Integrated tactical continuous production planning of two blending systems sharing supply sources: the case of a phosphate supply chain

Keywords: tactical planning, interdependent production systems, blending, alternative routings, alignment

This paper deals with a problem of tactical planning of production activities. It considers the case of the world's largest phosphate production site, with several mines, several washing plants, and a drying plant, with transport of merchantable phosphate ores (MOs) by rail or pipeline. The tightening of product quality requirements by customers prevents from continuing to plan its production with the current rules. Currently, the plants are managed quite independently, source ores (SOs) are pre-assigned to the MOs for blending, and the MO production routings in the washing plants are predetermined. We propose a model that ensures flexibility in the production of MOs through the choice of dynamic blends and routings. Our approach goes beyond any pre-allocation of resources and aims at synchronising the flows of the washing plants. This specific problem of blending production and planning has not been addressed in the literature. Still, it is widely encountered in many mining industries and offers perspectives for the application of the approach proposed. Numerous tests show that this model ensures the quality constraints related to the composition of several chemical components, with a generalised use of the most economical routings while ensuring horizontal and vertical alignment of decisions.

Introduction

As a result of current global developments (demographic, economic, environmental), the mining and primary processing industries are facing new challenges such as the scarcity and heterogeneity of raw materials, rising energy costs, increased customer diversity and requirements, etc. These issues have been the subject of a great deal of research based on the famous linear model of blending [START_REF] Dantzig | Reminiscences about the Origins of Linear Programming[END_REF], followed by extensions of this model and the development of suitable algorithms. However, it has received little attention and application in the specific case of the phosphate mining industry, which is the main supplier of raw materials to produce fertilisers and phosphoric acid and which have a major position in the agriculture and food industries.

These industries have a number of specific features: (i) they generally integrate several elements of the supply chain (extraction, homogenisation process, chemistry), (ii) they combine heterogeneous raw natural resources to obtain homogenous market products that meet precise and specific specifications, (iii) raw materials are supplied in push flow depending on the extraction's program, (iv) the homogenisation process often consists of several parallel treatment lines, (v) chemical plants (phosphoric acid) must be supplied continuously to avoid any defusing. For all these reasons, the traditional planning methods used in manufacturing supply chains are unsuitable. This paper focuses on the largest phosphate rock production supply chain (SC) of OCP Group, which provides 70% of the group's total production. In 2022, OCP's revenue will be US$ 11.5 billion, with a Morocco Gross National Product of US$ 133 billion making OCP a worldwide leader in phosphate and its derivatives.

This SC is faced with three sets of demands linked to the type of recipient and the method of shipment: (1) internal demand to the chemical complex delivered by pipeline, (2) external demand to the port delivered by the same pipeline and (3) external demand to the port delivered by train. Each demand (Merchantable ores, MO) must be fulfilled in quantity, delivery date and quality requirements outlined in a quality charter (QC). A MO is obtained by blending different raw materials (Source Ore, SO) to which it is possible to apply a washing treatment that will enrich it in phosphate (three different routings coexist).

Currently, the SC focuses on a unique chemical element for piloting flow (Bone Phosphate Lime -BPL, characterising the richness of phosphate in P2O5) whereas the QC of each MO requires limits for other elements (Cadmium, etc.). It uses almost fixed blends to prepare the final products, although the order specifications and SO availability and chemical quality may evolve over time. The current planning organisation therefore raises a number of issues: (1) how to ensure a finished product that satisfies QC for all components, (2) how to make better use of available SOs, and (3) how to improve the effectiveness and efficiency of SC.

To address these challenging issues, we propose a flexible and dynamic approach for piloting flow for this phosphate SC. This approach is twofold. First, we propose a new planning organisation of production in washing plants to manage the limited capacities, the parallel washing operations and the available SOs. Second, we develop an optimisation model (MILP class) to generate dynamic blends that fulfil a tactical orders book. This paper is then the result of a collaborative research [START_REF] Shani | Handbook of Collaborative Management Research[END_REF]van de Ven et Johnson, 2006). The aim of such research is not to consider previously identified theoretical hypotheses, but rather to explore the field to dissect the problem and identify avenues for further research and reflection. The suggested approach could be inspiring and provide valuable insights for several other mining industries adopting similar production processes. This paper is organised as follows: Section 2 presents a literature review on planning production activities in the process industries and aligning decision. Section 3 devoted to the formulation and explanation of the mathematical model. Numerical studies and analyses are proposed in Section 4. The final section draws some managerial insights before concluding with some perspectives.

Literature review

As the paper deals with a processing and blending problem in the phosphate industry, we have focused the literature review on blending issues, combined with treatment/processing in the mining industry, to address the gap. We have also reviewed the concept of alignment, which deals with the coherence between decisions. In most cases, these coherence problems caused by the use of models designed to solve a particular problem are ignored by the authors of these models, implicitly assuming that the constraints induced by their solution must be taken into account by the other decision entities (which is sometimes relevant). We decided to include this issue in the analysis of the consequences of the proposed model.

Blending production in the mining sector

We focus on the blending problem in the mining industry in a deterministic environment, which has three specific characteristics: i) the inputs are extracted and not purchased. Their characteristics depend mainly on nature, which implies a relatively high instability of the characteristics of the available inputs that need to be handled through blending and processing to satisfy customer needs; this makes the problem dynamic and impacts the optimal solution more than the cost; ii) the blending output is a semi-raw material used later by the industry for fertilizers and phosphoric acid production; iii) the blending process may involve the use of alternative routings and possibly several processors that may work in series or in parallel, as we will explain later.

The articles analysed are selected based on two keywords: 'Blend/blending' and the name of a specific ore or metal such as 'iron ', 'coal', 'phosphate', 'gold', etc., and the analysis of the abstract. Some articles were general and did not consider the case of a specific ore/metal.

Table 1 shows the analysis grid resulting from the analysis of 15 articles dealing with blending problems in a deterministic mining environment. This analysis was carried out on the basis of several criteria. We have selected the most relevant ones, mainly five (type of ore, type of production, mathematical formulation, processing and blending process, and objectives), to compare the main characteristics of our paper with those of the analysed articles:

• Type of ore: the blending problem was addressed in several mining industries like iron, phosphate, copper, and coal.

• Mathematical formulation: Linear programming, mixed integer linear programming, non-linear programming, mixed integer non-linear programming.

• Production's type: Outputs made to stock or on demand.

• Processing and/or blending: In mining industries, the production process is composed of at most two main operations which are processing and/or blending. Different production configurations (illustrated by Figure ) are possible: the first one (configuration A) is where only the blending of SO is realised to satisfy customer requirements, and the second (configuration B) consists of blending SO and then processing the blend (washing being not the only type of treatment available) with a specific routing for enrichment. For the processing stage of this configuration, it is possible that the main one is composed of several sequential sub-processing units which justifies the case of some articles mentioned in the grid with sequential process and configuration B. The third one (configuration C) aims to treat SO and then blend the necessary inputs (enriched products and/or SO) to satisfy customer requirements.

Configuration C is based on the parallel use of several ore processing lines during the same production period before blending to obtain the desired output. Other configurations using multiple processing lines at different times are possible but raise the complex problem of managing intermediate stocks combined with a scheduling problem. Recently papers were focused on phosphate blending problems and considered the case study of OCP group in Morocco [START_REF] Azzamouri | Flexibility of dynamic blending with alternative routings combined with security stocks : A new approach in a mining supply chain[END_REF]Hilali et al., 2022). Those papers are kind of complementary to each other and different from ours regarding several aspects. They are adopting configuration B with a unique production system, contrary to our paper which concerns configuration C which is a bi-production system. The rest of the features are presented in the grid (Table 1).

• Objective function: economic (maximisation of profit or minimisation of costs), environmental, requirements targets.

Alignment concept

The organisational alignment concept was defined several decades ago [START_REF] Venkatraman | Exploring the Concept of « Fit » in Strategic Management[END_REF][START_REF] Venkatraman | The Concept of Fit in Strategy Research : Toward Verbal and Statistical Correspondence[END_REF][START_REF] Tan | Environment-strategy co-evolution and co-alignment : A staged model of Chinese SOEs under transition[END_REF]. It is linked by some researchers with the concept of "congruence" and defined as it (Lawrence and Lorsch,1967). [START_REF] Wong | Towards a Theory of Supply Chain Alignment Enablers : A Systematic Literature Review[END_REF] have defined alignment as the 'fit' in terms of objectives, structures, and processes within and between the supply chain's various functions and production units. According to [START_REF] Porter | What is strategy?[END_REF] We distinguish two dimensions of alignment in a supply chain: vertical and horizontal.

• According to [START_REF] Kathuria | sOrganisational alignment and performance : Past, present and future[END_REF], vertical alignment consists in developing and elaborating action plans, strategies, and decisions at all levels of the organisation's decision-making. For [START_REF] Bhatnagar | Models for multi-plant coordination[END_REF], effective strategies leading to good performance focus on how decision-making at different organisational levels is coordinated (vertical alignment) so that operational policies are optimal for the organisation as a whole. According to [START_REF] Ivanov | An adaptive framework for aligning (re)planning decisions on supply chain strategy, design, tactics, and operations[END_REF], the vertical alignment of the three levels of decision is crucial, as it leads to feasible and balanced production planning and provides feedback for the audit and the adaptation of these plans to the actual performance and capacity of the processes of the supply chain. [START_REF] Kathuria | sOrganisational alignment and performance : Past, present and future[END_REF] point out that vertical fit/alignment requires a shared understanding of the objectives of the organisation by different managers at different decision-making levels and at different units of the organisation hierarchy.

• Furthermore, horizontal alignment is related to the coherence of decisions taken between the different production units of the supply chain for each decision level. [START_REF] Kathuria | sOrganisational alignment and performance : Past, present and future[END_REF] defined it as the coordination of efforts in the organisation, which is relevant in the lower levels of the strategy hierarchy. They defined it depending on the cross-functional and intra-functional integration. Cross-functional integration implies consistency of decisions between supply chain functions, such as decisions on production operations, human resources, etc., and other functions related to and complementing each other.

Intra-functional integration is achieved through coherence across decision areas to achieve synergy within each function. [START_REF] Malone | The interdisciplinary study of coordination[END_REF] defined horizontal

alignment as the coordination and the act of managing dependencies between entities and the joint effort of entities working together towards mutually defined objectives. [START_REF] Porter | What is strategy?[END_REF] shed light, through his paper, on the importance of horizontal alignment within several activities of companies rather than the key (one or two) ones, in maintaining a competitive advantage over time.

Tactical production planning

Section 3.1 presents the general description of the SC studied. Section 3.2 details the tactical planning model we propose, which must satisfy several operational constraints, but which does not depend on the order books used, whose design must accommodate continuous internal demand and batch export demand. This is achieved with an original solution presented in section 4.

SC description and organisation

Upstream the SC, ore extraction is carried out in a push-flow mode based on an annual extraction program, leading to significant variability over time in the composition and volume of SOs, which are available for MOs production (Azzamouri et al., 2018). The SO stocks built up at the mine and in the vicinity of the washing plants are significant and constitute a decoupling point in the SC [START_REF] Sun | Positioning multiple decoupling points in a supply network[END_REF][START_REF] Van Donk | The impact of the customer order decoupling point on type and level of supply chain integration[END_REF], implying the absence of stock management problems in the SC studied part and the possibility of local optimisation.

