safe-Dose Limits for Manganese Valence Measurements in Environmentally Relevant Manganese Oxides[END_REF]. The XANES spectroscopy at the L2,3-edges is often proposed as a powerful alternative and is increasingly used in the Earth sciences. Firstly, the X-ray energies required for XANES analysis are lower at the L2,3-edges (between ~640 and 655 eV) than at the Kedge (between ~6500 and 6580 eV), allowing higher resolutions, i.e. < 0.1 eV and ~30 nm at existing synchrotron facilities. Secondly, the X-ray incident beam is less destructive for samples than the TEM-EELS electron beam.

The XANES spectroscopy at the L2,3-edges is based on the 2p → 3d electronic transition, which is sensitive toamong other parametersthe metal valence (e.g. Garvie andCraven 1994). De Groot et al. (1994) describing in detail the complex physical basis of Mn L2,3-edges, underlined that Mn valence can be obtained from L2,3-edge spectra by a multiplet calculation. However, this approach remains difficult to use in the case of natural minerals whose structure has not been beforehand determined. Otherwise, the Mn valence can be evaluated by fitting L2,3-edge spectra with a combination of reference spectra, but this requires Mn 2+ , Mn 3+ , Mn 4+ reference compounds, with Mn in the same local coordination environment than the studied sample. Consequently, several authors have turned to empirical approaches, trying to find a spectral parameter depending only (or at least, mainly) on the Mn valence. The white-line ratio, calibrated by van Aken and Liebscher (2002), is probably the best known, linking the formal transition metal valence to the ratio of integral intensity (over a 2 eV window) of the L3 and L2 excitation peaks. Recently, Wang et al. (2018) used the integrated L-edge intensity, considering it is proportional to the total number of 3d holes localized in the X-ray absorber (normalized to this invariant edge jump), while [START_REF] Risch | Redox Processes of Manganese Oxide in Catalyzing Oxygen Evolution and Reduction: An in Situ Soft X-ray Absorption Spectroscopy Study[END_REF] proposed a linear correlation between Mn valence and the energy of the center of gravity of the Mn L3-edge. But these methods, a review of which was proposed by Tan et al. (2013), were often calibrated for Mn-oxides, but were not tested on Mn-silicates, which present specific structures. Moreover, synchrotron facilities make possible to carry out Mn L2,3-edge XANES spectroscopy with a scanning transmission X-ray microscope (STXM), one spectrum being one image pixel of the studied sample area (e.g. [START_REF] Bourdelle | Quantification of the ferric/ferrous iron ratio in silicates by scanning transmission X-ray microscopy at the Fe L-2,L-3 edges[END_REF]. This makes it possible to consider extracting quantitative maps of Mn valence over the entire area of interest, very useful for heterogeneous natural samples containing mixed oxidation state Mn species. [START_REF] Pecher | Quantitative charge state analysis of manganese biominerals in aqueous suspension using Scanning Transmission X-ray Microscopy (STXM)[END_REF] explore the feasibility of such maps extracted from STXM-XANES data, in order to characterize the Mn charge state distribution in biominerals. Unfortunately, in absence of empirical calibration based on a spectral intensity ratio rather than an integrated area or a center of gravity calculation, the resulting maps remain qualitative.

From these observations, we want to evaluate the potential of the scanning transmission X-ray microscopy at the Mn L2,3-edges as a probe for manganese redox state investigations in natural silicates, defining a suitable spectral empirical calibration allowing to construct quantitative Mn valence maps with a high spatial resolution (nanoscale).

Materials and methods

Natural samples

Samples used in this study were natural silicates, containing various Mn amount and covering the three common Mn redox state (2+, 3+, 4+). As the shape of the Mn L2,3-edge spectra can be influenced by, among others parameters, the Mn coordination, one oxide presenting Mn in tetrahedral coordination sites is also considered. Particles transparent to soft X-rays are needed to measure XANES spectra in the transmission mode of STXM, therefore samples are prepared as grounded powders dispersing in ethanol; a drop of which is placed (then evaporated) on a carbon holey support film placed on a 200 mesh copper grid.

