Edith Galy

Claudine Mélan

Effects of cognitive appraisal and mental workload factors on performance in an arithmetic task Running title: Cognitive appraisal effects on workload

Keywords: workload measures, cognitive load, time pressure, task difficulty, alertness, cognitive appraisal, arithmetic task

We showed in a previous study an additive interaction between intrinsic and extraneous cognitive loads and of participants' alertness in an 1-back working memory task. The interaction between intrinsic and extraneous cognitive loads was only observed when participants' alertness was low (i.e. in the morning). As alertness is known to reflect an individual's general functional state, we suggested that the working memory capacity available for germane cognitive load depends on a participant's functional state, in addition to intrinsic and extraneous loads induced by the task and task conditions. The relationships between the different load types and their assessment by specific load measures gave rise to a modified cognitive load model. The aim of the present study was to complete the model by determining to what extent and at what processing level an individual's characteristics intervene in order to implement efficient strategies in a working memory task. Therefore, the study explored participants' cognitive appraisal of the situation in addition to the load factors considered previously -task difficulty, time pressure and alertness. Each participant performed a mental arithmetic task in four different cognitive load conditions (crossover of two task difficulty conditions and of two time pressure conditions), both while their alertness was low (9 a.m.) and high (4 p.m.). Results confirmed an additive effect of task difficulty and time pressure, previously reported in the 1-back memory task, thereby lending further support to the modified cognitive load model. Further, in the high intrinsic and extraneous load condition, performance was reduced on the morning session (i.e. when alertness was low) on one hand, and in those participants' having a threat appraisal of the situation on the other hand. When these factors were included into the analysis, a performance drop occurred in the morning irrespective of cognitive appraisal, and with threat appraisal in the afternoon (i.e. high alertness). Taken together, these findings indicate that mental overload can be the result of a combination of subject-related characteristics, including alertness and cognitive appraisal, in addition to welldocumented task-related components (intrinsic and extraneous load). As the factors investigated in the study are known to be critically involved in a number of real job-activities, the findings suggest that solutions designed to reduce incidents and accidents at work should consider the situation from a global perspective, including individual characteristics, task parameters, and work organization, rather than dealing with each factor separately.

INTRODUCTION

 Since Miller's (1956)nominal paper suggesting that working memory capacity is limited to a defined number of digits of information, a central theoretical issue was to describe how people might organize information in a capacity-limited short-term memory store. Cognitive load theory (CLT) emphasizes the capacity limitations to process novel information in working memory in instructional or educational contexts, by distinguishing different load categories [START_REF] Sweller | Cognitive load during problem solving: effects on learning[END_REF]. "Intrinsic cognitive load" refers to the load induced by the material to be processed, such as task difficulty that is defined in particular by the number of items to be processed, and by item interactivity, and depends on the expertise of the learner [START_REF] Ayres | Using subjective measures to detect variations of intrinsic cognitive load within problems[END_REF][START_REF] Kalyuga | The expertise reversal effect[END_REF][START_REF] Sweller | Why some material is difficult to learn[END_REF]. "Extraneous mental workload" refers to the components of a learning environment that may be modified to reduce total load, in particular by adequate instructions in a learning context, and by adapting the to-be-learned material in terms of its relevance, presentation format, adequate presentation of domain elements [START_REF] Amadieu | Effects of prior knowledge and concept-map structure on disorientation, cognitive load, and learning[END_REF][START_REF] Debue | What does germane load mean? An empirical contribution to the cognitive load theory[END_REF][START_REF] Leppink | Effects of pairs of problems and examples on task performance and different types of cognitive load[END_REF][START_REF] Van Merriënboer | Cognitive load theory in health professional education: design principles and strategies[END_REF].

Finally, "germane mental workload" corresponds to the load induced by conscious application of strategies to solve tasks more efficiently [START_REF] Schnotz | A reconsideration of cognitive load theory[END_REF].

Though CLT has been developed in the field of instructional design, a growing number of studies showed its usefulness in non-instructional designs, including e-learning [START_REF] Amadieu | Effects of prior knowledge and concept-map structure on disorientation, cognitive load, and learning[END_REF][START_REF] Debue | What does germane load mean? An empirical contribution to the cognitive load theory[END_REF][START_REF] Leppink | Effects of pairs of problems and examples on task performance and different types of cognitive load[END_REF], clinical diagnosis [START_REF] Durning | The impact of selected contextual factors on experts' clinical reasoning performance (does context impact clinical reasoning performance in experts?)[END_REF] and ergonomics [START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF][START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: investigation in the field of aerospace activities[END_REF]. Though it is not yet clear to what extent cognitive load and workload refer to the same concept, the two latter studies revealed similar effects of three cognitive load factors in a controlled laboratory study and in field studies respectively. The relationships between these load factors and the load categories described by CLT, together with their assessment by specific load measures gave rise to a modified cognitive load model [START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF]. In a 1-back working memory task, intrinsic load variations by task difficulty affected participants' perceived cognitive effort, thereby confirming that subjective load ratings are most sensitive to small load variations [START_REF] Gimino | Students' investment of mental effort[END_REF]Paas andMerriënboer, 1993, Paas et al., 2003). Simultaneous intrinsic and extraneous load (time pressure) variations were revealed by participants' performance and their mental efficiency (a measure computed from both, performance and self-rated effort, according to [START_REF] Paas | The efficiency of instructional conditions: an approach to combine mental effort and performance measures[END_REF]. Thus, in agreement with CLT [START_REF] Sweller | Cognitive load during problem solving: effects on learning[END_REF] when the task was easy and/or had to be performed under low time pressure, it could be solved without requiring specific strategies (germane load virtually inexistent). Conversely, specific strategies, generating germane load, would have been required to solve the difficult task under high time pressure,. In agreement with de Jong's statement, we proposed that "intrinsic and extraneous cognitive load concern cognitive activities that must unavoidably be performed" (2010, p.113) and would represent the minimum cognitive resources that are required to solve a given task in a given context. Further, effects of participants' alertness were revealed by differential heart rate, shown to provide systematic and reliable relationships with task demands and mental effort [START_REF] Backs | Metabolic and cardio respiratory measures of mental effort: the effects of level of difficulty in a working memory task[END_REF][START_REF] Tattersall | Level of operator control and changes in heart rate variability during simulated flight maintenance[END_REF]. Hence, in the 1-back memory task, the additive effect of task difficulty and time pressure was only observed when participants' alertness was low (i.e. in the morning), leading to the proposal that alertness may have determined the mental resources available for implementing specific strategies in working memory. More especially, limited cognitive working memory resources in the morning, as a consequence of low alertness, would have been unsufficient to enable efficient strategies in the high difficulty/high time pressure conditions, while no effect was expected in the easy and/or low time pressure conditions as in these conditions the task could be solved without requiring specific strategies (germane load virtually inexistent). In other controlled laboratory studies, decreased alertness or arousal has also been shown to be associated with lower working memory performance [START_REF] Fabbri | Effect of time of day on arithmetic fact retrieval in a number-matching task[END_REF][START_REF] Smit | Mental and physical effort affect vigilance differently[END_REF], especially in the higher cognitive load condition [START_REF] Jackson | Low Cognitive Load and Reduced Arousal Impede Practice Effects on Executive Functioning, Metacognitive Confidence and Decision Making[END_REF]. Further, when the same load factors were explored in air traffic controllers performing a mental arithmetic task, time pressure improved performance in the low difficulty task condition, but only when controllers' alertness was high [START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: investigation in the field of aerospace activities[END_REF].

Resource theory also proposes that increasing task demands, fatigue or cognitive overload result in more resource consumption and this depletion of resources results in a vigilance decrement [START_REF] Helton | Brief mental breaks and content-free cues may not keep you focused[END_REF]. Accordingly, available mental resources that depend on an individual's functional state, together with the minimum resources necessary for intrinsic and extraneous load, would determine the amount of free processing resources that may be devoted to germane cognitive load and ultimately determine individual task efficiency, expressed by performance measures [START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF].

The purpose of the present study was two-fold: Testing in controlled laboratory conditions the modified cognitive load model in a different working memory task (i.e. a mental arithmetic task), and completing the model by including another factor known to affect cognitive load, i.e. individual characteristics. Before describing the study rationale in further detail, it may be useful to highlight that the load factors considered in the study have been reported to characterize job activity in a number of work situations. Accordingly, their combined investigation may provide a more contextualized application of CLT [START_REF] Jong | Cognitive load theory, educational research, and instructional design: some food for thought[END_REF], also has been suggested for CLT for health professional education for instance [START_REF] Van Merriënboer | Cognitive load theory in health professional education: design principles and strategies[END_REF]. In addition to the well-documented effects of work task difficulty in real-life settings, operating under time pressure figures among the major sources of stress in general [START_REF] Matthews | Sustained performance under overload: Personality and individual differences in stress and coping[END_REF] and in safety-related job-situations in particular (for a review, [START_REF] Tucker | Working time, health and safety: A research synthesis paper[END_REF]. In work environments time may be part of a process that influences perception of control [START_REF] Koslowsky | Commuting Stress: Causes, Effects, and Methods of Coping[END_REF], and short-term effects on brain and autonomous nervous system activity (increased heart rate) were reported in real and simulated work situations involving high tension and/or mental effort [START_REF] Ritvanen | Responses of the autonomic nervous system during periods of perceived high and low work stress in younger and older female teachers[END_REF][START_REF] Sloan | Effect of mental stress throughout the day on cardiac autonomic control[END_REF].

