Guillaume Gravier
email: guillaume.gravier@irisa.fr

Claire-H Él Ène Demarty

Siwar Baghdadi

Patrick Gros

Classification-oriented structure learning in Bayesian networks for multimodal event detection in videos

We investigate the use of structure learning in Bayesian networks for a complex multimodal task of action detection in soccer videos. We illustrate that classical score-oriented structure learning algorithms, such as the K2 one whose usefulness has been demonstrated on simple tasks, fail in providing a good network structure for classification tasks where many correlated observed variables are necessary to make a decision. We then compare several structure learning objective functions, which aim at finding out the structure that yields the best classification results, extending existing solutions in the literature. Experimental results on a comprehensive data set of 7 videos show that a discriminative objective function based on conditional likelihood yields the best results, while augmented approaches offer a good compromise between learning speed and classification accuracy.

Introduction

Automatic video analysis is one of the basic tools that enables the development of applications such as multimedia information retrieval or novel TV services. Understanding a video is a multifaceted objective that includes simple tasks like the recovery of the video structure or more complex ones such as the detection of specific events. In this paper, we focus on this last case, i.e., on the ability to detect specific extracts of a video that have a particular, and usually important, meaning for the user. Event detection is particularly important when videos have a weak structure since events are then the only anchors in the stream that allow non-linear browsing.

Events have no general definition and are in general specific to a particular context and application. Most of the time, the application context calls for a high-level semantic definition of an event (a goal in soccer, a dunk in basketball), but the definition may be much fuzzier: An interesting moment, or a moment similar to a set of examples. This suggests two main approaches to build an event detection system. First, a formal definition of the event can be given as a model which is then used for detection. Such approaches are usually based on rules that can be either defined by a human expert (see, e.g., [START_REF] Saraceno | Identification of story units in audio-visual sequences by joint audio and video processing[END_REF], [START_REF] Tovinkere | Detecting semantic events in soccer games: Towards a complete solution[END_REF], [START_REF] Lienhart | Scene determination based on video and audio features[END_REF], [START_REF] Zhong | Structure analysis of sports video using domain models[END_REF]) or inferred from examples as in [START_REF] Perlovsky | Conundrum of combinatorial complexity[END_REF]. Alternately, machine learning techniques can be used to train a system from examples with the goal of deciding whether a video extract contains the event or not. These approaches heavily rely on classification techniques, be they probabilistic (see, e.g., [START_REF] Huang | Integration of multimodal features for video scene classification based on HMM[END_REF], [START_REF] Xu | Motion based event recognition using HMM[END_REF], [START_REF] Mizutani | Commercial detection in heterogeneous video streams using fused multi-modal and temporal features[END_REF] or not (e.g., [START_REF] Bae | Semantic event detection in structured video using hybrid HMM/SVM[END_REF], [START_REF] Snoek | Multimedia event-based video indexing using time intervals[END_REF], [START_REF] Haering | A semantic event-detection approach and its application to detecting hunts in wildlife video[END_REF]). The goal of these classifiers is to establish a relation between what can be extracted from the videos, i.e., low-level multimodal features, and the event. Their performance is thus closely linked to their ability in finding the best combination of features and to derive a decision rule that allow discriminating the positive examples with an adequate level of generalization.

We focus here on probabilistic approaches to event detection which are, for the most part, based on the Bayesian theory. One of the interests of statistical models is that they allow to easily take into account the correlations between features and the temporal aspect of the videos. The variety of statistical models used in multimedia analysis includes naive Bayes classifiers, decision trees, Bayesian networks-often in a naive Bayes way-and hidden Markov models (HMMs). In particular, HMMs and their variants have been extensively used for event detection in videos, with a wide range of applications from commercial detection [START_REF] Mizutani | Commercial detection in heterogeneous video streams using fused multi-modal and temporal features[END_REF], video genre classification [START_REF] Gibert | Sports video classification using HMMs[END_REF] to structure analysis in videos [START_REF] Kijak | Audiovisual integration for tennis broadcast structuring[END_REF][START_REF] Qian | Soccer video event detection by fusing middle level visual semantics of an event clip[END_REF]. Hidden Markov models are well adapted to dense segmentation where every shot correspond to some well-defined event but not particularly suited for sparse event detection. Moreover, the model assumes that all observations are part of a single observation vector. This assumption is not well adapted to videos, in which several modalities are combined. Multistream extensions of the HMM framework have been proposed in audiovisual speech recognition, with application to multimedia analysis [START_REF] Huang | Integration of multimodal features for video scene classification based on HMM[END_REF][START_REF] Kijak | Audiovisual integration for tennis broadcast structuring[END_REF]. However, recent work on segmental multistream HMMs for tennis video structuring [START_REF] Delakis | Audiovisual integration with segment models for tennis video parsing[END_REF]) demonstrated the necessity of modeling the dependencies between features. Unfortunately, knowing which dependencies to model, and how, is not an easy task and requires a lot of human expertise, if possible at all. This paper therefore focuses on the necessity for algorithms to learn statistical dependencies between variables in a large set of variables, along with the corresponding model.

In this regard, Bayesian networks (BN) define a general framework for probabilistic modeling which encompasses all of the above mentioned models, including HMMs and segment models using so-called dynamic Bayesian networks [START_REF] Murphy | Dynamic Bayesian networks: representation, inference and learning[END_REF]. A Bayesian network, dynamic or not, is a directed acyclic graph (DAG) where nodes represent random variables and links represent the causal relations between variables, thus allowing for a wide variety of topologies and offering flexibility. Moreover, BNs have shown to be adapted to multimodal fusion in the framework of video analysis [START_REF] Huang | Semantic analysis of soccer video using dynamic bayesian network[END_REF][START_REF] Lakka | A Bayesian network modeling approach for cross media analysis[END_REF]) with application in event detection, for example in soccer videos [START_REF] Wang | Dynamic Bayesian network based event detection for soccer highlight extraction[END_REF] or in Formula 1 car races [START_REF] Petkovic | Multi-modal extraction of highlights from TV Formula 1 programs[END_REF].

Certainly one of the most appealing features of the Bayesian network theory is the ability to learn the structure of the graph that links together all the variables considered. In other words, one can learn the structure of the DAG in addition to the parameters of the model, a fact never satisfactorily achieved with HMMs. The main interest for structure learning is to avoid resorting to human expertise and heavy trial and error experimental protocols to define the best statistical model, yet avoiding unnecessary assumptions on the data such as the state conditional independence assumption for HMMs.

Several algorithms for structure learning in BNs, such as the K2 algorithm [START_REF] Cooper | A Bayesian method for the induction of probabilistic networks from data[END_REF], have been proposed in the literature. In particular, score based approaches seek to maximize an objective function that reflects a trade-off between the best fit of the training data and the generalization capabilities of the model. However, such algorithms are seldom used in the multimedia area where naive networks predominate [START_REF] Nefian | A coupled HMM for audio-visual speech recognition[END_REF].

Note however the work of [START_REF] Choudhury | Boosting and structure learning in dynamic Bayesian networks for audio-visual speaker detection[END_REF]; [START_REF] Friedman | Using Bayesian network to analyze expression data[END_REF]; [START_REF] Baghdadi | Structure learning in Bayesian network based video indexing[END_REF] which investigate structure learning successfully on rather simple tasks.

In this paper, we investigate the use of structure learning algorithms for a rather complex multimedia task which consists in detecting action shots in soccer videos from multimodal input. To the best of our knowledge, this constitutes the first attempt in the multimedia area to use BN structure learning algorithms on a large scale complex task. We illustrate that classical score-oriented structure learning algorithms such as the K2 one, whose usefulness has been demonstrated on simple tasks, fail at providing a good network structure for classification tasks where many correlated observed variables are necessary to make a decision.

We then compare several structure learning objective functions, which aim at finding out the structure that yields the best classification results, extending existing solutions in the literature. All structure learning algorithms are evaluated and compared on a realistic task, namely action detection in soccer videos from multimodal input, using a comprehensive data set of 7 games.

The paper is organized as follows. Section 2 defines Bayesian networks more formally and present classical structure learning strategies. In section 3, we exhibit a case where the K2 algorithm performs poorly and discuss the reasons for this. We then propose new objective functions oriented towards the classification goal in section 4 and provide an experimental comparative study in section 5.

Bayesian networks and structure learning

A Bayesian network can be seen as a graphical representation of a probabilistic distribution over a set of random variables, where the graphical representation depicts the causal relations between the variables. As with any classification model, using Bayesian networks faces two issues: inference and training. Inference aims at making a decision (as to whether or not the event considered is present in our case) based on the evidences, or observations, available, given a network. Training includes two usually distinct phases, namely the design of the model and the estimation of the parameters from examples given the structure. We first formally define Bayesian network and briefly discuss the inference issue, before discussing model design issues and presenting the general principles of structure learning in Bayesian networks.

a. Definition and inference

Formally, a Bayesian network is a statistical model of a set of random variables, representing relations between variables such as conditional independence or causality. A network can be represented as a graphical model, i.e., a direct acyclic graph (DAG) G where each node X i is a random variable, arcs representing a relation of conditional dependence between the two variables at stake. In other words, the arc X i → X j indicates that X j depends on X i . Assuming random variable taking values in a discrete observation space, a probability distribution table is associated to each node X i of the DAG to describe the probability of the random variable taking a value conditionally on the value of the set P i made of the parents of node X i , i.e. P i = {X j s.t. X j → X i }. Hence, the network encodes the relations within the set of random variables considered, {X i }, and can be used to factor the total probability of the collection according to

P [X 0 , X 1 , . . . , X n ] = n i=0 P [X i |P i ] , (1)
where P i denote the set of variables corresponding to the parents for node i, i.e., the set of random variables upon which X i is dependent.