The selected silicates are rhodonite, ardennite, piemontite and a Mn 4+ -silicate (Table 1), for which chemical composition has been verified by Energy-dispersive X-ray spectroscopy, the EDX probe being coupled to a Scanning electron microscopy (QUANTA 200 SEM instrument operating at 15 kV with a 1.5 nA current; mineral standards used for EDX probe calibration: albite, diopside, orthoclase, garnet and MnTiO3; ZAF correction applied). Rhodonite is a Mn 2+ pyroxenoid, where Mn is mainly in 6 coordination, sometimes in 7 [START_REF] Smyth | Crystal Structures and Cation Sites of the Rock-Forming Minerals London and Boston (Unwin-Hyman Ltd.)[END_REF][START_REF] Nelson | Crystal chemistry of Zn-rich rhodonite ("fowlerite")[END_REF]. Mn is therefore in distorted octahedral sites, defined by Mn-O bonds. The rhodonite sample used here, whose formula is Ca0.15Mn0.85SiO3, comes from Gambaseta (Liguria, Italia). Ardennite is a Mn 2+ sorosilicate described by the following formula: Mn4Al4(AlMg)(AsO4)(SiO4)2(Si3O10)(OH)6. In it, Mn is located in large polyhedron, based on 5 coordination via Mn-O bonds, and 2 additional coordination via Mn-OH bonds [START_REF] Donnay | Si3O10 Groups in the Crystal Structure of Ardennite[END_REF]). Here, one specimen of As-Ardennite from Salm-Château (Ardennes, Belgium) was studied; the composition does not present an excess of Mn (< 4 atoms per formula unit), all Mn is consequently assumed as Mn 2+ (Nagashima and Armbruster 2020). Piemontite is a Mn-rich epidote, where Mn is in trivalent form and occupies octahedral sites. The selected specimen comes from the Prabornaz mine (Aosta, Italia), with the verified chemical formula Ca2.05(Al1.68Fe 3+ 0.49Mn 3+ 0.83)(Si2.0O7)(Si1.0O4)O(OH). The last studied Mn-silicate, a rare type of silicates that contains tetravalent Mn similarly to stavelotite-(La), was sampled at Eveslogchorr (Murmansk Oblast, Russia) combined with pectolite and has the determined empirical formula: Na0.3Ca1.4Fe 3+ 0.3Mn 4+ 5SiO14. A jacobsite sample, from Langban, (Filipstad, Sweden), was also analysed. Jacobsite is an Mn 2+ oxide belonging to the spinel group, with the common formula MnFe2O4. As a "normal spinel", Mn 2+ occupies tetrahedral sites formed by 4 oxygens [START_REF] Bosi | Nomenclature and classification of the spinel supergroup[END_REF].

STXM and XANES spectroscopy

The STXM is able to record the transmitted soft X-ray intensity on each point of the pluri-micrometric-sized area of interest for each defined energy. Therefore, STXM gives 2D images for which each pixel represents a soft X-ray absorption spectrum. This is of great interest for mapping metal oxidation state variation into small crystallites (e.g. [START_REF] Bourdelle | Quantification of the ferric/ferrous iron ratio in silicates by scanning transmission X-ray microscopy at the Fe L-2,L-3 edges[END_REF]). In the present study, STXM analyses were acquired on the PolLux beamline at the Swiss Light Source (SLS, Villigen, Switzerland). The characteristics of the beamline are detailed by [START_REF] Raabe | PolLux: A new facility for soft X-ray spectromicroscopy at the Swiss Light Source[END_REF]; the beam was in circular-polarisation configuration to avoid crystal lattice orientation dependency of analysis (see below). The scanning transmission Xray microspectroscopy endstation allows to achieve stacks and linescans, i.e. a spectral map of an area and a sum of spectra for each pixel of a line, respectively. Stacks were recorded over the 635-660 eV energy range (Mn L2,3-edge) using a 0.2 eV spectral resolution and a 40 nm spatial resolution. Linescans were recorded over the same energy range, using a 0.1 eV spectral resolution. The dwell time per image-and energy-point was between 1 and 10 ms.

Focus was checked systematically for each particle. STXM-XANES data were post-processed using the aXis2000 software [START_REF] Hitchcock | XPS determination of Mn oxidation states in Mn (hydr)oxides[END_REF]. Beam damages caused by the incident beam were assessed by monitoring spectral changes at the Mn L2,3-edges with increasing dwell times up to 20 ms.