Further, the effects of certain cognitive load conditions at work, or of mental workload (i.e. overload but also underload), are most prominent on early morning hours or during the night, as indicated by a higher probability of an operator being involved in an accident or injuring himself at times when he/she would normally be asleep [START_REF] Tucker | Working time, health and safety: A research synthesis paper[END_REF]. As stated by Akerstedt (2007, p. 209), three conditions that are typically associated with night-or shiftwork, i.e. "being exposed to the circadian low, extended time awake, or reduced duration of sleep will impair performance". The short-term consequences of shift-scheduling systems on operators' cognitive performance and alertness, and thus on safety and security, and their longterm effects on physical and mental health are now well established [START_REF] Costa | Shift Work and Health: Current Problems and Preventive Actions[END_REF][START_REF] Tucker | Working time, health and safety: A research synthesis paper[END_REF]. In shift-work conditions, alertness but also task-requirements appear to determine operators' task performance in a complex way [START_REF] Mélan | Recall Performance in Air Traffic Controllers Across the 24hr Day: Influence of Alertness and Task Demands on Recall Strategies[END_REF]. On early morning hours, when shift-workers' alertness was low, their performance dropped in various discrimination or memory tasks, but only in the more demanding task conditions, while no such effect was observed when alertness increased in the afternoon [START_REF] Galy | Investigation of task performance variations according to task requirements and alertness across the 24-h day in shift workers[END_REF]Mélan et al., 2007;[START_REF] Mélan | Recall Performance in Air Traffic Controllers Across the 24hr Day: Influence of Alertness and Task Demands on Recall Strategies[END_REF]. These results strongly favor the idea that low alertness is associated with low mental resources and increasing alertness with higher mental resources. In these studies, subjective alertness ratings enabled determining the circadian variations of an operator's functional state. Thus, Thayer's adjective check-list and visual analogue scale ratings have been shown to closely match the variations of a shift-workers' body temperature, which is known as a prominent marker of circadian rhythms [START_REF] Cariou | Differential 24-h variations of alertness and subjective tension in process controllers: Investigation of a relationship with body temperature and heart rate[END_REF]. These studies, together with the finding of positive relationships between alertness and performance with task difficulty and time pressure on one hand, and of these measures with low job demands and high job activity in real-job situations [START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: investigation in the field of aerospace activities[END_REF], highlight time of day as a determinant factor of mental workload.

Elsewhere, in a recent formulation of CLT, Sweller (2010) stated that germane cognitive load is concerned only with learner characteristics. Several recent studies explored the role of various individual characteristics, either to further refine the definition of the different load types proposed by CLT or to point to the involvement of additional processes in selected CL tasks.

Thus, disorientation, a psychological state induced by the difficulties during e-learning has been reported in participants with low prior knowledge [START_REF] Amadieu | Effects of prior knowledge and concept-map structure on disorientation, cognitive load, and learning[END_REF], cognitive absorption or motivation during reading improved retention performance [START_REF] Debue | What does germane load mean? An empirical contribution to the cognitive load theory[END_REF][START_REF] Kuldas | Greater Cognitive Effort for Better Learning: Tailoring an Instructional Design for Learners with Different Levels of Knowledge and Motivation[END_REF], and irrelevant contextual factors impacted on expert physician performance [START_REF] Durning | The impact of selected contextual factors on experts' clinical reasoning performance (does context impact clinical reasoning performance in experts?)[END_REF]. Some earlier works already stressed the involvement of individual characteristics while implementing specific strategies in a cognitive task, including age, expertise [START_REF] Schnotz | A reconsideration of cognitive load theory[END_REF], and psychological processes, like stereotype threat [START_REF] Steele | A threat in the air. How stereotypes shape intellectual identity and performance[END_REF], and cognitive appraisal [START_REF] Lazarus | Stress, Appraisal, and Coping[END_REF]. "Stereotype threat" is a factor that inhibits stereotyped individuals to perform up to their full ability, and that occurs when a negative stereotype undermines performance of certain minority groups [START_REF] Steele | A threat in the air. How stereotypes shape intellectual identity and performance[END_REF] Working memory resources would be impaired (by three interrelated processes, i.e. a physiological stress response, self-monitoring of performance in order to find ways to restore the cognitive balance, and appraisal processes resulting in negative affect and cognition (for a review, [START_REF] Appel | Stereotypes and the Achievement Gap: Stereotype Threat Prior to Test Taking[END_REF][START_REF] Schmader | an integrated process model of stereotype threat effects on performance[END_REF][START_REF] Steele | Stereotype threat and the intellectual test performance of African Americans[END_REF]. [START_REF] Folkman | If it changes it must be a process: Study of emotion and coping during three stages of a college examination[END_REF] described for the first time the effects of cognitive appraisal on task performance. With a "challenge appraisal" participants were reported to be more heavily invested in task resolution [START_REF] Saxby | Active and passive fatigue in simulated driving: discriminating styles of workload regulation and their safety impacts[END_REF] and to display better performance than with a "threat appraisal". Tomaka and co-workers (1997) conceptualized threat and challenge responses as goal relevant multi-dimensional reactions in response to environmental demands.

Threat appraisal has been shown to occur when the demands are perceived as taxing or exceeding the individual's resources and to be associated with negative affect and inadequate mobilization of physiological resources. In contrast, a challenge appraisal would occur when the demands are appraised within the person's resources, and is characterized by positive emotion and efficient physiological activation. In a mental arithmetic task, threat appraisals predicted greater negative affect and perceived stress, whereas challenge appraisals were related to greater positive affect and task engagement [START_REF] Maier | Relation of cognitive appraisal to cardiovascular reactivity, affect, and task engagement[END_REF]. Further, fatigue induced by cognitive overload has been shown to elevate appraisals of threat and uncontrollability [START_REF] Saxby | Active and passive fatigue in simulated driving: discriminating styles of workload regulation and their safety impacts[END_REF].Taken together, the data from the literature suggest that cognitive appraisal may be a determinant factor while implementing efficient strategies for solving a task accurately.

The present experiment was designed to test whether, and to what extent, cognitive appraisal would interfere with load types defined by CLT. Cognitive load measures were those described in previous studies [START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF][START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: investigation in the field of aerospace activities[END_REF]; task performance, cognitive effort self-ratings, differential heart rate, mental efficiency). We used a mental arithmetic task, sensitive to cognitive appraisal effects [START_REF] Tomaka | Cognitive and physiological antecedents of threat and challenge appraisal[END_REF][START_REF] Maier | Relation of cognitive appraisal to cardiovascular reactivity, affect, and task engagement[END_REF], and that may provide an indication of the participants' confidence in their ability to perform the task [START_REF] Steele | A threat in the air. How stereotypes shape intellectual identity and performance[END_REF]. Visual analog scales enabled determining self-rated task-induced stress and resources to perform the task, and the ratio of both measures indicated participants' cognitive appraisal, as described by Tomaka and co-workers (1993).

In light of previous results, participants' performance was expected to be sensitive to all factors investigated. More especially, a simultaneous increase in task difficulty and time pressure would affect task performance in the morning (though not in the afternoon), and in those participants exhibiting a threat appraisal of the task (but not in those exhibiting a challenge appraisal). Despite comparable motivation and similar effort, underperformance with stereotype threat has been attributed to inefficient processing, as a result of negative affect and cognition, leaving only limited cognitive resources to perform efficiently [START_REF] Steele | Stereotype threat and the intellectual test performance of African Americans[END_REF]. Though for different reasons, similar cognitive, affective and physiological consequences would characterize threat appraisal [START_REF] Tomaka | Cognitive and physiological antecedents of threat and challenge appraisal[END_REF][START_REF] Maier | Relation of cognitive appraisal to cardiovascular reactivity, affect, and task engagement[END_REF].

Accordingly, in the present experiment, threat appraisal may be expected to affect cognitive load by reducing available resources that may be used for germane load, as has been shown previously for alertness [START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF]. In contrast, participants with a challenge appraisal of their mental arithmetic abilities would allocate sufficient cognitive resources to perform the task, thereby promoting efficient task solving [START_REF] Tomaka | Subjective, physiological, and behavioral effects of threat and challenge appraisal[END_REF].

METHODS

Participants

31 students (Mage = 23.3; SD = 1.86; range = 20-27) volunteered to take part in the experiment. 18 participants (9 women and 9 men) studied biology and 13 studied psychology (6 women and 7 men). Participants attended two individual test sessions in the laboratory and abstained from drinking tea or coffee for three hours before the start of the tests. All participants gave their full informed consent before participating in the experiment that was performed in accordance with the Ethical Principles of Psychologists and Code of Conduct of The French Federation of Psychologists and Psychology and with the Ethical standards in chronobiological research [START_REF] Touitou | Ethics, standards, and procedures of animal and human chronobiology research[END_REF].

Material and measures

Arithmetic task

Each subject performed the task in four experimental conditions, defined by task difficulty and time pressure (low difficulty and low time pressure; low difficulty and high time pressure; high difficulty and low time pressure; high difficulty and high time pressure). Prolab was used for random item presentation and for response recording (latency and accuracy). Task difficulty was manipulated by requiring participants to add either 5 (low task difficulty) or 36 (high task difficulty) to a number displayed on the screen. Two-and three-digit items were selected so that the algebraic sum with 5 (low task difficulty) or 36 (high task difficulty) changed either the tenths or the hundredths in half of the 32 trials. In the two low time pressure conditions, there was no time limit, although participants were instructed to respond as quickly and accurately as possible. In the two high time pressure conditions, the time limit was set at 8,000 ms. For each trial, participants entered the algebraic sum on a numeric keypad.

Differential heart rate

Changes in heart rate were recorded continuously throughout the experiment by an ambulatory heart rate (HR) monitor (Polar S610iä). These devices represent a convenient alternative to traditional electrocardiographs, as far as heart rate variability is concerned (Rezende [START_REF] Barbosa | Comparison of Polar(®) RS800G3(™) heart rate monitor with Polar(®) S810i(™) and electrocardiogram to obtain the series of RR intervals and analysis of heart rate variability at rest[END_REF][START_REF] Quintana | On the validity of using the Polar RS800 heart rate monitor for heart rate variability research[END_REF]. It is comprised of a transmitter worn around the chest and a receiver worn on the non-dominant wrist that stores the HR values. The HR values were then transferred over an infrared connection to a computer where they were subsequently analyzed using Polar Precision Performance Software. During measurements, participants were comfortably seated in an armchair, and were asked to relax for 20 min to make sure that baseline values were reached before starting the experiment. In each task condition, measures for differential heart rate were obtained between values of the 4-min test period and the corresponding baseline values of a 4-min rest period.

