François Mentec

Zoltán Miklós

Sébastien Hervieu

Thierry Roger

Conversational recommendations for job recruiters

Keywords: Conversational recommendation, Recruitment, Explainable recommendation

Recruitment is a long, complex, and crucial process for every company. Matching candidates to job offers is time-consuming and requires a broad knowledge of the different domains, in particular the relevant skills and qualifications and their relationships. By comparing the required skills with candidates' profiles, recruiters can identify potential collaborators for a given position. To support recruiters' work, we propose recommendation techniques that help the identification of suitable candidates. While job offers contain required skills for a position, the recruiter's preferences are not explicit: for example, some skills might be more important than others etc. These preferences are very hard to elicit, and they even might depend on the particular job offer. We propose conversational recommendation techniques that can support recruiters' work and recommend candidates to a given job offer, based on relevant skills, that can provide an explanation for the recommendation, so that the recruiter has specific information as to why a candidate is recommended. Interaction with the system that can reveal more details about preferences is possible. In this way, a new set of recommendations can be obtaines or he can reinitialize the recommendation procedure, if preferred. Our system is evaluated using a real Resume/Job Offer dataset from a company database. Performance of generated recommendations is compared to a reference Deep-Learning based matching system trained on the same dataset.

Introduction

Recruitment is a long, complex, and crucial process for every company. Recruiters and human resources experts often need to evaluate a large number of candidates. There are many tools to support the work of recruiters that have been in use for decades [START_REF] Tixier | Employers' recruitment tools across europe[END_REF]. These tools can help with various tasks, including information extraction or matching candidates to job offers.

Our work also focuses on this matching task and we propose a recommender system for recruiters that can support their work through recommendations. We do not aim to replace the human agent in the recruitment process, on the contrary we would like to empower the involved persons. In large companies, the number of potential candidates for a position can be overwhelming. In particular, we focus on reducing the number of candidates a recruiter has to look at using skill-based matching of job offers and candidates. Understanding how various skills listed in job offers or resumes relate to each other is often not self-evident. For example, for a "backend developer" position where the company searches 3rd Edition of Knowledge-aware and Conversational Recommender Systems (KaRS) & 5th Edition of Recommendation in Complex Environments (ComplexRec) Joint Workshop @ RecSys 2021, September 27-1 October 2021, Amsterdam, Netherlands francois.mentec@alten.fr (F. Mentec); zoltan.miklos@irisa.fr (Z. Miklós) http://people.irisa.fr/Zoltan.Miklos/ (Z. Miklós) 0000-0002-3701-6263 (Z. Miklós) for developers experimented with the "express" development framework, one might also consider candidates with similar competencies or experiences. For example, a candidate who knows well the "hapi" framework (that is a different framework for the same task) could be well suited for the job. Identifying such highly competent candidates requires a broad knowledge of the technical terms. Moreover these technologies evolve quickly. This means that it is not easy for the recruiters to understand the relation between these skills. Clearly, other factors than skills are highly relevant for the recruitment (such as geographic proximity or other factors), and our methods can be extended to deal with these aspects as well.

Our recommender system can help recruiters to identify potential candidates and is capable to suggest candidates beyond a simple keyword match, based on the relatedness of the necessary skills and the candidate's competencies. There are a number of challenges involved in designing and realising such a recommender system. A job offer in general should express all the requirements for the position in question, however in reality it contains only partial information. For example, some skills might be more important than others. In other cases, the recruiters can have specific politics: they might prefer someone with a broad range of skills, while in other cases, one specific skill is crucial for the position, so they seek someone who has this skill. These preference structures are not known in general. They might even be different for each position, or each company. It is difficult to elicit these preferences, as they might not even be clear to the recruiter: he might realize it as he consults the candidates resumes. To overcome these challenges, our system follows the conversational recommendation paradigm [START_REF] Jannach | A survey on conversational recommender systems[END_REF]. We have developed techniques that can propose a candidates based on some initial assumptions. The user can later refine the recommendations through interactions with the system or restart the recommendation process if he prefers so.

In our application context, it is particularly important that recommendations be explainable and configurable: a recruiter should be able to understand why a candidate has been recommended, that is, what is the relation between the candidate skills and the job offer.

Our contributions in this work are the following:

• We propose a recommender system for resumes to job offers, based on a domain-specific ontology. The rest of the paper is organised as follows. We formulate the job candidate recommendation problem in Section 2. We present our conversational recommender system for job recruitment in Section 3. We present the experimental evaluation of our approach in Section 4, including a comparison to a deep learning-based matching system. We discuss related works in Section 5. Section 6 concludes the paper.

The job-candidate recommendation problem

Our goal is to recommend candidates for a specific job offer to support recruiters' work. In our recommendation model, each recommendation is accompanied by an explanation and complementary information (see Section 3.2). The user can observe these pieces of information and can decide to change certain parameters of the recommendation process and obtain a new, more refined, set of recommendations. This process can be repeated as many time as necessary, resulting in a conversation between the system and the user that should lead to a few good recommendations.

In the following we describe the data model used to generate job recommendations. Positions are described in "job offers". We recommend job candidates, who are represented by their "resume". In this work we focus on recommendations based on skills only. The model could be extended to take into account other aspects, such as geographic location, education, etc. The Job Offer inform us on the skills required for the position, and the Resume on the skills possessed by the candidate. We assume that Resumes and Job offers are semi-structured, that is we can identify skill labels in these documents. A skill label represent a skill and is composed of a few words. However, different labels can refer to the same skill depending on the vocabulary used by the person which redacted the label, for example, "back-end development" and "serverside development" refer to the same skill, but expressed in a different vocabulary.

A Job Offer in our model is a document containing a set of labels of the necessary skills 𝑜 = {𝑙1, 𝑙2, . . . , 𝑙𝑛}. A Resume is also a document containing a set of labels, but they represent the skills possessed by the candidate 𝑟 = {𝑙1, 𝑙2, . . . , 𝑙𝑛}. Those labels can't be compared directly, because they are redacted by different persons, hence use different vocabulary. A function to translate those labels to the appropriate skill in a unified referential is required 𝑓 (𝑙) → 𝑠, 𝑠 ∈ 𝑆. For this referential, we propose to use an ontology. An Ontology is a hierarchical structure which takes the form of a Directed Acyclic Graph that represent a set of concepts and their relations. In our work we use a skill ontology, in which nodes correspond to skills and edges denote a "is more specific skill than" relation 𝑂 = {𝐼, 𝑟}.

