M Bunel

C Duchêne

A-M Olteanu-Raimond

M Villanova-Oliver
email: marlene.villanova-oliver@univ-grenoble-alpes.fr

G Bonhoure

T Jouan

An approach for identifying and analysing reference features and spatial relations used in mountain emergency calls

Keywords: indirect spatial referencing, spatial knowledge representation, spatial relation, reference features, sketch map, mountain rescue

The CHOUCAS project aims at helping mountain rescue services to locate a victim who describes her location by means of spatial relations with reference geographic features. In this context, the study presented in this paper aims at better understanding what reference features and spatial relations are used to locate oneself in a mountain area, with the ultimate aim of designing tools to help the rescuers. Audio tapes of real emergency calls were used as starting material. The core of the work is the design of a template to transcribe the location information contained in these calls while structuring it. A first analysis of the transcribed calls shows that projective or directional static spatial relations are the most used, and that a finer classification of reference features and spatial relations is needed. In order to synthetically present the location information contained in a call, an additional representation by means of a sketch map with a dedicated symbolisation is proposed.

Introduction

The project named CHOUCAS (choucas.ign.fr), funded by the French National Research Agency, aims at proposing methods and tools to improve the decision making process of rescue workers who have to localise victims in mountain areas from an emergency call they receive (Olteanu-Raimond et al., 2017a;[START_REF] Olteanu-Raimond | Projet CHOUCAS : Intégration de données hétérogènes et raisonnement spatial pour l'aide à la localisation des victimes en montagne[END_REF]. In several situations, it is not possible to localise the victim using technologies such as GPS. In such cases, the probable location has to be built from different clues collected from what is said during the emergency call. These clues are elements given by the caller to describe his or her location, like "I am on a footpath", "I can see a lake", etc. They give indications on the location by means of spatial relations ("on", "can see") with respect to a reference feature ("a footpath", "a lake"). This way of describing a location is called indirect spatial referencing (ISO, 2003) or indirect georeferencing [START_REF] Hill | Indirect Geospatial Referencing through Place Names in the Digital Library: Alexandria Digital Library Experience with Developing and Implementing Gazetteers[END_REF]. (Hill 2006, p.2) describes it as informal and used in ordinary discourse, contrary to a formal way of describing location that uses coordinates in a spatial reference system, which is call direct spatial referencing (ISO, 2003). The task of the rescuer who receives an emergency call is to transform the collected set of clues (indirect spatial referencing) into a set of possible locations expressed as coordinates on a map (direct spatial referencing). The CHOUCAS project tackles three major issues related to this process: the collection, enrichment and query of geographic data stemming from heterogeneous sources [START_REF] Gaio | Geoparsing and geocoding places in a dynamic space context. The case of hiking descriptions[END_REF][START_REF] Van Damme | Potential of crowdsourced data for integrating landmarks and routes for rescue in mountain areas[END_REF]; the conception of geovisualisation environments aiming at supporting the reasoning of the rescue workers [START_REF] Viry | Improving the search for victims in mountain with geovisualization and competing hypotheses management[END_REF]; and the conception of models for semi-automated spatial reasoning based on the clues extracted from the calls to compute an area for each clue [START_REF] Bunel | Référencement spatial indirect : modélisation à base de relations et d'objets spatiaux vagues[END_REF] and to fusion them to generate a probable location (a fuzzy area) where the victim can be. Underlying these issues (especially the second and third ones), is the necessity to understand and formalise the information contained in such clues in order to be able to exploit them. This is in line with the notion of Naïve Geography, defined by [START_REF] Egenhofer | Naive Geography, in Spatial Information Theory A Theoretical Basis for GIS[END_REF] as "the field of study that is concerned with formal models of the common-sense geographic world". This paper describes an on-going study that aims at formalising and better understanding the information contained in clues given by persons who call the French mountain rescue service, based on a corpus of audio tapes of emergency calls. The rest of the paper is structured as follows. Section 2 describes the objectives of the study and the audio corpus we started from. Section 3 describes a tabular template that was set up in order to transcribe and structure the information contained in the audio calls. Section 4 presents a first analysis of the collected structured information. Section 5 reports on an additional proposal, which consists in providing a visual synthesis of the information contained in a call under the form of a sketch map. Finally, section 6 concludes with a summary and a discussion on this study.

Objectives

In this paper, we present the approach we set up to collect and analyze spatial relations and reference features from an audio corpus of about forty-five real emergency calls provided by the mountain rescue team, the High Mountain Gendarmerie Platoon of Grenoble. Listening these recordings was very useful to better understand the nature of the information and to better perceive the content of the exchanges in real situations. For example, the following elements are noted:  Callers do not describe locations with a consensual vocabulary (neither for toponyms nor for conceptual terms used for describing reference objects);  Approximate information is often provided ("I walked one to two hours");  Information can be provided in terms of negation: "there is a hut: I am not there", which is in itself useful information;  Information is given on what the caller sees from his/her position which refers to intervisibility situations;

 The degree of reliability to be given to the information the caller gives may sometimes be questioned. Although very informative in their original form, these raw materials (audiotapes) obviously required being structured in a way allowing us for an efficient analysis of content that serves the different objectives of the CHOUCAS project. The goal of the information structuration is to formalize knowledge using a model that covers all the facets of information relevant to our scientific challenges.

A finer identification of salient references features and spatial relations employed by callers is also needed for the part of our work dealing with the design and development of a geovisualisation tool that support the reasoning process of rescuers. Callers can give more or less details, be sure of themselves or not when telling their trail, often employ vague, uncertain, imprecise words in their descriptions. The structuration of information is a first step to be able to provide relevant spatial data collect and delivery components for processing the emergency call.

For the collection, enrichment and query of geographic data, structuring the knowledge contributes to the constitution of a corpus of callers' expressions that guide the approaches of automatic matching of heterogeneous data. This will also help to identify, in relative positioning expressions of callers, some real objects of the terrain that are not currently explicitly referenced in data sources, but could be automatically computed by spatial analysis methods. Examples of such objects are yaw turns or crossroads that could lead us to propose semantic and geometric enrichment of geographic data sources.

For the research work dealing with spatial reasoning algorithm to compute areas based on different clues and to fusion them to determine possible localization areas, information structuration is important to explore more precisely the concepts of the terrain used as reference in real situations and in association with which spatial relations. Even slight variations in the vocabulary used, they are important to be detected to accurately transcribe the semantics of the situation the caller describes. It is not always the same to explain being under a bridge (in the sense of sheltered under the bridge) and being below a bridge (at a lower altitude for instance). In these cases, the methods to be used for transforming the associated clues into location areas are different.

Building a template to transcribe emergency calls

Our aim is not to annotate a verbal speech while keeping the words unchanged. It is to interpret the spatial information contained in it, and structure this information in a table. However, it is interesting to notice that some of the retained columns are close to the structuration of information proposed in ISO-Space [START_REF] Pustejovsky | ISO-Space: Annotating Static and Dynamic Spatial Information[END_REF], an annotation scheme dedicated to the semantic annotation of spatial relations directly in texts that has become an ISO standard.

A template was developed as a tabular file through a collective and iterative work based on the study of a few audio tapes. The template is to fill in from the listening of the audio files and allows the storage of complex expressions composed of verbs, spatial relations, references features, and modifiers. It is structured in three sections: metadata, interpretation of expressions, and spatial features.

The metadata tab describes the name of the audio file, the time of the call (e.g. year, month, day or hour and specifies if the caller is the victim or a third party. Beyond the descriptive aspect of the audio file, this section allows to collect the types of mountain activities and the real location of the victim (if the information is accessible), which can be used respectively for adapting methods that transform an indirect location into a direct location (an area) and to validate the proposed methods.

The tab named interpretation of expressions is structured into 17 columns. Three main categories can be distinguished: extract, context and expression. The first category (see Table 1) describes an extract (as heard in the audio call), identifiers of the extract, and timestamp (i.e. time where the extract occurs in the audio file). It allows to better understand the expression and to rapidly identify the time where the expression was mentioned in the audio file. We need to distinguish between extract and expressions, because sometimes two expressions are linked together and cannot be dissociated such as I'm at Grand Tollier, I'm just below" or "I'm in front of a rock which is on the left of the road". The identifiers are assigned by the transcriber. The Id expression allows to distinguish extracts having more than one expression, each expression being coded separately (a line of the table). In the example given in Table 1, the extract (Id extract = 3) contains two expressions: "I'm at the Grand Tollier" (Id expression = 1) and "I'm just below" (Id expression = 2).