Subjective measures

Immediately following the final trial in each task condition, the participant was asked to rate several visual analog scales. He/she indicated the mental effort induced by the task by a vertical mark on a 10-cm long horizontal line ranging from "little mental effort" (0 cm) to "considerable mental effort" (10 cm), and from "low subjective tension" (0 cm) to "high subjective tension" (10 cm). Cognitive appraisal was investigated following completion of each task condition, by using the procedure described by [START_REF] Tomaka | Subjective, physiological, and behavioral effects of threat and challenge appraisal[END_REF]. Primary evaluation and secondary evaluation were explored using 10-cm visual analog scales ranging from "little task-induced stress" to "considerable task-induced stress", and from "low resources to perform the task" to "high resources to perform the task" respectively. When the ratio of these measures was below the median value (cognitive resources higher than task-induced stress), the participant's cognitive evaluation was labeled "challenge appraisal", and when the ratio was above the median value (cognitive resources lower than task-induced stress), his/her cognitive evaluation was labeled "threat appraisal".

Mental efficiency

Mental efficiency proposed by [START_REF] Paas | The efficiency of instructional conditions: an approach to combine mental effort and performance measures[END_REF] was calculated using the formula E = (P -ME)/2, where P and ME corresponded to z-scores of performance and mental effort measures.

Subjective alertness

Each participant completed the French paper-and-pencil version of Thayer's Activation-Deactivation Adjective Checklist [START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF], by selecting one of the following responses for each of 20 listed adjectives: "not at all", "don't know", "little" and "much". These responses were weighted 1, 2, 3 and 4, but two of the adjectives were given negative weightings. The responses were totaled to yield four factors: general activation (GA), deactivation sleep (DS), high activation (HA), and general deactivation (GD). The GA/DS ratio was used as an alertness index.

Procedure

Each participant performed each of the four task conditions between 9 a.m. and 10 a.m. and between 4 pm. and 5 p.m. He/she was informed of the aim of the study before being equipped with the Polar monitor and was then asked to complete a background questionnaire (age, gender, etc.), and to rate the alertness checklist. Following 20' of relaxation, they were given the task instructions ("you must respond as quickly and accurately as possible"), and an opportunity to familiarize themselves with the task procedure for approximately 2 min.

Following a 4-min rest period, the experiment started with the administration of a randomly selected task condition, followed by subjective ratings including cognitive evaluation, and a rest period of 4 min. This procedure was repeated for the three remaining task conditions; each being preceded by a 4-min rest period.

Statistics

We first explored the effects of participants' gender and study field on the cognitive appraisal index, and alertness variations across the day with analyses of variance (ANOVAs). Thereafter, hierarchical regression analyses integrating difficulty, time pressure, alertness, task difficulty x time pressure, difficulty x alertness, time pressure x alertness, and difficulty x time pressure x alertness, and cognitive appraisal were performed according to the parsimony principle, on each load measure separately. Moreover, complementary analyses including intrinsic and extraneous load factors (task difficulty, time pressure, difficulty x time pressure) were conducted for each condition characterized as requiring low cognitive resources (morning session and/or threat appraisal) and for each condition requiring high cognitive resources (afternoon session and/or challenge appraisal).

RESULTS

A first analysis of variance (ANOVA), testing effects of gender and study domain (biology and psychology) on the cognitive appraisal index, revealed no significant effect indicating that variations observed fir this measure weren't induced by these factors. An ANOVA of time-ofday on alertness revealed that alertness was significantly lower in the morning than in the afternoon (F(1,29) = 8.76; p = .004, r 2 adj = 0,06). Details of the analysis are presented in Table 1.

Hierarchical regression analysis on participants' performance (number of correct responses;

Table 2) of all the factors considered in the study revealed a regression model with alertness, time pressure, task difficulty and time pressure x task difficulty explaining 81% of variance of performance (r 2 adj = .81). A significant effect of alertness on performance (β = .27, p = .04) indicates that the number of correct responses increased with alertness, and a significant interaction between task difficulty and time pressure (β = -1.55, p < .001) revealed a performance decrement when task difficulty and time pressure were simultaneously increased (Figure 1).

The same hierarchical regression analysis was conducted on perceived cognitive effort (Table 3), mental efficiency index (Table 4), perceived tension (Table 5), and on differential heart rate (Table 6). All factors were introduced into the analysis and after application of the parsimony principle, a model with difficulty, time pressure and difficulty x time pressure was obtained and explained 40% of variance of perceived mental effort (r 2 adj = .40). A significant effect of interaction between task difficulty and time pressure was observed (β = .55, p = .001).

Concerning mental efficiency, the same model than for perceived mental effort was obtained and explained 70% of variance (r 2 adj = .70), and a significant effect of interaction between task difficulty and time pressure was too observed (β = -.83, p = .001). Moreover, a similar model was obtained for perceived tension explaining 21% of variance (r 2 adj = .21) and revealing a significant interaction between both load factors (difficulty and time pressure; β = .464, p = .001). A similar analysis on differential heart rate revealed only a significant effect of alertness (β = .35, p < .001, r 2 adj = .11), indicating greater heart rate variations between the test and rest periods when participants' alertness was high.

Finally, complementary regression analyses were conducted on performance as a function of cognitive resources conditions. Thus, these analyses revealed variations of effect of interaction between task difficulty and time pressure according to cognitive resources conditions. Thus, this interaction affected the number of correct responses in the morning (β = -1.48, p = .0001, r 2 adj = .75), but not in the afternoon (β = -.41, ns, r 2 adj = .86). It also affected significantly more performance in participants with a "threat appraisal" (β = -1.37, p = .002, r 2 adj = .85) compared to those with a "challenge appraisal" (β = -.56, ns, r 2 adj = .79). When these two factors (cognitive appraisal and time of day) were considered, a significant interaction between task difficulty and time pressure reduced the number of correct responses in both "threat appraisal" (β = -1.41, p = .0001, r 2 adj = .78), and "challenge appraisal" participants (β = -1.38, p = .0001, r 2 adj = .72) in the morning, but only in "threat appraisal" participants (β = -1.54, p = .028, r 2 adj = .92) in the afternoon.

Correlations analyses between the different cognitive load measures revealed a significant negative relationship of task performance with perceived effort (r = -.530, p <.001), and perceived tension (r = -.454, p <.001), and a highly significant positive relationship of task performance with mental efficiency index (r = .878, p <.001). Moreover, each subjective measure was significantly correlated with each other (statistical details presented in table 7).

However, no significant relationship was observed between differential heart rate and any other measure.

DISCUSSION

The present findings confirm and extend those reported in previous studies investigating the relationships between cognitive load factors and load types, by testing intrinsic load (task difficulty), extraneous load (time pressure) and individual characteristics (participants' alertness and cognitive appraisal). They raised several issues that will be discussed separately.

Interaction between intrinsic and extraneous cognitive load factors

The study revealed that a simultaneous increment in intrinsic and extraneous load by task difficulty and time pressure during task completion respectively, resulted into a performance decrement. This effect was observed in a mental arithmetic task in the present study and in a nback memory task in a previous study [START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF]. It was quite robust as it still occurred when additional factors were included into the analysis (see below), both in the present and the previous study. In both studies, additive effects of intrinsic and extraneous mental load also affected participants' mental efficiency index which was computed from task performance and self-rated effort. However, results of the two studies differed in that in the arithmetic task an interaction of task difficulty and time pressure was observed for self-rated cognitive effort, as for the afore-mentioned load measures, while in the n-back memory task a main effect of task difficulty occurred for this measure. In other words, participants would have perceived time pressure as a greater constraint when calculating the sum of two numbers than when retrieving numbers from short-term memory. This may be explained by the fact that the arithmetic task was cognitively more demanding than the memory task, given that in the former case participants had to manipulate the numbers in addition to maintaining them in the short-term buffer, whereas in the latter case they only had to maintain the numbers. It seems thus plausible to propose that participants would more rapidly gain the impression that they reached their cognitive limits with mental calculation.

Taken together, these results favor the hypothesis of a functional link between the two load categories, as suggested previously (Galy et al., 20012;[START_REF] Sweller | Cognitive architecture and instructional design[END_REF]. In line with these considerations, we argued that mental efficiency and self-estimated effort required to perform a task would provide reliable indications of the combined effects of the two load categories [START_REF] Ayres | Using subjective measures to detect variations of intrinsic cognitive load within problems[END_REF]. There is, however, an ongoing debate concerning the measurement methods of the cognitive loads within CLT. Several authors stressed that multiple indicators of each cognitive load type would provide a broader evaluation of each load type than single items [START_REF] Debue | What does germane load mean? An empirical contribution to the cognitive load theory[END_REF][START_REF] Leppink | Effects of pairs of problems and examples on task performance and different types of cognitive load[END_REF]. In this respect, multidimensional subjective rating scales have been developed, and self-ratings have been performed together with objective ratings, including performance measures, eye-tracking components and differential heart rate [START_REF] Amadieu | Effects of prior knowledge and concept-map structure on disorientation, cognitive load, and learning[END_REF][START_REF] Debue | What does germane load mean? An empirical contribution to the cognitive load theory[END_REF][START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF][START_REF] Leppink | Effects of pairs of problems and examples on task performance and different types of cognitive load[END_REF][START_REF] Smit | Mental and physical effort affect vigilance differently[END_REF].

