V Dragos

D Battistelli
email: delphine.battistelli@parisnanterre.fr

A Etienne
email: aline.etienne@parisnanterre.fr

Y Constable
email: yolene.constable@onera.fr

Angry or Sad ? Emotion Annotation for Extremist Content Characterization

Keywords: Emotion annotation, social data analysis, extremist content

This paper examines the role of emotion annotations to characterize extremist content released on social platforms. The analysis of extremist content is important to identify user emotions towards some extremist ideas and to highlight the root cause of where emotions and extremist attitudes merge together. To address these issues our methodology combines knowledge from sociological and linguistic annotations to explore French extremist content collected online. For emotion linguistic analysis, the solution presented in this paper relies on a complex linguistic annotation scheme. The scheme was used to annotate extremist text corpora in French. Data sets were collected online by following semi-automatic procedures for content selection and validation. The paper describes the integrated annotation scheme, the annotation protocol that was set-up for French corpora annotation and the results, e.g. agreement measures and remarks on annotation disagreements. The aim of this work is twofold: first, to provide a characterization of extremist contents; second, to validate the annotation scheme and to test its capacity to capture and describe various aspects of emotions.

Introduction

Social platforms play an increasingly important role in the propagation of extremist ideas. As the growth of extremism online continues, the ability to detect this harmful content is paramount to restrain the spread of messages. Emotions associated to this type of content reflect the affiliations and aptitudes of users towards entities, events but also ideas and give clues about their activities online. A major barrier to the development of accurate models for extremist content detection is the limited number or relevant corpora and the absence of a reliable protocol for data annotation. More specifically, the need for corpora annotated by combining both sociological knowledge as to why the content is extremist has also emerged. The paper focuses on extremism analysis in French textual contents collected on social platforms and adopts an emotion annotation scheme to investigate emotions expressed in extremist and non-extremist bodies of texts. In this work, we show that extremist contents capture valuable emotional linguistic signals revealing, for instance, when extremist attitudes are associated with fear or sadness. Building a labeled corpus for extremism detection is not trivial, since there is no consensus among researchers in the field of sociology on the definition of extremist content or the identification of its main characteristics (Alava et al., 2020). In addition, detecting emotion in text is a difficult task even for humans ( Öhman, 2020). In order to cope with those difficulties, we developed an approach which consists of two main phases: (1) the development of a semiautomatic procedure guided by knowledge from sociology was implemented to create two distinct data sets containing extremist and non-extremist contents, respectively; and (2) the use of an annotation scheme designed to manually annotate emotions, where annotators identify linguistic markers that convey an emotion among a pre-defined set of emotions.

Based on this combination of sociological knowledge and emotion analysis, we are able to build a new data set, which provides interpretable associations of emotions that highlight differences between extremist and non-extremist contents. Overall, this paper makes three main contributions. First, we integrate both sociological knowledge and emotion annotations and show that emotions annotation correlate well with human judgments of extremist or non-extremist contents. Second, we provide fine-grained annotated data sets in french, which can be widely used for training data for machine learning approaches and can be considered as gold standards in text classification tasks. Finally, we carry out a manual validation of emotion annotation and a crossanalysis of annotation categories. The remainder of the paper is organized as follows. Next section discusses several related approaches and section 3. gives a brief overview of the corpora used for this work and explains the procedures adopted to build it. Section 4. elaborates on the annotation scheme used for emotion analysis of texts and provides examples of annotations. Section 5. discusses annotation validation and remarks on agreement measures. Section 6. concludes and presents directions for future work.

Related work

The analysis of affective states, including sentiments, emotions or opinions, received attention from several research communities, including natural language processing, sociolinguistics and machine learning, to the extent that building labeled data sets for training raises questions related to the nature of emotions and the representation scheme suitable to describe them. The section discusses several data sets labeled with emotion types and information related to their extremist nature, respectively.

Emotion labeled data sets

A large number of research efforts developed data sets annotated according to different emotion schema. Those re-sources can be classified into two main categories: data sets created to linguistically describe emotions (and sometimes also their causes) and data sets built to investigate how emotions correlate with other factors. The first category includes EmoBank, a data set released by Buechel and Hahn (Buechel and Hahn, 2017). EmoBank consists of 10k sentences in English, manually annotated according to the valence-arousal-dominance model (Mauss and Robinson, 2009). This model describes emotions according to there dimensions: valence or polarity, arousal, a concept capturing the degree of calmness or excitement, and dominance, which is to say the perceived degree of control over a situation. EmoBank builds on multiple genres and domains and the annotation highlights both the emotion expressed by the writer, and the emotion perceived by the readers. EmoInt is another labeled data set built by Mohammad and Bravo-Marquez (Mohammad and Bravo-Marquez, 2017) in order to associate paragraphs with various intensities of emotions. The collection focuses on social media and gathers 7,097 tweets altogether in English. The tweets were annotated via crowdsourcing with various intensities of four emotions: anger, joy, sadness, and fear, although most tweets are annotated with one emotion. The Emotion-Stimulus dataset was published by Ghazi and colleagues (O'Reilly et al., 2016) in order to predict the causes of emotions in the text. The resource consists of 1,549 sentences in English annotated with emotions and 820 enriched sentences annotated with emotions and their causes. The set of labels includes the list of basic emotions (anger, contempt, disgust, enjoyment, fear, sadness, surprise) to which shame is added. The second category includes research efforts intended to investigate the relations between emotions and other factors, such as context, news, events or actions. Hence, the Stance Sentiment Emotion Corpus, is a data set in English released by Schuff and colleagues (Schuff et al., 2017). The collection consists of 4,868 tweets annotated thank to a hybrid approach mixing linguistic expert annotations and crowd sourcing. Each tweet was labeled with multiple emotion labels following the Plutchik's wheel of emotions (Donaldson, 2017). The resource has several annotation layers, allowing the analysis of relationships among emotion types. Following a similar research line, Grounded-Emotions is an emotion tagged data set in English published by Liu and Mihalcea (Liu et al., 2017) in order to correlate emotions with other factors including weather, news and social aspects. The collection was built on social media and consists of 2,557 single labeled instances published by 1,369 unique users. The set of labels includes only two emotions: happy and sad. The resource was used in experiments showing the role played by contextual factors in predicting emotions. Taking a step forward, GoodNewsEveryone is a corpus built by Bostan and colleagues (Oberländer et al., 2020) in order to tackle emotions from a structured learning perspective. The collection consists of 5000 English news headlines, annotated via crowdsourcing by associating emotion types, semantic roles capturing emotion causes, experiencers and targets, as well as the reader's perception. By adding those annotation layers, different types of associations can be further inferred, such as correlations of emotions and their causes but also differences between the emotions as related by the author and perceived by the reader. Other resources develop even more complex structures to describe emotions in text, and for example AffectVec (Raji and De Melo, 2020) matches English words to numerical vectors, in which a given dimension quantifies the degree of association of that specific word with a specific emotion.

Data sets labeled for extremism detection

As shown in the previous section, annotation of emotions in texts has extensive literature, but there are not numerous studies considering emotions in contents dealing with extremist ideologies. More specifically, building labeled data sets for extremism detection received little attention.

De Gibert and colleagues developed a labeled data set for White Supremacy detection (de Gibert et al., 2018). The resource is in English and consists of data collected from the StormFront Website, a main portal of white supremacists. Although data was collected from an extremist source, the annotation focused mainly on hate detection, and several annotation rules were defined. For example, one rule labeled a text as Hate if an attack against a specific group of individuals was mentioned; another rule annotates as Hate any content explicitly supporting extremist ideas. The overall collection was annotated with a set of three labels: Hate, NoHate, and Skip (for undetermined contents).

Another extremist data set in English was built by scraping extremist content from Twitter feeds by using known white supremacist hashtags like white-privilege, and its-okto-be-white (Alatawi et al., 2021). Three different annotators annotated the collection with a set of four labels: Ex-plicitWhiteSupremacist, ImplicitWhiteSupremacist, Other-HateSpeech, and Neutral. Other contributions considered the binary (Extremist/NonExtremist) annotation of online profile, as it is the case in this study (Hartung et al., 2017) carried out by Hartnung and colleagues to detect right-wing extremism in German Twitter profiles.

Regarding the analysis of French contents, a first data set for sexism detection in French is presented in (Chiril et al., 2020). The collection gathers about 115,000 tweets among which 12,274 are manually annotated with two main categories Sexist and NonSexist. The annotation procedure also provides a deeper characterization of sexist contents, by making the distinction between tweets that are directly addressed to a target (a woman or women in general) and tweets that report or denounce sexism experienced by women. A review of methods and annotated corpora for online extremist detection is presented in (Gaikwad et al., 2021).

With this paper, we provide a data set in French annotated with both linguistic and sociological expert knowledge. Data was collected from Twitter and the resource provides information on right-wing extremist categories and on emotion types. Thus it allows us to explore the relationships between those two distinct annotation layers.

