domain: stat info

text:
Akilimali Pascal

Doctorant Bamalembuko

Prof Expédit

Wakitwanga Sindano

Enseignant-Chercheur

P O Paulin
email: paulinbapo@gmail.com

Bapolisi Bahuga

P A Deogratias

Mbilizi Mwisimbwa
email: mbilizidembi@gmail.com

Kasambi Bally
email: ballykasambi@gmail.com

Balimwengu

VALIDATION D'UN ENVIRONNEMENT INFORMATIQUE INTERACTIF « AKBAL » D'AIDE A LA REVISION-APPRENTISSAGE A L'ECOLE MATERNELLE. VALIDATION OF THE "AKBAL" INTERACTIVE COMPUTER ENVIRONMENT FOR REVISION AND LEARNING IN NURSERY SCHOOLS

Keywords: Exercices informatisés, logiciels éducatifs, exercices interactifs, évaluation de logiciels éducatifs, environnement d'apprentissage informatique Computerized exercises, educational software, interactive exercises, evaluation of educational software, computer learning environment

Cette recherche présente le résultat d'évaluation d'un environnement informatique dédié à la révision-apprentissage d'enfants d'âge de l'école maternel en RDC, ville de Bukavu, dans la commune urbaine d'Ibanda. L'évaluation a consisté à soumettre les situations ludopédagogiques interactives à l'appréciation par des juges enseignantes d'école maternelle, experts psychopédagogues et didacticiens de leur conformité au programme d'enseignement national d'enseignement maternel en conformité aux différents critères ergonomiques, pédagogiques et technologiques de validité d'un logiciel pédagogique. Pour quantifier de la concordance des opinions émises par des évaluateurs sur le degré de satisfaction (validité) ou acceptabilité de l'environnement d'exercices AKBAL, nous avons appliqué les tests statistiques kappa de Fleiss sur des données quantitatives récoltées auprès de 32 juges au moyen du logiciel statistique SPSS v26, généré les coefficients de Kappa de Fleiss et les tableaux de corrélations inter-variables pour mesurer la concordance ou le degré d'accord entre les juges/évaluateurs pour les valeurs ergonomiques, les valeurs psycho pédagogiques et technologiques de trois modules d'exercices interactifs conçus pour accompagner les activités pluridisciplinaires de la section. Les juges évaluateurs ont été à l'unanimité d'accord sur les critères de validité des composants de l'environnement d'apprentissage, exprimé à travers le coefficient Kappa de degré moyen de Fleiss k=0,508.

Introduction

Depuis l'avènement de l'introduction du programme de la discipline informatique [PNEM 2013], les enseignants se heurtent aux multiples difficultés de se créer d'eux-mêmes des situations d'enseignement d'informatique ou utiliser des outils disponibles, jugés plus intelligents et inadaptés tels que les logiciels offices de l'environnement Windows avec les logiciels bureautiques. L'état de lieu d'utilisation les ressources informatisés dans certaines écoles primaires, fait remarquer qu'il existe des petits logiciels offrants des activités plus ludiques que pédagogiques et non conçu en contexte du programme en vigueur comme ce le cas sous d'autres cieux [START_REF] Belabbes Sanaa | L'importance des activités ludiques dans l'enseignement/apprentissage du vocabulaire.-Exemple des apprenants de 1ére année moyenne[END_REF][START_REF] Bugmann | Chronique• Technologies en éducation[END_REF][START_REF] Ferone | Numérique et apprentissages : Prescriptions, conceptions et normes d'usage[END_REF][START_REF] Komis | Une analyse cognitive et didactique du langage de programmation ScratchJr[END_REF][START_REF] Porcher | Quels logiciels installer sur les ordinateurs de l'école?-Circonscription de Senlis[END_REF][START_REF] Préat | Les pratiques ludiques des enseignants et enseignantes du primaire[END_REF][START_REF] Rousson | UN MODELE DE CONCEPTION D'UN JEU-SITUATION[END_REF]. Cette étude est partie alors de ce manque des ressources interactives adaptées, répondant aux aspirations des directives méthodologiques et objectifs du PNEM 2021 stipulant que les encadreuses de l'école maternelle et primaire doivent recourir à certains logiciels Ludo-pédagogiques pour leurs activités de cours d'informatique et faciliter l'apprentissage des autres disciplines de base. C'est dans le processus d'intégration des activités de la discipline informatique, qu'un environnement AKBAL doté des exercices (ou situations pédagogiques numérisées) interactifs a été conçu. Après la conception, nous avons soumis cet environnement de révision-apprentissage à l'appréciation/validation au moyen des critères scientifiques de niveau ergonomique, pédagogique et technologique de trente-deux juges (c'est-à-dire 32 évaluateurs). Ces derniers se sont accordés sur l'acceptation d'AKBAL en tant que ressource d'enseignement-apprentissage [START_REF] Scapin | Ergonomic criteria for evaluating the ergonomic quality of interactive systems[END_REF][START_REF] Bach | Critères Ergonomiques pour les Interactions Homme-Environnements Virtuels : Définitions, justifications et exemples[END_REF][START_REF] Bastien | The ergonomic criteria and the ISO/DIS 9241-10 dialogue principles : A pilot comparison in an evaluation task[END_REF].

Tous les logiciels conçus ne sont pas forcément adaptés selon un contexte d'utilisation présagé. Certains sont purement ludiques, d'autres dans des contextes d'éducation étrangère [START_REF] Depover | Pour une appropriation éducative réelle des nouveaux outils multimédias par les pays en voie de développement[END_REF][START_REF] Depover | Les TIC ont-elles leur place en milieu scolaire africain?[END_REF][START_REF] Pingwinde | B@angr-bulga un environnement pédagogique informatisé pour l'apprentissage de l'histoire de la colonisation africaine RESSOURCES[END_REF][START_REF] Guay | La lecture interactive : Un outil de développement et d'adaptation. Langage et littératie chez l'enfant en service de garde éducatif[END_REF] (Crozat, Trigano, et al., 1999) pour l'ensemble et d'autres auteurs [START_REF] Bach | Critères Ergonomiques pour les Interactions Homme-Environnements Virtuels : Définitions, justifications et exemples[END_REF], le logiciel est pris et vu sous différents angles comme un tout composé de plusieurs facettes, composantes ou dimensions. Ces composants sont à leurs tour détaillés en de sous critères ou indicateurs sousjacents que nous rapprochons à la structure du model Technology Adoption Model (TAM) [START_REF] Silva | Information seeking behavior and technology adoption: Theories and trends[END_REF] ou le facteur ergonomique [START_REF] Tricot | Utilité, utilisabilité, acceptabilité : Interpréter les relations entre trois dimensions de l'évaluation des EIAH[END_REF] est associé à la composante factorielle d'utilité perçue, le facteur psycho-technologiques est associé à la fois à la composante factorielle d'utilisabilité perçue et la composante risque pressenti, le facteur pédagogique (Crozat, Hû, et al., 1999) englobant à la fois la composante factorielle d'efficacité ou pertinence perçue de contenus situations pédagogiques, et la composante au niveau de motivation perçue [START_REF] Hû | Une aide à l'évaluation des logiciels multimédias de formation[END_REF].

Nous nous inspirons alors du modèle TAM de Davis [START_REF] Rose | Predicting general IT use : Applying TAM to the Arabic world[END_REF] pour structurer les parties de la grille d'évaluation en intégrant les trois grands aspects : ergonomiques, pédagogiques, technologiques de logiciel pour Crozat et Hû (1999) puis les jumelons aux différentes composantes du modèle TAM (utilité perçue, utilisabilité perçue, pertinence perçue de contenu, motivation perçue, le risque perçu.). Nous définissons des méta-critères caractéristiques d'un bon logiciel pédagogique, les apprêtons à la vérification de leur cohérence et corrélations quelles entretiennent ensemble pour exprimer une convergence à l'acceptation et par conséquent, l'adoption ou rejet du logiciel en tant qu'une technologie éducative.

Démarches méthodologiques

La démarche est incrémentale : La conception des situations pédagogiques interactives en prenant en charge les critères et spécifications ergonomiques, pédagogiques et psychotechnologiques-la soumission du prototype au test hors contexte par les juges experts-la réintégration au prototype des nouvelles spécifications, critiques et suggestions des experts pour l'amélioration des modulesle test final et expérimentation contrôlée hors contexte en milieu familial (en classe).

Au moyen d'une grille de 23 items/critères (c'est-à-dire qu'un item montre un aspect d'un logiciel) groupés en 5 facteurs, les juges ont évalué après expérimentation dans des ateliers, 3 modules de maternelle 1 (Mat1), Maternelle (Mat2), Maternelle (Mat3). Les 32 enseignants qui participent à l'étude sont choisis au hasard parmi les 50 enseignants d'enseignement maternel, primaire, secondaire et universitaire (c'est-à-dire la population totale). Un petit Ensemble/groupe différent de 4 juges non-uniques a été choisis respectivement parmi les 32 pour évaluer chacun 1 module, puis quatre autres enseignants sélectionnés au hasard ont évalué le module suivant, et ainsi de suite, jusqu'à ce que les 3 modules aient été évalués par 32 juges experts. Nous utilisons le coefficient kappa de Fleiss pour mesurer le niveau d'accord entre les évaluateurs non uniques.

Méthodologie d'analyse du coefficient Kappa de Fleiss

Pour déterminer le niveau d'accord entre les juges évaluateurs d'AKBAL, nous avons utilisé le test statistique kappa de Fleiss [START_REF] Falotico | Fleiss' kappa statistic without paradoxes[END_REF][START_REF] Senn | Review of Fleiss, statistical methods for rates and proportions[END_REF] qui est une mesure de l'accord inter-évaluateurs utilisé pour déterminer le niveau d'accord entre deux ou plusieurs évaluateurs dont la variable est mesurée sur une échelle catégorielle.

Pour appliquer ce test, nous avons tenu à respecter les exigences/hypothèses d'analyse statistique de Fleiss de kappa suivant :

Respect des Exigences de base et hypothèses du kappa de Fleiss

Le kappa de Fleiss [START_REF] Statistics | Fleiss' kappa using SPSS Statistics. Statistical tutorials and software guides[END_REF] 1) 4juges--->mat1 4) 4juges--->mat1 7) 4juges--->mat1 12 grilles de mat1

2) 4juges--->mat2 5) 4juges--->mat2 8) 4juges--->mat2 12 grilles de mat2

3) 4juges--->mat3 6) 4juges--->mat3 8 grilles de mat3 2.1.3. L'équation [START_REF] Fleiss | Measuring nominal scale agreement among many raters[END_REF] L'équation Kappa est définie comme :

k = P ̅ -P ̅ e 1-P ̅ e (1)
Soit N le nombre total de sujets, soit n le nombre de classification par sujet, et soit k le nombre de catégorie dans laquelle les attributions sont faites. Les sujets sont indexés par i = 1, ... N les catégories sont indexées par j = 1, ... k. Soit pij qui représente le nombre d'observateurs qui attribuent le i-ème sujet à la j-ème catégorie [START_REF] Vanbelle | Accord entre observateurs et coefficient Kappa de Cohen[END_REF].

Calculons d'abord pj, la proportion de toutes les attributions à la j-ème catégorie :

N= nombre total de sujets/items évalués n = nombre de juges évaluateurs K=nombre de catégories nominales (pas du tout d'accord, pas d'accord, neutre, d'accord, tout à fait d'accord.