In real-world settings, task load is not simply defined by task difficulty/complexity or item interactivity, but also by the perception of various dimensions of the environment, including physical, psychological and psychosocial aspects. Thus, assessing simultaneously various external and internal sources of load may enable determining the capacity that is left in working memory to implement efficient strategies to solve a particular task or a problem at work. Even though this methodology has been shown to be less specific than when each load type is assessed by different and multiple indicators, it may have an operational value in applied contexts. It is however noteworthy that "it is not entirely clear to what extent workload and cognitive load refer to the same concept across contexts" (Lepping et al., 2014, p.33). In safetyrelated job situations in particular, high demands or work overload have been found to be positively related to job strain and safety behavior [START_REF] Li | Job demands, job resources and safety outcomes: The roles of emotional exhaustion and safety compliance[END_REF]. In another study cognitive load in the arithmetic task described here was assessed together with air traffic controllers' job perception (job demands, control and social support), and control operations that were recorded following the psychological tests. Results revealed that controllers' performance in the high difficulty and high time pressure task conditions was associated with their real job activity and supervisor support [START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: investigation in the field of aerospace activities[END_REF]. Thus, assessing intrinsic and extraneous load with the same load measure may be informative in applied contexts when combined with more specific, job-related dimensions. Further, experimental paradigms like the one used in this study may be regarded as simplified models of real-job activities that involve similar cognitive processes. For instance, operating several flights at the same time or solving conflicts between aircrafts (intrinsic load) require air traffic controllers to make the right decisions under high time pressure and to give ground-to air instructions in a limited time (extraneous load; [START_REF] Mélan | Recall Performance in Air Traffic Controllers Across the 24hr Day: Influence of Alertness and Task Demands on Recall Strategies[END_REF].

Modulation of cognitive resources by alertness

The second issue raised by the present study was the finding of a main effect of participants' alertness on task performance and differential heart rate. Both measures were specifically reduced when participants performed either working memory task in the morning, while their self-rated alertness was low [START_REF] Galy | What is the relationship between mental workload factors and cognitive load types?[END_REF]. These results are in agreement for instance with the performance decrement reported when a number-matching task involving working memory was performed in the morning rather than later during the day [START_REF] Fabbri | Effect of time of day on arithmetic fact retrieval in a number-matching task[END_REF]. Likewise, a mental effort has been shown to be associated with decreased subjective alertness and increased theta power in the EEG, reflecting both an arousal decline [START_REF] Smit | Mental and physical effort affect vigilance differently[END_REF].

Interestingly, a physical effort induced a vigilance increment that was associated with higher subjective performance ratings but not with higher effective task performance. In contrast, in a driving simulation task, moderate cognitive load and moderate arousing motion improved participants' subsequent performance in various cognitive tasks, while these effects declined following either a low cognitive workload task or the absence of arousing motion [START_REF] Jackson | Low Cognitive Load and Reduced Arousal Impede Practice Effects on Executive Functioning, Metacognitive Confidence and Decision Making[END_REF].

In line with these findings, the free working memory capacity that participants may have devoted to genuine load in the present study was proposed to be determined by both the minimal resources that were necessarily used to deal with intrinsic and extraneous load, as has been outlined above, and by individual's functional state, expressed by alertness and assessed by differential heart rate [START_REF] Cariou | Differential 24-h variations of alertness and subjective tension in process controllers: Investigation of a relationship with body temperature and heart rate[END_REF]. This is in agreement with the idea that ''mental load refers to the load that is imposed by task (environmental) demands. Mental effort refers to the amount of cognitive capacity or resources that is actually allocated to accommodate the task demands'' (Sweller et al., 1998, p. 266). According to Jonge (2010, p. 113), "germane cognitive load is the space that is left over that the learner can decide how to use, so this can be labelled as cognitive effort". This hypothesis was favored by studies investigating alertness effects on cognitive task performance by asking participants to perform a task at different times of day, either in controlled laboratory conditions or in field studies. In field studies, alertness variations may, however, depend on the job-situation considered and in particular on specific workload or on job demands (Mélan et al., 2007;[START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: investigation in the field of aerospace activities[END_REF]. In the latter study for instance both air traffic controllers and satellite controllers reported higher alertness on shift-beginning rather than on later shift-phases, as a result of task organization across the shift. Further, the relation between alertness and task performance is not a simple linear relation, as time of day has been shown to interact with task load factors, including memory load, discrimination difficulty and presentation modality, suggesting that [START_REF] Galy | Investigation of task performance variations according to task requirements and alertness across the 24-h day in shift workers[END_REF]Mélan et al., 2007). In other words, the entrainment of cognitive efficiency rhythms is driven by the circadian rhythm of arousal and is dependent on the amount of resources used to solve a task [START_REF] Fabbri | Effect of time of day on arithmetic fact retrieval in a number-matching task[END_REF].

Further, when satellite controllers performed the arithmetic mental task while they were on duty, their alertness ratings were positively related to task performance (high extraneous load) on day-shifts and with self-rated cognitive effort during task completion on night-shifts.

Conversely, high alertness was associated with low perceived job demands on day-shifts (physical demands), and on night-shifts (psychological demands). Further, both job activity (perceived job demands and real-job activity) and alertness were higher on day-shifts than on night-shifts. These data stress the need to consider shift-scheduling features, but also task organization within shifts when investigating workload in a given job-situation. This more especially as the consequences of reduced alertness in terms of safety and security in real-job situations are now well documented [START_REF] Tucker | Working time, health and safety: A research synthesis paper[END_REF]. Findings of laboratory and field studies investigating cognitive load factors may also be accounted for by resource theory that posits that a performance decrement is due to resource demand, mental fatigue and cognitive overload [START_REF] Helton | Brief mental breaks and content-free cues may not keep you focused[END_REF].

Cognitive appraisal: modulatory effect on cognitive resources versus effect on germane load

Analysis of cognitive appraisal effects yielded similar effects than those described in the previous section for alertness. Task performance was only affected by a task difficulty x time pressure interaction in the morning (low alertness) but not in the afternoon (high alertness), and in those participants who had a "threat appraisal", whilst not in those exhibiting a "challenge appraisal" in this situation. Even though the same effects were observed for the two factors, it is not clear from a theoretical point of view whether they intervened on the same processes, i.e.

exerting their effects at the same level of the CL model. Strictly speaking, they would have somehow prevented efficient implementation of particular strategies, as their effects became apparent only in the high difficulty and time pressure condition, requiring the use of such strategies for high task performance.

This raises the possibility that cognitive appraisal may have decreased available cognitive resources that participants may have devoted for strategy implementation, as has been suggested in the previous section for alertness. According to [START_REF] Folkman | If it changes it must be a process: Study of emotion and coping during three stages of a college examination[END_REF], cognitive appraisal determines participants' task investment and the use of available cognitive resources for additional strategic cognitive processing. Engagement has been reported to correlate with challenge appraisal, high task focus and positive affect [START_REF] Maier | Relation of cognitive appraisal to cardiovascular reactivity, affect, and task engagement[END_REF][START_REF] Matthews | Profiling task stress with the Dundee Stress State Questionnaire[END_REF]. The present study, the combined effects of intrinsic and extraneous load on cognitive appraisal may be explained by lower task investment in those participants with a "threat appraisal" compared to those with a "challenge appraisal". Accordingly, the latter would have been able to use more appropriate strategies as a result of their task investment, in particular in the more demanding task condition. From this point of view, cognitive appraisal played a similar role than alertness in the present experiment, and determined an individual's cognitive resources available for germane load, once the minimal resources (i.e. intrinsic and extraneous load) have been subtracted. If this was indeed the case, it is tempting to speculate that the modulatory effect of cognitive appraisal on cognitive resources were mediated by processes that are not under participants' conscious control, as is the case for alertness that is controlled by endogenous mechanisms. The influence of learner motivation, involving both conscious and unconscious processes, could be a good candidate for mediating these effects.

The role of learner motivation in CLT (Moreno and Mayer, 2007) has been neglected until recently (for a review, see [START_REF] Kuldas | Greater Cognitive Effort for Better Learning: Tailoring an Instructional Design for Learners with Different Levels of Knowledge and Motivation[END_REF], despite the fact that an individual's motivation is certainly a key process in learning and performance. [START_REF] Sweller | Element interactivity and intrinsic, extraneous, and germane cognitive load[END_REF] proposed that germane load could be related to individual characteristics, i.e. to learner motivation and may reflect the cognitive resources devoted to dealing with the to-be-learned material. [START_REF] Debue | What does germane load mean? An empirical contribution to the cognitive load theory[END_REF] found that germane load was positively associated with several dimensions of cognitive absorption, representing a measure of user motivation.

Alternatively, it may be argued that threat appraisal would act directly on the implementation of efficient strategies, independently of cognitive resources. The multiple effects of a threat response, and in particular the negative affect [START_REF] Maier | Relation of cognitive appraisal to cardiovascular reactivity, affect, and task engagement[END_REF][START_REF] Matthews | Sustained performance under overload: Personality and individual differences in stress and coping[END_REF] may indeed hamper participants' to apply adequate strategies to solve the task, as the result of either a loss of control, motivation or allocation of effort or attention [START_REF] Debue | What does germane load mean? An empirical contribution to the cognitive load theory[END_REF][START_REF] Kuldas | Greater Cognitive Effort for Better Learning: Tailoring an Instructional Design for Learners with Different Levels of Knowledge and Motivation[END_REF]Moreno and Mayer, 2007).

Recent evidence from the literature suggests that cognitive appraisal of the situation may have directly interfered with implementation of specific task strategies, rather than indirectly by diminishing overall resources available for germane load. As a threat response is associated with negative affect [START_REF] Maier | Relation of cognitive appraisal to cardiovascular reactivity, affect, and task engagement[END_REF][START_REF] Tomaka | Cognitive and physiological antecedents of threat and challenge appraisal[END_REF], it may generate task-irrelevant affective and/or cognitive processing (for a review, [START_REF] Kuldas | Greater Cognitive Effort for Better Learning: Tailoring an Instructional Design for Learners with Different Levels of Knowledge and Motivation[END_REF]. Negative emotions may for instance bring about task-irrelevant thoughts that are retrieved from long term-memory probably at the same time as numerical facts required for solving the present task. Alternatively, when information is perceived as frustrating or aversive, learners would exert no more cognitive effort for processing the information, in particular when demanding mental math skills are necessary, and this even more when performing under time pressure. Inhibitory effects of negative emotions may also emerge when learners make a conscious effort to avoid failures while solving a task. Likewise, attempts to suppress stereotype-related thoughts generate anxiety and narrow participants' attention, thereby consuming cognitive resources that are unavailable for task performance [START_REF] Steele | Stereotype threat and the intellectual test performance of African Americans[END_REF]. More recent studies suggested that in such a context several processes would impair working memory resources which are necessary for test taking. Physiological stress and inadequate arousal would directly impair processing.