Data collection and characterization

Collecting data sets for the specific purposes of usagedriven approaches relies on one major hypothesis, namely that the content of corpus is representative of the phenomenon under scrutiny. The representativeness of corpus raises methodological and practical questions, and for this work, concepts and dynamics from sociology guided the construction of data sets. Extremist content can be gleaned after explicitly defining the notion of extremist or by selecting several sources generally accepted as being extremist. Defining extremism in general as a process or concept, suffers from a lack of consensus within the sociology field itself (Thorburn et al., 2018). If we consider the specific case of right-wing extremism in Europe, the features of this ideology change considerably from one country or region to another. Several authors pointed in to the fluid nature of extremism and its multifaceted nature including a verity of discourses from revisionists, racists, skinheads and extremist hooligans, nationalists or identity-based groups, paramilitary, xenophobic or anti-migrant groups (Araque and Iglesias, 2021). In order to avoid the difficulty of defining the concept of extremism we restricted the application area of this study to the analysis of extremism in French blogosphere and we also focused on information sources. The data collection step consists at the first run on selecting several sources considered as extremist and collecting streams of data released by those sources. A source can be a user, a hashtag, a keyword or a combination of those three elements. Data was collected from December 2019 to December 2020 by an interdisciplinary team of researchers in sociology, linguistics and computer science. The sets of data have been scraped from various online platforms using the MediaCentric tool 1 . The corpus was built iteratively in an effort to select only texts which were clearly connected with a certain ideology. The data set includes data from Twitter, forums, and online sources. Streams collected from different sources were merged together. Merging those contents, although provided by distinct sources, allows us to build a homogeneous corpus according to the principle of homophily (Oussalah et al., 2018) stating that users within a certain group setting have a tendency to develop a similar use of language when developing the ideas of the group. In spite of using keywords, the subject matter and the homogeneity of the corpora were difficult to establish after the collection step, because online users user can write about any subject. After collecting rows of online date, several validation and characterization steps were performed on the entire collection to ensure that data sets are relevant and to detect finer categories of extremist contents. Those steps are described in fig. 1. First, the initial collection gleaned on social platforms was manually explored by two experts in sociology (one is a senior researcher in education sciences and the other one is a post doc in sociology with a background in social communication) in order to discard non-relevant contents. The initial corpus and was further roughly divided into two sub-1 https://www.chapsvision.fr/data Using statistical tools for textual analysis (IRAMUTEQ 2 ) and tagging collected from 56 information sources we identified categories of texts based on internal similarity (lexical similarity estimated by the tool) and external distances (semantic distances estimated by the tool). The identification of social categories was carried out by the same team of two researchers in sociology who have a sufficient understanding of online platforms. They were provided with a set of symbols, hashtags and notions associated to extremist ideologies. This input was used as a baseline to decide of which content is considered extremist and which is not. Researchers carefully studied both the information comprised in texts and about the texts (namely the source or keywords used to collect the tweet) to infer the main category associated to the texts. They also identified textual units carrying relevant extremist or nonextremist contents. The length of textual units ranges from one to eight sentences (clearly, one sentence only is often not enough to identify extremist data). Keywords and topics that seemed to characterize the content were highlighted and discussed. When textual units corresponded to several categories, each category would be indicated accordingly. When this was not the case, new categories would be proposed inductively. By following this approach, four right-wing extremist categories were generated, see tab. 1.

Category

Frequent At the est of this process, each textual unit was labeled either as extremist (1), non-extremist (0) or unknown (x) by each person involved. For the final collection, only the extremist and non-extremist textual units were selected. The total number of textual units in the final data set is 1728, out of which 1129 were labeled extremist and the remaining 599 were labeled non extremist. For each textual unit we stored the text together with the right-wing extremist categories associated to it and the binary extremist/ non extremist distinction.

Emotion annotation

The annotation scheme used for this work was developed independently of the task of extremism detection ( Étienne and Battistelli, 2021). This paragraph introduces the elements of the scheme and the annotation procedure.

Description of annotation scheme

The annotation scheme uses SitEmo units to describe emotional situations, which is to say emotions expressed by linguistic markers and thus spatially and temporally anchored. Labelled emotions are explicitly mentioned through an emotional label, such as happy, anger, etc.. This expression mode corresponds to the use of emotional lexicon's words (Creissen and Blanc, 2017;Micheli, 2014).

Displayed emotions are shown directly through the characteristics of statements, which occurs when the enunciator experiences an emotion at the time of the utterance. The statement then includes linguistic markers, which show that the speaker felt an emotion and on which the reader relies to infer the emotional state of the enunciator. According to (Micheli, 2014), Displayed emotions can be shown by syntactic structures, lexical marks (interjections, judgments etc.) or typographical signs (exclamation points, etc). Suggested emotions are inferred by the reader from the description of socio-cultural conventions associated to feelings. The emotion is therefore neither directly presented, nor translated by a behavior, nor visible in the structure of the statement. The reader will analyze the overall picture, and this analysis serves as a support to build the emotion: the emotion felt by the character (or Narrator/Writer) is inferred by the reader based on the situation described. (Creissen and Blanc, 2017;Micheli, 2014) Behavioral emotions are expressed by using the description of behaviors or physical manifestations of the character who feels the emotion. Affective states are often associated to a variety of behavioral and emotional reactions, but sometimes only behaviors are reported, and the nuances of emotions will then be inferred from their descriptions (Creissen and Blanc, 2017). The Type of emotion (basic or complex) and the emotional category (fear, joy, etc.) also characterize SitEmo units. More specifically, the annotation scheme introduces 11 categories of emotions. The list of emotion categories comprises the 6 basic emotions introduced by (Ekman, 1992) and 4 complex emotions taken from (Blanc and Quenette, 2017) and (Davidson, 2006). We added a fifth complex category, Admiration, to better balance basic and complex emotions. Values of Type and Category elements are corre-lated and each of the 11 emotional categories is previously associated to the basic or complex types, as shown in table 3.

Basic Those categories are defined in order to regroup several more specific emotions. For example, the category Anger can be used to annotate textual segments expressing not only Anger but also annoyance, fury, indignation and disapproval.

The set of emotional categories implemented in the scheme is not exhaustive. In order to keep the annotations in line with the content under analysis, the unit Other can be used to annotate segments expressing an emotional category not foreseen by the annotation scheme.

The last element of SitEmo units is the Trigger, understood as the core of the annotated emotional expression. The trigger of emotions is the shortest segment (term or group of terms) which, within the annotated segment, constitutes the most salient emotional element, the one that focuses the emotional meaning of the textual segment and thus motivates the annotation. In some practical situations, several triggers can be identified for the same SitEmo unit.

Annotation procedure

The annotation scheme was designed to be implemented within the Glozz annotation platform (Widlöcher and Mathet, 2012). Glozz was selected because it can be customized by plugging specific annotation schemes and allows linguistic annotations at different levels (words, grammatical categories, sentences, groups of sentences) . The annotation starts with distinguishing a seed from a whole sentence in terms of emotion, see fig. 3. Emotions are described from the perspective of the writer, and the annotators need to be able to identify such emotions within the content and to pinpoint precise textual segments carrying emotions as basic SimEmo units.

In many cases, emotions can be clearly specified, see fig. 5 for an explicit example of Pride annotation, but in some cases emotions are hidden and their identification is not that simple.

Figure 5: Labelled annotation of type Pride Fig. 6 shows an example of implicit annotation of type Sadness. The type is not directly indicated in the sentence but rather inferred from the seed catastrophique (catastrophic). The annotation procedure identifies distinct emotions within the sentence and explicitly annotates their modes, types and categories. Used jointly, the annotation procedure and scheme allows to built complex descriptions of emotions, such as:

• Mode: Suggested

• Type: Basic The annotation procedure creates a fine-grained enriched corpus.

Validation and first results

Validation of annotations

The task of annotating the entire corpus in terms of emotions was given to three annotators: two of them authored the paper (A1 and A2) and the other is a master student in computational linguistics (A3). The annotation started with a set of 267 annotations created by A2. Two validation procedures were carried out, focusing on two different aspects. The first question was whether annotators agreed on values assigned to categories of emotions. This procedure is intended to validate the annotation scheme and the number and/or categories of emotions, as sometimes disagreement means adding emotions that are not included in the annotation scheme. For the first procedure, the initial annotation set was reviewed by annotator A1 in order to check the degree of agreement regarding the category of emotions. This validation identified 37 disagreements. When a1 and a2 are the sets of anchors annotated by A1 and A2, respectively, the recall of A2 with respect to A1 is given by :

Recall(A2||A1) = |a1 ∩ a2| |a2| (1)
For emotion category, the value of Recall is 0.86 and fig. 8 illustrates cases that annotators disagreed on.

As shown in the examples in fig. 8, the disagreement is related to the limitations of the annotation scheme, and adding additional categories or clearly indicating secondary emotions covered by categories in the scheme can improve the agreement.