P j = 1 Nn ∑ p i N i-1 ; 1 = ∑ P j k j-1 (2)
Calculons maintenant Pi, qui représente à quel point les observateurs sont d'accord entre eux pour le i-ème sujet [START_REF] Vanbelle | Accord entre observateurs et coefficient Kappa de Cohen[END_REF] :

P i = 1 n(n -1) ∑ p j k j=1 (p j -1) = 1 n(n -1) ∑(p 2 j -n k j=1 ) = 1 n(n-1) [(∑ p 2 j) -(n)] k j=1 (3)
Maintenant calculons P ̅ , la moyenne de 's, et P ̅ eutilisé dans la formule de k

P ̅ = 1 n ∑ P i N i=1 (4) = 1 Nn(n -1) (∑ ∑ n 2 ij -Nn) k j=1 N i=1
P ̅ e = ∑ P 2 k j=1 j (5)

Groupons ( 4) et ( 5)

k = P ̅ -P ̅ e 1 -P ̅ e
Le facteur 1 -P ̅ e ̇ donne le degré de concordance qui est réalisable au-delà du hasard, et, P ̅ -P ̅ e donne le degré de concordance réellement atteint au-dessus du hasard, si les observateurs sont en accord complet, alors k=1. S'il n'y a pas de concordance parmi les observateurs (autre que ce qui aurait pu être atteint par hasard) alors k≤0 [START_REF] Haley | Kappa coefficient calculation using multiple ratings per subject : A special communication[END_REF][START_REF] Kılıç | Kappa testi[END_REF][START_REF] Strube | A general program for the calculation of the kappa coefficient[END_REF].

C

  'est dans ce cadre que l'environnement AKBAL a été conçu pour répondre à ce besoin courant et fréquent dans l'enseignement maternel. Cet environnement interactif doté des situations interactives pédagogiques destinées à la révision-apprentissage d'activités pluridisciplinaires des enfants d'école maternelle en contexte congolais. Il [AKBAL] facilite l'intégration des connaissances spécifiques de la discipline informatique et appui l'application effective des directives méthodologiques du nouveaux Programme d'Enseignement National de Maternel en vigueur depuis octobre 2022 (P. AKILIMALI & B. KASAMBI, 2023). L'environnement AKBAL est-il valide et adapté pour faciliter l'intégration effective des activités informatiques à l'école maternelle ? Nous avions émis l'hypothèse selon laquelle l'environnement AKBAL serait valide et adapté aux critères théoriques de validité ergonomique, pédagogique et technologique reconnus à un logiciel pédagogique. Et permettrait d'offrir des situations interactives pédagogiques basées sur le programme en vigueur à l'école maternelle. Nous structurons cette étude en quatre points dont le fondement didactique et revue de la littérature de la validation d'AKBAL ; la démarche méthodologique de validation de notre environnement en respectant les critères d'utilisation du coefficient de Fleiss de Kappa ; les résultats d'analyse statistique des valeurs du coefficient Kappa de Fleiss pour différents facteurs d'utilité perçue, utilisabilité perçue, pertinence de contenus perçu, la motivation 1. Fondement didactique et revue de la littérature de la validation d'AKBAL Les outils d'enseignement et les matériels didactiques tels que les logiciels pédagogiques, pour leur adoption et intégration en situation de classe et activité extrascolaire, nécessitent une évaluation, un test minutieux (pour déterminer la cohérence faciale, interne, hors contexte, par les juges), une censure donnée par les experts d'enseignement, didacticiens et psychopédagogues en ce qui concerne sa valeur pédagogique, ergonomique et psycho technologique. Ces instruments/grilles d'évaluation de logiciels eux-mêmes nécessitent la mesure de leur validité et fiabilité pour se rassurer de la valeur du logiciel.

  et d'autres sont destinés uniquement aux activités de divertissement, de jeux et où le coté plaisir prime sur l'apprentissage scientifique basé sur un programme d'éducation nationale ; et pour d'autres encore les contenus n'ont pas d'objectifs pédagogiques visés et n'ont pas des liens avec les textes légaux de la politique d'éducation. Il existe cependant, dans cet ensemble de ces logiciels pédagogiques certains qui véhiculent uniquement l'éveil technologique, d'autres encore, combinent à la fois les aspects pédagogiques et aspects de divertissements/ludiques. Il est alors du devoir des didacticiens et spécialistes d'éducation de pouvoir les diagnostiquer, juger leur pertinence, évaluer si les objectifs attendus d'eux y sont présents et détiennent les contenus, les compétences et connaissances à transmettre qu'ils sont sensés véhiculer. Ils pourront ainsi se rassurer de leur choix raisonné comme outils éducatifs, leur utilisation dans le contexte bien déterminé, soit pour accompagner des activités en classe, soit utilisés à des Revue Internationale du Chercheur ISSN: 2726-5889 Volume 4 : Numéro 4 activités extrascolaires de révision-apprentissage ; ou encore à l'exercisation et l'autoévaluation. Pour faire ce diagnostic, les auteurs en sciences des technologies éducatives ont recensé des critères de leur acception et adoption comme outil pédagogique. Ces critères pour différents auteurs tels que Stéphane Crozat, Phillipe Trigano et Olivier Hû

  n'est qu'un des nombreux tests statistiques qui sont utilisés pour évaluer l'accord entre deux évaluateurs ou plus lorsque la méthode d'évaluation (c'est-à-dire la variable de réponse) est mesurée sur une échelle catégorielle par exemple[START_REF] Scott | Reliability of content analysis : The case of nominal scale coding[END_REF];[START_REF] Cohen | A Coefficient of Agreement for Nominal Scales[END_REF];[START_REF] Fleiss | Measuring nominal scale agreement among many raters[END_REF];Landis & Koch (1977a). Chacun de ces différents tests statistiques a des exigences et des hypothèses de base qui doivent être satisfaites pour que le test donne un résultat valide/correct. Le kappa de Fleiss ne fait pas exception. Par ces critères nous voulons nous rassurer que la conception de notre étude réponde aux exigences/hypothèses de base du kappa de Fleiss. Le respect de l'exigence/Hypothèse #1 de Fliess de kappa (a) pour analyser nos données nous conduit à spécifier le choix test statistique coefficient k (c'est-à-dire le kappa de Fleiss) pour déterminer ; (b) le niveau d'accord des 32 juges évaluateurs regroupés en 8 petits groupes. Ils ont été sélectionné pour évaluer le niveau de satisfaction/acceptation de 3 modules(Mat1, Mat2 et Mat3) interactifs de révisionapprentissage à l'école maternelle, au moyen d'une grille d'évaluation composée de Revue Internationale du Chercheur ISSN: 2726-5889 Volume 4 : Numéro 4 pédagogique et du risque perçu à l'utilisation et accès à distance) ; (c) les cibles évalués sont les items/critères de validité des 3 modules Mat1, Mat2, Mat3 d'apprentissage à l'école maternelle ; et (d) les catégories de notre variable de réponse sont en 5 échelles de Likert « Pas du tout d'accord », « Pas d'accord », « Neutre », « et « Tout à fait d'accord », pour souligner que la variable de réponse est une variable catégorielle. Notre échantillon d'évaluateurs non unique (selon l'Exigence/Hypothèse #4 ) est (a) de 32 enseignants sélectionnés occasionnellement, (au hasard) selon leur disponibilité dans une population estimée à 50 enseignants qui avaient bien avant donné leurs accords pour participer aux ateliers de test et validation d'AKBAL (b) 2018, 2021 et 2022, des encadreuses d'écoles maternelles de la commune d'Ibanda/Quartier Nguba et Ndendere pour nous permettre d'utiliser le kappa de Fleiss de manière appropriée, conformément à l'exigence/hypothèse n° #4 (c'est-à-dire que les deux évaluateurs ou plus ne sont pas uniques), et à l'exigence/hypothèse n° 6 respectivement. Tableau 1 : Choix et élaboration de l'échantillon des juges/experts évaluateurs des modules

Figure 1 :

 1 Figure 1: Notre représentation schématique des exigences de K de Fleiss

2. 1

 1 .2. Procédure SPSS Statistique pour effectuer une analyse kappa de Fleiss Nous avons calculé le coefficient kappa de Fleiss à l'aide du logiciel SPSS Version 26 dans son option « Analyse de fiabilité » en 3 étapes. Comme le test FLEISS KAPPA n'est pas une procédure intégrée dans SPSS Statistics de la version 26, nous avons d'abord téléchargé son plugin « STATS_FLEISS_KAPPA.SPE » à partir du lien (IBM, s. d.); puis l'avons intégré en tant qu' "extension" à l'aide de l'Extension Hub dans « SPSS Statistics v.26». Pour atteindre la commande kappa de Fliess, avons clique sur le menu Analyser, puis sur Échelle, puis sur Analyse de fiabilité.

  Grace aux suggestions d'interprétations suggérées par Altman (1999) pour le coefficient kappa de Cohen, et adapté de Landis & Koch (1977a) de niveaux d'accord situé entre « pas du tout d'accord », « pas d'accord », « neutre », « d'accord » ou « tout à fait d'accord », nos coefficients de concordance par facteurs représentent de façon globale un accord modéré.

Figure 2 :

 2 Figure 2: Interprétation de Kappa de Cohen

Figure 4 :

 4 Figure 4: Capture d'interface d'exercice interactif de repérage de point géographique sur une carte/plan.

Figure 5 :Figure 6 :

 56 Figure 5: Capture d'interface d'exercice interactif d'ajustage d'image au nombre : Activité mathématique ; sous activité les nombres.

. Le facteur d'utilité perçue Tableau 3 : Coefficient Kappa de Fleiss pour le facteur d'utilité perçue Overall Kappa

		Interprétation (Landis)	Cohen
	< 0	Pauvre concordance	<0.20	Poor
	0.01 -0.20 Faible concordance	0.21 -0.40 Fair
	0.21 -0.40 Légère concordance
	0.41 -0.60 Concordance Moyenne	0.41 -0.60 moderate
	0.61 -0.80 Concordance importante	0.61 -0.80 Good
	0.81 -1.00 Concordance presque parfaite 0.81 -1.00 very Good
			Source : Landis et Koch [22]
	Son interprétation exprime à quel point la valeur de concordance observée parmi les
	observateurs dépasse ce qui aurait pu être attendu si tous les observateurs avaient fait leur
	classification totalement au hasard.
	3. Resultants
	3.1Kappa	Asymptotic Standard Error	Z	P Value	Lower 95% Asymptotic CI Bound	Upper 95% Asymptotic CI Bound
	Overall	.728	.037	19.654	.000	.655	.800
	Source : Nos résultats obtenus de la commande de coefficient k de Fleiss au moyen du
	logiciel statistique SPSS v26.
	Les résultats de l'analyse du coefficient kappa de Fleiss kappa, κ (c'est-indiqué dans la
	colonne "Kappa" du tableau Kappa global) pour le facteur de l'utilité perçue est de k=0.728,
	p=0.000, c.à.d. p<0.005, ce qui implique que ce résultat de coefficient kappa est
	statistiquement significatif avec un intervalle de confiance (IC) à 95 % entre 0.655 et 0,800. Il
	a une grande chance qu'il tombe entre les valeurs 0.655 et 0,800pour z=19.654
	Les juges évaluateurs se sont accordés à l'unanimitéé de façon "bonne", de coefficient
	important (k=0.728)

Table de classification de coefficient kappa de Landis & Koch (1977b) s'inspirant aussi de celui de Cohen. En observant les catégories individuelles 4 "d'accord" et 5. "Tout à fait d'accord " Tableau 4:

Coefficient individuel de Kappa de Fleiss par catégorie Kappas for Individual Categories

							Lower 95%	Upper 95%
		Conditional		Asymptotic		P Value	Asymptotic CI	Asymptotic CI
	Rating Category	Probability	Kappa	Standard Error	Z	sig	Bound	Bound
	3	.000	-.014	.039	-.352	.725	-.089	.062
	4	.909	.760	.039 19.698	.000	.684	.835
	5	.833	.737	.039 19.108	.000	.661	.813
	Source : Nos résultats obtenus à partir de la commande de coefficient k de Fleiss au moyen du
	logiciel statistique SPSS v26

Les juges experts lors de l'évaluation de chaque catégorie individuelle de la variable de réponse, les coefficients kappas individuels indiquent que les juges experts sont « fortement d'accord » de niveau de signification « bon » pour leurs affectations/classements ou attribution des rangs aux items/critères définissant le facteur d'utilité perçue (5) /« tout à fait d'accord » et au rang (4) « d'accord ». Les résultats kappa (k=0.778) individuels sont affichés dans le tableau Kappa pour les catégories individuelles, comme indiqué ci-dessus : 3.

