Federico Rollo

Andrea Zunino

Nikolaos Tsagarakis

Arash Enrico Mingo Hoffman
email: enrico.mingo-hoffman@inria.fr

Enrico Mingo

Arash Ajoudani

CARPE-ID: Continuously Adaptable Re-identification for Personalized Robot Assistance

come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

To accomplish Human-Robot Interaction (HRI) tasks in human-populated environments, robots need to recognize their human counterparts and tailor their actions accordingly. Such a personalization step is generally overlooked in traditional HRI settings, which assume that the robot collaborates with the nearest person and that there won't be other human interventions/distractions during the task execution. This assumption is not always realistic, especially when a task involves mobility and a larger workspace. For this reason, future collaborative robots must have the capacity to identify and recognise their human counterparts to deliver personalisable assistance.

Earlier works to address this focused on an offline human identification step followed by online tracking, e.g., for an omnidirectional mobile robot to follow a person [START_REF] Rollo | Followme: a robust person following framework based on visual re-identification and gestures[END_REF]. In another work [START_REF] Ye | Robot person following under partial occlusion[END_REF], the authors introduced a re-identification application in the presence of partial occlusions. Despite the progress made, these frameworks lack real-time adap-tation to target appearance changes and cannot recover reidentification after total occlusions. In fact, they are relatively robust in tracking a target in the camera field of view (FOV), but when the target is lost for a moment, they often need a reinitialization of the tracking through human actions [START_REF] Javed | Visual object tracking with discriminative filters and siamese networks: a survey and outlook[END_REF] [START_REF] Luo | Multiple object tracking: A literature review[END_REF].

Given these limitations, our objective is to minimize human intervention in robot recognition and (re)identification for the human counterparts. Our first attempt to achieve this was presented in [START_REF] Rollo | Followme: a robust person following framework based on visual re-identification and gestures[END_REF]. The limitation of this approach was that, if a person changed his/her appearance after the calibration step (e.g., by changing the outfit), the reidentification module was not able to track the target person. To tackle this challenge, in this work, we provide a novel reidentification module which uses a deep learning approach based on feature extraction and a continual adaptation to be compliant with the target appearance changes. The robot constantly acquires images during the tracking and uses the new person's learned appearance to continuously update an ideal target representation which is used to re-identify the target when the tracking fails.

We present an adaptive person re-identification layer that takes advantage of a Multi-Object Tracking (MOT) algorithm 1 based on the well-known YOLO framework [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF] and the StrongSORT tracker [START_REF] Du | Strongsort: Make deepsort great again[END_REF], to supply a Re-identification system capable to handle the IDs' jumps that often occur in MOT 2 .

The contributions of this work can be summarized in:

• proposing a Continual Adaptation Personalized Reidentification framework 3 (CARPE-ID) to accomplish HRI tasks with a specific target; • testing the tracking algorithm with a real Human-Robot collaborative scenario; • evaluating limitations and possible solutions. Videos of experiments can be found in the playlist at this link.

The rest of the paper is structured as follows. In Sect II the state-of-the-art in Single and Multi-Object Tracking and HRI re-identification works and surveys are reviewed. Our approach is presented in Sect III. Experiments and results are reported in Sect IV with a discussion on achievements, performances, and limitations. Finally, in Sect V the whole work is summarized and conclusive statements are presented.

II. RELATED WORKS

Many systems were proposed in the literature to cope with the object-tracking objectives. Multi-object tracking (MOT) and Single-object Tracking (SOT) are commonly used methods to track all objects or a single selected object in the image, respectively. MOTs algorithms generally perform both detection and tracking of multiple classes, while SOTs require only the initial guess (i.e., the object bounding box) to track the object of interest in that specific area, no matter which is its class type.

Based on a recent survey [START_REF] Soleimanitaleb | Single object tracking: A survey of methods, datasets, and evaluation metrics[END_REF], the SOT techniques can be divided into four categories: (i) feature-based, (ii) segmentation-based, (iii) estimation-based and (iv) learningbased. They focused on learning-based approaches and then presented an overview of the datasets and the metrics used to evaluate the SOT algorithms. Similarly, the authors in [START_REF] Zhang | Recent advances of single-object tracking methods: A brief survey[END_REF] analyzed the recent advancements in SOT focusing on correlation-based and deep learning-based algorithms while a broader analysis of Discriminative Correlation Filters and Siamese Network for Visual Object Tracking is presented in [START_REF] Javed | Visual object tracking with discriminative filters and siamese networks: a survey and outlook[END_REF]. Instead, in the review presented in [START_REF] Luo | Multiple object tracking: A literature review[END_REF], the recent evolution of MOT systems and their applications are presented.

Considering the objectives of SOT and MOT algorithms, it is clear that they do not fulfil the requirements of personalisable HRI since they often lack robustness in the target re-identification after partial or total occlusions. For this reason, other approaches for person re-identification are proposed in the literature, especially for personalized robotics applications.

The most common approach for personalized reidentification for robotic assistance uses skeleton or face cues to track the target. For example, the authors in [START_REF] Patruno | People re-identification using skeleton standard posture and color descriptors from rgb-d data[END_REF] proposed the use of soft biometric features extracted from depth and colour to build an informative descriptor of the target. They use 3D skeleton points extracted with AlphaPose [START_REF] Hao-Shu Fang | Alphapose: Whole-body regional multi-person pose estimation and tracking in real-time[END_REF] to create a skeleton standard posture which is used to partition the target with a grid. For each grid cell, the mean colour is used for the re-identification, but it is limiting because, when people wear similar clothes, it could be prone to error. The authors in [START_REF] Ye | Robot person following under partial occlusion[END_REF] developed a robot person-following robotic system which is robust to the partial occlusion often caused by the limited camera FOV. They used the target person's skeleton and a prior model to identify and localize it. The tracking and the identification are based on skeleton heuristics information such as joints, height, and bounding box position to identify the person. Even if this work is promising for a person-following scenario, a big assumption they make is that the person remains always inside the camera FOV.

Regarding face recognition for person re-identification and tracking, the authors in [START_REF] Liu | Online rgb-d person reidentification based on metric model update[END_REF] train a metric model offline using labelled data, then use online face information to match the target and update the metric model. They propose the feature funnel model (FFM) to merge appearance information to the skeleton one. Also, in the work presented in [START_REF] Wang | A realtime and unsupervised face re-identification system for human-robot interaction[END_REF], the authors use a face Re-id approach to enhance human-robot interaction. They pre-trained a feature extractor CNN that is used to re-identify target faces in an unsupervised manner. Both these works assume that the human collaborator always faces the robot though this is not always the case as we have seen in our experiments.

The authors in [START_REF] Koide | Monocular person tracking and identification with on-line deep feature selection for person following robots[END_REF] use an RGB monocular approach. They first use OpenPose [START_REF] Cao | Realtime multi-person 2d pose estimation using part affinity fields[END_REF] for the skeleton extraction and then track the target using an unscented Kalman filter due to the information of the ground plane prior and the person height estimation. They combine convolutional channel features and online boosting to identify the person through deep features. The proposed method at the start needs a calibration process to learn the deep feature appearance that will be used to re-identify the target. A distinct approach is proposed in [START_REF] Cos | Human re-identification with a robot thermal camera using entropy-based sampling[END_REF], where the authors use a thermal camera to track and re-identify the target. They acquire a small dataset of thermal images to train a neural network and then use an entropy-based sampling to obtain a thermal dictionary for each person. A Support Vector Machine (SVM) classifier is trained using some geometric distribution obtained by the thermal dictionaries and then used to classify the people. The integration of a thermal camera is intriguing for solving standard camera problems. However, the need for extensive training and its inability to adapt to target changes restrict its applicability to our intentions.

As reported in the literature review, it becomes evident that all these works have certain limitations, which could hinder the development of a robust and personalized persontracking system. Our approach solves online the problem of re-identification after partial and total occlusion and target appearance changes which, to the best of the authors' knowledge, is still an open problem for tracking systems in HRI applications.

III. METHODOLOGY

Our person-tracking method is represented in the pipeline in Fig. 1 and a pseudocode implementation is proposed in Algorithm 1. The tracking starts when an ID is selected by the user, meaning that before the ID selection, we run the MOT inference and store detected person appearances into a database to let the user choose the person to track. After the ID selection, the initial tracking step is to acquire an RGB image and pass it into the MOT algorithm which provides an instance segmentation and a first object tracking, assigning different IDs to each detection. For each detection, the features representing their appearances are extracted with a deep neural network trained for person recognition (see details in Sect. IV) and then used to track or re-identify the target. These steps are repeated during the application which is conceptually divided into two steps that run sequentially for each frame: (i) target re-identification and (ii) target ideal representation update.

A. Target re-identification

The features x extracted from the people detections are used to compute the statistical distance: Fig. 1: The figure shows the framework pipeline starting from the image input to the target re-identification output. The first module is MOT, where a neural network gives the first coarse tracking of objects in the image. From the MOT module, we obtain the detections that are passed into a feature extractor outputting the output feature vectors x i where i goes from zero to the number of the input detections. The feature vectors x i permits to compute the statistical distance d µ,σ (x) (see Eq. 1) that will be used by the re-identification module. If the MOT can correctly track the target, we proceed directly to use its output, otherwise, if no target is found by the MOT, our re-identification module searches for a correspondence between the ideal target and the ones in the image. If the target keeps the same ID or if it is re-identified, the target statistical distance d µ,σ (x) and the target features x i are used to update respectively the re-identifier threshold λ d and the ideal target representation µ and σ (dashed lines). Otherwise, if no target is re-identified, the framework does not give any output and skips to the next RGB frame.

d µ,σ (x * ) = 1 D D i=1 x * i -µ i σ i 2 , (1)
where the subscript i represents the i-th index of the corresponding vector and µ and σ correspond to the distribution representing the ideal target we want to track. In the following step, we check if there exists a feature vector with an associated ID equal to the user-picked one; if this is the case then we directly output the detection paired with its ID. Otherwise, the re-identification module finds the feature with the smallest distance from the target ideal representation and checks if this distance is less than the adaptive threshold λ d .

If no person is re-identified among the detected ones then the framework continues to analyze the next RGB frame.

B. Target ideal representation update

Once the target is re-identified, we use its feature vector and corresponding statistical distance to continuously adapt the ideal target representation µ and σ and the threshold λ d , used in the re-identification step, which is computed as:

λ d = µ d + 2 σ d , (2)
where µ d and σ d are the mean and the variance of the statistical distances of the target. To update online the variables µ, σ, µ d and σ d we used a Damped version of the Exponential Moving Average χ dema that we will call DEMA now on. The DEMA formula is expressed in the following equation:

χ dema [k] = α damp ψ + (1 -α damp ) χ dema [k -1], ( 3
)
where ψ is the new value, [k] represents the discrete-time instant of the DEMA and α damp is an adaptive weight which encodes the importance of the new values ψ with respect to the previous DEMA value χ dema [k -1] and is computed as:

α damp = 2 N damp + 1 , (4)
with end if 30: end while N = 0 to speed up the initial convergence and to set a fixed upper-bound N M AX otherwise as time passes the DEMA won't be affected by new values because as N increases, α damp tends to 0.