A simple example of a Bayesian network is illustrated in Fig. 1, where the three variables X 1 , X 2 , X 3 are all independent conditionally on the knowledge of X 0 . The total probability can therefore be decomposed as

P [X 0 , X 1 , X 2 , X 3 ] = P [X 0 ]P [X 1 |X 0 ]P [X 2 |X 0 ]P [X 3 |X 0 ] .
As can be seen, a Bayesian network over a given collection of random variables is fully defined by its structure, i.e., the topology of the direct acyclic graph, and by the conditional probability tables (CPT) at each node. In practice, Bayesian networks are mostly used to make decisions based on the inference of the value of unobserved variables given the observed ones. For example, in the framework of multimedia content classification that we are studying, one is interested in inferring the class value given observations. This can be done using so-called naive structures as the one depicted in Fig. 1 where X 0 represents the unknown class to be inferred-here, a binary class stating whether an event is present or not-given observations X 1 , X 2 , X 3 . Inference algorithms, such as [START_REF] Kim | A computational model for causal and diagnostic reasoning in inference systems[END_REF] and [START_REF] Jensen | Bayesian updating in recursive graphical models by local computations[END_REF], are the key to solving marginalization or posterior problems so as to find an optimal configuration for unobserved variables.

b. Graphical model design

Apart from the inference issue, model design is a crucial step in implementing a Bayesian network classifier. Model design can be seen as a two-step process where the first step consists in defining the topology of the model while the second one relates to the estimation of the conditional probability tables from training data.

Maximum likelihood approaches have been designed for parameter estimation in a variety of networks, exploiting the factorization of the total probability in the network [START_REF] Heckerman | A tutorial on learning with Bayesian networks[END_REF][START_REF] Ghahramani | Adaptive Processing of Sequences and Data Structures[END_REF][START_REF] Murphy | Dynamic Bayesian networks: representation, inference and learning[END_REF]. For simple networks such as the ones considered in this study, with discrete variables, all of them observable in the training data, maximum likelihood estimation boils down to estimating conditional probabilities with empirical frequencies.

On the contrary, only a few algorithms have been proposed for the estimation of an optimal graph topology given training data. Moreover, these algorithms are seldom used in practice for real-life classification problems such as the one targeted here. Approaches to structure learning can be grouped into two main approaches. The first one consists in using statistical dependency tests to search for causalities between variables, such as in the IC and SGS algorithms [START_REF] Pearl | A statistical semantics for causation[END_REF][START_REF] Spirtes | Causation, Predection and Search[END_REF]). The second family groups methods targeting the optimization of a score that evaluates the quality of a structure. Several scores have been proposed in the literature, along with efficientbut suboptimal-strategies to review a large set of candidate structures to choose from.

For example, restricting the possible set of structures to trees, one can search for the best tree structure using the maximum weight spanning tree (MWST) algorithm [START_REF] Kruskal | On the shortest spanning subtree of a graph and the traveling salesman problem[END_REF]), assuming the availability of a causality score between any two variables [START_REF] Chow | Approximating discrete probability distributions with dependence trees[END_REF][START_REF] Heckerman | A tutorial on learning with Bayesian networks[END_REF]. For structures more general than trees, most algorithms, including the popular K2 algorithm [START_REF] Cooper | A Bayesian method for the induction of probabilistic networks from data[END_REF] and its variants, imposes an ordering on the nodes such that the set of possible parents for a given node is limited to those nodes with a higher rank, thus drastically reducing the search space. Finally, greedy search heuristics were also proposed in the literature for efficient exploration of the space of all possible structures [START_REF] Chickering | Learning Bayesian networks: Search methods and experimental results[END_REF].

Most score-oriented structure learning algorithms exploit a score which seeks for a tradeoff between accurately modeling the training data and obtaining a low complexity network.

In particular, a popular score function which derives from a simplification of the K2 algorithm, is the Bayesian information criterion (BIC) for which the objective function to optimize is given for a graph G over N variables by

Q BIC (G) = ln P G [X] - λ 2 C(G) ln(K) = N i=0 ln P [X i |P i ] - λ 2 C i (G) ln(K) (2)
where K is the number of training examples, X is the set of variables, C(G) is the total number of free parameters in the network and C i (G) is the number of free parameters in node i. As explicitly shown in the above equations, the objective function is decomposable as a sum over all nodes of the network, thus limiting the amount of computation to get a new score when the structure is changed.

However, this approach suffers from severe drawbacks in a complex classification task, in particular because of the fact that the objective function is oriented towards description of the data, rather than towards optimal prediction. Indeed, in classification networks, the classification node, denoted X c in the sequel, plays a particular role and should be treated differently. Few criteria were proposed for the purpose of classification. The tree augmented network (TAN) consists in augmenting a naive network with a tree structure using a MWST algorithm [START_REF] Geiger | An entropy-based learning algorithm of Bayesian conditional trees[END_REF][START_REF] Friedman | Bayesian network classifiers[END_REF]). More recently, [START_REF] Grossman | Learning Bayesian network classifiers by maximizing conditional likelihood[END_REF] proposed to use the conditional likelihood-i.e., conditionally to the classification node-rather the likelihood in the objective function.

In the next section, we study the use of the Bayesian information criterion as an objective function to learn the structure for the task of event detection in soccer videos and show the limitations of likelihood-based objective functions in this case. A classification-oriented objective function is proposed in section 4 and compared to the TAN algorithm and to a K2 augmented network.

Limitations of K2 structure learning for soccer video indexing

In preliminary work, we demonstrated the benefit of using Eq. 2 as the objective function for structure learning in the task of multimodal advertisement detection in videos [START_REF] Baghdadi | Structure learning in Bayesian network based video indexing[END_REF]). Elaborating on these results, the same structure learning paradigm is here applied to a more complex task, where more variables are to be considered, namely the detection of actions in soccer videos based on low-level audio and visual features.

We first describe the task and experimental protocol that is used throughout the paper before presenting results which demonstrate that K2 fails at such a complex classification task.

a. The action detection task in soccer videos

We consider the task of detecting actions in soccer videos, where an action is defined as a period of time in the match when a player is about to shoot to score. Such an action usually takes place near the goal mouth and comes with the cheering of the crowd and an excitement of the speaker, thus requiring multimodal input. Some replays of the action also usually follow. Action detection in soccer video is a complex task which requires that multiple features be considered simultaneously, thus being far more challenging for structure learning algorithms than previous case studies. In particular, in comparison with advertisement detection, the number of features required to accurately identify actions is greater and no straightforward features such as monochrome frames are available.

In this work, detection is performed at the shot level, all videos being automatically segmented into shots. From each shot, the following set of 8 binary audio and visual features is automatically extracted, a value of one indicating the presence of the feature:

i. crowd excitement: this feature usually is strongly related with a noticeable event;

ii. transition shot: some transition effects, classically detected by the shot segmentation algorithm, are usually added to increase the attractiveness of an event;

iii. wide shot: a shot is classified as wide based on the detection of green as the dominant color and on the detection of terraces in the background; iv. lull scene: a lull scene, as opposed to a peak scene, corresponds to a game sequence where nothing special is happening and for which directors usually alternate between However, actions are mostly characterized by the temporal evolution of the features and classification can hardly be performed on the base of a single shot. Hence, the primary features of a shot are augmented with features from the neighboring shots, taking 2 shots of context on the left and right side respectively. This amounts to a total of 40 contextual features which are to be modeled using a Bayesian network classifier. With respect to our previous study, it is important to note that this constitutes a larger set of features. Moreover, features are highly correlated, in particular due to the use of context shots. Finally, it should also be noted that not all features are always directly relevant for the classification task.

Experiments are carried out on a data set of 7 games broadcasted during the 2006 World Cup, amounting to about 14 hours of video. Automatic shot segmentation yielded 9,632 shots in total, among which 192 were labeled by a human expert as action shots (about 2 % of the total number of shots). Table 1 provides details on a per video basis. Due to the limited number of data available a cross-validation protocol with 7 folds was adopted, retaining one match as test material for each fold. The training set for each fold is used both for structure learning and maximum likelihood parameter estimation, the two being performed jointly regardless of the structure learning criterion used. Results are reported in terms of recall and precision on the action shots, where a shot is deemed to be an action shot if the posterior probability P (X c /X 1 , X 2 , ...X n ) of the classification node is above a threshold. The threshold is varied so as to achieve different trade-offs between recall and precision.

b. K2 structure learning for soccer videos

Following exactly the same methodology as in [START_REF] Baghdadi | Structure learning in Bayesian network based video indexing[END_REF] where the K2 algorithm demonstrated effectiveness for advertisement detection, the K2 algorithm using the score function given in Eq. 2 was first used for event detection in soccer video. The structure was initialized using the MWST algorithm of [START_REF] Chow | Approximating discrete probability distributions with dependence trees[END_REF], taking the classification node X c as the root for the tree. Node ordering in the K2 algorithm was derived from the tree structure obtained from the initialization step.

Results are reported in Fig. 2 and compared with a naive structure. Contrarily to previous results on advertisement detection, the K2 structure fails at capturing the complex relations between variables, resulting in poorer performance than the naive structure. This result is counter-intuitive as one would expect the model to benefit from taking into account the correlations that might exist between variables. An example of a structure learned from the data is given in Fig. 3, where variables were assigned arbitrary numbers, and illustrates two important points regarding the behavior of the K2 algorithm. On the one hand, structure learning succeeds to some extent in capturing the relations between variables, resulting in a network structure rather different from the naive one. This structure nevertheless remains difficult to interpret, even with some expert knowledge in soccer. But, most of all, it also appears that only a few feature (observed) nodes are directly connected to the event classification node (red links), contrary to the naive network where, by definition, all features are connected to X c . This last observation is the key to understanding the poor results obtained with structure learning when, contrarily to the advertisement detection use case, a large number of variables is at stake. Indeed, for a graph structure G, the likelihood term in the score function Q BIC can be rewritten as

ln P G [X] = ln(P G [X 1 , ..., X n ]) + ln(P G [X c |X 1 , ..., X n ]) . ( 3
)
From this formulation, it can be seen that as the number n of observed variables increases, the first term on the right hand side of the equality decreases rapidly. Since the second term does not depend on n, structure learning with a large number of variables is dominated by the maximization of the term ln(P G [X 1 , ..., X n ]), regardless of the class node X c . The result is a structure that represents the relationships between the observed variables, regardless of their impact on the classification task considered.

These preliminary results show that for classification tasks with a large number of observed variables, structure learning algorithms searching for a trade-off between the best fit of the data and the complexity of the resulting model are not suited. A solution to skirt this issue is feature selection so as to limit the number of observed variables, a solution that has proven experimentally valid. However, feature selection might result in information loss. An alternate solution consists in using objective functions for structure learning that account for the specificity of classification tasks, paying special attention to the peculiarity of X c .