Spectrum processing

Spectra were extracted from stacks and linescans in form of optical density spectra (noted OD), obtained as OD =ln(I/I0), where I is the X-ray intensity transmitted from the sample, and I0 is those recorded without samples. Then two steps of processing were applied on spectra:

(i) a linear background correction was applied to remove the contribution of lower energy absorption edges, so that the pre-edge region is set to 0 optical density.

(ii) the two edge steps resulting from transitions to unoccupied states in the continuum were subtracted using a double arctan function [START_REF] Chen | Experimental confirmation of the X-ray magnetic circular-dichroism sum-rules for iron and cobalt[END_REF]van Aken and Liebscher 2002;[START_REF] Brotton | Valence state fossils in Proterozoic stromatolites by L-edge X-ray absorption spectroscopy[END_REF]) as:

𝑓(∆𝐸) = ℎ 1 𝜋 (tan -1 [ 𝜋 𝑤 1 (∆𝐸 -𝐸 1 )] + 𝜋 2 ) + ℎ 2 𝜋 (tan -1 [ 𝜋 𝑤 2 (∆𝐸 -𝐸 2 )] + 𝜋 2 ) (1)
where h1 and h2 are the step heights of the two arctan functions, w1 and w2 are fixed peak widths and E1 and E2 are the positions of the inflection points resulting in an energy near the edge onset. [START_REF] Brotton | Valence state fossils in Proterozoic stromatolites by L-edge X-ray absorption spectroscopy[END_REF] proposed setting the function slope w at 5 eV, to account for the slow onset of the continuum. Following this recommendation, w1 and w2 were fixed to 5

eV. For each sample, four or five spectra on different particles were extracted to evaluate the spectral variability. A total of 23 spectra were thus used in this study.

Results and discussion

3.1. Influences of Mn redox state, coordination and atomic environment on the shape of Mn L2,3-edge XANES spectrum X-ray absorption near edge structure spectra at the Mn L2,3-edges for Mn-silicates and jacobsite are shown in Figure 1, where peaks are identified by letters (from L3-a to L3-h and from L2-a to L2-e) and linear background is subtracted. These spectra result from transitions from 2p core electrons to 3d state, 4s state or continuum as follow:

-two strong absorption peaks, usually noted L3 and L2, due to the spin-orbit splitting of 2p level (van Aken and Liebscher 2002;[START_REF] Nishida | Effect of local coordination of Mn on Mn-L2,3 edge electron energy loss spectrum[END_REF]) involving transitions from 2p3/2 and 2p1/2 states to empty 3d atomic orbitals, respectively. From a 2p 6 3d n ground state, the absorption process leads to a core-excited 2p 5 d n+1 final state, as 3d 5

for Mn 2+ , 3d 4 for Mn 3+ and 3d 3 for Mn 4+ , implying variations in absorption energy.

-edge jump steps at the bottom of L3 and L2 peaks, corresponding to 2p → continuum transitions.

-negligible contributions of 2p → 4s transitions, which are 20 times weaker in intensity than 2p → 3d transitions.

Each L3 and L2 peak consists of one major peak accompanied on both sides by several minor peaks. The energy position of these major peaks mainly depends (but not only) on the core-excited final state, i.e. Mn redox state: 641.6 and 654.1 eV for Mn 2+ (L3-b and L2-c, respectively; rhodonite, ardennite, jacobsite), 643.2 and 654.4 eV for Mn 3+ (L3-e and L2-d, respectively; piemontite), 644.6 and 655.2 eV for Mn 4+ (L3-f and L2-e, respectively; Mn 4+silicate). In this way, spectra are qualitatively similar to those described in several previous studies, obtained using different analytical techniques (e.g. Garvie and Craven 1994;[START_REF] Morales | In Situ X-ray Absorption of Co/Mn/TiO2 Catalysts for Fischer-Tropsch Synthesis[END_REF]Zhang et al. 2010;[START_REF] Kubin | Probing the oxidation state of transition metal complexes: a case study on how charge and spin densities determine Mn L-edge X-ray absorption energies[END_REF].

Minor peaks arise from factors other than redox as their number, intensity and shape vary from one sample to another. Therefore, Mn 2+ spectra present 3 minor peaks (L3-a, L3-d and L3-g with a shoulder peak noted L3-h) around L3-b, and 2 minor peaks (L2-a, L2-b) before L2-c, more intensive (related to the intensity of major peaks) for rhodonite than for ardennite.