Table 1: Columns describing the extract "I'm at Grand Tollier, I'm just below"

The second category allows describing and understanding the context of each expression. The columns of this category require on interpretation of the extract such as speaker (i.e. specify if the expression is used by the victim, the rescuer, or the (third party) caller), and a confidence (expresses the confidence allowed by the transcriber to what it said: strong, normal, or weak). In the example illustrated in Table 1, the speaker is the victim and the confidence is normal (the speaker has no doubt about his/her location). Finally, the last category allows interpreting and coding each expression. The following columns are defined: subject (identifies if the subject is the victim or another reference feature), reference feature (specifies the used reference feature), spatial relation, and modifiers. The modifiers allow to better describe characteristics of subjects, verbs (walk slowly), spatial relations (just in front) and reference features (round lake). They are intended to be used later to better tune the parameters of the methods that compute a possible area of location given an expression. Table 2: Columns describing the expressions: "I'm at Grand Tollier" "I'm just below", I see partially a lake just in front", "I have to my left a round lake", "I was walking slowly to a ski station".

Let us mention that for ternary spatial relations, two references features are present in the expression (e.g. "I'm between Rosay village and a huge bridge"). For modelling ternary spatial relations, two new columns are added for identifying the second reference feature and its modifier.

Finally, the entity tab describes for each reference feature identified in the expression its type (e.g. lake) and its name if appropriate (Lake of Roselette). This section allows identifying the types of reference features used by people as a landmark when describing their location and the followed itinerary in the context of different mountain activities. Let us mention that coding these two columns sometimes requires that the transcriber takes into account the spatial context by looking on a map and consider the whole extract or other extracts found in the same given audio file. If the caller says "I'm in Chalence", it is difficult to know the type of the feature or if the name of the entity is correct. In the given example, the correct name is Coomb of Chalence, and the type is coomb.

For each element of the template, a definition and explanation of how to fill it is provided, and different examples of how extracts and expressions should be coded into the template are also given to the transcriber.

First analysis of the location information within the transcribed emergency calls 4.1 Semantic Classification

The template has been filled with two corpora of emergency calls. The first corpus is composed of 15 emergency calls, transcribed in the template by a rescuer and partially verified. The second corpus is composed of 30 emergency calls, transcribed and verified by the authors. In total, 374 clues containing a spatial relation have been identified. The spatial relations are classified in two classes according to their semantic properties: static relations (i.e. describes a fixed position) vs dynamic relations (i.e. describes a movement or a route). These classes are similar to those proposed by [START_REF] Borillo | L'espace et son expression en français[END_REF] for classifying spatial prepositions, but, unlike [START_REF] Borillo | L'espace et son expression en français[END_REF], we chose to classify the spatial relations instead of spatial prepositions. This choice is motivated by the semantic variability of the French spatial prepositions (Vandeloise, 1986, p.18;Borillo, 1998, p. 84). A same preposition can be static or dynamic according to the context. For example, the French preposition "à" is dynamic in the sentence "Je vais à la montagne" ("I'm going to the mountain") and static in the sentence "Je suis à la montagne" ("I am in the mountain"). The static relations are subdivided into five classes: topologic relations (denote inclusion or connection), projective and directional relations, qualitative distance relations, quantitative distance relations (including quantitative absolutes altitudes) and visibility relations. This subcategorization also helps us to distinguish multiples semantics of a same preposition. To use again the example of the French "à" preposition, it may be static and topological, like in the expression "Je suis au sommet" ("I am at the summit") or static and denoting a quantitative distance, like in the expression "Je suis à 500 mètres du sommet" ("I am 500 meter away from the summit"). This subcategorization is inspired by the classification of spatial relations proposed by [START_REF] Clementini | Directional relations and frames of reference[END_REF]. However, we chose to add to this classification a class for the visibility relations, and we distinguish qualitative and quantitative distances. [START_REF] Borillo | L'espace et son expression en français[END_REF] proposed another classification distinguishing topological and projective prepositions. But, these two classes are too broad and the terms used to name them have a meaning different from that usually used in geomatics. Despite these modifications, some categories are still not totally satisfactory, some spatial relations being difficult to classify. For example, the expression: "I am on the bottom of the ski slope", can be classified as a topologic relation but also as a projection and directional relation. For this kind of spatial relations, we choose to categorize them as projection and directional relation, but this choice is questionable. We chose not to detail the classification of dynamic relations, indeed theses spatial relation have not yet been analyzed, especially because their modeling supposes to make hypotheses about the route followed by the victim (or the caller).

Quantitative analysis

Among the 374 identified instances of relations, 286 are static and 88 are dynamic (Table 3). Among the corpus, the visibility relations are the less used (18 occurrences). Distance relations, whether qualitative or quantitative are also rather rarely used (respectively 24 and 31 occurrences), contrary to the topologic relations (113 occurrences) and the projective or directional relations (95 occurrences). We did not identify any significant differences between the two corpora. Each spatial relation is associated with a reference feature. In our corpus, a lot of reference features are specific to the mountain context. For example the most used reference features (around 38 %) are related to orography (e.g. "summit", "rock", or "plateau"). This category is wide, and contains objects of very variable size, such as mountains and glaciers or rocks and passes. Furthermore, some types of orographic features are missing from spatial databases, which require an enrichment work. The orographic features are mainly used with static relations, whether topologic ("in a valley") or projective ("on the other side of the ridgeline"). A majority of references features are named (around 58 %); they are generally summit or other natural features, like lakes or salient rocks. Another important part (32 %) of named entities denotes villages, city and more generally, localities. But no visibility relation refers to this latter type of entities in the analyzed emergency calls: the visibility relations are mainly related to salient natural objects, like summits or lakes. In addition to the previous categories, including a majority of references features, we note the use of immaterial objects (coordinates, altitude) in some cases. Sometimes, the caller describes her/his position using map elements, like in the expression "I am under the red dashed line". This case is rare, but it shows the importance of the referential (in that case the map) and more generally of the context in the interpretation of an utterance in natural language, as defended by [START_REF] Bateman | A linguistic ontology of space for natural language processing[END_REF].

Spatial relations

However, this quantitative analysis needs to be improved in further research. First, the classification of spatial relations is too broad to characterize their semantics, and by extension, to make a precise analysis. Therefore, we are currently working on the definition of an ontology of spatial relations, based on the GUM-Space ontology proposed by [START_REF] Bateman | A linguistic ontology of space for natural language processing[END_REF]. Similarly, the classification of reference features needs to be improved: some classes, like the orography class, are too broad. We are therefore also working on the definition of an ontology of reference features, focused on mountain context. This one is based on the GEONTO ontology proposed by [START_REF] Mustière | Analyses linguistiques et techniques d'alignement pour créer et enrichir une ontologie topographique[END_REF].

Synthetic visualisation of the location information contained in an emergency call by means of a sketch map

Utility of a synthetic visualisation

As reported in the previous section, a quantitative analysis of the terms used to locate oneself is not sufficient and a qualitative analysis is needed, in order to understand the actual semantics of a given term denoting a spatial relation in a given situation. In this respect, the transcription template, once filled for a given emergency call, gives access to the location information contained in the call in a much more practical form than the initial audio tape: only the relevant part of the information remains, it is structured and can easily be read without being constrained by the sequential aspect of the audio tape. However, looking line by line at a table containing lots of columns is still not a very easy way of getting a global view of the used reference features and terms denoting spatial relations in a call. To make the access to the situation described in a call easier, we propose to represent the location information contained in a call as a sketch map, i.e. a (schematic) map "which is drawn from observation rather than to exact scale measurements and which shows the main features of an area" (Collins online dictionary). In our case, only the victim, the caller (if different), the reference features and the related spatial relations used for location should be represented on this sketch map. One sketch map corresponds to one call, therefore if several calls are to be analysed together, one sketch map per call should be drawn. The intended users of those sketch maps are the researchers who work on the analysis of the information contained in the emergency calls (in our case, they are members of the CHOUCAS project). The intended use is to help them figure out very quickly what pairs of (spatial relation, reference features) have been used by the caller to describe the location of the victim in a call. A sketch map could then be viewed side by side with a topographic map of the zone where the reference features that have been identified without ambiguity are highlighted (Figure 1), as well as the actual position of the victim, if known from the filled transcription template, in order to understand the semantics of the used spatial relations. Several sketch maps (and associated annotated topographic maps) could also be observed together to detect cases where similar spatial relations have been used and investigate if their semantics seems similar, or on the contrary, situations that seem spatially similar but where the used spatial relations are different.

Designing the sketch maps

A design for the sketch maps was proposed and assessed in the context of a student project. Symbols were designed for the reference features and spatial relations that appeared the most frequently in the first corpus of calls transcribed in the template. It was assessed that there is no need to distinguish between all types of reference features, therefore all features are represented by the same red dot symbol labelled with its type and name (if known), except for features that usually have a "big" linear or polygon spatial extension and on/in which the victim can be situated (forest, road/path). Most of the relations are represented by means of labelled arrows.