This SC part (see Figure ) is made of i) five mines (extending over several hundred km 2 ) connected to ii) three washing plants (with five washing lines) feeding either a drying plant or tanks in a Head Station, iii) the Head Station is connected, through a 183 km pipeline, with phosphoric acid production plants (whose demand is regular) and the Jorf port for exportation (of irregular demand); iv) MOs produced by the drying plant are delivered by trains to the Casablanca port for exportation. Two interdependent production systems coexist, the first dedicated to the order book of customers downstream of the pipeline and the second to the order book of customers downstream of the train. These two systems (which we will refer to as the pipeline production system and the train production system) share mining resources, and the former supplies the latter with WSOs. Currently, the production subsystem centred on the washing plants, and the one centred on the drying plant, are managed separately, using a pre-allocation of ores, with poor efficiency in terms of QC and poor effectiveness in terms of ore consumption.

As mentioned in the introduction, this SC production is a pull-flow process. The organisation of this production must be based on the strongest constraints, which are undoubtedly those of pipeline transport due to its fixed transfer rate and the constraints of not saturating the storage tanks of limited capacity located upstream and downstream of the pipeline and not defusing downstream for internal demand. The train export order book does not pose any particular problem (except that of respecting the production capacity of the drying plant), unlike the pipeline production and transport order book, which has to satisfy both continuous demand (defined by a flow rate) and discrete demand (quantities to be loaded onto a ship), that cannot be used directly. To improve the organisation, we propose a new master production schedule for the production carried out by the washing plant, based on two principles.

• Production is organised cyclically in a succession of the same set of two several alternate sequences. In the first sequence, all the washing lines produce an order for internal demand (mono-production), which increases the stock located downstream of the pipeline (delivery tank). In the second sequence, the washing lines are shared between an order for internal demand and an order for export demand on the other (bi-production), which reduces this stock. This cycle, defined to avoid saturation and depletion in the delivery tank, is arbitrarily designed using several rules presented in Section 4.1 and illustrated in Table 3.

• In mono-production as in bi-production, the lines assigned to an MO order work synchronously to produce, each of them, a WSO obtained by treating a selected SO with a selected routing. This simultaneous production, mobilising several lines over the same period with a chosen routing, implies a pre-determination of the number and quantities of inputs (SOs) used in the blending selected to produce the outputs (MOs).

Our modelling does not depend on the definition of the order book, which is considered as an input parameter to the model, whose construction logic makes it possible to reconcile continuous and discontinuous demand flows, is nevertheless a contribution of this paper.

Mathematical model

As the model is relatively technical, this paragraph describes the structure related to orders. A final order is broken down into several small orders in the case of export demands (train and pipeline) and is described by a set of orders in the case of local demands. With the production cycle described previously, each washing line produces a batch intended for a precise order (if routed by pipeline) or for an export-train final order assigned by the model. Thereby, a batch is defined by the couple (l, k) where l is the number of the line mobilised, and k is associated with an order for: i) the local customer (same index k since the local orders use washed ingredients only), ii) an export-pipeline customer (index r), or iii) an export-train customer (index p).

All orders routed by pipeline are constituted of a blend of WSO, whereas orders routed by train are constituted of a blend of SO and/or WSO. A local order k is obtained by blending the five mono-production or three bi-production batches produced by the lines assigned to that local MO order. An export-pipeline order r is constituted by two orders k, (assigned to r), each produced by two washing lines, which leads, consequently, to a blend of four batches. In this last case, the model will intrinsically assign, if necessary, the export-train orders to the different final commands.

Each order concerns a given MO with an associated volume and quality charter (index j). The link between an order and the merchantable ore is made through a conversion parameter ( ). A parameter is used to identify the type of order to which each elementary order is attached .

After listing the used indexes, parameters, and variables, we first explain some restrictions with predicate definitions. These predicates will be useful for the optimisation by

λ ,ρ , π k r p { } (A 1, 2,3 ) k =
reducing the number of variables. Then, we describe the mathematical model before commenting on the introduced relations.

Description of the used indexes, parameters, and variables.

Index Description

t Index of time.

i Index of a raw ingredient/ input/ SO. p Index of a drying plant order performed to meet an export-train order.

r Index of export-pipeline orders.

k Index of an order produced in the washing plants by blending the batches of WSO produced by the washing lines assigned to that order.

Parameters Description

General parameters

Volume of order k produced in washing plants (in m 3 ).

Volume of export-train order p (in m 3 ).

Volume of the export-pipeline order r (in m 3 ).

Output index of local elementary orders.

Output index of export-pipeline orders.

Output index of export-train orders.

Technical parameters

Proportion of component c in the weight of input i.

Weight reduction coefficient of input i by routing h. If the routing h is not used to process SO i, then .

Distortion coefficient of component c in input i by using routing h.

λ k j = ρ r j = π p j = D k D p ¢ D r ¢¢ λ k ρ r ρ p ¢ α ci η ih η 0 ih = γ cih
Lower and upper bounds of the proportion (%) of component c in the weight of output j.

Boolean is worth 1 if the elementary order k involves washing plant l.

Equal to 1 if k corresponds to the local customer, to 2 for the exportpipeline customers, and to 3 for the export-train customers.

Mine from which the input i is extracted.

Boolean is worth 1 if the mine m feeds the washing plant l.

Boolean is worth 1 if the mine m feeds the drying plant.

Index of the export-pipeline order r to which the elementary order k belongs.

Conversion ratio from volume (m 3 ) to weight (in tons) (in ton/m 3 ).

Conversion ratio linked to the drying plant from entering volume of input i to exiting volume.

Hourly production rate of washing plant line l (in m 3 /h) corrected by an average percentage of availability.

Maximum volume of each input to be used for each order.

Minimum volume of each input to be used for each order.

Time parameter

Production time of the elementary order k.

First period of production of the elementary order k (then the last period of production is ) .

Latest delivery period to start the feeding of order p in the drying plant, considering the drying time and the train transportation time and the earliest loading date on the boat.

Product transportation time by conveyor between entities (mines, washing plants, drying plant), oversized to avoid explicitly treating potential conflicts in conveyor use at a tactical level.

Inventory parameters

Initial stock of input i at t=0 (in tons). At the tactical level, the stock of input i available in a mine is merged with the ones of that input i kept beside a washing, as transportation issues (involving short transport times) can be easily treated at the operational level.

Min Max

[β β ] cj cj - B kl A k μ i ml P m ¢ P C k κ χ i d l M M θ k ω k ω θ 1 k k + - π p ζ init S i
Forecasted stock feeding (in tons) of input i at the beginning of period t (pushed once a day by the production program of mines).

Cost parameter

Average unitary cost of extraction of one ton of SO.

Treatment unitary cost of one ton of SO in a washing line (energy, water, chemicals, sludge disposal...) involved by routing h.

Variables Description

Decision variables

Boolean equals 1 if input i is processed by routing h on washing plant l to produce elementary order k forwarded via pipeline.

Boolean equals 1 if input i is processed by routing h on washing line l to produce elementary order k to include in preparing orders p to forwarded via trains to export customers.

Quantity (in tons) of input i used to produce export-train order p delivered at time t.

Boolean equals 1 if input i is carried to the drying plant since period t for the train-export order p.

Auxiliary variables

Weight of component c in the total weight of the product made (WSO) on the line l for the elementary order k.

Weight of component c in the total weight of the export-train order p of the volume .

Level of stock of input i at the end of period t (in tons).

Predicates

The decision variables will not exist in the whole space defined by the combination of all the index spaces. Therefore, to reduce the size of the model, we define some predicates associated with all variables. A predicate is a logical expression ("true" or "false") that defines the domain of an index, which in turn binds the existence of a decision variable, depending on the parameters' values.

Q

it E σ W σ h ihlk x ihlkp y itp z itp u μ clk μ cp ¢ ' D p S it
exists if four conditions of existence are present: (1)

, meaning that k concerns only orders related to local customer and export pipeline ones, (2) , meaning the production of order k calls for the line l, (3) , meaning the mine from which the SO i is extracted is linked to the washing line l by a conveyor, and (4) , meaning that routing h can be used to treat the input i. These four conditions yield the assignment condition predicate and the physical existence predicate .

exists if (1) (order k deals with the production of a WSO made for a drying plant order), (2) the above predicates and are true, and (3) this WSO is produced time units prior its transportation ( ) and use by the drying plant order p leading to the predicate exists if input i can be transported to the drying plant , before the latest production period in the drying plant (considering the oversized time of conveyor transportation, ), yielding the predicate . exists if is true.

Flow characteristics

The table 2 shows the characteristics of the three types of orders (local-pipe, export-pipeline and export-train), where the production of order k aggregates the production of the lines used for this order. including the volumes/quantities of ingredients to consume and blend to prepare the final products according to the specificities related to the transformation process.

ihlk x A 3 k < B 1 kl = μ Π 1 i l = μ i η 0 ih > 1 (B 1) kl W º = 2 μ Π 1 ( 0) η i l ih = Ù > W º ihlkp y A 3 k = 1 W 2 W (ω θ ) k k + ζ 3 (ω θ 1 ζ< π ) k k p W º + -+ itp z μ ( 1) i
¢ P = ζ 4 μ ) 1 ( π i p t z ¢ Ù º + < = W P itp u 4 W 3.2.

Model relations and justifications

We first present all the constraints (3.2.4.1 to 3.2.4.3); the objective-function is described in 3.2.4.4. Three production constraints exist: those dealing with the production sent by pipeline (decision variables ), those dealing with the production sent by train (decision variables and ) and those dealing with SO Stocks (intermediate variables ).

Production constraints of the pipeline production system

(1)

Relation (1) forces the production elementary order k shipped by pipeline ( ), to use a unique allocated line ( ), a unique input reachable by that line and a unique routing usable on that line for the input i. As presented in 3.2.1., existence of the variable is determined by the predicates et which will be inserted in all the constraints and in the objective function, involving the variable .

q k w k w k +q k -1 d l .q k. k/h ih d l .q k .k D k q k w k w k +q k -1 relation (7)

Local customers

Order k where A k =1 made of WSO batches where x ihlk =1

S l,i,h d l .q k x ihlk = D k

Export-pipe customers

Order r made of several orders k where A k =2˄C k =r Batch of a WSO produced by line l for order k (x ihlk =1) Batch of SO i used for order p where S t u itp =1 before drying delivered from period

Export-train customers

Order p made of orders k where A k =3˄ S ihl y ihlkp =1 -AND/OR batches of SO i used for order p where

x ihlk =1 Demand (m 3 ) Production Weight (ton) Volume (m 3 ) D p ¢ D r ¢¢ itp t t u × å . itp i t z c å /κ itp t z å .χ /κ itp i t z å itp t z å d .θ l k d .θ .χ l k i d .θ .κ.χ i l k C A 2 D D k k r k k = Ù = ¢¢ = å ihlk x ihlkp y itp z it S 2 1 , 1, | A 3, ihlk k i h x k l W = " < " W å A 3 k < B 1 kl = ihlk x 1 W 2 W ihlk x (2)
Technical constraints (2) prevent feeding simultaneously two washing lines with the same input.

( (5)

Relation ( 5) enforces the QC respect for pipe-export customers for the mixing of all the elementary orders included in the pipe-export order r. Remember that an export-pipeline order is formed by combining two orders k.

An additional constraint prohibiting some combinations of routings and washing lines, in washing plants owning two lines, easy to formalise, is not presented in this paper.