Conversational recommendation of job candidates

Section 3.1 presents an ontology-based recommendation approach, that can produce interpretable job candidate recommendations, which represents the basis of our conversational recommendation approach. This method generate recommendations to identify potentially relevant candidates. For each recommendation explanations are generated that we describe more in detail in Section3.2. Section 3.3 discusses how the user can interact with the system and further refine the recommendations.

Ontology-based recommendation

Our recommendations are based only on skills from the candidate's resume and the job offer. In order to deal with the linguistic differences between the various terms that denote skills we rely on a widely adopted ontology of skills: ESCO (There are a number of alternatives which could also be used, including the American ontology O*NET, or company specific proprietary skill catalogs). Our recommendation technique can identify a set of candidates who are likely to suit for a given job offer. The recommendations are generated if a user -who is the agent in charge of the recruitment-is engaged in searching for a candidate. We obtain recommendations for a given job offer in the following way:

• Skill matching. We first match skill labels of the resume and the offer to nodes of the ontology. This is a preparatory step, that we execute only once, we do not need to repeat this step for each recommendation. • Skill similarity. We estimate the similarity of individual skills in the job offer and resume using the ontology. • Aggregation. We aggregate individual skill similarities (between the skills in the offer and resume) depending on the search politic of the user. • Generating recommendations. We generate candidate recommendations for the job offer, together with an explanation.

In the following, we detail these steps. evaluation (we input this the larger amount of data used for training). We used every label in French, English, Spanish, German, and Italian to do so. Despite using multiple languages, we made sure that every label would only appear once in the dataset for a given skill to prevent the same label to appear in multiple subsets (i.e. train, dev, or test) because it is the same for multiple languages (e.g. SQL would appear in every language, it is never translated).

Skill matching

For each label from the ontology, the model was trained to predict the skill it comes from, as well as each of its ancestors up to the top of the ontology. This ensured strong accuracy for skills placed higher in the hierarchy 1.

This approach enables us to compare individual skills (of the Resume and Job offer): we can compare the corresponding terms in the ontology.

Skill similarity

Skills from the offer are requirements and those from the resume can match/fill those requirements. They can be related to each other using a similarity function based on the ontology. One could use different similarity function. We have chosen a similarity function that works particularly well for skills: we would like that the sim-ilarity function respects the structure of the ontology. We have decided to use the similarity function that was proposed by Panagiotis et al. [START_REF] Mavridis | Using hierarchical skills for optimized task assignment in knowledge-intensive crowdsourcing[END_REF] for comparing skills in a hierarchical structure (Equation 1) :

𝑆𝑖𝑚(𝑎, 𝑏) = 𝑑𝑚𝑎𝑥 -𝑑𝑒𝑝𝑡ℎ(𝑙𝑐𝑎(𝑎, 𝑏)) 𝑑𝑚𝑎𝑥 , (1)
where 𝑎 and 𝑏 are skills from the ontology, 𝑑𝑚𝑎𝑥 is the maximal depth of the ontology, and 𝑙𝑐𝑎(𝑎, 𝑏) their lowest common ancestor.

Aggregating skill similarity scores

We are reducing Resumes and Job Offers to a list of skills which can be compared using their relationships in an ontology. We want a scoring function that measure how much a Resume fits to a Job Offer using only their skills and the ontology, and keep it simple enough that it can be easily explained. The higher the score, the higher the match. Also, the score should be easy to interpret for a human: 1 is a perfect match, and 0 is no match at all. A resume scoring higher than another resume for the same offer is to be interpreted as a better match. Also, 𝑆𝑐𝑜𝑟𝑒(𝑟1, 𝑜1) > 𝑆𝑐𝑜𝑟𝑒(𝑟2, 𝑜2) means the resume 𝑟1 is a better match for job offer 𝑜1 than 𝑟2 is for 𝑜2.

Using this measure we can associate each skill from the offer with its most similar counterpart from the resume. From there we can design multiple possible aggregation politics to match offers and resumes that can correspond to different preferences or recruitment strategies:

1. Average: compute the average of the best association for each skill of the Offer (this is the politic used by default). 2. Min: only consider the association with the lowest similarity. 3. Max: only consider the association with the highest similarity.

Average politic:

𝑆𝑐𝑜𝑟𝑒(𝑜, 𝑟) = ∑ 𝑎∈𝑆𝑜 max 𝑏∈𝑆𝑟 𝑆𝑖𝑚(𝑎, 𝑏) |𝑆𝑜| (2)
The Min politic:

𝑆𝑐𝑜𝑟𝑒(𝑜, 𝑟) = min 𝑎∈𝑆𝑜 max 𝑏∈𝑆𝑟 𝑆𝑖𝑚(𝑎, 𝑏) (3)
The Max politic:

𝑆𝑐𝑜𝑟𝑒(𝑜, 𝑟) = max 𝑎∈𝑆𝑜 max 𝑏∈𝑆𝑟 𝑆𝑖𝑚(𝑎, 𝑏) (4)
𝑜 denotes the job offer 𝑜, 𝑟 the resume, 𝑆𝑥 the skills set of 𝑥, and 𝑆𝑖𝑚 the similarity between two skills (equation 1).

Generating recommendations

Usually a recommendation consists in presenting a user with an item he could be interested in. In the case of recruitment the item isn't for the user (i.e. the recruiter), but for a job from a customer. So given an offer, we would present the user with a list of candidates that could match the offer. Candidates are recommended based on their score.

The most straightforward way to make recommendations given an offer and a set of resumes, is to rank the resumes based on their matching score with the offer according to our model, and recommend the top-k to the recruiter. On our 6181 offers and resumes, with 𝑘 = 10, this would lead to an average score for the top-k of 0.98 which ensure high precision, but only 2204 resume would ever be recommended meaning that almost two third of our consultants would never be attributed a job.

An other approach would be to probabilistically recommend a resume based on its score. The probability to recommend a resume 𝑖 is its score divided by the sum of every score: 𝑃 (𝑖) = 𝑆 𝑖 ∑ 𝑗∈𝑆 𝑆 𝑗 . This method reduce the average score of the recommendation to 0.74 but increase the catalog coverage to almost 100% (6124 resumes are now recommended). We could also use the exponential of the score instead of the score itself; this leads to an average score of 0.71 and 6179 resumes being recommended.

Explanation

By using a manually designed scoring function and a human-understandable representation of skills (skill ontology), we can generate an explanation for each recommendation. An example of such explanation can be seen in Figure 1. The resume match the job offer at 69% because its skills are close to those contained in the job offer: SQL is close to Mongo, Python to Javascript, Flask to Node, and Flask is also not too far away from Angular. If the user wants to know why a skill is matched to another one with a certain score, he can click on the link between them to see where are the corresponding nodes located in the ontology and how they are linked.

