L ' Impact

D U Nombre D'ingredients

Sur Le Traitement De L'information, L'imagerie

Mentale De

L A Saveur

L E Choix

D U Produit

Fanny Thomas
email: fanny.thomas@univ-lyon3.fr

Sonia Capelli
email: sonia.capelli@univ-lyon3.fr

THE NUMBER OF INGREDIENTS DEPICTED ON FOOD PACKAGING IMPACT INFORMATION PROCESSING, MENTAL TASTE IMAGERY AND PRODUCT CHOICE?

Keywords: charge cognitive, évaluation, Ingrédients, produit alimentaire, Besoin de cognition, packaging DOES cognitive load, evaluation, ingredients, food product, need for cognition, packaging

Dans un contexte fortement concurrentiel des produits alimentaires en supermarchés, les consommateurs ont des difficultés à traiter en profondeur les informations mentionnées sur un packaging. Cette recherche examine comment le nombre d'ingrédients représentés sur les packagings a une incidence sur l'évaluation du produit, en fonction de la capacité des consommateurs à traiter l'information. Une première étude révèle que, sous forte charge cognitive, les packagings illustrés avec plusieurs ingrédients induisent plus d'imagerie mentale de la saveur, favorisant une augmentation de l'intention d'achat. Dans une deuxième étude, il est montré que les consommateurs ayant un besoin de cognition fort et sous forte charge cognitive, le packaging sans ingrédients illustrés, est préféré lorsque les consommateurs sont motivés par la faim. En l'absence de charge cognitive, l'information est traitée centralement et l'évaluation ne dépend pas du nombre d'ingrédients représentés sur le packaging.

Introduction

Adding a product picture on packaging when products cannot be seen directly is a classic managerial application; it has a proven positive effect on judgment [START_REF] Underwood | Packaging as brand communication: effects of product pictures on consumer responses to the package and brand[END_REF]. Visual or textual cues on packaging facing are used to present arguments on intrinsic product features. For instance, Pillsbury's© 'simply' chocolate chip cookie packaging depicts five ingredients included in the recipe on the facing. The presence of a product picture on packaging facing develops mental imagery and intrinsic sensory properties of products [START_REF] Paivio | Mental representation: A dual coding approach[END_REF]Hirschman, 1986;[START_REF] Babin | A modified scale for the measurement of communication-evoked mental imagery[END_REF], Gavard-Perret, 1997;Gallen, 2005). Adding visual cues on the packaging also increases information to process [START_REF] Winkielman | The hedonic marking of processing fluency: implications for evaluative judgment. The psychology of evaluation: Affective processes in cognition and emotion[END_REF], consumers evaluate products using a heuristics strategy during product evaluation [START_REF] Chaiken | Heuristic and systematic information processing within and beyond the persuasion context[END_REF]. At the opposite, given the purchase context of food products, increasing information may be a counter-productive strategy. A shopper must choose in 25 seconds from among thousands of references [START_REF] Chandon | Do We Know what We Look At?: An Eyetracking Study of Visual Attention and Memory for Brands at the Point of Purchase, INSEAD, 1, 2-41. coding?[END_REF]. Shoppers are thus under heavy cognitive load and this can affect decisions made by shoppers [START_REF] Malhotra | Information and sensory overload. Information and sensory overload in psychology and marketing[END_REF]. In this context, it is harder for them to process the messages presented [START_REF] Iyengar | When choice is demotivating: Can one desire too much of a good thing?[END_REF], leading to failure to memorise and process information [START_REF] Shiv | Heart and Mind in Conflict: The Interplay of Affect and Cognition in Consumer Decision Making[END_REF]. The more (versus the less) consumers are involved and can process messages, the more they take the central (versus peripheral) route to evaluate the promoted product [START_REF] Cacioppo | Central and peripheral routes to persuasion: An individual difference perspective[END_REF]. Consequently, consumers' ability to process several pictures depicted on a package should depends on whether they experience information overload. It also depends on their capacity to enjoy mobilising cognitive effort to process messages through the need for cognition [START_REF] Cacioppo | The need for cognition[END_REF]. The present research investigates the efficiency of adding many ingredient pictures on a food product package according to consumers' ability to process information. This ability depends on both the context (cognitive load) and the consumers' characteristics (need for cognition). Two experimental studies shows the positive impact of the number of ingredients depicted on food packaging facing on intrinsic product perception, purchase intent and preference for the packaging is investigated in a high cognitive load condition.