2. Utilisabilité ou facilité d'usage perçue Tableau 5: Coefficient Kappa de Fleiss pour le facteur d'utilisabilité perçue Overall Agreement a

	Tableau 6:
						Lower 95%	Upper 95%
			Asymptotic		P Value	Asymptotic CI	Asymptotic CI
	Kappa	Standard Error	Z	Sig.	Bound	Bound
	Overall	.485	.065	7.504	.000	.359	.612
	Source : Nos résultats obtenus à partir de la commande de coefficient k de Fleiss au moyen du
	logiciel statistique SPSS v26.
	Le coefficient k=0.485, statistiquement significatif au seuil de p=0.000 et est < 0.005. Il
	représente un degré de concordance moyenne (0.41 -0.60) entre les évaluateurs en ce qui
	concerne le facteur technique d'utilisabilité ou facilité d'usage des exercices des modules
	AKBAL. Les juges évaluateurs se sont accordés à l'unanimité de façon "modérée", de
	coefficient de concordance modérée évalué à (k=0.485).

Coefficient individuel de Kappa de Fleiss par catégorie de facteur d'utilisabilité Kappas for Individual Categories

							Lower 95%	Upper 95%
	Rating	Conditional		Asymptotic			Asymptotic	Asymptotic CI
	Category	Probability	Kappa	Standard Error	Z	P Value	CI Bound	Bound
	3	.000	-.032	.072 -.447	.655	-.174	.109
	4	.667	.565	.072 7.824	.000	.423	.706
	5	.865	.493	.072 6.827	.000	.351	.634
	Source : Nos résultats obtenus à partir de la commande de coefficient k de Fleiss au moyen
	du logiciel statistique SPSS v26.

Il découle des résultats de ce tableau de kappa individuel que les juges experts sont « moyennement d'accord » de niveau de signification « modéré » pour leurs affectations/classements ou attribution des rangs aux items/critères définissant le facteur d'utilisabilité ou facilité d'usage perçue (4) « d'accord » et au rang (5) « tout à fait d'accord » Les résultats kappa (k=0.565) et (k=0.493) individuels sont affichés dans le tableau Kappas pour les catégories individuelles, comme indiqué ci-haut.

3.3. La pertinence perçue de contenu pédagogique L'évaluation a été réalisée sur base des items 12,13, 14 et 15 Tableau 7:

Coefficient Kappa de Fleiss pour le facteur de pertinence perçue des contenus Overall Kappa

	Tableau 8:
					Lower 95%	Upper 95%
			Asymptotic		Asymptotic CI	Asymptotic CI
		Kappa	Standard Error	Z	P Value	Bound	Bound
	Overall	.404	.070	5.750	.000	.267	.542
	Source : Nos résultats obtenus à partir de la commande de coefficient k de Fleiss au moyen
	du logiciel statistique SPSS v26
	Les résultats de l'analyse du coefficient kappa de Fleiss kappa, κ (indiqué dans la colonne
	"Kappa" du tableau Kappa global) pour le facteur d'utilité perçue est de k=0.404, p=0.000,
	c.à.d. p<0.005, ce qui implique que ce résultat de coefficient kappa est statistiquement
	significatif avec un intervalle de confiance (IC) à 95 % entre 0.267 et 0,542. Il a une grande
	chance qu'il tombe entre les valeurs 0.267 et 0,542 pour z=5.750
	Les juges évaluateurs se sont accordés à l'unanimitéé de façon "modérée" (k=0.404)

Coefficient individuel de Kappa de Fleiss par catégorie de facteur de pertinence perçue des contenus Kappas for Individual Categories

							Lower 95%	Upper 95%
		Conditional		Asymptotic		Asymptotic	Asymptotic CI
	Rating Category	Probability	Kappa	Standard Error	Z	P Value	CI Bound	Bound
	3		.000	-.008	.072 -.109	.913		-.149	.134
	4		.602	.414	.072 5.735	.000		.272	.555
	5		.806	.409	.072 5.672	.000		.268	.551
	Source : Nos résultats obtenus à partir de la commande de coefficient k de Fleiss au moyen
	du logiciel statistique SPSS v26
	On observe en deux catégories individuelles les variables à réponse nominale 4 « d'accord »
	et 5 « tout à fait d'accord », les juges qui ont affecté le rang (a) de catégorie « d'accord » et
	ceux qui ont affecté le rang de catégorie 5 « tout à fait d'accord » ont été concordants de façon
	modérée ( 0.41 -0.60), leurs k=0.414 et k=0.409 pour la pertinence perçue de contenu
	pédagogique des exercices.
	3.4. La motivation perçue
	Tableau 9:Coefficient de Kappa de Fleiss pour le facteur de motivation perçue
				Overall Kappa Agreement a
							Lower 95%	Upper 95%
			Asymptotic			Asymptotic CI	Asymptotic CI
	Kappa	Standard Error	Z	P Value	Bound		Bound
	Overall	.467		.070	6.623	.000		.328	.605
	Source : Nos résultats obtenus à partir de la commande de coefficient k de Fleiss au moyen
	du logiciel statistique SPSS v26.
	Le coefficient kappa pour le facteur de motivation perçue est de k=0.467, p=0.000, c.à.d.
	p<0.005, ce qui implique que ce résultat de coefficient kappa est statistiquement significatif
	avec un intervalle de confiance (IC) à 95 % entre 0,448 et 0,467, ce coefficient révèle un
	accord modéré entre le jugement des encadreuses (0.328 et 0.605). Il y a une grande chance
	qu'il tombe entre les valeurs 0.328 et 0.605 pour la valeur z=.6.623.
	Tableau 10 : Coefficient individuel de Kappa de Fleiss par catégorie de facteur de la
	motivation perçue

(d'utilité perçue, d'utilisabilité ou facilite d'usage, de pertinence de contenu

Source : Nos résultats obtenus à partir de la commande de coefficient k de Fleiss au moyen du logiciel statistique SPSS v26.


Marie Colmont

Céline Darie

Alexander A Tsirlin

Anton Jesche

Claire Colin

Olivier Mentré

Communication Compressibility of BiCu 2 PO 6 : polymorphism against S=1/2 magnetic spin ladders

BiCu 2 PO 6 is an unique example of S=1/2 ladder where the magnetic exchanges are mainly confined in 1D-∞ [BiCu 2 O 2 ] 3+ cationic ribbons, although the existence of shortest Cu-Cu separation between them. Its original magnetic topology gives the most representative example of frustrated quantum ladder to investigate the complex physics behind. Herein, we report the synthesis and characterization of one high-pressure polymorph. In this new phase, the preservation of 1D-∞ [BiCu 2 O 2 ] 3+ units somewhat restacked leads to the preservation of its gapped magnetic ground state and ladder topology. The comparison between both compounds highlight a scare thermodynamic conjuncture, where both the stable ambient pressure (AP) and the metastable high pressure (HP) forms display the same equilibrium volume and superposed volume dependence of the energy , leading to a 1 st order AP  HP transition undetected by DTA.