The second procedure investigated whether annotators would recognize the same linguistic units as seeds, and therefore triggers of SitEmo units. For this second validation, we started again with the set of annotations created

Cross-analysis and remarks

The cross analysis of results was carried out by highlighting the distribution of SitEmo units in extremist and nonextremist data, respectively. As shown in fig. 10 , extremist data contains mainly emotions of Anger (45%). The second predominant emotion is Fear (19%) then, to a lesser extent, we detected emotions of Sadness (13%). Regarding the distribution of basic vs. complex emotions, the main complex emotion detected in non-extremist data is Pride. However, the percentage of Pride in extremist data (5% ) is slightly higher than in non-extremist data (4%). Moreover, Joy is approximately twice as represented in non-extremist data (16% vs. 7% that in extremist data) and Fear is less dominant (17 % for non-extremist data vs. 19% in extremist data).

Conclusion and perspectives

This paper explores some of the issues that are faced when exploiting emotions correlated to extremist contents released on social platforms. The paper presents a French annotated corpus in which extremist categories were originally constructed by exploring extremist contents and emotion labels were provided by a linguistic annotation scheme defined independently of this work. The manual labelling of data sets is a labor-intensive task and semi-automatic procedures are needed (Canales et al., 2019). For this work, the annotation task might be made easier by first considering clusters of data sets according to sociology-driven perspectives and then labelling all textual units within a given cluster based on the manual review of a limited set of examples within the cluster. Ontologies of appraisal categories (Dragos et al., 2018) or hate (Battistelli et al., 2020) can also be used to guide the annotation. Future work will address training machine learning algorithms for automatic classification of extremist contents and analyze the relevance of different features for extremist content detection. We will also extend the data sets by including new contents gleaned with additional keywords. The annotation of this new content could give a good overview of the robustness of the emotion annotation scheme and can help us verify if the annotation procedure is easily adaptable to other contents.

Acknowledgements

This document has been produced in the context of the FLYER project 4 funded by ASTRID, a research program supported by ANR (The French National Research Agency) and DGA (The French Defence Procurement Agency). The authors are grateful to Aurore Lessieux for her contribution to the annotation task.

Data availability statement

Data sets presented in this article are not available because of the nature of the material collected and analyzed.

Figure 1 :

 1 Figure 1: Data sets validation and exploration

Figure 2 :

 2 Figure 2: Extremist and non-extremist textual units

Figure 3 :

 3 Figure 3: Annotation process

Figure 4 :

 4 Figure 4: Examples of seeds and annotation units

Figure 6 :

 6 Figure 6: Suggested annotation of Type Sadness

Figure 7 :

 7 Figure 7: Examples of behavioural annotations

Figure 8 :

 8 Figure 8: Examples of disagreements on Category

Figure 9 :

 9 Figure 9: Examples of disagreements on seeds (Trigger)

Figure 10 :

 10 Figure 10: Categories of emotions in extremist data

Figure 11 :

 11 Figure 11: Categories of emotions in non-extremist data

Table 1 :

 1 Categories of right-wing extremism

		key-words
	Fundamentalists	Faith, Identify, Culture, Origin
	Defenders	Victim, Danger, Threat, Manipulation
	Nostalgics	Value, Nation, New order
	Fighters	Fight, Conflict, Planning, Action

Table 2 :

 2 Elements of SitEmo unitsEmotion Mode indicates how the emotion is linguistically expressed in the textual segment. The scheme considers that emotions are expressed in four main ways: through an emotional label, displayed by the linguistic characteristics of an utterance, suggested by a situation or inferred from behavior, thus values of Mode fit into four sub-types 3 : Labelled, Displayed, Suggested and Behavioral.

	Expression Mode	Labelled, Displayed, Sug-
		gested, Behavioral
	Type of emotion	Basic, Complex
	Category of emotions Anger, Joy, Fear, Pride.
		etc.
	Emotion trigger	Core of emotional expres-
		sion

SitEmo units are characterized by using 4 elements shown in tab. 2: 2 http://www.iramuteq.org/

Table 3 :

 3 Associations of emotional types and categories

	emotions Complex emotions
	Anger	Admiration
	Disgust	Guilt
	Joy, Fear	Embarrassment
	Surprise	Pride
	Sadness	Jealousy

The scheme was developped in French. We translate the sub-types as follows: Désigné is Labelled, Montré is Displayed, Suggéré is Suggested and Comportemental is Behavioral.


Ali Moscatiello
email: 1amoscatiel@laas.fr

Benjamin Cerdan #

Camille Gironde $

Christophe Furger $

David Dubuc
email: 3dubuc@laas.fr

Katia Grenier
email: 4grenier@laas.fr

Dosimetry Performances of a MultiWell-Plate-Based Near-Field RF Applicator for the Investigation of EM Impact on Biological Cells

Keywords: Dosimetry, RF applicator, RF effects, SAR, biological cells

While electromagnetic fields are now quasiubiquitous on earth and are constantly growing in use, RF radiation impact on living beings still continues to question. Within this context, a near-field RF applicator compatible with routine in vitro microplates for cellular investigations is proposed. This paper specifically focuses on its dosimetry performances, which are evaluated through simulation and measurements at 225 MHz, and its facility in biological postanalysis enabled by the use of standard bio-microplates.

I. INTRODUCTION

Evaluating the effect of electromagnetic fields on living beings remains a challenging topic due to controversial scientific results, as mentioned for instance in [START_REF] Lin | Cancer Occurrences in Laboratory Rats from Exposure to RF and Microwave Radiation[END_REF] with the cancer occurrences in laboratory rats. Such an investigation is however requested, as new equipment and standards such as 5G are developed, and the presence of ElectroMagnetic (EM) waves in our environment is continuously spreading out.

To evaluate the effect of RadioFrequency (RF) fields on living models, studies are conducted at different scales: in vitro using cultured cells, in vivo with animals and through epidemiological investigations at the human level. These different types of studies currently help to evaluate if there may be or not any beneficial or harmful effect of electromagnetic fields on living systems, depending on the RF exposure conditions [START_REF] Vander | RF/Microwave Interaction with Biological Tissues[END_REF][START_REF] Staebler | Human Exposure to Electromagnetic Fields[END_REF]. As far as experimental studies are concerned, they require developing appropriate RF exposure systems and test setups in conjunction with post-analysis performed by biologists and physicians. Actually, a large variety of RF exposure systems exist, with various electromagnetic approaches (far-field, near-field, antennas, rectangular waveguides) [START_REF] Hagan | A novel waveguide-based radio frequency/microwave exposure system for studying nonthermal effects on neurotransmitter Release-finitedifference time-domain modeling[END_REF][START_REF] Zhadobov | Exposure System and Dosimetry for In Vitro Studies of Biocompatibility of Pulse-Modulated RF Signals of Ultrahigh Field MRI[END_REF][START_REF] García-Fernández | Dosimetric Characteristics of an EMF Delivery System Based on a Real-Time Impedance Measurement Device[END_REF]. For in vitro evaluation, most of these solutions employ traditional Petri dishes, which present limitations in terms of compactness, dosimetry, and handling.

This paper therefore introduces an original near-field RF applicator specifically designed to radiate electromagnetic fields to cells, which are located into a standard biological 96well plate. The structure permits not only to illuminate biological cells with controlled and calibrated electromagnetic conditions, but it drastically facilitates the biological postanalysis of the cells due to the use of a standard biological accessory employed in routine analysis by biologists.

After describing the microwell plate-based near-field RF applicator in a first section, its electromagnetic characterization performed at 225 MHz is presented. The results obtained with electromagnetic simulation are given in section III, whereas the section IV is dedicated to the experimental dosimetry of the applicator. The next section provides then the application of the RF applicator with biological cells and its association with a biological postanalysis.

II. DESCRIPTION OF THE MULTIWELL-PLATE-BASED NEAR-

FIELD RF APPLICATOR Figure 1 presents a photography of the RF applicator. It includes two radiating elements, RF1 and RF2, located on the top of a Printed Circuit Board (PCB). The biological microplate may then be placed on top of the PCB, whereas the back side of the board is used to connect the applicator to the RF generation chain. Metallic vias through the PCB are also employed to interconnect the two sides of the PCB. The configuration of illuminating two well plates simultaneously with the same electromagnetic field may appears astonishing at a first sight. Nevertheless, it is defined on purpose. Biological studies request to systematically replicate the experiments due to the intrinsic inhomogeneity of living beings. The integration of two radiating elements powered by one cable consequently permits to apply the same electromagnetic field to two wells without needing to replicate RF cables on the back side. This configuration is presented in The dimensions are defined to illuminate the well, which presents an internal diameter of 6.35 mm, with a center to center distance of 9 mm.

The two next sections are dedicated to the dosimetry study of the applicator with electromagnetic simulation and experiments respectively.