Monitoring performance to restore the cognitive balance would both elicit appraisal processes resulting in negative affect and cognitions. These processes and subsequent efforts to suppress negative thoughts and emotions would consume cognitive resources that are unavailable for the to-be-performed task [START_REF] Schmader | an integrated process model of stereotype threat effects on performance[END_REF][START_REF] Appel | Stereotypes and the Achievement Gap: Stereotype Threat Prior to Test Taking[END_REF].

From the above considerations it is clear that the affective and/or cognitive processes potentially activated by threat appraisal are not relevant to the to-be-performed task. For this reason, Kuldas et al. (2014, p. 365) consider that "cognitive load as task-irrelevant thoughts associated with negative emotions need to be distinguished from the intrinsic and extraneous load".

Accordingly, irrelevant thoughts and emotions may directly impact on, or interfere with, the implementation of mental calculation strategies. According to these considerations, effects of alertness and cognitive appraisal would involve different pathways and act at different levels of the CL model. Cognitive appraisal would act on a cognitive level, because the thoughts, though irrelevant, generate cognitive load that would hamper strategy implementation required for the task to be performed. In other words, the load induced by cognitive appraisal would be the result of superfluous processes that do not directly contribute to learning. As this is precisely the definition of extraneous load in CLT [START_REF] Sweller | Element interactivity and intrinsic, extraneous, and germane cognitive load[END_REF] it may be considered as extraneous load.

Instead, alertness would intervene at a non-cognitive level, and would reduce available cognitive resources in a nonspecific manner, as suggested in the present study by its effects on a psychophysiological measure.

CONCLUSION

The present findings lend further support to the model illustrated on figure 2. Briefly, alertness may have determined overall cognitive resources available, whereas task difficulty and time pressure would have determined the cognitive load necessarily involved while solving the task (intrinsic plus extraneous load). The combined action of these factors would determine the remaining cognitive resources can be for germane cognitive load and execution of appropriated strategies. This vision implies that alertness and other cognitive load factors would act on two different components of the cognitive system confirming the asymmetric nature of the relationship between germane load on one hand, and intrinsic and extraneous loads on the other [START_REF] Schnotz | A reconsideration of cognitive load theory[END_REF], and explaining the absence of an interaction between alertness and task difficulty or time pressure. As task performance varied with alertness, task difficulty, and time pressure, this load measure would be most sensitive to variations of total load. The remaining measures used in the study were sensitive to task difficulty and time pressure, suggesting that they assessed mainly intrinsic and extraneous mental workload. The latter measures were also sensitive to alertness variations what is not surprising given that alertness variations are associated with task performance variations in difficult task conditions [START_REF] Galy | Investigation of task performance variations according to task requirements and alertness across the 24-h day in shift workers[END_REF]Mélan et al., 2007;[START_REF] Mélan | Recall Performance in Air Traffic Controllers Across the 24hr Day: Influence of Alertness and Task Demands on Recall Strategies[END_REF][START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: investigation in the field of aerospace activities[END_REF]Smit et al., 2007).

Cognitive appraisal would also determine germane load, by acting either on overall resources available, like alertness, or by interfering directly with strategy implementation. The results did not allow deciding which explanation is the most likely, as alertness and cognitive appraisal effects were similar. Given that intrinsic and extraneous load only affected performance in participants with a threat appraisal, cognitive appraisal may specifically affect the ability to implement additional strategies. This would also account for the observation that cognitive appraisal did not interact with alertness, so that cognitive appraisal may act on the third level (represented in figure 2). Further studies are necessary to test this hypothesis and the idea that cognitive appraisal and alertness act via different pathways. For instance, investigating taskunrelated thoughts by a specific questionnaire [START_REF] Helton | Brief mental breaks and content-free cues may not keep you focused[END_REF], should thus reveal whether such thoughts are more frequent in participants with a threat appraisal than in those exhibiting a challenge appraisal. Further, in line with the motivation hypothesis, encouraging participants may increase their self-confidence and thereby decrease threat appraisal.

Figure 1 .

 1 Figure 1. Bars: Mean number of correct responses in the morning and in the afternoon as a

Figure 2 .

 2 Figure 2. Graphical representations of putative relationships between cognitive load factors and

Table 6 .

 6 Differential heart rate as a function of task difficulty, time pressure and alertness

	Differential heart rate			Confidence interval to 95%
			Mean	Standard	Inferior born Superior
				error		born
	Low	Low pressure	4.358	.748	3.030	5.914
	difficulty	High pressure	6.099	.966	4.184	8.087
	High	Low pressure	4.573	.792	3.154	6.306
	difficulty	High pressure	4.286	.595	3.242	5.619
	r 2 adjusted	.120
			Time	Difficulty X	Alertness
		Difficulty	pressure	time pressure
	β	.251	.422	-.495	.348
	Sig value	.359	.117	.182	.000*

Table 7 .

 7 Correlations between cognitive load measures

Author Contributions

EG and CM made equivalent contributions to the different aspects of the present work and are both considered first author.

Conflict of interest statement:

The authors declare that the research was conducted in the absence of any commercial or financial relationship that could be construed as a potential conflict of interest.


J De Clermont-Gallerande

Maggy Colas

F Celarie

Y Gueguen

M Bergler

D De Ligny

T Hayakawa

P Thomas

; M Dutreilh-Colas

; F Célarié

; Y Gueguen

; M Bergler

; D De Ligny

; T Hayakawa

; P Thomas

Correlation between

come

Introduction

Tellurite glasses have interested researchers in the field of photonic application for many years. Indeed, they are good candidates for optical fibers thanks to their high linear refractive index, high dielectric constant, wide infrared transmittance, and their high third order non-linear optical values [START_REF] El-Mallawany | Tellurite glasses handbook: physical properties and data[END_REF][START_REF] Mirgorodsky | Ab initio study of the nonlinear optical susceptibility of Te O 2 -based glasses[END_REF][START_REF] Wang | Tellurite glass: a new candidate for fiber devices[END_REF][START_REF] Kim | Linear and Nonlinear Optical Properties of TeO2 Glass[END_REF].

Ab-initio studies showed that the pure TeO2 glasses have the highest non-linear optical properties among tellurite glasses (5) (fifty times more than fused silica glasses [START_REF] Kim | Linear and Nonlinear Optical Properties of TeO2 Glass[END_REF][START_REF] Duclère | Third order nonlinear optical properties of a paratellurite single crystal[END_REF]), but extreme quenching conditions are needed to obtain glass [START_REF] Sarjeant | New Glassy and Polymorphic Oxide Phases Using Rapid Quenching Techniques[END_REF]. Consequently, modifier oxides are required. Different systems have been studied in their abilities to form glasses (glassy domains) and their structural, linear and non-linear optical properties for many years in IRCER laboratory [START_REF] Udovic | Thermal characteristics, Raman spectra and structural properties of new tellurite glasses within the Bi2O3-TiO2-TeO2 system[END_REF][START_REF] Udovic | Formation domain and characterization of new glasses within the Tl2O-TiO2-TeO2 system[END_REF][START_REF] Linda | New glasses within the Tl2O-Ag2O-TeO2 system: Thermal characteristics, Raman spectra and structural properties[END_REF][START_REF] Noguera | Dynamics and crystal chemistry of tellurites. II. Compositionand temperaturedependence of the Raman spectra of x(Tl2O)+(1-x) Te2O glasses: evidence for a phase separation?[END_REF][START_REF] Dutreilh-Colas | The TeO 2 -rich part of the TeO 2 -Ga 2 O 3 system: equilibrium and non-equilibrium phase diagram[END_REF][START_REF] Blanchandin | New heavy metal oxide glasses: investigations within the TeO2-Nb2O5-Bi2O3 system[END_REF][START_REF] Jeansannetas | Glass Structure and Optical Nonlinearities in Thallium(I) Tellurium(IV) Oxide Glasses[END_REF]. Among them, adding TiO2 is well known to increase the glass forming ability resulting in homogeneous glasses with only slight changes in the structure of pure TeO2 glass [START_REF] Udovic | Thermal characteristics, Raman spectra and structural properties of new tellurite glasses within the Bi2O3-TiO2-TeO2 system[END_REF][START_REF] Soulis | The role of modifier's cation valence in structural properties of TeO2-based glasses[END_REF][START_REF] Zaki | Synthesis, thermal, structural and linear optical properties of new glasses within the TeO2-TiO2-WO3 system[END_REF].

Adding ZnO in tellurite glasses significantly increases the glass forming domain (up to 40mol% ZnO) [START_REF] Ahmmad | Physical and optical properties of zinc arsenic tellurite glasses[END_REF]. Binary TeO2-ZnO glasses are useful media for ultra-low loss optical fibers (1 dB/km) in the wavelength range of 3.4-4 µm [START_REF] Van Uitert | ZnCl2 glass: A potential ultralow-loss optical fiber material[END_REF]. Different studies have been done on TeO2-ZnO glasses based on Raman spectroscopy data [START_REF] Sekiya | Raman spectra of MO-TeO2 (M = Mg, Sr, Ba and Zn) glasses[END_REF][START_REF] Bürger | Glass formation, properties and structure of glasses in the TeO2-ZnO system[END_REF][START_REF] Duverger | Raman spectroscopic investigations of the effect of the doping metal on the structure of binary tellurium-oxide glasses[END_REF][START_REF] Hoppe | Structure of zinc and niobium tellurite glasses by neutron and x-ray diffraction[END_REF][START_REF] Kozhukharov | Atomic arrangement of a zinctellurite glass[END_REF], and neutron and X-ray diffraction [START_REF] Thorbahn | Compositional dependence of the stress-optic response in zinc tellurite glasses[END_REF]. The different studies showed that adding ZnO to the original TeO2 glass matrix results in (i) a structural transformation of TeO4 into TeO3 units and so a linear decrease of the optical properties (ii) a band gap decrease as the glasses turn more transparent upon adding ZnO [START_REF] Ghribi | Thermal, optical and structural properties of glasses within the TeO2TiO2ZnO system[END_REF].