N damp = N • ∆,
There are two different damping factors ∆ for the DEMA, one for the ideal target features represented by µ and σ called ∆ f , see [START_REF] Ge | Mutual mean-teaching: Pseudo label refinery for unsupervised domain adaptation on person re-identification[END_REF], and one for the threshold λ d computed with µ d and σ d that is called ∆ λ d , see [START_REF] Han | Mmptrack: Largescale densely annotated multi-camera multiple people tracking benchmark[END_REF]. In Fig. 2, the EMA with and without the damping factors are compared. This image shows how the damping factor ∆ λ d removes high-frequency noise from the threshold λ d (in red) and smooths its behaviour mitigating the EMA peaks that could lead to wrong re-identifications when the threshold becomes too high.

∆ f = min(1, d µ,σ 2 ), (5)
∆ λ d = max(1, 2 d µ,σ λ d ). (6)
Substituting the damping factor ∆ f in (5) in DEMA (3) and N damp , we are disfavouring that situations in which the distance in (1) from the current feature is small because in that case, the current feature is similar to the ideal one and this will overfit the ideal representation, especially in a situation in which the target is stationary in the same pose. Instead, the damping factor ∆ λ d in [START_REF] Han | Mmptrack: Largescale densely annotated multi-camera multiple people tracking benchmark[END_REF], is used to avoid the excessive growth of the threshold when the ratio between the distance d µ,σ and the threshold λ d is too large, leading to wrong re-identification.

To improve the robustness of the algorithm we added a blacklist manager that evaluates which IDs provided by the MOT are associated with distractors, to be able to discard in advance them during the re-identification step. When the target ID provided by the MOT does not change during the tracking, the manager adds the IDs associated with the other people present in the image (the distractors) to the blacklist. In this way, we nullified the few re-identification errors we could have in challenging situations.

IV. EXPERIMENTS

To validate our framework we performed two different experiments. We validate the framework per se using a fixed camera that acquires videos in a laboratory setup from different view perspectives (see sect. IV-A) and, to further validate the proposed method, we consider a second experiment that shows the use of the framework in a humanrobot interaction application, i.e. a robot person-following scenario (see sect. IV-B). Finally, in sect. IV-C, we discuss the results obtained in the experiments.

The framework runs on a notebook with an Intel® Core™ i9-11950H processor and an NVIDIA Geforce RTX 3080 Laptop GPU. We used an Intel Realsense D455 camera for image acquisition and a Robotnik RB-Kairos+ 5e as the assistant robot. For the feature extraction network, we pretrained an IBN-ResNet-50 [START_REF] Pan | Two at once: Enhancing learning and generalization capacities via ibn-net[END_REF] on the popular MSMT17 [START_REF] Wei | Person transfer gan to bridge domain gap for person re-identification[END_REF] dataset using [START_REF] Ge | Mutual mean-teaching: Pseudo label refinery for unsupervised domain adaptation on person re-identification[END_REF] and set the output feature dimension to 256.

A. Individual framework validation

We tried to use a person-tracking dataset, i.e., Person-Path22 [START_REF] Shuai | Large scale real-world multi person tracking[END_REF], to analyze the individual framework, however, we realized that this dataset (which has the same format as other visual person-tracking datasets [START_REF] Han | Mmptrack: Largescale densely annotated multi-camera multiple people tracking benchmark[END_REF]) is not suitable for the evaluation of our framework for the following reasons:

• The videos do not represent a human-robot collaboration scenario but are mainly composed of security cameras or person-view videos in crowded environments where people are far from the camera and appear in the image only for small instants of time. • The videos are too short to correctly validate the reidentification module.

• In almost all the cases, the MOT algorithm we used in our framework already performed the right tracking because, when people disappear from the camera fieldof-view (FOV), they do not enter it anymore, making unnecessary our re-identification module. Due to such limitations, we decided to acquire a custom dataset for the validation. This dataset comprises 18 videos for a total of 53 minutes. Moreover, in the videos in which more actors are present, the framework is evaluated one time for each person, which brings the total minutes analyzed to 113. The videos capture different working scenarios in two laboratory setups where a single person or group is present in the image. People in the videos are asked to exit and re-enter in camera FOV and to change their appearance (e.g., by wearing a sweatshirt) to test both the capabilities to re-identify when partial or total occlusions occur and adapt to new target appearances. The analysis of these videos provided the following performances (more details are reported in Fig. 3):

• The min, mean, and max tracking lengths for the stateof-the-art MOT were 3.02, 21.2, and 52.2 seconds (with some outliers which extended the max to 97.17 seconds). • The min, mean, and max Re-ID delay, i.e. the time the framework takes to re-identify the target, was 0.06, 1.1, and 2.6 seconds. There have been two cases in which the tracker took 6.5 and 12.1 seconds for the re-identification even if the target was in the scene. • The MOT algorithm had min and max failure rates of 2 and 7 times with a mean failure rate of 4 times for each video. Instead, our framework failed only 2 times for all the videos which demonstrate high robustness to partial and total occlusions. • The min, mean, and max number of re-identification by our framework were 1, 4, and 7.

B. Application validation

To validate the framework on a real application we set up a robot person-following scenario in the same way as in [START_REF] Rollo | Followme: a robust person following framework based on visual re-identification and gestures[END_REF]. The target person is asked to move around and the robot has to follow him/her avoiding obstacles. However, in our case, the targets change their appearances during the following (condition not satisfied in [START_REF] Rollo | Followme: a robust person following framework based on visual re-identification and gestures[END_REF]) and pass among obstacles to test robustness to partial or total occlusions. We stated that in all the experiments the robot was able to correctly track, re-identify and follow the target person which moved the robot around in a laboratory setup where other people were working. In Fig. 4, an experiment sample is plotted to give an idea of the experimentation setup. The target has to roughly follow the red dashed line, while the robot (blue line) has to follow him/her from start to finish. We performed the experiment 10 times with 5 different people as targets for a Fig. 4: A FollowMe experiment sample: the target person has to roughly follow an ideal path (red dashed line) while the robot (blue line) has to follow him/her. The target positions computed using the CARPE-ID framework tracking are represented with green plus signs. The robot is initially placed in the green start position and has to follow the target until the red finish position is reached. total of 837 meters of following. A video example can be found here.

C. Results discussion

In this section, we analyze the results obtained from the considered evaluation tests to demonstrate the contributions presented in our work. The individual results obtained in Sect. IV-A, clarify that human-robot interaction tasks require a personalized approach for re-identifying the target person. These application scenarios often require more specific recognition capabilities, e.g., when the person exits and reenters in the camera FOV. For this reason, common SOT and MOT algorithms, are not enough for such scenarios and a more robust framework is necessary. This statement can be supported by the results presented in Fig. 3a where we can see that the MOT algorithm has a mean tracking time of 21.2 seconds while the mean video time is 176 seconds and the minimum video time is 94 seconds. In Fig. 3b, we presented the delay between the target person's appearance in the camera FOV and the time in which the target is re-identified. The mean delay is 1.1 seconds which is acceptable for an HRI application scenario. There have been 2 cases in which the re-identifier was not able to re-identify the target in less than 6 seconds. These cases happened due to a limitation of this framework: the target person should not change his/her appearance outside of the camera's field of view. In these cases, the targets re-entered into the camera's field of view with a different appearance e.g., they opened their sweatshirt, and the framework was not able to re-identify them with a non-negligible delay, therefore, they were considered as errors. Instead, in Fig. 3c and Fig. 3d, the times of the MOT algorithm losing track of the target are compared with the number of times the Re-ID framework was able to reidentify the target. The fact that both the plots have a mean of 4 indicates that most of the MOT errors are recovered by our framework. Anyway, from the figure is clear that there are more MOT errors than Re-identifications. This is caused by the quick ID switching of the MOT algorithm and the re-identification delay; e.g., in a dataset video, the MOT changed the three target IDs in 1.4 seconds and the re-identifier was able to re-identify only the last one in realtime.

The application scenario considers an example of a possible application for our framework. The video linked above and Fig. 4 show example experiments where the robot constantly follows the target in a laboratory environment where other people are working. Except for some small delays in the re-identification, the robot was always able to accomplish the following task for all the experiments without human intervention.

V. CONCLUSION AND FUTURE WORKS

In this work, we presented a continuously adaptable person re-identification framework that can be used along with other human-robot interaction applications to enhance personrobot co-existence. We presented our pipeline composed of a MOT algorithm for detection and preliminary person tracking, a feature extraction network for appearance representation of the detected people and a re-identification structure based on a statistical distance, an adaptable ideal target representation and threshold computation with a custom version of the exponential moving average where we added a damping factor (DEMA -damped exponential moving average). Using this setup we can perform person tracking when partial or total occlusions occur as well as when the target person changes his/her appearance during the tracking (e.g., by wearing a sweatshirt) which are challenging situations to be handed by MOT algorithms, as the experiments revealed.

A limitation of this work is that it suffers from catastrophic forgetting, i.e., the algorithm forgets the appearance of the target as time passes because it adapts to the new information it gathers. To overcome this problem a Continual Learning approach can be implemented where the feature extractor network can be trained online using a batch of target and nontarget people images acquired during the re-identification. Such a solution could enhance the ability of the feature extractor to personalize the output features on the target's common appearance. Another limitation is the difficulty of recognizing people at really high distances. This situation does not occur often in human-robot collaboration scenarios because the human is generally near to the robot and the camera but it is reasonable to highlight this point.

Future improvements will consider the enhancement of the re-identification capabilities when the target changes appearance outside the camera FOV. These cases could be recovered using a specialized network which can recognize the target through face identification. Another improvement is to implement the continuous learning approach cited above to make the algorithm more robust. This technique can specialize the feature extraction network on the target appearance with online self-supervised training using the images of the target and of other people (the distractors).

  where N is the number of the DEMA updates made till now and ∆ is the damping factor that, as we will explain later, depends on what kind of information we are trying to update. It is a good practice to initialize Algorithm 1 CARPE-ID framework Input: tracked id 1: µ, σ, µ d , σ d , λ d ← initialize DEM A variables() 2: while True do 3: I rgb ← camera.get rgb image() 4: detections ← mot network.inf erence(I rgb ) 5: f eatures ← reid network.inf erence(detections) 6: min dist ← M AX F LOAT N U M BER 7: tracked f eat ← N ull ▷ Target Re-identification 8: for f eat ∈ f eatures do 9: if tracked id = f eat.id then 10: σ ← get distance(f eat, µ, σ), 14: if d µ,σ < min dist & d µ,σ < λ d then 15: min dist ← d µ,σ 16: tracked f eat ← f eat 17: tracked id ← f eat.id 18: if target f eat ̸ = N ull then 22: var ← compute variance(µ, tracked f eat) 23: µ ← DEM A(µ, tracked f eat, ∆ f ) 24: σ ← DEM A(σ, var, ∆ f ) 25: var d ← compute variance(µ d , min dist) 26: µ d ← DEM A(µ d , min dist, ∆ λ d ) 27: σ d ← DEM A(σ d , var d , ∆ λ d ) 28: λ d ← µ d + 2σ d 29:

  (a) Representation of the effects of the EMA function. (b) Representation of the effects of the DEMA function.