Classification-oriented structure learning algorithms

Two main strategies can be envisioned to learn the structure of a Bayesian network for classification. The first one consists in forcing relations between the observed variables and the classification node, leaving structure learning to the sole relations between observed variables. The second one consists in explicitly accounting for classification issues in the objective function. The first option benefits from an easy implementation but is suboptimal, while the second one is optimal but difficult to implement because most classification-oriented objective functions are not decomposable.

For each of the two strategies, an efficient algorithm for Bayesian network structure learning in the framework of classification is proposed. Firstly, pursuing the philosophy of the tree augmented network structure learning algorithm of [START_REF] Friedman | Bayesian network classifiers[END_REF], we impose constraints on the optimal structure, forcing all observed variables to be directly related to the classification node. This strategy yields a K2 augmented network structure which is still learned based on the likelihood-complexity trade-off. Secondly, a discriminative objective function [START_REF] Grossman | Learning Bayesian network classifiers by maximizing conditional likelihood[END_REF] is used in replacement of the K2 likelihood based one. Unfortunately, this new objective function is not decomposable over the set of nodes in the network and we resort to genetic algorithms for greedy optimization.

a. K2 augmented structure

As naive networks have proven successful for classification tasks on many an occasion, [START_REF] Friedman | Bayesian network classifiers[END_REF] proposed to augment the naive structure by adding arcs between observed variables using a MWST algorithm to generate a tree structure between the observed nodes. A score based on the mutual information between each pair of nodes, conditionally on X c , was used as input to MWST computation. This algorithm therefore results in a structure where each observed node has two parents: the classification node and another feature node.

Restricting the search of the structure to the set of trees clearly limits the complexity of the structure learning process. However, the relative simplicity of the resulting structure has also some drawbacks. First the tree structure will not allow to have connections between more than two features nodes, a fact that is likely to appear when a large set of variables is used. This is particularly true in our case because of the use of contextual features from the neighboring shots in the description of each shot, likely to be highly correlated one to another. Additionally, accounting for features not related to any other (i.e., a feature that should exhibit a unique connection to X c ) is impossible.

As a workaround, we propose to augment the naive structure using K2 structure learning with the BIC criterion, thus extending the tree augmented network philosophy. Using K2 structure learning to augment the naive structure clearly enlarges the set of possible structures, enabling more complex structures that do not suffer from the limitations stated.

K2 augmented structure learning relies on a modified version of the Bayesian information criterion which accounts for the compulsory link between each feature and the event node.

Formally, the objective function is defined as

Q (c) BIC (G) = N i=0 ln P (X i |P i , X c ) - λ 2 C(X i , G) ln(K) , (4)
and remains decomposable, thus making it possible to use the same efficient exploration strategy based on node ordering as for the initial K2 algorithm described in section 3.

b. Discriminative objective function

Even if the classification goal is explicitly considered in Eq. 4, the rationale still consists in finding the structure that best fits the training data, subject to the simplicity of the structure. Given a large number of observed variables, this structure might still be dominated by the search for a good explanation of the relations between features rather than by the search for the structure that best classifies the data. We therefore propose a new structure learning criterion with the goal of directly maximizing the class conditional probability P [X c |X 1 , ..., X n ] rather than the joint probability P [X c , X 1 , ..., X n ]. The use of the class conditional probability was introduced in [START_REF] Greiner | Structural extension to logistic regression: Discriminative parameter learning of belief net classifiers[END_REF] for parameter estimation and studied in [START_REF] Grossman | Learning Bayesian network classifiers by maximizing conditional likelihood[END_REF] for structure learning using the BNC algorithm.

We detail here a variant of the BNC algorithm using a genetic algorithm to explore the space of possible network structures.

As in [START_REF] Grossman | Learning Bayesian network classifiers by maximizing conditional likelihood[END_REF], the objective function for structure selection is defined as

Q CLL = N i=1 ln P G [X c |X 1 , ..., X n ] . (5)
Unfortunately, the discriminative score is not decomposable and cannot be written as a sum of local scores calculated separately for each node. We therefore resort to a genetic algorithm in order to explore the set of possible structures. Genetic algorithms are iterative algorithms that require an initial structure as a starting point. From this initial structure, a set of candidate structures is generated by adding, reverting or deleting one single arc. The discriminative score is calculated for each of the structures resulting from these mutations and the one that maximizes the score-given maximum likelihood estimates of the parameters-is then chosen as the starting point for the next iteration. The algorithm stops if none of the generated structures increases the score. The choice of the initial structure is crucial and will be discussed along with experimental results in the next section.

Experimental results

Recall vs. precision trade-off curves are plotted in Fig. 4 for the tree and K2 augmented networks as well as for the discriminant objective function. Performance for the naive network is also reported as a baseline. It should be noted that for the K2 augmented network, λ was experimentally set to 3 in Eq. 4.

Results show that the two augmented approaches clearly improve over the naive baseline network. Indeed, by forcing the classification node to be connected to all the feature nodes, these techniques build a structure which benefits from the whole feature information, as with the naive Bayesian network, while also taking into account correlations between the features themselves. Moreover, the K2 augmented method provides better results than the TAN approach for the classification task, due to the fact that the resulting network is less constrained in the K2 augmented case. This allows for more flexibility to take into account the correlations between several features when they exist, or on the contrary to avoid nonrelevant connections between features when this is not needed, a fact that is crucial in such a complex classification task as the one we are targeting. Finally, the classification-oriented approach based on a discriminative objective function actually outperforms all techniques.

The maximization of this new score, dedicated to the classification task, is one explanation for these good results, the other being the absence of format restriction in the choice of the final structure. The resulting network will therefore better describe the correlations between the classification node and the features. An analysis of the resulting structure with this classification-oriented scheme is proposed in the following section.

An example of a structure obtained with the classification-oriented objective function is shown in Fig. 5, where node 1 corresponds to the classification node. An analysis of this structure highlights the few number of nodes used for the classification process: 13 nodes are directly connected to the classification node (red links) and 10 additional nodes are indirectly used. A total of 17 nodes was therefore rejected from the final structure, as non relevant for the classification task at hand. Connections with these nodes were indeed not increasing the discriminative score and the algorithm therefore applies implicit feature selection. It is interesting to note that implicit feature selection cannot, by construction, occur in augmented techniques. This reduction of the structure size consequently results in a more reliable parameter learning step, hence in an increased performance for the classification.

As mentioned previously, the choice of the initial point for the genetic exploration of the set of possible structures for the conditional probability maximization is usually of utmost importance. Three initial points were tested, namely naive, TAN and K2 augmented networks. We observed no impact on performance after structure learning. However, training time is significantly affected by the initialization point, as reported in Tab. 2. The much reduced training time when starting from one of the augmented structure highlights the quality of the latter, thus making good starting point for the genetic algorithm.

Conclusion

Taking action detection in soccer videos as a use case for multimodal event detection, we have shown how structure learning in Bayesian networks, associated with the adequate objective function, can efficiently detect complex multimodal events in videos. We have demonstrated that, while using an information criterion for structure learning in BNs suffers major drawbacks for complex classification tasks with a large number of correlated observed variables, classification-oriented objective functions can efficiently deal with such matter. In particular, we proposed a new K2 augmented network structure and a genetic implementation of the conditional likelihood objective function which both turned to outperform state-ofthe-art structure learning methods. Experimental results however call for a few remarks and suggestions for further work.

Firstly, we observed that the ability to select relevant variables, i.e., to decide that some variable has no direct or indirect relation with the classification node, is crucial. While the conditional likelihood criterion embeds feature selection, it is not the case for the BIC and augmented approaches which might benefit from explicit feature selection. However, we believe that embedding structure learning and feature selection is better suited than performing feature selection as a required preliminary step to structure learning.

Secondly, we considered that the observed variables directly contribute to the classification if at all. In other terms, we only have two types of variables, the observed ones and the classification node. For complex classification tasks, it appears interesting to consider hidden variables which act as intermediate concepts between the observation and the decision.

We are convinced that training such networks will help improve the structure inferred and thus classification by summarizing complex information from the features in a few concepts.

However, extensions of the existing structure learning algorithms to handle hidden variables are required to do so.

Finally, the temporal dimension of videos was limited in this work to the use of contextual features from the neighboring shots, classification being performed on a per shot basis.

As for shot-based classification, learning the temporal structure of the video with a goal-

oriented

  wide shots and other shots to maintain the dynamics of the video. The detection of such scenes is mostly rule based, relying on the result of the classification of shots into wide or not; v. presence of face: shots containing mostly a face, as indicated by a face detection algorithm, are likely to be close-up which are strongly related to action; vi. green shot: shots where the green color is sufficiently present are marked as so to indicate whether the field is visible or not; vii. replay logo: this feature indicates the presence of a replay logo which indicates the start or end of a replay sequence; viii. goal mouth: this indicates whether the goal mouth is visible or not, thus acting as an indicator of the action importance.

Fig. 3 .

 3 Fig. 3. Structure obtained with K2 structure learning, where red links denote direct connections between X c (node 1 in the picture) and the observed variables.

Fig. 5 .

 5 Fig. 5. Example of a structure resulting from the use of the discriminative objective function.

Table 1 .

 1 objective function is likely to improve classification performance and requires further investigation. Directly learning the structure of a dynamic BN is intractable, except in some rare cases. Combining BNs and segmental HMMs appears like a plausible alternative, where the structure and parameter of BNs are trained to predict the posterior probabilities required for Viterbi decoding in segmental HMMs. Number of shots, number of action shots and total duration of the video per game. Note that the Germany -Portugal video was truncated but kept as is.

	Game	#shots #action duration
			shots	of video
	Germany -Argentina	1,983	20	2h52
	Saudi Arabia -Ukraine 1,234	27	2h01
	France -Brasil	1,736	30	2h10
	Germany -Italy	1,490	38	2h33
	Italy -Ukraine	1,181	23	1h52
	Germany -Portugal	694	17	1h00
	Brasil -Ghana	1,122	37	1h56
	Total	9,440	192	14h24

Table 2 .

 2 Impact of the initial structure on the learning time of the discriminative approach. Recall vs. precision trade-off curves comparing the K2 (red) and naive (blue) Structure obtained with K2 structure learning, where red links denote direct connections between X c (node 1 in the picture) and the observed variables. 33 4 Recall precision trade-off curves for i) a naive Bayesian network (dark blue),ii) a tree augmented network (green), iii) a network resulting from the K2 augmented technique (red) and, iv) a discriminatively trained network (light Fig. 1. Example of a simple Bayesian network with four variables.

	structures.