An explanation can have different forms, graphical or textual, and pursue different aims [START_REF] Tintarev | Explanations of recommendations[END_REF]. Law et al. [START_REF] Law | A comparison of graphical and textual presentations of time series data to support medical decision making in the neonatal intensive care unit[END_REF] compared a graphical explanation to a textual one, and if the first was preferred by users, the last one yielded the best accuracy in terms of decision making. In our case and given the use of an ontology, we can generate an explanation by making sentences of the form "𝑠1 is 𝑎𝑑𝑗 to 𝑠2 because both are 𝑙𝑐𝑎(𝑠1, 𝑠2)". If skills 𝑠1 and 𝑠2 would be matched together, 𝑎𝑑𝑗 would be an adjective selected based on the similarity between the skills, and 𝑙𝑐𝑎(𝑠1, 𝑠2) their lowest common ancestor. For example, the link between Mongo and SQL from Figure 1 give: SQL is close to Mongo because both are database management systems. 1

Conversational recommendation

The explanation enables also to refine the search and guide the user to identify her (or her company's) preferences. In this way, the user can fine-tune the query and obtain a new set of recommendations. To allow this fine-tuning, we propose a slight variation from our initial scoring function where a weight is associated to each skill from the Offer. 𝑊 is a weighting function that associates to each skills of the job offer a weight between 0 and 1. Those weights can be seen in the Figure 1.

𝑆𝑐𝑜𝑟𝑒(𝑜, 𝑟, 𝑊 ) =

∑

𝑎∈𝑆𝑜 𝑚𝑎𝑥 𝑏∈𝑆𝑟 𝑆𝑖𝑚(𝑎, 𝑏) × 𝑊 (𝑎) ∑ 𝑎∈𝑆𝑜 𝑊 (𝑎) (5) If the recruiter notice a lot of resumes are recommended because they contain a skill he doesn't find that important, he can lower the weight attributed to the skill, or even remove it. On the opposite, if he notice a very important skill is always missing from recommended resumes, he can increase its weight.

For example, if a recruiter is looking for an "Angular" developer and gets a lot of recommendations that do not contain the "Angular" skill, but javascript and other web frameworks (e.g. Vue) he can increase the weight of this "Angular" skill to get more recommendations containing it.

Experimental evaluation

Dataset

To evaluate our model, we have access to a database of 343.802 resumes from the ALTEN company. It uses a specific format called "Technical Files", that is a structured resume which contains a list of professional experiences that include a job title, a description and a set of skills. We have a total of 249,721 experiences, less than the number of resumes. This means that some resumes are incomplete and do not contain any experiences. After preprocessing we keep only resumes that contain at least 2 experiences, so we're left with 30,907 resumes and 154,033 experiences. Most of these resumes are in French, but we also have some in English. We generated a resume/job matching dataset by creating pairs 1 Our example is hypothetical, as in the ESCO ontology, that we use, there is currently not any mention of Mongo, Angular, Flask or Node. Though we can find SQL, JavaScript and Python along other IT technologies like CMS (e.g. Wordpress). ESCO is being extended, and also one can use a company specific enriched version that would contain all relevant skills and competences.

(𝑅𝑒𝑠𝑢𝑚𝑒, 𝐽𝑜𝑏𝑂𝑓 𝑓 𝑒𝑟), and we considered the last experience of a resume as a job offer.

Evaluation methodology

We evaluate our system as a Job Recommender System and as a Conversational Recommender System through the following aspects:

• Raw accuracy compared to Deep Learning on a binary classification task. • Weighting techniques, to understand the impact the user can have. • Utility/Efficiency of its conversational components.

Evaluation as binary classification

We evaluate the performance of our techniques on the following task: given a resume and a job, the system must predict if they constitute a match or not. For this evaluation we can rely on a variety of classification metrics: accuracy, precision, recall, and F1-Score. A high precision would greatly improve the efficiency of the recruiters (less irrelevant resumes to look at), and a high recall would reduce the risk of missing a good resume. Also too low a recall would raise ethical concerns, some resume might never be recommended, hence preventing their owners from getting a job.

We're going to compare our ontology-based recommender system to a system entirely based on Deep Learning.

Dataset for binary classification

We constructed a new evaluation dataset from our dataset introduced in section 4.1. The original includes a number of resumes matched with an appropriate job. For this evaluation we also need pairs of resumes with jobs that do not match. We duplicated every pairs and replaced the job with an experience randomly selected from another resume. In this way, we obtained an equal amount of good and bad pairs of resume and job. This procedure is depicted in Figure 2.

This methodology has a few shortcomings:

• If an Experience is part of a Resume, this does not mean the person was a good fit to the job (staffing errors can occur). • Taking an Experience at random for bad pair may sometimes land a good match, especially since all jobs are from the same company, and as such in in similar fields. However, the fact that ALTEN employ a wide variety of profiles can mitigate this effect.

We split our dataset into 3 subsets:

Deep Learning Recommender System

We use as a baseline a full deep learning recommender system that we trained using BERT [START_REF] Devlin | Bert: Pre-training of deep bidirectional transformers for language understanding[END_REF]. We use the Transfomers library from Hugging Face [START_REF] Wolf | Transformers: State-of-the-art natural language processing[END_REF] for implementation. The pairs were fed to the model using the following structure : <cls>Resume<sep>job Offer<sep>. <cls> is the classification token, it indicates the position at which the model makes its prediction (i.e. does the resume and the job offer match). The resume and job offer in the input are the list of skills they contain separated by a comma followed by a space (", "). <sep> is the separator token, it indicates the end of a document (resume/job offer). We used the BertForSequenceClassification model from the Transformers library which use a cross entropy loss when the number of labels is 1. It was trained with a batch size of 16 until the accuracy on the dev set stopped showing any improvement for 3 consecutive epochs. The best model (3 epochs prior) was kept. We used the optimization function AdamW [START_REF] Loshchilov | Decoupled weight decay regularization[END_REF] with an initial learning rate of 5e-5.

Metric

Full

Results for binary classification

We now have 2 Job Recommender Systems which can be compared on the same dataset. The results in table 2 are in favor of Deep Learning with a strong accuracy of 83.03% higher than the Ontology-based one, which is only 62.76%. This result is not surprising as the ontology based similarity distances cannot compete with deep learning based ones. However, as we show below, one can obtain much better figures through conversational interactions.

Weighting evaluation

We test the impact of the weighting paradigm introduced in section 3.3 on the accuracy by randomly generating a thousand weighting for each pair, and measuring the portion of those weightings that led to a good prediction.