3.2.4.2 Production constraints of the train production system

2 1 , 1, , | A 3 ihlk k h l x ik W W Ù £ " < å 2 1 , | μ (κ.d .θ ). α .γ , , , |A 3 clk l k ci cih ihlk k i h x c k l W = × " <Ù W å (A 3) k < α ci γ cih (κ.d .θ ) l k 1 Min Max λ λ | β .D μ / κ β .D , , |A 1 k k c k c l k c k k l c k W £ £ " = å Min Max [β β ] cj cj - 1 Min Max ρ ρ A 2 , A 2 C C C A 2 β . D μ / κ β . D , , r r k k k k k k r r r k c k c l k c k k k l c r = Ù = Ù ÙW Ù = = = = £ £ " å å å (6)
Relation ( 6) enforces the production of the elementary order k of an export-train order p by the allocated washing line to yield a WSO to include in the blending of the train order p . This is realized by respecting assignment existence condition ( ), physical existence conditions ( ) and time existence conditions ( ). It should be noted that this relationship does not force the two WSOs produced by the two washing lines assigned to a given order k to be integrated into the same train order, which gives greater flexibility in the search for an optimal solution.

(

) 7
The demand of the export-train order p mixes (i) either, 0, 1 or several SOs, assuming that SO i can be conveyed to the drying plant before its use (predicate ). This corresponds to the first sum of the right side of relation ( 7) and (ii) either 0, 1 or several WSOs (second sum of the relation 7). During the drying process, the weight of each input i is reduced by the factor because of the existence of a screening process before the drying one.

(8)

Binary variable , only if a positive amount of SO i is forwarded to the drying plant from the period t onward, to be integrated into export-train order p. The volume must be neither too low nor too high . In addition, Relation (8) verifies and enforces the quantity bounds to be respected if .

(9) ( κ . d. θ) . α . γ . χ. , ,

2 3 1 , , 1, , | A 3 ihlkp k i h p y lk W ÙW = " = ÙW å (A 3) k = 1 W 2 W 3 W μ 3 1 2 3 , | , , , 1 κ D χ / χ d .θ . , i p i itp i l k ihlkp i t i h k l z y p ¢ P W W Ù W = ÙW Ù ¢ = × + × " å å D p ¢ 4 W χ i 4 M. , , | M. itp itp itp itp z u i t p z u ³ ì ï " W í £ ï î 1 itp u = itp z itp z (M. M. ) itp itp itp u z u £ £ 0 0 itp itp u z = Û = itp z 1 itp u = 4 1 2 3 , | , , , μ α . χ.
cp ic i ipt l k ic hci i ihlkp i t i h k l z y c p W W Ù W Ù W ¢ = + " å å
Relations ( 11) and ( 12) model the SO Stock evolution. The recurrent Relation ( 12) is a classical stock conservation equation, where the removal of an SO from its stockpile is wholly completed at the beginning of such removal. Three removals can take place: (1) SO forwarded directly to the drying plant ( ), (2) SO forwarded to a washing lines(plants) for a pipeline orders ( ) and ( 3) SO forwarded to a washing lines for a train orders ( ).

The considered tactical horizon allows a reservation of SO depending on the need and availability. Thus, the SO are considered available upstream of washing lines, and there is not any convoying time from mines.

Optimisation criteria

The objective-function relates to an efficiency point of view, trying to minimise the sum of the SO extracting costs P E (linked to train orders for first and second lines of the mathematical

Min Max cρ c ρ β .D κ β .D , μ , / p p c p p p c p ¢ ¢ ¢ £ £ " ¢ ¢ D p ¢ init 0 , S 0 S S , it i i i t ï í ï î " ì = ³ 1 4 1 2 2 , 1 | , , , 3 , A
, 3 ω A ω S =S κ. Q d .θ κ. , . / η d .θ . η , / k k k k i t it ipt l k ihlk ih p h k l l k ihlkp ih h p k l it t t z x i t y Ù - W W ÙÙ < W W Ù = = ÙW = Ù - - " + -å å å ipt z ihlk x ihlkp y
formulation, and to pipeline orders for third one) and washing costs P W (linked to pipeline orders for the first part in the relative mathematical formulation and train orders for the second one). The conveyors' and drying costs are not considered because they depend little on the chosen solution and are of low relative importance compared to other costs.

(13)

Numerical experiments

Twenty tests of this model were carried out, combining randomly generated data (based on observed structures) relating to the order books of pipeline and train customers (volumes, dates, and MOs) and the availability of the SOs over the horizon under consideration, resulting from the push-flow production of SOs. This section uses the data from the first test as an illustration.

Section 4.1 describes the principles retained for the design of the washing plant order book to reconcile the requirements of internal continuous demand and discrete export demand. Section 4.2 describes the other data used. Section 4.3 provides the detailed optimal solution of this test and summarises the solutions of all the tests performed. These data, generated randomly, respect the characteristics observed in the field in terms of physical production and transport systems, order books (dates, volumes, MO references) and SOs supply schedules (in volume and quality).

Design of the washing plants order book

As mentioned in section 3.1, to meet both continuous demand (internal MO) and discrete demand (export MO) to be produced by the washing plants and transported by the pipeline, we have retained an organisation that alternates between a mono-production where all washing

5 1 2 3 1 2 , | E E , , , , , , , , A 3 P
σ κ . d . θ / η κ.d .θ / η k ipt i t l k ihlkp ih i h k l p l k ihlk ih i h k l p z y x W W ÙW ÙW < ÙW ÙW é ù + ê ú ê ú = × × + ê ú ê ú × ê ú ë û å å å 1 2 1 2 3 W W , , |A 3 , , , | P σ .( κ.d .θ / η κ.d .θ / η ) h l ki h l k i h l k i h l k p i h h i k l i k lp x y < ÙW ÙW W ÙW ÙW = × + × å å å E W
Min(P P ) + lines are allocated to the internal MO and a bi-production where the allocation of these lines is shared between internal and export demand. To facilitate the understanding, we will rely on the reasoning using the numerical data of the case study (close to the actual one) where the internal MO is considered as its supply is mandatory.

• At the tactical level, it is impossible to consider fluctuations in the MO chemistry demand and preventive maintenance operations and setup time in washing lines. Then the nominal production capacities are reduced in the proportion observed in the last months.

• In mono-production, the internal MO production rate is 3,240 m 3 /h. In bi-production, a systematic assignment of the last three lines to the internal MO production leads to a production rate of 1,980 m 3 /h for the internal MO and then 1,260 m3/h for the export MO with the first two lines. In both cases, these production rates consider a 10% unavailability rate (maintenance, breakdown...). This decision defines the assignments of the washing lines to the order processed for the production sent by pipeline and the WSO used by the production sent by train (parameters and ).

• The capacity of internal MO tanks downstream of the pipeline is 22,500 m 3 . In monoproduction, these tanks, considered initially empty, are filled in 22,500/(3,240-2,500) = 30,4

hours by a produced quantity of 98,514 m 3 of internal MO. In bi-production, these tanks being initially full, are emptied in 43.3 hours, by a produced quantity of 85,734 m 3 . During that period, the two other washing lines may produce 54,558 m 3 , used in priority for pipeline export MOs, the residual being used (WSO) for export train MO.

• Then a possible production organisation may be based on a succession of cycles of approximately 73 hours made of a sequence of a 30-hour period of mono-production (gradually leading to saturation of the internal MO tanks downstream of the pipeline), followed by a sequence of 43-hour period of bi-production (gradually leading to emptying • This type of organisation, which requires large quantities of SOs to be used simultaneously to produce MOs, in a context of relative scarcity of these SOs, not only makes it more difficult to comply with the MO quality charter but may also prevent a solution from being obtained that complies with the QC. So, the organisation chosen is based on the repetition of a 73-hour cycle in which several mono-and bi-production sequences are alternated to reduce the size of the batches to be produced and make good use of the available SOs. We have arbitrarily selected 5 sequences in a cycle comprising an alternation of 5 monoproduction batches (22,680, 19,440, 19,440, 19,440 and 16,200 m 3 , for durations of 7, 6, 6, 6 and 5 quarters of an hour) and 5 bi-production batches (17,820, 17,820, 17,820, 15,840, 15,840 m3, for durations of 9, 9, 8, 8 and 8 quarters of an hour during which export-pipe QSLs and train QSLs can be produced). This alternation, illustrated in Table 3, uses arbitrarily chosen values that respect the constraints of non-saturation and non-de-priming.

This production organisation has an impact on the data used by the planning problem, but not on the mathematical optimisation model.

• There are three additional points to consider in bi-production: i) each pipeline export order, whose the number and characteristics vary in time, must be split into two elementary orders (allowing a blend of 4 batches of WSO) or more, to ensure QC constraints; ii). a size constraint exists for the batches of WSO produced for train as an export-train order will be transported in several full trains of limited capacity (3,600 tons), where each load have to comply with the QC; to be used in the blend of a trainload, the size of WSO batches must be small enough, to allow the use of SOs in addition to WSO in blending; iii) a batch of WSO cannot be used immediately by the drying plant because it has to be drained and transported by conveyor belt; this implies a neutralisation period of about 42 hours at the beginning of the order book for MOs transported by train and a neutralisation period of the same length at the end of the order book for washing plants, in order to ensure that all the batches of WSO produced are used.

• It can be added that, with a transfer rate of 4,000 m 3 /h, the pipeline utilisation cannot exceed 3,240/4,000 = 81%. Pipeline transport induces a time lag between internal MO production and the feeding of delivery tanks (downstream of the pipe), which can be ignored here as we are only interested in the production problem. Three important observations can be made from the result of this test, which is representative of the 20 tests carried out.

• Among the 20 tests, all batches tested in a washing line use the h=1 routing, corresponding to a simple washing for all batches (WSO), whatever the type of order (this routing is the least expensive and consumes less water). This observation made on the optimal solution

shows that an important use of the less efficient routings 2 and 3 can be avoided.

• As can be seen in 11 and 20; orders 3, 12 and 21). This is due to the temporal and spatial interdependence of the decisions, which involves a trade-off in the use of SOs, taking into account their scarcity, which evolves over time. This observation made on the optimal solution shows that the systematic use of fixed blending recipes is not relevant.

• The WSOs produced during the first production cycle are used by orders from the drying unit in a very varied way (Table 8): an order may not include any WSOs produced during the first cycle (this is the case for the first 4 orders) or one or more WSOs from these WSOs produced during the first cycle, possibly mixed with WSOs produced late.

Conclusions

It is important to stress that this work is not only a comprehensive case study, but also the an original scientific approach that can and must be applied in other mining companies with similar configurations (section 5.1). This study also has interesting implications for OCP management (section 5.2).

Scientific contribution and dissemination of the approach

From a scientific point of view, the proposed model can be analysed as a joint planning problem for two logistics chains: i) which differ in the production processes used and the demands to be met (fairly stable continuous demand + highly irregular discrete demand for the first SC and highly irregular demands for the second SC); ii) but which are linked by the sharing of primary inputs (ores extracted from 5 distant mines) and the supply, on an ancillary basis, of intermediate inputs (WSOs) produced by the first SC, to use its residual capacities, at the request of the second SC in addition to the primary inputs it can use. This type of tactical problem is specific and modelling it using mathematical programming. The problem treated in this paper represents an original assembly of primitives. The originality that can be mentioned is found upstream of the mathematical model with the construction of order books based on a cyclical organisation of the production of SC of washing plants, which makes it possible to reconcile the joint satisfaction of a regular demand and an irregular demand (this order book constituting an input data of the model).