Acknowledgments

This work was partially funded by OSEO, French state agency for innovation, in the framework of the Quaero project.

List of Tables


Guillaume Guery
email: gguery@clemson.edu

J David Musgraves

Christine Labrugere

Evelyne Fargin

Thierry Cardinal

Kathleen Richardson

Evolution of glass properties during a substitution of S by Se in Ge 28 Sb 12 S 60-x Se x glass network

Keywords: Chalcogenide glass, Raman spectroscopy, X-ray photoelectron spectroscopy, Glass properties

In this paper, a detailed study to examine the influence of chalcogen S/Se mole % in the Ge 28 Sb 12 S 60-x Se x glass system, with x=0, 15, 30, 45 and 60, is presented that provides insight into the effect of chalcogen content on the glass network and properties. Specifically, we report results of a systematic study to evaluate the relationship between compositional variation, glass properties and dominant bonding configurations. These materials are important to applications in optics manufacturing where correlation of physical and optical properties is required to predict fabrication behavior and ultimate material performance. It has been found that the dominant bonds in the glass system change upon reaching a specific molar ratio (percentage, %) of chalcogen substitution, between 30<x<45 mol %, changing from Ge-Se to Sb-Se bonds as the dominant bond type. This singularity has been observed using micro-Raman spectroscopy and X-ray photoelectron spectroscopy. This effect of the dominant bond configurational change was also shown to impart changes in important physical properties including micro-hardness, thermal properties, and the glass' viscometric behavior. Results indicate that the observed dominant bond change was responsible for a constant value in the evolution of both the micro-hardness and calorimetric glass transition temperature. The viscosity was also affected by the change in dominant bond type, breaking the monotony of the viscosity evolution during the S substitution, due to the total strength of the vitreous system which doesn't linearly increase.

Introduction

Chalcogenide glasses (ChG's) have attracted the attention of many investigators due to the fact that they are used in applications for infrared optics, reversible optical recording, photonic devices, memory switching [1,2] and more recently, in precision glass molding (PGM) [3]. Additionally, selenide and sulfide-containing ChG materials have been identified as possible materials for nonlinear optical applications. Several investigations [4][5][6][7][8] have evaluated the difference in physical and optical properties between both chalcogen systems (based solely on sulfur or selenium), but these works have not systematically investigated the influence of S substitution for Se on the structure and glass properties yet. glasses and the influence of Se for S substitution on the linear and nonlinear optical properties of the material. These compositions were largely in the Ge 23 Sb 7 S x Se 70-x (written here as 23-7-70) composition space, which is lower in Ge content than commercially available Ge 28 Sb 12 Se 60 compositions manufactured by Schott Glass and Amorphous Materials under the trade names IG-5 and AMTIR-3. These latter glasses (IG's and AMTIR compositions) are widely used in commercial optical systems and thus, are of importance to optical designers interested in fabricating precision optical components via conventional (grinding and polishing) or more advanced (precision glass molding, PGM) methods [START_REF] Gleason | An introduction to the Dyna Technologies Inc. precision molding machine[END_REF]. Thus, as optical properties (transmission, refractive index and dispersion) and thermo-mechanical attributes (viscosity, hardness and structural relaxation behavior) of these materials have been shown to vary with chalcogen type, the current study aims to evaluate how S/Se ratio impacted properties important to optical design and manufacturing efforts. This paper examines glasses in the Ge-Sb-S-Se system with high crystallization stability, T>100 o (defined as T x -T g ), and has systematically evaluated physical property changes in the glass associated with a substitution of Se for S in the amorphous network. Glasses in the amorphous system Ge 28 Sb 12 S 60-x Se x with x=0, 15, 30, 45 and 60 have been investigated and the resulting variation in physical properties quantified. Raman spectroscopy and X-ray photoelectron spectroscopy (XPS) have been used to evaluate the modifications in glass structure as S is progressively replaced by Se. A correlation is established between molecular units in the glass network and the corresponding fluctuation of glass properties. The impact of these structural changes on mechanical (micro-hardness) and thermal (viscosity) behavior has also been quantified.

Experimental procedure

Sample preparation

Sulfide glasses in the vitreous system Ge 28 Sb 12 S 60-x Se x with x = 0, 15, 30, 45 and 60 were examined in this study and were prepared in 10 g batches. The glasses were prepared from high purity elements (Ge 99.999% (Alfa Aesar), Sb 99.999% (Sigma-Aldrich), S 99.998% (Aldrich), Se 99.999% (Alfa Aesar)). The starting materials were weighed and batched inside a nitrogen-purged glove box and sealed using a gas-oxygen torch under vacuum into quartz ampoules. The ampoule was then heated for 16 h at between 875 and 925 °C, depending on the glass composition. A rocking furnace was used to rock the ampoule during the melting to increase the homogeneity of the melt. Once homogenized, the melt-containing ampoule was air-quenched to room temperature. To avoid fracture of the tube and glass ingot, the glasses were subsequently returned to the furnace for annealing for 15 h at 40 °C below the respective glass transition temperature, T g , of the glass. The sulfo-selenide glass samples were then cut, optically polished, and inspected visually.

Glass compositions were verified by Energy-dispersive X-ray spectroscopy (EDS) and were found to be identical to the initial concentrations introduced in the batch. No loss of sulfur was observed within the accuracy of the measurement (±2%). X-ray diffraction was carried out on each sample to confirm the amorphous state of the investigated samples.

Property measurements

Raman spectra were obtained using a Senterra (Bruker Optik) micro Raman system using a 785 nm excitation wavelength with a laser power level of 1 mW. The use of this near-infrared (NIR) radiation for Raman excitation was specific to our study, in that excitation was at an energy and power level well below the band gap region for these samples, thus eliminating the possibility of inducing photostructural modification in the glass from the probe beam during measurements. Confirmation that this analysis did not change the glass structure was obtained by repeating the analysis on the same spot twice in a row for each measurement.

XPS data were collected using a VG Scientific 220i-XL ESCALAB system. The non-monochromatized MgKα X-ray source (1253.6 eV) was used to acquire the surveys at 150 eV of constant pass energy and the high-resolution spectra at 20 eV.

Binding energies were referenced to the C(1s) energy at 284.7 eV. Experimental peaks were fitted using Gaussian-Lorentzian mixtures with the "AVANTAGE" software provided by ThermoFisher Scientific. Freshly fractured surfaces were analysed after cleaving the glasses and introducing them immediately into vacuum. The residual pressure in the analysis chamber was in the 10 - 7 Pa range.

In this study, a Shimadzu DUH-211S Micro-hardness tester was used, with a Vickers diamond indenter with a square base and an angle of 136 degrees between opposite faces. A static load of 2000 mN made with a loading rate of 13.3240 mN/min, generating indentations with no residual lateral cracking was used for the experiments; the reported micro-hardness values represent the average of fifteen tests. The diagonal length of indentation was measured after the test and the micro-hardness was then calculated.

The glass transition temperatures (T g ), the onset of the crystallization peak (T x ) and the crystallization temperature (T p ) were determined by Differential Scanning Calorimetry (DSC) at a heating rate of 10 o C/min from 50 to 550 o C using a commercial DSC apparatus (DSC 2920, TA instruments). The instrumental error of all measured values is ±2°C. The measurements were carried out in hermetically sealed aluminium pans. The glass transition temperature (T g ) was taken as the inflection point of the endotherm (obtained by taking the first derivative of the curve), and the crystallization temperature (T p ) at the maximum of the exothermic peak. Crystallization stability, T=T x -T g , was calculated to confirm the vitreous nature of the glasses (T>100 o C) within the temperature ranges examined, permitting glasses to be crystal-free, and maximizing the IR transparency of the specimens.

The glass viscosity properties in the softening region (across the range of Log η = 3.0 -6.0 Pa.s) were measured with a PPV-1000 parallel-plate viscometer from Orton Ceramics. As the sample height changes as a function of time and temperature, a LVDT (Linear Variable Differential Transformer) coil, residing on the compensation arm and attached to the adjacent sample arm, monitors the magnitude and direction of the initial specimen's (4 mm high) height change. The compensation arm is attached via a hollow, fused quartz support rod to an Inconel ® compensation block (12 mm thickness), which houses the sample temperature thermocouple. By attaching the LVDT to an Inconel ® compensation block, system movement and Inconel ® plate expansion are nullified from the LVDT signal. The insulation acts as the top of the furnace in the raised position for experimental measurements. The 1000 °C, Kanthal wound, ceramic fiber-lined furnace can be raised and lowered with a motor to house the glass sample.

Results

The purpose of this study was to investigate the effect of the substitution of S for Se on the glass network in the GeSbbased glasses. Raman spectroscopy and X-ray photoelectric spectroscopy (XPS) have been used to track these structural evolutions during the chalcogen specie substitution. Discussion will be focused on the evolution of the bands in the Raman spectra, related to the evolution of features within the XPS spectra.

The Raman spectra of the investigated glasses are shown below in Figure 1.

The spectrum of the sulphide glass (x=0) in the Ge-Sb system exhibits 4 broad bands with the maximum intensity peaking at around 160, 210, 260 and 330 cm -1 . A vibration at 150 cm -1 is assigned to the F 2 mode of GeS 4/2 groups [START_REF] Kamitsos | [END_REF].

Vibrations between 210 and 260 cm -1 have been attributed to the molecular entities containing fewer than 4 sulfur atoms around Ge centers (the glass is sulfur deficient), and vibrations related to homopolar bonds are clearly observed. A vibration related to the presence of Sb-Sb linkages has been reported at 163 cm -1 [11], while the band at 260 cm -1 is associated by Luvosky et al. to the stretching of Ge-Ge homopolar bonds in the S 3 Ge-GeS 3 units [12]. The main band around 342 cm -1 has been assigned by Sugai et al. to the A 1 symmetric stretching vibration of S atoms in GeS 4 units. The vibration around 375 cm -1 , called the companion A 1 C band, is attributed to edge sharing tetrahedral sites [13]. According to Jackson et al. and also reported by Petit et al., the weak band located around 400 cm -1 may arise from the T 2 mode of corner-sharing GeS 4 units [7]. Bands at 287 and 308 cm -1 have been attributed by Frumarova et al. to E and A 1 modes of SbS 3 units respectively [14].