Processing packaging information

Processing information

Information processing depends on the number of elements included in the message conveyed by a package. Most often, whatever the kind of information, seven elements (plus or minus 2) are processed simultaneously in the short term [START_REF] Miller | The magical number seven, plus or minus two: some limits on our capacity for processing information[END_REF]. Beyond this limit, the information processing task becomes too complex: the higher the quantity of information, the less the message is understood and perceived by consumers [START_REF] Winkielman | The hedonic marking of processing fluency: implications for evaluative judgment. The psychology of evaluation: Affective processes in cognition and emotion[END_REF]. Similarly, the more (versus less) consumers are involved and motivated, the more they process advertising messages via the central route (versus peripheral, which entails concentrating on elements such as typography, illustration colours, etc...) [START_REF] Cacioppo | Central and peripheral routes to persuasion: An individual difference perspective[END_REF]. In the Elaboration Likelihood Model [START_REF] Cacioppo | Central and peripheral routes to persuasion: An individual difference perspective[END_REF], involvement depends on the motivation, ability and opportunity to process the message. When consumers' involvement is high, they implement the central route, or the persuasion route, mobilising previous knowledge related to the advertising message. Along this route, the process generates thoughts and arguments in line with the presented elements. Consumers can thus integrate and retain information. When consumer involvement is low, information is processed via the peripheral route. The peripheral route helps consumer create beliefs about the product regarding secondary superficial and peripheral elements more than on arguments and product benefits presented in the message. This information processing strategy consumes fewer cognitive resources; it is used by consumers who are less motivated to process information or who have fewer cognitive resources available. Consumers then create cognitive heuristics, facilitated by familiar information or information that contains few cues [START_REF] Chaiken | Heuristic and systematic information processing within and beyond the persuasion context[END_REF]. This simplifies and accelerates the decision process. Central and peripheral routes are related to the matching resources theory based on advertising message persuasion and supplement the ELM model. These two constructs highlight available and required resources. Available resources correspond to individuals' mental capacities to process the advertising message. Required resources reflect necessary abilities to adequately process the message [START_REF] Anand | Strategies for Designing Persuasive Messages: Deductions from the Resource Matching Hypothesis[END_REF]. Based on the ELM model and matching resources theory, consumers who are able to process information should process food packaging via a central route and be convinced by the arguments more than the pictures presented. On the contrary, consumers who are not able to process information should adopt the peripheral route and be more convinced by peripheral cues such as pictures conveyed by the package.

Cognitive load

Cognitive load induces an overload in working memory and leads to failure to memorise and process information [START_REF] Shiv | Heart and Mind in Conflict: The Interplay of Affect and Cognition in Consumer Decision Making[END_REF] and then, can affect decisions made by consumers [START_REF] Malhotra | Information and sensory overload. Information and sensory overload in psychology and marketing[END_REF]. The effect of cognitive load on information processing varies with message fluency. Studies of fluency show that message simplicity makes cognitive processing easier and enhances positive evaluation (Novemsky, Dhar, Schwarz, & Simonson, 2007). The consumers react to an overload of information by becoming more incited, bringing to a reduction of the attention concerned an aspect limited by the incoming information [START_REF] Kahneman | Attention and effort[END_REF]. As information can't be process in depth, a high cognitive load should thus encourage consumers to use a peripheral route to process information, and then favour a message that includes numerous coherent images.

Need for cognition (NFC)

As mentioned, the route consumers use to process a message partly depends on their ability; message processing can be observed through the NFC. [START_REF] Cacioppo | The need for cognition[END_REF] define the NFC as a stable interindividual difference, like a tendency to enjoy cognitively challenging activities. The measure of NFC is strongly correlated with intrinsic motivation. Individuals low in NFC are more influenced by peripheral distractors and tend to process information peripherally. They use cognitive heuristics to form an opinion. Individuals high in NFC do not mind making efforts to process information. They stay focused on a processing activity that requires significant cognitive efforts and are less distracted by peripheral elements. They process information more deeply [START_REF] Cacioppo | The need for cognition[END_REF]. They are more likely to form impressions or change their attitude about the central elements of an argument rather than the peripheral elements [START_REF] Cacioppo | Central and peripheral routes to persuasion: An individual difference perspective[END_REF].To summarise, without cognitive load, high NFC individuals should appreciate getting ample information about the product they are considering. Conversely, under high cognitive load, high NFC individuals are uncomfortable processing ample information, and consequently prefer to see little information on the package, which lets them control their cognitive process via the central route.