Fig. 2 :

 2 Fig. 2: Comparison between DEMA and EMA effects on threshold filtering and ideal target representation. In subfigure (a) the distances mean, variance, and threshold (in dark blue, green, and red) closely follow the behaviour of the distances plot (light blue line) with a small delay. In subfigure (b) the damping factor ensures that the mean, variance, and threshold do not follow the behaviour of the distance during big peaks and wait for the ideal representation to adapt to the new appearances of the target.

  (a) MOT tracking time (in seconds) w.r.t. mean video time. (b) CARPE-ID delay (in seconds) before target re-identification. (c) MOT number of errors for each video experiment. (d) CARPE-ID number of re-identification for each video experiment.

Fig. 3 :

 3 Fig. 3: Statistical evaluation of the obtained results.

yolo tracking (MOT): link

A detected object could switch the identification number (ID) due to partial and total occlusion or quick appearance changes.

The authors will grant access to the source code based on the GPL 3.0 license, upon paper acceptance.


Khelifa Berriah
email: khelifaberiah@gmail.com

Bendouma Doumi
email: bdoummi@yahoo.fr

Allel Mokaddem
email: mokaddem.allel@gmail.com

Mohammed Elkeurti

Adlane Sayede

Abdelkader Tadjer

João Pedro Araújo

B Khelifa Berriah

• João

Pedro Araújo

Theoretical investigation of electronic performance, half-metallicity, and magnetic properties of Cr-substituted BaTe

Keywords: Cr-substituted BaTe, TB-mBJ approach, Half-metallic ferromagnetism, Electronic properties

come

Introduction

In recent years, a new field of electronics called spintronics has been developing rapidly [START_REF] Matsukura | Control of magnetism by electric fields[END_REF][START_REF] Nie | Quest for high-Curie temperature Mn x Ge 1-x diluted magnetic semiconductors for roomtemperature spintronics applications[END_REF][START_REF] Tang | Spin transport in Ge nanowires for diluted magnetic semiconductor-based nonvolatile transpinor[END_REF]. In this approach, the electron spin is used as another degree of freedom for information processing, offering a promising method to meet new challenges [START_REF] Nie | Quest for high-Curie temperature Mn x Ge 1-x diluted magnetic semiconductors for roomtemperature spintronics applications[END_REF][START_REF] Wang | Spintronics for nanoelectronics and nanosystems[END_REF]. Spintronics devices offer several advantages compared with conventional electronics, including higher speed and lower power, because they are based on spin direction and spin coupling [START_REF] Yu | Spintronic Materials and Technology[END_REF]. In particular, transitionmetal-doped III-V and II-VI semiconductors have emerged as a new type of compounds called dilute magnetic semiconductors (DMSs). These materials are main candidates for progress of spintronics applications, because they are ferromagnetically stable at higher temperatures than room temperature [START_REF] Sato | Material design of GaN-based ferromagnetic diluted magnetic semiconductors[END_REF][START_REF] Wu | Synthesis, characterization, and modeling of high quality ferromagnetic Crdoped AlN thin films[END_REF] and exhibit half-metallic ferromagnetic behavior [START_REF] Doumi | Investigations of structural, electronic, and half-metallic ferromagnetic properties in (Al,Ga,In) 1-x M x N (M = Fe, Mn) diluted magnetic semiconductors[END_REF][START_REF] Doumi | First-principle investigation of half-metallic ferromagnetism in octahedrally bonded Cr-doped rock-salt SrS, SrSe, and SrTe[END_REF][START_REF] Berber | Investigation of electronic structure and half-metallic ferromagnetic behavior with large half-metallic gap in Sr 1-x V x O[END_REF].

The BaX (X = S, Se, Te) barium chalcogenides belong to the group of alkaline-earth chalcogenides, which are widegap insulators with closed-shell ionic systems [START_REF] Bhardwaj | Pressure induced structural phase transitions-A review[END_REF]. BaX compounds have attracted increasing attention because of their potential applications in light-emitting and laser diodes [START_REF] Heng | Prediction of semiconductor material properties by the properties of their constituent chemical elements[END_REF][START_REF] Tuncel | A firstprinciples study on the structural, elastic, vibrational, and thermodynamical properties of BaX (X = S, Se, and Te)[END_REF][START_REF] Feng | First-principles study of electronic and optical properties of BaS, BaSe and BaTe[END_REF] as well as luminescent and magnetooptical devices [START_REF] Partin | Lead strontium telluride and lead barium telluride grown by molecular-beam epitaxy[END_REF][START_REF] Weir | Pressure-induced metallization of BaSe[END_REF][START_REF] Pandey | Spectroscopic properties of defects in alkaline-earth sulfides[END_REF][START_REF] Lin | Electronic properties of barium chalcogenides from first-principles calculations: Tailoring wide-band-gap II-VI semiconductors[END_REF]. BaTe forms closed-shell ionic coordination and crystallizes as an NaCl-type (B1) phase at ambient conditions [START_REF] Feng | First-principles study of electronic and optical properties of BaS, BaSe and BaTe[END_REF][START_REF] Kholiya | Pressure-induced phase transition and elastic properties of barium chalcogenides[END_REF]; it has been widely researched owing to its interesting structural and electronic properties [START_REF] Feng | First-principles study of electronic and optical properties of BaS, BaSe and BaTe[END_REF]. Syassen et al. [START_REF] Syassen | Optical response and band-structure calculations of alkaline-earth tellurides under pressure[END_REF] found that optical and absorption spectra of BaTe appear in the pressure range of 0-400 kPa at temperature of 300 K. Besides, Feng et al. [START_REF] Feng | First-principles study of electronic and optical properties of BaS, BaSe and BaTe[END_REF] investigated the effect of spin-orbit coupling on the optical properties of BaTe, including the reflectivity and the real and imaginary parts of the dielectric function. BaTe has an indirect gap located between the and X high-symmetry points, exhibiting a reduction of about 0.27 eV in its bandgap on application of spin-orbit coupling [START_REF] Pourghazi | Electronic and optical properties of BaTe, BaSe and BaS from first principles[END_REF].

Recently, several experimental and theoretical works have been carried out on the half-metallic and magnetic properties of DMSs based on II-VI semiconductors, e.g., on the room-temperature ferromagnetism of half-metallic Ni-doped ZnS [START_REF] Akhtar | Room temperature ferromagnetism and half metallicity in nickel doped ZnS: experimental and DFT studies[END_REF], half-metallic ferromagnetism of Fe-doped ZnS thin films formed by chemical bath deposition [START_REF] Akhtar | Chemical bath deposition of Fe-doped ZnS thin films: investigations of their ferromagnetic and half-metallic properties[END_REF], halfmetallic ferromagnetism of Co-and Fe-doped CdSe [START_REF] Tian | First-principles study on the half-metallic ferromagnetism and optical properties of Fe-doped CdSe and Co-doped CdSe[END_REF], half-metallic ferromagnetism in V-doped ZnS [START_REF] Rabbani | An ab-initio calculation of halfmetallic ferromagnetism in vanadium doped ZnS[END_REF], and halfmetallic ferromagnetic properties of V-doped BaS [START_REF] Addadi | Electronic and ferromagnetic properties of 3d(V)-doped (BaS) barium sulfide[END_REF] and V-doped SrO [START_REF] Berber | First-principle predictions of electronic properties and half-metallic ferromagnetism in vanadium-doped rock-salt SrO[END_REF].

extended up to G max = 14 (a.u.) -1 , where G max is the largest vector of the Fourier expansion. We extended the basis functions and potential in combination with spherical harmonics around atomic sites with cutoff of l max = 10. In the interstitial region, the Fourier series were extended in plane waves with cutoff of R MT K max = 9 (where R MT is the mean radius of the muffin-tin spheres). For Brillouin zone sampling, we utilized a Monkhorst-Pack mesh [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF][START_REF] Pack | Special points for Brillouin-zone integrations"-a reply[END_REF] of (4 × 4 × 4) for BaTe, Ba 0.75 Cr 0.25 Te, and Ba 0.25 Cr 0.75 Te, and (4 × 4 × 3) for Ba 0.5 Cr 0.5 Te, with self-consistent convergence of the total energy of 0.1 mRy. Note that the number of k-points was reduced in the tetragonal structure of Ba 0.5 Cr 0.5 Te in space group P4/mmm (no. 123) due to its lower number of symmetry operations compared with the cubic structure of Ba 0.75 Cr 0.25 Te and Ba 0.25 Cr 0.75 Te in space group Pm 3m (no. 221).

Results and discussion

Structural parameters

Barium telluride (BaTe) crystallizes in a rocksalt NaCl (B1) phase; its conventional structure has two types of atoms, viz. Ba and Te, located at (0, 0, 0) and (0.5, 0.5, 0.5) positions, respectively, with space group Fm 3m (no. 225). In the Ba 4 Te 4 structure with eight atoms, we substituted one, two, or three atoms of chromium (Cr) at Ba sites to create supercells of Ba 0.75 Cr 0.25 Te, Ba 0.5 Cr 0.5 Te, and Ba 0.25 Cr 0.75 Te with concentration x = 0.25, 0.5, and 0.75, respectively. The Ba 0.75 Cr 0.25 Te and Ba 0.25 Cr 0.75 Te supercells have cubic structure in space group Pm 3m (no. 221), while Ba 0.5 Cr 0.5 Te has tetragonal structure in space group P4/mmm (no. 123). Note that the description of the Ba 0.75 Cr 0.25 Te, Ba 0.5 Cr 0.5 Te, and Ba 0.25 Cr 0.75 Te alloys using smaller supercells would necessarily introduce side effects on their ordered structure. Therefore, our calculations are valid only for ordered structures close to the stoichiometries of the ordered Ba 0.75 Cr 0.25 Te, Ba 0.5 Cr 0.5 Te, and Ba 0.25 Cr 0.75 Te compounds.