Figure 2 shows the final proposed symbols. The absolute position of the different elements (victim, reference features) is considered unknown, so that it is possible to draw a sketch map even if the reference features have not been identified on a map/dataset and the actual location of the victim has not been indicated in the metadata tab of the template. On the sketch map, the victim is positioned in the center, and the used reference features are positioned around. If possible, the features such that the victim is above them are positioned below, and reversely. Only one example sketch map was produced in the context of this work (Figure 3).

Evaluation

The proposed symbols and sketch map were assessed through a user test performed on 28 persons with skills in cartography and geomatics, therefore representative of the intended users of the sketch maps. Three test sessions were organized in sequence, first with 25 students and teachers, then with 1 then with 2 (other) researchers from the CHOUCAS team, with an improvement of symbols every time. During the first session, two tests were performed (12 and 13 persons): the tasks were respectively to interpret the sketch map of Figure 3 without its key (aim: test if the chosen symbols are intuitive), and to draw a sketch map for another transcribed call from the key (aim: test if choosing and placing the symbols on the sketch map is easy). Only the first task was repeated at the second and third sessions.

The drawing test showed that the choosing and placing the symbols from the key seems relatively straightforward. The interpretation test enabled us to improve in particular the symbols proposed for relations "in the forest" (forest represented by a filled region with a fuzzy shape and no boundary line rather than by an empty region with an ellipsoidal crisp boundary line), and "above/below an object" (label + arrow needed). The footprints indicating a place the victim comes from were logically interpreted as denoting a trip by foot. An adaptation for other modes of locomotion has to be made.

It is difficult to draw general conclusions from a test performed on just one occurrence of sketch map, but it is likely that the statement for the relations would also be valid for other relations (label + arrow needed). Further work is needed to consolidate this sketch maps proposal, among others the notion of "frame of reference" for directions [START_REF] Clementini | Directional relations and frames of reference[END_REF] was not addressed.

Discussion and conclusion

The context of the reported study is the need to gain knowledge on how people describe their location by means of spatial relations with reference features in the context of mountain rescue, in order to later propose tools to support the work of the rescuers (GUIs, tools to automatically compute a possible location from a clue, tools for data integration and enrichment). The objective of the reported study is to set up a method to (manually) structure information contained in emergency calls and related to the description of the location of the victim or caller. Such a method was set up and applied to a real corpus of calls: a template dedicated to the manual transcription of the information contained in the calls was defined and used to transcribe 45 calls. A first analysis of the content of these 45 transcriptions was performed and an additional representation of a call by means of a sketch map was proposed. Now, beyond the possible improvements already identified in previous sections, some issues raised during this study deserve discussion.

First, we gained feedback on the designed transcription template. Its use by several people (a rescuer and researchers part of the CHOUCAS team, students) showed that it was not so easy to get familiar with it. As a result, transcriptions of a same call by different people can be heterogeneous, which requires the transcriptions to be consolidated. This is probably due to the complexity of the template, and the fact that the examples provided with it are not necessarily read. A face to face training might be more relevant. Clues that are transcribed with difficulties are especially those where an absolute altitude is used as a reference feature (it is not natural to consider an altitude a reference feature), and those using a projective relation where the referential of directions is intrinsic [START_REF] Clementini | Directional relations and frames of reference[END_REF] as in "I have a lake at my left" (often wrongly transcribed as "I am to the right of a lake").

Another issue that emerged is the multiplicity of possible interpretations for a given spatial relation (e.g. "below" cf. [START_REF] Bunel | Référencement spatial indirect : modélisation à base de relations et d'objets spatiaux vagues[END_REF], and the possible consequences in the future geovisualisation interface that will be built to support the rescuers: provided each relation corresponds to a possible choice in a scrolling list, how to ensure the interface includes the "right" number of possible choices, i.e. enough to distinguish between situations that need to be processed differently to build a possible location, but not too much so that it remains usable by the rescuer?

To enable a good interoperability between the methods dedicated to the computation of a possible location and the interface components, and because the used spatial relations and reference features are not homogeneous from one speaker (caller, rescuer) to another one, it appeared obvious that a shared vocabulary is needed. Therefore, as mentioned in Section 4, a work has been undertaken to build ontologies dedicated to spatial relations and reference features used in the context of location in mountainous areas.

Figure 1 .

 1 Figure 1. Example of an annotated topographic map highlighting the identified reference features used in a call (same call as sketch map of Figure 3).

Figure 2 .

 2 Figure 2. Symbols proposed for recurrent reference features and spatial relations (final version)

Figure 3 .

 3 Figure 3. Sketch map describing the following clues (the caller is with the victim): "We started from the Plateau of Pra mountain hut", "We are below the Plateau of Pra mountain hut". "We are above the Oursière chalet", "We are above the Oursière Waterfall", "We are on the Oursière Waterfall track", "We are in a forest", "We are at an altitude of 1500 meter". Blue labels = English translation, added afterwards for the purpose of this paper.

  The subject can also be characterized by a modifier. The last allows clarifying the subject in time: victim now, victim at a given time, victim at his departure, victim at the picnic break. For all the examples illustrated in Table2, the subject is the victim. The modifier is respectively "victim now" for the first four examples and "victim from the starting point" for the last example.

						Thus,
	four columns are defined for modifiers: subject modifier,
	verb modifier (Verb mod), spatial relation modifier
	(Spatial relation mod) and reference feature modifier (Ref
	feature mod).
	Examples illustrating the interpretation and transcription
	for different expressions are given in Table 2.
	Verb	Verb	Spatial	Spatial	Ref	Ref
		mod	relation	relation	Feature	feature
				mod		mod
	be		at		Grand
					Tollier
	be		below	just	Grand
					Tollier
	see		in front	just	a lake	partially
	have		to my		a lake	round
			left
	walk	slowly to		ski
					station

Table 3 .

 3 Occurrences of spatial relations for our corpus

		Static	Dynamic
	Projective or directional	95
	Topological	113
	Qualitative distance	24	88
	Quantitative distance	31
	Visibility	18

Proceedings of the International Cartographic Association, 2, 2019. 29th International Cartographic Conference (ICC 2019), 15-20 July 2019, Tokyo, Japan. This contribution underwent single-blind peer review based on submitted abstracts. https://doi.org/10.5194/ica-proc-2-12-2019 | © Authors 2019. CC BY 4.0 License.

Acknowledgements

The work reported in this paper is founded by the French National Research Agency (ANR), the French national research agency (ANR-16-CE23-0018 -CHOUCAS).


Cassandre Kouvatas

Nasima Kanwal

Julien Trébosc

Claire Roiland

Laurent Delevoye

Sharon E Ashbrook

Eric Le Fur

Laurent Le Pollès

Julien Trebosc

Rationalization of solid-state NMR multi-pulse decoupling strategies: Coupling of spin

Keywords: Solid state NMR, Multi-Pulse decoupling, heteronuclear scalar interaction, half integer quadrupolar nucleus, simulations, resolution improvement, characterization of inorganic materials

come

INTRODUCTION

In solid-state NMR spectroscopy, improving the spectral resolution is vital for the detailed structural investigation of solid materials. In particular, homonuclear and heteronuclear decoupling have been widely used to remove the significant dipolar couplings that typically affect NMR spectra of solids, but are removed in solution by rapid molecular tumbling. In recent years, attention has been focused on improving the resolution of NMR spectra of nuclei with spin quantum number I = ½ that are broadened by heteronuclear interactions (such as scalar and dipolar coupling) with highly abundant surrounding nuclei. There are several possible ways to remove these interactions. For example, magic-angle spinning (MAS), where the sample is rotated around an axis inclined at an angle of 54.7° with respect to the external field B 0 , leads to a time-dependence of the heteronuclear dipolar coupling, which results in a manifold of spinning sidebands. In addition, the application of radiofrequency (RF) pulses to the coupled heteronucleus during the signal acquisition can be used typically to remove (or in some cases to selectively retain) heteronuclear interactions.