Packaging visual cues and consumers' beliefs

Packaging as a silent salesman is a rich advertising medium to convey intrinsic and extrinsic product attributes. The number of elements and the level of similarity between the elements on facing determine the level of complexity [START_REF] Pieters | The stopping power of advertising: measures and effects of visual complexity[END_REF][START_REF] Berlyne | Novelty, complexity, and hedonic value[END_REF]. The more (versus less) the message contains distinct elements, the more (less) complex it is. This determines the difficulty of message processing. In this research, it is considered the number of ingredients depicted visually on a package. Because information processing is hierarchical, visual information is more fixed, better memorised than textual information [START_REF] Piqueras-Fiszman | Using combined eye tracking and word association in order to assess novel packaging solutions: A case study involving jam jars[END_REF] and processed faster (Hirschman, 1986).They are more vivid and able to attract attention [START_REF] Mitchell | The effects of verbal versus visual components of advertisements on Novemsky[END_REF][START_REF] Paivio | Picture superiority in free recall: Imagery or dual coding?[END_REF]. Including a product image or graphical representations yields benefits regarding consumer attitudes and beliefs about a product [START_REF] Underwood | Packaging communication: attentional effects of product imagery[END_REF][START_REF] Underwood | Packaging as brand communication: effects of product pictures on consumer responses to the package and brand[END_REF][START_REF] Bone | Package graphics and consumer product beliefs", brand attitudes and attitude toward the advertisement[END_REF]. Product pictures elicit imagery processing (Pavio, 1986;[START_REF] Babin | A modified scale for the measurement of communication-evoked mental imagery[END_REF]Gavard-Perret, 1997;Gallen, 2005), multisensory imageries (e.g., taste, Hirschmam, 1986) and communicate information on intrinsic product and sensory characteristics [START_REF] Pantin-Sohier | L'impact des stimuli informationnels d'un nouveau produit alimentaire sur les réactions affectives et cognitives du consommateur[END_REF]. The more consumers pay attention to iconographic elements, the more they form product judgments [START_REF] Underwood | Packaging as brand communication: effects of product pictures on consumer responses to the package and brand[END_REF]. Ingredients depicted on packaging facing induce a representation of the naturalness of the product [START_REF] Rozin | The meaning of "natural" process more important than content[END_REF], which conveys healthiness in the product composition owing to the familiarity of natural ingredients and linked to tasty product [START_REF] Werle | Unhealthy food is not tastier for everybody: The "healthy= tasty" French intuition[END_REF]. Also, ingredients depicted increase perceived pleasantness [START_REF] Lancelot Miltgen | Communicating Sensory Attributes and Innovation Through Food Product Labeling[END_REF].To summarise, the literature highlights that visual cues on packaging might elicit representations of sensory information such as taste, along with increased judgment on product evaluation, depending on consumers' ability to process the packaging, level of cognitive resources and need for cognition. Hence the following hypotheses: H1: The number of ingredients depicted on packaging impacts the purchase intent via increasing of perceived mental taste imagery and

H1a : In presence of cognitive load, perceived mental taste imagery increases when packaging is with many ingredients

H1b : In absence of cognitive load, perceived mental taste imagery doesn't depend on the number of ingredients depicted on packaging

To better capture those effects, consumers under high cognitive load are investigated, introducing the potentially counter-balancing effect of motivation to process. For food products, to create motivation to process information centrally is to consider hungry consumers. First, they find the presentation of a food product more attractive [START_REF] Lewin | The Conceptual Representation and the Measurement of Psychological Forces[END_REF]. Then, hunger impacts strategic decision-making especially in the case of task-solving with cognitive effort (De Ridder,, Kroese, Adriaanse, & Evers, 2014) as with a cognitive load.