At least a dozen other mining industries that extract and process ores of various types (See Table 9 in Appendix) produce constrained composition outputs by blending previously processed inputs in treatment lines. Many mining industries are now forced to exploit lowgrade, distant deposits that require a combination of beneficiation and blending to meet quality standards, as is currently the case in the OCP supply chain studied. The increasing scarcity of phosphate ore makes this trend ineluctable.

In addition, it can be noted that the principle of alternating mono-production and biproduction should be of interest for other continuous production industries facing to a nondefusing constraint (chemical process, etc.).

Managerial impacts for OCP

The numerous tests have shown that it is possible to meet the QC requirements with minimal ore and chemical consumption, and our main contribution is to demonstrate the possibility of a more efficient management mode based on flow control, taking into account the characteristics of several chemical components and without the need for additional information, based on several advances.

The first two ones are technical.

• The change from a single component (BPL) to several components to be taken into account in the QC no longer makes it possible to manage the washing lines independently without a sharp deterioration in effectiveness (non-compliance with the QC) and efficiency (significant use of routings 2 and 3, which mobilise larger quantities of SOs and chemicals).

• The flexibility offered by replacing MO's largely fixed blend recipes by dynamic ones that take into account the entire order book and the entire ore delivery schedule, dramatically increases planning efficiency.

The other advances are of a managerial nature. Currently, the washing lines are managed independently, which is no longer possible with the scientific approach of blending, which forces a horizontal and a vertical alignment of decisions taken by productive entities.

• The replacement of parameters (predetermined 'ores' allocation and blending recipes) by decision variables in the optimisation model guarantees a horizontal alignment of the tactical decisions taken in these two productive subsystems at three levels: i) through the optimal allocation of SO between the production sent by pipeline and the production sent by train; ii) through the coordination of the production decisions of different production units (drying plant, washing lines) that must cooperate to ensure the satisfaction of MO demands; iii) through the synchronisation of the production.

• This model allows a vertical alignment between tactical decisions and operational decisions, in particular the combined decisions on the production of washing lines and the transport of these products by pipe, for which an operational model has been created and successfully tested [START_REF] Bamoumen | Un modèle de blending pour la planification dynamique d'une chaine logistique minière. 13ème Conférence Francophone de Modélisation[END_REF]. This alignment is facilitated using the same level of detail for inputs and outputs, as well as the use of a common hourly time breakdown, which eliminates the occurrence of classical disaggregation problems. Furthermore, the operational model uses the same principle of alternating between mono and bi production.

Finally, WSO production decisions made at the tactical level can be retained at the operational level, as can the sharing of WSOs between the two production systems, which can then be managed separately. Of course, all this requires tactical planning to be updated fairly frequently, which is essential because of the hazards encountered in mining and therefore in making newly extracted SO available.

For implementing this new approach, it is now necessary to carry out some additional benchmarks to convince the OCP top management of the need for this change of perspective.

It is also necessary to consider encapsulating this model in a DSS coupled with the database fed by the extraction schedule and the MOs order book.

Data availability statement

The data supporting this article's results are available in the Mendeley data (doi: 10.17632/5hpbyvv3rt.1). For confidentiality reasons, some data are fictitious. However, the structure of this information is close to that of the actual data.

Figure 1

 1 Figure 1 Caption. The different production configurations in mining industries Figure 1 Alt text. The scheme represents three main production configurations in mining industries, configuration A concerns blending only, configuration B is related to blending raw materials before processing, and configuration C aims to blend after processing raw materials.

  s ability to maintain a competitive advantage is based on its ability to acquire and deploy resources consistently and aligned with the competitive need of the organisation.

Figure 2 Figure 2

 22 Figure 2 Caption. The studied supply chain Figure 2 Alt text. The studied supply chain is composed of five mines, five washing lines, a drying unit, and a Head Station, linked by conveyors of several kilometres. It transforms source ores into merchantable ores for two types of customers delivered by train or pipeline.

j

  Index of output related to an order, with for the order k of the local customer, for the order r of the export-pipeline customers, and for the order p of export-train customers. m Index of mines. h Index of routings. c Index of chemical components. l Index of washing lines.

  ) Relation (3) calculates the weight of the chemical component c characterizing the quality of the WSO obtained from the production of line l for the elementary order k performed for the pipeline . This production transforms SO i (represented by its chemical characteristics ) with routing h (represented by the distortion rate ) for a downstream total weight equal to . enforces the QC respect for local customers for each elementary order k. Recall that the Quality Charter is defined for each chemical component c and for each order j by the interval , while considering the volume Dk of the elementary orders k to prepare for the local customers.

Relation ( 9

 9 ) calculates the weight of the chemical component c characterizing the quality of export-train orders p. This is realized while considering the contributions of raw products/ SO in the first part of relation 9, and of WSO in the second one.(10) Relation (10) enforces respecting the QC for each chemical component c and for the train-

  of the pipeline). With this cycle length, the time horizon used for the tactical planning is 10 cycles (730 hours), which is approximately one month.

Table 1

 1 Caption. Synthetic grid for the analysis of blending literature Table 1 Alt text. The table represents the classification of the analysed articles treating the blending concept, depending on several criteria

, Parallel processors Sequencial processors Williams and Haley 1959

				C		X B	X	X	X
		Sherali and Puri	1993	C		X C	X	X	X	X
		Chanda and Dagdelen	1995	C		X A X		X	X	X
		Shih and Frey	1995	C	X	A X		X	X
		Pendharkar and Rodger	2000	C		X A	X	X	X
		Kumral	2003	Fe		A X		X	X
		Gholamnejad and Kasmaee 2012	Fe		A X		X	X
		Liu and Li	2013	Fe		X A X		X	X
		Siemon et al	2019	Cu		X B	X		X X
	10	Yuan et al	2020	C	X	B	X	X	X
	11	Haonan et al	2020	-	X	A	X	X		X

12 Azzamouri et al 2021 PO₄³⁻ X B X X X 13 Yan et al 2022 C X B X X X X 14 Hilali et al 2022 PO₄³⁻ X B X X X 15 Ahmad et al 2023 C X C X X X 16 US 2023 PO₄³⁻ X C X X X Environmental

Table 2

 2 Caption. Flow characteristicsTable 2 Alt text. The table represents the flow characteristics depending on customer types,

Table 3

 3 Caption. Order books for washing plants and drying plantTable3Alt text. The table represents the components of the proposed sequencing program for the two first and last production cycles, including the volumes to produce, production duration and the starting production dates

	4.2 Other data of the planning problem
	These data relate to MOs and their QCs (section 4.2.1), and to the SOs and their
	transformation by the routing used in the washing plants (section 4.2.2). For confidentiality
	reasons, the different unit costs (	and	) used in the objective function (relation 13) will

Table 7

 7 Caption. Optimal solution extract (Cycle 2 of oder book & MO scenario 1 -Supply scenario 1) Table7Alt text. The table represents the production recipes proposed by the model to satisfy orders to forward via pipeline for the first production cycle, including the starting production dates, volume of SO and WSO, washing line, alternative routings and product quality.

	Production of Internal MO sent by pipe during cycle 1	Production of pipe export MO sent by pipe during cycle 1
	Order k	Start date	# SO	R# L#	SO WSO S Quantity	c=1 (%) Composition c=2 (%) c=3 (ppm) Chemical	order r	Order k	Start date	SO# R# L #	SO WSO S Quantity	c=1 (%) Composition c=2 (%) c=3 (ppm) Chemical
						BPL	MgO	Cd					BPL	MgO	Cd
	1 1			22680	71.99 0.89	14.92	1	12 23 3 8		7560	72.98	0.60 15.48
	2 8			17820	70.96	0.87 14.37		21 38 30 53		8820	72.98 0.60 15.48
	10 17			19440	71.34 0.92 14.77	3	56 96 47 81		7560	72.98	0.60 15.48
	11 23			17820	70.6	0.84 15.07	4	65 111 73 126		10080	72.98 0.60 15.48
	19 32			19440	72.48 0.90 13.88
	20 38			17820	71.26	0.86 12.88
	28 47			19440	72.48 0.90 13.88
	29 53			15840	71.26	0.86 12.88
	35 61			16200	72.48 0.90 13.88
	36 66			15840	71.26	0.86 12.88

Table 8

 8 Caption. Extract of optimal solution for the drying plant focused on the orders that include WSO Table8Alt text. The table represents the production recipes proposed by the model to satisfy the export train orders using WSO (k) produced during cycle 1 in washing plants, and including the volume of SO and WSO, the alternative routings, starting production periods and products quality.

			Production of WSO sent to drying plant		Production of Internal MO sent by train during the first cycle (first orders p that includes WSO produced during cycle 1)
		Order k	Start date	SO# R# L#	SO Quantity WSO S	Order p	Start date	SO#	Order k (WSO)	Line l	SO (ton) Quantity WSO (m3)	S (ton)	c=1 (%) (BPL) Chemical Composition c=2 (%) (MG O) c=3 (ppm) (Cd)
		4 5	11 12	5 1 1 12 1 2 12 1 2 5 1 1	523 941 941 523	450 810 810 450	1260 1260	5 55	6 13 15 12	---5	-2536 --72 --182 -2 -810	3600	71.02 0.6 15.30
	Cycle 1	6 7	13 14	5 1 1 12 1 2 12 1 2 5 1 1	523 941 941 523	450 810 810 450	1260 1260	.. .. .. 6 13 15 7 58	.. ---	.. .. -2536 -.. -72 --182 -	.. 3600	.. 71.02 0.6 15.30 .. ..
		8	15	12 1 2 5 1 1	941 523	810 450	1260	12 … … …	9 …	2 … … -	810 …	…	…	…	…
		9	16	12 1 2 5 1 1	941 523	810 450	1260			5 5	5 6	1 1	--	450 450
		13 14	26 27	5 1 2 5 1 1 5 1 1 5 1 2	941 523 523 941	810 450 450 810	1260 1260	10 77	5 5 5 5	16 24 27 13	1 1 1 2	----	450 450 450 810	3600	72	0.50 15.54
	Cycle 2	15 16	28 29	5 1 2 5 1 1 5 1 1 5 1 2	941 523 523 941	810 450 450 810	1260 1260	11 80	5 6 15 5	26 --17	2 -2027 --810 -19 -2 -810	3600	72	0.53 15.21
		17	30	5 1 2 5 1 1	941 523	810 450	1260			12 13	8 -	2 -17 -	810 -
		18	31	5 1 2 5 1 1	941 523	810 450	1260			15 5	-4	-128 1 -	-450
		22 23	41 42	5 1 1 5 1 2 5 1 1 5 1 2	523 941 523 941	450 810 450 810	1260 1260	12 83	5 5 5 5	14 17 22 23	1 1 1 1	----	450 450 450 450	3600	72	0.50 15.54
	Cycle 3	24 25	43 44	5 1 1 5 1 2 5 1 1 5 1 2	523 941 523 941	450 810 450 810	1260 1260	5 5 … … … WSO produced during cycle 1 WSO produced during cycles> 1 14 2 -810 16 2 -810 … … … … … … … …
		26	45	5 1 2 5 1 1	941 523	810 450	1260
		27		5 1 1 5 1 2	523 941	450 810	1260

Table 7 (

 7 and more extensively in the Mendeley file), a same MO order can be obtained with different SO blends (see for example orders 10, 19 and 28; orders 2,

Characteristics of the MOs

Each order is characterised by a quantity, its availability date, and its MO. This last piece of information was not included in the definition of the order books (in the previous section)

because the tests carried out assigned to each of the 5 order sets 2 sets of MOs randomly generated from the observed demand structures, resulting in a set of 10 order sets defined by dates, quantities and products.