Mn 3+ and Mn 4+ spectra have fewer minor peaks: only two, at the same (or very close) energy position than the L3 and L2 Mn 2+ major peaks, and one more at 642.3 eV (L3-c) only for Mn 4+ spectra. These minor peaks are also observed in previous studies (e.g. [START_REF] De Groot | Insitu scanning transmission X-ray microscopy of catalytic solids and related nanomaterials[END_REF][START_REF] Cuartero | X-ray absorption and emission spectroscopy study of Mn and Co valence and spin states in TbMn1-xCoxO3[END_REF][START_REF] Risch | Redox Processes of Manganese Oxide in Catalyzing Oxygen Evolution and Reduction: An in Situ Soft X-ray Absorption Spectroscopy Study[END_REF], especially on Mn-oxide spectra, and are influenced by the Mn valence and coordination environment, the crystal field strength, the nature and the length of the metal-ligand bonds, and the intra-atomic 3d-3d and 2p-3d Coulomb and spinorbit interactions in the 2p core and 3d orbitals.

Here, no complex calculations or multiplet analyses were used to describe spectrum shape in detail as the aim of the present study is to propose an easy-to-use approach to empirically map the Mn valence in silicates. However, some comments can be made to explain (i) the general shape of the Mn-silicate spectra and (ii) the great similarity of them with Mn-oxide spectra.

In fact, 3d orbitals consist of five d orbitals, as three have lobes between x, y, z-axis (noted dxy, dxz, dyz) and two have lobes on the axes (noted dz² and dx²-y²). In octahedral coordination site, the 6 ligands approach Mn along the axes, increasing by electrostatic repulsion the energy of dz² and dx²-y² orbitals (called eg). Conversely, dxy, dxz, dyz orbitals (called t2g) point between the ligands, that lowered their energies. This difference of energy between eg and t2g orbital groups defines the crystal field strength (Δo or 10Dq) [START_REF] Burns | Mineralogical Applications of Crystal Field Theory (Cambridge Topics in Mineral Physics and Chemistry)[END_REF]).

In the case of 6 coordinated Mn 2+ , the t2g spectral contribution is often assigned to the L3-a minor peak, while eg is associated to the L3-b major peak (Garvie and Craven 1994;[START_REF] De Groot | X-ray absorption and dichroism of transition metals and their compounds[END_REF]), 10Dq can be deducting from the energy distance between these two peaks. In the Figure 2, focused on the L3-edge part of Mn 2+ absorption spectra (edge jump steps were subtracted), the energy gap between L3-a and L3-b is very weak (< 1 eV), suggesting a low 10Dq value. The comparison with 10Dq calculations and estimates from experiments previously published (Garvie and Craven 1994;Garvie et al. 1994;[START_REF] Pérez-Dieste | Unoccupied orbitals of 3d transition metals in ZnS[END_REF] confirms that 10Dq value is probably around 0.5 or 1 eV. The energy difference between t2g and eg orbital groups remains therefore weak enough for Mn to be in high-spin state [START_REF] Burns | Mineralogical Applications of Crystal Field Theory (Cambridge Topics in Mineral Physics and Chemistry)[END_REF], which is the most common spin configuration for Mn (Garvie and Craven 1994;[START_REF] De Groot | X-ray absorption and dichroism of transition metals and their compounds[END_REF]. The Figure 2 also shows that the energy position of L3-a is always the same whatever the Mn 2+ mineral studied in our conditions, but that its intensity (related to L3-b major peak intensity) is variable. This observation is also suitable for other minor peaks L3-d and L3-g, suggesting the contribution of another significant factors. In fact, Mn 2+ in rhodonite, ardennite and jacobsite is located in different coordination sites, with different Mn-ligand bond length and different type of ligands. In rhodonite, Mn 2+ occupies octahedral sites slightly distorted, elongated, due to the global structure, linked to 6 O [START_REF] Smyth | Crystal Structures and Cation Sites of the Rock-Forming Minerals London and Boston (Unwin-Hyman Ltd.)[END_REF]. This configuration leads to an energy splitting between dx²-y² and dz² orbitals (Edx²-y² > Edz²) on the one hand, and between dxy and dxz, dyz orbitals (Edxy > Edxz and Edyz) on the other hand. In ardennite, Mn 2+ is located in large polyhedron with a 6 or 7 coordination configuration, with O and OH as ligands [START_REF] Donnay | Si3O10 Groups in the Crystal Structure of Ardennite[END_REF], also implying a substantial change in orbital energies. In jacobsite, Mn 2+ is surrounded by 4 O in a tetrahedral site. But in this case, the 4 ligands are closer to the dxy, dxz, dyz orbitals (t2) than to the dz², dx²-y² orbitals (e), leading to an inversion of the splitting energy, t2 orbital group having higher energy than e orbital group [START_REF] Burns | Mineralogical Applications of Crystal Field Theory (Cambridge Topics in Mineral Physics and Chemistry)[END_REF]. Differences in spectrum shapes, especially the intensities of t2g or tg -L3-a (virtually disappeared in the case of jacobsite), L3-d and L3-g peaks, must be related to the coordination and the ligands of Mn. From an empirical point of view, the intensity of minor peaks decreases proportionally to the number of Mn-O bonds. On the other hand, the similarity of Mn-silicates (i.e. Mn 2+ , Mn 3+ and Mn 4+ -silicates) and Mn-oxides spectra (from this study and literature) tends to indicate that, as a first approximation, the extended atomic environment (i.e. beyond the coordination site receiving Mn) has negligible influence compared to that of the near coordination.