In the case in which the expert always finds the perfect configuration regarding the importance of each skills in the job offer, the accuracy may rise up to 87%. Obviously it is unlikely even an expert would always find the one in a thousand best weighting, but we could easily expect

Figure 3:

The influence of weighting on the accuracy of the ontology-based RS. We can see that 63% of pairs have about 50% of their weighting that led to a correct prediction. And 87% of the pairs have at least one weighting that led to the right prediction, which is better than the Accuracy of the DL RS.

him to do better than average. Empirical testing would be required to evaluate how and with which accuracy a recruiter would find a good weighting.

Evaluation of conversational interactions

We take a subset of 100 pairs of offers with the right resume from the test set, and for each offer we recommend 𝑛 resumes, the set of recommended resumes is denoted by 𝑅. If the correct resume is recommended it's a success, otherwise we take a step to fine-tune the recommendation until it is recommended or we reached the maximum number of steps (100).

In the absence of real users, We adopted heuristic techniques to try to mimic human reasoning. The actions that can be taken are the following:

• Add a skill: we consider the recruiter has an idea of the kind of profile he wants, and that profile is the right resume for the offer. So if a skill from the correct resume is infrequent among recommended resume, it can be added to the offer. • Increase the weight of a skill: if a skill from the offer is in the correct resume but is infrequent among recommended resumes, its weight can be increased. • Decrease the weight of a skill: if a skill from the offer is not in the correct resume but is frequent among recommended resumes, its weight can be decreased. If its weight reaches 0, this action is equivalent to removing the skill from the offer.

Actions are determined and weighted in the following way:

• Add skill: for each skill in the correct resume but not in the offer, the probability of adding it to the offer is the inverse of its frequency among recommended resumes (equation 6). • Increase the weight of a skill: for each skill in the correct resume and in the offer, the probability to increase its weight, is also the inverse of its frequency among recommended resumes (equation 6). • Decrease the weight of a skill: for each skill in the offer but not in the correct resume, the probability to decrease its weight is its frequency among recommended resumes (equation 7).

𝑃 𝑎𝑑𝑑/𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 (𝑠) = |𝑅| |𝑟 ∈ 𝑅 ∧ 𝑠 ∈ 𝑟| + 1 (6) 𝑃 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 (𝑠) = |𝑟 ∈ 𝑅 ∧ 𝑠 ∈ 𝑟| |𝑅| (7)
At each step/turn, we only apply the action with the highest probability.

We also evaluated our conversational recommendation w.r.t. the following metrics: success rate, low rank rate, average number of turns, see Sun et al. [START_REF] Sun | Conversational recommender system[END_REF]. For a list of 100 offers and 100 resumes, and 𝑛 = 5 recommendations per step/turn, we achieve a 74% success rate, 8.69 average turns/steps, and 26% low rank rate.

Related work

Recommender systems for recruitment

There are a number of systems that try to support the recruitment process through recommendations. Surveys of these methods include [START_REF] Al-Otaibi | A survey of job recommender systems[END_REF], [START_REF] Siting | Job recommender systems: A survey[END_REF]. A commonly used approach is to try to match job candidates to job offers, based on different available sources of information. For example, Lin et al. [START_REF] Lin | Machine learned resume-job matching solution[END_REF] propose a machine learned resume-job matching method. Their method is composed of three phases: First, they use unsupervised feature extraction methods to identify relevant features from job offers and resumes. Then they train different classifiers to match these features. Finally they rely on ensemble learning techniques to combine these classifiers. Another technique based on machine learning methods was proposed by Malinowski et al. [START_REF] Malinowski | Matching people and jobs: A bilateral recommendation approach[END_REF]. Papparizos et al. [START_REF] Paparrizos | Machine learned job recommendation[END_REF] proposes a job recommendation technique that is based on the job transition graphs, which is constructed using the candidates resumes. A conceptually similar approach was proposed by Heap et al. [START_REF] Heap | Combining career progression and profile matching in a job recommender system[END_REF] and [START_REF] Heap | Combining career progression and profile matching in a job recommender system[END_REF] who exploit the job history of the candidates to offer better recommendations. Other methods of job candidate matching include [START_REF] Paparrizos | Machine learned job recommendation[END_REF]. Yang et al. [START_REF] Yang | Combining content-based and collaborative filtering for job recommendation system: A cost-sensitive statistical relational learning approach[END_REF] developed a job recommendation technique that combines content-based filtering techniques with collaborative filtering.

More recent proposals rely on bilateral preference matching methods [START_REF] Malinowski | Matching people and jobs: A bilateral recommendation approach[END_REF], [START_REF] Hong | Ihr: An online recruiting system for xiamen talent service center[END_REF] or on deep learning [START_REF] Luo | Resumegan: An optimized deep representation learning framework for talent-job fit via adversarial learning[END_REF], [START_REF] Qin | Enhancing person-job fit for talent recruitment: An ability-aware neural network approach[END_REF], [START_REF] Zhu | Person-job fit: Adapting the right talent for the right job with joint representation learning[END_REF]. A major shortcoming of machine learning and deep learning based techniques in this context is the lack of interpretability. This poses even an ethical problem in this context. Even if recruitment decisions are finally made by humans, recommendations that influence the process are not interpretable and they are not transparent. The usage of ontologies inside Recommender Systems isn't new, they can be used to overcome the cold-start problem and improve accuracy, by displaying the profile of a user in a human-readable format he can easily edit to fine-tune his recommendations [START_REF] Middleton | Ontology-based recommender systems[END_REF].

The article [START_REF] Zhang | Explainable recommendation: A survey and new perspectives[END_REF] surveys explainable recommendation techniques [START_REF] Zhang | Explainable recommendation: A survey and new perspectives[END_REF]. One can distinguish model-intrinsic methods and model-agnostic methods. For model-intrinsic techniques the decision mechanism is transparent, one can derive explanations directly for the model decisions, while for model-agnostic (or post-hoc) explanations the recommendation decision is black box, and explanations try to give some insights event if they are not directly derived from the model. Our method is model-intrinsic, we obtain explanations directly from our recommendation model. This choice has a price: one could potentially obtain more accurate recommendations with the help of deep learning based methods, but then we could not have transparent model-intrinsic explanations. An interpretable job-person recommendation, with post-hoc explanations was presented in [START_REF] Le | Towards effective and interpretable person-job fitting[END_REF].