III. ELECTROMAGNETIC SIMULATION OF THE APPLICATOR AT

225 MHZ An electromagnetic simulation is conducted with the finite element software named HFSS ® to evaluate the dosimetry characteristics of the applicator. The corresponding results are indicated in Figure 4, which presents the Specific Absorption Rate (SAR) distribution within the two illuminated wells, as well as in surrounding ones. The illuminated wells are easily recognizable with the red color in their center, whereas the non-illuminated ones exhibit a blue color. One may notice the symmetry versus both x and y axis of the applicator and wells configuration. The electromagnetic study may consequently be simplified by evaluating SAR values in specific locations, mentioned as a, b and c in Fig. 4.

A SAR value of 15 W/kg is obtained in the center of the two radiating elements (location a in Fig. 4), whilst an incident power of 1W is applied. At a distance of 2 mm from this center (location b in Fig. 4), the SAR presents a lower simulated value (9.7 W/kg). This is however not an issue as cells beyond this limit will not be considered in biological experiments during the RF effects investigations.

One may also notice that the surrounding wells, which are not directly exposed to an electromagnetic field, present nevertheless a light blue color of SAR in the vicinity of the RF illuminated wells. This is due to parasitic electromagnetic fields, with SAR values a decade lower than the maximal one in the radiating elements (see location c in Fig. 4). All these SAR values have been defined while wells are filled with a culture medium (Dulbecco's Modified Eagles Medium -DMEM in our case) and at a height of 10 µm from the bottom of the plastic well. This height corresponds to the average value for the size of the cells used later for RF impact evaluation. To complete this study, the experimental dosimetry is also conducted and presented in the next section.

IV. EXPERIMENTAL DOSIMETRY OF THE RF APPLICATOR

A. Method applied to extract the SAR value and the thermal increment

The experimental protocol applied to evaluate the SAR value and the thermal increment within the device at 225 MHz is based on temperature measurements, as mentioned in [START_REF] Wu | Safe for generations to come[END_REF] (cf. pp. 67, eq. ( 3)). Wells are filled with culture medium (DMEM), whereas a strong incident power is applied on the RF applicator to obtain a measurable thermal increment. A fiber optic temperature sensor permits to get the temperature versus time at the bottom of the well. Based on the corresponding curve, the SAR value may be directly extracted from the slope, which starts once RF power is ON. Further details on the experimental test setup, temperature measurements and SAR extraction are similar to those in [START_REF] Augé | Experimental Dosimetry Study of a Miniature RF Applicator Dedicated to the Evaluation of Severe RF Exposure Impact on a 3D Biological Model[END_REF].

For the experiments, the RF applicator and the temperature probe are both placed in an incubator at 37°C. In order to perform the dosimetry study of the structure, the characterization method mentioned above is performed at different locations above the RF applicator and in some surrounding wells. These positions are summarized in Fig. 5. The two red circles symbolize the RF applicator, whereas the two blue circles are surrounding wells. Three different locations on RF1 are identified: A at the center, B and C at a distance of 2 mm from A, with B toward the radiating element RF2 and C toward the opposite direction respectively. As far as the adjacent and non-illuminated wells are concerned, three positions are tested, similarly as with RF1, and referenced as E in the middle, D and F for the two others. Due to the symmetries of the structure, only the points indicated above are measured. Each point is measured with three independent experiments.

B. Experimental results

Table 1 gives a summary of the measured SAR values and thermal increments with an incident power of 1W in continuous wave mode, at 225 MHz. The initial temperature is 37°C. Above the center of the RF1 element, an average SAR value of 16.9 W/kg is measured with a standard deviation of 0.9 W/kg, whereas the temperature increment is of 0.7°C. These values are also reached in point B at 2 mm from A on RF1. On the opposite side of RF1, in point C, the SAR value is decreased by 1 W/kg, leading to a global SAR homogeneity of 94% in a 4 mm disk diameter in the RF1 well.

V. APPLICATION OF THE RF APPLICATOR TO HUMAN LIVING CELLS To validate the developed applicator regarding its interest for EM effect evaluation on living cells, this one is applied to biological human cells and associated to a biological postanalysis, which evaluates the homeostasis of cells [START_REF] Gironde | Use of LUCS (Light-Up Cell System) as an alternative live cell method to predict human acute oral toxicity[END_REF]. This technique, called LUCS (for Light Up Cell System) is relevant of any perturbation of the cellular equilibrium and is based on a fluorescence detection realized directly with cells placed in standard 96-well microplates. The detection is only performed within a 4 mm diameter disk at the bottom of the wells, due to the high SAR homogeneity in this location. Three independent experiments have been performed on the human liver HepG2 cell line culture in DMEM medium. Fig. 6 presents the results of one representative experiment for the two conditions: with or without (negative control) RF application. Due to the parasitic fields in the nearest neighbor wells as indicated in section IV.B, negative controlled wells are chosen several columns further on the microplate. Fig. 6. LUCS homeostasis assay readout obtained for HepG2 cells submitted or not to an electromagnetic illumination at 225 MHz, with a SAR of 16.9 W/kg, for 24 hours.

No significative impact for this specific RF scenario applied to HepG2 cells is obtained for all the experiments. VI. CONCLUSIONS A near-field RF applicator specifically designed to radiate a controlled and calibrated electromagnetic field on cultured cells, which are located in standard biological microplates, is introduced. Its dosimetry study is performed at 225 MHz, leading to a homogeneous SAR value on a large surface at the bottom of the microplates' wells. This applicator has then been applied to illuminate biological cells with a SAR value of 16.9 W/kg. No significant effect on cells was detected. But the key issue of this experiment was to demonstrate the power of allying specific RF applicators with standard biological consumables, i.e microplates. The bio-post-analysis are extremely facilitated due to the use of standard biomicroplates, which are compatible with all the traditional and routine bio-equipment.

Homeostasis readout

No RF RF

Fig. 1 .

 1 Fig. 1. Photography of the RF applicator developed to radiate cells with a biological 96 well plate placed on top and composed of two radiating elements, RF1 and RF2.

Figure 2 aFig. 2 .

 22 Fig. 2. Schematics of the RF applicator board (green) with the microwell plate placed above (grey): (a) Tilted version and (b) Cross section. Back side RF cable is in red, whereas the RF connector in purple.

Figure 3

 3 Figure3presents the dimensions of the applicator with both top and bottom views. The radiating elements exhibit a coplanar configuration. The metallization is indicated in yellow, whereas the capacitive slots are presented in green respectively. Vias are present in the middle of the signal patch to interconnect both sides of the PCB. The purple strip on the back side is used to convey the electromagnetic field to the two radiating elements. The ground is specifically designed to allow the soldering of an SMA connector.

Fig. 3 .

 3 Fig. 3. Schematics and dimensions of the RF applicator, which radiates electromagnetic waves into 2 wells: (a). Top view (b). Bottom view.

Fig. 4 .

 4 Fig. 4. Simulated SAR distribution in the wells placed above the RF applicator and their nearest neighbors.

Fig. 5 .

 5 Fig. 5. Location of temperature kinetic measurements for SAR evaluation.

Table 1 .

 1 Measured dosimetry characteristics of the RF applicator for an incident power of 1W at 225 MHz.

ACKNOWLEDGMENT

This work was supported in part by the French National Research Program for Environmental and Occupational Health of Anses (2019/2 RF/25) and in part by the French Direction Generale de l'Armement and the French Direction Generale des Entreprises with the funding of the RAPID project "CELL FI".


José P Carvalho

Wassilios Papawassiliou

Andrew J Pell
email: andrew.pell@mmk.su.se

Half-integer-spin quadrupolar nuclei in magic-angle spinning paramagnetic NMR: The case of NaMnO 2

Keywords: Paramagnetic NMR, Solid-state NMR, Magic-angle spinning, Quadrupolar interaction, TOP-STMAS, RAPT, MAT;

A combination of solid-state NMR methods for the extraction of 23 Na shift and quadrupolar parameters in the as-synthesized, structurally complex NaMnO 2 Na-ion cathode material, under magic-angle spinning (MAS) is presented. We show that the integration of the Magic-Angle Turning experiment with Rotor-Assisted Population transfer (RAPT) can be used both to identify shifts and to extract a range of magnitudes for their quadrupolar couplings. We also demonstrate the applicability of the the two-dimensional one pulse (TOP) based double-sheared Satellite Transition Magic-Angle Spinning (TOP-STMAS) showing how it can yield a spectrum with separated shift and second-order quadrupolar anisotropies, which in turn can be used to analyze a quadrupolar lineshape free of anisotropic bulk magnetic susceptibility (ABMS) induced shift dispersion and determine both isotropic shift and quadrupolar products. Combining all these experiments, the shift and quadrupolar parameters for all observed Na environments were extracted and yielded excellent agreement with the density functional theory (DFT) based models that were reported in previous literature. We expect these methods to open the door for new possibilities for solid-state NMR to probe half-integer quadrupolar nuclei in paramagnetic materials and other systems exhibiting large shift dispersion.