H2: Under high cognitive load, packaging with no ingredients is preferred more (versus less) to packaging with many ingredients by hungry consumers with high (versus low) NFC .

Study 1: Ingredient number impact on mental taste imagery and purchase intent

Methodology

A 2 (number of ingredients depicted on the package: few vs many) x 2 (low vs high cognitive load) between-subject experiment was conducted. To manipulate the number of ingredients depicted on the packaging, four stimuli of a chocolate-nut brownie package branded with an unknown name were created and pre-tested (sample of 145 respondents). Subjects were grouped into two levels of information illustrated on the facing: few ingredients (0 and1) versus many ingredients (3 and 5).Natural ingredients (nuts, chocolate, eggs, butter and flour), pretested before the experiment, were perceived positively and belonged to the component list illustrated. Packaging also contained a traditional product picture for the category. Measures. Explained variables are assessed via seven-point measurement scales: perceived mental taste imagery (Adapted from [START_REF] Miller | A scale for measuring advertisementevoked mental imagery[END_REF]α= .90), purchase intent (Bearden, Lichenstein & Teel, 1984;α= .94). Level of perceived naturalness of the ingredients: by asking respondents to choose from among a list of 20 ingredients, 50% of which were natural, those they thought the product contained. The difference between natural and artificial ingredients selected is calculated to produce a score. Perceived healthiness (1 item in 7point Likert: 'This product is healthy'), perceived naturalness (adapted from [START_REF] Rozin | The meaning of "natural" process more important than content[END_REF], simplicity perception [START_REF] Cox | Beyond first impressions: The effects of repeated exposure on consumer liking of visually complex and simple product designs[END_REF], brownie appreciation and brand name awareness were controlled. The questionnaire ends with questions about gender and age. Procedure and participants. A sample of 217 students (63% women, average age 22.5, SD = 5.75) was tested in laboratory. Data were collected for two weeks. Participants were informed that there was a project on a new product launch and that they could enter a drawing (for a digital tablet) as an incentive. For the cognitive load condition, each participant was asked to memorise a 6-digit and to restore at the end of the experiment. Then, one of the four packaging pictures was presented on a digital tablet for 25 seconds and the respondent was asked to complete a paper questionnaire.

Results study 1

Results. After checking the measuring validity, hypotheses were sequentially tested via SPSS software with linear regressions as recommended by [START_REF] Hayes | An index and test of linear moderated mediation[END_REF] with model 8 (table 1). Perceived healthiness, naturalness and natural/artificial estimated ingredients difference were integrated as co variable for mental taste imagery and purchase intent.

Annex 1 Results of study 1

x:Few (coded 0) vs many ingredients (1)-y:Purchase Intent w: Low (coded 0) versus high ( 1 Results indicate a positive and non-significant effect of (x) on (y) (p >.10). Also it indicates a negative and non-significant effect of (x) on (m) ( p >.10). Perceived mental taste imagery does not differ according to the number of ingredients depicted (M manyingredients = 5.27, SD = 1.45; M fewingredients = 5.36, SD = 1.21). (m) and (y) are correlated to the perceived healthiness of the product (p < .05 ; p < .01) and to the level of naturalness of the ingredients in the product recipe (p =.05 ; p < .01), however they are not correlated to the perceived naturalness (p > .10 ; p > .10).

When consumers are under high cognitive load, results indicate a positive and significant interaction term between (x) and (w) on (m) (p < .05); packaging depicting many ingredients increases perceived mental taste imagery of the product under high cognitive load. And then, (m) has a positive and significant effect on (y) (p < .05). Results indicate a negative and nonsignificant interaction term between (x) and (w) on (y) (p >.10). The indirect effect of (x) on (y) through (m) moderated by (w) is positive and significant, 0 is not included (β = .11; 90% CI = .0403 to .2305), indicating a total moderated mediation (Zhao et al 2010). Packaging depicting many (vs few) ingredients increases purchase intent, under high cognitive load, via the increasing of mental taste imagery. H1 is then validated.