Recommender systems (for movies, products, services, etc.) try to exploit and reconstruct the user's preferences, based on some signals or patterns in the data. Yan et al. [START_REF] Yan | Interview choice reveals your preference on the market: To improve job-resume matching through profiling memories[END_REF] try to reconstruct the preference structures for person-job recommendation from the interview history of candidates. Such information is rarely available and in general, the preferences of the recruiter are not present in the data. For example, the required skills in job descriptions correspond to some ideal candidate, but finally the companies hire candidates, who do not have all of the required skills in the offer. The preference structure is not present in the data. For example, for some jobs the recruiter might prefer someone who has a specific skill that is of high importance for the position, while in other cases, some closely relevant skills could be enough and a candidate with a diverse set of skills is better. Moreover, these preferences might be tacit to the recruiter, he might not be aware his own preferences prior to the selection process or the preference might depend on some other factors, such as situations where the company needs someone urgently for a project, in which case, they might opt for a less qualified candidate. To the best of our knowledge there is no job recommender system that could deal with this problem of tacit preference structures. As preference structures are not available to the recommendation process we argue that a conversa-tional recommendation technique is a suitable approach.

Conversational recommendation

Conversational recommender systems (CRS) [START_REF] Jannach | A survey on conversational recommender systems[END_REF] rely on interactions with the users to compute recommendations. This exchange with the user can take the form of a conversation in natural language, but isn't limited to this modality. For example, Yo et al. [START_REF] Yu | A visual dialog augmented interactive recommender system[END_REF] use visual dialogues in the conversation. CRSs often realize the following the following phases: Request, Recommend, Explain, and Respond. In our work we adopt the conversational recommendation process. In our context, the Request corresponds to the situation where the recruiter starts the search for candidates and asks for potential resumes. He can obtain recommendations, together with complementary information that serves as explanation as to why a given candidate was recommended. Based on these pieces of information the user can respond, refine or restart the search for candidates. The excellent survey paper [START_REF] Jannach | A survey on conversational recommender systems[END_REF] highlights a number of application areas of CRS, but to the best of our knowledge they have not yet been applied to the recruitment domain.

Discussion and Conclusion

We have proposed a job candidate recommendation technique based on conversational recommendation principles. Our system helps identifying suitable candidates, based on the skills in the resumes and their relation to the required skills in the job offer. Our recommendation is completely transparent and for each recommendation, it is clear, why a given candidate is recommended (or not recommended). The explanations serve also as a basis of a conversation with the user, who can then refine the recommendation process. We evaluated our recommendation technique through extensive experimentation.

Currently the deep-learning baseline showcase much stronger performances. There are 3 ways our system could catch up: improve the mapping between skill labels from documents and skills from the ontology, refine the ontology by adding new skills and relationships, use more complex similarities metrics.

Figure 1 :

 1 Figure1: Our model can show why a recommendation was made and how the score was computed. We can see how important each skill from the job offer is (this value can be adjusted by the recruiter), we can see with which skill from the Resume it has been matched, how similar both skills are, and how this similarity has been estimated based on the ontology.

Figure 2 :

 2 Figure 2: From pairs (𝑅𝑒𝑠𝑢𝑚𝑒, 𝐽𝑜𝑏𝑂𝑓 𝑓 𝑒𝑟) to a Matching Dataset. Every pair is duplicated and the Job Offer is replaced by another Job Offer randomly picked from another pair, thus generating bad pairs.

Table 1 ESCO

 1 Job Offers and Resumes are usually written by different people, hence use different vocabularies. To deal with this problem we use an ontology and map each skill in the Resume and in the Job offer to the corresponding skill in the ontology. To realize this task, we use deep learning-based matching techniques.We trained a classifier on top of a multilingual version of BERT because we can find documents in French and English in our dataset, and the multilingual model showcased stronger performances during experimental

	Level	0	1	2	3	4
	Accuracy	99% 96% 94% 93% 91%

Skill Classifier performances by level of the ontology.

Table 2

 2 Recommender Systems performances. This table show the accuracy, precision, recall and F1-Score on our binary classification dataset for a full Deep Learning model based on BERT and our ontology-based recommender system.

		Deep Learning Ontology-based
	Accuracy	83.03%	62.76%
	Precision	86.96%	61.29%
	Recall	77.92%	70.32%
	F1-Score	82.20%	65.50%

We plan to introduce more sophisticated conversational techniques to better guide the user, by exploiting the different statistics of skill distributions in the data. Also we would like to investigate more realistic preference structures also including multi-objective variants. We also plan to evaluate our system in use, w.r.t. perception of the recommendation process and interpretability of recommendations and the guiding suggestions with real users.


Yang Song

Isabel Gómez-Recio

Ram Kumar

Cristina Coelho Diogo

Sandra Casale

Isabelle Génois

David Portehault
email: david.portehault@sorbonne-universite.fr

4

 Hence, a synthesis procedure for high purity Na 4 Si 4 (ca. 90 mol%) is yet to be developed.

 Overall, the resulting material encompasses Na 4 Si 4 and excess elemental silicon and/or sodium. For instance, a stoichiometric mixture A straightforward approach to high purity sodium silicide Na 4 Si

Silicon-based materials are involved in many domains from electronic devices, to catalysts, to biomedical technology. [1][START_REF] Canham | [END_REF][3][4][5] Research efforts towards novel forms of silicon and siliconbased materials have yieldedamong otherssilicon clathrates, 6,7 a variety of new silicon allotropes, [8][9][10] and transition metal silicides. 5,11,12 Silicon-based nanomaterials also provide an additional dimension to the phase space, in order to adjust properties with e.g. silicon nanoparticles, 13,14 nanoporous and mesostructured frameworks, 15 as well as metal silicide nanocrystals. 5,11 These materials can be produced by planar deposition methods that use gas-phase silicon-containing molecules, 13,16,17 or by solid-state reactions employing elemental silicon or alkali silicides. 7,8 These reactions can also be mediated in liquid phase. 6,11,14,18 Herein we focus on a specific silicon source: sodium silicide Na 4 Si 4 . [19][20][21] Na 4 Si 4 synthesis from Si nanoparticles: 470 mg of NaH (20 mmol) and 500 mg of Si nanoparticles (20 mmol) were firstly ball-milled for 2 minutes at 20 Hz (Retsch MM400 ball mill airtight stainless-steel vial of 50 mL, one steel ball of 62.3 g with a diameter of 23 mm). Then, the fine powder was loaded in a pyrolytic h-BN crucible (cylinder ∅ 25 × H60 mm) covered with a cap of pyrolytic h-BN, then placed in a bottom closed quartz tube. The tube was heated in a vertical furnace at 395 °C with different reaction times from 2 to 24 hours, under argon flow. The as-synthesized sample was made of a dark pellet with another white pellet on the top. The latter corresponds to Na 2 O and NaOH coming from the reaction between NaH and the native silicon oxide layer on the surface of Si nanoparticles (Fig. S2). The upper white pellet was scratched away. The synthesis of Na 4 Si 4 under the optimal conditions described in the Results and discussion section was repeated 20 times to ensure reproducibility.