Experimental and Simulation Details

Synthesis procedure

The synthetic procedure was carried out based on previous literature [START_REF] Billaud | β-NaMnO 2 : a high-performance cathode for 714 sodium-ion batteries[END_REF][START_REF] Abakumov | 722 Multiple twinning as a structure directing mechanism in layered rock-salt-723 type oxides: NaMnO 2 polymorphism, redox potentials, and magnetism[END_REF]. Appropriate amounts of Na 2 CO 3 and Mn 2 O 3 were mixed and ground to account for the evaporation of Na 2 O during the firing process. The samples were then fired up under oxygen at 950 • in two separate steps for 24 hours each.

After those steps, the samples were quickly quenched to room temperature and placed inside an Ar-filled glovebox, due to air sensitivity.

Powder X-ray diffraction

Powder X-ray diffraction was performed on a Panalytical X'Pert PRO diffractometer operated with Cu-K α 1 radiation and in θ -2θ diffraction geometry. Diffraction patterns were measured in a 2θ range of 5-90 • . Subsequent Rietveld analysis was performed with the software FullProf Suite [START_REF] Rodriguez-Carvajal | FULLPROF: a program for Rietveld refinement 726 and pattern matching analysis[END_REF].

Solid-state NMR

The solid-state NMR spectra were acquired on a 500 Avance NEO spectrometer and on a 600 Avance III Bruker spectrometer, at magnetic fields of 11.7 and 14.1 T, corresponding to Larmor frequencies of 132.294 and 158.744 MHz for 23 Na, respectively. In both cases 1.3 mm HX probes were used at 60 kHz MAS frequency. Both the 23 Na shifts and RF field strength were calibrated on solid NaCl, with 23 Na signal referenced at 7.21 ppm. At 11.7 T, all pulses were applied with a RF field strength with 225 kHz, corresponding to 0.56 and 1.11 µs π/2 and π CT selective pulses. RAPT pulses [START_REF] Yao | Sensi-729 tivity enhancement of the central transition NMR signal of quadrupolar 730 nuclei under magic-angle spinning[END_REF] operated at 159 kHz nutation frequency. At 14.1 T, all pulses operated with an RF field strength with a nutation frequency of 195 kHz, corresponding to 0.64 and 1.28 µs π/2 and π CT selective pulses.

In the discussion that follows, the observed 23 Na shifts are defined as

δ obs = δ iso + δ QIS , (1)
where δ QIS is the second-order isotropic quadrupolar induced shift given by

δ QIS = A 0 (I, q) 3 4I(2I + 1) 2 P 2 q ν 0 , (2)
where ν 0 is the Larmor frequency, δ iso the isotropic shift, P q the quadrupolar product,

P q = C q 1 + η 2 q 3 , (3)
and A 0 (I, q) is a spin (I) and transition (q) dependent coefficient [START_REF] Ashbrook | High-resolution NMR of quadrupolar nu-733 clei in solids: the satellite-transition magic angle spinning (STMAS) ex-734 periment[END_REF]. C q is the quadrupolar coupling given by

C q = e 2 qQ 2I(2I -1) , ( 4
)
where eQ is the nuclear quadrupole moment and eq is the zz component of the electrical field gradient (EFG) tensor, Ṽii in the principal axis frame (PAF). The components of the EFG in the PAF are ordered as Ṽzz ≥ Ṽyy ≥ Ṽxx . The quadrupolar splitting frequency ω q and asymmetry parameter η q are defined as

ω q = 3πC q 2I(2I -1) , (5)
η q = Ṽxx -Ṽyy Ṽzz . (6)
The shift tensor is characterized by the three principal components that are ordered according to the Haeberlen convention, δzzδ iso ≥ δxxδ iso ≥ δyyδ iso where

δ iso = 1 3 δxx + δyy + δzz (7)
and δxx , δyy and δzz are the components of the shift tensor in the PAF and δ iso the isotropic shift. The shift anisotropy (SA), ∆δ, and asymmetry parameter, η, are given by, ∆δ = δzzδ iso (8)

η = δyy -δxx ∆δ . (9)
We note that SA corresponds to a generalization of the chemi-156 cal shift anisotropy (CSA) to include the contribution from un-157 paired electrons. For 23 Na, the orbital contributions [START_REF] Pennanen | Nuclear magnetic resonance chemical shift in 737 an arbitrary electronic spin state[END_REF] to the 158 SA tensor are generally negligible.

159

RAPT pulse trains applied prior to a rotor-synchronised Hahn-echo sequence, using xx pulses, as shown in figure 2(a), saturate the populations of the satellite transitions (STs) so that their net polarization reduced to zero and, consequentially, yields a sensitivity enhancement of the central transition (CT) signal by a factor of I + 1/2, where I corresponds to the nuclear spin which for 23 Na is 3/2, giving a maximum theoretical enhancement of 2 [60]. The repetition frequency, defined as ν = 1/(2τ 1 ), where τ 1 is the interpulse delay, corresponding to an experimental setup that gives the largest enhancement when ν is equal to the quadrupolar splitting frequency [58-60, [START_REF] Yao | Sen-740 sitivity enhancement of the central transition NMR signal of quadrupo-741 lar nuclei under magic-angle spinning[END_REF][START_REF] Prasad | Zim-745 mermann, A combined 17 O RAPT and MQ-MAS NMR study of l-746 leucine[END_REF][START_REF] Ash | Solid-state NMR characterization of 69 Ga 749 and 71 Ga in crystalline solids[END_REF],

ν = ω q 2π . ( 10
)
The maximum enhancement is, therefore, independent of η q .

160

The enhanced CT polarization is then excited using a conven- The spectrum was recorded with a recoupling time of two rotor periods and 128 complex increments (480 kHz spectral width in the indirect dimension), 2800 scans per increment and a recycle delay of 33 ms. The MAT pulse sequenced was preceded by a RAPT pulse train identical to that used for the one-dimensional spectrum.

The TOP-STMAS experiment was performed using the zfiltered STMAS pulse sequence [57,[START_REF] Ashbrook | High-resolution NMR of quadrupolar nu-733 clei in solids: the satellite-transition magic angle spinning (STMAS) ex-734 periment[END_REF] as shown in figure 1(c), preceded by a simple saturation pulse train for preparation of the magnetization. This experiment uses the fact that the transition pathway that goes through a satellite transition (ST) during t 1 and ends on the CT in t 2 , does not form simultaneous echoes for the isotropic nuclear shielding, isotropic quadrupolar and anisotropic quadrupolar contributions, as shown in Figure 3 of the SI, and only after double-shearing transformation the isotropic shift and quadrupolar anisotropy is separated into orthogonal dimensions [57, [START_REF] Hung | 752 Q-shear transformation for MQMAS and STMAS NMR spectra[END_REF][START_REF] Kobera | Biaxial Q-755 shearing] of 27 Al 3QMAS NMR spectra: Insight into the structural dis-756 order of framework aluminosilicates[END_REF]. Here, we employed a TOPbased protocol [54][55][56][START_REF] Blümler | Two-dimensional one-pulse rotational 759 echo spectra[END_REF], by carrying out active shearing transformations of the discretely-sampled-data, exploiting the Fourier shift theorem [START_REF] Grandinetti | Symmetry pathways in solid-762 state NMR[END_REF], after the generation of all four timedomain quadrants, and by swapping the direct and indirect dimensions, as described in Carvalho et al. [57] (see Figure 3 of the SI for a schematic of STMAS time-domains before and after the shearing transformations). The center-of-gravity of the lineshape in each dimension is given by

δ Shift = δ iso + δ q • S C δ q,1 , (11)
δ Quad = δ q • S C δ q,2 , (12)
where

δ q = 3 4I(2I + 1) 2 P 2 q ν 0 , (13)
and S C δ q,1/2 corresponds to the quadrupolar shift coefficients, given in Ref. Haberkorn-Rubens method [START_REF] States | A 2D NMR experiment with pure 765 absorption phase in four quadrants[END_REF].

201

The final one-dimensional MAS spectra were recorded us-

(c) t 2 t 2 t 2 t 1 =
Figure 1: Pulse sequences and coherence transfer pathways (CTP) for the experiments used to extract shifts and quadrupolar parameters: (a) Rotorsynchronised Hahn echo sequence preceded by a train of x x pulses for RAPT with repetition frequency given by ν = 1/(2τ 1 ). (b) Five π-pulse MAT pulse sequence also preceded by a RAPT train, with an evolution time of N rotor periods, where N is an integer that is not a multiple of 3. Pulses at (2/6)Nτ r and (4/6)Nτ r are fixed and the timings of the remaining π pulses are shifted according to echo or anti-echo types as shown in the pulse-timings below, where n is the number of increments acquired in the indirect dimension. (c) z -filtered STMAS experiment where dashed red and black pathways correspond to the N-type and P-type datasets. n is incremented from 1 in steps of a single rotor period. A representation of the STMAS time-domains before and the TOP based double-shear transformation is shown in figure 2 of the SI. All π/2 and π correspond to CT selective pulses.