Heteronuclear dipolar-decoupling schemes are commonly employed in solid-state NMR experiments, with the primary aim of improving spectral resolution. Originally employed in solution-state NMR spectroscopy, continuous wave (CW) decoupling [START_REF] Bloom | Effects of Perturbing Radiofrequency Fields on Nuclear Spin Coupling[END_REF] is now also routinely used in solid-state NMR MAS. Owing to the limitations of this simple decoupling scheme, a number of more complex decoupling schemes have been specifically developed for use on rotating solids, some using continuous irradiation or adiabatic pulses, including TPPM (and its related variant XiX) [START_REF] Bennett | Heteronuclear decoupling in rotating solids[END_REF][START_REF] Detken | Simple and efficient decoupling in magicangle spinning solid-state NMR: the XiX scheme[END_REF][START_REF] Equbal | Relative merits of r CW A and XiX heteronuclear spin decoupling in solid-state magic-angle-spinning NMR spectroscopy: A bimodal Floquet analysis[END_REF], the SPINAL schemes [START_REF] Fung | An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids[END_REF], DFS [START_REF] Thakur | Swept-frequency two-pulse phase modulation for heteronuclear dipolar decoupling in solid-state NMR[END_REF], PISSARO or rCW [START_REF] Weingarth | Efficient heteronuclear decoupling by quenching rotary resonance in solid-state NMR[END_REF][START_REF] Equbal | Efficient heteronuclear decoupling in MAS solid-state NMR using non-rotor-synchronized rCW irradiation[END_REF][START_REF] Sharma | Systematic evaluation of heteronuclear spin decoupling in solid-state NMR at the rotary-resonance conditions in the regime of fast magic-angle spinning[END_REF] and other approaches [START_REF] Agarwal | Amplitude-modulated low-power decoupling sequences for fast magic-angle spinning NMR[END_REF][START_REF] De Paëpe | Improved heteronuclear decoupling schemes for solid-state magic angle spinning NMR by direct spectral optimization[END_REF][START_REF] Riedel | Heteronuclear decoupling in rotating solids via symmetry-based adiabatic RF pulse schemes[END_REF][START_REF] Hodgkinson | Heteronuclear decoupling in the NMR of solids[END_REF][START_REF] Madhu | Heteronuclear Spin Decoupling in Solid-State Nuclear Magnetic Resonance: Overview and Outlook[END_REF].

The choice of decoupling scheme depends upon the type of heteronuclear interactions that broadens the spectral lines [START_REF] Paul | On the choice of heteronuclear dipolar decoupling scheme in solid-state NMR[END_REF][START_REF] Delevoye | Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei[END_REF]. It has been shown that the heteronuclear scalar coupling between nuclei with spin quantum number I = ½ spin and surrounding quadrupolar nuclei (I > 1/2) with half-integer spin quantum number can dramatically decrease the spectral resolution and hinder the extraction of structural and chemical information [START_REF] Delevoye | Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei[END_REF][START_REF] Kao | The First Observation of Heteronuclear Two-Bond J-Coupling in the Solid State: Crystal Structure and Solid-State NMR Spectroscopy of Rb4(NbO)2(Si8O21)[END_REF][START_REF] Du | A Solid-State 93 Nb and 19 F NMR Spectroscopy and X-ray Diffraction Study of Potassium Heptafluoroniobate(V): Characterization of 93 Nb, 19 F Coupling, and Fluorine Motion[END_REF][START_REF] Delevoye | Double-Resonance Decoupling for Resolution Enhancement of 31 P Solid-State MAS and 27 Al → 31 P MQHETCOR NMR[END_REF][START_REF] Girard | 31 P MAS NMR spectroscopy with 93 Nb decoupling and DFT calculations: A structural characterization of defects in a niobium-phosphate phase[END_REF][START_REF] Mazoyer | Heteronuclear NMR Correlations To Probe the Local Structure of Catalytically Active Surface Aluminum Hydride Species on γ-Alumina[END_REF]. Although the heteronuclear dipolar coupling can, in principle, be averaged by MAS, the introduction of other time-dependent phenomena, such as RF irradiation (as applied during a decoupling sequence for example), can lead to an interference effect if the two happen on a similar timescale. This can result in an unwanted recoupling of the heteronuclear dipolar interaction, leading to an increased broadening of spectral lines, which is added to the broadening due to the 2nI+1 multiplet that results from the heteronuclear scalar coupling (where n is the number of neighboring quadrupolar nuclei with spin quantum number I).

In recent years, the Rotor Asynchronized -MultiPulse RA-MP decoupling scheme [START_REF] Delevoye | Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei[END_REF] (showed in Fig. 1) has been developed to overcome this problem, and has shown good efficiency for the decoupling of the heteronuclear scalar interaction between a spin I = ½ nucleus and a proximate half-integer quadrupolar nucleus, without reintroducing heteronuclear dipolar coupling. This scheme is based on the application of a series of moderate strength RF-field pulses (of duration τ p ) spaced by a time interval or "delay" (of duration τ d ), chosen such that τ p + τ d ≠ τ r , where τ r is the MAS rotor period. However, the efficiency of this decoupling scheme has been shown to be limited for the case of strong heteronuclear dipolar and scalar couplings or the presence of a large quadrupolar interaction on the coupled spin [START_REF] Girard | 31 P MAS NMR spectroscopy with 93 Nb decoupling and DFT calculations: A structural characterization of defects in a niobium-phosphate phase[END_REF][START_REF] Mazoyer | Heteronuclear NMR Correlations To Probe the Local Structure of Catalytically Active Surface Aluminum Hydride Species on γ-Alumina[END_REF]. To date, the RA-MP scheme has not been widely used, despite showing excellent efficiency (often offering significant improvements over CWbased approaches) when employed in the appropriate case. When applicable, this approach requires an appropriate selection of the decoupling parameters (i.e., τ p and τ d ) with respect to the nature of the nuclei involved in the coupling and the other experimental parameters (i.e., MAS rate and RF field strength) employed, in order to obtain the best possible results.

Here we investigate the influence of instrumental parameters and those parameters intrinsic to the material studied on the MP decoupling of the heteronuclear scalar interaction between spin I = ½ nuclei and half-integer quadrupolar nuclei while considering possible recoupling of dipolar interaction. Using a combination of simulation and experimental verification we will develop a time-saving guide to the optimum choice of experimental parameters in order to access the best decoupling performance as the nature of the specific system of interest varies.

EXPERIMENTAL METHODS

Synthesis

γ-VOPO 4

γ-VOPO 4 was synthesized by thermal decomposition of VOHPO 4 .0.5H 2 O, a precursor that was synthesized according the VPO preparation route [START_REF] Dummer | Vanadium Phosphate Materials as Selective Oxidation Catalysts[END_REF], by refluxing V 2 O 5 in a 90/10 vol mix of isobutanol and benzylic alcohol for 16 h. A stoichiometric amount of phosphoric acid (1 M) was added, followed by one hour of additional reflux. The resulting compound was filtered and washed with a mixture of isobutanol and benzylic alcohol (90/10 ratio), and subsequently dried at 140 °C. The resulting blue powder was recovered and decomposed in air at 750 °C for 5 h. A powder X-ray diffraction pattern obtained for the final yellow powder confirmed the formation of the γ-VOPO 4 polymorph [START_REF] Harlow | The crystal structure of the gamma phase of vanadyl phosphate, gamma-VOPO 4 , solved and refined using both synchrotron and neutron powder diffraction data[END_REF].

Y 2 Sn 2 O 7

The procedures used for the synthesis and 17 O enrichment of Y 2 Sn 2 17 O 7 can be found in Refs. [START_REF] Fernandes | 17 O solid-state NMR spectroscopy of A 2 B 2 O 7 oxides: quantitative isotopic enrichment and spectral acquisition?[END_REF][START_REF] Ashbrook | Y Magic-Angle Spinning NMR of Y 2 Ti 2-x Sn x O 7 Pyrochlores[END_REF].

Solid-state NMR spectroscopy

γ-VOPO 4

31 P solid-state NMR experiments were performed using a Bruker Avance III spectrometer equipped with a 14.1 T magnet and a 2.5 mm probehead at Larmor frequencies of 242.938 and 157.852 MHz for 31 P and 51 V, respectively. 31 P experiments were carried out using an RF field strength ν 1 P = 40 kHz (corresponding to a RF pulse duration for a π/2 pulse of 6.25 μs) at a MAS rate of 22 kHz, using a recycle interval of 60 s. Two 51 V decoupling strategies were tested during 31 P acquisition, using CW and MP schemes. For CW decoupling, the 51 V RF field was set to be the highest possible field that could be used without broadening the 31 P signals due to the reintroduction of dipolar interaction, i.e., ν 1 v (CW) = 28.8 kHz. Further details for the MP decoupling schemes used are given in the relevant figure captions. Experimental 31 P chemical shift scales are shown relative to 1 M H 3 PO 4 (aq) at 0 ppm. The RF field strengths used for 51 V decoupling were determined using CsVO 3 in HCl.