The goal of the present study is to highlight a correlation between the evolution of the mechanical properties and the structure of (100-x)TeO2-5TiO2-xZnO (x=15, 17.5,[START_REF] Bürger | Glass formation, properties and structure of glasses in the TeO2-ZnO system[END_REF]22.5,25 (TTZ) glasses as a function of temperature especially around the glass transition temperature (Tg). In this study, the medium-range structure of TTZ glasses is studied using in-situ Raman spectroscopy and mechanical properties by Resonance Frequency and Damping Analysis (RFDA) and Brillouin experiments [START_REF]Standard Test Method for Dynamic Young's Modulus, Shear Modulus and Poisson's Ratio by Impulse Excitation of Vibration[END_REF]. By looking at the properties of the glass as a function of temperature, it might be possible to have an idea of their ability to fiber shaping..

Experimental

Sample preparation

The relevant amount of the different initial powders (commercial: α-TeO2: Toldini 99,9%, TiO2: Aldrich 99%, ZnO : Alfa Aesar 99,99%) within the ternary system (100-x)TeO2-5TiO2-xZnO %mol, with x= 15; 17.5; 20; 22.5 and 25 (respectively named TTZ15, TTZ17.5, TTZ20, TTZ22.5 and TTZ25) were ground in a mortar then melted in a platinum crucible at 850°C before being quenched on a brass mold preheated at 150°C. The glass domain is smaller than the one found in [START_REF] Ghribi | Thermal, optical and structural properties of glasses within the TeO2TiO2ZnO system[END_REF] due to the amount of powder used (13g) to synthesize the samples for mechanical experiment. The obtained glasses were then annealed at 30°C below the glass transition temperature (taken from [START_REF] Ghribi | Thermal, optical and structural properties of glasses within the TeO2TiO2ZnO system[END_REF][START_REF] Kabalci | Optical properties and crystallization kinetics of (TeO2)(ZnO)(TiO2) glasses: Optical properties and crystallization kinetics of (TeO2)(ZnO)(TiO2) glasses[END_REF]) for 12 hours in order to release stresses resulting from the melt-quenching method. The final concentrations of the samples have been controlled by EDS experiments which evidence a deviation less than 2% from the theoretical composition.

As many experiments have been done, the size and synthesis conditions of the samples have been adapted to the needs of each measure. All the relevant information are summarized in the Table 1.

Experiment

Initial mass (g) Raman spectra were recorded in the 10-1000cm -1 spectral range, using a T64000 HORIBA Jobin-Yvon spectrometer operating in the triple subtractive configuration at 514.5 nm. Samples were heat using a LINKAM TMS600 device (5°C/minute).

All Raman spectra were normalized (total area normalization) and baseline corrected (linear correction).

The normalized spectra were then decomposed using the Focus program [START_REF] De Sousa Menses | FOCUS version 1.0, software utility for the creation of optical function[END_REF] based on previous studies [START_REF] Linda | New glasses within the Tl2O-Ag2O-TeO2 system: Thermal characteristics, Raman spectra and structural properties[END_REF][START_REF] Ghribi | Thermal, optical and structural properties of glasses within the TeO2TiO2ZnO system[END_REF][START_REF] Ghribi | Structural, mechanical and optical investigations in the TeO2-rich part of the TeO2-GeO2-ZnO ternary glass system[END_REF], with 10 oscillators: 9 Gaussian functions and 1 log-normal function. As the spectra are recorded at different temperature, all functions were independently corrected from the Bose-Einstein factor. Due to the width and overlapping of the bands of the normalized Raman spectra (figure 1) all Gaussian functions were width at half maximum (FWHM) and frequency fixed, and only the intensity was left free. As the log-normal function is well defined, all fitting parameters were left totally free (frequency, FWHM and intensity).

The TTZ glass Raman spectra's frequencies range can be divided in two different parts: the low wavenumber region with the Boson peak (BP), the high wavenumber region (300-800 cm - 1 ) with the deformation of bridges (Zn-O-Zn or Zn-O-Te and asymmetric and symmetric Te-O-Te) and the elongation vibrations of Te-O bonds for TeO3 and TeO4 polyhedra (figure 2). The mechanical properties have been obtained by Resonance Frequency and Damping Analysis (RFDA). Details on this technique can be found in the ASTM international base [START_REF]Standard Test Method for Dynamic Young's Modulus, Shear Modulus and Poisson's Ratio by Impulse Excitation of Vibration[END_REF]. Sample have been heat until the loss of the signal (10°C/minute).

Brillouin measurements have been done on the ARABICA platform (Associated Raman Brillouin Calorimetry) [START_REF] Veber | Combined Differential scanning calorimetry, Raman and Brillouin spectroscopies: A multiscale approach for materials investigation[END_REF]. Samples have been heated at 10°C/min until 420°C. Time accumulation from Brillouin signal is 30 seconds (spectrum each 5°C).

Results and discussion

Raman spectroscopy

Vibrational studies of TeO2-ZnO glasses have been extensively done [START_REF] Sekiya | Raman spectra of MO-TeO2 (M = Mg, Sr, Ba and Zn) glasses[END_REF][START_REF] Bürger | Glass formation, properties and structure of glasses in the TeO2-ZnO system[END_REF][START_REF] Duverger | Raman spectroscopic investigations of the effect of the doping metal on the structure of binary tellurium-oxide glasses[END_REF] at room temperature. It has been reported [START_REF] Bürger | Glass formation, properties and structure of glasses in the TeO2-ZnO system[END_REF] that adding ZnO in the glasses has different consequences. By Raman spectroscopy, a shift of the band corresponding to the vibration of the TeO4 polyhedra toward higher frequencies and a shift of the band corresponding to the vibration of the non-bridging oxygen in TeO3 and TeO4 polyhedra to higher values accompanied by a progressive increase in intensity are observed. A decrease of the intensity of the band corresponding to the vibration of the Te-O-Te bridges and a shift to lower frequencies is also noted. According to Bürger et al. [START_REF] Bürger | Glass formation, properties and structure of glasses in the TeO2-ZnO system[END_REF], it has been evidenced that the introduction of zinc oxide in TeO2 glasses will induce Non Bridging Oxygens (NBO) species. The length of one of the Te-O bond of the TeO4 units gradually increase, leading into TeO3+1 units and then TeO3 units with an increase in zinc oxide content.

Kozukharov et al. reported that ZnO is introduced as ZnO6 octahedra either within tellurite chains or between them [START_REF] Kozhukharov | Atomic arrangement of a zinctellurite glass[END_REF]. At low content of ZnO, a part of the TeO4 trigonal bipyramids (tbps) becomes asymmetric, producing TeO3+1 units observed in the Zn2Te3O8 crystalline phase. For higher concentration of ZnO, the TeO3+1 units loose one oxygen to become TeO3 trigonal pyramids (tp) found in ZnTeO3 crystalline phase [START_REF] Kozhukharov | Atomic arrangement of a zinctellurite glass[END_REF].

Thorbahn et al. [START_REF] Thorbahn | Compositional dependence of the stress-optic response in zinc tellurite glasses[END_REF], evidenced by Raman spectroscopy and EXAFS experiments for binary TeO2-ZnO glasses that Zn coordination number decreases from 6±1.6 to 4±0.6 with a Zn-O bond length that remained constant with increasing ZnO content. It was also reported that rather than the ZnO6 configuration discussed above, ZnO is present in the form of ZnO4 tetrahedra for high ZnO content [START_REF] Thorbahn | Compositional dependence of the stress-optic response in zinc tellurite glasses[END_REF].

In a previous study in IRCER laboratory, Ghribi et al. have studied the TeO2-TiO2-ZnO and the TeO2-GeO2-ZnO system at room temperature [START_REF] Ghribi | Thermal, optical and structural properties of glasses within the TeO2TiO2ZnO system[END_REF][START_REF] Ghribi | Structural, mechanical and optical investigations in the TeO2-rich part of the TeO2-GeO2-ZnO ternary glass system[END_REF]. They concluded that adding ZnO in glassy matrix will in a first step lead to breaking Te-O-Te bridges, including network depolymerization, and in a second step, with more ZnO content, to the formation of Te-O-Zn and Zn-O-Zn bridges.

As the role of ZnO in still unclear, we proposed here a structural investigation of the ternary system TTZ on a wide ZnO range content (15-25 mol%) from RT up to crystallization temperature. However, the crystallization of the samples won't be discuss in this paper.

Nevertheless, as parent crystallized phases give good indications of the unit, which can be evidence in glasses, an overview of crystallized phases in the TeO2-ZnO binary system is proposed.

Two stable crystalline phases respectively ZnTeO3 for 50% mol TeO2 -50% mol ZnO and Zn2Te3O8 for 60% mol TeO2 -40% mol ZnO [START_REF] Hanke | Die Kristallstruktur von Zn2Te3O8[END_REF][START_REF] Hanke | Zinktellurit: Kristallstruktur und Beziehungen zu einigen Seleniten[END_REF] can be found [START_REF] Ghribi | Synthesis, structural and mechanical investigations of new tellurite materials for non-linear optical applications[END_REF].

The Zn2Te3O8 structure is composed of chain-like structure with Te3O8 groups made with one TeO4 and two TeO3+1 units with ZnO5+1 in octahedra-like structures between the chains.

Whereas, the ZnTeO3 has Zn substituting Te to form new Zn-O-Te chains. Pure ZnO crystal is made of chains of tetrahedra units. By comparing each crystallized phases, it can be hypothesized that at low concentration of ZnO, the zinc polyhedra could be between the tellurite chains in a pseudo-octahedral form (looking like the Zn2Te3O8 crystalline phase). And as ZnO content increases, the TeO4 and TeO3+1 polyhedra will decrease for an increase in TeO3 polyhedra, the ZnO5+1 polyhedra will also go toward a ZnO4+1 and will substitute the tellurium oxide inside the chains to form Te-O-Zn bridges as shown in the ZnTeO3 crystalline phase. It is possible that in glasses with high concentration in zinc oxide, the ZnO will be tetrahedra-formed inside the chains (as shown in the pure ZnO crystal). The crystallization of the samples have been presented elsewhere [START_REF] Ghribi | Synthesis, structural and mechanical investigations of new tellurite materials for non-linear optical applications[END_REF].