The spectrum of the sulfur-free selenide glass (x=60) in the Ge-Sb system exhibits three broad bands located around 160, 200 and 260 cm -1 . The first broad band at around 160 cm -1 , contains what are believed to be two convolved peaks. Vibrations at 152 cm -1 correspond to the homopolar bond Sb-Sb in the Se 2 Sb-SbSe 2 molecular unit [11,15]. The vibration at 174 cm -1 is attributed to Ge 2 Se 6/2 [16]. Regarding the second broad band at around 200 cm -1 , three contributions have been reported. The vibration at 192 cm -1 represents the Sb-Se linkage in SbSe 3/2 pyramids [17]. In accordance with Lucovsky and al., the band at 200 cm -1 has been assigned to the ν 1 mode of corner-sharing of GeSe 4/2 [12,18,19]. The frequency at 215 cm -1 is correlated to A C 1 breathing vibration of edge-sharing of Ge 2 Se 8/2 [7]. The vibration at 260 cm -1 is linked to the F 2 vibration of GeSe 4/2 molecular units [18,19]. The vibration located at 280 cm -1 is related to the electronic density of germanium [20]. The frequency at 300 cm -1 is associated to F 2 asymmetric vibration modes of GeSe 4 tetrahedra [17].

When sulfur is replaced by selenium, namely x (% Se) increases, the relative intensity of the bands associated with sulfur, located between 275 cm -1 and 450 cm -1 progressively decrease and new bands appear below 230 cm -1 . Two main bands at 152 and 192 cm -1 emerge, respectively attributed to the homopolar bond Sb-Sb in the Se 2 Sb-SbSe 2 molecular unit, and to Sb-Se linkage in The XPS Sb spectrum in Ge 28 Sb 12 S 60-x Se x (with x = 0, 30 and 60) is represented by a main double peak corresponding to Sb3d 5/2 and Sb3d 3/2 The studied system presents complex spectra due to overlaps of peaks (i.e. Sb3d 5/2 with O1s, Se3p with S2p, Sb4d with Ge3d). The most important result is the shift of the peak to lower energy as the sulfur is replaced for selenium.

Indeed, we can observe in Figure 2, a shift of the peaks during the substitution from 529.3 -528.3 eV (for x = 0) to 528.6 -527.4

eV (for x = 60). The presence of the oxygen contribution is due to oxygen contamination during the batch preparation or during the fresh fracture.

The XPS Ge3d -Sb4d5/Sb4d3 spectrum consists of two bands described by a single Gaussian contribution for Ge3d around 32 eV and by two Gaussians for Sb4d5 and Sb4d3 around 34 -35 eV, as shown in Figure 3. According to the average coordination number <r> = 2.68 as defined by Phillips et al. [21], taking into account that the coordination numbers of Ge, Sb and S is respectively 4, 3 and 2, in agreement with previous investigation mainly Sb 3+ species are expected in the glass matrix as discussed by Jiang et al. for sulfide [22].

In the bulk sulfide glass (x = 0), the peak related to Ge3d is more intense than those for Sb4d5/Sb4d3, whereas during the substitution (x = 30), this tendency changes. Finally in the selenide glass (x = 60), the peak assigned to Sb4d5 is the most intense in the spectrum. Furthermore, the Ge3d peak becomes narrower, with a full width at half maximum (FWHM) changing from 2.17 eV to 1.83 eV.

The Vickers micro-hardness of the investigated glasses is shown below in Figure 4 for the glasses examined. In this glass system, a decrease of the hardness is clearly observed when sulfur is substituted for selenium. This can be explained by the average bond strengths present in the glass (E Ge-Se =230 kJ/mol, E Ge-S =279 kJ/mol, E Sb-Se =225 kJ/mol, E Sb-S =205 kJ/mol, [22,23]), which are higher in the sulfide glasses than in the selenide glass. Similar results were obtained previously in related compositions [7].

Table 1 summarizes the variation in glass transition temperature (T g ), temperature of crystallization onset (T x ), crystallization temperature (T p ) and the crystallization stability (ΔT = T x -T g ) with chalcogen type and ratio. T g and T x decrease during the substitution of S for Se, due to a difference in the bond strengths as noted above. As shown in Figure 5, T g decreases during the substitution with a constant value at 30 -45 mol%. Furthermore, all compositions have a ΔT > 100 o C, which means that glasses have excellent stability against crystallization and no evidence of crystallization was noted in any glasses prepared or measured in this study.

Viscosity of the investigated glasses has been measured between Log η = 3.0 -6.0 Pa.s using a parallel plate viscometer (PPV) and the data are shown below in Figure 6 a). The system isokom, indicating the temperatures at which each glass has a viscosity of 10 5 Pa.s is shown in Figure 6 b). This viscosity region represents the working region, where the glass is soft enough to be manipulated for obtaining different shapes (e.g. fiber, aspherical lens).

Trends in the data points from the PPV measurements indicate that when sulfur is substituted by selenium, the log (viscosity) curve shifts to a lower temperature.

Discussion

The aim of this study was to investigate the effect Se substitution for S on the glass structure and physical properties in Ge-Sb-based sulphide glasses. Raman spectroscopy and X-ray photoelectron spectroscopy were used to evaluate and track the structural modification through systematic substitution of Se atom for S. This discussion will be focused on the evolution of the Raman bands, their features and the relative fraction of various species in the glass network, and will be linked to changes in relevant structure-sensitive thermal and physical properties.

The Ge 28 Sb 12 S 60-x Se x glass system is not a stoechiometric composition. Indeed, in a stoichiometric composition, Sb 2 S 3 and GeS 2 are the primary molecular units and there are no homopolar bonds present. In the present case, all glasses examined are deficient in sulfur (chalcogen) meaning that homopolar bonding of the non-chalcogen species can be expected. Homopolar bonds such as Ge-Ge and Sb-Sb can be assumed to be present, in this case.

As noted ealier, the Raman band at 342 cm -1 decreases whereas the bands at 152 and 192 cm -1 increase during the substitution of sulfur for selenium. This evolution indicates that the fraction of GeS 4 molecular units, which are dominant in the sulfur-rich end of the glass system, decreases and are replaced by Sb-based bonds such as the homopolar Sb-Sb bond and SbSe 3/2 pyramidal units.

X-ray photoelectronic spectroscopy measurements have been performed in order to corroborate the evolution of the glass network suggested by the Raman spectra. Changes of peak intensity seen in Raman spectra, which translate to switch of dominant bonds present in the glass network, is here studied by XPS, showing the evolution of the atomic fraction of each component present in the vitreous system. Focusing on the 530-540 eV range shown in Figure 2, we can observe that the peaks assigned to Sb3d5/2 shift in energy during the chalcogen substitution from 529.3 -528.3 eV to 528.6 -527.3 eV. This shift is due to the change of cation linked to the Sb atoms, i.e. Sb-S to Sb-Se. The 30-40 eV range examined in Figure 3 shows that the intensity ratio Ge3d to Sb4d5 features has changed. Indeed, during the chalcogen substitution, the highest peak intensity shifts from the Ge3d (for x = 0) to the Sb4d5 (for x = 60) feature. The significance of these changes is related to the contribution of each species, indicating a change in the dominant bond type in the glass network [24,25]. Regarding the germanium contribution, based on the width and the area of its peak, we can observe that the FWHM decreases from 2.17 eV to 1.83 eV. Such an evolution is indicative of a narrower distribution of sites for the germanium centers. In the selenium glass (x=60) the site distribution around germanium is the narrowest. The increase of the selenium content tends to limit the distribution of sites for germanium centers and increase the variety of antimony sites. Such a hypothesis is in accordance with the appearance in the Raman spectra of significant Sb-Sb vibration contribution for selenium rich samples, which were not evident in the sulfur rich glass.

This change of dominant bond type in the glass network is at the origin of the glass property modifications exhibited by this family. As shown in Figure 4, the physical properties (i.e. microhardness) are only modestly changed. The micro-hardness slowly decreases during the S substitution, but it can be seen that in the x=30-45 region, a flat evolution appears which reflects a non-linear evolution in the total bond strength in the vitreous system; because the ratio of the different species (GeS 4/2 to SbSe 3/2 )

is not linear with the S substitution, the total bond strength, reflected in the hardness, is not linear.

Thermal properties are also dependent on the nature of the dominant bonds present in the glass network. Figure 5 shows the evolution of the glass transition temperature of the system as function of the atomic percent of Se in the glass. Here we can observe that T g does not decrease monotonically across the composition space. A constant value is present in the x=30-45 region, which again reflects a change in dominant bonds in the network; indeed, as T g represents onset of mobility in the network this temperature is dominated by the majority network structure.

Note again that glasses at x=30 and 45 exhibit similar viscosity behavior, shown in Figure 6 a), and more explicitly in Figure 6 b), indicating the evolution of the specific drawing temperature. This trend is expected, considering again that the strength of the Se bonds is lower than that of the S bonds, and thus require less thermal energy to cause weakening of the glass network and the onset of flow. As soon as the sulfur is present (x=45), the material properties tends to the pure sulfide making a significant break with the behavior of the pure selenide.

Conclusion

In this paper, we have shown that the progressive introduction of Se for S in germanium-antimony based-sulfide glasses does not follow a linear trend of the relative fraction of various species in term of thermal and mechanical properties.

Raman spectroscopy and X-ray photoelectron spectroscopy provided evidence of a clear change of dominant bonds in the chalcogenide glass network, upon substitution of S by Se. This change of dominant bond was correlated to variations in glass properties: decreasing micro-hardness and glass transition temperature with, each time, the same value in x=30-45 region. This observation was also seen into the evolution of the viscosity. We observed that viscosities of Ge 28 Sb

  Prior efforts from Richardson et al. Frumar et al., Giridhar et al., Narasimham et al. have widely investigated GeSbS

SbSe 3 /

 3 2 pyramids. Above x = 15, the intensity of the broad band at 200 cm -1 increases, and at x = 45, two contributions are clearly seen at around 200 cm -1 and 215 cm -1 . These bands may be related to the Sb-Se linkage in SbSe 3/2 pyramids proposed by L. Petit et al. at 192 cm -1 , to the ν 1 mode of corner-sharing of GeSe 4/2 proposed by G. Lucovsky et al. at 200 cm -1 [12], and thus to A 1 C breathing vibration of edge-sharing of Ge 2 Se 8/2 also proposed by L.Petit et al. at 215 cm -1 [7].