Simulations

211

Numerical simulations of the NMR spectra were all per-212 formed using SIMPSON [START_REF] Bak | SIMPSON: a general simula-767 tion program for solid-state NMR spectroscopy[END_REF] considering 579 crystallite orien-213 tations using the Alderman, Solum, Grant (ASG) scheme [START_REF] Alderman | Methods for analyzing spectro-770 scopic line shapes. NMR solid powder patterns[END_REF]. 274 and the spin-dipolar interaction, which dominates the SAs. We 275 note that at lower sodium content, Na x MnO 2 , we expect higher 276 sodium shifts, since the oxidation of Mn 3+ to Mn 4+ leads to a 277 higher hyperfine shift [START_REF] Clément | Structurally stable Mg-doped P2-Na 2/3 Mn 1-y Mg y O 2 709 sodium-ion battery cathodes with high rate performance: insights from 710 electrochemical, NMR and diffraction studies[END_REF][START_REF] Billaud | β-NaMnO 2 : a high-performance cathode for 714 sodium-ion batteries[END_REF][START_REF] Clément | 717 Insights into the nature and evolution upon electrochemical cycling of 718 planar defects in the β-NaMnO 2 Na-ion battery cathode: An NMR and 719 first-principles density functional theory approach[END_REF]. 23 Na resonances extracted from the MAT spectra with increasing repetition frequency of the RAPT pulses. The data points are indicated by red circles. The smooth black curves were obtained by employing a moving-average filter and were used to estimate the maximum enhancement factor. Considering frequency interval corresponding to ±5% of the maximum enhancement factor and using equation [START_REF] Bryce | NMR crystallography: structure and properties of materi-523 als from solid-state nuclear magnetic resonance observables[END_REF], the range of magnitudes of the quadrupolar couplings C q was determined. The spectral lineshapes were all simulated considering Gauss-Lorentz curves whose centers-of-gravity were used to determine the quadrupolar products, P q (3 ± 0.2 MHz for (1) and 3 ± 0.3 MHz for (2)), and isotropic shifts using equations [START_REF] Van Der Klink | NMR in metals, metal particles and 526 metal cluster compounds[END_REF] and [START_REF] Papawassiliou | Resolving Dirac 530 electrons with broadband high-resolution NMR[END_REF]. The STMAS spectrum was recorded while spinning at 60 kHz MAS and at 11. All NMR parameters were fixed in accordance with the fitting models shown in figure 6, with corresponding NMR parameters given table 1. The total intensity of each site and relative intensity of the satellite transitions (ST) and central transition (CT) was allowed to vary. The relative intensity of the satellite transitions was constrained to never exceed their theoretical limit. The 14.1 T spectrum was fitted with the relative ST-to-CT intensities fixed intensity ratios set to match the 11.7 T data, and only the relative intensity of each site was allowed to vary. Taking into account the relative intensities of the spectrum recorded at 11.7 T, the relative quantification of each sodium environment was computed and is also given in table 1. The observed shifts, δ obs = δ iso + δ QIS , were calculated using equation ( 2) for the two different magnetic fields. The small peak at ∼ 0 ppm is due to a Na + in a residual diamagnetic impurity not predicted by the fitting model. Additional details pertaining to the simulated lineshapes are given in the Experimental and Simulation Details section.

DFT [START_REF] Clément | 717 Insights into the nature and evolution upon electrochemical cycling of 718 planar defects in the β-NaMnO 2 Na-ion battery cathode: An NMR and 719 first-principles density functional theory approach[END_REF]. (b) and (c) Range of DFT predicted NMR parameters for two mixed α/β-NaMnO 2 structures, proposed in [START_REF] Clément | 717 Insights into the nature and evolution upon electrochemical cycling of 718 planar defects in the β-NaMnO 2 Na-ion battery cathode: An NMR and 719 first-principles density functional theory approach[END_REF], that contain twin boundaries between structural domains of both phases. Na(1) and Na(2) feature similar Mn-O-Na interactions, and only differ in the spatial arrangement of the atoms around the sodium ion, leading to similar isotropic shifts, δ iso , and different shift anisotropy (∆δ and η) and quadrupolar parameters (C q and η q ). The same argument holds true for the Na(β)/pseudo β and Na(α)/pseudo α sites, respectively. All DFT based NMR parameters were transcribed from [START_REF] Clément | 717 Insights into the nature and evolution upon electrochemical cycling of 718 planar defects in the β-NaMnO 2 Na-ion battery cathode: An NMR and 719 first-principles density functional theory approach[END_REF] and used B3LYP functional with 20 and 35% Hartree-Fock exchange implemented in the CRYSTAL09 code [START_REF] Dovesi | CRYSTAL: a computational tool for the ab initio study 788 of the electronic properties of crystals[END_REF]. (d) 23 Na NMR parameters obtained obtained by fitting the extracted one-dimensional slices of the MAT spectrum shown in figure 6. Three resonances were assigned to β (β 1 and β 2 ) and α-"like" environments and two resonances were assigned to sites in the vicinity of a stacking fault (SF 1 and SF 2 ). The Na environment corresponds to sodium ions in a different local environment in the orthorhombic sodium deficient phase shown in 2(c). Relative quantification of each sodium environment was obtained considering the fitted signal intensities of each site of spectrum recorded at 11.7 T, shown in figure 7. The observed shifts, δ obs = δ iso + δ QIS , were calculated considering an external magnetic field of 11.7 T.

1

 1 Solid-state NMR (ssNMR) has become an established tool 2 to study a wide range of systems in chemistry, physics, ma-uniform excitation or inversion more difficult and complicates 57 the extraction of the NMR parameters. 58 Notable pulse schemes have been proposed for integer 59 quadrupolar systems such as the application of the Delays Al-60 ternating with Nutation for Tailored Excitation (DANTE) [45] 61 to achieve broadband inversion and excitation, and the low-62 power excitation of double-quantum coherences in spins sub-63 ject to large quadrupolar interactions [46, 47]. Pulse sequences 64 designed for the separation separation of shift and quadrupo-65 lar interaction have also been proposed, for static samples the 66 shifting p-echo [48], shifting d-echo [49], adiabatic shifting 67 d-echo [50], and, more recently phase adjusted spinning side-68 band (PASS) [51] for spinning samples. 69 For half-integer quadrupolar nuclei in paramagnetic systems 70 we have the additional problem of differentiating between the 71 central transition (CTs) of different environments, and their ac-72 companying satellite transitions (STs), both of which are broad-73 ened by the paramagnetic SA and are generally seen under 74 high-power conditions used to obtain the spectrum. The most 75 widely used method of achieving high-resolution, the multiple-76 quantum magic angle spinning experiment (MQMAS) [52], 77 has not been widely successfully applied to paramagnetic sys-78 tems, likely due to the interference between paramagnetic and 79 quadrupolar effects. A rival experiment, the satellite transi-80 tion magic angle spinning experiment (STMAS) [53], however, 81 has been successfully applied to systems with low concentra-82 tions of a paramagnetic dopant ion and when combined a dou-83 ble shearing transformation based on the two-dimensional one 84 pulse (TOP) scheme [54-57], yields a spectrum where shift and 85 quadrupolar interactions are separated. Alternatively, the rotor-86 assisted population transfer (RAPT) method [58-60] has some 87 success at estimating the quadrupolar parameters in paramag-88 netic systems [60]. 89 In this work, we explore the performance and limitations of 90 the state-of-the-art methods for extraction of both quadrupo-91 lar shift anisotropy tensor parameters in an as-synthesized 92 NaMnO 2 system, which belongs to a class of layered sodium in-93 tercalation compounds that have been a focus of recent studies 94 due to its applications as high-capacity Na-ion cathodes [61-95 64]. The complexity of NaMnO 2 stems from the fact that it 96 may crystallize into several polymorphs. The assignment and 97 validation of the proposed models for the structure of NaMnO 2 98 by Clément et al. [65] have hitherto been made solely based 99 on a comparison of experimental isotropic shifts with DFT-100 calculated values. However, useful NMR parameters, such as 101 the shift-anisotropy (SA) and quadrupolar interaction parame-102 ters, are not routinely used, despite containing potentially use-103 ful additional information. This is largely due to the difficulty 104 in obtaining reliable experimental values, particularly for the 105 quadrupolar parameters where the second-order spectral line-106 shapes are smeared out by paramagnetic line broadening. 107 This paper explores how far the current state-of-the-art ex-108 perimental methods can be used to identify the different CTs 109 and STs from different environments, obtain both isotropic 110 shifts and quadrupolar tensor parameters for the different lo-111 cal environments, and how this additional information may be 112 used to obtain a more detailed picture of the different struc-tures within this complex paramagnetic material. More specifically, we will employ a combination of Hahn-echo and MAT experiments in conjunction with RAPT for site identification and coarse determination of the quadrupolar couplings. Subsequently, we refine our analysis via the TOP-STMAS experiment, for differentiation of the contributions from shifts and second-order quadrupolar effects, and ensuingly by fitting the slices of the MAT spectra, for extraction of the full NMR tensor parameters. Lastly, using the obtained parameters, we fit the Hahn-echo spectra acquired at two different external magnetic fields, to obtain an unambiguous assignment, and quantify the different sodium environments.