Structural parameters of BaTe and Ba 1-x Cr x Te at various concentrations were determined by fitting the variation of the total energy as a function of volume using the Murnaghan equation [START_REF] Muranghan | The compressibility of media under extreme pressures[END_REF]. The structural parameters such as the lattice constant (a), bulk modulus (B), and its pressure derivative (B ) calculated for BaTe and Ba 1-x Cr x Te at different concentrations using the GGA-WC approximation, together with other theoretical [START_REF] Bhattacharjee | Effects of barium (Ba) doping on structural, electronic and optical properties of binary strontium chalcogenide semiconductor compounds -A theoretical investigation using DFT based FP-LAPW approach[END_REF][START_REF] Chattopadhyaya | Theoretical study of structural, electronic and optical properties of Ba x Pb 1-x S, Ba x Pb 1-x Se and Ba x Pb 1-x Te ternary alloys using FP-LAPW approach[END_REF][START_REF] Drablia | Ab initio calculations of the structural, electronic, thermodynamic and thermal properties of BaSe_1 -xTe_x alloys[END_REF][START_REF] Bahloul | Ab initio calculations of structural, electronic, optical and thermodynamic properties of alkaline earth tellurides BaxSr 1-x Te[END_REF] and experimental data [START_REF] Grzybowski | Band-overlap metallization of BaTe[END_REF], are summarized in Table 1. The a and B parameters obtained for BaTe are in good agreement with experimental [START_REF] Grzybowski | Band-overlap metallization of BaTe[END_REF] and recent theoretical calculations [START_REF] Bhattacharjee | Effects of barium (Ba) doping on structural, electronic and optical properties of binary strontium chalcogenide semiconductor compounds -A theoretical investigation using DFT based FP-LAPW approach[END_REF][START_REF] Chattopadhyaya | Theoretical study of structural, electronic and optical properties of Ba x Pb 1-x S, Ba x Pb 1-x Se and Ba x Pb 1-x Te ternary alloys using FP-LAPW approach[END_REF] using the GGA-WC approximation [START_REF] Wu | More accurate generalized gradient approximation for solids[END_REF]. In addition, the To the best of the authors' knowledge, no experimental and theoretical studies have been performed on BaTe doped with chromium (Cr) atom. In the work presented herein, we investigated the half-metallic ferromagnetic behavior and improved electronic structure of Cr-doped BaTe to explore its ferromagnetic features for use in spintronic applications. For these calculations, we used first-principles calculations based on density functional theory (DFT) using the WIEN2k code [START_REF] Blaha | WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties[END_REF] [START_REF] Hohenberg | Inhomogeneous electron gas[END_REF][START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF], treating the exchange and correlation potential using the Wu-Cohen generalized gradient approximation (GGA-WC) [START_REF] Wu | More accurate generalized gradient approximation for solids[END_REF] and Tran-Blaha-modified Becke-Johnson (TB-mBJ) approach [START_REF] Tran | Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential[END_REF][START_REF] Koller | Merits and limits of the modified Becke-Johnson exchange potential[END_REF].

Calculation methods

We employed the WIEN2k package [START_REF] Blaha | WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties[END_REF] based on the fullpotential linearized augmented plane-wave (FP-LAPW) method for first-principles DFT calculations [START_REF] Hohenberg | Inhomogeneous electron gas[END_REF][START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF]to study the structural, electronic, and magnetic properties of Ba 1-x Cr x Te compounds with various compositions x = 0.25, 0.5, and 0.75 of chromium (Cr) impurity. First, we calculated the structural parameters, electronic structure, and magnetic properties, using the Wu-Cohen generalized gradient approximation (GGA-WC) [START_REF] Wu | More accurate generalized gradient approximation for solids[END_REF]. We then used the accurate Tran-Blaha-modified Becke-Johnson (TB-mBJ) exchange potential combined with the local density correlation potential [START_REF] Tran | Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential[END_REF][START_REF] Koller | Merits and limits of the modified Becke-Johnson exchange potential[END_REF] to improve the electronic properties and give the exact gaps of the band structure.

We chose the average of the muffin-tin radii of Ba, Te, and Cr atoms in such a way that the muffin-tin spheres do not overlap. Besides, the charge density was Fourier results of these parameters are better than recent calculations [START_REF] Drablia | Ab initio calculations of the structural, electronic, thermodynamic and thermal properties of BaSe_1 -xTe_x alloys[END_REF][START_REF] Bahloul | Ab initio calculations of structural, electronic, optical and thermodynamic properties of alkaline earth tellurides BaxSr 1-x Te[END_REF] using the generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] and local density approximation (LDA) with Teter-Pade parameterization [START_REF] Goedecker | Separable dual-space Gaussian pseudopotentials[END_REF]. This is due to the precise GGA-WC exchange potential for structural properties. For the doped Ba 1-x Cr x Te system, the lattice constant decreased with increasing concentration of chromium owing to the difference between the ionic radii of the Ba atom and the substituted Cr impurity. Consequently, Ba 1-x Cr x Te becomes harder with increasing Cr concentration. Note that there are no experimental and theoretical calculations to compare with our results for the structural parameters of Ba 0.75 Cr 0.25 Te, Ba 0.5 Cr 0.5 Te, and Ba 0.25 Cr 0.75 Te.

Electronic structure and half-metallic performance

We calculated the spin-polarized densities of states (DOS) and band structures of the BaTe and Ba 1-x Cr x Te materials using the optimized lattice constants. Firstly, we used the GGA-WC approximation to calculate the electronic structure 3.08 [START_REF] Zolweg | Optical absorption and photoemission of barium and strontium oxides, sulfides, selenides, and tellurides[END_REF], 3.1 [START_REF] Saum | Fundamental optical absorption in the IIA-VIB compounds[END_REF] Experimental of the compounds. We then improved the bandgap calculations of the electronic structure using the TB-mBJ approach.

The spin-polarized band structure of the compounds is shown in Figs. 1, 2, 3, and 4 for the GGA-WC and Figs. 5, 6, 7, and 8 with the TB-mBJ potential. Figures 1 and5 show that the two spin channels of BaTe have similar semiconducting band structures with indirect bandgap (E X) located between and X high-symmetry points. The remaining figures for Ba 1-x Cr x Te with each concentration reveal a half-metallic feature resulting from the metallic nature of the majority spin and a bandgap for the minority spin. The minorityspin bands of Ba 1-x Cr x Te reveal two types of bandgap, viz. tions, using the GGA-WC and TB-mBJ exchange potentials, together with other theoretical [START_REF] Bhattacharjee | Effects of barium (Ba) doping on structural, electronic and optical properties of binary strontium chalcogenide semiconductor compounds -A theoretical investigation using DFT based FP-LAPW approach[END_REF][START_REF] Chattopadhyaya | Theoretical study of structural, electronic and optical properties of Ba x Pb 1-x S, Ba x Pb 1-x Se and Ba x Pb 1-x Te ternary alloys using FP-LAPW approach[END_REF][START_REF] Drablia | Ab initio calculations of the structural, electronic, thermodynamic and thermal properties of BaSe_1 -xTe_x alloys[END_REF][START_REF] Bahloul | Ab initio calculations of structural, electronic, optical and thermodynamic properties of alkaline earth tellurides BaxSr 1-x Te[END_REF] and experimental [START_REF] Zolweg | Optical absorption and photoemission of barium and strontium oxides, sulfides, selenides, and tellurides[END_REF][START_REF] Saum | Fundamental optical absorption in the IIA-VIB compounds[END_REF] data, are presented in Table 2. The agreement is very good between our computed E X for BaTe and calculations [START_REF] Bhattacharjee | Effects of barium (Ba) doping on structural, electronic and optical properties of binary strontium chalcogenide semiconductor compounds -A theoretical investigation using DFT based FP-LAPW approach[END_REF][START_REF] Chattopadhyaya | Theoretical study of structural, electronic and optical properties of Ba x Pb 1-x S, Ba x Pb 1-x Se and Ba x Pb 1-x Te ternary alloys using FP-LAPW approach[END_REF] using the same GGA-WC and TB-mBJ approaches. Also, our result for E X with TB-mBJ is better than other calculations [START_REF] Drablia | Ab initio calculations of the structural, electronic, thermodynamic and thermal properties of BaSe_1 -xTe_x alloys[END_REF][START_REF] Bahloul | Ab initio calculations of structural, electronic, optical and thermodynamic properties of alkaline earth tellurides BaxSr 1-x Te[END_REF] using the GGA-PBE [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] and LDA [START_REF] Goedecker | Separable dual-space Gaussian pseudopotentials[END_REF] approximations. Note that the calculated E X , G HMF , and G HM gaps obtained with TB-mBJ are higher than obtained with the GGA-WC, because the TB-mBJ semilocal exchange correlation potential can provide perfect bandgaps compared with the LDA and different versions of the GGA approxima- a direct half-metallic ferromagnetic (HMF) gap and halfmetallic (HM) gap. The direct HMF gap is situated at high-symmetry point between the valence-band maximum (VBM) and conduction-band minimum (CBM). The HM gap is defined as the minimum of the lowest energy of the majority (minority)-spin conduction bands with respect to the Fermi level and the absolute value of the highest energy of the majority (minority)-spin valence bands [START_REF] Yao | Half-metallic ferromagnetism of zinc-blende CrS and CrP: a first-principles pseudopotential study[END_REF][START_REF] Gao | Half-metallic ferromagnetism in zinc-blende CaC, SrC, and BaC from first principles[END_REF]. This factor describes the minimal energy bandgap for a spin-flip excitation needed to create a hole or electron with minority spin [START_REF] Doumi | First-principle investigation of half-metallic ferromagnetism in octahedrally bonded Cr-doped rock-salt SrS, SrSe, and SrTe[END_REF][START_REF] Doumi | A novel theoretical design of electronic structure and half-metallic ferromagnetism in the 3d (V)-doped rock-salts SrS, SrSe, and SrTe for spintronics[END_REF][START_REF] Cherfi | A novel theoretical investigation of electronic structure and half-metallic ferromagnetism in 3d (V)-doped InP for spintronic applications[END_REF].

The calculated indirect gap (E X ) of BaTe, HMF (G HMF ) and HM (G HM ) gaps of Ba 1-x Cr x Te at all concentra- tion for semiconductors and insulators [START_REF] Koller | Merits and limits of the modified Becke-Johnson exchange potential[END_REF][START_REF] Bhattacharjee | Effects of barium (Ba) doping on structural, electronic and optical properties of binary strontium chalcogenide semiconductor compounds -A theoretical investigation using DFT based FP-LAPW approach[END_REF][START_REF] Chattopadhyaya | Theoretical study of structural, electronic and optical properties of Ba x Pb 1-x S, Ba x Pb 1-x Se and Ba x Pb 1-x Te ternary alloys using FP-LAPW approach[END_REF]. Moreover, we understand that the half-metallic ferromagnetic gap of Ba 1-x Cr x Te decreases with increasing chromium concentration, due to broadening of 3d states of the Cr impurity in the gap. We found that Ba 0.75 Cr 0.25 Te, Ba 0.5 Cr 0.5 Te, and Ba 0.25 Cr 0.75 Te compounds exhibited half-metallic character with HM gap of 0.329, 0.435, and 0.469 eV, making them promising materials for use in spintronics applications.

The contribution to the DOS around the Fermi level (E F ) determines the metallic or semiconductor nature of a material and its polarization. The spin polarization (P) of a material arises from the difference in the contribution of the densities of states of the majority spin N ↑ (E F ) and minority spin

P = N ↑ (E F ) -N ↓ (E F ) N ↑ (E F ) + N ↓ (E F ) . ( 1
)
The spin-polarized total (T) and partial (P) densities of states (DOS) of Ba 0.75 Cr 0.25 Te, Ba 0.5 Cr 0.5 Te, and Ba 0.25 Cr 0.75 Te compounds are shown in Figs. 9, 10, and 11, respectively. These plots depict that the valence bands of the two spin directions are dominated by the major contribution of p (Te) and 3d (Cr) states and minor p (Ba) states in the energy ranges of -2.5 to -0.1 eV for Ba 0.75 Cr 0.25 Te, -2.7 to -0.6 eV for Ba 0.5 Cr 0.5 Te, and -3.5 to -0.3 eV for Ba 0.25 Cr 0.75 Te. The crystal field of the octahedral (Te) surrounding splits the 3d (Cr) levels into two types of states, viz. three low-lying t 2g (d xy , d xz , and d yz ) levels and two high-lying e g (d z 2 and d x 2 -y 2 ) states [START_REF] Doumi | First-principle investigation of half-metallic ferromagnetism in octahedrally bonded Cr-doped rock-salt SrS, SrSe, and SrTe[END_REF][START_REF] Doumi | A novel theoretical design of electronic structure and half-metallic ferromagnetism in the 3d (V)-doped rock-salts SrS, SrSe, and SrTe for spintronics[END_REF], as shown in Fig. 9. For Ba 1-x Cr x Te at all concentrations, the metallic nature of the majority spin results from p-d hybridization between p (Te) and 3d (Cr) states around E F , while the minority-spin states show a gap. Consequently, the Ba 1-x Cr x Te compounds exhibit half-metallic ferromagnetic behavior with spin polarization of 100 %, making them potential candidates for use in spintronics applications.