Consequently, an empirical calibration linking a spectral parameter to the Mn mean valence must be mainly based on major peaks, most sensitive to redox, without taking into account an energy window (as white line ratio method) that might include minor peaks, most sensitive to the Mn coordination and the surrounding atomic environment. An empirical calibration is possible especially since the 10Dq is weak (van der Laan and Kirkman 1992).

Mn redox state estimation from L2,3-edge XANES spectra

As three valence states of Mn could be present in silicates, it is not possible to determine easily, directly and empirically the relative proportion of each of them. As an alternative, XANES spectra allow to assess the Mn mean valence which, coupled to a structural formula obtained with an independent method, gives a strong indication of the likely xMn 2+ + yMn 3+ + zMn 4+ combination.

As referenced in the Figure 1, the main variation in the XANES spectra of silicates with the Mn valence involves the energy position of the L3 major peak. More precisely, the L3 major peak shifts to higher energies with increasing Mn charge, by a step of 1.4-1.6 eV.

However, because this step and Mn valence are not linearly linked, [START_REF] Risch | Redox Processes of Manganese Oxide in Catalyzing Oxygen Evolution and Reduction: An in Situ Soft X-ray Absorption Spectroscopy Study[END_REF] prefer to use the center of gravity of the L3-edge. From Mn-oxides, authors propose a linear correlation implying to take in consideration the L3 minor peaks in addition to major peaks. A such correlation was established here for silicates (Figure 3), and demonstrates the influence of minor peaks, i.e. of the type of coordination sites in which Mn occurs. Considering only the mineral phases where Mn occupies octahedral sites (piemontite, rhodonite) and Mn 4+ -silicate, the relationship between nominal Mn valence and the L3 center of gravity is linear, with a R² = 1. However, taking into account the ardennite in which Mn occupies large polyhedron or jacobsite in which Mn is in tetrahedral sites, the energy position of the L3 center of gravity for Mn 2+ phases depends on L3-a, L3-d and L3-g peak weight and not only of Mn redox state.

Mainly, the L3 center of gravity is a spectral parameter including a peak area, not extractable from a stack. This approach therefore does not allow to easily map the Mn valence from STXM-XANES data.

In order to construct a redox map, it becomes therefore necessary to propose a new purely-empirical calibration of Mn valence with a simple spectral parameter, using selected energy points (and not a spectral surface as white line ratio or center of gravity), that does not need to have any physical significance (as an intensity ratio). Considering only the silicates (jacobsite is excluded) and the 13 identified peaks (Figure 1), 78 ratios of two peak intensities can be calculated, plus their inverses, namely 156 possibilities. But only 12 peak intensity ratios are in correlation with the Mn valence with a coefficient of determination higher than 0.98. In fact, the R² is very poor for intensity ratios implying major peaks of Mn 3+ and minor peaks of Mn 2+ (Figure 2). On the 12 peak intensity ratios correlated to Mn valence, 3 only used peaks from L3 peak, 6 only used peaks from L2 peak, and 3 used peaks from L3 and L2 peaks. Among them, we prefer those using peaks common to several valences and major peaks. Two correlations are therefore selected as calibration. The selected spectral parameter in the first calibration is a ratio between the intensities at two energy points of the L2-edge, i.e.