161

  tional Hahn-echo sequence, as shown in figure2(a), and corre-162 sponds to an enhanced signal. The one-dimensional spectra shown in figure 3(a) was acquired with a RAPT pulse train with 20 loops, 525 kHz repetition frequency and using 4096 scans and 125 ms recycle delay. The experimental signal enhancements shown figure 4 were measured by varying the repetition frequency in a total of 27 steps of 25 kHz (from 250 kHz to 900 kHz), accumulating 2048 transients per frequency step and using 125 ms recycle delay. The enhancement profiles were benchmarked on the four-coordinate 27 Al resonance of yttrium aluminium garnet (see figure 1 of the SI). The 2D MAT [27] experiment, shown in figure 1(b), uses a sequence of 5 π-pulses to manipulate the spinning sidebands and separate them by isotropic shift in the indirect dimension.

  [57]. Along the quadrupolar dimension, the lineshapes can be analyzed without shift-dispersion induced broadening arising from ABMS effects. The STMAS spectrum, will also exhibit a CT-CT and ST-ST diagonal peaks, with the latter generally being negligible, that form echoes simultaneous with the isotropic nuclear shielding and thus appear at δ Quad = 0, since these pathways cannot be filtered via phasecycling. The time-dependent contributions of the chemical shift anisotropy and quadrupolar interactions are refocused along the time-dependent echo ridge represented in figure 2 of the SI. After the double shearing transformation these contributions ap-pear in both dimensions. The spectra shown in figure 5 was 195 recorded employing 1.35 µs pulse for both the excitation and 196 reconversion of the satellite coherences and 0.56 µs for the fi-197 nal CT selective pulse. 256 complex increments were recorded 198 with a sampling interval of 16.67 µ in t 1 and 2048 transients 199 per increment using a 33 ms recycle delay using the States-200

202

  ing a two-rotor period synchronised Hahn-echo sequence. At 203 11.7 T external magnetic field, 32768 transients were accu-204 mulated with a relaxation delay of 125 ms to ensure quanti-205 tative results. In table 1 of the SI the T 2 coherence lifetime 206 and T 1 spin-lattice relaxation time, determined using rotor syn-207 chronised Hahn-echo and echo-detected saturation recovery, re-208 spectively, are shown for each observed site. At 14.1 T, 65536 209 transients were accumulated with a relaxation delay of 50 ms.

214

  The quadrupolar and CSA parameters were obtained by fitting 215 slices of the MAT spectra including only the contribution aris-216 ing only from the CT and 20 γ angles. Constraints on C q and 217 on δ iso for one of the sodium environments were imposed in 218 accordance with the results of the TOP-STMAS spectrum and 219 RAPT signal enhancement curves. The errors of the fitted pa-220 rameters where determined using Monte-Carlo error estimation 221 as described in Aleksis et al. [50]. 222 RAPT buildup curves were obtained by first fitting the one-223 dimensional spectrum acquired with a RAPT pulse train with 224 repetition frequency of 525 kHz, using six mixed Gauss-225 Lorentz functions for the centerband of each observed reso-226 nance. Each slice of the buildup pseudo-2D spectrum together 227 with the one-dimensional spectrum acquired without the RAPT 228 pulse train were then also fitted using the fitting function, al-229 lowing only the parameters governing the signal intensity to 230 vary. The enhancement ratios were obtained considering the 231 intensities of the one-dimensional spectra and subsequentially 232 used to normalize the buildup data. The buildup curves were 233 smoothed using a moving-average filter to mitigate the impact 234 of the noise. 235 The final one-dimensional MAS spectra were fitted simply 236 by allowing the intensity arising from the CT and STs of each 237 site to vary, with fixed NMR parameters. The contribution of 238 the signals from the satellite transition was constrained to never 239 exceed the maximum theoretical intensity ratio with respect to 240 the central transition. Each one-dimensional lineshape was sim-241 ulated in SIMPSON with 100 γ-angles.

242 3 .

 3 figure 2 of the SI, revealed a ratio of roughly 62 : 18 : 20 245

Figure 2 :

 2 Figure 2: Crystal structure of the three forms of Na x MnO 2 : (a) orthorhombic β-NaMnO 2 in Pmnm space group exhibiting corrugated layers, (b) a Jahn-Teller distorted α-NaMnO 2 structure with a monoclinic C2/m space group and (c) orthorhombic sodium deficient Na 2/3 MnO 2 in Cmcm space group.

278

  As previously shown by Billaud et al.[START_REF] Billaud | β-NaMnO 2 : a high-performance cathode for 714 sodium-ion batteries[END_REF] the lineshape 279 exhibits multiple23 Na environments, with three clear distinct 280 main resonances at 309, 500 and 830 ppm. These environments 281 have been previously assigned to an ideal β-"like" environment, 282 a sodium site in the vicinity of a stacking fault, and an α-"like" 283 environment, respectively. The spectral lineshapes are also rela-284 tively broad due to a combination of structural disorder, ABMS 285 and second-order quadrupolar effects. 286 The application of a RAPT pulse train yields an enhance-287 ment of approximately 1.4, corresponding to less than half of 288 the maximum theoretical enhancement 2. Nevertheless, it is a 289 useful tool to enhance CT signal-to-noise ratio while simultane-290 ously suppressing the contributions from the satellites. Further-291 more, evaluating the repetition frequency that yields the maxi-292 mum enhancement for each site gives an estimate of the mag-293 nitude of their corresponding C q . Since we are in the presence 294 of multiple sodium environments, we first need to separate the 295 overlapping spinning sideband manifolds, in order to identify 296 the different resonances.297 The MAT experiment was only designed for spin systems 298 with rank 2 SA broadening, since the time-dependent modula-299 tion of rank 4 terms, introduced by the second order quadrupo-300 lar interaction, are not refocused. Considering that the rank 2 301 interactions are much larger in magnitude and we are operating 302 at a spinning frequency that is much larger than the width of the 303 MAS lineshape, as clearly evidenced in the one-dimensional 304 lineshapes shown in figure 3(a), and, therefore, with adjacent 305 sidebands that do not overlap with each other, there is little jus-306 tification version of MAT experiment that refocuses the contri-307 butions arising from the second order quadrupolar interaction 308 [82-84]. 309 In figure 3(b) the 2D MAT spectrum is shown exhibiting six 310 distinct sodium peaks, including the three main resonances at 311 309, 500, 830 ppm, and additional, at lower intensity, that were 312 not distinguishable in the 1D spectrum, at shifts of 356, 539 313 and 1170 ppm. The resonances at 356 and 539 ppm are at-314 tributed to sodium environments near the planar defects that 315 have similar Mn-O-Na hyperfine interactions to the β and stack-316 ing fault environments observed by Billaud et al. [64], respec-317 tively, and, hence, similar Fermi contact shifts. These reso-318 nances, however, differ in the spatial arrangement of the atoms 319 around the central sodium ion [65], which in turn correspond 320 to differences in the observed shift of approximately 40 ppm in 321 induced shift. Nevertheless, these environments are hard to dis-322 tinguish in the experimental NMR spectrum since the inherent 323 linewidth of the sodium resonances is roughly 20 ppm. Fur-324 thermore, since the separation between the satellite and central 325 transition resonances considering the quadrupolar couplings re-326 ported in Billaud et al. [64] corresponds to roughly 40 ppm at 327 an external magnetic field of 11.7 T, these sites also overlap 328 with signal contributions arising from the STs of the main sites 329 at 309 and 500 ppm. However, since we saturate the satellite 330 transition populations with a RAPT train it is unlikely that con-331 tributions arising from STs would be significant. The resonance 332 observed at 1170 ppm has also been reported in Clément et al. 333 [65] in Na x MnO 2 samples with low sodium content, x ∼ 0.4, 334 and was attributed to sodium environments in a different phase 335 and local environment. This site likely arises from the presence 336 of the orthorhombic sodium deficient phase revealed by XRD, 337 also observed by Clément et al. [63], since higher sodium shift 338 is consistent with the oxidation of Mn 3+ to Mn 4+ . 339 We proceed to investigate the enhancement factors of the ob-340 served resonances in the RAPT buildup curves, as shown in fig-341 ure 4. The integrals were all evaluated considering the Gauss-342 Lorentz functions used to deconvolve the one-dimensional line-343 shape shown in 2(a). For each slice of the RAPT buildup curve, 344 only the intensities of each Gauss-Lorentz function were al-345 lowed to vary, ensuring the effect of the overlap of the line-346 shapes was minimized. All six sites clearly show an enhance-347 ment of the signal intensity which further evidences that they 348 correspond, predominantly, to CT lineshapes. Additionally, the 349 maximum in the profiles permitted the estimation of a range of 350 C q values. It is worth noting that the ranges are of the order of 351 1 MHz which is relatively quite large, which reflects the limi-352 tations of the method to estimate C q accurately, particularly in 353 the presence of overlapping resonances.