Y 2 Sn 2 O 7

119 Sn solid-state NMR experiments were performed using a Bruker Avance III spectrometer equipped with a 9.4 T magnet and a 4 mm triple resonance probehead at Larmor frequencies of 149.115 MHz and 54.243 MHz for 119 Sn and 17 O, respectively. 119 Sn experiments were carried out using an RF field strength ν 1 Sn = 100 kHz (corresponding to a RF pulse duration for a π/2 pulse of 2.5 μs) at a MAS rate of 10 kHz, using a recycle interval of 30 s. An RF nutation rate ν 1 O of 35 kHz was used for MP and CW decoupling. 119 Sn NMR spectra are shown relative to (CH 3 ) 4 Sn at 0 ppm (measured using a secondary reference of SnO 2 at -604 ppm.

Density matrix simulations

Numerical density matrix simulations were performed using the SIMPSON program [START_REF] Bak | SIMPSON: A General Simulation Program for Solid-State NMR Spectroscopy[END_REF]. Considering the computational effort to carry out these simulations, we have considered a two-spin system composed of a spin I = ½ nucleus on the observe channel, and a half-integer quadrupolar nucleus on the decoupled channel. Our simulations were close to those obtained with a three-spin system, validating our two-spin approach. The two nuclei were coupled through both heteronuclear dipolar and isotropic scalar couplings. The simulations included both first-and second-order quadrupolar interactions on the coupled spin. The FIDs were Fourier transformed using 10 Hz apodization and the maximum intensity of the corresponding spectra were used in subsequent plots. The number of gamma angles was set to 19. Testing of several sets of Euler angles were conducted, but their influence is not significant on the results. By comparing simulations carried out with and without considering anisotropy, the results obtained were very close. As a consequence, we did not take into account the CSA interaction in the numerical approach, as its effect is considered as negligible. Other simulation parameters are given in the relevant figure captions.

RESULTS AND DISCUSSION

The conditions required for optimum MP performance as the system and experimental parameters varied were considered using both numerical simulation and experimental verification. The effect of varying the magnitude of the quadrupolar coupling, heteronuclear scalar and dipolar interactions, and the influence of instrumental and acquisition parameters such as the decoupling RF field and the MAS rate have been investigated systematically. In the following, we have considered the signal intensity (obtained in simulation or experimentally) as a reliable reflection of the decoupling efficiency. Figure 2 shows the calculated amplitude of the 1 H NMR signal under 27 Al decoupling, as a function of the decoupling sequence parameters τ p and τ d values, at two different decoupling RF field strengths (2 and 70 kHz for Figs. 2a and2b, respectively). The SIMPSON simulations were performed using the 1 H and 27 Al spin system parameters typical of aluminum hydride species grafted on -alumina [START_REF] Mazoyer | Heteronuclear NMR Correlations To Probe the Local Structure of Catalytically Active Surface Aluminum Hydride Species on γ-Alumina[END_REF]. In this system, the 1 H/ 27 Al pairs are constrained to the surface, leading to large values of the quadrupolar and dipolar couplings (C Q = 15 MHz, D IS = -9.3 kHz, J = 375 Hz). Experimentally the 1 H sextet resulting from the scalar coupling to 27 Al (I = 5/2) shows an asymmetry, due to the presence of both a large heteronuclear dipolar interaction and the significant quadrupolar coupling. The secondorder dipolar/quadrupolar cross term that results in this case is significant, and the scalar interaction cannot be removed simply by MP decoupling used directly during the acquisition. The cross-term interaction is not considered in the simulation, and so to facilitate later comparison. A J-HMQC filter was employed prior to the 27 Al MP decoupling to efficiently filter the couplings with the 27 Al outermost satellite transitions. This leads to a doublet in the 1 H NMR spectrum arising from the coupling with only the 27 Al central transition. In this situation, 27 Al MP decoupling was then used in acquisition to suppress the residual scalar coupling.

Numerical approach  Large quadrupolar coupling and large heteronuclear dipolar interaction

The SIMPSON simulations (Fig. 2b) carried out with the set of parameters extracted from the study of Mazoyer et al. [START_REF] Mazoyer | Heteronuclear NMR Correlations To Probe the Local Structure of Catalytically Active Surface Aluminum Hydride Species on γ-Alumina[END_REF] shows a very low 1 H signal amplitude under 27 Al decoupling (ν 1 Al = 70 kHz), at all conditions considered. This can be explained by the strong recoupling of heteronuclear dipolar interaction observed for large dipolar couplings (-9.3 kHz in this case). At the lower decoupling RF field (ν 1 Al = 2 kHz, Fig. 2a), the simulated 1 H NMR signal amplitude is low, unless short pulse durations (τ p = 3-5 μs) are used, again a result of the strong heteronuclear dipolar recoupling. This recoupling decreases dramatically the MP decoupling efficiency, making this scheme as poorly effective to decouple scalar coupling as the CW in that case. Moreover, in the regions where calculated amplitude is the highest (τ p < 3 μs), the corresponding simulated 1 H MAS NMR spectra still show the 1 H- 27 Al J-multiplet corresponding to the heteronuclear scalar coupling (Fig. 1 SI 2). These calculations show the inefficiency of MP decoupling in the case of a large heteronuclear dipolar interaction (revealed here through the large second-order cross terms) in agreement with the results obtained by Mazoyer et al [START_REF] Mazoyer | Heteronuclear NMR Correlations To Probe the Local Structure of Catalytically Active Surface Aluminum Hydride Species on γ-Alumina[END_REF]. Similarly, as in the case of CW decoupling, the MP scheme is not favored for the case of a large dipolar coupling. However, when associated with a preliminary pulse sequence to filter out the couplings with satellite transitions, MP decoupling outperforms CW [START_REF] Mazoyer | Heteronuclear NMR Correlations To Probe the Local Structure of Catalytically Active Surface Aluminum Hydride Species on γ-Alumina[END_REF]. The combination of RA-MP with filtering techniques to remove the effect of satellite transitions will not be discussed any further in this article.

 Influence of MAS rate and decoupling RF field strength

Figure 3 shows the calculated intensities of the 31 P NMR signal under different 51 V MP decoupling conditions, as a function of pulse lengths, τ p , and interpulse delay, τ d . The simulations were carried out considering a 51 V -31 P spin system with a 51 V (I = 7/2) quadrupolar coupling constant of 3 MHz, typical of that found in VOPO 4 materials (usually between 0.5 and 4 MHz) [START_REF] Siegel | Hirschinger, 51 V magic angle spinning NMR in VOPO 4 phases[END_REF][START_REF] Lapina | Practical aspects of 51 V and 93 Nb solid-state NMR spectroscopy and applications to oxide materials[END_REF][START_REF] Truflandier | Détermination de paramètres RMN par la théorie de la fonctionnelle de la densité : Application aux éléments 3d en RMN de l'état solide[END_REF], together with a J coupling of 30 Hz, and a dipolar coupling constant of -396 Hz (calculated for an internuclear distance of 3.18 Å). The simulations were performed with increasing RF field strengths and at two different spinning rates, the two most important experimental parameters to consider. Their influence on the decoupling efficiency can be evaluated together with the influence of the quadrupolar coupling (parameterized using either C Q or ν Q ) through the adiabatic passage parameter α, described by Grey and Vega [START_REF] Vega | MAS NMR Spin Locking of Half-Integer Quadrupolar Nuclei[END_REF][START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF]. The parameter , where ν 1 is the decoupling RF field strength, ν r the spinning rate and ν Q the quadrupolar frequency of the half-integer quadrupolar nucleus (defined in this case as ). When α >>1, the regime is considered as adiabatic, i.e., the population transfer is facilitated, and a direct consequence is that the reintroduction of dipolar coupling is facilitated as well, as it is in the TRAPDOR sequence [START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF]. In contrast, when α << 1, the regime is considered sudden (i.e., not in favored of dipolar recoupling). In the following figures, we have considered different cases with increasing α, ranging from 0.1 to 4.8. Figure 3a shows the amplitude of the 31 P NMR signal intensity as a function of (τ p , τ d ) for a RF field strength of 14 kHz, corresponding to an α value of 0.09. As previously observed [START_REF] Delevoye | Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei[END_REF], the rotor synchronized condition (i.e., τ p + τ d = τ r ) should be avoided as it leads to a minimum intensity (i.e., poor decoupling performance). However, significant regions of efficient decoupling of heteronuclear scalar interaction on either side of this rotor synchronized condition are observed, making the choice of (τ p , τ d ) pair straightforward. For example, the (50 μs, 35 μs) or (60 μs, 60 μs) pairs, highlighted with triangles in Fig. 3a, produce similarly good efficiencies of the 51 V MP decoupling of 31 P-51 V scalar interaction. Indeed, when α is small (i.e., a large quadrupolar coupling constant or low RF field strength), the decoupling pulses do not generate a reintroduction of dipolar interaction, with the result that MP and CW schemes should show similar efficiencies (this is later in this article supported by experimental data). When the decoupling RF field strength is increased (Fig. 3b), the regions that correspond to maximum decoupling efficiencies move towards shorter pulse lengths and longer interpulse delays, although still close to the rotor synchronized condition. For example, in Fig. 3b (α = 0.2), a maximum efficiency is found for (τ p , τ d ) of (35 μs, 55 μs). The (τ p , τ d ) pair of (45 μs,75 μs) gives similarly good efficiency. This regime is characterized by an interpulse delay that is always larger than the pulse duration. For larger α parameters (e.g., 0.76 and 4.76 in Figs. 3c and3d), the maximum efficiency is found towards shorter pulse durations, with a reduced region of efficiency found around the rotor synchronized condition. At α = 4.76, maximum efficiency is obtained for τ p = 20 μs and τ d = 90 μs. Any slight variation from this (τ p , τ d ) pair results in a dramatic loss of MP decoupling efficiency. Finally, increasing the decoupling RF field strength is always favorable in terms of maximum decoupling efficiency. For example, the maximum calculated amplitude for Figs. 3a and 3d are 25 and 60 (arbitrary units), respectively. For a higher MAS rate of 22 kHz (Figs. 3e to 3h), a similar general trend is observed, i.e., shorter τ p and longer τ d are favoured as the decoupling RF field strength (and, concomitantly, α) increases. However, the regions corresponding to maximum intensity are larger, leading to a MP decoupling efficiency that is less dependent on the choice of (τ p , τ d ).