Study 2: Ingredient number impact on product choice according to hungry consumers' need for cognition

As in study 1, cognitive load is manipulated and the focus is on the case of high cognitive load condition. Moreover, consumers' NFC is integrated to investigate the role of consumers' ability to moderate the relationship between the number of depicted ingredients and packaging preference.

Methodology

The same product and cognitive load manipulation as in study 1 were used. A 2* between subject (low vs high cognitive load) *1 (choice between two packages) experiment is conducted. To contrast the results and base them on the dichotomisation of the NFC (low vs high), two packages with major variance in visual signals represented (via number of ingredients depicted) were compared. A Bonferroni test showed that packaging with no ingredients is less hard to understand ( measure of scale of Pieters et al, 2010; α =.86) (M noingredients = 1.76, SD = .99; M 5ingredients = 2.42, SD = 1.59; p < .05) than a package with five ingredients.

Measures. NFC (Cacioppo & Petty, 1992;α =.75) and level of hunger were measured and the sample was divided into high and low groups based on median split on NFC scores (median = 4.5; SD =.64) and Level of hunger scores (median = 4; SD = 1.87). Gender, age and brand name knowledge were also controlled. Procedure and participants. A sample of 122 students was used and surveyed in laboratory. Data were collected for one week. 50 % of consumers reporting being very hungry; they were retained for the study. The final sample was composed of 52% females, mean age = 21 years, SD = 1.13.

4.2Results study 2

An exploratory analysis via logistic regression was computed with choice between a package with no ingredients depicted (coded 0) and one with 5 ingredients depicted (coded 1) as the dependent variable. Covariables are: low NFC (coded 0) and high NFC (coded 1) ; low cognitive load (coded 0) and high cognitive load (coded 1). Results show a direct effect of cognitive load (β = -2.614, Wald 2 (1) = 5.198, p < .05). In the presence of cognitive load and high NFC, participants preferred packaging without ingredients. 29% of participants chose packaging without ingredients depicted, while 16% of participants chose packaging with 5 ingredients depicted, H2 is thus affirmed. Results also show that there is a difference in choice between participants in low or high cognitive load conditions (β = 2.83, Wald 2 (1) = 7.467, p < .01). 29% of the participants chose packaging with 5 ingredients, while 21% chose packaging without ingredients under cognitive load. Those results are in line with study 1.

Discussion and conclusion

Results show in study 1 that, under high cognitive load, a package depicting many ingredients induces more mental taste imagery and a better purchase intent. Multisensory imagery induced product taste judgment through peripheral message processing and then purchase intent.

Processing is then peripheral due to message processing overload. Mental imagery is based on visual cues, beliefs and judgment. Because the supermarket context induces high cognitive load, it is advisable to use packaging with many ingredients, which increases purchase intent. These results confirm the positive impact of using images when information is processed peripherally: ingredient pictures are used as signals for increasing mental taste imagery [START_REF] Underwood | Packaging as brand communication: effects of product pictures on consumer responses to the package and brand[END_REF]. Anymore, the storage of information increases when the message contains coherent images (Heckler & Childers,1992).As expected, in a context of motivation (study 2) and high cognitive load, packaging is processed via a peripheral route due to the lack of cognitive resources, inducing a preference for packaging including many ingredients. When considering consumers' NFC, the results emphasise an interaction between high cognitive load and high NFC, which induces a preference for packaging with no ingredients because the participant processes information conveyed by the packaging via a central route, which entails greater cognitive effort. The research is limited, first, the storage of packaging in a competitive environment on store shelves is not considered, and cognitive load is manipulated fictitiously. Second, the sample is represented by students. Third, familiarity with iconic representations for this product category was not considered.


Thermodata -

B Cheynet

P Chaud

P-Y Chevalier

E Fischer

P Mason

M Mignanelli

Ca, Sr, O, Fe ) Ba

Mg Rho Al

Cr Fe

Cr, Fe, O, Mg Spinel Al

B, O Si Al

C, Cr C B Fe

Ni Mc

) Ag

In Al

Nuclear Thermodynamic Database Version 2007-01 developed by

transposing the Directive 96/9/EC of the European Parliament and the Council of 11 March 1996 on the legal protection of databases.

Extraction and/or re-utilization of the whole or of a substantial part, evaluated qualitatively and/or quantitatively, is strictly prohibited.