BiCu 2 PO 6 (BCPO) is a S=1/2 ladder system with a unique magnetic behaviour due to frustration of spin ladders along their legs [START_REF] Mentré | Incommensurate spin correlation driven by frustration in BiCu2PO6[END_REF][START_REF] Tsirlin | Bridging frustrated-spin-chain and spin-ladder physics: Quasi-one-dimensional magnetism of BiCu2PO6[END_REF]. In this compound, there is a strong discrepancy between the structural ladders and the magnetic ones in that sense that the shortest Cu-Cu distance of 2.89 Å along the structural rungs, leads to only a weak magnetic coupling J3, following cancellation of ferromagnetic and antiferromagnetic terms. On the opposite, longrange interactions (J4), mediated by oxygen and bismuth bridges with Cu-Cu distances exceeding 5 Å, turn out to be strong and reinstate the ladder-like interaction topology, but now with spin ladders formed between the structural ladder-like units (see Figure 1). This would be a mere oddity, unless further long-range interactions had come into play. Such interactions, labelled J2 hereinafter, connect next nearest neighbour (NNN) along the legs (Figure 1c). They naturally compete with nearest-neighbour (NN) interactions J1 and render BiCu 2 PO 6 a unique representative of copper-based quantum magnets that triggers long-standing interest of the physics community [START_REF] Mentré | Structural features of the modulated BiCu2(P(1-x)V(x))O6 solid solution; 4-D treatment of x = 0.87 compound and magnetic spin-gap to gapless transition in new Cu 2+ two-leg ladder systems[END_REF][START_REF] Alexander | Impurity effects in coupled-ladder BiCu2PO6 studied by NMR and quantum Monte Carlo simulations[END_REF][START_REF] Casola | Direct Observation of Impurity-Induced Magnetism in a Spin-1 2 Antiferromagnetic Heisenberg Two-Leg Spin Ladder[END_REF][START_REF] Casola | Field-Induced Quantum Soliton Lattice in a Frustrated Two-Leg Spin-1/2 Ladder[END_REF][START_REF] Choi | Evidence for Dimer Crystal Melting in the Frustrated Spin-Ladder System BiCu 2PO6[END_REF][START_REF] Koteswararao | Spin-gap behavior in the two-leg spin-ladder Bi Cu2PO6[END_REF]. On the physics side, the main interest in BCPO stems from the fact that this compound lacks long-range magnetic order and instead exhibits an unusual spin gap, i.e., a gap Δ/kB =32-45 K separating the first excited state from the ground state. Unlike in the conventional spin-dimers systems, two excitations branches are formed owing to the giant anisotropic spin interactions [START_REF] Plumb | J Quasiparticle-continuum level repulsion in a quantum magnet[END_REF][START_REF] Jeon | Giant suppression of phononic heat transport in a quantum magnet[END_REF][START_REF] Plumb | J Incommensurate dynamic correlations in the quasi-two-dimensional spin liquid BiCu2PO6[END_REF]. Closing the gap in applied magnetic fields leads to a cascade of magnetic transitions into a plethora of novel magnetic states, including soliton lattices, whereas excitations over the gap serve as a model case for quasiparticle-continuum level repulsion, as probed in inelastic neutron scattering experiments [START_REF] Kohama | Anisotropic Cascade of Field-Induced Phase Transitions in the Frustrated Spin-Ladder System BiCu2PO6[END_REF][START_REF] Kohama | Entropy of the quantum soliton lattice and multiple magnetization steps in BiCu2PO6[END_REF]. In addition recent evidences of the suppression of the BCPO thermal conductivity at low temperature increasing the magnetic field due to strong spin-phonon coupling opens the perspectives of strong magnetoelectric coupling [START_REF] Jeon | Giant suppression of phononic heat transport in a quantum magnet[END_REF][START_REF] Nagasawa | Thermal Conductivity in the Frustrated Two-Leg Spin-Ladder System BiCu2PO6[END_REF]. From the structural viewpoint, these peculiar properties result from a specific ladder topology induced by the aptitude of both Cu 2+ and Bi 3+ ions to occupy the corners of oxo-centered tetrahedra arranged in edge-sharing units, i.e. the double ∞ [BiCu 2 O 2 ] 3+ zig-zag chains in BCPO shown in the figure 1 (see ref. [START_REF] Krivovichev | Anion-Centered Tetrahedra in Inorganic Compounds[END_REF] for a review), which naturally create the Cu 2+ zig zag chains. Here, due to the strongly covalent O-Cu and O-Bi bonds compared to the external Bi/Cu ---OPO 3 bonds, the magnetic units form the rigid framework of the crystal structure. High pressure/high temperature (HP/HT) treatments have been applied in order to probe the possibility of reorganization between them in a denser polymorph. In this paper, the ambient-pressure BiCu 2 PO 6 (AP-BCPO) and its high-pressure variant (HP-BCPO) will be presented and juxtaposed. Single phase HP-BCPO material was achieved by the HP/HT transformation of AP-BiCu 2 PO 6 at 5GPa/800°C. The AP-BiCu 2 PO 6 polycrystalline precursor was preliminary prepared at 800°C from a stoichiometric mixture of Bi 2 O 3 , CuO, and (NH 4 )H 2 PO 4 as reported in [START_REF] Mentré | Structural features of the modulated BiCu2(P(1-x)V(x))O6 solid solution; 4-D treatment of x = 0.87 compound and magnetic spin-gap to gapless transition in new Cu 2+ two-leg ladder systems[END_REF][START_REF] Abraham | Crystal structure of a new bismuth copper oxyphosphate: BiCu2PO6[END_REF]. It was then packed into a platinum capsule, jointly pressed and heated using a belt system apparatus. Details about the synthesis are given in Supplementary informations, S1. After releasing the pressure, HP-BCPO is stable and its XRD pattern shows drastic changes compared to AP-BCPO. It was fully indexed in the orthorhombic unit cell a= 12.26003(8) Å, b= 5.21763(4) Å and c= 7.27982(5) Å with respect to the Pnma symmetry, reminiscent of the BiCu 2 AsO 6 (BCAO) crystal lattice [START_REF] Radosavljevic | Synthesis and structure of bismuth copper arsenate, BiCu2AsO6[END_REF]. The Rietveld refinement using the BCAO starting model leads to final agreement factors R Bragg = 4.36% and R f = 2.67% using constrained P-O distances due to the slightly "out-of range" P-O bonds. A more accurate model for oxygen positions was obtained after DFT relaxation of the refined structure fixing the experimental lattice parameters, see S2 by comparison to AP-BCPO. The main interatomic distances and angles in these units for the two BCPO forms are compared in the table 1. In this table, the labels J1 to J4 respects the nomenclature used in ref [START_REF] Mentré | Structural features of the modulated BiCu2(P(1-x)V(x))O6 solid solution; 4-D treatment of x = 0.87 compound and magnetic spin-gap to gapless transition in new Cu 2+ two-leg ladder systems[END_REF], as shown in figure 1. Density-functional band-structure calculations performed on the GGA+U level (U d =9.5 eV and J d =1eV) lead to the exchange couplings Ji compared in table 1 for both the AP and HP forms. At this stage, several main features should be noted: i) the ratio between the cell volumes of AP-BCPO and HP-BCPO is 1.02, i.e. 474.56 Å3/465.67 Å3, confirms the HP transformation into a more dense crystal packing. ii) the conservation of the nearly unchanged ∞ [BiCu 2 O 2 ] 3+ oxo-centered units suggests that basic features of the magnetic lattice, along with its exotic magnetic ground state, should be preserved, see figure 1 c,d. In the AP-form, ∞ [BiCu 2 O 2 ] 3+ magnetic ladders grow parallel, whereas in HP-BCPO the ladders are rotated by ca. 100° and arranged in a crisscrossed pattern. iii) Similar to AP-BCPO, the coupling J3 between the magnetic units (i.e., within the structural ladders) is expected to be relatively weak because of the nearly orthogonal orbital overlaps (i.e. Cu-O-Cu = 92.1°). On the other hand, the rung super-super-exchange coupling J4 can be substantial, because the Cu-O…O-Cu dihedral angle is small (i.e., ~10.1°) and the O…O contact distances (2.749 Å) are within the Van der Waals distance [START_REF] Whangbo | Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels[END_REF]. This reinstates remarkably similar spin ladder topologies between AP-BCPO and HP-BCPO, although the main structural context is drastically modified.

68 95 Cu1-Cu1 (Å) O2-O2 (Å) Cu1-O2-O2-Cu1 (°) O1-O1 (Å) Cu1-O1-O1-Cu1 (°) 5.17 2.56 0 2.55 0 5.22 2.56 0 2.60 0 J2'/Kb (K) SSE (NNN- legs) Cu-O-(P)-O-Cu and Cu-O-(Bi)-O- Cu 117 108 Cu2-Cu2 (Å) O2-O2 (Å) Cu-O2-O2-Cu (°) O1-O1 (Å) Cu-O1-O1-Cu (°)
Experimentally, the absence of a magnetic ordering transition and the sharp decrease of the magnetic susceptibility (T) below T max = 43K indicate a spin gap, similar to AP-BCPO. Our data collected at several applied fields between 0.1 and 7T show a significant, fielddependent upturn below 10K typical of defect paramagnetism. Due to the presence of a minor ferromagnetic impurity not detected by XRD, we have focused on the 1T data after checking that the shape of (T) is field-independent above 10K. We have used several approaches to the magnetic modelling, ranging from an analytical approximation to the exact diagonalization, to elucidate this complex case. First, we fitted the susceptibility using the high-temperature series expansion for a simple S= 1/2 ladder  L (g, J1, J4), see details in S3. In view of the sizable inter-ladder coupling J3 the expression was modified taking into account the inter-ladder interactions on a mean-field level via an effective temperature θ int . The Curie-type impurity term and the 0 temperature-independent term were included as well:

 = 0 + ximpC/(T-θimp) + (1-ximp) L/[1-(θint L /C)] (1)
with C = 0.375 cm 3 K mol -1 , θ int = z S(S+1) J 3 /3K b and z=4 surrounding ladders via J 3 . After fixing g=2.2 and J 1 /J 4 = 1.8 (from DFT calculations below) we found antiferromagnetic J1/K b = 88.8(3)K (i.e. J 4 /K b =49K) and ferromagnetic J 3 /K b = -4.85(2) K,  0 =2.2.10 -4 cm 3 mol -1 x imp = 1.75(2)% and θ imp = -2.44(6) K giving a rough approximation of the J's involved and the deduced gap of 22 K (see S3). The shortcomings of this approach are the absence of the secondneighbour couplings J2, J2' and, consequently, the neglected effect on the gap, which can be remedied by a simple fit using the relation:

 = 0 + ximpC/(T-θimp) + A exp(-/T)/ T (2)
in the low-temperature part. This leads to the accurate  = 27.9(1)K value very similar to the gap of 32K in the AP-form [START_REF] Tsirlin | Bridging frustrated-spin-chain and spin-ladder physics: Quasi-one-dimensional magnetism of BiCu2PO6[END_REF]. Including J2 and J2' in a full temperature range is more difficult, because magnetic frustration is introduced, and the analytical expression for  L no longer holds. Nevertheless, we can use the exact result for a single spin ladder with J1, J2, J2', and J4, but neglect J3. This leads to a very good fit above 100 K (g=2.15 and the approximation J1=200K, J2=J2'=J1/2 and J4 =140K) and compares favourably with the exchange couplings obtained from DFT, see S3. On the other hand, the low-temperature part is not reproduced, because the interladder coupling J3 is crucial for the size of the spin gap. The model without J3 overestimates the gap and, therefore, shifts the susceptibility maximum toward higher temperatures. All fits are presented in Figure 2a. The exchange couplings in BCPO are far from trivial. It is striking that most exchanges are calculated to be stronger in the HP form despite the longer Cu-Cu distances. This confirms the primordial role of the SE and SSE mechanisms in these compounds. For example, the leg coupling J1 is strongly enhanced due to the increase in the Cu-O-Cu bridging angle. On the other hand, J4 is reduced in the HP polymorph, because the bigger dihedral angle of 10.1° (see iii) above and table 1) renders the super-superexchange pathway more curved and, consequently, less efficient [START_REF] Whangbo | Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels[END_REF]. Finally, the sharp difference between J2 and J2' in the AP-form, despite the equal Cu-Cu distances of 5.17 Å, was discussed in the previous literature, but remains largely unclear. The HP-form gives new insights here for better rationalization of the hierarchy of magnetic exchanges. By comparing the structural parameters of the AP and HP polymorphs, we find a clear correlation between the size of J2(J2') and the O-O distances within the Cu-O-(P)-O-Cu and Cu-O-(Bi)-O-Cu paths, see figure 1e,f,g,h. The sizes of J2 and J2' are scaled by the length of the O-O contact, which are differentiated at the bismuth side. We now study the compressibility and thermodynamic stability of the two forms. Although HP-BCPO is denser than AP-BCPO, most of the cation-cation and cation-anion bond distances involved in the structural and spin ladders are slightly longer in the HP-form, which is rather unusual and may be due to the sterically active Bi 3+ lone pair that is external to these units. We computed total energies of the AP-and HP-polymorphs as a function of volume and fitted the resulting E(V) dependencies using the Birch-Murnaghan equation of state (EOS), see figure 2b. [START_REF] Birch | Finite Elastic Strain of Cubic Crystals[END_REF]. Dertails are given in S3. The results highlight a very unusual behavior giving E 0 (eV/cell), V 0 (Å 3 ), B 0 (GPa), B 0' = -225.302, 487.7, 82.6, 5.96 for the AP-form and -225.082, 487.8, 53.3, 8.37 for the HP-form. DFT systematically overestimates equilibrium cell volumes V 0 , but provides a surprising result of nearly the same V 0 in both structures despite the drastic structural reorganization. The equilibrium energy E 0 (i.e. the energy at the minimum) for the HP structure is 0.22 eV/cell (i.e. 55 meV/f.u. ~ 5.33 kJ/mol) higher than that of the AP structure, which confirms metastable nature of the HP-form at ambient conditions. More intriguingly, both the bulk modulus B 0 (inversely proportional to the compressibility) and its pressure derivative B'= dB 0 /dP (which scales the pressure effect of the bulk modulus) reveal higher compressibility of the HP-form. The HP-BCPO is thus as soft as Bi 4 Ge 3 O 12 (B 0 = 48 GPa, B' = 9), although formed under pressure. [START_REF] Meng | Optical phonon modes and phase transition in the Bi4Ge3-xTixO12 ceramic system[END_REF], [START_REF] Arora | Stability of bismuth orthogermanate at high pressure and high temperature[END_REF] To the best of our knowledge, this counter-intuitive hardness hierarchy AP hard >HP soft has not been previously seen in compounds of lone-pair cations, where pressureinduced phase transition typically produce a harder structure, e.g. PbCrO 3 I (B 0 =59 GPa)  II (B 0 = 187 GPa) [22] with its giant volume collapse, or α-BiB 3 O 6 I(B 0 = 38GPa)  II(B 0 =114 GPa) [START_REF] Dinnebier | High-pressure crystal structure of the non-linear optical compound BiB3O6 from two-dimensional powder diffraction data[END_REF][START_REF] Haussühl | Piezoelectric and elastic properties of the nonlinear optical material bismuth triborate, BiB3O6[END_REF]. In contrast, less compressible (i.e. high bulk modulus) structures are generally stable in a broad pressure range, e.g. Bi 2 Al 4 O 9 (B 0 = 122 GPa), Bi 2 Mn 4 O 10 (B 0 = 138 GPa) [START_REF] López-De-La-Torre | High-pressure behavior of the ternary bismuth oxides[END_REF]. The high compressibility of the HP-form compared to the AP one can be explained by structural arguments, keeping in mind its analogy with BiCu 2 AsO 6 compound. It is well established that the compressibility of Bi 3+ compounds is driven by the flexibility of the BiO x polyhedra, including the stereo-activity of the lone electron pair [START_REF] Wiehl | Structural compression and vibrational properties of Bi12SiO20 sillenite from experiment and theory[END_REF]. The four PO 4 groups in the vicinity of Bi 3+ involve the BiO 4 +6 main polyhedron in the AP-form, in contrast to the BiO 4 +5 polyhedron in the HP-form, where the four short Bi-O bonds point toward the magnetic units, see figure 1f,g. Dealing with the long Bi-O bonds, the oxygen packing shows O---O bonds in the order of magnitude of the Van der Waals distances, which involves a less dense (i.e. more compressible) HP form due to its lower Bi coordination. In addition, the comparison between the BCAO and the HP-BCPO structures shows significant shrinkage of Bi-O bonds in the former by up to 4.5% as shown by arrows on the figure 1,h. This shrinkage compensates for the presence of longer As-O bonds compared to P-O bonds, thus leaving a room for the large compression of HP-BCPO with its smaller PO 4 groups, in agreement with our EOS fits.