Figure 3 :Figure 4 :

 34 Figure 3: High resolution XPS spectrum of Ge3d levels for the investigated a) Ge 28 Sb 12 S 60 , b) Ge 28 Sb 12 S 30 Se 30 and c) Ge 28 Sb 12 Se 60

Figure 5 :

 5 Figure 5: Evolution of the glass transition temperature T g as function of the substitution of S by Se in glass system.

Figure 6 :

 6 Figure 6: a) Evolution of the transition range viscosity behavior in the Ge 28 Sb 12 S 60-x Se x glass system as a function of Se content (x, mol%). b) Evolution of the drawing temperature of Ge 28 Sb 12 S 60-x Se x glass system as function of Se content (x, mol%).

  12 S 30 Se 30 and Ge 28 Sb 12 S 15 Se 45 glasses were switched, due to this change of the dominant bonds. A gap in term of thermal and mechanical properties is observed between the Ge 28 Sb 12 S 15 Se 45 and Ge 28 Sb 12 Se 60 compositions which is related to the formation of different antimony sites and significant formation of Sb-Sb bonds.Figure 1: Raman spectra of Ge 28 Sb 12 S 60-x Se x versus x.. High resolution XPS spectrum of Sb3d 5/2 levels for the investigated a) Ge 28 Sb 12 S 60 , b) Ge 28 Sb 12 S 30 Se 30 and c) Ge 28 Sb 12 Se 60

		a) c) a)						Sb4d5	Ge3d
									529.3
									528.6
	Counts / s Counts / s Counts / s	Normalized Intensity (U.A.)	0.2 0.4 0.6 0.8 1.0		Sb4d3		O1s 530.0	528.3	527.4 Ge 28 Sb 12 S 60	0.2 0.4 0.6 0.8 1.0	Ge 28 Sb 12 S 45 Se 15
			0.0				O1s						0.0
						100 O1s		200	300	400		500	600	0	100	200	300	400	500	600
								Wavenumber (cm -1 )					Wavenumber (cm -1 )
	0 532 532 36 0.0 0.2 0.4 0.6 0.8 1.0 Figure 2: 52 100 200 300 400 500 600 0 0.0 0.2 0.4 0.6 0.8 1.0 Ge 28 Sb 12 S 30 Se 30 Normalized Intensity (U.A.) A Wavenumber (cm -1 ) 52 526 527 528 529 530 531 533 534 Binding Energy (eV) b) 526 527 528 529 530 531 533 534 Binding Energy (eV) 28 29 30 31 32 33 34 35 37 38 Binding Energy (eV) b)	100	200	300 Wavenumber (cm-1)	400	500 Ge 28 Sb 12 S 15 Se 45 600
	Counts / s Counts / s	Normalized Intensity (U.A.)	0.0 0.2 0.4 0.6 0.8 1.0	0	100 Sb4d3	200 Sb4d5 O1s	300 529.2 Ge3d 528.2 400		500 Ge 28 Sb 12 Se 60 600
					O1s		Wavenumber (cm-1)
	534	533		532	531	530	529	528		527	526	52
	38	37	36		Binding Energy (eV) 31 32 33 34 35	30	29	28
						Binding Energy (eV)

Composition T g (°C) T x (°C) T p (°C)


Sophie Tencé

Etienne Gaudin

Olivier Isnard

Bernard Chevalier
email: chevalie@icmcb-bordeaux.cnrs.fr

Magnetic and magnetocaloric properties of the high-temperature modification of TbTiGe

Keywords: Terbium, Ternary germanide, Structural properties, Ferromagnetism, Magnetic structure, Magnetocaloric properties PACS numbers: 61.05.cp, 61.05.F-, 75.25.-j, 75.30.Sg, 75.50.Cc

come

Introduction

The investigation of the isothermal section at 1070 K of the Tb-Ti-Ge system reveals that the structural properties of the ternary germanide TbTiGe are depending on the temperature [1].

In this last reference [1], it was reported that the high temperature (HT) modification (tetragonal CeFeSi-type; space group P4/nmm) was obtained by quenching from the liquid during electric arc furnace melting whereas the low temperature (LT) modification (tetragonal CeScSi-type; space group I4/mmm) was detected in the sample after annealing at 1070 K. But after this last thermal treatment, the two HT and LT phases coexist. These results were confirmed by Welter et al. [2] who have investigated the crystallographic properties of the HT modification (CeFeSi-type) using X-ray diffraction on a single crystal extracted from the ascast ingot of TbTiGe. To date, the crystal structure of the TbTiGe ternary compound adopting the CeScSi-type was determined by X-ray powder diffraction performed on a sample containing a mixture of the two HT and LT modifications [1].

Recently, we have shown that the ternary germanide CeTiGe exhibits a structural phase transition as a function of the temperature, the tetragonal HT and LT modifications adopting respectively the CeScSi-and CeFeSi-type [3]. This behavior is opposite to that previously reported for TbTiGe. It is interesting to note that this structural change influences the magnetic properties of CeTiGe. A decrease of the hybridization coefficient J cf between 4f(Ce) and conduction electrons is evidenced in the sequence LT-CeTiGe (CeFeSi-type)  HT-CeTiGe (CeScSi-type); the HT modification is classified as a non-magnetic strongly correlated electron system [3] as shown by an enhanced Sommerfield coefficient γ = 0.308 J mol -1 K -2 .

More recently, we have shown that the ternary germanide GdTiGe can be obtained as single phase crystallizing in the CeScSi-type by melting of the elements followed by a quenching [4]. This study agrees with that performed on CeTiGe revealing that the HT modification of the RETiGe (RE = rare earth) compounds adopts the tetragonal CeScSi-type.

In this view, it is interesting to obtain as pure phase the crystallographic form of TbTiGe adopting the CeScSi-type and to determine its magnetic properties. We remind that an antiferromagnetic ordering around 286-288 K was reported for TbTiGe crystallizing in the tetragonal CeFeSi-type [5][6][7]. In this paper, we report on the synthesis of the two forms HT and LT of TbTiGe. The first one (CeScSi-type) was much less investigated in the past, we consequently present a more detailed study of this HT form, using X-ray and neutron powder diffractions, specific heat and magnetization measurements. Also, the magnetic structure and the magnetocaloric properties of this HT modification of TbTiGe are determined and discussed in relation to those reported previously for the LT modification showing an antiferromagnetic behaviour.

Experimental

Sample with the following composition 32 % Tb: 35 % Ti: 33 % Ge as atomic ratio percentage was prepared by melting precisely weighted amounts of high purity elements Tb, Ti and Ge (99.9 %) in a levitation induction furnace. This starting composition was deduced from the phase equilibrium in the Tb-Ti-Ge system [1] in order to inhibit the presence of Tb 5 Ge 3 or Tb 5 Ge 4 (ordered magnetic compounds) in the final sample. Melting was performed several times to ensure a good homogeneity, in a water-cooled copper crucible, under a purified argon atmosphere. The weight losses during the overall melting process were less than 0.1 wt. % and finally the as-cast sample (HT-TbTiGe) was quenched by switching off the power supply. Then, the annealed sample (LT-TbTiGe) was obtained after thermal treatment of a part of the as-cast sample enclosed in evacuated quartz tube at 1073 K for seven weeks.

No reaction between the sample and the quartz tube was observed.

Both the composition and homogeneity of the as-cast and annealed samples were checked by microprobe analysis using a Cameca SX-100 instrument. The analysis was performed on the basis of intensity measurements of Tb-Lα 1 , Ti-Kα 1 and Ge-Kα 1 X-rays emission lines, which were compared with those obtained for the high purity elements Tb, Ti and Ge used as reference materials.

X-ray powder diffraction was performed with the use of a Philips 1050-diffractometer (Cu-K radiation) for the characterization of the structural type and for the phase identification of the as-cast and annealed samples. To determine the crystal structure of HT-TbTiGe, X-ray patterns were recorded at room temperature with a high-resolution Bruker D8 powder diffractometer in transmission geometry (10° < 2θ < 100°, step size of 0.02°). It operates with a focusing Ge(111) monochromator selecting the Cu-K 1 radiation and eliminates the fluorescence by using a Moxtek-type solid state detector.

Neutron diffraction experiments were carried out at the high flux reactor of the Institut Laue Langevin. (Grenoble, France) using the high flux powder diffractometer D1B operated by the French CNRS. The neutron diffraction patterns as function of temperature were obtained in the range of 1.5 to 310 K. The neutron wavelength of 2.52 Å was selected. All powder neutron diffraction data were analyzed using the Rietveld line profile technique implemented with the program FULLPROF [8]. A pseudo-Voigt type peak shape function was used in the refinements and, in the case of the D1B data, the peak shape was very close to pure Gaussian. The coherent neutron scattering lengths were b Tb = 0.738 10 -12 cm, b Ti = -0.3438 10 -12 cm, and b Ge = 0.8185 10 -12 cm for Tb, Ti and Ge, respectively [9]. A full description of the Rietveld method used in this article as well as the definition of the agreement factors can be found elsewhere [10].

Magnetization measurements were performed using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design MPMS-XL) in the temperature range 2-350 K. The field dependence at 10 K of the magnetization for HT-TbTiGe was performed at ambient pressure using the extraction method in applied fields from zero to 10 T [11]. The same type cryostat was used with another insert enabling any temperature between 300 and 850 K to be regulated. This set up has been used to investigate the magnetic properties of HT-TbTiGe above room temperature [12] and in this case the maximum field used was 1T.

Heat capacity was determined with a standard relaxation method with a Quantum Design PPMS device. Sample of approximately 40 mg was glued to the sample holder using Apiezon N-grease. The heat capacity of the sample holder and grease was measured just before the sample was studied.

Results and discussion

Structural properties from X-ray diffraction investigation

Microprobe analysis performed on the as-cast and annealed samples indicates their high chemical purity. These samples contain a major phase TbTiGe (> 99 % in volume) with some amounts of the binary compound Ti 5 Ge 3 . The presence of this last binary germanide agrees with the choice of the nominal composition (32 % Tb: 35 % Ti: 33 % Ge as atomic ratio percentage) used for the synthesis of the samples.