Finally, it can be noted that the maximum calculated amplitude increases with increasing decoupling RF field strength for a given spinning rate, but also increases with increasing spinning rate for a given α parameter. This is illustrated in Fig. 2 SI where simulated 27 Al MAS NMR spectra are shown for conditions shown by the triangles in Fig. 3. Figure 4 shows the influence of both the scalar and dipolar coupling constants on the efficiency of the MP decoupling for different values of (τ p , τ d ). The simulations were performed by considering a spin pair, 51 V-31 P, with a 51 V quadrupolar coupling constant C Q , that corresponds to the upper value (C Q = 3 MHz) of those encountered in vanadophosphates.

 Competition effect between heteronuclear scalar and dipolar coupling

For a small scalar coupling constant of 10 Hz with a small dipolar coupling (-100 Hz, corresponding to an internuclear distance of 5 Å), most (τ p , τ d ) pairs provide efficient decoupling of the heteronuclear scalar interaction (as shown in Fig. 4a). This means that no dipolar recoupling occurs and the weak scalar interaction can be easily decoupled. As the dipolar coupling increases (from top to bottom in Fig. 4), the region that corresponds to maximum decoupling efficiency moves towards shorter τ p and longer τ d values, on either side of the rotor synchronized condition, i.e., the use of longer τ p , where the dipolar recoupling would dominate, should be avoided.

For the larger scalar coupling constant of 50 Hz and for a weak dipolar coupling (100 Hz, Fig. 4d), the overall intensity (and therefore MP decoupling efficiency) is significantly reduced with respect to that obtained when J = 10 Hz, and region corresponding to optimum efficiency moves towards longer τ p values, still ensuring that rotor synchronization is avoided. This illustrates that larger scalar couplings require longer pulse lengths for optimum MP decoupling. However, when the dipolar coupling is increased, dipolar interaction is reintroduced for long τ p , such that the signal amplitude decreases rapidly and the pulse lengths for optimum MP decoupling performance tend to decrease. This dependence illustrates the competitive effect of scalar decoupling and reintroduction of dipolar interaction, which has been clearly observed in the case of CW [START_REF] Delevoye | Double-Resonance Decoupling for Resolution Enhancement of 31 P Solid-State MAS and 27 Al → 31 P MQHETCOR NMR[END_REF] but can also occur for MP.

Experimental results

The conclusions about the influence of the various experimental and system parameters on MP decoupling efficiency determined from the simulations were tested experimentally on systems containing a spin I = ½ nucleus ( 31 P or 119 Sn) J-coupled to a quadrupolar nucleus ( 51 V, 93 Nb or 17

O).

 γ-VOPO 4 : Small C Q and moderate 31 P-51 V scalar and dipolar interactions Figure 5 compares experimental (Fig. 5a) and calculated (Fig. 5b) 31 P signal amplitude under 51 V MP decoupling for different (τ p , τ d ) values. The γ-VOPO 4 polymorph was used for the experimental measurements, while calculations were performed using the corresponding NMR and structural parameters [START_REF] Harlow | The crystal structure of the gamma phase of vanadyl phosphate, gamma-VOPO 4 , solved and refined using both synchrotron and neutron powder diffraction data[END_REF][START_REF] Truflandier | Détermination de paramètres RMN par la théorie de la fonctionnelle de la densité : Application aux éléments 3d en RMN de l'état solide[END_REF]. The γ-VOPO 4 polymorph exhibits a moderate dipolar coupling of -396 Hz (corresponding to a internuclear P-V distance of 3.18 Å), and a small quadrupolar coupling constant, C Q , of 1.5 MHz, shown above to be favorable for MP decoupling. The experimental and calculated contour plots show good agreement, with similar regions of decoupling efficiency located at pulse lengths slightly shorter than the interpulse delays, on either side of the rotor synchronized condition. This is typical of behavior expected in the intermediate regime (here,  = 0.35), as shown in Fig. 2.

The resolution enhancement provided by MP decoupling was evaluated by comparing the experimental 31 P MAS NMR spectrum obtained with MP decoupling (Fig. 5c), with τ p = 15 μs and τ d = 37 μs (corresponding to the circle in Fig. 5b), with a spectrum acquired using optimized CW scheme (Fig. 5d) and a final spectrum recorded without decoupling (Fig. 5e). The spectrum acquired without decoupling exhibits two major, broad signals centered at -16.7 and -20.73 ppm (FWHM around 900 and 695 Hz, respectively). The use of (optimized) CW decoupling slightly improves the resolution, and allows the two signals overlapping at -16.7 ppm to be distinguished. However, the spectrum acquired using 51 V MP decoupling shows the most spectacular improvement in resolution, enabling the unambiguous assignment of three 31 The best fit simulations of the three spectra in Figs. 5c, 5d and 5e are shown in the supplementary information (Fig. 4 SI), together with a table summarizing the fitting results (Table 1 SI). The analytical fits of each spectrum show that the relative integrated intensities of the three 31 P signals at -20.76, -17.43, and -15.83 ppm, are approximately 50%, 30% and 20%, respectively (isotropic chemical shifts are determined using the fit of MP decoupled 31 P spectrum in Fig. 5c, then rightly adjusted as such for all best-fit simulations). The lowest linewidth is found for the MP decoupled spectrum. Indeed, for the signal at -20.76 ppm, the linewidth decreases by 38%, from 695 Hz (when no decoupling is applied) to 430 Hz (when MP decoupling is used). CW also gives a lower linewidth (573 Hz) for this site (corresponding to a decrease of 18%). The CW scheme used here employs a decoupling RF field optimized to be just lower than that which would reintroduce the dipolar coupling, which means that the resolution enhancement using this approach has reached its limit. Thus, for the same decoupling RF field of 28.8 kHz, the analytical fits show that MP is more efficient for decoupling the heteronuclear scalar interaction than the CW approach.

 NbOPO 4 : High C Q and moderate 31 P-93 Nb scalar and dipolar interactions Figure 6a shows the 31 P linewidth extracted from a 31 P MAS NMR spectrum of NbOPO 4 as a function of the 93 Nb CW decoupling RF field [START_REF] Girard | 31 P MAS NMR spectroscopy with 93 Nb decoupling and DFT calculations: A structural characterization of defects in a niobium-phosphate phase[END_REF]. It is clear that there is a decrease in linewidth as the RF field increases. However, as described by Girard et al., even at the maximum available RF field strength of 55 kHz, the 31 P signal linewidth is still decreasing. In other words, under these conditions there is no apparent effect of dipolar recoupling which usually broadens the signal, as was observed in aluminophosphates [START_REF] Delevoye | Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei[END_REF]. This could be explained by the magnitude of the 93 Nb quadrupolar coupling (C Q = 21 MHz), which considerably reduces the recoupling of the heteronuclear dipolar interaction [START_REF] Vega | MAS NMR Spin Locking of Half-Integer Quadrupolar Nuclei[END_REF][START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF].

Figs. 6b and 6c show the 31 P signal amplitude determined from a SIMPSON simulation under 93 Nb MP decoupling, as a function of (τ p , τ d ), for a spin system similar to NbOPO 4 , i.e., D IS = -304 Hz (calculated from the structure of Longo et al. [START_REF] Longo | The crystal structure of NbOPO 4[END_REF]), C Q = 21 MHz, J = 40 Hz. Two decoupling RF field strengths were tested: 30 kHz and 55 kHz in Figs. 6b and6c, respectively.