In fine, HP-BCPO is metastable at ambient pressure and has been quenched upon cooling inside our high-pressure setup. A harder HP polytype may be expected at higher pressures, similar to assumptions given for the Bi 12 SiO 20 sillenite (B 0 =63.4) with no detected transition up to ca. 17 GPa. [START_REF] Wiehl | Structural compression and vibrational properties of Bi12SiO20 sillenite from experiment and theory[END_REF]. HP-BCPO transforms abruptly back into the AP-form at ca. 690°C as shown by high temperature XRD that reveals a 1st order transition, see figure 3a. However, the splitting of XRD peaks suggests a distribution of compositions after quenching to RT, i.e., a phase separation into two AP-related compounds in the approximatively 1:1 ratio with the lattice parameters a=11. stoichiometric compound when similar thermal treatments (heating rate = 5°C/min) are used, Figure 3b.

In conclusion, we have prepared at 5GPa, 800°C a new highpressure (HP) polymorph of the well-known BiCu 2 PO 6 compound, fascinating due to its unique spin-gap ground state that results from frustrated S=1/2 ladders. In the HP-form, the magnetic layers are preserved but twisted, such that a novel spin-gap ground state is reached with the reinforced leg couplings (J1) and plethora of potential specificities with regards to the intensive properties previously explored in the ambient-pressure (AP) parent compound. The structural relationship between the AP and HP polytypes validates the role of the covalent oxocentered ∞ [BiCu 2 O 2 ] 3+ units holding the magnetic ladders as structural templates. Finally, the rearrangement between them leads to a scare thermodynamic conjuncture, where both the stable AP and metastable HP forms have nearly the same equilibrium volume and superposed volume dependence of the energy. As a matter of fact, it is responsible for a specific 1st order HP AP transition at 690°C in air, observed by DSC but undetected by DTA, likely due to almost unchanged Gibbs energy G, and entropy S= -dG/dT at the HP/AP boundary, see figure 3d. Besides this original phase diagram the achievement of a novel frustrated ladder systems with counter-intuitive hierarchy of magnetic couplings offers a novel playground for exotic magnetic fundamental states.

Figure 1 :

 1 Figure 1: Projection along the b-axis of the BiCu2PO6 crystal structure with evidence of polycationic ribbons surrounded by XO4 groups with (a) X= P and (b) X= As. The Cu 2+ zigzag ladders are formed between the two ribbons, asshown by the dotted lines. The ribbons and ladders stretched along the b,-axis with the distance labelling scheme with different J-J coupling schemes for (c) X= P and (d) X= As. e) two paths of the J2 exchange. The interaction between the XO4 groups and oxo-centered units in f) AP-BCPO; g) HP-BCPO; and h) BiCu2AsO6.

Table 1 :

 1 Geometrical parameters associated with the SE and SSE paths in the AP and HP (ICSD# 434030)polymorphs of BiCu2PO6.

Figure 2 :

 2 Figure 2: a) Experimental magnetic susceptibility under 1T and its fits using models described in the text. b) Fit of the energy-vs-volume curves for the HP and AP polymorphs.

Figure 3 :

 3 Figure 3 : a,b) HT-XRD of HP-BCPO with transition into biphased APtypes at 690°C. c) DTA of the melting and recrystallization of both polymorphs. d) Thermal analyzes of the HP AP transformation.

ACKNOWLEDGMENTS

This work was carried out under the framework of the LOVE-ME project supported by the ANR (Grant ANR-16-CE08-0023). The onds urop en de veloppement gional ( ), , gion ord Pas-de-alais, and inist re de l' ducation ationale de l' nseignement up rieur et de la echerche are acknowledged for funding the X-ray diffractometers. The authors thank M. legendre at Institut Néel for technical support of the high pressure synthesis.

AUTHOR INFORMATION

*E-mail: Olivier.mentre@ensc-lille.fr *E-mail: altsirlin@gmail.com A metastable high pressure polymorph of BiCu 2 PO 6 was prepared, with frustrated S=1/2 magnetic ladders similar to those of the ambient-pressure form, but drastically reorganized. It forms an original dual-system with specific relative thermodynamic stability of both forms.

Entry for the


Malcolm Doering
email: doering@i.kyoto-u.ac.jp

Dražen Brščić

Takayuki Kanda
email: kanda@i.kyoto-u.ac.jp

Learning Social Robot Behaviors for Interacting with Staff and Customers

Keywords: Human-robot interaction, imitation learning, machine learning, human-robot teaming

Data-driven imitation learning has been used to train social robots to interact with human customers in service domains. However, up till now previous works on imitation learning of social interaction behaviors for human-robot interaction have focused only on customer-shopkeeper interactions, but not on how the robot should interact with fellow staff members. This work presents work in progress on training social service robots to both perform customer service and work together with human staff. Interviews of people with retail work experience were conducted to discover what types of tasks staff members work together on and how they work together. From this, representative interaction scenarios for role-play were created for the purpose of data collection. Finally, a preliminary interaction behavior learning system is proposed.

I. INTRODUCTION

Recently social robots have been applied in a variety of domains, such as elder care [START_REF] Kuwamura | Designing Robots for Positive Communication with Senior Citizens[END_REF], personal companions [START_REF] Samani | Towards a formulation of love in human-robot interaction[END_REF], hotel concierges [START_REF] Guo | Conversational bootstrapping and other tricks of a concierge robot[END_REF], workout partners [START_REF] Rea | is this all you can do? harder!" the effects of (im) polite robot encouragement on exercise effort[END_REF] and in day-today interaction [START_REF] Rosenthal | An effective personal mobile robot agent through symbiotic human-robot interaction[END_REF], which require various social interaction behaviors. One approach to developing interaction behaviors is to manually code them or use integrated development environments such as choreograph [START_REF] Pot | Choregraphe: a graphical tool for humanoid robot programming[END_REF] or interaction composer [START_REF] Glas | Human-robot interaction design using interaction composer: Eight years of lessons learned[END_REF], but this is tedious, time-consuming, and requires the developer to anticipate a myriad social scenarios. Another approach, which overcomes these limitations, is to use datadriven imitation learning to learn social interaction behaviors automatically from example interaction data without manual data annotation. With this approach, interaction data can be collected via passive sensor networks in places that people frequently interact and the repeatable, formulaic behaviors, which characterize many domains where social service robots might be useful (e.g. retail, restaurants, and museum tours), can be learned via machine learning with reduced effort by developers.

Previous work on data-driven imitation learning has focused on one-to-one interactions [START_REF] Liu | Data-driven hri: Learning social behaviors by example from human-human interaction[END_REF], one-to-many interactions [START_REF] Nanavati | Autonomously learning one-to-many social interaction logic from human-human interaction data[END_REF], learning proactive behaviors [START_REF] Liu | Learning proactive behavior for interactive social robots[END_REF], curiosity-driven learning [START_REF] Doering | Curiosity did not kill the robot: A curiosity-based learning system for a shopkeeper robot[END_REF], resolving ambiguity [START_REF] Doering | Modeling interaction structure for robot imitation learning of human social behavior[END_REF], remembering customer preferences [START_REF] Doering | Neural-network-based memory for a social robot: Learning a memory model of human behavior from data[END_REF] and adapting to changing product inventory [START_REF] Doering | Data-driven imitation learning for a shopkeeper robot with periodically changing product information[END_REF]. Furthermore, these works focused on retail scenarios where one shopkeeper robot interacts with customers, but the case where a shopkeeper robot must also work together with other staff members has been less explored. This work reports on work-in-progress on a data-driven imitation learning approach to train a robot to both interact appropriately with other staff and perform customer service.

II. RELATED WORKS A. Data-driven Imitation Learning of Social Interaction Behaviors

Data-driven systems for designing behaviors for virtual humans were explored early on: The 'Restaurant Game' was a virtual restaurant in which two human players, playing the roles of customer and waiter, could navigate around the restaurant and interact via text and predefined actions [START_REF] Orkin | The restaurant game: Learning social behavior and language from thousands of players online[END_REF], [START_REF]Automatic learning and generation of social behavior from collective human gameplay[END_REF]. 'Plan networks' were automatically extracted from the interaction data, enabling the automation of virtual characters. The 'Mars Escape' game used a similar approach, and went a step further by embodying the learned behaviors in a real robot [START_REF] Chernova | Crowdsourcing hri through online multiplayer games[END_REF]- [START_REF] Breazeal | Crowdsourcing human-robot interaction: New methods and system evaluation in a public environment[END_REF]. In contrast, data collected in the real, physical world, which we propose to collect and use for training, has the additional challenge of sensor noise, which is absent in virtual worlds.

[8], [START_REF] Liu | How to train your robot-teaching service robots to reproduce human social behavior[END_REF] introduced the concept of training a camera shopkeeper robot from examples of natural human-human interaction without any manual data annotation, on which this work is based. The approach consists of clustering the raw interaction data to find discrete common actions, and then training a neural network classifier using the interaction state at each point in time as inputs and the action cluster IDs as target outputs.

Much research has been done in extending the data-driven imitation learning approach to HRI. [START_REF] Nanavati | Autonomously learning one-to-many social interaction logic from human-human interaction data[END_REF] focused on applying the data-driven imitation learning framework to one-to-many interaction (i.e. one shopkeeper, many customers). [START_REF] Doering | Modeling interaction structure for robot imitation learning of human social behavior[END_REF] focused on the problem of modeling the hidden structure of interaction, which enabled resolution of ambiguous customer speech. [START_REF] Doering | Neural-network-based memory for a social robot: Learning a memory model of human behavior from data[END_REF] showed how gated recurrent neural networks could be used to learn a memory model of customer behavior.

[11] presented a system that could explore different robot behaviors and learn online, which resulted in more varied, interesting robot behaviors than previous approaches and enabled some customization to customers' individual differences. [START_REF] Doering | Data-driven imitation learning for a shopkeeper robot with periodically changing product information[END_REF] introduces an approach that automatically adapts the robot's behavior to account for changing products in the store. Those works focused on customer-staff interactions. In contrast, the current work focuses on staff-staff interactions and customer-staff-staff interactions.