The comparison of the X-ray powder patterns obtained on the as-cast or annealed TbTiGe sample evidences strong differences (Figure 1). For instance, the strong peak observed near 2θ = 28° on the pattern of the as-cast sample, disappears after annealing. This analysis reveals that TbTiGe undergoes a structural transition as a function of temperature. After melting (HT modification) TbTiGe crystallizes in the tetragonal CeScSi-type structure (space group I4/mmm) whereas after annealing (LT modification) the ternary germanide adopts the tetragonal CeFeSi-type structure (space group P4/nmm). This structural transition evidenced for TbTiGe is similar to that reported by us during the synthesis of CeTiGe [3]. On the contrary, the results obtained in our study are in disagreement with those reported previously [1,2].

The Rietveld analysis of the X-ray powder pattern of HT-TbTiGe recorded at room temperature confirms that it crystallizes with the CeScSi-type structure (space group I4/mmm) (Figure 2). Some extra weak peaks correspond to the presence of a small amount (≈ 4 wt %) of the impurity phase Ti 5 Ge 3 , in agreement with the microprobe analysis. (At this stage it is important to mention that Ti 5 Ge 3 shows a weak Pauli paramagnetism [START_REF] Sychev | Izvestiya Vysshikh Uchebnykh Zavedenii[END_REF] therefore its presence will not influence the magnetic properties of the HT-TbTiGe sample). The unit cell parameters are refined to a = 404.84( 5) and c = 1530.10(9) pm, i. e. they are slightly smaller than those of GdTiGe (a = 406.45( 5) and c =1544.8(2) pm) [4] which is consistent with the lanthanide contraction. The remaining discrepancies between calculated and measured intensities come mostly from the existence of preferred orientation, visible for instance on the (00l) lines which are too small in comparison to the (110) or (200) lines without any correction. Therefore, the preferred orientation has been taken into account and partly corrected to improve the refinement. The final Rietveld refinement of the atomic positions with the isotropic atomic displacement parameters leads to the reliability factor R Bragg = 6.7 % and the profile factors R p = 13.2 % and R wp = 12.0 % (Figure 2). These structural parameters are gathered in Table 1.

At this stage it is important to mention that Ti 5 Ge 3 shows a weak Pauli paramagnetism therefore its presence will not influence the magnetic properties of two samples

The positional parameters determined here for the HT-TbTiGe ternary germanide agree with those reported previously for this compound during the investigation by X-ray powder diffraction of a mixture containing HT-and LT-TbTiGe [1]. The comparison between the interatomic distances d existing respectively in the HT-[this work] and the LT- [2] forms of TbTiGe shows: (i) a small increase of the d Tb-Tb distances from 370.4 to 371.4 pm in the sequence LT-TbTiGe  HT-TbTiGe and (ii) a decrease of the d Tb-Ge (298.0  294.4 pm) and d Tb-Ti (335.0  332.9 pm) distances in the same sequence. These changes could lead to different magnetic behavior for the two crystallographic forms of TbTiGe.

Magnetic properties

The temperature dependence of the magnetization M of HT-TbTiGe divided by low applied magnetic field H = 0.05 T is strongly dependent upon its cooling history as observed by the occurrence of a strong irreversibility between the zero field cooled (ZFC) and field cooled (FC) curves (Figure 3). The features characteristic of a ferromagnetic ordering are clearly seen in the data near T C = 300(1) K (temperature defined by a minimum in the derivative curve (dM ZFC /H)/dT). A broad maximum is observed around 275(5) K just below T C in the ZFC curve, which is followed by a drastic fall in the M value, whereas the FC curve continuously rises with decreasing temperature. In the ferromagnetic systems, a bifurcation of ZFC-FC curves appears if the coercive field becomes larger than the applied magnetic field (see below). Also, such a bifurcation is observed in anisotropic systems based for instance on rare earth having an orbital moment (Nd, Tb,…). This study suggests that the HT-TbTiGe phase exhibits a ferromagnetic behaviour as reported previously for the GdTiGe compound crystallizing in the CeScSi-type [4,14].

On the contrary, the M/H versus T curve corresponding to the LT-TbTiGe phase (inset of Figure 3) shows a maximum near T N = 280(1) K characteristic of the occurrence of an antiferromagnetic ordering. The Néel temperature T N determined by us is close to that reported previously in ref. [5,7] (286-288 K) but smaller than that observed in ref. [6] (312 K). But with this investigation, it is clear that the structural transition CeScSi-type (HT-TbTiGe)  CeFeSi-type (LT-TbTiGe) induces a magnetic transition from ferromagnetism to antiferromagnetism. [15].

As shown in

At 10 K, the hysteresis curve M versus µ 0 H for HT-TbTiGe (Figure 5) agrees with the behaviour of a polycrystalline ferromagnet. The loop exhibits an important coercitive field of 1 T and the magnetization M is not completely saturated at 10 T revealing most probably a significant magnetocrystalline anisotropy. In these last conditions, M is close to 7.79 (5) μ B /mol, a value smaller than that expected for a Tb 3+ moment (g J J = 9.0 µ B /Tb).

In order to confirm the conclusions of the magnetization measurements, specific heat C p measurements were performed on the HT-TbTiGe sample. The temperature dependence of C p in zero applied magnetic field is shown on Figure 6. The C p versus T curve exhibits only a λtype peak; its maximum is around 289(2) K and with decreasing temperature C p starts to increase near 299(2) K. These results are in excellent agreement with the magnetization data and confirm that HT-TbTiGe has only one magnetic transition below 320 K. It is interesting to note that the λ-peak observed here for the ferromagnetic HT-TbTiGe compound is much higher than that reported for the antiferromagnetic LT-TbTiGe [16]. In addition to the different nature of the magnetic structure, this can also indicate that the quality of the two samples is different.

Nuclear and magnetic structures from neutron diffraction investigation

A neutron diffraction pattern was recorded at 310 K, namely above the Curie temperature T C , in order to only have the nuclear contribution and to determine precisely the crystallographic structure of HT-TbTiGe modification. At this temperature, all Bragg peaks can be indexed with the space group I4/mmm. It is worth noticing that small peaks resulting from the λ/2 harmonics (0.8 % of the λ contribution) are present and taken into account in the refinements.

The model using the CeScSi-type structure and as starting atomic coordinates the values of the X-ray diffraction converge immediately to a similar solution. Then, the refined parameters are a = 404.87(1) and c = 1529.62(7) pm, z Tb = 0.3255(3) and z Ge = 0.1249 (2), values in fair agreement with the X-ray data at room temperature (Table 1). The accuracy of the atom position is somewhat limited by the preferred orientation, in particular for X-ray diffraction measurements a technique more sensitive to preferred orientation. At this point it is worth to remark also that a large contrast of neutron scattering length exists between the elements and even a negative sign for the Ti nucleus opposite to that of Tb and Ge. Consequently the structural parameters deduced from neutron diffraction can be expected to be more precise than that derived above from X ray diffraction. In addition, no significant deviation from the stoechiometric composition is observed by neutron diffraction.

Below T C , magnetic contributions appear on the nuclear peaks indicating the onset of a ferromagnetic state in agreement with the magnetization measurements. Thus, all the observed magnetic reflections can be indexed with the propagation vector k = (000) down to 2 K. According to the magnetic symmetry analysis, used to determine the irreducible representations (IR) with their basis vectors, only four IR are allowed for the Tb site 4e for k = (000) and the space group I4/mmm. Only two IR correspond to a ferromagnetic structure:

one with the Tb-moments along the c-axis and one with the Tb-moments within the basal (a, b)-plane. Since there is no magnetic contribution on the reflections (00l), the solution is likely the former one. Indeed, the model with magnetic Tb-moments parallel to the c-axis leads to the best refinement of the data with R B-nucl = 9.8 % and R B-mag = 7.6 %. Therefore, the magnetic structure consists of ferromagnetic Tb-planes ferromagnetically coupled with next adjacent Tb-planes along the c-axis (Figure 7). Figure 8 shows the final refinement for which the Tb-moment value amounts to 8.90(4) μ B at 2 K. This value corresponds to the trivalent state of the Tb 3+ ions (μ Tb +3 = 9.00 μ B ) and is slightly higher than the maximum value of M = 7.79(5) µ B deduced from the magnetization curve recorded at 10 K (Figure 5). This difference is most probably due to the fact that the magnetization is not completely saturated at 10 T.

The different patterns recorded between 2 and 310 K allow us to study the thermal evolution of the Tb-moment and the unit cell parameters by using the same collinear ferromagnetic model. On figure 9, showing the temperature dependence of these parameters, we observe an interesting anisotropic magnetostriction effect at the Curie temperature:

whereas the a parameter decreases with decreasing temperature, the c parameter increases On the contrary, for the antiferromagnetic isotype compounds TbMgSn and TbMgPb, the orientation of the Tb-moments is within the basal (a, b)-plane [18,22,23]. This result is explained by the modification of the crystal electric field (CEF) interaction via the sign of the second order crystal field term B 2 0 = α j <r 2 >(1 -σ 2 )K 2 0 A 2 0 , depending on the signs of the Stevens factor α j and of A 2 0 determined by the electrostatic field experienced at the Tb site due to the environment [24,25]. The Stevens factor depending only on the rare earth element (negative for Tb), the change of the easy magnetization direction for isotype compounds results from the modification of the CEF on the Tb site due to local environment, in particular due to the nature of the transition metal. Indeed, TbTi 0.85 Mo 0.15 Ge presents for example, a canted ferromagnetic structure below T C2 = 75(3) K [19], i.e. a slight reorientation of the magnetic moment compared with HT-TbTiGe, which must reflect the influence of the substitution of Mo for Ti on the CEF.

In the low temperature form LT-TbTiGe crystallizing in the CeFeSi-type structure, the Tb-moments are also parallel to the c-axis with μ Tb = 9.0(6) μ B at 2 K but the structure is antiferromagnetic [6]: the magnetic cell is doubled along the c-direction and the Tb-moments are coupled in the sequence (+ + --). Therefore, the magnetic interactions are ferromagnetic within the layers of [Tb 4 ] tetrahedra in both forms HT-and LT-TbTiGe, but are antiferromagnetic between these layers in LT-TbTiGe contary to those in HT-TbTiGe. This is related to very similar distances d Tb-Tb within these Tb layers in both forms and very different distances d' Tb-Tb between these layers since d' Tb-Tb distances decrease drastically from 598 to 528 pm in the sequence LT-TbTiGe  HT-TbTiGe.