Na 4 Si 4 synthesis from bulk Si powder was prepared following the same procedure and reagents proportion described above, but bulk Si powder was used instead of Si nanoparticles. The thermal treatment was performed at 395 °C for 10 hours.

Si clathrates synthesis: The Na 4 Si 4 powder (4 mmol) synthesized as described above was loaded in a pyrolytic h-BN crucible (∅ 25 × H60 mm) previously dried at 400 °C under vacuum (10 -3 mbar) for 10 hours to remove adsorbed moisture. The crucible was placed in a bottom-closed quartz tube. The tube was heated in a vertical furnace. Na 8 Si 46 (type I) and Na x Si 136 (type II) were obtained by heat treatment at 470 °C and 440 °C, respectively, under dynamic vacuum (10 -3 mbar) for 90 min. These temperatures were chosen according to the literature. 7 For Na 8 Si 46 (type I), the h-BN crucible was covered with an h-BN cap prior heating, to maintain a higher Na vapor pressure. For Na x Si 136 (type II), the crucible was maintained opened. During the reaction, a thin deposit of Na appeared on the upside cold part of the quartz tube. After dwelling and cooling down, the quartz tube with the h-BN crucible and its containment was transferred into an argon-filled glovebox without exposure to air.

Powder X-ray diffraction (XRD) was performed on a Bruker D8 Advance diffractometer equipped with an X-ray source working with Cu Kα radiation. Due to the air-sensitivity of Na 4 Si 4 , the powder was loaded in an airtight sample holder into an argon-filled glovebox and capped with a protective plastic dome. Beam scattering by the dome gives rise to a broad bump between 15-25° (2θ Cu Kα) (Fig. S3). Powder XRD patterns used for Le Bail analysis were acquired with a step size of 0.029° and an acquisition time of 10 s per step, which correspond to 13 h of measurement. Over this long dur-ation, the sample holder shows evidences of air leaks (see Results and discussion). Otherwise, 5 min fast acquisitions with a step size of 0.050° and an acquisition time of 0.19 s per step were performed as standard program to avoid sample degradation during XRD measurement. Na 4 Si 4 , Na, Si (diamond structure, d-Si) and NaOH were identified according to the ICDD database and the reference cards 04-015-9208, 00-022-0948, 00-027-1402 and 00-035-1009, respectively. of silicon and sodium yields a mixture of Si and Na 4 Si 4 with a purity of ca. 44 mol% (Table S1). 6 Another approach involves the reaction of sodium with silica gel to yield ca. 15 mol% Na 4 Si 4 mixed with Na 2 SiO 3 (Table S1). 28,29 A third method was first reported by Ma et al. 24 and enabled a decrease by few hundreds of degrees of the synthesis temperature, by triggering the reaction between previously ball-milled sodium hydride and silicon powders at 420 °C under argon flow over several days. The procedure did not require any specific container nor sealing and then appeared simple, but a long ballmilling pretreatment of 0.5-1 h was required. 19,30 More importantly, the outcome strongly depended on experimental parameters, including the preliminary ball-milling time and especially the argon flow rate, since reaction intermediates (sodium) and by-products (dihydrogen) are volatile or gaseous at the reaction temperature. Therefore, despite the attractiveness of this procedure, reaching high purity (ca. 90 mol%) sodium silicide remains an arduous task: a large excess of sodium hydride is required, while elemental silicon and sodium are commonly encountered as impurities.

Herein we report a procedure to enhance the reactivity of silicon with sodium hydride by using silicon nanoparticles as reagents and by carefully controlling experimental parameters (Fig. 1). Thanks to this approach, we demonstrate the ability with regular lab equipment to reproducibly produce sodium silicide with a purity of ca. 98 mol% and at the scale of several hundreds of milligrams, both features strongly exceeding those previously reported. 24 We then deliver a simple scalable protocol that will enable wide-spread use of this material.

Experimental methods

Commercial NaH (95%, Sigma-Aldrich) and bulk Si powder (99%, Sigma-Aldrich) were used as received. Commercially available silicon nanoparticles (99%) were obtained from Nanomakers© (Fig. S1 andS2), France. All the reagents and products were stored and manipulated in an argon-filled glovebox free of H 2 O (<0.5 ppm) and O 2 (<0.5 ppm) and with standard Schlenk procedures. Caution: the Na 4 Si 4 powders produced by the procedure described herein are air sensitive and burn spontaneously when exposed to water. All manipulations described were performed by handling these powders under inert atmosphere, except when stated otherwise.

4NaH ðsÞ þ 4Si ðsÞ À! Δ Na 4 Si 4ðsÞ þ 2H 2ðgÞ ð1Þ
A slight excess of NaH was used in order to account for reaction (2) below, which accounts for the reactivity between sodium hydride and the native oxide layer of silicon particles (simplified as SiO 2 ):

10NaH ðsÞ þ 4SiO 2ðsÞ À! Δ Na 4 Si 4ðsÞ þ 3Na 2 O ðsÞ þ 5H 2 O ðgÞ ð2Þ
Besides, neither broad signal of amorphous SiO 2 and Si centered at ca. -110 and -40 ppm 32,33 nor any contri-bution of d-Si expected at ca. -80 ppm 34 were observed. It thus confirms the high purity of Na 4 Si 4 . The 23 Na spectrum (Fig. 3b) shows two quadrupolar resonance patterns at 56.3 ppm (C Q = 1.32 MHz, η Q = 0.47) and 49.8 ppm (C Q = 2.34 MHz, η Q = 0.27) corresponding to two Na crystallographic sites in Na 4 Si 4 . In addition, no peak at ca. 50 ppm corres-ponding to Na 2 O could be detected, 35 suggesting no contami-nation from the upper white pellet made mainly of Na 2 O and of a minor portion of NaOH (Fig. S4). The thin peak at 18.5 ppm is assigned to crystalline NaOH accounting for less than 5% of the total amount of sodium. 36 As mentioned above, crystalline NaOH could not be detected by XRD in fast acquisition mode (Fig. S3). Its observation by NMR is then ascribed to the degradation of Na 4 Si 4 during preparation of NMR analyses.