at L2-a in Mn 2+ spectra (651.7 eV) and at the L2-e major peak in Mn 4+ spectra (655.2 eV). The spectral parameter is then expressed as follows:

𝑅 𝐿 2 = 𝐼(𝑎𝑡 655.2 𝑒𝑉)
𝐼 (𝑎𝑡 651.7 𝑒𝑉) From this parameter, the first calibration equation is (Figure 4a):

𝑀𝑛 𝑚𝑒𝑎𝑛 𝑣𝑎𝑙𝑒𝑛𝑐𝑒 = 𝑅 𝐿 2 +6.705 3.512 (2)
It shows a coefficient of determination (R²) of 0.999. The same RL2 value is obtained for ardennite and rhodonite (and jacobsite, not used for calibration), showing that R 2 is not influenced by the Mn atomic environment but only by the Mn valence. This perfect correlation can be used to map Mn valence on unknown samples, since only two images (at fixed energy, i.e. 651.7 and 655.2 eV) are required.

The spectral parameter defined in the second calibration is the ratio between the intensity at L3-egde energy point (i.e. 641.6 eV, the energy position of the L3-b major peak of Mn 2+ spectra) and the intensity at L2-edge energy point (i.e. 655.2 eV, the energy position of the L2-e major peak of Mn 4+ spectra). The calibration equation is expressed as follows (Figure 4b): The coefficient of determination for this second calibration (R²) is 0.984, slightly lower than the one of the first calibration. The difference between RL2,3 values for rhodonite and ardennite (and jacobsite) suggests a contribution of Mn atomic environment in addition to the Mn valence dependence. However, taking an intensity on the L3-edge (which is more intense than the L2) and one on the L2-edge improves the signal to noise ratio. As for the first correlation proposed, the construction of a Mn valence map from STXM-XANES data is made possible by equation 3.

𝑀𝑛 𝑚𝑒𝑎𝑛 𝑣𝑎𝑙𝑒𝑛𝑐𝑒 = 𝑅 𝐿 2,

STXM-XANES coupling: Mn redox mapping

The scanning properties of the microscope allow to record a stack of 125 energy images over the 635-660 eV with a spectral resolution of 0.2 eV. Equations 2 and 3 permit the Mn mean valence to be estimated from the spectrum intensities at two energies. This gives the possibility to easily map the Mn valence from two energy images, and use one of the two calibrations proposed.

In fact, two other XANES images are required in addition to the two images used for mapping, in order to subtract the background at each pixel of the images. Therefore, only four energy images should be selected to calculate the R parameter. In the Figure 5, the calibration procedure that uses the equation 3 and the RL2,3 parameter is drawn as example (piemontite sample). It is obtained by extracting one image at 641.6 eV, one at 655.2 eV, one in the preedge (to apply the ''linear background correction'' at each pixel of the 641.6 eV image), and one beyond the energy corresponding to the L2 peak (to remove the linear background and the second edge step of the arctan function at each pixel of the 655.2 eV image). The ratio of corrected 641.6 and 655.2 eV images can then be used to determine the RL2,3 for each pixel and to obtain the map of Mn redox state. In this way, the linear background is represented by only one energy at one energy position, so this point should be fairly close to the first peak (638 eV in Figure 5). In the case of spectra with a strong background noise, it is possible to make an "image average" (giving an average value of the linear pre-peak background) by selecting about 10 images between 625 and 639 eV, by adding them and then by dividing the resulting "image sum" by 10 thanks to the aXis2000 software.

If the equation 2 is chosen for calibration, the images required to calculate the RL2 parameter need to be selected at 651.7 eV (L2-a), at 655.6 eV (L2-e), at the inflexion point between the L3 peak and the L2 peak (to remove the background from the 651.7 eV), and one beyond the L2 peak (to remove the linear background and the second edge step of the arctan function for each pixel of the 655.2 eV image). By applying the same procedure as before, the Mn map can be reconstructed only from the L2-edge data.