For the export train order, the 8 most requested MOs were retained in these tests and are described in Table 3, together with their QCs, as well as the ones corresponding to the local and export pipeline orders.

Characteristics of the SOs

The washing and drying plant are supplied by 6 mines that produce around 33 SOs in a push flow, the supply of which is considered at the beginning of each day. There is a desynchronisation between the production of a WSO prepared in a washing line and its use in an order of a drying plant, due to the time needed for draining and transport (about 30 hours).

Table 4 shows the composition of some SOs among the 33 used (more details in the Mendeley file), and Figure 2 (in the appendix) shows one of the two scenarios for the evolution of the supply of these SOs, starting from the initial stocks.

Results

The model was tested with 20 problem sets (detailed in the Mendely files) the solutions of which were obtained on a MacBook Air computer with an M2 chip and 24 GB of unified memory, of which 18 GB was allocated to the Parallels virtual machine running the used XPress-IVE optimisation software. which is based on AML-type modelling [START_REF] Fourer | Algebraic modeling languages for optimization[END_REF].

These problems involved around 2,800,000 variables and 5,000 variables; their resolution times were between 1,000 and 5,000 seconds, with gaps less than 0.002 from the theorical best solution.

The numerical results illustrate that the model perfectly meets all the constraints imposed. .d .θ . /


Daphne Vandemeulebroucke
email: daphne.vandemeulebroucke@uantwerpen.be

Maria Batuk

Amirhossein Hajizadeh

Myriam Wastiaux

Pascal Roussel

Joke Hadermann

Incommensurate Modulations and Perovskite Growth in La 𝑥 Sr 2-𝑥 MnO 4-𝛿 Affecting Solid Oxide Fuel Cell Conductivity

Ruddlesden-Popper La 𝑥 Sr 2-𝑥 MnO 4-𝛿 materials are interesting symmetric solid oxide fuel cell electrodes due to their good redox stability, mixed ionic and electronic conducting behavior and thermal expansion that matches well with common electrolytes.

In reducing environments -as at a solid oxide fuel cell anode -the x = 0.5 member, i.e. La 0.5 Sr 1.5 MnO 4-𝛿 , has a much higher total conductivity than compounds with a different La/Sr ratio, although all those compositions have the same K 2 NiF 4 -type I4/mmm structure. The origin for this conductivity difference is not yet known in literature. Now, a combination of in-situ and ex-situ 3D electron diffraction, high-resolution imaging, energy-dispersive X-ray analysis and electron energy-loss spectroscopy uncovered clear differences between x=0.25 and x=0.5 in the pristine structure, as well as in the transformations upon high-temperature reduction. In La 0.5 Sr 1.5 MnO 4-𝛿 , Ruddlesden-Popper n=2 layer defects and an amorphous surface layer are present, but not in 1

Introduction

In solid oxide fuel cells (SOFC), electricity is generated by means of redox reactions, requiring oxygen at the cathode and a fuel -e.g. methane or hydrogen gas -at the anode.

Their electrolytes are solid ceramics with ionic conductivities that increase with temperature. Therefore, the first SOFCs could only operate at very high temperatures: from 750°C to 1000°C. Since then, many efforts have been made to reduce the performance temperature, and intermediate-temperature SOFCs have been created, working between 500°C and 750°C. [START_REF] Cooper | An Introduction to Solid Oxide Fuel Cell Materials[END_REF] One way to optimize the performance, is the use of Mixed Ionic and Electronic Conductors (MIEC) as electrode materials, since they exhibit both electron and oxide ion mobility. [START_REF] Sandoval | Sr, Ca) en vue de leur application en tant que materiaux d'electrode de pile a combustile a oxide solide (SOFC)[END_REF] A particular group of MIECs for symmetric SOFCs -where the cathode and the anode consist of the same material -are the Ruddlesden-Popper (RP) manganites La 𝑥 Sr 2-𝑥 MnO 4-𝛿 . This series structurally belongs to the layered Ki 2 NiF 4 -type RP materials, which can be derived from a perovskite oxide with general formula ABO 3 (Figure 1a). RP oxides consist of an alternation between one rock salt layer AO and 𝑛 perovskite layers ABO 3 , leading to the general formula A 𝑛+1 B 𝑛 O 3𝑛+1 or (AO)(ABO 3 ) 𝑛 with 𝑛 = 1, 2, 3, ... (Figure 1). For the particular composition La 𝑥 Sr 2-𝑥 MnO 4 with 0 ≤ x ≤ 1 and space group I4/mmm, only one perovskite layer is situated in between the rock salt layers (𝑛 = 1), as illustrated in Figure 1b. Here, A is Sr or La, and B is Mn.

It was reported that the La 𝑥 Sr 2-𝑥 MnO 4-𝛿 compositions with 0 ≤ x ≤ 1.4 have comparable thermal expansion properties to most common electrolytes, and possess a good stability up to 800°C in air, which is crucial for their performance as a SOFC cathode. [START_REF] Munnings | Structure, stability and electrical properties of the La(2-x)SrxMnO4 solid solution series[END_REF] Moreover, symmetric SOFCs also require stability in reducing conditions. In-situ powder X-ray diffraction (XRD) and neutron diffraction (ND) showed that La 𝑥 Sr 2-𝑥 MnO 4-𝛿 with 0.25 ≤ x ≤ 0.6 remains stable under flowing hydrogen gas, as in the operational environment at the anode. From this series, La 0.5 Sr 1.5 MnO 4-𝛿 possesses the best combination of conductivities in oxidizing and reducing conditions at 800°C, i.e. 35.6 S cm -1 (air) and 1.9 S cm -1 (3% H 2 /Ar). With these values, it breaks the decreasing (in air) and increasing (in hydrogen gas) conductivity trends of the other compositions with increasing La content. For x= 0.25, 0.4 and 0.6, these are 38.6 S cm -1 , 33.6 S cm -1 and 28.8 S cm -1 in air, and 0.4 S cm -1 , 0.5 S cm -1 and 0.8 S cm -1 in 3% H 2 /Ar, all at 800°C. [START_REF] Sandoval | In depth study of the RuddlesdenPopper LaxSr2-xMnO4 family as possible electrode materials for symmetrical SOFC[END_REF] The reasons for this were not yet uncovered.

On top of that, despite the reported space group stability for 0.25 ≤ 𝑥 ≤ 0.6, the insitu powder XRD and ND experiments by Sandoval et al. [START_REF] Sandoval | In depth study of the RuddlesdenPopper LaxSr2-xMnO4 family as possible electrode materials for symmetrical SOFC[END_REF] displayed complex cell parameter changes upon heating and cooling in reducing atmosphere, that could not be explained by thermal expansion only. During reduction by heating in diluted H 2 , non-linear steep changes happen for cell parameters 𝑎 and 𝑐 between 500°C and 600°C, which are reversed between 250°C and 350°C upon reoxidizing in air. Further, the anisotropic atomic displacement parameters (ADP) gave anomalous values after heating in H 2 : one component of the ellipsoid was significantly larger than expected for thermal expansions, which indicates a structural transformation that could not be further quantified by in-situ powder XRD or ND experiments.

Therefore, we investigated these compounds using single-crystal 3D electron diffraction (3DED). For 3DED, crystals of a few tens of nanometers -sizes from which X-rays and neutrons can only produce powder patterns -already suffice to obtain single-crystal diffraction data. We already showed 5 that in-situ electron diffraction can pick up oxygen vacancy ordering that was overlooked in in-situ XRD or ND experiments. But ordering of oxygen vacancies has a significant effect on ionic transport properties. For instance, for SrCo 0.8 B' 0.2 O 3-𝛿 (with B'= Cr, Fe, Co, Cu) and for La 0.6 Sr 0.4 CoO 3-𝛿 , the transition from a low-temperature vacancy-ordered state to a high-temperature disordered perovskite leads to an increase in oxygen permeability with 5 to 6 orders of magnitude (up to 3• 10 -7 mol cm -2 s -1 ). [START_REF] Kruidhof | Influence of order disorder transitions on oxygen permeability through selected nonstoichiometric perovskite-type oxides[END_REF] With this research, we investigated whether differences in structural order might explain the differences in SOFC electrode performance for La 𝑥 Sr 2-𝑥 MnO 4-𝛿 with different La content. In addition to 3DED, we also performed high-resolution high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM), energy-dispersive X-ray spectroscopy (EDX) and electron energy-loss spectroscopy (EELS) on pristine and high-temperature reduced La 𝑥 Sr 2-𝑥 MnO 4-𝛿 with x = 0, 0.25 and 0.5, both in-situ and ex-situ.

Results

To study potential ordering phenomena upon reduction, La 0.25 Sr 1.75 MnO 4-𝛿 (I4/mmm, a = 3.8324(3) Å, c = 12.422(1) Å) was first annealed in N 2 at 550°C for 1h and then in 5% H 2 /Ar at 700°C for 1h. The prior nitrogen heating cycle was performed to remove any potentially adsorbed water and other molecules from the surface, and did not lead to any structural changes from the pristine state -as checked by 3D electron diffraction (3DED) and powder X-ray diffraction (XRD). After the hydrogen treatment at 700°C, precession 3DED revealed the transformation to an incommensurate 2D modulated structure with cell parameters a = 3.8324 (7) Å and c = 12.6725(5) Å, and superspace group I4/mmm(𝛼𝛼0)0000(𝛼-𝛼0)0000