Magnetocaloric properties

To determine the magnetocaloric properties (MCE) of HT-TbTiGe, isothermal magnetization measurements were performed around its Curie temperature T C (Figure 10). The M versus µ 0 H measurements have been carried out with increasing magnetic field from 0 to 5 T and for various temperatures between 330 and 100 K with a temperature step of ΔT = 5 K around T C = 300 K. In this temperature range, no remanent magnetization persists, which should not disturb the MCE determination.

The isothermal magnetic entropy change m S  was determined from the magnetization data by using the Maxwell relation:

dH T H T M H T S H H m            0 ) , ( ) , (
The results for  0 ΔH = 2 and 5 T are reported in Figure 11. A single maximum centered between 290 and 295 K, i.e. close to T C , is observed, as expected for the magnetocaloric effect. m S  reaches a maximum value of -4.3 JK -1 kg -1 for  0 ΔH = 5 T and -2.0 JK -1 kg -1 for  0 ΔH = 2 T. These values are modest but spread over a large temperature range around T C , which is typical of a second order magnetic transition. Note that a similar m S  value was found for TbTiGeB x (-4.7 JK -1 kg -1 [18]) as expected, and a slightly smaller value for TbTiGeC x (-3.5 JK -1 kg -1 [START_REF] Mazet | Proceedings of the 2 nd International Conference of the IIR on Magnetic Refrigeration at Room Temperature[END_REF]). Also, the maximum of the magnetic entropy change for the LT-TbTiGe was found to be equal to 0.09 JK -1 kg -1  0 ΔH = 5 T only [16], which arises from the antiferromagnetic behaviour of this compound.

The adiabatic temperature change T ad was determined by combining the heat capacity at zero field (Figure 6) and the magnetization data through the relationship:

) ( ) ( ) ( T S T C T T T m p ad    
(This calculation method leads to overestimated ΔT ad values as reported previously by Pecharsky et al. [START_REF] Pecharsky | [END_REF]. Indeed, due to the fact that C p was measured at zero magnetic field only, it is impossible to get a more accurate estimation of ΔT ad ). The thermal evolution of ΔT ad for HT-TbTiGe is plotted in Figure 11 for  0 ΔH = 5 and 2 T. As expected, a peak around the T C temperature in the ΔT ad versus T curves is observed with a maximum of ΔT ad of 4.2 and 2.0 K for  0 ΔH = 5 and 2 T, respectively. This MCE amounts to around 35 % of that of pure gadolinium (ΔT ad = 5.8 K for  0 ΔH = 2 T [28]) which is the reference for the magnetocaloric compounds.

Conclusion

The structural properties of TbTiGe are dependent on the temperature of its synthesis. After melting and quenching, the high temperature modification (HT-TbTiGe) adopts the tetragonal CeScSi-type whereas after annealing at 1073 K, the low temperature form (LT-TbTiGe) presents the tetragonal CeFeSi-type structure. This structural transition induces different magnetic behaviours for TbTiGe: (i) HT-TbTiGe is characterized by a ferromagnetic ordering below T C = 300(1) K and on the contrary (ii) LT-TbTiGe is an antiferromagnet below T N = 280(1) K. The investigation of these two modifications by neutron powder diffraction reveals that the Tb-moments are in both case aligned along the c-axis. HT-TbTiGe shows a magnetocaloric effect around the room temperature; its magnetic entropy change m S  is equal to -2.0 JK -1 kg -1 for a magnetic field change of 2 T. This m S  -value is comparable to that determined previously for GdScGe ( m S  = 1.91 JK -1 kg -1 ) which adopts also the CeScSitype [29].

  Figure 4 the temperature dependence of the reciprocal magnetic susceptibility χ m -1 = f(T) of HT-TbTiGe compound follows a Curie-Weiss law above 310 K with a value of the paramagnetic Curie temperature θ p equal to 285(2) K. A paramagnetic behaviour is then observed in this temperature range, and the positive value of θ p confirms the ferromagnetic ordering of this ternary germanide. The experimental value of the effective magnetic moment µ eff. = 10.41(5) μ B /Tb is slightly larger than the theoretical free ion value of 9.70 μ B /Tb for Tb 3+ ion. The enhancement of µ eff. suggests a contribution to the magnetic properties of HT-TbTiGe compound from the polarization of the conduction electrons as observed for instance in the ternary stannide Tb 6 Co 2.35 Sn 0.65

  below T C till 200 K and then decreases normally. It is noteworthy that the magnetic structure of HT-TbTiGe is similar to those of closely related compounds crystallizing in the CeScSi-type structure. For examples, the compounds TbTiGeC x (T C = 310(5) K), TbTiGeB x (T C = 301(5) K), TbTi 0.85 Mo 0.15 Ge (T C1 = 280(3) K, canted below T C2 = 75(3) K), TbScGe (T C = 216 K) and TbZrSb (T C = 65 K) also exhibit aferromagnetic structure with the c-axis as easy magnetization direction[16][17][18][19][20][21]. We observe similar values for the Tb-moment around 9 μ B except for TbZrSb for which μ Tb = 5.6 μ B[21].

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Rietveld profile refinement of the X-ray powder pattern recorded at room temperature for the HT-TbTiGe ternary germanide (λ = 1.54059 Ǻ). The Ti 5 Ge 3 phase was included in the refinement. The observed data, the calculated profile and the difference between observation and calculation are given respectively in red circles, black and blue (bottom) solid lines. The green ticks correspond to 2θ-Bragg peak positions of HT-TbTiGe (1) and Ti 5 Ge 3 (2).

Figure 3 .

 3 Figure 3. Temperature dependence of the magnetization M of HT-TbTiGe measured under an applied magnetic field H = 0.05 T determined in the zero field cooling (ZFC) and in the field cooling (FC) process. The inset presents the thermal dependence of M recorded for the LT-TbTiGe phase.

Figure 4 .

 4 Figure 4. Temperature dependence of the reciprocal magnetic susceptibility χ m -1 of HT-TbTiGe measured in an applied magnetic field of 0.1 T. The dashed line presents the Curie-Weiss law.

Figure 5 .

 5 Figure 5. Field dependence at 10 K of the magnetization M of the ternary germanide HT-TbTiGe.

Figure 6 .

 6 Figure 6. Temperature dependence of the specific heat C p of the ternary germanide HT-TbTiGe.

Figure 7 .

 7 Figure 7. Comparison of the magnetic structure obtained at 2 K for the two inequivalent crystal structures: LT-TbTiGe (a) and HT-TbTiGe (b).

Figure 8 .

 8 Figure 8. Rietveld refinement of the neutron diffraction pattern at 2 K of HT-TbTiGe (λ = 2.52 Ǻ). The observed data, the calculated profile and the difference between observation and calculation are given respectively in red circles, black and blue (bottom) solid lines. The green ticks correspond to 2θ-Bragg peak positions of HT-TbTiGe (nuclear), HT-TbTiGe (magnetic) and Ti 5 Ge 3 from top to bottom respectively.

Figure 9 .

 9 Figure 9. Temperature dependence of the Tb-moment (upper part) and of the unit cell parameters (lower part) as deduced from the analysis of the neutron diffraction data.

Figure 10 .

 10 Figure 10. Field dependence at various temperature (100 K  T  330 K) of the magnetization M of the ternary germanide HT-TbTiGe.

Figure 11 .Figure 1 .

 111 Figure 11. Temperature dependence for  0 ΔH = 2 and 5 T of the isothermal magnetic entropy change ΔS m (upper part) and of the adiabatic temperature change ΔT ad (lower part) for HT-TbTiGe.

Figure 2 .

 2 Figure 2. Rietveld profile refinement of the X-ray powder pattern recorded at room temperature for the HT-TbTiGe ternary germanide (λ = 1.54059 Ǻ). The Ti 5 Ge 3 phase was included in the refinement. The observed data, the calculated profile and the difference between observation and calculation are given respectively in red circles, black and blue (bottom) solid lines. The green ticks correspond to 2θ-Bragg peak positions of HT-TbTiGe (1) and Ti 5 Ge 3 (2).

Figure 3 .

 3 Figure 3. Temperature dependence of the magnetization M of HT-TbTiGe measured under an applied magnetic field H = 0.05 T determined in the zero field cooling (ZFC) and in the field cooling (FC) process. The inset presents the thermal dependence of M recorded for the LT-TbTiGe phase.

Figure 4 .

 4 Figure 4. Temperature dependence of the reciprocal magnetic susceptibility χ m -1 of HT-TbTiGe measured in an applied magnetic field of 0.1 T. The dashed line presents the Curie-Weiss law.

Figure 5 .

 5 Figure 5. Field dependence at 10 K of the magnetization M of the ternary germanide HT-TbTiGe.

Figure 6 . 24 Figure 7 .Figure 8 .Figure 9 .Figure 11 .

 62478911 Figure 6. Temperature dependence of the specific heat C p of the ternary germanide HT-TbTiGe.

Table 1 .

 1 Lattice, positional and isotropic displacement parameters at room temperature for HT-TbTiGe (CeScSi-type structure with space group I4/mmm) as deduced from Rietveld

	refinement of X-ray powder diffraction (first line) and neutron powder diffraction (second
	line)
				positional parameters
	Atom	site	x	y	z	B iso (Ǻ 2 )
	Tb	4e	0	0	0.3273(2)	1.5(3)
			0	0	0.3260(6)	1.03(3)
	Ti	4c	0	1/2	0	1.4(3)
			0	1/2	0	0.9(4)
	Ge	4e	0	0	0.1277(2)	0.3(2)
			0	0	0.125(2)	1.2(3)
	a = 404.84(5) and c = 1530.10(9) pm R Bragg = 6.7 %, R p = 13.2 % and R wp = 12.0 %
	a = 404.87(3) and c = 1529.62(7) pm R Bragg = 6.7 %, R p = 17.1 % and R wp = 13.9 %

Acknowledgment

This work was supported by the ANR (Agence Nationale pour la Recherche) through the research project "MAGCOOL" (ANR-2010-STKE-008).