Overall, EDS, XRD and NMR support the formation of crystalline Na 4 Si 4 . EDS yields a purity of ca. 98 mol%, and amorphous Si is the main impurity. The synthesis yield is about 80%, which corresponds to ca. 700 mg of powders, i.e. a10 fold increase compared to previous approaches using the reaction between sodium hydride and silicon (Table S1. This result is achieved with only a slight excess of sodium hydride reagent (10 mol%) compared to previous reports (60-90 mol% excess) (Table S1), 19,30 which enables bypassing purification steps (Table S1). The preliminary ball-milling time is also shortened from over 30 min to only 2 min and the reaction time is further reduced to 24 h. A comparison with the most commonly used reaction between elemental sodium and silicon occurring above 650 °C (Table S1) shows that the reaction time and the temperature are strongly reduced with the approach we describe herein, while purification steps and complex set-ups encompassing metal containers are avoided. 29 Si and 23 Na magic angle spinning solid-state nuclear magnetic resonance (MAS solid-state NMR) spectra were acquired on a 700 MHz AVANCE III Bruker spectrometer operating at 139.05 MHz and at 185.20 MHz respectively and using a 3.2 mm Bruker triple resonance probe. Samples were transferred to ZrO 2 rotors spun at a MAS rate of 10 kHz for 29 Si and 20 kHz for 23 Na. A single-pulse excitation was used with a recycle delay of 500s and 400 scans for 29 Si and 1 s and 1960 scans for 23 Na. 29 Si and 23 Na chemical shifts were referenced to TMS and 0.1 M NaCl (aq) respectively. The spectra were treated with the DMFIT program. 31 Energy-dispersive X-ray spectroscopy (EDS) (Oxford Instruments -X-max) on the scanning electron microscope (SEM) was performed on a SEM HITACHI S3400N at 20 kV to determine the composition of the Na 4 Si 4 sample. Carbon deposition was required to enable the EDS analysis on insulating sample. In order to avoid equipment damage and for safety concern, air-sensitive Na 4 Si 4 samples were pre-neutralized by exposure to air during 4 days.

Transmission electron microscope (TEM) and high resolution TEM (HRTEM) was performed with JEOL JEM 2100 FEG microscope operating at 200 kV. For sample preparation, the powders were dispersed in ethanol. The suspensions were drop casted onto carbon coated copper grids.

Results and discussion

Optimal synthesis of Na 4 Si 4 Reaction (1) described below between NaH and Si nanoparticles (1.1 : 1 mol ratio) was performed for 24 hours at 395 °C with an argon flow of 55 mL min -1 : Under these optimal conditions, Na 4 Si 4 with optimized purity was obtained. The atomic ratio between Na and Si was evaluated to Na : Si = 1 : 1.02 by EDS analysis. The formation of Na 4 Si 4 (S.G. C2/c) was supported by Le Bail analysis of the powder XRD pattern (Fig. 2 and Table S2). NaOH was also detected (Fig. 2) and ascribed to leakage of air into the XRD sample holder during the long acquisition of the XRD diagram. This is confirmed by the fact that no crystalline NaOH was observed in a prior fast acquisition on a fresh sample (Fig. S3).

The 29 Si MAS solid-state NMR spectrum of Na 4 Si 4 (Fig. 3a) shows two resonances centered at -362 and -366 ppm corresponding respectively to the two crystallographic non-equivalent Si sites in the crystal structure. 23 This upfield shift compared to silicon is due to electron transfer from Na to Si. 25 the reaction was performed over 10 to 24 h compared to more than two days as reported for bulk silicon. 24 Impact of the reaction time By using Si nanoparticles, we varied the reaction time from 2 to 24 hours to investigate the course of the reaction. XRD (Fig. 5) shows that a 2 h reaction produces crystalline Na 4 Si 4 together with Na and Si, as minor phases. The absence of peaks assigned to Na 2 O confirmed the thorough separation of Na 4 Si 4 from oxidic side-products. NaOH observed is again attributed to air leaks of the XRD sample holder over XRD pattern acquisition. Increasing the reaction time to 10 h decreases the relative intensity of Na and Si peaks. Further decrease of these peaks occurs from 10 to 24 h. It confirms that Si nanoparticles allow shortening the reaction time to 24 h. Note that the XRD pattern obtained at 10 hours is similar to the one previously reported for Na 4 Si 4 produced from bulk silicon over 2 days. 24 Comparison of the results from bulk Si and Si nanoparticles shows a dramatic reduction of reaction time that we ascribe to the reactivity of Si nanoparticles, in relation to their larger interface between NaH and Si, and shorter atomic diffusion paths.

Impact of the Si source

To assess the role of the silicon source in the synthesis, we have followed the same protocol as above but by using bulk Si powder as precursor. The reaction was performed over 10 h under a 15 mL min -1 Ar flow rate. The initial NaH : Si ratio was kept at 1.1 : 1 mol. The resulting product was pale grey aggregates. According to XRD (Fig. 4), the main crystalline phases are unreacted Na and Si. Therefore, silicon nanoparticles play a primary role in the completion of the reaction at low temperature and short time. Their higher reactivity ensures a reaction in close-to-stoichiometry reagents ratio compared to bulk Si that required a large excess of NaH (NaH : Si = 1.9 : 1 mol.) to yield Na 4 Si 4 as major product. 24,37 Note also that while bulk Si required ball-milling over 1 hour, 19,24 using Si nanoparticles enables shortening the milling step down to 2 min. Likewise, range of elemental substitutions to tune thermal, electrical and thermoelectric properties among others. [START_REF] Beekman | [END_REF]40 To assess the usefulness of the as-synthesized sodium silicide as precursor for inorganic synthesis, we have studied its thermal decomposition as a well-known pathway to type I Na 8 Si 46 and type II Na x Si 136 (0 ≤ x ≤ 24) silicon clathrates. Type I and type II silicon clathrates are generally obtained by thermal decomposition 7,19 or oxidation 6 of Na 4 Si 4 . Thermal decomposition of Na 4 Si 4 under vacuum at 400-500 °C yields type I and type II clathrates, 7,19 with phase selectivity depending on various factors that are related to the vapor pressure of sodium. The impurities were the other type I/type II clathrate and d-Si. By using a setup to control the Na relative pressure, Krishna et al. reported a phase selective approach to type II clathrates. 19 By aiming for a simple and straightforward procedure, we have thermally decomposed the as-synthesized Na 4 Si 4 in a very simple setup. It consists of an h-BN crucible introduced in a bottom-closed quartz tube heated in a vertical oven under dynamic vacuum (10 -3 mbar).