Magnetic properties

The ferromagnetic state of Ba 1-x Cr x Te can be explained using the Zener carrier-mediated model [START_REF] Zener | Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure[END_REF], because the ferromagnetism is mediated by acceptor hole carriers generated by partially filled 3d (Cr) levels. Besides, the partially occupied 3d (Cr) states stabilize the ferromagnetic state configuration [START_REF] Sato | Ab initio materials design and Curie temperature of GaN-based ferromagnetic semiconductors[END_REF][START_REF] Sato | Curie temperatures of III-V diluted magnetic semiconductors calculated from first-principles in mean field approximation[END_REF] associated with the double-exchange mechanism [START_REF] Akai | Ferromagnetism and its stability in the diluted magnetic semiconductor (In, Mn)As[END_REF]. Therefore, the ferromagnetic state arrangement of Ba 1-x Cr x Te is stabilized by the contributions of p-d exchange and double-exchange mechanisms.

To describe the effect of the p-d exchange mechanism on the magnetic behavior, we calculated the total magnetic moment per Cr atom and local magnetic moments within the muffin-tin spheres of the relevant Cr, Ba, and Te atoms in Ba 1-x Cr x Te compounds. The total and local magnetic moments of Ba 0.75 Cr 0.25 Te, Ba 0.5 Cr 0.5 Te, and Ba 0.25 Cr 0.75 Te are presented in Table 3, revealing that the total magnetic moment per Cr atom for each compound was equal to 4µ B , principally due to the local magnetic moment of Cr atom. The total magnetic moment of 4µ B originates from the 3d (Cr) majority-spin states, which are partially filled with four electrons. On the other hand, the predicted magnetic moment of Cr atom is reduced to below 4µ B and minor local magnetic moments are induced at Ba, Te, and interstitial sites due to the p-d exchange interaction between p (Te) and 3d (Cr) levels. For Ba 1-x Cr x Te at all concentrations, the magnetic spins of Cr and Te atoms have opposite sign, indicating antiferromagnetic interaction between Cr and Te. The interaction between Cr and Ba atoms is ferromagnetic for Ba 0.75 Cr 0.25 Te and Ba 0.5 Cr 0.5 Te, but becomes antiferromagnetic in the case of Ba 0.25 Cr 0.75 Te compound.

Fig. 1

 1 Fig.1Spin-polarized band structure obtained with GGA-WC for BaTe: a majority spin (up) and b minority spin (dn). The Fermi level is set to zero (horizontal dotted line)

Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8

 2345678 Fig. 2 Spin-polarized band structure obtained with GGA-WC for Ba 0.75 Cr 0.25 Te: a majority spin (up) and b minority spin (dn). The Fermi level is set to zero (horizontal dotted line)

Fig. 10

 10 Fig.[START_REF] Berber | Investigation of electronic structure and half-metallic ferromagnetic behavior with large half-metallic gap in Sr 1-x V x O[END_REF] Spin-polarized total and partial densities of states of Ba 0.5 Cr 0.5 Te. The Fermi level is set to zero (vertical dotted line)

Fig. 9

 9 Fig.[START_REF] Doumi | First-principle investigation of half-metallic ferromagnetism in octahedrally bonded Cr-doped rock-salt SrS, SrSe, and SrTe[END_REF] Spin-polarized total and partial densities of states of Ba 0.75 Cr 0.25 Te. The Fermi level is set to zero (vertical dotted line)

Fig. 11

 11 Fig. 11 Spin-polarized total and partial densities of states of Ba 0.25 Cr 0.75 Te. The Fermi level is set to zero (vertical dotted line)

Table 1

 1 Calculated lattice constant (a), bulk modulus (B), and its pressure derivative (B ) for BaTe and Ba 1-x Cr x Te with composition x = 0.25, 0.5, and 0.75 of Cr atoms

	Compound	a (Å)	B (GPa)	B	Method
	This work				GGA-WC
	BaTe	6.944	31.89	4.56
	Ba 0.75 Cr 0.25 Te	6.735	33.51	5.02
	Ba 0.5 Cr 0.5 Te	6.457	38.27	5.47
	Ba 0.25 Cr 0.75 Te	6.073	50.66	6.42
	Other calculations
	BaTe	6.934 [37]	28.81 [37]	5.191 [37]	GGA-WC
		6.955 [38]	30.91 [38]	4.012 [38]	GGA-WC
		7.075 [39]	27.04 [39]	4 . 6 3 [ 39]	GGA-PBE
		7.0667 [40]	28.5384 [40]	4.0526 [40]	GGA-PBE
		6.8690 [40]	35.3052 [40]	4.4247 [40]	L D A
		7.005 [41]	29.4 [41]	7 . 4 [ 41]	Experimental

Table 2

 2

	Calculated indirect bandgap (E X) for BaTe,	Compound	G HMF (eV)	G HM (eV)	E X (eV)	Method	Behavior
	half-metallic ferromagnetic gap (G HMF ), and half-metallic gap (G HM ) of minority-spin bands	This work BaTe			1.455	GGA-WC
	for Ba 1-x Cr x Te at	Ba 0.75 Cr 0.25 Te	1.491	0.136			HMF
	concentrations x = 0.25, 0.5, and 0.75 of Cr atoms	Ba 0.5 Cr 0.5 Te Ba 0.25 Cr 0.75 Te	1.298 0.816	0.282 0.360			HMF HMF
		This work				TB-mBJ
		BaTe			2.256
		Ba 0.75 Cr 0.25 Te	2.167	0.329			HMF
		Ba 0.5 Cr 0.5 Te	1.923	0.435			HMF
		Ba 0.25 Cr 0.75 Te	1.250	0.469			HMF
		Other calculations
		BaTe			1.325 [37], 1.822 [38]	GGA-WC
					1.656 [39], 1.6516 [40]	GGA-PBE
					1.3649 [40]	L D A
					2.453 [37], 2.254 [38]	TB-mBJ
					2.365 [39]

Table 3

 3 Calculated total and local magnetic moments of relevant Cr, Ba, and Te atoms, and at interstitial sites (in Bohr magneton µ B per Cr atom) for Ba 1-x Cr x Te with compositions x = 0.25, 0.5, and 0.75 of Cr atoms

	Compound	Total	Cr (µ B ) Ba (µ B ) Te (µ B ) Interstitial
		(µ B )			(µ B )
	This work
	Ba 0.75 Cr 0.25 Te 4	3.996	0.001	-0.261 0.265
	Ba 0.5 Cr 0.5 Te	4	3.952	0.0005	-0.242 0.290
	Ba 0.25 Cr 0.75 Te 4	3.788	-0.006 -0.189 0.408
	N ↓ (E F ) around E F , defined by the expression [50]

Conclusions

We predicted the structural, electronic, and ferromagnetic properties of rocksalt BaTe doped with Cr atoms, i.e., Ba 1-x Cr x Te with compositions x = 0.25, 0.5, and 0.75, based on first-principles calculations in DFT with the GGA-WC and TB-mBJ exchange potentials using WIEN2k code. The electronic structure showed that the Ba 1-x Cr x Te compounds are half-metallic ferromagnetic with spin polarization of 100 %. The total magnetic moment per Cr atom has integral value of 4µ B , being principally formed by the main contribution of the local magnetic moment of Cr atom. The ferromagnetic state arrangement is stabilized by both p-d exchange and double-exchange mechanisms. The improved HM gaps of the Ba 1-x Cr x Te materials make them potential candidates for use in future spintronics applications.


Gauthier Lefevre

Sébastien Saitzek

Rachel Desfeux

Adlane Nathalie Kunkel

Adlane Sayede
email: adlane.sayede@univ-artois.fr

Hydrogen storage in

Keywords: Hydrogen storage, Magnesium based alloy, Metal hydrides, DFT prediction, Evolutionary algorithm

come

Introduction

Currently, environmental and political concerns regarding global warming and the search for alternative fuels greatly impact scientific research. As a consequence, hydrogen technology, which promises green energy producing only water as combustion product, is of great interest and highly efficient hydrogen fuel cells already exist [START_REF] Zulkepli | Review on the Recent Developments of Photovoltaic Thermal (PV/T) and Proton Exchange Membrane Fuel Cell (PEMFC) Based Hybrid System[END_REF]. However, despite many years of research -except for a few pilot projects -hydrogen technology has still not been established as a broadly used technology in the renewable energy sector. This is mainly because the requirements for an effective, safe and reliable way to store hydrogen are not yet met. Next to storage in gas containers under high pressure, solid storage in form of metal hydrides seems to be one of the most promising options, because it is intrinsically safe and allows a volumetric capacity higher than liquid and compressed hydrogen and, all the more reason, it can operate at low pressure [START_REF] Schlapbach | Hydrogen-storage materials for mobile applications[END_REF]. Recently, a lot of attention has been paid to novel solid state hydrogen storage systems, such as nano-structured materials [START_REF] Jeon | Airstable magnesium nanocomposite provide rapid and high-capacity hydrogen storage without using heavy-metal catalysts[END_REF] and Liquid Organic Hydrogen Carriers (LOHCs) [START_REF] Teichmann | Liquid organic hydrogen carriers as an efficient vector for the transport and storage of renewavle energy[END_REF][START_REF] Wulf | Assessment of system variations for hydrogen transport by liquid organic hydrogen carriers[END_REF]. However, these methods still suffer from significant drawbacks and further developments remain challenging [START_REF] Rusman | A review on the current progress of metal hydrides material for solid-state hydrogen storage applications[END_REF].