B. Human-robot Teaming

Human-robot teaming focuses on how humans and robots can work together to complete tasks. One approach to humanrobot teaming is to create a top down model of how the robot should interact with other team members. Robots can act as team members by merely reacting to the state of the world, planning its actions to reach a goal, with or without a model of the humans in the space, and with or without a model of the human's mental model of the robot (trust and expectations of the robot) [START_REF] Chakraborti | Ai challenges in human-robot cognitive teaming[END_REF], [START_REF] Wooldridge | An introduction to multiagent systems[END_REF]. Examples of the model of the human include its cognitive and physical state (abilities, preferences, intentions, goals, model of reality, etc.) [START_REF] Gombolay | Coordination of human-robot teaming with human task preferences[END_REF], [START_REF] Clodic | Key elements for human-robot joint action[END_REF].

Another approach to human-robot teaming is apprenticeship learning, i.e. learning from an expert's demonstrations. Inverse reinforcement learning (IRL) is one technique for apprenticeship learning, which tries to learn a reward function from demonstration data and a state-action policy from that [START_REF] Abbeel | Apprenticeship learning via inverse reinforcement learning[END_REF]. [START_REF] Nikolaidis | Efficient model learning from joint-action demonstrations for human-robot collaborative tasks[END_REF] uses IRL to learn different policies for teaming with different types of users and demonstrates their technique in a task where a robot arm holds an object for a human to work on. Our proposed method, based on [START_REF] Liu | Data-driven hri: Learning social behaviors by example from human-human interaction[END_REF], [START_REF] Doering | Neural-network-based memory for a social robot: Learning a memory model of human behavior from data[END_REF], is another type of apprenticeship learning, called imitation learning which tries to directly learn a state-action policy without learning a reward function first.

III. TASKS IN A RETAIL STORE

A. Interviews of Retail Store Staff

It is currently difficult to collect data of customer-staff and staff-staff interactions in a real retail store, so we propose to collect data from role-played interactions in the lab instead. To create representative role-play scenarios, we interviewed people with retail work experience to learn more about the types of tasks and interaction that occurs there.

12 native level Japanese speakers with retail experience were recruited to participate in the interviews (7 female, 5 male, average age 39.3, s.d. 9.8). The interview format was semi-structured and consisted of first informing the participant of the interview's purpose and then asking 13 questions about what tasks they worked on in the retail store, how they worked and interacted with other staff, how they interacted with customers, etc. Participants were encouraged to respond freely and an interpreter helped translate between English and Japanese. Each interview took between one and two hours and each participant was payed 6000 JPY (about 54 USD).

The participants had experience in a variety of different retail stores, including large department stores, grocery stores, specialty shops (ballet, pets, alcohol, suits), apparel shops, shopping malls, and convenience stores. The roles of participants in these stores ranged from store manager, section manager, owner, part-time staff, customer service manager, regional manager, direction leader of marketing, department store direction leader, and general full-time staff. We focused the interviews on their experience on the floor, where we envision robots to be most useful.

B. Summary of Tasks 1) Tasks: The tasks collected fit into 11 broad categories: managing the cash register, supervising and managing junior workers, managing stock, customer service, shoplifting prevention, communication among staff, cleaning the store, spying on rival stores, store-specific tasks (e.g. various tasks dealing with animals in the pet shop), and other tasks (advertising, organizing shopping carts, etc.).

2) Customer-staff Interactions: We found that many customer-staff interactions occur in all types of retail stores, for example greeting customers, answering customer questions, asking customer preferences, recommending products, answering phones, walking around the store to ask if any customer needs help, guiding customers who ask for a specific product, etc. Some interactions only occur in certain types of stores, for example helping customers try on makeup, measuring customers for suit fitting, helping customers try on shoes, and gift wrapping. Sometimes certain types of customers need to be classified and dealt with in different ways, such as customers who need help vs. just browsing, customers who are likely to complain, and regular customers. Some types of interaction occur only with regular customers, such as making small talk or taking actions based on their preferences.

3) Staff-staff Interactions and Communication: Many types of staff-staff interaction occur where the staff are co-present, such as when one staff member trains another to do some task, asks another to do some task, asks another a question, needs access to a restricted resource, or when multiple staff collaborate on a task (e.g. stocking shelves or taking inventory).

More generally, communication among staff is important for running a retail store. In many stores the day opens or closes with a staff meeting in which important information is shared (e.g. about events in the area expected to draw many customers, recent shoplifting events in the area, which displays to put out, and the status of ongoing tasks such as product orders). During busy times, staff communicate where they are going and what they are doing. Non-verbal communication is also important, for example eye gaze can be used to signal they need assistance with a customer. At the end of a shift, staff will tell the person taking over the state of on-going tasks, what must be done, etc. Communication is often face-to-face, but in some large stores staff communicate via microphones and ear pieces or some idiosyncratic system (e.g. in one store staff communicated which department needs help by sending by cell phone a number representing the department). When staff are not co-present but must communicate, written notes are used. Sometimes staff must also communicate with other branches, for example to coordinate their displays. During non-busy times, small talk is important to let staff learn about each other (including their skills and preferences) and build good relationships (which makes it easier to later ask for help). Staff also communicate among themselves to share the most efficient ways of performing tasks. 4) 3-way Customer-staff-staff Interactions: Some interactions involve a customer and multiple staff, such as when one staff member brings a trainee along to demonstrate customer service or when a customer asks a question requiring the staff member to bring someone more knowledgeable with information about a product or how to perform some process (like using a printer at a convenience store).

5) Planning and Coordination:

We found that most frequently staff split up the tasks and worked on them individually, in parallel (e.g. managing the cash register, announcing sales, and stocking shelves). Sometimes multiple staff worked together on the same task at the same time, for example in stock management one person would count product while another checks a list. Sometimes multiple staff worked together on the same task at different times for example when a product arrives and must later be given to a certain customer. Sometimes lower level workers must coordinate with higher level workers because they do not have access to certain resources, such as using a computer to make orders. 6) Task Allocation: When coordinating multiple tasks to decide who will do which tasks, sometimes staff decide among themselves and other times a manager decides. In either case, several attributes of each staff member are considered when making the decision, including their preferences, skills, job title or position, and gender (e.g. in some stores it is better to let female staff help female customers). Furthermore, attributes of the task are also considered, including task priority, department or section of the task, and time of day or required sequence of tasks. Fig. 2. Example of staff-staff-customer 3-way interaction. When the customer asks for information unknown to the staff member, she goes to fetch a second, more knowledgeable, staff member and introduces her to the customer.

IV. PROPOSED DATA COLLECTION

We set up a (7x8m) lab space to look like a camera shop. We plan to invite participants to role-play staff-staff, customerstaff, and customer-staff-staff interactions, and record their audio and motions. Each data collection session will have two staff members (two-recurring participants with service experience) and one customer, who will role-play multiple scenarios. Kinect Azure sensors will be used to track participants motions (32 joint positions) over time, wireless lapelmounted microphones will record audio data, inter-channel suppression [START_REF] Ishi | Hearing support system using environment sensor network[END_REF] will be used to isolate individual participants' audio, and automatic speech recognition will transcribe their speech. To make the social interaction behaviors feasible to learn within time and resource constraints, we specified the camera attributes customers should mainly talk about (price, weight, color, resolution, and camera-specific features). To elicit various behaviors, we will assign staff roles (manager, junior who likes customer service, junior who dislikes customer service, etc.) and customer roles (portrait photographer, nature photographer, novice photographer, curious customer, or window shopper) per scenario.

We found that staff tended to work together in two different ways: First, splitting up tasks and working on them independently, in parallel and second, working together on tasks that required staff to interact.

Independent tasks done in parallel include things like managing the cash register, stocking shelves, and helping customers (Fig. 1). From the staff interviews, we found that staff would communicate among themselves to split up the tasks based on their skills, preferences, etc. and then perform them independently. Interesting dynamics occur when the state of the world changes while they are performing these tasks, such as a customer asking for help, requiring one staff member to call over another who is more knowledgeable but prefers not to interact with customers (Fig. 2). To record training data containing examples of such interactions, we assigned staff participants preferences such as 'liking customer service,' 'disliking customer service,' 'in-depth knowledge of products,' and 'sparse knowledge of products.' Tasks requiring staff to work together include situations where one staff member has access to a restricted resource, such as access to a stock room, a computer, or a license to handle prescription medications, requiring staff without access to interact with that staff member to complete the task, for example when fetching a product from behind the counter for a customer. To record such interactions, we gave one staff participant permission to access a 'stock room' and a 'behind the counter' area containing products which needed to be brought to the customer.

The data collection procedures were approved by the Kyoto University and ATR internal ethics review boards

V. PROPOSED LEARNING SYSTEM

The goal of the system is to learn the social interaction behaviors of a shopkeeper from examples of human-human interaction, such that a robot could perform as a shopkeeper in interaction with real humans. Fig. 3 shows an overview of the complete system that would enable a robot shopkeeper to function at runtime.

The proposed system is based on those in [START_REF] Liu | Data-driven hri: Learning social behaviors by example from human-human interaction[END_REF], [START_REF] Doering | Neural-network-based memory for a social robot: Learning a memory model of human behavior from data[END_REF]. Data collected from the human-human interactions (Sec. IV) is used for training a neural network to predict the next shopkeeper action given the current interaction state. To reduce the dimensionality and make the learning problem more tractable, the raw data is abstracted to a higher level of meaningful information, such as typical stopping locations (via stopping location clustering), proxemics formations (via existing HRI models of proxemics formations, such as waiting, face-to-face, and present object [START_REF] Liu | Two demonstrators are better than one-a social robot that learns to imitate people with different interaction styles[END_REF]), and common shopkeeper actions (via clustering of speech and locomotion actions). Furthermore, the interaction data is discretized into sequences of discrete actions by segmenting the data whenever a customer action is detected (moving to a new location or saying an utterance) or a timeout occurs. In this way, interaction state input -action output training pairs can be extracted from the data without manual data annotation.

After training the network, it can be used to automate a robot to interact with a human customer (Fig. 3). The same sensor network used for human-human data collection is used at run time. To decide the robot's actions in real time, the raw data coming from the sensor network is discretized and abstracted in the same way as was done to prepare the training data. It is then fed into the trained neural network. The neural network then outputs the robot's next action -a shopkeeper action cluster ID corresponding to a spatial state, state target, and speech cluster. The robot moves to the location indicated by the output spatial state and state target and synthesizes the medoid utterance of the speech cluster with text-to-speech. In this way, the robot can respond to the constantly changing state of the interaction with the various interaction behaviors learned from the human-human training data.

The focus of this work is for the robot to interact with fellow staff, not only customers (as the previous work focused on [START_REF] Liu | Data-driven hri: Learning social behaviors by example from human-human interaction[END_REF]). Therefore, it remains to be discovered how well this proposed approach, which is based on the previous work, generalizes to situations with both staff-staff, staff-customer, and 3-way interactions among multiple staff and customers. Specifically, it is anticipated that it may be necessary to integrate into the imitation learning approach a method of modeling the human staff member's mental state (e.g. preferences and intentions) so that the robot can smoothly coordinate its behaviors with fellow staff [START_REF] Chakraborti | Ai challenges in human-robot cognitive teaming[END_REF], [START_REF] Wooldridge | An introduction to multiagent systems[END_REF], [START_REF] Clodic | Key elements for human-robot joint action[END_REF].

VI. FUTURE WORK

This paper reports work in progress towards the goal of training a shopkeeper robot to interact socially with both other staff and customers using a data-driven imitation learning approach. Thus far, we have conducted interviews of people with retail work experience to identify the types of tasks performed in retail stores and the ways in which staff interact with each other and with customers. Based on the interviews, we crafted representative retail interaction scenarios that participants can role-play in an in-lab data collection area to be recorded with a passive sensor network. Data collection, training, and evaluation of the proposed learning approach remains to be done.