where 𝛼 = 0.2848 (1). This is illustrated in Figure 2b, 2e and 2h, showing the reconstructed [001] and [010] zones from 3DED, and modulation vectors ⃗ 𝑞 1 and ⃗ 𝑞 2 . A very similar (3+2)D structure was already found for oxygen deficient LaSrCuO 3.5 with in-zone electron diffraction by Hadermann et al., [START_REF] Hadermann | The (3 + 2)D structure of oxygen deficient LaSrCuO3.52[END_REF] with a somewhat different modulation wavelength (𝛼 ≈ 0.22) where the modulation was driven by oxygen vacancy order. Starting from a similar model and using precession 3DED, we could dynamically refine the atomic positions, positional and occupancy modulation parameters and atomic displacement parameters for modulated La 0.25 Sr 1.75 MnO 4-𝛿 to the values listed in the supplementary information. Precessing the electron beam and the method of dynamical refinement are crucial to deal with the effects of multiple scattering in electron diffraction. In Figure 3, the Mn-O plane is shown for the 𝑡 = 0, 𝑢 = 0 section through five-dimensional space. Vacancy ordering occurs for the equatorial oxygen positions, and gives rise to an alternation between manganese octahedra, square pyramids and tetrahedra. A graphical representation of the occupancy modulation function of the equatorial oxygen atoms has been included in the supplementary information. For La 0.5 Sr 1.5 MnO 4-𝛿 (I4/mmm, a = 3.86007(7) Å, c = 12.4135(5) Å), the identical heat treatment leads to a 1D incommensurate modulation, with a slightly longer modulation wave vector ⃗ 𝑞 = 𝛼 (⃗ 𝑎 * -⃗ 𝑏 * ) with 𝛼 = 0.318(2), an orthorhombic superspace group Fmmm(0,0,𝛼)000 and cell parameters a = 5.4537(6) Å, b = 12.711(2) Å and c =5.4403 (5) Å (rotated 45°along the 𝑐 axis with respect to the I4/mmm parent cell). For the x = 0.5 composition, the satellites are much weaker than for the x = 0.25 composition (and even weaker after hydrogen treatment without the N 2 cycle), as can be seen in Figure 2c, 2f and 2i. For this particular crystal, some weak reflections also appear along the ⃗ 𝑎 * + ⃗ 𝑏 * direction in the [001] zone, but they stem from twinning and this composition is not two-dimensionally modulated. First, such reflections are not systematically present in all crystals. Moreover, no satellites are observed that arise from the combination of two different q vectors as e.g. in the [010] zone of 2D modulated La 0.25 Sr 1.75 MnO 4-𝛿 (Figure 2h). As a reference sample, also Sr 2 MnO 4 (I4/mmm, a = 3.78839(6) Å and c = 12.4955(3) Å) was annealed in 5% H 2 /Ar at 550°C for 1h, with prior N 2 heating cycle as described above. This caused a conversion to the known P2 1 /c superstructure of Sr 2 MnO 3.5 as expected from literature 8 9 with a = 6.82 (EDX) confirms the amorphous layer is indeed a lanthanum strontium manganite, but the relative lanthanum concentration of this layer is ⟨𝐿𝑎/𝑆𝑟⟩ = 1.0 (𝜎 = 0.1), which is more than twice as large as in the bulk RP 𝑛 = 1 structure: ⟨𝐿𝑎/𝑆𝑟⟩ = 0.36 (𝜎 = 0.03) (Figure 4b). Note that for the quantification of the composition of the bulk RP n=1 structure, only non-oriented low magnification maps where taken into account. This is because quantification of EDX (as for EELS) of in-zone-oriented crystals is unreliable due to the excitation of guided light modes and relativistic losses. [START_REF] Vatanparast | Bandgap measurement of high refractive index materials by off-axis EELS[END_REF] Additionally, many higher order RP 𝑛 = 2 layer defects were observed in the pristine material -at the surface and in the bulk area -that also contain relatively more lanthanum than the 𝑛 = 1 structure. This can e.g. be seen by the brighter Z-contrast of the A cation layer in between the two perovskite layers in Figure 4c, and in the EDX map in Figure 4d. In some pristine La 0.5 Sr 1.5 MnO 4-𝛿 crystals, perovskite blocks are present that epitaxially grew during synthesis on the {001} face of the RP 𝑛 =1 phase (Figure 4c) and also have a higher lanthanum content than the n=1 RP bulk (Figure 4d).

After annealing La 0.5 Sr 1.5 MnO 4-𝛿 in N 2 and in 5% H 2 /Ar as described above, high-resolution HAADF-STEM also revealed many perovskite domains on the surface of the crystals, as illus- in-situ 3DED using the same reduction treatment in diluted hydrogen gas as above, both with and without prior nitrogen cycle. However, none of the crystals exhibited the satellites observed after the ex-situ reduction. The reason for this is the formation of an unexpected silica shell around the crystals during the in-situ reaction, as revealed by EDX and electron energy-loss spectroscopy (EELS) (see e.g. Figure 5). This shell originates from Si migration to the crystals from the electron transparent silicon nitride window of the in-situ heating chips, likely hindering the reduction of the sample. Nevertheless, the formation of a per-ovskite phase takes place here for both the x = 0.25 and the x = 0.5 compounds. This is evidenced by reflections in the 3DED patterns in agreement with a perovskite structure with a ≈ 3.9 Å. Figure 6 Due to the extra reaction with the silicon nitride window, these in-situ results cannot be used to represent the actual circumstances as found in the applications. Several attempts were made to prevent the formation of the silica shell and to obtain an effective reduction in-situ in the closed cell, unfortunately without success. Details of these attempts can be found in the Supporting Information.

To circumvent this shell formation, and still be able to follow the transformation, we turned to in-situ heating in vacuum, which is well-known to be a reducing atmosphere as well. As a test, the reference sample Sr 2 MnO 4 was successfully reduced to Sr 2 MnO 3.5 at 550°C in vacuum, as its P2 1 /c superstructure could be observed by in-situ 3DED. Next, La 0.5 Sr 1.5 MnO 4-𝛿 was heated in-situ to 700°C in vacuum. No silica shell was observed. However, in-situ 3DED data still only showed the partial transformation to perovskite, but no structural modulation corresponding to an oxygen-vacancy ordering.

In-situ high-resolution HAADF-STEM of one and the same La 0.5 Sr 1.5 MnO 4-𝛿 crystal at room temperature and at 700°C in vacuum -without electron beam exposure in betweenshows that it is the 2-3 nm amorphous surface layer that crystallizes into perovskite, whereas the bulk RP 𝑛 = 1 phase remains unchanged (Figure 7a and7b). Perovskite reflections were never observed at room temperature when using the illumination conditions as we use for 3DED (parallel beam with selected area aperture). So, the 3DED acquisition does not change the sample in a way that would influence the 3DED analysis. HAADF-STEM images of pristine La 0.25 Sr 1.75 MnO 4-𝛿 do not show any amorphous layer or RP 𝑛 = 2 defects (Figure 7c).

There, the RP n=1 bulk phase always stretches until the very edge of the crystals. Nevertheless, in-situ 3DED in diluted hydrogen gas also evidences perovskite formation upon heating to 700°C (Figure 6h).

To determine the manganese valence state -and thus the effectivity of the reduction treatment -monochromated STEM electron energy-loss spectroscopy (mono STEM-EELS) was performed. In Figure 8, the L 2 and L 3 edges of the Mn fine structure are given for La 0.5 Sr 1.5 MnO 4-𝛿 after in-situ heating in vacuum to 700°C (8a) and ex-situ heating in 5% H 2 /Ar to 700°C (8b).

In the in-situ gas heating experiments, the thickness of the double-chip Nano-reactor rendered the signal-to-noise ratio too low for a valid interpretation of the measurements (see Supplementary Information). Since the same structural transformation was observed in the 3DED data for in-situ heating in hydrogen as in vacuum, the mono STEM-EELS spectra for in-situ vacuum heated La 0.5 Sr 1.5 MnO 4-𝛿 are used in this comparison. For this latter case (8a) the Mn L 3 edge is positioned at 643 eV at the outer surface, and gradually shifts to 644 eV at a depth of 60 nm, with an energy resolution of 0.5 eV. Comparing with MnO 2 , Mn 2 O 3 and MnO reference spectra, [START_REF] Tan | Oxidation state and chemical shift investigation in transition metal oxides by EELS[END_REF] this gives a mixture of Mn 3+ and Mn 4+ . However, the Mn L 3 edge of ex-situ annealed La 0.5 Sr 1.5 MnO 4-𝛿 in a 5% hydrogen atmosphere is shifted to 641 eV. This indicates a lowering of the Mn valence to 2+ over the whole edge of the measured crystal (from the surface up to 50 nm into the bulk). Thus, the degree of reduction is much lower for the in-situ vacuum heated material -where indeed no oxygen-vacancy ordering was observed with 3DED -as opposed to the ex-situ reduced sample.

Discussion

Although according to literature [START_REF] Sandoval | In depth study of the RuddlesdenPopper LaxSr2-xMnO4 family as possible electrode materials for symmetrical SOFC[END_REF] Ruddlesden-Popper manganites La 𝑥 Sr 2-𝑥 MnO 4-𝛿 with 0.25 ≤ x ≤ 0.6 have the same I4/mmm structure, the x = 0.5 has a conductivity that breaks In the former case, the L 3 peak shift indicates a mixture of Mn 3+ and Mn 4+ , while for the latter case Mn 2+ is observed.

the trend of the other compositions. Especially in reducing SOFC anode conditions, its conductivity is large in comparison to the compounds with a higher or lower lanthanum content.

With ex-situ 3D electron diffraction (3DED) it was now possible to detect an incommensurate modulation in La 0.25 Sr 1.75 MnO 4-𝛿 and La 0.5 Sr 1.5 MnO 4-𝛿 due to ordering of the oxygen vacancies, when reduced in 5% H 2 at 700°C. While the resulting satellite reflections are very cleary visible in the reconstructed zones from 3DED (see Figure 2), the materials were previously reported to retain oxygen-vacancy disorder upon high-temperature reduction. [START_REF] Sandoval | In depth study of the RuddlesdenPopper LaxSr2-xMnO4 family as possible electrode materials for symmetrical SOFC[END_REF] The satellite reflections in modulated La 0.5 Sr 1.5 MnO 4-𝛿 are much weaker than in modulated La 0.25 Sr 1.75 MnO 4-𝛿 (Figure 2), suggesting that a smaller fraction of the overall crystal transforms into the modulated structure and thus the compound is less ordered. For both samples, 3DED data were repeated with a CCD as well as a direct electron detector under the same illumination conditions, giving systematically the same results. Goff et al. [START_REF] Goff | Defect structure of yttriastabilized zirconia and its influence on the ionic conductivity at elevated temperatures[END_REF] showed that for yttria-stabilized zirconia, the ionic conductivity decreases with an increasing degree of order in the oxygen vacancies. Thus, the decreased oxygen-vacancy order might explain the much higher conductivity for La 0.5 Sr 1.5 MnO 4-𝛿 at 800°C in diluted hydrogen gas (1.9 S cm -1 ) with respect to compositions with higher and lower lanthanum content : (x = 0.25: 0.4 S cm -1 , x = 0.4: 0.5 S cm -1 and x= 0.6: 0.8 S cm -1 ).

The x = 0.5 compound does not only break the conductivity trend with lanthanum doping in reducing conditions, but also in air (x = 0.25: 38.6 S cm -1 , x = 0.4: 33.6 S cm -1 , x = 0.5:

35.6 S cm -1 and x = 0.6: 28.8 S cm -1 ). [START_REF] Sandoval | In depth study of the RuddlesdenPopper LaxSr2-xMnO4 family as possible electrode materials for symmetrical SOFC[END_REF] This might be related to the abundant RP 𝑛 = 2 layer defects in La 0.5 Sr 1.5 MnO 4-𝛿 , whereas they are absent in La 0.25 Sr 1.75 MnO 4-𝛿 . In-situ neutron diffraction studies of the vacancy localization and atomic displacement parameters of the (La,Sr) 𝑛+1 (Co,Fe) 𝑛 O 3𝑛+1 Ruddlesden-Popper series suggest that oxygen transport pathways are rather located in the perovskite layers than the rocksalt layers, causing the RP 𝑛 = 1 structure to have to lowest oxygen mobility. [START_REF] Tomkiewicz | Oxygen transport pathways in Ruddlesden-Popper structured oxides revealed via in-situ neutron diffraction[END_REF] The presence of RP 𝑛 = 2 defects could thus explain why La 0.5 Sr 1.5 MnO 4-𝛿 breaks the downward trend in conductivity in air with increasing x. However, the x = 0.25 composition still has a somewhat higher conductivity in the oxidized form than the x = 0.5 composition, because the effect of the defect structure does not exceed the influence of the doping concentration.