Resulting quantitative Mn redox maps are a useful tool to identify the Mn mean valence of unknown nanometric particles, but have some limitations. On a map built from RL2,3 parameter for a no-pure piemontite sample constructed with equation 3 (Figure 6), the Mn-free crystallites appear in white (Figure 5G and Figure 6) while in areas where the particle is too thick and/or highly concentrated in Mn, valence is overestimated (Figure 6B). In the first case, the absence of Mn leads to calculate the ratio between two too weak absorption pixels (Figure 5E andF). In the second case, a too high X-ray absorption cause an absorption saturation of the L3 peak, which is more intense than the L2 peak. This phenomenon generates a nonlinear response of the absorption detection, artificially modifying the relative peak intensities, affecting the RL2,3 calculation and overestimating the Mn valence. Although more sensitive to the signal/noise ratio, the use of the RL2 parameter and equation 2 to map the Mn valence, based exclusively on the L2 peak, may provide a favourable way to circumvent absorption saturation issues encountered with the L3 peak (Figure 6C).

The spatial averaging effect of the X-ray beam over the pixel size (i.e., 40 nm) must also be taking into account. This effect fixes the limit of the minimum distance over which phase contacts or phase rims can be discriminated.

Surpassing these limitations easily identifiable, the STXM-based XANES quantitative map becomes a precise tool, giving an estimate of Mn valence with a high spatial resolution, as demonstrated by the map of piemontite in the Figure 6.

Assessment of saturation and beam damage effects

Although EELS is known to cause more damage than STXM on the structure of minerals (e.g. de Groot et al. 2010), the latter is nonetheless a method that damages particles during analysis if precautions are not taken. Potentially, the repeated scan of particles at each energy point of a spectrum can altered the structure of the crystallites, and consequently the Mn mean valence estimate. A stack recorded on a 5x5 µm area, obtained with a spatial resolution of 50 nm, a spectral resolution of 0.2 eV and a dwell time of 5 ms per energy-and image-point results in a total analysis time of 2.5 hours (dead time excluded) and of 0.875 s per image-point. To evaluate beam damages, spectral changes at the Mn L2,3-edges were monitored with increasing dwell times, from 1 to 20 ms per energy-and image-point. The resulting XANES spectra do not show significant changes, while RL2 and RL2,3 parameters are only slightly affected, varying by less than 5%. Consequently, the effect of beam damages on the Mn valence estimate is negligible in the typical dwell time range used during routine analyses.

The saturation of spectrum can also alter assessment of RL2 and RL2,3 parameters (see section 3.3). This phenomenon occurs when particles are too thick or too rich in Mn (or a combination of both), leading to a distortion of the spectrum. [START_REF] Hanhan | Optimization of analysis of soft X-ray spectromicroscopy at the Ca 2p edge[END_REF] for Ca and [START_REF] Bourdelle | Quantification of the ferric/ferrous iron ratio in silicates by scanning transmission X-ray microscopy at the Fe L-2,L-3 edges[END_REF] for Fe proposed to evaluate the maximum intensity of the major peak not to be exceeded to avoid saturation effect. Applying a similar approach, the maximum Mn L3 peak intensity, below which the L3/L2 peak intensity ratio varies linearly and the spectrum is undistorted, was determined. For this, a stack was recorded on a powder of piemontite sample (Mn 3+ ) with particles of various thicknesses. Figure 7 plots the intensity of the L3 major peak according to the one of L2 major peak for each image-point. The intensities of these two peaks increase linearly until ~0.25 OD. When the particle is thick enough for the L3 major peak intensity to exceed 0.25 OD, the L3/L2 intensity ratio no longer evolves linearly, i.e. the intensity of L2 major peak increases faster than that of L3 major peak, reflecting the spectra distortion for the considered image-points. This observation is also valid for Mn 2+ and Mn 4+ spectra. Consequently, all the quantitative data in this study were therefore obtained from areas presenting a L3 major peak intensity lower than 0.25 OD. It should be noted that Mn is much more sensitive to saturation phenomena than Fe (saturation effects at > 1.5 OD at the Fe L2,3-edges; [START_REF] Bourdelle | Quantification of the ferric/ferrous iron ratio in silicates by scanning transmission X-ray microscopy at the Fe L-2,L-3 edges[END_REF], i.e. saturation effects appear at relatively low Mn content (concentration or weak sample thickness). On an indicative basis, piemontite, which is a phase that is not very rich in Mn, presents saturated spectra for a crystallite thickness higher than ~150 nm, while Mn-rich jacobsite shows saturation effects on spectrum when crystallite thickness is around 70 nm.