If successful, the work will demonstrate a method for training a human-robot interaction system to interact with retail staff and customers, without requiring expensive manual data annotation or hand-coding of interaction behaviors. In the future, such an approach could be applied to a variety of domains, wherever interaction training data can be collected, towards the goal of making social service robots more ubiquitous and helpful to society.

Fig. 1 .

 1 Fig. 1. Example of staff executing multiple tasks in parallel. They coordinate among themselves based on skills, preferences, etc. and the state of the world (e.g. presence of customers) to decide who will do which tasks.

Fig. 3 .

 3 Fig. 3. System Overview. Before runtime, speech features, typical stopping locations, and shopkeeper speech clusters are learned from the training data and the neural network is trained. During runtime, speech and tracking data are collected from a sensor network in the real world, the raw data is abstracted using the models of typical behavior patterns, vectorized, and input to the trained neural network. The neural network outputs the robot's next action.

This work was supported in part by JST, AIP Trilateral AI Research, Grant Number JPMJCR20G2, Japan (problem formulation) and in part by JST CREST under Grant Number JPMJCR17A2, Japan (data collection).


Marie Colmont
email: marie.colmont@ensc-lille.fr

Olivier Mentre

Natacha Henry

Alain Pautrat

Bastien Leclercq

Frédéric Capet

Nora Djelal

Pascal Roussel

Olivier Mentré

Undulated oxo-centered layers in PbLn_3O_4

Keywords: Lanthanum, Lead, Vanadium, Oxo-centered tetrahedra, Flux growth synthesis, Crystal structure, Optical and magnetic properties

come

Introduction

The search for new luminescent materials is a hot topic of today's solid state chemistry. Indeed, it is of necessity to save energy through the replacement of light bulbs with LED-based solid-state white lighting. Most of the actual commercialized white LEDs are based on the conversion of LED light via inorganic phosphors [1]- [3]. Running towards new advanced materials with high quantum yields and a good thermal stability is on a roll. In this context, lanthanum based oxides are promising because of their ability to host emitters, turning then to phosphors. [4]- [6] Following the recent discovery of the new KLa 5 O 5 (VO 4 ) 2 [7] structure and its promising luminescent properties [8], we investigated another ternary system PbO-La 2 O 3 -V 2 O 5 . To the best of our knowledge, the title compound is the first lead, vanadium and lanthanum ternary system. Here, in order to overpass the problem of stability of lanthanum orthovanadate (i.e.LaVO 4 [9]) and lead vanadates (i.e. Pb 3 (VO 4 ) 2 [10], Pb 2 V 2 O 7 [11]…) currently obtained after heating a mixture of primary oxides, an alternative synthetic flux growth route was used. It is known to be a method of choice to grow original architectures from various compositions. Here PbO was chosen both as flux and a reactant, as proposed in [12], leading to the title compound: PbLa 3 O 4 (VO 4 ). This compound appears to be one of the broad series of compounds described using the anion-centered tetrahedra [13] around the four oxo-anions of the above formula. This means that its cationic backbone is built on the association by edges of O(La/Pb) 4 tetrahedra. Accordingly to this anti-tetahedra description, vanadates are considered as isolated and surrounding the [PbLa 3 O 4 ] 3+ polycationic body.

Herein we report on the synthesis and structural characterization of a new lead lanthanum vanadate oxide, and discuss structural relations with the related Nd 4 O 4 (GeO 4 ). Then, its structural stability under air at low (100K) and high temperature (until 1073K) was checked. In a second step, the neodymium compound was synthesized bringing ff electronic transitions and paramagnetism.

Results and Discussion

Single crystals of PbLa 3 O 4 (VO 4 ) were grown using the flux growth method, at 900 °C and in a platinum crucible from a mixture of PbO, La(OH) 3 and V 2 O 5 mixed in a 3 : 1 : 1 molar ratio (see Experimental section below). The crucible was fitted with a platinum lid. It is interesting to note that, due to the refractory behaviour of lanthanum hydroxide, the flux growth technique is often preferred to isolate crystals of novel members [12], [14]. The combined choice of Pb 2+ and La 3+ is governed by their matching within oxo-centered tetrahedra (OPb 4 ) [15] (OBi 4 ) [16], [17] or (OCu 4 ) [18]… The "flexibility" induced by highly polarizable lone pair Pb 2+ species is another key-parameter, this cation being susceptible of sizeable Pb-O distances and the inherent possibility for mixed oxo-centred units, for example in O(Pb,Bi) 4 [19], [20], or O(Pb,Cu) 4 [21].

Small orange crystals (0.11 × 0.09 × 0.02 mm 3 ) of PbLa 3 O 4 (VO 4 ) were studied using singlecrystal X-ray diffraction analysis ( ), [22]. In this compound the ionic mobility of the substoechiometric oxo-centred anions was shown after substitution of Ge 4+ by Ga 3+ . [23] Selected structural data and main distances for both structures are compared in Table 1. 3+ cationic layers are growing parallel to the (a,c) plane, built on the edge-sharing of (OLa 4 ) and (OPbLa 3 ) tetrahedra and connected according to a zig-zag cross section, with 3 tetrahedra long segments (figure 1a)). The co-presence of La 3+ /Pb 2+ in the oxo-centered tetrahedra is extremely rare. To the best of our knowledge this new phase is the second example of a structure hosting such mixed units (i.e. (OPb 3 La) and (OPb 2 La 2 ) in Pb 6 LaO 7 X, X= Cl, Br). [24] It is noteworthy that the La 3+ /Pb 2+ ordering located Pb 2+ at the Cresnel-edge of the zig-zag layers so that its lone pair (LP) is able to point outward between two V 5+ cations. The position of the lone pair of Pb 2+ was estimated using the Verbaere and co-workers method as implemented in the HYBRIDE software. [25] This is based on the local electric field E calculation in the whole crystal using the Ewald's method. [26] Under the influence of this electric field on the cation center, the lone pair is displaced by an amount d deduced by the relation μ= q*d= α*E with q corresponding to the lone pair charge (equal to -2) and μ corresponding to Pb 2+ -E dipolar momentum. We have used Pb 2+ Shannon polarizability of α= 6.58 Å 3 .

The description of the method is described elsewhere [27], [28]. The results are given Table S1. The In the literature, Nd 4 O 4 (GeO 4 ) crystal structure was first reported by Merinov et al. [22] in an orthorhombic P-centered unit cell. The cross-substitution of Nd (ionic radius R=0.983Å) by La and Pb (R=1.032Å and 1.19Å, respectively), and Ge (R= 0.39Å) by V (R= 0.355Å), induced significant modifications of the unit-cell volumes (767.44Å

O 2 (V 1-x P x O 4 )
case. [30], [31] In our case, the matching between the r X /r Ln ratio is considerably modified driving the symmetry loss. It involved in Nd 4 O 4 (GeO 4 ) two Nd atoms (i.e. Nd1 and Nd2 figure 2b)) located on crystallographic sites with local symmetry m out of the mirror plane perpendicular to c-axis compared to a single La1 located on a mm site, and to the tilting of the GeO 4 tetrahedra. The higher symmetry of the title compound comes together with the location of V 5+ on a mm site, compared to m for the twisted Ge 4+ ions. This difference of symmetry is responsible for different structural complexity as expressed by the Shannon information's content per atom and per unit cell. [32] These values, calculated using the ToposPro software [33], showed a larger structural complexity for the low-symmetric Nd-based structure (I G = 4.24 bits/atom, I G,total = 220.42 bits/cell) than La-based structure ((I G = 2.93 bits/atom, I G,total = 76.21 bits/cell) putting both compounds in a very common area in terms of complexity taking into account the complexity distribution reported for inorganic structure database. [34] To probe potential symmetry loss at low temperature, XRD data of the same La-based single crystal were collected at 100K. Results of the refinement are presented in Table S1. Apart from the thermal contraction no sign of phase transition was evidenced.

Powder synthesis

A powder of PbLa 3 O 4 (VO 4 ) was then synthesized from a mixture of PbO, La(OH) 3 and V 2 O 5, finely grinded in an agate mortar. The sample was then successively heated at 600° and 900° in an alumina crucible. Several intermediate grindings were necessary until achievement of a phase almost pure (additional small peak at 26° figure S1) assigned to LaVO 4 ). The lattice parameters refined from the powder diffraction pattern (using JANA 2006 software [35]) led to a= 5.8812(3)Å, b= 17.9429(9)Å and c= 7.9014(4)Å which is in good agreement with those refined from the single crystal data.

Temperature dependent XRDP study.

The stability in temperature was studied at high temperature by Differential Thermal Analyses (DTA) and in situ High Temperature X-Ray Diffraction. Figure S2a) shows the typical DTA plot obtained for PbLa 3 O 4 (VO 4 ) under air from RT to 800°C at a heating rate of 10°C.min -1 . A small, endothermic peak is observed on heating at 310°C. In agreement with results of ref [36], it was assigned to the LaVO 4 minor impurity. We also checked the sample by in situ HTXRD under air in similar conditions. The refinement of both unit cell parameters and volume allowed the determination of the linear thermal expansion coefficients: α V = 35.3, α a = 9.8, α b = 16.9 and α c = 8.3 (10 6 . K -1 ). The thermal expansion of this material is twice higher along b-axis (so anisotropic), matching well with the rigid oxo-centered units and 2D-lattice growing in the (a,b) plane. In contrast we expect the more ionic external Ln/Pb---O-V to vary more strongly upon heating.

Infrared spectroscopy

The infrared spectrum of PbLa 3 O 4 (VO 4 ) is displayed figure S3, where bands between 700 and 800cm -1 are assigned to [VO 4 ] 3-vibrations mode, the one around 440cm -1 to La-O and at 490 cm -1 and 840cm -1 to Pb-O vibrations. [37] [38][36]The main information arise from absence of peaks around 3600cm -1 , usually attributed to O-H vibrations, excluding the presence of hydroxyl groups or water molecules, although lanthanum oxides are known to be easily decomposable by hydroxylation or incorporation of water molecules at the surface.

Ln substitution

The possibility to substitute La 3+ by Nd 3+ was checked using the same experimental route than the one described above starting from Nd 2 O 3 oxide precursors. Despite several attempts changing parameters during the solid-state synthesis (temperature, precursors, time…), PbNd 3 O 4 (VO 4 ) was systematically accompanied with a small amount of NdVO 4 (estimated to 8% in weight) (figure S4)

The refined lattice parameters are a= 5.7760(1)Å, b= 17.7534(3)Å and c= 7.7330(2)Å.

Optical properties: UV-vis spectroscopy

Figure 3a) shows the UV-vis diffuse reflectance spectrum (DRS) of the La-compound between 300 and 800nm (or 4.13 and 1.55eV). One can note a broad absorption edge below 3.3eV with a bump at lower energy (around 2.6eV). This corresponds to an absorption in blue-green responsible for the orange colour of the compound (V3d transitions). Then, this broad absorption edge includes Pb 2+ , La 3+ and VO 4 interactions. However its continuous decay above the fermi level shows the important contribution of defect levels.

Concerning the Nd-compound, the global behaviour of the UV visible absorbance is almost similar to La-compound. In that case, the breaking occurs around 3.05V and the bandgap is estimated to be around 2,85eV, which also justifies the pale green colour of the powder. In addition, the peaks observed at low energy are assigned to the main f-f transitions of Nd as detailed on figure 3.a). the temperature for 2 applied magnetic field (0.1 and 0.01T). In the inset is shown the inverse of susceptibility as function of the temperature, the linear part corresponds to the Curie Weiss domain.