Thus, research on metal hydrides, such as MgH 2 , LiH and new ternary and quaternary alloys, is still ongoing and light-weight and reversible systems are intensively searched for. The use of hydrogen as a fuel would be convenient, because the only combustion product is water, no other exhaust fumes, that might be possibly toxic or detrimental for the climate, are emitted. Light metals, such as magnesium, are of particular interest due to their high gravimetric hydrogen density. However, their use remains limited because of their high thermodynamic stability and their slow dehydrogenation kinetics. Several ways to overcome this problem have been proposed, such as the use of solid solutions of hydride and fluoride [START_REF] Tortoza | Thermodynamics and performance of the mg-h-f system for thermochemical energy storage applications[END_REF][START_REF] Sheppard | Hydriding characteristics of namgh 2 f with preliminary technical and cost evaluation of magneisumbased metal hydride materials for concentrating solar power thermal storage[END_REF] or the use of magnesium-based alloys [START_REF] Reilly | Reaction of hydrogen with alloys of magnesium and copper[END_REF][START_REF] Bobet | Study of Mg-M (M=Co, Ni and Fe) mixture elaborated by reactive mechanical alloying hydrogen sorption properties[END_REF][START_REF] Pistidda | Hydrogen storage systems from waste mg alloys[END_REF][START_REF] Hardian | Waste mg-al based alloys for hydrogen storage[END_REF]. For instance, in the system magnesium-nickel, it is known that the intermetallic compound Mg 2 Ni shows a lower desorption temperature and improved hydrogenation kinetics [START_REF] Reilly | Reaction of hydrogen with alloys of magnesium and nickel and the formation of mg2nih4[END_REF][START_REF] Iturbe-Garca | Hydrogen desorption process in Mg 2 Ni hydrides[END_REF]. However, the disadvantage of this system is the low hydrogen storage capacity that is less than 4 %wt. It is also worth noting that the synthesis technics such as ball milling, infiltration in nano-scaffold and the use of selected additives can also influence the hydrogenation and dehydrogenation kinetics [START_REF] Mao | Recent advances in the use of sodium borohydride as a solid state hydrogen store[END_REF].

Recently, a new material, MgNi 3 , which crystallizes in the cubic space group Pm ¯3m, has been synthesized by mechanochemistry [START_REF] Liu | A new phase MgNi 3 synthesized by mechanical alloying[END_REF][START_REF] Yartys | Hydrogen-assisted phase transition in a trihydride MgNi 2 H 3 synthesized at high H 2 pressures: Thermodynamics, crystallographic and electronic structures[END_REF]. Similarly, Watanabe et al. [START_REF] Watanabe | High Pressure Synthesis of Novel Compounds in Mg-TM Systems (TM = Ti ∼ Zn)[END_REF] showed that at high pressure syntheses, novel compositions of magnesium-copper system can appear, which may be potentially interesting for hydrogen storage applications. In this context, theoretical prediction of new structures, for instance of magnesium binary alloys, could support the experimental quest. With the substantial progress in computational science as well as in global structure search methods, it is nowadays possible to explore new crystalline phases using reliable calculations based on the electronic properties. In the present work, our aim is to investigate in silico the effect of pressure on MgX (X = Ba, Co, Cu, Ni, Ti, V) systems. Using an evolutionary algorithm (EA) in combination with first-principles optimization, to explore the compositional and configurational space, allows mapping the high-pressure phase diagram of Mg-based binary systems. Particular attention is paid to the compositions MgNi 3 and MgCu. For these compounds, new hypothetical crystalline phases of hydrides were found. Detailed structures, as well as electronic and mechanical properties are presented and our results are promising and encourage the search for hydrogen storage alloys.

Computational details

Crystal structure prediction approach

For many years, the resolution of a crystal structure by theoretical means has been an almost insolvable problem. Recently, the rapid improvement of computational resources and methods has led to the appearance of many new methods for crystal structure prediction [START_REF]Modern Methods of Crystal Structure Prediction : CRYSTAL -METHODS O-BK[END_REF], which use physical phenomena (simulated annealing) or mathematical algorithms (Basin Hopping, Genetic Algorithm...). The widely used evolutionary algorithm (EA) belongs to one of the most effective methods and shows pertinent results [START_REF] Zheng | Pressure-induced phase transition and electronic properties of MgB 2 C 2[END_REF][START_REF] Sun | New phases of 3d-transition metalcerium binary compounds: an extensive structural search[END_REF].

In the present work, the USPEX code developed by Oganov et al. [START_REF] Oganov | Crystal structure prediction using ab initio evolutionary techniques: Principles and applications[END_REF][START_REF] Oganov | How Evolutionary Crystal Structure Prediction Works and Why[END_REF][START_REF] Lyakhov | New developments in evolutionary structure prediction algorithm USPEX[END_REF], a prediction code based on the variable-composition evolutionary algorithm (VC-EA) was used for the prediction of crystal structures. Depending on the size of the system, unit cells containing 8-16 (for Mg -Ba, Mg -Co and Mg -Cu systems) or 12-25 (for Mg -Ni, Mg -Ti and Mg -V systems) atoms were considered. The calculations were performed both at 0 and 40 GPa external pressure. To ensure an unbiased and complete prediction, the following parametrization if the USPEX code was used: an initial population of 150 structures was generated randomly and afterward, 60 generations of 80 candidates were generated and considered. These 60 gehardynerations were obtained by applying variation operators on previous structures found, including heredity operations (i.e. combination of slices of two parents lattices), random production, and mutation operators (i.e. random exchange of different atoms, distortion of the crystal lattice, atomic displacements along the softest phonon mode eigenvectors). Finally, the additional inclusion of known crystal structures yielded an extra generation. Further and more detailed technical information on the USPEX evolutionary structural searches are given in the Supporting Information. Global searches for hydrides were carried out for the interesting alloys MgNi 3 and MgCu and consisted of an exploration of various hydride compositions with hydrogen ratios ranging from 1 to 5 atoms per unit cell. In order to relax the crystal structures at ab initio level using the density functional theory (DFT), calculations were carried out with the VASP package [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF]. The energy calculations were based on the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) parametrization [START_REF] Perdew | Generalized gradient approximation made simple[END_REF].

Projected-augmented wave (PAW) potentials [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] were used, which had a [Ne] core (radius 2.0 u) for magnesium, [Ar] core (radius 2.3 u) for cobalt, copper, nickel, titanium, vanadium and [Pd] core (radius 2.8 u) for baryum. To improve the quality of the calculations, a multi-step relaxation of the structures was carried out using USPEX coupled with VASP. Once the final level of relaxation was reached, Monkhorst-Pack grid centered at the Γ-point with the resolution of 2π × 0.05 Å-1 to describe the Brillouin zone and a energy cut-off of 500.0 eV were used. Convergence criteria of 10 -4 eV for the electronic properties and less than 1 meV Å-1 for the ionic forces were applied. The Hellman-Feynman forces were minimized using a quasi-Newton algorithm. Such variable-composition calculations were executed both at 0 and 40 GPa external pressure.

Structure and electronic calculations

Once a set of candidate structures was identified (as discussed below), a more careful analysis was performed applying the criteria of 800.0 eV, 10 -5 eV Å-1 and 10 -8 eV for the cut-off energy, the convergence of total energy and Hellmann-Feynman forces, respectively. Both spin and non-spin polarized calculations were performed for the structure that had been identified by the USPEX prediction calculations. The obtained energy difference were compared and since they were almost identical, a non-spin polarized state was assumed for all calculations. To obtain the accurate total energy as well as for the determination of the densities of states (DOS), the linear tetrahedron method with Blöchl corrections was used on the relaxed structures. In order to guarantee dynamic stability, phonon dispersion curves were calculated with the Phonopy code using density functional perturbation theory (DFPT) [START_REF] Togo | First principles phonon calculations in materials science[END_REF]. This allowed to apply the zero point energy (ZPE) correction for the calculation of formation energies. Additionally, the mechanical stability of the structures was examined based on the calculated elastic constants (bulk modulus B, shear modulus G and Poisson's ratio ν ) and using the stress-strain relations implemented in the VASP code. Furthermore, the charge distribution on the atoms was evaluated using Baders topological analysis [START_REF] Tang | A grid-based Bader analysis algorithm without lattice bias[END_REF]. Within this approach, the electron density is partitioned into regions linked by the minima of the charge density. Electronic density charge transfer and electron localization function (ELF) mapping as well as the 3D visualization of crystal structures were performed using the VESTA code [START_REF] Momma | VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data[END_REF].

The enthalpy of formation of magnesium based alloys Mg x X y is defined as follows:

∆H = E el (Mg x X y ) -xE el (Mg) -yE el (X) (1)
where E el denotes the calculated energy of various compounds. For hypothetical hydrides, the enthalpies of absorption are deduced from the equation :

∆H abs = E tot (A m H n ) -mE tot (A) - n 2 E tot (H 2 ) (2)
where E tot (A) represents the total energy of the theoretical and experimental structures MgNi 3 or

MgCu and E tot (H 2 ), E tot (A m H n ) are the total energies of the hydrogen molecule and the magnesiumbased hydrides, respectively. These total energies include the contributions from the zero point energies (ZPE) [START_REF] Milonni | The quantum vacuum: An introduction to quantum electrodynamics[END_REF] of compounds in the following way :

E tot (X) = E el (X) + E ZPE (X) (3)
The ZPE correction is of great importance for the correct calculation of hydride formation energies since the ZPE correction from hydrogen atoms in compounds present a substantial value and has a stabilizing effect, which is due to the low mass of hydrogen atom [START_REF] Kohlmann | Crystal structure and hydrogenation properties of Pd 5 As[END_REF].

The energy of a H 2 molecule is approximated by DFT calculations using the molecule in a box approach, where hydrogen dimer was placed in a box with edges of 10 Å × 11 Å × 12 Å using Γ-point sampling. The results E ZPE (H 2 ) = 0.29 eV, d H-H = 0.757 Å and E binding (H 2 ) = 4.51 eV are in good agreement with those reported in previous works [START_REF] Alapati | Using first principles calculations to identify new destabilized metal hydride reactions for reversible hydrogen storage[END_REF][START_REF] Kresse | Dissociation and sticking of H 2 on the Ni(111), (100), and (110) substrate[END_REF].

Results and discussions

Extensive structural searches on numerous magnesium-based binary alloys were carried at simulated pressures of 0 and 40 GPa. Since hydrogen storage for mobile applications, such as transportation, requires compounds with densities as low as possible, light elements of the first row Transition Metals (TM) have been studied, as well as an element of the alkaline earth metals for comparison. The goal of simulations at 40 GPa, a pressure that is difficult to reach experimentally, was rather to investigate if these systems were more favorable for alloys formation in a severe and drastic environment. These predictions could then give insight to scrutinize new alloys for systems sensitive to pressure. In this perspective, we investigate MgX (X = Ba, Co, Cu, Ni, Ti, V) systems and the results for transitions metals show that the pressure effect tends to stabilize new combinations with magnesium. At low pressure, a high number of 3d electrons of the transition metal seems to favor mixing with magnesium. Moreover, at high pressure, enthalpy of formation of simulated Mg-TM alloys decreases further. In contrast, attempts with an alkaline earth metal, namely barium, shows a destabilization of the simulated alloys with increasing pressure, leading to a complete immiscible system where even the composition Mg 2 Ba is unstable. Even though we have studied a number of Mg-TM systems in our work, we could not identify stable intermetallic phases for all of them. In the magnesium-titanium and magnesium-vanadium systems (see fig. S1 andS2), for example, no compounds were estimated as stable, even though at 40 GPa metastable intermetallics were found.