The crystal orientation compared with the direction of polarisation of the X-ray beam may also influence the spectrum shape. This process is called linear dichroism [START_REF] Benzerara | Study of the crystallographic architecture of corals at the nanoscale by scanning transmission X-ray microscopy and transmission electron microscopy[END_REF], and can be thwart using a circular polarized beam as here. The residual dichroism effect was evaluated by comparing spectra from different piemontite particles with various orientation. No change in spectrum shape was observed, and the impact of particle orientation on the Mn mean valence estimate remained undetectable.

Conclusion

In the present work, we explore the possibility to construct quantitative Mn redox maps for silicates using the STXM coupled with XANES spectroscopy at the Mn L2,3-edges.

With fairly limited precautions, we demonstrate that this type of maps could be obtained from two easy-to-use empirical calibrations linking the Mn mean valence to a simple ratio of intensities from selected energy positions. We applied this approach on a mix of piemontite and no-Mn phase sample, demonstrating the potential of it to assess the Mn valence at the nanoscale through micrometric areas. Even if calibrations and map construction have yet to be tested on silicates containing Mn under several oxidation states, as Mn-phyllosilicates, these results pave the way for the study of nanochemical zonations in heterogeneous silicates.

wish also to thank the editor and the two anonymous reviewers for comments and suggestions that improved the paper.

Figure captions

Fig. 1 Representative XANES spectra at the Mn L2,3-edges for the Mn-silicates and jacobsite. The spectra have been normalised to the major L3 peak intensity, and some of the spectra have been shifted

vertically for clarity (normalised intensity with arbitrary units). The vertical lines indicate major peaks (solid lines) and minor peaks (dashed lines). Each peak is indexed, redox states and core-excited final state configurations are mentioned Fig. 2 Focus on L3-edge for Mn 2+ phases (rhodonite, ardennite, jacobsite). The spectra have been normalised to the major L3 peak intensity. Coordination (number of O ligands and sites) is specified for each phases Fig. 3 L3-edge center of gravity from XANES spectra versus Mn valence for the selected silicates.

Error bars represent the standard deviation calculated on the base of 4 or 5 spectra for each sample.

Value for jacobsite is given for information, but not taken into account for calibration calculation (2). The spatial averaging effect of the X-ray beam over the pixel size (i.e., 40 nm) sets the limit of the minimum distance (turquoise rims, underlined by a yellow square). No-Mn silicates, identified by blue dashed polygon on the OD image, appear in white on the redox map B and in black for no Mn absorption on the redox map C and image E of the Fig. 5. Areas where the particle thickness is too high to obtain no-saturated images (see section 3.4.)highlighted by a purple polygon on the OD imagelead to the overestimate of Mn valence (pink and red zones of the redox map B), up to the total saturation (appearing in white on the map). Areas presenting no-too-thick piemontite particles (i.e. the rest of the OD image) appear in blue on the Mn redox maps, testifying of trivalent manganese

Fig. 4 Fig. 5 Fig. 6

 456 Fig.4L2,3-edge intensity ratio from XANES spectra versus Mn valence for the selected silicates. (A)

Fig. 7

 7 Fig.7Difference, pixel by pixel, of intensity detected between the L3 major peak and the L2 major

Figure7

  Figure7

Table 1

 1

	: Samples used for STXM-XANES Mn L2,3-edge investigations to Mn mean valence
	quantification
	Type	Sample	Location	Mn	Position of major
				valence	peaks (eV)
					L3	L2
	Silicate	Rhodonite	Gambaseta (Liguria, Italia)	2+	641.6	654.1

  This study was financially supported by LGCgE.

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Acknowledgements

We are most grateful to the PSI SLS synchrotron, especially Benjamin Watts (PolLux beamline) for technical advice. Thanks are extended to Philippe Recourt (LOG, Univ. Lille) for sample preparation and to Francis Coune for providing ardennite sample. The authors

This study was financially supported by LGCgE (laboratory funds).

Conflicts of interest/

.bourdelle@univ-lille.