For an in-depth understanding of the vibration modes of the Raman spectroscopy of Zn2Te3O8 and ZnTeO3crystalline phases, computational studies by using LADY software [START_REF] Smirnov | LADY: Software for lattice dynamics simulations[END_REF] were done, and a theoretical Raman spectra was calculated for each phases. By comparing the Raman spectra of the two crystalline phases (figure 2), the evolution of the Raman spectra as a function of the concentration can be explained. An increase of ZnO content causes : (i) an increase of the Zn-O-Zn/Zn-O-Te bonds (300-400 cm -1 ), (ii) a decrease of the Te -O-Te bridges (400-550 cm -1 ), (iii) a decrease of TeO4 polyhedra and an increase of TeO3 polyhedra (550-800 cm -1 ) is expected.

As the Boson peak (BP) is a manifestation of the excess of Vibrationnal Density of States (VDoS), phonon scattering is caused by intrinsic density fluctuations domains in the structure (within which short and medium range order is maintained and beyond which the material is isotropic). The BP, which is characteristic of the glassy state, will give important information allowing the correlation of the mechanical and structural approaches. This paper will focus on its evolution. Most of the graphs will be presented in a non-conventional way, namely abscissa and ordinate will be normalized by the value of the parameter under study at TgDSC (obtained from DSC measurements,) to facilitate the comparison between samples.

Figure 3 represents the evolution of the Boson peak (BP) intensity. A decrease of the BP intensity before Tg is first observed and then followed by an increase up to crystallization temperature.

Figure 4a, b, c summarized the Boson peak wavenumber evolution. Figure 4a illustrates the general evolution of the Boson peak wavenumber of each sample as a function of temperature. A slight shift to lower wavenumber up to Tg, and after this temperature, a strong difference of the wavenumber evolution is observed. Figure 4b shows the Boson peak wavenumber as a function of the composition at Room temperature (RT). A decrease of the wavenumber with an increase of the ZnO concentration is observed until TTZ20 and a strong increase of this intensity is noted for further concentrations. To illustrate the evolution of the Boson peak wavenumber after Tg, Figure 4c represents the evolution of the slope of the curve shown in Figure 4a; this slope represents the rate at which the wavenumber of the Boson peak is decreasing after Tg. A slight decrease of the value between TTZ15, TTZ20 and TTZ25 can be noted and an abnormal behavior compared to the previous three samples was observed for TTZ17.5 and TTZ22.5 samples.

As a glass is considered composed of small domains with organized structure. Those domains (thereafter named blobs), are randomly arranged inside the glass, explaining its nonexistent long order structuration.

When the BP intensity decreases, heterogeneity between blobs decreases [START_REF]Inelastic light, neutron, and X-ray scattering related to the heterogeneous elasticity of glasses[END_REF][START_REF] Champagnon | Boson peak, structural inhomogeneity, light scattering and transparency of silicate glasses[END_REF]. The present evolution means that with an increase in temperature, there is a rearrangement at short and intermediate distance of the glass to reach an energy minima at each temperature. After the glass transition temperature, the transition toward a viscous liquid will increase the heterogeneity of the glass. After the crystallization temperature, there is a decrease of intensity of the Boson peak due to the disappearance of the glass phase.

Duval et al. [START_REF] Duval | Vibrational dynamics and the structure of glasses[END_REF] and Elliott et al. [START_REF] Elliott | A Unified Model for the Low-Energy Vibrational Behaviour of Amorphous Solids[END_REF] independently proposed a relationship between the size of the blobs ξ ,the BP frequencies ωBP and the mean sound velocities Vav (see equation 3) calculated from the mechanical properties of the glasses. The evolution of ωBP then gives a first understanding of the evolution of the size of the blobs as a function of the temperature. ξ = 𝑉 𝑎𝑣 /𝜔 BP (1) In the present study, before Tg, a classical trend as a function of temperature is observed, as glass is relaxing the size of the blobs increases, and after Tg, the samples goes toward a state of a viscous liquid, increasing the size even further (figure 4a).

Figure 4b evidences that at RT, ωBP decreases up to TTZ20 and then increases meaning that blobs size firstly increases and then decreases.

ωBP fluctuations clearly evidences a change in the structural behavior of the glass.

Mechanical approach

𝐺 = 𝐺 𝑇𝑔 ( 𝑇𝑔 𝑇 ) 𝛼 (2)
The obtained parameters of both simulated curves are reported on respectively table 2 (Wachtman parameters) and table 3 (Rouxel parameters). The intersection of both calculated curves gives the value Tg. As this temperature is dependent of the thermal history of the sample, this temperature will be denoted mechanical Tg: TgRFDA. This TgRFDA will be used to normalize the data. The B parameter of the Watchman equation is quite constant for both E and G data, which means that the evolution of the properties are equivalent up to Tg. On the opposite, the evolution of the simulated alpha coefficient from the Rouxel equation evidences huge variations which means that after Tg, Young and shear modulus have special trend which has to be studied. As a function of temperature, for each sample, a slight decrease of E and G before TgRFDA is observed which is exacerbated after (figure 6a and7a). The Poisson ratio, which is calculated using G and E, presents also strong variations around Tg (figure 8a). This evolution will be further discussed in the discussion part.

The evolution of the E, G and ν values (figure 6b, 7b, 8b respectively) at room temperature and as a function of the concentration show an equivalent variation: a decrease of their values from TTZ15 to TTZ17.5 and then an increase from TTZ17.5 to TTZ25 is observed. Those results are consistent with the results previously published by Ghribi et al. [START_REF] Ghribi | Synthesis, structural and mechanical investigations of new tellurite materials for non-linear optical applications[END_REF], using ultrasonic echography experiments.

As Poisson ratio gives an information on the average connectivity of the glass [START_REF] Greaves | Poisson's ratio and modern materials[END_REF], an increase of the connectivity of the network before TTZ17.5 and a decrease of the connectivity after is observed. Those results are consistent with the proposed theory: at low concentration of ZnO, Zinc oxide polyhedra are localized between the tellurite chains, linking them together by weak bonding, increasing by consequence the connectivity of the network but decreasing E and G values. At higher concentration, zinc atom substitutes Te atom within the chains, so it does not link the chains as it did at lower concentration. This in turn will decrease the connectivity of the network and increase once more E and G values compared to the lower concentration of zinc oxide.

The alpha coefficient (extracted from the Power law equation), which expresses the softening rate and which is correlated to the liquid fragility index [START_REF] Mezeix | Elasticity and viscosity of BaO-TiO2-SiO2 glasses in the 0.9 to 1.2Tg temperature interval[END_REF], was calculated by measuring the slope of the curve obtained after plotting log(G/G(Tg)) versus f(log(Tg/T)) for temperatures higher than Tg (figure 9a). The same way is used for log (E/E(Tg))=f(log Tg/T)) (figure 9b).

The α coefficient evolution as a function of the concentration (figure 10) shows that the two glasses with the highest α value are the TTZ17.5 and TTZ22.5 samples. The other three glasses have a linear increase of the α coefficient value.

An higher value of α coefficient means a higher rate of decreasing mechanical properties, so the linear increase in the α coefficient value between TTZ15, TTZ20 and TTZ22.5 glasses means that the more ZnO content inside the glass, the faster the mechanical properties will decrease after Tg. The α coefficient for the two glasses TTZ17.5 and TTZ22.5 shows that the mechanical properties of these two glasses decrease at a faster rate.

Comparing the evolution of the TTZ17.5 glass to the previous conclusion on the structural properties, another hypothesis can be added: when the Zinc oxide is between the tellurite chains, the bonds between the Zinc oxide and the tellurium oxide are weak, and become even weaker after the glass transition temperature (decreasing at the same time the mechanical properties faster (higher α coefficient value)).

The evolution of the TTZ22.5 glass sample is still under study and other experiments are being done to understand the strange behavior of this sample compared to other compositions.

ARABICA experiment

In the Brillouin spectra, due to the backscattering geometry used in the experimental setup only longitudinal mode are observed. The position of the Brillouin band strongly depends on the temperature (figure 11). A slight shift of the Brillouin position to lower energy before the glass transition temperature (TgDSC) is observed. Around 20°C before the glass transition temperature, a sharper decrease of the Brillouin shift is observed followed by a second slope break. The variation just before the glass transition temperature will be further discussed in the discussion part. As the Brillouin shift is proportional to the longitudinal velocity of the glasses, so proportional to the mechanical properties of each samples (equation 4). It is then possible to compare the mechanical properties obtained by RFDA experiments to the results from the Brillouin shift.

𝑉 𝐿 (𝐵𝑟𝑖𝑙𝑙𝑜𝑢𝑖𝑛) = 𝜆.(𝐵𝑟𝑖𝑙𝑙𝑜𝑢𝑖𝑛𝑠ℎ𝑖𝑓𝑡) 2𝑛 (4)
With λ the wavelength of the measurement (488nm in this work) and n the linear refractive index at the same wavelength. Thanks to the figure 12, which compare the variation of the longitudinal velocities obtained by Brillouin experiment and RFDA experiment as a function of the ZnO content, a good agreement of the variation is found between the two different techniques, with a decrease of the longitudinal velocities between TTZ15 and TTZ17.5 followed by an increase thereafter. By normalizing the Brillouin shift in the same way as for the mechanical properties to extract the alpha coefficient of the power law equation, it is possible to compare the evolution of the mechanical properties and the variation of the Brillouin energy by calculating the slopes in the second part of the graphic in figure 13a.

Hence, by comparing the values of slope calculated showed in figure 13b to the one from the α coefficient (figure 10), it is shown that the evolution as a function of the concentration has the same linear evolution between the three samples TTZ15, TTZ20 and TTZ25 with two anomalies being TTZ17.5 and TTZ22.5.