In contrast, the magnesium-transition metal systems with cobalt, nickel and copper showed a radically different behavior with a wide range of new compositions at high pressure. Novel alloys, especially in the magnesium-rich area, are found and may serve as starting points for further experimental or theoretical examinations. We then focused on Mg -Ni and Mg -Cu systems in order to seek for positive effects of pressure on the stability of new phases and possible applications for hydrogen storage. It is worth noting that in spite of the extensive searches carried out in our study, we are not able to predict all the possible stable structures of the present systems. Since complex phases may be composed of more than thirty atoms in their primitive cell, and supposing that hydrides with high hydrogen ratio may exist, current predictions lack the necessary computational power to deal with phases that require high computational costs. High pressure new phases discussed here might be obtained experimentally using approaches such as high energy ball milling, and therefore in conditions far from equilibrium. It therefore should be noted that their utilization might be limited by the fact that upon cycling their re-formation might be hindered or not possible.

Structure prediction in the magnesium-nickel system

Fig. 1 shows the enthalpy of formation of the generated structures in the magnesium-nickel system according to their composition. Without taking pressure into account, theoretical and experimental results are in perfect agreement: only the two well-known structures, the hexagonal phases Mg 2 Ni and MgNi 2 with the space groups P 6 2 22 and P 6 3 /mmc respectively, are on the thermodynamic convex hull.

This latter is a complete set of phases stable against transformation or decomposition into any other phases. Interestingly, we can note a metastable phase closest to stability with the MgNi 3 composition, which will be discussed later.

Under pressure of 40 GPa (fig. 1), a broad variety of new compositions appeared to be stable, meaning that all structures are mechanically and dynamically stable according to calculations, even if some of them exhibit no particular geometry (see As mentioned previously, stable phases could have a particular and complex structure, as it is the case for the metastable Mg ∼6 Ni [START_REF] Todorova | Mg 6 Ni formation in rapidly quenched amorphous MgNi alloys[END_REF] phase that have been experimentally identified as a Mg 6 Pd-type structure containing more than a hundred atoms in its unit cell. Due to computational limits, one could not predict such an important structure in variable-composition studies. Nevertheless, a Mg 6 Ni low symmetry phase has been found on the convex hull, demonstrating the efficiency of ab initio prediction for obtaining the right stable compositions, in default of the right structures. The composition MgNi 3 has also been synthesized experimentally under severe conditions [START_REF] Liu | A new phase MgNi 3 synthesized by mechanical alloying[END_REF][START_REF] Yartys | Hydrogen-assisted phase transition in a trihydride MgNi 2 H 3 synthesized at high H 2 pressures: Thermodynamics, crystallographic and electronic structures[END_REF]. In the present study, depending on pressure, two competing phases for the ground state structure are found, a metastable phase at 0 GPa (with tetragonal structure, space group P 4m2) and a stable cubic phase at 40 GPa (space group P m 3m, which is also found experimentally).The structural changes between the Ambient-(AP) and High- is generally employed in order to illustrate these structural modifications [START_REF] Bärnighausen | Group-subgroup relations between space groups : a useful tool in crystal chemistry[END_REF][START_REF] Weil | The phase transition of Pb 8 F 14 I 2[END_REF]. Using the symmetry group analysis [START_REF] Aroyo | Bilbao crystallographic server: I. databases and crystallographic computing programs[END_REF][START_REF] Müller | Relating crystal structures by groupsubgroup relations[END_REF], there is no direct group-subgroup relation between AP and HP space groups. But there is a possible way using a hypothetical intermediate structure according to the following sequence :

N i M g 4 N i M g 2 N i M g N i M g N i 2 M g N i 3 M g N i 5 M g N i 7 M g N i
P m 3m (HP phase) --→ P 4/mmm --→ P 4m2 (AP phase). This pathway seems perfectly consistent with the model prediction.

A careful theoretical examination of all possible phases was also carried out in the range of 0 -40 GPa.

With a step size of 10 GPa, a number of structures (ground state phases found by prediction and some interesting metastable phases) was completely relaxed to observe the convex hull aspect with respect to pressure (fig. 1). Interestingly, from 10 GPa simulated pressure, one can observe the formation of the Mg 6 Ni composition, in good agreement with the mild conditions of synthesis [START_REF] Todorova | Mg 6 Ni formation in rapidly quenched amorphous MgNi alloys[END_REF].

By mechanical alloying, Liu et al. found a new cubic phase MgNi 3 with the space group P m 3m and conclude that their process reached a pressure higher than 8 GPa, which is high enough for Mg to substitute Ni in its cubic phase with space group F m 3m. The EA prediction performed at 40 GPa confirms this cubic phase of MgNi 3 as the global minimum energy structure. However, as mentioned previously, another structure, a tetragonal phase MgNi 3 with space group P 4m2, was predicted without pressure consideration. According to the low value of the energy of formation (see table 1), this tetragonal phase may be seen as a potential phase. The theoretical change of the ground state phase from the tetragonal to the cubic phase occurs between 20 and 30 GPa (see fig. 1) whereas the cubic phase was experimentally formed at 8 GPa. This lead us to think, in agreement with Liu et al., that kinetic effects aided by the grinding energy are governing this phase formation rather than pressure and thermodynamic. The formation of other Mg -Ni compositions seems to require drastic synthesis conditions, because a minimum pressure of 20 GPa is calculated. Moreover, the found Ni-rich alloys are not interesting in terms of light systems for hydrogen storage, and some of the structures found seem questionable given their low symmetry structure.

Structure prediction in the magnesium-copper system

The previous study has been repeated in the Mg -Cu system. From prediction at 40 GPa (fig. 2 [START_REF] Rahman | The structural, elastic, electronic and optical properties of MgCu under pressure: A first-principles study[END_REF][START_REF] Mao | First-principles calculations of structural, elastic and electronic properties of AB2 type intermetallics in MgZnCaCu alloy[END_REF]. These discrepancies are related to the high value of cut-off energy and k-points sampling we found necessary to obtain for a good convergence of elastic moduli (see Supporting Information section 3). Stabilities of Mg -Cu compositions are shown in fig. 2 and the stabilizing effect of pressure on considered alloys can clearly be seen. It also indicates that significant pressure stresses is needed to obtain a spontaneous formation of these compounds.

We have not been further interested by the study of the hexagonal Mg-rich phase Mg 3 Cu since it becomes stable only for high pressure superior to 30 GPa. However, it is interesting to note that Mg 3 Cu hydride has already been synthesized [START_REF] Torres | Short communication: High-pressure synthesis and crystal structure of a novel Mg 3 CuH x ternary hydride[END_REF] at 3.5 GPa and ∼1100 K but the hydrogen free alloy was not observed. In contrast, the CsCl-type phase MgCu is the easiest affordable new composition and was experimentally discovered by Okada et al. under 6 GPa pressure at 1073 K [START_REF] Watanabe | High Pressure Synthesis of Novel Compounds in Mg-TM Systems (TM = Ti ∼ Zn)[END_REF]. Hydrogenation of this phase was not achieved but the authors assumed hydrogenation may be possible under suitable conditions. According to them, the experimental temperature of 423 K during their hydrogenation attempt was likely too high for the hydride synthesis, meaning that an interesting low stability hydride might exist. This hypothesis is in excellent agreement with our present results shown in the next section. Furthermore, the calculated stability of the MgCu compound suggests that a direct and lower temperature synthesis is possible if the pressure conditions are set to approximately 10 GPa. At such pressure, hydrogenation at low temperature could be likely achieved. Okada et al. have also synthesized a novel compound Mg ∼51 Cu ∼20 similar to the Mg 51 Zn 20 phase with space group Immm. This structure with numerous atoms in the primitive cell is out of range of our proof of principle calculations. However its composition ratio Cu/(Mg + Cu) of 0.28 is closed to the 0.25 of the Mg 3 Cu predicted crystal and demonstrates that genetic algorithm method are a efficient tool to predict possible mixed compounds.

The hypothetical hydrides of MgNi 3 and MgCu

As mentioned previously, the novel compounds MgNi 3 and MgCu have been synthesized recently and particular attention has been paid to these compositions in the present study in order to shed more light on possible hydrogenation. The electronic structure calculations show that the two alloys exhibit a metallic character as can be seen in the total and partial electronic densities of states (DOS and PDOS) In spite of a shorter distance, the ionic bond for MgNi 3 , denoted by the charge transfer between atoms, is very weak and one could then expect an easier distortion of the lattice for the latter compound.

To ensure totally unbiaised searches of hydrides, no starting geometry was given or recommended to the genetic algorithm. More than six thousand different structures were generated and among the most stable hydrides predicted, two were kept for further investigations since they exhibit high symmetry structures (see table 3), namely MgNi 3 H 2 and MgCuH 3 with a trigonal structure.

To explore hydrogenation, one usually considers the process as presented into different contributions [START_REF] Miwa | First-principles study on 3d transition-metal dihydrides[END_REF][START_REF] Smithson | First-principles study of the stability and electronic structure of metal hydrides[END_REF] : conversion of the crystal, expansion of the structure and hydrogen insertion ; the first two being destabilizing steps compared to the third. Particularly, the conversion step is really energy demanding when alloy and hydride have a rather different crystal structure, as, for instances, shown in our previous work on the arsenic-palladium system [START_REF] Kohlmann | Crystal structure and hydrogenation properties of Pd 5 As[END_REF].

Interestingly, a simple ab initio relaxation of hydride structures with hydrogen atoms removed leads directly to the ground state structure of MgNi 3 and MgCu, meaning that structures of hydride and hydrogen hosts are very close to each other in the energy landscape. For MgNi 3 and its hydride (fig. 7), this point was confirmed with further calculations and is in agreement with the work of Miwa and Fukumoto [START_REF] Miwa | First-principles study on 3d transition-metal dihydrides[END_REF] who showed that the lattice expansion is a dominant factor for d-metals around the 8 th column. The hydride structure can be considered as a distorted Cs -Cl structure. In contrast, it is somewhat surprising to see how easily MgCuH 3 hydride structure relaxes to Cs -Cl ground state symmetry. Nevertheless, the compound crystallizes in the strongly distorted cubic closest packing, as can be seen on fig. 4.

The calculated absorption enthalpies of the studied hydrides (table 3) are singularly different regarding the fact that both hydrides and alloys have the same structure type. It is worth noting that neglecting the ZPE correction would lead to incorrect enthalpies, especially for MgCuH 3 hydride where its omission leads to a non-spontaneous formation. Furthermore, one could expect the hydrogen richest compound MgCuH 3 to be the most stable since hydrogen has generally a stabilizing effect. To explain the difference, a precise study on electronic structures was carried out, especially using electron localization function (ELF) and electron charge density transfer. In ELF, electrons localization information is given by the probability for finding a second like-spin electron near a reference point. It allows to view the system in more chemical aspects, particularly different bonding interactions. The charge density transfer is an Overall, the stabilization of both hydrides is confirmed by the strong electron gain (transfer) and electron localization around the hydrogen sites (fig. 6). The densities of states (fig. 5) also demonstrate hydrides) and that a large transfer for MgCuH 3 may be a reason for the large structure distortion.

In MgCuH 3 , five H atoms form a deformed square-based pyramid around the Mg atoms and Cu atoms are surrounded by four hydrogen atoms in a distorted tetrahedral environment, with the resulting polyhedra constituting of puckered sheets. Thus, the hydrogen atoms interact with copper as well as with magnesium, which leads to an overlap between hydrogen and metals orbitals, as indicated by the PDOS.