Le Bail analysis of powder XRD patterns (Fig. 7 and Table S3) shows that the samples obtained by decomposition of Na 4 Si 4 at 470 °C with a closed crucible and 440 °C with an open crucible containing Na 8 Si 46 and Na x Si 136 as major phases, respectively. HRTEM images of the corresponding powders are also indexed against the Na 8 Si 46 (Fig. 7c) and Na x Si 136 (Fig. 7d) structures, respectively, thus confirming the identity of the phases. In Fig. 7c, the amorphous oxide layer on the surface is ascribed to SiO x or sodium silicate generated during sample manipulation.

Dalton Transactions Paper

Impact of the argon flow rate Ma et al. described that a large argon flow rate (50 mL min -1 ) resulted in excess Si, while residual Na was observed when using moderate argon flow rate (10 mL min -1 ). 24 This sensitivity of the reaction to the gas-flow rate comes from vaporization of two products.Firstly,H 2 gas forms during the reaction (1). Secondly, reaction (1) proceeds by decomposition of NaH at ca. 317 °C38 into Na, which then reacts with silicon. Nonetheless, Na is also volatile at the temperature of synthesis and can leave the reaction medium depending on the argon flow rate. Herein, the reaction was performed at 395 °C in 10 hours under different Ar flow rates (NaH : Si = 1.1 : 1) to study the impact of Ar flow on the completion of the reaction. XRD (Fig. 6) shows that the relative peak intensities for the Na impurity barely changed with the Ar flow rates and that the product Na 4 Si 4 is always the major crystalline product. Therefore, the influence of Ar flow on the reaction appears negligible in the range 15-100 mL min -1 when using silicon nanoparticles, contrary to the bulk silicon source. 24 Hence, the higher reactivity of Si nanoparticles ensures reaction of sodium and silicon before sodium leaves the reaction medium by evaporation. The ability to perform the reaction with low dependency versus the Ar flow rate improves strongly the repeatability of the synthesis.

Simple approach to silicon clathrates

Silicon clathrates hold cage structures based on 4-coordinated silicon atoms. These tetrahedral frameworks can adopt a wide

The electronic and thermal properties of Na x Si 136 (0 ≤ x ≤

Conclusion

Herein we have shown that using silicon nanoparticles as chemical reagents provides a convenient way to solve the usual limitations of the synthesis of silicon compounds with poor thermal stability and from poorly reactive elemental silicon: the high reactivity of silicon nanoparticles enables synthesis at high yield, close to the theoretical reagent stoichiometry, and at lowered temperature below the decomposition threshold of the product, thus significantly enhancing its purity. It also enhances the robustness of the synthesis versus experimental conditions, especially by eliminating the dependence of the reaction versus gas flow. We demonstrated that the as-obtained Na 4 Si 4 powder is a convenient precursor towards the selective synthesis of type I and type II silicon clathrates, thus supporting the relevance of the material for further use towards silicon-based materials. 24) type II clathrates depend strongly on the occupancy of structural cages by Na. 40 Therefore, we have estimated the x value according to the dependency of the a cell parameter as a function of x (Fig. 8). We retrieve an overall composition of Na 11.86 (2) Si 136 corresponding to a partial occupancy of Na sites. 7,41 French Region Ile de France SESAME program and the ERC Consolidator Grant GENESIS (D. P. and I. G. R.) with Agreement Number 864850. The silicon nanoparticles were kindly provided by Nanomakers© and by ICMCB in the frame of the LabEx AMADEus (ANR-10-LABX-42) and of IdEx Bordeaux (ANR-10-IDEX-03-02).

Fig. 1

 1 Fig. 1 Scheme of the synthesis route towards high purity Na 4 Si 4 .

Fig. 2

 2 Fig. 2 Le Bail analysis of the XRD pattern of the powder obtained after 24 h at 395 °C under 55 mL min -1 Ar flow. The observed pattern, calculated pattern and difference curve are shown in red dots, black curve and blue curve, respectively. Upper blue and lower red tick marks correspond to Na 4 Si 4 and NaOH, respectively.

Fig. 4

 4 Fig. 4 Powder XRD patterns of the Na 4 Si 4 samples synthesized respectively with Si nanoparticles (black bottom curve) and bulk Si powder (blue top curve) at 395 °C for 10 hours with an Ar flow rate 15 mL min -1 . Red lines indicate Na 4 Si 4 reference. Si, Na, and NaOH impurities are marked on the most informative peaks.

Fig. 3

 3 Fig.3(a)29 Si and (b)23 Na solid-state NMR spectra of the Na 4 Si 4 powder obtained after 24 h at 395 °C under 55 mL min -1 Ar flow. Asterisks indicate spinning sidebands. The measured spectra are shown by the blue curves, and the fitting curve is shown in red.

Fig. 5

 5 Fig. 5 (a) Powder XRD patterns of Na 4 Si 4 samples synthesized during various reaction times at 395 °C with a 15 mL min -1 Ar flow. Red lines account for Na 4 Si 4 reference. Si, Na, and NaOH impurities are marked on the most informative peaks. An enlarged view of the XRD pattern in the range of 26-32°is shown in (b).

Fig. 6

 6 Fig. 6 (a) Powder XRD patterns of Na 4 Si 4 samples synthesized with different Ar flow rates at 395 °C with a reaction time of 10 hours. Red lines account for Na 4 Si 4 reference. Si, Na, and NaOH impurities are marked on the most informative peaks, where NaOH is ascribed to incidental oxidation of sample. (b) An enlarged view of the XRD pattern in the range of 26-32°.

Fig. 7

 7 Fig. 7 (a and b) Le Bail analysis of the powder XRD patterns of products obtained by Na 4 Si 4 thermal decomposition at (a) 470 and (b) 440 °C. The observed pattern, calculated pattern and difference curve are shown in red, black line and blue, respectively. Blue, green and red tick marks correspond to Na 8 Si 46 (type I), Na x Si 136 (type II) and Si, respectively. HRTEM images and corresponding Fast Fourier Transforms (FFTs) of powders obtained at (c) 470 °C and (d) 440 °C. FFTs are indexed along the (c) type I and (d) type II silicon clathrate structures.

Fig. 8 a

 8 Fig.8a lattice parameter evolution with the Na content of Na x Si 136 (0 ≤ x ≤ 24) clathrate. Solid red square, blue circle, yellow and green triangles represent data reported by Beekman et al.,42 Stefanoski et al.,43 Beekman et al.,44 and Reny et al.,40 respectively, while the empty red square corresponds to this work. The broken line corresponds to data linear fit.

Acknowledgements

This work was financially supported by the China Scholarship Council, the French state funds within the framework of the Cluster of Excellence MATISSE led by Sorbonne Université, the

Conflicts of interest

There are no conflicts to declare.