Figure 3 :Figure 4 :

 34 Figure3: RAPT-enhanced23 Na solid-state NMR spectra of NaMnO 2 . (a) Onedimensional Hahn-echo spectrum of NaMnO 2 with and without the application of a RAPT pulse train illustrating the enhancement of the signal intensity of the central transition. Observed centerbands and sidebands marked with by stars ( ) and asterisks ( * ), respectively. (b) MAT spectrum of NaMnO 2 exhibiting six resonances with distinct observed shifts. Inset spectra correspond to extracted direct-dimension slices, and the observed shifts correspond to the centerbands marked by stars ( ). RAPT pulses were applied before the MAT experiment to enhance the signal-to-noise ratio and suppress the signals arising from the satellite transitions. Both spectra were recorded at 60 kHz MAS and at an 11.7 T external magnetic field. RAPT pulse trains were employed with a repetition frequency of 525 kHz.

Figure 5 :

 5 Figure 5: (a) Sheared z -Filtered TOP-STMAS spectrum showing the CT-CT diagonal peaks of five observed resonances, around 0 kHz in the indirect dimension, and the Satellite Transition (ST)-CT diagonal peak for the sites whose central transition is observed at 309 and 500 ppm, at around -2.6 kHz in the indirect dimension. Sidebands are marked with ( ). Extracted slices along the shift and quadrupolar dimensions together with the best fits are shown in figures (b) and (c), respectively.The spectral lineshapes were all simulated considering Gauss-Lorentz curves whose centers-of-gravity were used to determine the quadrupolar products, P q (3 ± 0.2 MHz for (1) and 3 ± 0.3 MHz for (2)), and isotropic shifts using equations[START_REF] Van Der Klink | NMR in metals, metal particles and 526 metal cluster compounds[END_REF] and[START_REF] Papawassiliou | Resolving Dirac 530 electrons with broadband high-resolution NMR[END_REF]. The STMAS spectrum was recorded while spinning at 60 kHz MAS and at 11.7 T.

0 Figure 6 :

 06 Figure 5: (a) Sheared z -Filtered TOP-STMAS spectrum showing the CT-CT diagonal peaks of five observed resonances, around 0 kHz in the indirect dimension, and the Satellite Transition (ST)-CT diagonal peak for the sites whose central transition is observed at 309 and 500 ppm, at around -2.6 kHz in the indirect dimension. Sidebands are marked with ( ). Extracted slices along the shift and quadrupolar dimensions together with the best fits are shown in figures (b) and (c), respectively.The spectral lineshapes were all simulated considering Gauss-Lorentz curves whose centers-of-gravity were used to determine the quadrupolar products, P q (3 ± 0.2 MHz for (1) and 3 ± 0.3 MHz for (2)), and isotropic shifts using equations[START_REF] Van Der Klink | NMR in metals, metal particles and 526 metal cluster compounds[END_REF] and[START_REF] Papawassiliou | Resolving Dirac 530 electrons with broadband high-resolution NMR[END_REF]. The STMAS spectrum was recorded while spinning at 60 kHz MAS and at 11.7 T.

440

  els based purely on mixed cell 1 predict higher proportion of 441 α-like environments than stacking-fault like environments, and 442 models based purely on mixed cell 2 would result in more 443 α-like environments. Nevertheless, considering the good the 444 agreement between the NMR parameters of environments in the 445 vicinity of the twin boundary and the Na(1) and Na(2) sites, the 446 stacking sequences should be closer to those in mixed cell 1. 447 In order to verify the consistency of our model, Hahn-Echo 448 spectrum recorded at 14.1 T was fitted using the same model, as 449 shown in figure 7(b). Both lineshapes fit the experimental data 450 considerably well. We also note that the Rietveld refinement 451 of the diffraction pattern, shown in figure 1 of the SI, which 452 indicated a 62 : 18 : 20 ratio between the β, α and distorted 453 P2 phases, is also reasonable agreement with the quantification 454 obtained using NMR.

456Figure 7 :

 7 Figure7: One-dimensional Hahn-echo23 Na experimental spectra and best-fits of NaMnO 2 at 11.7 (a) and 14.1 T (b) both at 60 kHz MAS. The fitting model comprises of 6 distinct sodium sites, taking into account the contribution of both central and satellite transitions. All NMR parameters were fixed in accordance with the fitting models shown in figure6, with corresponding NMR parameters given table1. The total intensity of each site and relative intensity of the satellite transitions (ST) and central transition (CT) was allowed to vary. The relative intensity of the satellite transitions was constrained to never exceed their theoretical limit. The 14.1 T spectrum was fitted with the relative ST-to-CT intensities fixed intensity ratios set to match the 11.7 T data, and only the relative intensity of each site was allowed to vary. Taking into account the relative intensities of the spectrum recorded at 11.7 T, the relative quantification of each sodium environment was computed and is also given in table1. The observed shifts, δ obs = δ iso + δ QIS , were calculated using equation (2) for the two different magnetic fields. The small peak at ∼ 0 ppm is due to a Na + in a residual diamagnetic impurity not predicted by the fitting model. Additional details pertaining to the simulated lineshapes are given in the Experimental and Simulation Details section.

  . Additional details pertaining to the simulated lineshapes are given in the Experimental and Simulation Details section.

	430	Fixing the obtained NMR parameters extracted from the
	431	MAT slices, shown in table 1, the one-dimensional fully relaxed
	432	Hahn-Echo spectrum recorded at 11.7 T, shown in figure 7(a),
	433	was fitted to obtain the relative quantifications of sodium envi-
	434	ronments (see table 1 of the SI for relaxation measurements).
	435	About 61% and 23% of Na nuclei are in β-like and stacking-
	436	fault like environments, respectively, and 8% are α-like and
	437	Na environments. It is worthwhile to note that for this fit the
	438	contributions arising from both the CT and ST were included.
	439	As noted by Clément et al. [65], these results also suggest the
		presence of different stacking sequences, since structural mod-

Table 1 :

 1 (a) Range of DFT predicted NMR parameters for α and β-NaMnO 2 considering both experimental and optimized structures reported in

	parameters:	Site	δ obs	δ iso [ppm]	∆δ [ppm]	η	C q [MHz]	η q
	(a) α/β-NaMnO 2
		β	51 -372	61 -388	509 -585	0.63 -0.78	2.53 -3.04	0.38 -0.86
		α	548 -1099 567 -1109	999 -1139	0.17 -0.19 -3.60 --2.39 0.24 -0.81
	(b) Mixed cell 1
		Na(β)	156 -367	169 -379	563 -585	0.63 -0.67	2.80 -2.95	0.41 -0.56
		Na(1)	392 -692	404 -704	-568 -561	0.96 -0.98	2.70 -2.77	0.64 -0.70
		Na(2)	454 -761	469 -776	991 -1003	0.10 -0.13 -2.83 --2.77 0.99 -1.00
		Na(α)	735 -1165 750 -1179	1077 -1126	0.16 -0.18 -2.89 --2.81 0.83 -0.87
	(c) Mixed cell 2
		pseudo β	184 -426	199 -441	877 -897	0.05 -0.07	2.85 -2.88	0.89 -0.92
		pseudo α	628 -1085 640 -1097	-666 --617 0.60 -0.67	2.60	0.85
	(d) Experimental	Assignment	Obs. Shift	δ iso [ppm]	∆δ [ppm]	η	C q [MHz]	η q	Quantification [%]
		β 1	309 ± 6	319 ± 2	570 ± 60	0.2 ± 0.6	2.4 ± 0.2	0.9 ± 0.4	49 ± 1
		β 2	356 ± 8	378 ± 3	800 ± 100	0.9 ± 0.6	3.5 ± 0.2	0.9 ± 0.2	12 ± 2
		SF 1	500 ± 5	513 ± 3	630 ± 90	0.0 ± 0.5	2.7 ± 0.1	0.9 ± 0.2	19 ± 1
		SF 2	539 ± 8	554 ± 4	800 ± 900	0.0 ± 0.8	2.9 ± 0.1	0.9 ± 0.4	4 ± 1
		α	830 ± 10	843 ± 5	710 ± 90	0.0 ± 0.7	2.6 ± 0.4	0.9 ± 0.4	8 ± 1
		Na	1170 ± 10	1181 ± 7	800 ± 100	0.0 ± 0.7	2.7 ± 0.6	0 ± 1	8 ± 1

Acknowledgements 493

Declaration of Competing Interest

The authors declare that they have no known competing fi- [61] H. Xia, X. Zhu, J. Liu, Q. Liu, S. Lan, Q. Zhang, X. Liu, J. K. Seo, 701 T. Chen, L. Gu, et al., A monoclinic polymorph of sodium birnessite for 702 ultrafast and ultrastable sodium ion storage, Nature communications 9 [START_REF] Spiess | 50th anniversary perspective: The importance of NMR 498 spectroscopy to macromolecular science[END_REF]