In pristine La 0.5 Sr 1.5 MnO 4-𝛿 , there is also an amorphous 2-3 nm La-rich surface layer. Previously Gonell et al. [START_REF] Gonell | Structure Activity Relationship in Manganese Perovskite Oxide Nanocrystals from Molten Salts for Efficient Oxygen Reduction Reaction Electrocatalysis[END_REF] already reported such an amorphous edge in La 0.5 Sr 1.5 MnO 4-𝛿 formed during synthesis. Crystallization of an amorphous surface layer on a Ruddlesden-Popper manganite into a perovskite phase was observed earlier in RP Pr 0.5 Ca 1.5 MnO 4 by Mierwaldt et al. [START_REF] Mierwaldt | Environmental TEM Investigation of Electrochemical Stability of Perovskite and Ruddlesden-Popper Type Manganite Oxygen Evolution Catalysts[END_REF] after 7 minutes of electron beam exposure in 0.5 Pa H 2 O, but the perovskite did not form in vacuum. This suggests that water vapour played an important role in the formation mechanism. However, for La 0.5 Sr 1.5 MnO 4-𝛿 perovskite growth upon heating to 700°C was also observed in vacuum conditions with HAADF-STEM, and the addition of a molecular sieve to absorb water molecules (in-situ in a diluted hydrogen atmosphere, see Supporting Information for details) did not prevent perovskite formation either. No amorphous surface layer was observed in pristine La 0.25 Sr 1.75 MnO 4-𝛿 , although in-situ 3DED upon heating to 700°C in diluted hydrogen gas also showed perovskite growth. This suggests that in La 0.25 Sr 1.75 MnO 4-𝛿 the perovskite forms from the layered RP 𝑛 = 1 phase.

For both La 0.5 Sr 1.5 MnO 4-𝛿 and La 0.25 Sr 1.75 MnO 4-𝛿 , the creation of perovskite domains can be explained by thermodynamics and their different elemental distribution at the surface.

As shown in Figure 4, pristine La 0.5 Sr 1.5 MnO 4-𝛿 has a lanthanum rich region at the surface compared to the bulk. But the La/Sr ratio has a crucial influence on the stability of phases in the La-Sr-Mn-O system. According to the calculated phase diagrams by Grundy et al. [START_REF] Grundy | Assessment of the La-Sr-Mn-O System. Computer Coupling of Phase Diagrams and Thermochemistry[END_REF] using the compound energy formalism, [START_REF] Hillert | The compound energy formalism[END_REF] the stable coexisting phases at 800°C in reducing atmosphere (log(P(O 2 )= 10 -18 ) for La 0.5 Sr 1.5 MnO 4-𝛿 , La 0.25 Sr 1.75 MnO 4-𝛿 and Sr 2 MnO 4 are SrO, MnO and RP 𝑛 = 1 (La,Sr) 2 MnO 4 . But when the lanthanum content locally gets doubled or more -as seen by EDX at the surface of La 0.5 Sr 1.5 MnO 4-𝛿 in Figure 4 -also the perovskite form (La,Sr)MnO 3 and higher order RP 𝑛 = 2 (La,Sr) 3 MnO 7 become stable. This is why no perovskite formation was observed in the case of Sr 2 MnO 4 . It must be noted that oxygen nonstoichiometry was not taken into account there, due to a lack of thermodynamic literature data for the relevant Ruddlesden-Popper phases.

Upon annealing in-situ in hydrogen gas, none of the samples displayed oxygen vacancy ordering, and EDX detected the formation of a shielding shell containing silicon. This layer around the crystals stems from the silicon nitride window of the heating chip on which the sample is drop casted for in-situ heating experiments. Wang et al. [START_REF] Wang | Direct Environmental TEM observation of sil-24[END_REF] already recorded the migration of SiO 2 from the support to diverse metal nanoparticles like Pt, Co, Ni, ... upon heating to 750°C in 10% H 2 /Ar with in-situ high-resolution TEM images and EDX. Although the vacuum heating chips contain similar silicon nitride electron transparent windows as the gas heating chips, no such shell was detected by EDX upon heating in vacuum. However, as proven by mono STEM-EELS and in-situ 3DED, the high-temperature vacuum conditions (700°C-800°C) did not suffice to effectively reduce the x = 0.25 and the x = 0.5 compounds, although Sr 2 MnO 4 was successfully reduced to Sr 2 MnO 3.5 in vacuum at 550°C. Probably, the reaction with Si takes place in both experimental in-situ set-ups -gas and vacuumbut the silicon migration happens more slowly under vacuum conditions (10 -7 mbar) than near-atmospheric pressure (± 700 mbar). Because of the lower reduction temperature for the undoped x = 0 material compared to the other samples (550°C versus 700°C), oxygen vacancies could apparently still be created in Sr 2 MnO 4 in vacuum before the silicon shell got too thick to prevent this.

The perovskite formation evidenced in our experiments, is not reversible upon either cooling or another heating cycle in oxidizing conditions. Therefore, it is important to take this effect into account in degradation studies of the materials as SOFC electrodes. But as mentioned, a higher amount of perovskite blocks has a positive effect on oxygen mobility, [START_REF] Tomkiewicz | Oxygen transport pathways in Ruddlesden-Popper structured oxides revealed via in-situ neutron diffraction[END_REF] so this phenomenon might also contribute to the conductivity of the La 𝑥 Sr 2-𝑥 MnO 4-𝛿 series in a SOFC. Further research is required to determine the precise effect of perovskite formation during SOFC cycling on the cell's performance and lifetime.

Conclusion

Ruddlesden-Popper La 𝑥 Sr 2-𝑥 MnO 4-𝛿 solid oxide fuel cell (SOFC) electrode materials were examined for x = 0, 0.25 and 0.5 by different ex-situ and in-situ electron microscopy techniques, to examine the structural reasons behind the high conductivity for the x = 0.5 composition compared to compositions with a higher or lower La content, especially in reducing atmosphere as at the anode. 3D electron diffraction (3DED) discovered a structural transformation to an incommensurate 2D (La 0.25 Sr 1.75 MnO 4-𝛿 ) and 1D ( La 0.5 Sr 1.5 MnO 4-𝛿 ) modulated structure upon annealing at 700°C in 5% H 2 /Ar. This was previously undetected with powder X-ray and neutron diffraction. The systematically weaker satellites for x = 0.5 point to a lower degree of oxygen vacancy order, which can lead to a higher conductivity in reducing anode conditions. [START_REF] Goff | Defect structure of yttriastabilized zirconia and its influence on the ionic conductivity at elevated temperatures[END_REF] In pristine La 0.5 Sr 1.5 MnO 4-𝛿 , a 2-3 nm amorphous surface layer is systematically observed by high-resolution HAADF-STEM, as well as many higher-order RP 𝑛 = 2 layer defects. The presence of these defects can also play a role in the enhanced conductivity, since they contain more perovskite blocks which are assumed to be the oxygen transport pathways, [START_REF] Tomkiewicz | Oxygen transport pathways in Ruddlesden-Popper structured oxides revealed via in-situ neutron diffraction[END_REF] and no such 𝑛 = 2 defects are observed in La 0.25 Sr 1.75 MnO 4-𝛿 . Upon ex-situ or in-situ annealing in reducing environment at 700°C -diluted hydrogen gas or vacuum -also perovskite domains are created. In-situ high-resolution HAADF-STEM shows that for La 0.5 Sr 1.5 MnO 4-𝛿 , these domains originate from the crystallization of an originally amorphous surface layer. Such perovskite formation at high temperature is important to take into account in conductivity and degradation studies for applications as an SOFC electrode. However, due to silicon migration of the dedicated heating chips, it was not possible to fully reduce the materials in-situ and monitor the transformation to the modulated structure by in-situ 3DED. The precise mechanism leading to the perovskite growth is not clear, but based on thermodynamics of the La-Sr-Mn-O system, [START_REF] Grundy | Assessment of the La-Sr-Mn-O System. Computer Coupling of Phase Diagrams and Thermochemistry[END_REF] pellets of approximately 10 mm diameter. Then, the powders were calcined using three successive heating cycles at 1300 °C for 6h for x = 0.5. The x = 0.25 composition required three cycles at 1300°C for 6h, followed by 3 cycles at 1450°C for 6h and 1 cycle at 1450°C for 18h, performing intermediate grinding steps in all cases (note that pellets were always put on a sacrificial bed of powder to avoid any possible diffusion between the alumina crucible and the pellet).

Powder X-ray Diffraction

After synthesis, the quality of the samples was checked with powder X-ray diffraction (XRD) using a Huber powder diffractometer with Cu-K 𝛼1,2 equipped with a G670 Imaging Plate Guinier Camera. Powder XRD for ex-situ hydrogen annealed La 0.25 Sr an admixture was created, consisting of the more stable 𝛼-phase, i.e. a mixture of SrO and Sr 7 Mn 4 O 15 (P2 1 /c, a = 6.7931(4) Å, b = 9.6120(7) Å, c = 10.4259(5) Å, 𝛽= 92.053(5)°).

But since 3DED series of each crystal were also acquired in the pristine state, it was possible to select only the 𝛽-phase for tracking during heating. Also the ex-situ annealed samples were examined with powder XRD (see Supplementary Information for details of the Le Bail fit). All reported cell parameters were determined from powder XRD.

TEM Sample Preparation

After crushing the sample powder with mortar and pestel for about one minute, a suspension in ethanol was made and sonicated for about ten minutes in an ultrasonic bath, cooled with icepacks to prevent sample heating. This suspension was drop casted on a carbon coated Cu or Au grid, a DensSolutions EDX compatible Nano-Reactor consisting of an O-ring sealed top and bottom chip (gas heating) or a DensSolutions Nanochip for heating (in vacuum). Both types of chips contain electron transparent silicon nitride windows. After drop casting the sample, the (bottom) chip was plasma cleaned for 4 times 5 seconds in a 25% O 2 /Ar mixture at 30% power to reduce contamination in the transmission electron microscope (TEM).

3D Electron Diffraction (3DED)

3DED data were acquired with a CCD camera (Gatan US1000XP) in a stepwise manner with tilt steps of 0.5°, or -for the dynamical refinement of ex-situ reduced La 0.25 Sr 1.75 MnO 4-𝛿with a direct electron detector (ASI CheeTah) with a 1°tilt step and 1°precession semi-angle.

The total angular tilting range was about -20°to 20°for the DensSolutions Climate holder (gas heating), -30°to 30°for the DensSolutions Wildfire heating holder (vacuum heating)

and -70°to 70°for the Fischione tomo holder (ex-situ 3DED). All 3DED experiments were recorded in TEM mode at a Thermo Fisher Tecnai G2 or Titan 3 at 200 kV and 300 kV respectively. Either a 200 nm selected area aperture or a 300-600 nm parallel beam was used, depending on the crystal size. The acquisition was done manually (total acquisition about 30'-45') or semi-automatically, using either an in-house written Digital Micrograph script that allows intermediate manual crystal position adjustment (total acquisition 15'-20'), or the fast-ADT software 19 with prior crystal tracking in image mode (total acquisition about 10'). If specified explicitly, the data were acquired while precessing the beam at 150

Hz with a 1°semi-angle, using the Nanomegas system. After data acquisition, all diffraction patterns were processed with the PETS2 software 20 to reconstruct the three-dimensional reciprocal space and make two-dimensional reconstructions of selected crystallographic zones.

Dynamical refinement was done with Jana2020 including Dyngo. 21 In-Situ Gas Electron Diffraction

In-situ gas experiments were performed using the Climate single-tilt holder and an EDX compatible Nano-Reactor from DensSolutions, creating a 10 𝜇m thick sealed volume. Before heating in gas, 3DED series of the pristine sample were taken at room temperature in vacuum (10 -7 mbar), in air or nitrogen gas (700 mbar). As a reducing agent, H 2 was diluted with He or Ar (concentration explicitly mentioned). Before introducing the gases, each gas line was vacuum pumped 1 to 3 times in order to eliminate as much remaining oxygen as possible.