The electronic structure shows a non-metallic character with a band gap of 2 eV. Compared to the DOS of the MgCu alloy, one can see clearly that this band gap results from the displacement of Mg-states to lower energy levels due to Mg -H interactions, and the down-shift of the Fermi level to the top of the copper d-band. The overall DOS appearance is comparable to the DOS found for the intermediate, but not the late 3d transition metal hydrides as described in the detailed study of Smithson et al. [START_REF] Smithson | First-principles study of the stability and electronic structure of metal hydrides[END_REF]. Here, the destabilizing effect of hydrogen atoms on copper is counteracted by the partial substitution of Cu by Mg in the structure.

Moreover, the average ELF value between Mg or Cu and H is less than 0.3, which suggests the absence covalent bonding but the presence of ionic bonds. The latter is confirmed by the difference in the charge density and Bader charge analysis, as described previously.

In the MgNi 3 H 2 structure, hydrogen atoms are partially filling octahedral sites of the distorted Cs -Cl structure (fig. 7). The PDOS shows a dominant interaction of hydrogen with magnesium at a new lowenergy region, which leads, apart from this new region, to a similar DOS as the hydrogen-free MgNi More generally, the calculated enthalpies for both studied hydrides make theses last very interesting for hydrogen storage applications.

Conclusions

We have performed a systematic study on the phases stability of the binary alloys of magnesium and a number of 3d-transition metals systems at ambient and high pressure, using the USPEX code with ab initio calculations. Novel structures were predicted for the systems Mg -Ni and Mg -Cu and the calculations indicate that the new predicted phases are dynamically and mechanically stable. Moreover, our investigation points out the existence of possible hydrides of MgNi 3 and MgCu. The results obtained are in agreement with the electronic study concerning their structure and relative stability. As expected, there is a stronger hybridization between hydrogen and magnesium atoms than hydrogen and transition metals. For the considered systems, hydrogen interactions have stabilizing effects. The presence of magnesium plays a crucial role on the stability of the hydride of MgCu. The impact is lower in MgNi 3 since the Ni -3d states are not completely filled. The fundamental destabilizing factor in hydride formation remains the phase change and this step can be tailored by alloying different elements to form an appropriate host for hydrogen. In this context, finding the ground-state of hydride is an important point and genetic algorithms represent an efficient approach.

Besides the limitations of evolutionary algorithms for structure investigations such as crystals with large unit cells or amorphous phases, it can be clearly seen that this approach is a powerful tool to screen the composition variations of binary alloys, as shown in the present study with respect to pressure modifications. At least, a stable composition range can be highlighted and give useful insights and trends as shown for the predicted Mg 6 Ni and Mg 3 Cu alloys. The found theoretical hydrides seem to reflect experimental expectations. That is the reason why the genetic algorithm approach should belong to every rigorous structural study since it allows tailoring exotic and non conventional structures, which are common, especially in compounds composed of highly heterogeneous atom combinations.

Results and outlooks presented here are encouraging and motivate for further studies on the design of hydrogen storage alloys.

Figure 1 :

 1 Figure 1: Stability of predicted structures in the Mg -Ni system with respect to pressure

Figure 3 :

 3 Figure 3: Total and partial density of states of MgCu (left) and MgNi 3 (right).

(fig. 3 )

 3 . Due to the low electronegativity of magnesium compared to copper and nickel, Mg acts as a partial electron donor. This observation is confirmed by the Bader charge analysis, which yields a 0.20 e and 0.89 e electron transfer from Mg to Ni and Cu, respectively. In Ni-based alloy, the excess electron on Ni is located in the d-band and the Fermi surface lies in the highest metal d-states. In MgCu, the d-states of Cu are filled so that the Fermi level lies beyond them. The magnesium-metal atom distance is smaller for MgNi 3 (d Mg-Ni = 2.58 Å compared to d Mg-Cu = 2.74 Å for MgCu).

Figure 4 :

 4 Figure 4: Left : Relationship of the hydrogen free crystal structure of MgCuH 3 to a cubic closest packing. Trigonal unit cell is indicated by solid lines, pseudo-cubic cells by dashed lines. Right : Structure of MgCuH 3 , as seen as a stack of Mg hydride pyramid and Cu hydride tetrahedron.

  that the stabilization occurs by interaction of metals states with hydrogen s-states in wide energy range below the Fermi level, causing delocalization of metal states in the low-energy region. A medium loss of the d-orbital occupation of the transition metals is seen in the electron charge density in the direction pointing towards the hydrogen atoms, which arises from the formation of a bonding-antibonding pair between the directly overlapping H s and Ni or Cu e g orbitals. Nevertheless, the electron density change on transition metals is weak, because the d-states are filled or almost filled. The Bader charge analysis also confirms the hydridic behavior by the negative charge of the hydrogen atoms, and the values of -0.58 e for MgCuH 3 and -0.85 e for MgNi 3 H 2 are consistent with the electronegativity of metals and results reported in other works[START_REF] Aboud | A Density Functional Theory Study of the Charge State of Hydrogen in Metal Hydrides[END_REF][START_REF] Batalovi | Density functional theory guide to structure and thermodynamics of metal hydrides. Case study of (Ti, Zr, Hf)Ni intermetallic compounds[END_REF]. In addition, the Bader analysis indicates that electron transfer originates mainly from Mg atoms (Mg net charges are respectively 1.59 e and 0.80 e for MgCu and MgNi 3

Figure 5 :Figure 6 :

 56 Figure 5: Total and partial density of states of MgCuH 3 (left) and MgNi 3 H 2 (right).

NiFigure 7 :

 7 Figure 7: Left : Trigonal unit cell of MgNi 3 H 2 (in solid lines) and its distorded Cs -Cl type structure (in orange lines). Right : Representation of octahedra sites containing hydrogen atoms.

table 1 )

 1 . Only the hexagonal phase MgNi 2 remains identical to

		0	M g 6
	Enthalpy of formation (eV/atom)	-0.5 -0.4 -0.3 -0.2 -0.1
		-0.6
		0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
					Composition ratio : Ni/(Mg+Ni)

Table 1 :

 1 Calculated enthalpy of formation, structural and elastic parameters of stable and metastable phases in Mg -Ni HP) phases of MgNi 3 should be related by group-subgroup relations. The Bärnighausen tree

	system
	Structure and Space group	Lattice parameters		B (GPa)	G (GPa)	ν	∆H (eV/atom)
					0 GPa
	Mg 2 Ni	a = 5.20(5.205[37])	Å	65.47	30.80	0.297	-0.20
	P 6 2 22(180)	c = 13.18(13.236[37])	Å
	MgNi 3 P 4m2(115)	a = 4.75 Å ; c = 6.74 Å	136.7	67.92	0.287	-0.17
					40 GPa
	Mg 6 Ni P 1(2)	a = 4.95 Å ; b = 4.96 β = 86.9 • ; γ = 84.8 • Å c = 7.76 Å ; α = 80.1 •	246.8	73.29	0.365	-0.22
	Mg 4 Ni P 2 1 /m(11)	Å c = 6.41 Å ; β = 101.2 • a = 4.93 Å ; b = 8.34	122.7	72.40	0.253	-0.25
	Mg 2 Ni I4/mmm(139)	a = 2.87 Å ; c = 8.77 Å	163.1	74.30	0.302	-0.43
	MgNi P 4/mmm(123)	Å Å a = 2.72(2.99[38]) c = 2.97(3.13[38])	204.5	103.3	0.284	-0.56
	MgNi 2 P 6 3 /mmc(194)	Å c = 14.78(15.832[17]) a = 4.50(4.826[17]) Å	256.0	103.7	0.322	-0,44
	MgNi 3 P m 3m(221)	a = 3.72(3.7163[17]) Å	264.3	96.68	0.337	-0.34
	MgNi 5 Cmmm(65)	Å a = 3.40 Å ; b = 10.24 c = 3.38 Å	280.8	115.6	0.319	-0.25
	MgNi 7 Cmcm(63)	Å a = 4.78 Å ; b = 13.56 c = 4.78 Å	163.1	74.30	0.302	-0.19
	MgNi 11 C2/m(12)	Å c = 7.16 Å ; β = 125.1 • a = 8.25 Å ; b = 4.77	326.9	121.4	0.335	-0.13

  ), three new compositions in addition to known Mg 2 Cu and MgCu 2 intermetallics, and an alternative structure for Mg 2 Cu were found. For this system, all predicted structures exhibit reasonable geometry and are also determined to be stable (see table2). Calculated values of the elastic moduli for MgCu and MgCu 2 in

		0			M g 3 C u M g 2 C u	M g C u		M g C u 2 M g C u 3
	Enthalpy of formation (eV/atom)	-0.3 -0.25 -0.2 -0.15 -0.1 -0.05	0 GPa 10 GPa 20 GPa 30 GPa			I4/mmm Fddd
		-0.35	40 GPa
		0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
					Composition ratio : Cu/(Mg+Cu)

Figure 2: Stability of predicted structures in the Mg-Cu system with respect to pressure

table 2 differ from those reported in the references

Table 2 :

 2 Calculated enthalpies of formation, structural and elastic parameters of stable and metastable phases in the Mg -Cu system at 40 GPa

	Structure and Space group	Lattice parameters	B (GPa)	G (GPa)	ν	∆H (eV/atom)
	Mg 3 Cu P 6 3 /mmc(194)	a = 5.30 Å ; c = 4.25 Å	152.1	50.12	0.352	-0.197
	Mg 2 Cu I4/mmm(139)	a = 2.95 Å ; c = 8.64 Å	161.2	79.02	0.289	-0,261
	MgCu P m 3m(221)	a = 2.85 Å ; a = 3.16 Å	326.9	121.4	0.335	-0.338
	MgCu 2 F d 3m(227)	a = 6.49 Å	220.4	84.89	0.329	-0.237
	MgCu 3 I4/mmm(139)	a = 3.49 Å ; c = 7.03 Å	228.8	79.56	0.344	-0.233

Table 3 :

 3 Enthalpy of absorption, structural and elastic parameters of predicted hydrides

	Structure and Space group	Lattice parameters	B (GPa)	G (GPa)	ν	∆H(eV/atom)/ (kJ mol -1 • H 2 )
	MgNi 3 H 2 P 3 1 21(152)	a = 5.30 Å c = 6.47 Å	31.83	24.96	0.189	-0.134 / -77.7
	MgCuH 3 P 3 2 (145)	a = 4.92 Å c = 7.41 Å	139.3	71.93	0.280	-0.00971 / -0.312
	efficient way to visualize changes in electron density upon hydrogen insertion into alloys. It is obtained
	by calculating the difference in charge density between the hydride and the same hydride structure with
	hydrogen atoms removed.

Acknowledgment

The authors thank the Centre de Ressources Informatiques of the Universit de Sciences et Technologies de Lille (CRI) for computational facilities. Furthermore, N.K. would like to thank the Fonds der Chemischen Industrie for a Liebig and a doctoral fellowship (Li 197/02).