In the simulation the instrumental parameters were set to be comparable to those used in the 31 P NMR study of NbOPO 4 by Girard et al. [START_REF] Girard | 31 P MAS NMR spectroscopy with 93 Nb decoupling and DFT calculations: A structural characterization of defects in a niobium-phosphate phase[END_REF] (i.e., 93 Nb decoupling RF field of 55 kHz, MAS rate of 20 kHz, B 0 = 18.8 T). For these settings, the two-dimensional contour plot simulated for a decoupling RF field strength of 30 kHz (Fig. 6b) shows regions of good decoupling efficiency located at rather long pulse lengths, largely at values that are longer than the interpulse delays. This behavior is quite similar to that observed for the CW scheme, and is in agreement with the observations of Girard et al. In the particular case where the quadrupolar coupling is large relative to ν 1 2 /ν r , CW may sometimes be better than the MP decoupling scheme. For the higher decoupling RF field of 55 kHz (Fig. 6c), MP could prove useful, as the plot shows areas of higher decoupling efficiency and these are observed for wider ranges of τ p and τ d . This is an intermediate situation where MP scheme becomes more efficient than CW owing to the increased dipolar recoupling which occurs for CW (in this case) at rather high decoupling RF field due to large quadrupolar coupling. 119 Sn signal at -582.5 ppm. Simulations were carried out using the spin system parameters extracted from the published available data [START_REF] Riedel | Heteronuclear decoupling in rotating solids via symmetry-based adiabatic RF pulse schemes[END_REF], and by the best fit simulation (Fig. 6 Figure 7 shows experimental (Fig. 7a) and simulated (using SIMPSON) (Fig. 7b) twodimensional contour plots of 119 Sn signal amplitude under 17 O MP decoupling, as a function of (τ p , τ d ) values. In both experiment and simulation the MAS rate and decoupling RF field strength were 10 kHz and 35 kHz, respectively. Experiments have been performed on Y 2 Sn 2 O 7 , and plots show the peak height of the signal at -582.5 ppm. Figs. 6c, 6d and 6e show experimental 119 Sn MAS NMR spectra, acquired using 17 O MP decoupling (ν 1 O = 35 kHz) at τ p and τ d corresponding to the circle in Fig. 7b (Fig. 7c), under optimized CW decoupling at ν 1 Al = 35 kHz (Fig. 7d) and without decoupling (Fig. 7e).

The contour plot (Fig. 7b) for simulated data was generated using the spin system parameters extracted from the published available data and fits of the 119 Sn MAS NMR spectra (Fig. 7c to 7e, and [START_REF] Matteucci | Crystal structural and optical properties of Cr-doped Y 2 Ti 2 O 7 and Y 2 Sn 2 O 7 pyrochlores[END_REF]): C Q = 4 MHz, D IS = -680 Hz, J = 90 Hz (see supplementary information). This plot shows regions of good MP decoupling efficiency areas close to the rotor synchronization condition, for τ p slightly smaller than τ d . The (τ p , τ d ) pair of (50 μs, 80 μs) corresponding to the circle in Fig. 7b, was used to acquire the 17 O MP decoupled spectrum.

An attempted fit (in red) of the complex lineshape of the 119 Sn MAS NMR spectrum is proposed in Fig. 6SI As shown in Fig. 7d, the application of 17 O CW decoupling partly suppresses the component of the lineshape due to the coupling with the oxygens. Although the spectrum is narrowed using this approach, the effect of scalar decoupling is more impressive on the MP decoupled spectrum (Fig. 7c). Indeed, the linewidth is smaller due to an efficient scalar decoupling, which suppresses the multiplet 119 Sn- 17 O component, even though the 119 Sn lineshape is still affected by the 119 Sn-117 Sn scalar coupling.

Conclusion

In the present article, we propose a guideline for the choice of experimental and instrumental parameters for MP decoupling of half-integer quadrupolar nuclei during the acquisition of spectra of nuclei with spin I = ½, in the case of a moderate heteronuclear dipolar interaction. This case is commonly encountered in inorganic materials when studying nuclei with relatively low  (i.e., not 1 H or 19 F) that are coupled to each other. We have not treated this less common case where a large dipolar and a large quadrupolar coupling are present (direct 1 H-27 Al bonding for example). The evaluation of the decoupling efficiency was first evaluated with a numerical approach and confirmed experimentally for various halfinteger quadrupolar nuclei (e.g., I = 5/2 ( 17 O), 7/2 ( 51 V) and 9/2 ( 93 Nb)) coupled to nuclei with spin I = ½. We have shown that the MP decoupling scheme is characterized by a pulse length (τ p ) and an interpulse delay (τ d ), values that need to be carefully chosen, as efficiency can vary quite considerably. This efficiency also depends on the instrumental parameters (e.g., decoupling RF field strength, MAS rate) and intrinsic parameters of the material under study (e.g. heteronuclear dipolar and scalar interaction, quadrupolar coupling). We have considered three regimes (named as slow, fast and intermediate as a function of adiabatic passage parameter value), and for each of them typical regions of efficient decoupling have been determined in terms of the values of τ p and τ d .

In all cases, the decoupling RF field strength should be chosen to be the highest possible, as this results in better decoupling efficiency. The MAS rate should be chosen to be reasonably high, removing the broadening due to the chemical shift anisotropy, in addition to a rotorperiod τ r of the order of >10 μs (e.g a MAS rate up to 100 kHz). This results in a broad region of efficient decoupling and ensures that the choice of (τ p , τ d ) be less restricted.". However, high spinning rates, where the rotor period becomes of the the same order as the pulse length, should be avoided. As matter of fact, setting a very high spinning rate would imply that the regions of rotor-synchronization conditions (for instance 0.5τ r , τ r or 1.5τ r ) would be close from one another, so difficult to avoid. This would lead to a very picky choice of τ p and τ d away. For instance, if MAS rate is 150 kHz, then τ r = 6.7 μs, 0.5 τ r = 3.3 μs).

The optimal MP decoupling should be obtained following three main steps. Firstly, the rotor synchronized condition should always be avoiding. Secondly, one should validate or eliminate the extreme regime condition (α<0.05 and α>2-3). As a matter of fact, when α < 0.05 (sudden passage regime), long pulse lengths τ p , much larger than interpulse delays τ d , are chosen. Sometimes, CW decoupling can as well be used.

When α > 2-3 (adiabatic regime), one should use small τ p compared to interpulse delay. Finally, if the regime is intermediate (α ϵ [0.1 ; 2-3]), τ p and τ p are quite close, and one might probe a few (τ p ; τ d ) pair chosen on either side of the rotor synchronized condition, to determine the best τ p /τ d ratio to choose in order to have the best MP decoupling efficiency possible.

To summarize, we have studied in detail the influence of experimental conditions and the parameters intrinsic to the material on the efficiency of MP decoupling efficiency for NMR observation of nuclei with spin I = ½ coupled to half-integer quadrupolar nuclei. The decoupling efficiency was investigated as a function of the decoupling RF field, MAS rate, and the magnitude of the heteronuclear interactions and the quadrupolar coupling constant of the remote spin. The consideration of simulated and experimental data for a variety of spin systems helped a series of general, time-saving guidelines to be proposed, designed to expediate experimental implementation of MP schemes. Heternonuclear interactions with proximate quadrupolar spins can limit the resolution in NMR spectra of spin I = ½ nuclei, even under MAS conditions. Improving this resolution, enabling the extraction of more accurate site specific information, will be a vital step for the future structural characterization of complex materials.

Figure 1 :

 1 Figure 1 : MP decoupling sequence. The half-integer quadrupolar nucleus S is irradiated by a series of pulses of a duration τ p , and an interpulse delay τ d , during signal acquisition on the observed ½ spin nucleus I channel.

Figure 2 :

 2 Figure 2 : Two-dimensional contour plots showing the variation in the 1 H NMR signal amplitude (obtained from a SIMPSON simulation) under 27 Al MP decoupling, as a function of τ p and τ d . Decoupling RF field strengths are set to (a) ν 1 Al = 2 kHz and (b) ν 1 Al = 70 kHz, with 27 Al C Q = 15 MHz and η Q = 0. Heteronuclear dipolar and scalar couplings were set to 9300 Hz and 375 Hz, respectively. The MAS rate was 20 kHz. The parameters τ p and τ d were varied from 0 to 50 μs in steps of 1 μs.