Inside the sealed Nano-Reactor, the gas pressure was 700 mbar, and the gas flow varied

Figure 1 :

 1 Figure 1: Schematic representation of a single perovskite with chemical formula AMnO 3 (a) and Ruddlesden-Popper structures A 2 MnO 4 with 𝑛 = 1 (b) and A 3 Mn 2 O 7 with 𝑛 = 2 (c). Here, A is Sr or La, and B is Mn.

  (1) Å, b = 10.89(1) Å, c = 10.95(2) Å and 𝛽 = 113.5(2)°, as in Figure 2a, 2d and 2g (main reflections in I4/mmm in white, two twins of P2 1 /c in yellow and green). The cell declared in the original paper is 𝑎 = 1 2 (-𝑎 𝑡 -𝑏 𝑡 + 𝑐 𝑡 ), 𝑏 = 2(-𝑎 𝑡 + 𝑏 𝑡 ), 𝑐 = 2(𝑎 𝑡 + 𝑏 𝑡 ) (with the index 𝑡 referring to the tetragonal subcell). The latter two equations correspond to a two-dimensional commensurate modulation with vectors 𝑞 1 = 𝛼 (-⃗ 𝑎 𝑡 * + ⃗ 𝑏 𝑡 * ) and 𝑞 2 = 𝛼 (⃗ 𝑎 𝑡 * + ⃗ 𝑏 𝑡 * ) where 𝛼 = 0.25, similar to the one we observe for La 0.25 Sr 1.75 MnO 4-𝛿 , but commensurate instead of incommensurate. Therefore, that cell could be described by a supercell in the original paper. The first equation implies an additional shift of the whole vacancy ordered layer over tions with higher lanthanum content x = 0.75 and x = 1, i.e. La 0.75 Sr 1.25 MnO 4-𝛿 (I4/mmm, a =3.81784(4) Å and c = 12.9040(3) Å) and LaSrMnO 4-𝛿 (I4/mmm, a = 3.81624(2) Å and c = 13.1324(2) Å) were heated to 700°C in 5% H 2 /Ar after a prior nitrogen cycle at 550°C. This gave the cell parameters a =3.8224(2) Å and c = 12.84(1) Å for La 0.75 Sr 1.25 MnO 4-𝛿 , and a =3.80592(7) Å and c = 13.1152(4) Å for LaSrMnO 4-𝛿 , but did not lead to any structural change to the space group observable by 3DED.

Figure 2 :

 2 Figure 2: Reconstructed [001] and [010] zones from 3DED for annealed La 𝑥 Sr 2-𝑥 MnO 4-𝛿 at 700°C in 5% H 2 /Ar with x = 0 (d, g), 0.25 (e, h) and 0.5 (f, i). The main reflections from I4/mmm are indexed in white with 3 indices hkl, while the satellites are indexed by 4 or 5 indices and q vectors are indicated by arrows. Two twins of P2 1 /c are indexed in green and yellow. In a-c, details from the [001] zones in d-f are given to illustrate the trend in the modulation wavelength. 𝛼 is 0.25, 0.29 and 0.32 for x = 0, 0.25 and 0.5 respectively.

Figure 3 :

 3 Figure 3: Schematic representation of the manganese coordination for the 𝑡 = 0, 𝑢 = 0 section through five-dimensional space of reduced La 0.25 Sr 1.75 MnO 4-𝛿 , seen along 𝑐. A threshold of 56% is applied to plot the oxygen position as filled. The vacancy ordering causes a pattern of octahedra and square pyramids.

Figure 4 :

 4 Figure 4: a-d: HAADF-STEM images and EDX maps (in counts) of pristine La 0.5 Sr 1.5 MnO 4-𝛿 . In the EDX maps, lanthanum is represented as blue, strontium as green. In the models on top of the high-resolution images, La/Sr atoms are shown in green, Mn atoms in pink. (a,b) An amorphous layer is visible at the surface (red arrow) with a higher La content than the bulk structure, while (c,d) some crystals show perovskite on the edge, and many show Ruddlesden-Popper (RP) 𝑛 = 2 layer defects, both in the bulk as at the surface. All areas deviating from RP 𝑛 = 1 are La-rich. e: HAADF-STEM image of the [110] zone of La 0.5 Sr 1.5 MnO 4-𝛿 , first annealed at 550°C in N 2 and then at 700°C in 5% H 2 /Ar. Perovskite domains are observed here as well, but instead of sharp domain boundaries, a distorted transition region of up to 2 nm is present.

  shows the [001] and [100] reconstructed zones from the same La 0.5 Sr 1.5 MnO 4-𝛿 crystal (Figure6a, b, d, e) and La 0.25 Sr 1.75 MnO 4-𝛿 crystal (Figure6g, h) at room temperature before heating and at 700°C in 5% H 2 /Ar (after the heating cycle in nitrogen). Reoxidation by another heating cycle in 20% O 2 or cooling in 20% O 2 to room temperature did not recover the original RP 𝑛 = 1 structure, so the perovskite formation is not reversible. However, the undoped x = 0 composition did not show any perovskite reflections upon in-situ reduction.

Figure 5 :

 5 Figure 5: HAADF-STEM image and elemental EDX maps of two La 0.5 Sr 1.5 MnO 4-𝛿 crystals after in-situ heating to 700°C in 5%H 2 /Ar. All maps are given in counts. On the bottom, the deconvoluted EDX spectra are shown for three regions indicated in red on the HAADF-STEM image. The Ar peak is from the gas environment, N and a part of the Si stem from the support window. A silica shell is formed around the crystals.

Figure 6 :

 6 Figure 6: Experimental reconstructed [001] and [100] zones from 3DED and simulations. La 0.5 Sr 1.5 MnO 4-𝛿 at room temperature in the pristine state in air (a, d) and at 700°C in 5% H 2 /Ar (b, e). La 0.25 Sr 1.75 MnO 4-𝛿 at room temperature in the pristine state in air (g) and at 700°C in 5% H 2 /Ar (h). The simulated [001] and [100] zones of the multiphase crystal consisting of the RP 𝑛 = 1 and the perovskite structure (c,f). I4/mmm reflections are indexed in white, newly appeared perovskite reflections in green.

Figure 7 :

 7 Figure 7: High-resolution HAADF-STEM images. (a): Pristine La 0.5 Sr 1.5 MnO 4-𝛿 at room temperature. (b): The same crystal in-situ heated in vacuum at 700°C. In (b), perovskite domains (indicated as p) were created where the amorphous phase was previously present in (a) (red arrow). (c): Pristine La 0.25 Sr 1.75 MnO 4-𝛿 where no amorphous phase or RP 𝑛 = 2 layer defects are observed.

Figure 8 :

 8 Figure 8: The L 2 and L 3 edge of the Mn fine structure from mono STEM-EELS of (a) La 0.5 Sr 1.5 MnO 4-𝛿 after in-situ heating to 700°C in vacuum and (b) La 0.5 Sr 1.5 MnO 4-𝛿 afterex-situ heating to 700°C in 5%H 2 /Ar. In the former case, the L 3 peak shift indicates a mixture of Mn 3+ and Mn 4+ , while for the latter case Mn 2+ is observed.

  an important role is played by the La rich surface -as observed by EDX -and different structural phases are stable at the edge compared to the bulk structure in reducing environment. To completely understand this phenomenon, further research has to be performed, especially into the experimental set-up for in-situ electron microscopy, so that the reaction with silicon at high-temperatures can be avoided for this group of manganites and individual crystals can be tracked throughout the reaction in actual SOFC anode conditions. MnO 4 , La 0.25 Sr 1.75 MnO 4-𝛿 and La 0.5 Sr 1.5 MnO 4-𝛿 were synthesized by means of the solid state reaction. For Sr 2 MnO 4 , stoichiometric amounts of SrCO 3 (Sigma Aldrich 99.9%) and Mn 2 O 3 (Sigma Aldrich 99.9%) powder were pressed into pellets of 1 cm in diameter using a hydraulic press. These pellets were heated for 18h hours at 1500°C in air.For La 0.25 Sr 1.75 MnO 4-𝛿 and La 0.5 Sr 1.5 MnO 4-𝛿 , stoichiometric amounts of La 2 O 3 (Alfa Aesar 99.9%), SrCO 3 (Sigma Aldrich 98%) and MnCO 3 (Sigma Aldrich 99.9%) were mixed and milled in an agate mortar for 2 hours. The resulting powders were uniaxially pressed into

	Experimental
	Synthesis
	Sr 2

  1.75 MnO 4-𝛿 was performed with a high-flux Rigaku rotated Cu anode with Ni filter in Bragg-Brentano geometry. For as-synthesized Sr 2 MnO 4 , it was determined with XRD and Rietveld refinement, that apart from the intended 𝛽-Sr 2 MnO 4 (I4/mmm, a = 3.78839(6) Å and c = 12.4955(3) Å)

https://doi.org/10.26434/chemrxiv-2023-s7m48 ORCID: https://orcid.org/0000-0002-4511-4410 Content not peer-reviewed by ChemRxiv. License: CC BY-NC-ND 4.0

(-𝑎 𝑡 -𝑏 𝑡 + 𝑐 𝑡 ). Due to the glide plane perpendicular to 𝑐 𝑡 with a translation along 𝑎 𝑡 + 𝑏 𝑡 , satellites in the ⃗ 𝑎 * 𝑡 + ⃗ 𝑏 * 𝑡 direction are extinct (Figure2d). Additionally, two more composi-6 https://doi.org/10.26434/chemrxiv-2023-s7m48 ORCID: https://orcid.org/0000-0002-4511-4410 Content not peer-reviewed by ChemRxiv. License: CC BY-NC-ND 4.0

Acknowledgement

The authors thank Michael Hayward for the synthesis of La 0.75 Sr 1.25 MnO 4-𝛿 and LaSrMnO 4-𝛿 , and for his help regarding the use of zirconium for oxygen molecule absorption while heating in-situ, Olesia Karakulina for providing the smoothing script for EELS visualisation and Nicolas Gauquelin for his help with the mono STEM EELS acquisition. This research was financially supported by FWO I003218N, University of Antwerp BOF TOP 38689 and the European Commission NanED Grant number 956099.

between 0.1 ml (pure argon) and 0.5 ml (pure helium) per minute. Detailed descriptions of all in-situ gas heating experiments are provided in the supplementary information.

High-resolution HAADF-STEM

High-resolution high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) images were acquired at 300 kV with a Thermo Fisher Titan 3 instrument. For the in-situ HAADF-STEM experiments in vacuum, the double tilt heating holder from DensSolutions was used, and images were taken at room temperature and at 700°C.

(Monochromated STEM) Eelectron Energy-Loss Spectroscopy (EELS) (Monochromated STEM) electron energy-loss spectroscopy (EELS) experiments were performed at a Thermo Fisher Titan 3 at 300 kV with a Quantum 966 or Enfinium Gatan Image Filter and a US1000XP CCD camera. If the monochromator was used, it was excited to 0.7.

For energy calibration, dual EELS was performed to include the zero-loss peak.

Energy-Dispersive X-ray Spectroscopy (EDX)

Energy-Dispersive X-ray Spectroscopy (EDX) mapping was performed in STEM mode at 300 kV at a Thermo Fisher Titan 3 instrument or at 200 kV at a Tecnai G2 with a Super X detector. All spectra were processed using the Esprit software. The additional EDX maps in the Supporting Information were taken at a Thermo Fisher Quanta 250 FEG Scanning Electron Microscope at 20 kV, and processed using the Aztec software. icon diffusion-induced strong metal-silica interaction for boosting CO2 hydrogenation.