Magnetic properties

The magnetic susceptibility of polycrystalline PbNd 3 O 4 (VO 4 ) was measured under magnetic fields of 0.01T and 0.1T using field cooling and zero field cooling procedures, from room temperature down to 4K (figure 3.b)). In this compound the magnetic moments are given by the three Nd 3+ per FU.

Within experimental resolution, all curves are observed to be superimposed, in agreement with a pure paramagnetic regime and in absence of magnetic ordering. As shown in the inset of figure 3.b), a Curie-Weiss behaviour is observed for T≳50K, and fitting the linear part of  -1 (T) gives a molar Curie constant C mol = 5.02emu.mol -1 .K, giving an effective moment  eff ≈(8.C mol ) 1/2 ≈6.3  B /f.u. (i.e. gives 3.64  B /Nd) and a Weiss temperature  W ≈-38K, a priori indicating moderate antiferromagnetic interactions.

It is in very good agreement with the free ion value of Nd 3+ which is 4f 3 (S=3/2, L=6, J=8/2,

 eff =(2g J 2 J(J+1)) 1/2  B ≈3.62 B )
. The consideration of a small amount of NdVO 4 impurity (NdVO 4 is also a paramagnet with Nd 3+ ion) should not change significantly the experimental value.

Note that the deviation from a simple Curie Weiss law observed at low temperature T≲50K is very similar to what was previously reported in other paramagnetic oxides containing Nd 3+ . This deviation was shown to be due to splitting of the ion ground state by the crystal field. [39] It follows that the negative Weiss constant that we inferred from the Curie-Weiss fitting of the experimental data reflects likely such crystal field effects of the Nd 3+ ground state and not antiferromagnetic interactions.

Conclusions

In an attempt to find new inorganic phosphors able to host emitters for white LEDs applications a new lanthanum lead vanadate was isolated and fully characterised from a structural point of view. Its structure is similar to Nd 4 O 4 (GeO 4 ), already reported in the literature. This crystal structure is flexible as it may host different kind of atoms in its cationic backbone and around with different nature of XO 4 tetrahedra. It opens the door to further design of structures, playing both on the nature of atoms and on the size and shape of the layers. Indeed, in the present case, the height of steps is 2x2 but it has been shown in other systems that it can 3x4. [7], [40] This series of materials can thus be tuned in order to build 2D materials from sizable 2D building units. This approach was already successfully applied in the case of Bi-based materials [17], [41] and we believe that it may be extended to La-based materials, after optimization of synthesis routes. Concerning the possibility of introducing emitters, the insertion of neodymium is very promising and opens the door to introduction of other lanthanides and especially Sm 3+ , Eu 3+ , Tb 3+ or mixtures of them.

Experimental Section

Synthesis of I: Single crystals of PbLa 3 O 4 (VO 4 ) have been prepared by the flux growth method.

A mixture of V 2 O 5 (2mmol, Alfa Aesar, 99%), La(OH) 3 (1mmol, Alfa Aesar, 99,5%) and PbO (5mmol, Aldrich, 99,9%) was solely ground and loaded into a platinum crucible. The crucible was loaded into a tubular furnace heated to 1000°C for 10 hours. Then the temperature was lowered to 800 °C during 48 hours. Afterwards, the furnace was switched off. Block-shaped orange single crystals of the titled compound were found in large amount.

X-Ray crystallography. A suitable orange crystal of PbLa 3 O 4 (VO 4 ) with approximate dimensions 0.023 × 0.047 × 0.072mm3 was selected under polarizing optical microscope and glued on a glass fibre for a single-crystal X-ray diffraction experiment. X-ray intensity data were collected on a Bruker APEX2 CCD 4K area-detector diffractometer using an Incoatec Mo-Kα Microfocus source (λ=0.71073 Å) at room temperature and at 100K. Any important difference is observed between both temperatures and so only the room temperature refinement is presented in this paper. An orthorhombic unit cell with a=5.8858(4)Å, b=17.9380(12)Å, c=7.99079(5)Å and V= 834(10)Å 3 was revealed.

Several sets of narrow data frames were collected at different values of θ (3.44 to 28.31°), using 0.3° increments of ɸ or ɷ to obtain a full sphere of three-dimensional data. Data reduction was accomplished using SAINT V7.53a. [START_REF]SAINT: Area-Detector Integration Software[END_REF] The substantial redundancy in data allowed the use of a semi-empirical absorption correction (SADABS [START_REF]SADABS: Area-Detector Absorption Correction[END_REF]), on the basis of multiple measurements of equivalent reflections. The systematic absences of reflections are consistent with the space group Cmcm. The structures were solved using SUPERFLIP [START_REF] Palatinus | [END_REF] and refined by full-matrix least-squares procedures on F using JANA2006 program. [35] The final R value of 2.37% was obtained for 578 unique reflections with I>3σ(I) with all structure refinement details given Table 1.

Powder X-Ray diffraction was performed at room temperature in the angular range 10-80° with a scan step width of 0.02° using a D8 Advance Bruker AXS diffractometer in Bragg Brentano geometry equipped with a 1D LynxEye detector with a CuKα1,2 radiation (λ = 1.540598 Å and 1.54439Å). Full pattern matching was performed using JANA2006. [35] The X-ray thermodiffraction experiments were also performed with a diffractometer D8 ADVANCE (Bruker-AXS) in Bragg Brentano geometry and equipped with a 1D LynxEye detector. The patterns were measured in air every 100°C from RT to 850°C (heating rate of 10°C.min -1 ) using an Anton-Paar XRK900 furnace.

Infrared spectra was measured on a Perkin Elmer Spectrum Two spectrometer between 4000 and 400 cm -1 , equipped with a diamond attenuated total reflectance (ATR) accessory.

UV/Vis spectra were collected at room temperature using a Perkin Elmer Lambda 650 spectrophotometer in the 300-800nm range. Before the measurement, the blank was measured using BaSO 4 (standard for 100% reflectance) in order to calibrate the device.

Magnetic properties were measured using a Squid MPMS (Magnetic properties measurement system, Quantum Design) in dc mode. The temperature range was 4-300K and magnetic field values were 0.1 and 0.01T.

Acknowledgement

This work was carried out under the framework of the Multi-InMaDe project supported by the ANR (Grant ANR 2011-JS-08 00301). The onds Europ en de eloppement gional ( E ), C , gion ord as-de-Calais, and Minist re de l'Education ationale de l'Enseignement up rieur et de la echerche are ac nowledged for funding the X-ray diffractometers. The author thank J.F. Blach for fruitful discussion and Laurence Burylo for X-ray diffraction.

Figure 1 .

 1 Figure 1. Projection of the crystal structure of PbLa 3 O 4 (VO 4 ) a) along a-axis, b) along c-axis, c) along b-axis. It is built on stacking of [PbLa 3 O 4 ] 3+ zig-zag cationic layers d) surrounded by e) isolated VO 4 tetrahedra. The lone pair of Pb 2+ are highlighted in dark grey. They point outward the layers, between two V 5+ cations

  refined lone pair coordinates are [0.5, 0.2141, 0.75] corresponding to a Pb-LP distance of about 1.36 Å. This is a realistic value and the LP exactly takes place in the empty space between two VO 4 tetrahedra aligned along a-axis (figure1b)). The geometry of the VO 4 tetrahedron is quite regular with V-O distances ranging between 1.689(5) and 1.751(5)Å and O-V-O angles between 104.2 and 110.5°. This compound is structurally closed to Nd 4 O 4 (GeO 4 ) (figure2) where La 3+ , Pb 2+ and V 5+ are replaced by Nd 3+ , another Nd 3+ and Ge 4+ .

Figure 2 .

 2 Figure 2. Projections of the crystal structure of Nd 4 O 4 (GeO 4 ) [23] along a) b-and b) a-axis. It is built on the same kind of [Nd 4 O 4 ] 4+ polycationic layers surrounded by isolated GeO 4 . The differences with PbLa 3 O 4 (VO 4 ) are highlighted to evidence the reduction of symmetry leading to

Figure 3 .

 3 Figure 3. a) Optical absorption spectra for PbLa 3 O 4 (VO 4 ) (blue) and PbNd 3 O 4 (VO 4 ) (red). The f-f transitions of Nd 3+ cations are detailed, b) Molar magnetic susceptibility of PbNd 3 VO 8 as function of the temperature for 2 applied magnetic field (0.1 and 0.01T). In the inset is shown the inverse of susceptibility as function of the temperature, the linear part corresponds to the Curie Weiss domain.

Table

  ). The compound crystallizes in the Cmcm space group with

	unit	cell	parameters:	a = 5.8686(6) Å,	b = 17.8980(18)Å,	c = 7.9190(7)Å,	Z = 4,
	R 1 [I > 3σ(I)] = 0.0237, GOF = 1.70. The atomic positions, displacement parameters are given in
	Supplementary Information S1, S2 and S3. The crystal-structure data for PbLa 3 O 4 (VO 4 ) phase were
	deposited with the depository number CSD-431424.
		PbLa 3 O 4 (VO 4 ) is isotypic with the previously reported Nd 4 O 4 (GeO 4

Table 1

 1

	. Crystallographic data and selected bond distances (Å) for PbLa 3 O 4 (VO 4 ) (I), and
	Nd 4 O 4 (GeO 4 ).[22]

PbLa 3 O 4 (VO 4 ) Nd 4 O 4 (GeO 4 )[22]

	Space group	Сmсm	Pb2 1 m
	a / Å	5.8686(6)	5.727(2)
	b / Å	17.8980(18)	17.927(5)
	c / Å	7.9190(7)	7.475(2)
	V / Å 3	831.78(14)	767.4(4)
	Z	4	4
	D calc /g•cm -3	6.409	6.730

Selected distances in PbLa 3 O 4 (VO 4 ) (Å) V5-O6x2

		1.689(5)	O5-La1x	2.481(5)
	V5-O2x2	1.751(5)	O5-Pb1x1	2.188(5)
	O4-La3x2	2.364(3)	O5-La3x2	2.415(3)
	O4-La1x2	2.490(3)

Selected distances in Nd 4 O 4 (GeO 4 ) (Å) Ge1-O6x2

		1.765	Ge2-	1.733
			O8x2
	Ge1-O4	1.777	Ge2-O5x2	1.737
	Ge1-O2	1.820	Ge2-O7	1.758
	O1-Nd3	2.272	O3-Nd3	2.183
	O1-Nd5x2	2.275	O3-Nd1	2.417
	O1-Nd1	2.416	O3-	2.424
			Nd5x2
	O9-Nd4	2.187	O10-	2.280
			Nd6x2
	O9-Nd2	2.284	O10-Nd4	2.284
	O9-Nd6x2	2.373	O10-Nd2	2.471
	O11-Nd5	2.256	O12-Nd5	2.242
	O11-Nd2	2.548	O12-Nd1	2.377
	O11-Nd1	2.264	O12-Nd6	2.388
	O11-Nd6	2.411	O12-Nd2	2.44

  3 for Nd compound versus 831.78Å3 for the La counterpart; and symmetries. Oxo-centered structures with counter oxo-anions often display versatile symmetries depending on the size-matching between OM 4 and XO 4 groups. For instance, the BiM 2 O 2 (XO 4 ) series show a plethora of distortions[29] sometimes accompanied by large supercell ordering and/or incommensurate modulations tuning the X chemical nature, see the BiCu 2

Entry for the Table of Contents

This paper reports the crystal structure of PbLn3O4(VO4), (Ln= La and Nd) and its structural relationship with Nd4O4(GeO4). Optical and magnetic properties were also studied when appropriated.