Figure 3 :

 3 Figure 3 : Two-dimensional contour plots showing the variation in the 31 P signal amplitude (obtained from a SIMPSON simulation) under 51 V MP decoupling, as a function of τ p and τ d . The quadrupolar coupling constant, C Q , was set to 3 MHz and the asymmetry parameter η Q to 0. The dipolar and scalar coupling constants were set to -396 Hz and 30 Hz, respectively. Several decoupling RF field were tested for two different MAS rates. Decoupling field strengths of (a) ν 1 Al = 14 kHz, (b) ν 1 Al = 20.7 kHz, (c) ν 1 Al = 40.4 kHz and (d) ν 1 Al = 101 kHz were used for an MAS rate of 10 kHz. Decoupling field strengths of (e) ν 1 Al = 21.7 kHz, (f) ν 1 Al = 30 kHz, (g) ν 1 Al = 60 kHz and (h) ν 1 Al = 150 kHz were used for an MAS rate of 22 kHz. The adiabatic passage parameter α is (a, e) 0.09 (b, f), 0.2 (c, g), 0.76 and (d, h) 4.76. The parameters τ p and τ d were varied in steps of 3 μs. The triangles represent (τ p ,τ d ) pairs of (50 μs, 35 μs) and (60 μs, 60 μs) in Fig 2a, (35 μs, 55 μs) and (45 μs,75 μs) in Fig. 2b, (20 μs, 90 μs) in Fig. 2d, and (24 μs, 32 μs) in Fig. 2f.

Figure 4 :

 4 Figure 4 : Two-dimensional contour plots showing the variation in the 31 P NMR signal amplitude (obtained from a SIMPSON simulation) under 51 V MP decoupling, as a function of τ p and τ d . These parameters were both incremented in steps of 3 μs. The quadrupolar coupling constant C Q was set to 3 MHz and asymmetry parameter η Q to 0. The decoupling RF field strength was set to ν 1 V = 30 kHz and the MAS rate to 22 kHz. Two scalar coupling constants of (a-c) J IS = 10 Hz and (d-f) J IS = 50 Hz were considered with dipolar coupling constants of (a, d) D IS = -100 Hz, (b, e), -400 Hz and (c, f) -800 Hz. The adiabatic passage parameter α = 0.2.

  P signals at -20.76, -17.43, and -15.83 ppm. Another signal, belonging to a small impurity of the β-VOPO 4 polymorph is observed at -10.59 ppm.

Figure 5 :

 5 Figure 5 : Two-dimensional contour plots showing the variation in the P NMR signal amplitude, and experimental 1D 31 P MAS NMR spectra. These plots are obtained (a) in experiment and (b) from a SIMPSON simulation, under 51 V MP decoupling, as a function of τ p and τ d . The decoupling RF field strength was ν 1 V = 28.8 kHz and the MAS rate was 22 kHz. Experimental data were obtained for the γ-VOPO 4 polymorph, and is shown for the 31 P site at -22.7 ppm. Simulations were carried out using the spin system parameters extracted from the published data [23,29]: C Q = 1.5 MHz (ν Q = 107.1 kHz), η Q = 0.5 ; δ aniso = -942 ppm ; η σ = 0.07; D IS = -396 Hz, J IS = 30 Hz. (τ p , τ d ) steps were (1.5 μs, 1.5 μs) and (3 μs,3 μs) for experimental and simulated plots, respectively. Experimental 31 P MAS NMR spectra of the γ-VOPO 4 phase were acquired at B 0 = 14.1 T, at an MAS rate of 22 kHz (c) under MP decoupling (ν 1 V = 28.8 kHz), with (τ P , τ d ) = (15 μs, 37 μs) corresponding to the circles in (a) and (b); (d) with optimized CW decoupling (ν 1 V = 28.8 kHz) and (e) without decoupling. At these conditions, the adiabatic passage parameter, α, is 0.35.

Figure 6 :

 6 Figure 6 : Two-dimensional contour plots showing the variation in the 31 P NMR signal amplitude. (a) 31 P linewidth (FWHM in Hz) of the 31 P MAS NMR spectrum of NbOPO 4 acquired under 93 Nb CW decoupling, as a function of the 93 Nb decoupling RF field strength, at B 0 = 18.8 T and an MAS rate of 20 kHz. Fig. 6a is extracted with permission 1 from [20], (b, c) Two-dimensional contour plots showing the variation in the 31 P NMR signal amplitude, obtained from a SIMPSON simulation, under 93 Nb MP decoupling, as a function of τ p and τ d . Simulations were conducted with typical spin system parameters for NbOPO 4 (C Q = 21 MHz (ν Q = 875 kHz), scalar coupling of 40 Hz, dipolar coupling of -304 Hz [20,32]), at an MAS rate of 20 kHz, with (b) ν 1 Nb =30 kHz and (c) ν 1 Nb = 55 kHz. The adiabatic passage parameter α is (a) 0.05 and (b) 0.18.

 Y 2

 2 Sn 2 O 7 : Moderate C Q and dipolar interaction with high scalar coupling.

Figure 7 :

 7 Figure 7 : Two-dimensional contour plots showing the variation in the 119 Sn NMR signal amplitude. These plots are obtained (a) in experiment and (b) from a SIMPSON simulation, under 17 O MP decoupling, as a function of τ p and τ d . Experimental data were obtained for Y 2 Sn 2 O 7 , and peak heights are shown for the119 Sn signal at -582.5 ppm. Simulations were carried out using the spin system parameters extracted from the published available data[START_REF] Riedel | Heteronuclear decoupling in rotating solids via symmetry-based adiabatic RF pulse schemes[END_REF], and by the best fit simulation (Fig.6SI): C Q = 4 MHz (ν Q = 600 kHz), η Q = 0; η σ = 0, δ aniso = 0 ppm; D IS = -680 Hz, J IS = 90 Hz. (τ p , τ d ) steps were (1 μs, 1 μs) and (5 μs, 5 μs) for experimental and calculated SIMPSON plots, respectively. Experimental 119 Sn MAS NMR spectra of Y 2 Sn 2 O 7 were acquired at B 0 = 9.4 T at an MAS rate of 10 kHz. The 119 Sn spectra are: (c) under MP decoupling (ν 1 O = 35 kHz) with (τ P , τ d ) = (50 μs, 80 μs) corresponding to the circle in (b); (d) with optimized CW decoupling (ν 1 O = 35 kHz), and (e) without decoupling. At these conditions, the adiabatic passage parameter α is 0.2.

  SI): C Q = 4 MHz (ν Q = 600 kHz), η Q = 0; η σ = 0, δ aniso = 0 ppm; D IS = -680 Hz, J IS = 90 Hz. (τ p , τ d ) steps were (1 μs, 1 μs) and (5 μs, 5 μs) for experimental and calculated SIMPSON plots, respectively. Experimental 119 Sn MAS NMR spectra of Y 2 Sn 2 O 7 were acquired at B 0 = 9.4 T at an MAS rate of 10 kHz. The 119 Sn spectra are: (c) under MP decoupling (ν 1 O = 35 kHz) with (τ P , τ d ) = (50 μs, 80 μs) corresponding to the circle in (b); (d) with optimized CW decoupling (ν 1 O = 35 kHz), and (e) without decoupling. At these conditions, the adiabatic passage parameter α is 0.2.

  on the basis of J-couplings, considering a three component signal (a "singlet" component corresponding to uncoupled119 Sn species in agreement with the pyrochlore structure of Y 2 Sn 2 O 7 described by Matteucci et al.[START_REF] Matteucci | Crystal structural and optical properties of Cr-doped Y 2 Ti 2 O 7 and Y 2 Sn 2 O 7 pyrochlores[END_REF][34][35] (purple), a doublet component corresponding to Sn experiencing a 119 Sn-117 Sn 2 J coupling of 180 Hz (green), and 11 line multiplet corresponding to Sn experiencing a 1 J coupling to two17 O of 92 Hz (grey)). This tentative decomposition is by no means unambiguous, but was useful to point out the multiplet rising from the J coupling between 119 Sn and17 O. The exact interpretation of the obtained 119 Sn NMR lineshape would probably require additional experiments at multiple fields.

Reprinted from Solid State Nuclear Magnetic Resonance, 84[START_REF] Thakur | Swept-frequency two-pulse phase modulation for heteronuclear dipolar decoupling in solid-state NMR[END_REF], G. Girard, F. Vasconcelos, L. Montagne, L. Delevoye),[START_REF] Grey | Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/ 27 Al TRAPDOR NMR[END_REF] P MAS NMR spectroscopy with93 Nb decoupling and DFTcalculations: A structural characterization of defects in a niobium-phosphate phase,

210-215, Copyright (2017), with permission from Elsevier.

Acknowledgment

This work benefited from a grant from Agence Nationale de la Recherche (ANR MOSAIC 13-BS08-0018-01).