The results of the Brillouin experiment are in a good agreement with the mechanical properties as a function of the concentration but also as a function of temperature, with a slight decrease of the Brillouin shift as the mechanical properties decrease, and so even after Tg. A first interesting comment can be done on the difference between the values of Tg obtained as a function of the technique used. Using the same method as for RFDA data to extract a mechanical Tg, Raman data have been fitted with linear functions before and after the slope break observed on data, the value of Tg is extracted at the intersection of the two fitted parts. Comparing TgRaman and TgRFDA to TgDSC, it can be seen that TgRaman is lower and TgRFDA is higher. This difference partly come from the difference of sample's size, the difference of the heating rate (5°C/min for Raman spectroscopy and 10°C/min for the RFDA and ARABICA measurements). Moreover Raman data are obtained in a semi-dynamic way (Stop of the heating ramp during acquisition time) and not a dynamic one like RFDA and ARABICA data recording. Now, looking at Brillouin and RFDA experiments (in particular the Poisson coefficient) more in details, some interesting facts can be noted:

Discussion

In Brillouin experiment (figure 11), Brillouin shift evolution exhibits an intermediate slope break between the glassy state and the liquid one: This intermediate domain is characteristic of relaxation events suggesting that the heating rate of 10°C/min used for the experiment was too fast, creating strains inside the glass. The intercept between the intermediate and the liquid part is equivalent to the TgDSC and was used to define the TgBrillouin (results shown on table 4).

By comparing the Brillouin data to the Raman data it can be noticed in Figure 14 that the TgRaman corresponds to the intercept of the linear extrapolation between the glassy state and the liquid one of the Brillouin shift (relaxation temperature (TR) values in table 5). This also corresponds to the strong variation around Tg found on the Poisson ratio curve (figure 9), where the variation in Poisson ratio starts to fluctuate (values in table 5). This means that the relaxation of the sample due to the high heating rate will strongly affect the connectivity of the network before the glass transition temperature, due to a rearrangement of the glassy network.

With Vav the average between the transversal velocity (VT) and the longitudinal velocity (VL). It is possible to calculate the two required velocities with the two equation below (4) With K the Bulk modulus. Vav is then calculated with the equation below.

(5) Figure 15a represents the evolution of the size of the domains as a function of temperature. Before the glass transition temperature, a slight increase of this parameter is evidenced, with a steeper increase after the glass transition temperature. This evolution is in accordance to the previous evolution of the Boson Peak, and correspond to the relaxation of the glass before Tg and then the transition toward a viscous liquid after Tg.

As a function of the concentration (Figure 15b), two different evolutions can be seen: a sharp decrease of the size of the blobs between TTZ15 and TTZ17.5 and hereafter data are almost constant. This means that drastic changes of the structure after TTZ17.5 are observed, which can be explained by the change of the Zn atom coordination number as a function of ZnO content.

The discrepancy between the evolution of the size of the blobs as a function of the concentration and the evolution of the Boson peak wavenumber comes from the evolution of the sound velocities, and by this bias the evolution of the mechanical properties. This also means that having the Boson peak wavenumber evolution isn't enough to understand exactly how the size of the blobs evolve, even if it can give a rough understanding of this evolution as shown as a function of temperature.

Conclusion

Correlation between structural properties of glasses to different kind of macroscopic physic one has been one of the most important field of research on glasses for years. In this study, some interesting facts have been pointed out.

By comparing RFDA experiments and Raman spectroscopy, it has been possible to understand the structural properties of a glass having a complex structure with two entities that have a coordination number which change as a function of the TeO2 and ZnO content. glass, (ii) RFDA experiment gave an understanding on the strength of the different bonds as a function of the concentration, and (iii) from both Raman and RFDA experiments by calculating the blobs size, the structural evolution of the glass at intermediate-distance has been evidenced. Lastly, the behavior of the samples after the glass transition temperature has been evidenced and links to the particular behavior of Zinc polyhedra were noted. Indeed, the variation of the alpha coefficient of the mechanical properties studied by RFDA experiment, the variation of the slope after Tg of the Brillouin experiment and the variation of the slope of the shift in wavenumber of the Boson peak recorded in Raman spectroscopy, some anomalies stood out exactly at the same ZnO content : 17.5%ZnO and 22.5%ZnO.

Concerning mechanical properties, a higher slope value after the glass transition means that the decrease of the mechanical properties is faster

In Raman spectroscopy, a shift toward lower wavenumber means that the blobs size increases. So a higher slope value after the glass transition means that the blobs size increases at a higher rate.

From the two previous point, it can be porposed that: when the blobs size increase at a faster rate, the mechanical properties will decrease at a slower rate. Thanks to this hypothesis, it will be easier to predict how the mechanical properties will evolve at temperature close and higher than Tg which will be helpful for optical fiber shaping.

Figure 1 :

 1 Figure 1 : Raman bands attribution of a typical TTZ sample (Example of the TTZ15 sample)

3 Figure 2 :

 32 Figure 2 : Simulated Raman spectra of the Zn2Te3O8 and ZnTeO3 crystalline phases

Figure 3 :

 3 Figure 3: BP intensity as a function of Tg/T. Inset: zoom of the variations around Tg

Figure 4 :

 4 Figure 4: a) ωBP as a function of Tg/T. Inset: zoom of the variations around Tg b) ωBP as a function of ZnO content at 30°C (RT). c) Average slope of data extracted from figure 4-a) after Tg

2. 2

 2 .1. RFDA The temperature dependence of the elastic moduli and the shear moduli are illustrated figure 8. As explained by Mezeix et al. (39) for silica glasses, a good description of the comportment of glasses at temperatures before Tg is obtained by using the model proposed by Wachtman et al. (40) (equation 2) and after Tg, this temperature dependence can be modeled by a power law equation proposed by Rouxel et al. (41) (equation 3). 𝐺 = 𝐺 0𝐾 -𝐵𝑇. exp (

Figure 5 :

 5 Figure 5: Example of the shear modulus simulations as a function of temperature for the TTZ25 sample.

Figure 6 :Figure 7 :Figure 8 :

 678 Figure 6: a) Shear modulus as a function of temperature in the TTZx (x=15; 17.5; 20; 22.5; 25) system. b) Shear modulus as a function of the concentration in ZnO at 30°C (RT)

Figure 9 :

 9 Figure 9: a) G/G(Tg)=f(Tg/T); b) E/E(Tg)=f(Tg/T); Insets: zoom of the variations around Tg

Figure 10 :

 10 Figure 10 : Alpha coefficient as a function of the ZnO concentration

Figure 11 :

 11 Figure 11: TTZ glasses Brillouin position as a function of temperature

Figure 12 :

 12 Figure 12: Variation of the longitudinal velocities calculated from the Brillouin and RFDA experiments as a function of the concentration in zinc oxide at room temperature.

Figure 13 :

 13 Figure 13: a) Brillouin peak energy normalized with the Brillouin peak energy at the glass transition temperature as a function of Tg/T. Inset: zoom of the variations around Tg b) Variation of the slope in the second regime after the glass transition temperature

Figure 14 :

 14 Figure 14 : Example of how the relaxation temperature and the glass transition temperature are obtained (TTZ15 glass)

Figure 15 :

 15 Figure 15 : Evolution of the size of the blobs as a function of a) temperature; b) the concentration in ZnO (at RT)

  (i) As usual Raman spectroscopy gave informations on the change of the Te-O polyedra inside the

Table 1 :

 1 Information on the different experimental procedures for each experiment.

*Associated Raman, Brillouin Calorimetry. D: diameter; h: height of a cylinder; l: length of a parallelepiped; L: width of a parallelepiped; e: thickness of a parallelepiped.

Table 2 :

 2 Wachtman equation simulation parameters for E and G curves

	Sample		E			G
	Wachtman parameters	E0K	B	T0	G0K	B	T0
	TTZ15	52.45	0.023	531	21.30	0.011	588
	TTZ17.5	47.43	0.019	494	19.87	0.010	574
	TTZ20	51.34	0.018	353	20.87	0.009	503
	TTZ22.5	55.39	0.021	481	22.08	0.011	723
	TTZ25	54.25	0.029	700	21.89	0.011	634
	Sample		E			G
	Rouxel parameters	ETg	Tg(E)	α	GTg	Tg(G)	α
	TTZ15	48.38	593	1.26	30.06	383	1.01
	TTZ17.5	27.43	691	4.31	39.10	527	4.65
	TTZ20	30.33	722	2.79	24.20	514	1.45
	TTZ22.5	51.27	639	4.11	30.46	570	3.72
	TTZ25	29.82	717	3.66	26.09	547	2.25

Table 3 :

 3 Rouxel equation simulation parameters for E and G curves

Table 4 :

 4 Glass temperature measured by the different experiments (The values of TgDSC shown in table3were measured thanks to the ARABICA setup at the same time as the Brillouin shift measures).

	Sample	TgRaman (°C)	TgRFDA (°C)	TgBrillouin (°C)	TgDSC (°C)
		(±10°C)	Tg(E)	Tg(G)	(±10°C)	(±5°C)
			(±5°C)	(±5°C)
	TTZ15	310	339	336	336	335
	TTZ17.5	313	353	354	339	337
	TTZ20	321	354	347	341	339
	TTZ22.5	324	372	372	340	341
	TTZ25	331	355	351	345	343

Table 5 :

 5 Relaxation temperatures for each samples in RFDA and Brillouin experimentsTo go further, as explained before, Duval et al.[START_REF] Duval | Vibrational dynamics and the structure of glasses[END_REF] and Elliott et al.[START_REF] Elliott | A Unified Model for the Low-Energy Vibrational Behaviour of Amorphous Solids[END_REF] independently found a relationship that links the size of density fluctuations domains ξ with the position of the Boson peak frequency ωBP and the sound velocities inside the glasses.

	ξ =	𝑉 𝑎𝑣 𝜔 𝐵𝑃

Acknowledgement

The authors thank Dr. J. Cornette for valued assistance with Raman experiments and O. Noguera for his help on Raman spectra simulation. J. de CLERMONT-GALLERANDE also gratefully acknowledges the financial support from Conseil Régional du Limousin and the PICS.