"Extraction" means the permanent or temporary transfer of all or a substantial part of the contents to another medium by any means or in any form.

"Re-utilization" means any form of making available to the public all or a substantial part of the contents by the distribution of copies, by renting, by on-line or other forms of transmission.

The user is not allowed to make changes or amendments to the database. Completeness and intactness have to be respected.

Disclaimer

The data have been carefully evaluated by experts, they have been checked, but THERMODATA can give no guarantee for the correctness of the data provided. In any important research, results should be carefully examined and rechecked before final conclusions are drawn.

I. INTRODUCTION

Since 1990 some people were interested in the assessment of thermodynamical data for a number of compounds of reactor materials and fission products based on the recommendations of a specialists meeting held at JRC-Ispra, Italy in 1990 [*]. Critical assessments have been made on a very large number of compounds and systems. NUCLEA is a Thermodynamic Data Base built for collecting all this knowledge. This database has to cover the entire field from metal to oxide domains. It allows the user to calculate the thermochemical equilibrium state at any step of a severe accident and to use the results of the thermodynamic approach for improving the predictions of thermo-hydraulic or other accidents codes.

NUCLEA

The Gibbs energy of all possible multicomponent condensed or gaseous substances and solution phases are modelled. The binary and ternary Gibbs energy parameters were critically assessed by means of sophisticated optimisation procedures.

Applications of a global thermodynamic approach, i.e. the simultaneous use of a highquality thermodynamic database and an equilibrium calculation code, are numerous :

condensed state phase diagrams, transitions, liquidus/solidus, compositions and proportions, coupling thermodynamics and thermo-hydraulic, viscosity, segregation, residual power distribution, gaseous fission products release in any external conditions … Such a database in much more than a compilation of thermodynamic data from various sources, its constitution needs a considerable work for self-consistency analysis, to ensure that all the available experimental information is satisfactorily reproduced.

Updating and improving the database has to be a regular task, tightly linked to the needs of end-users.

[*] Fission Product Chemistry in Severe Nuclear Reactor Accidents, Specialist's Meeting at JRC-Ispra, 15-17 January 1990, EUR 12989 EN (1990), A.L. Nichols ed.

GENERAL DESCRIPTION

PURE COMPONENTS.

The NUCLEA Thermodynamic Database for In-and Ex-Vessel Applications contains the 18 + 2 following elements :

O-U-Zr-Fe-Cr-Ni-Ag-In-B-C-Ba-La-Ru-Sr-Al-Ca-Mg-Si + Ar-H.

Ar and H are not taken into account in condensed solution phases.

CONDENSED SOLUTION PHASES.

The condensed solutions (48 non-stoichiometric phases, based on 281 reference substances) were deduced from the analysis of the assessed sub-systems (binary, ternary, …) ; some of them present possible miscibility gaps.

The list of condensed solutions stored in NUCLEA is presented in table 1.

CONDENSED SUBSTANCES.

The condensed stoechiometric compounds are presented in table 2.

Hydrogen was added because it is a major component of the system, but the dissolution of hydrogen in condensed solid and liquid solutions is not taken into account at this time.

GASEOUS SPECIES.

The gaseous species were added as an ideal mixture. The list is presented in table 3

STATE of VALIDATION

The state of validation of a thermodynamic database is characterised by the good agreement between calculated and available experimental results (phase diagrams and thermodynamic properties) concerning basic sub-systems (binary, ternary, …) or practical global experiments, made in similar conditions and at thermodynamic equilibrium.

For user information, a quality criterion, based on comparison between calculation and available experimental data, has been established for each assessed sub-system.

Estimated

No experimental data available.

Perfectible

Some domains need more experimental information (phase diagram or thermodynamic properties).

Acceptable

The system is well known and satisfactorily modelled.

High quality

The system is quite known and modelled.

The complete list of the 153 (18*17/2) metal-metal or metal-oxygen binary systems based on pure elements and 105 (15*14/2) oxide pseudo-binary systems based on pure oxides are presented in tables 5 and 6 respectively.

Due to the very high number of possible ternary (18*17*16/3*2 = 816) and pseudo-ternary (15*14*13/3*2 = 455) systems, it is completely unimaginable to assess all of them in a human delay. For that reason it was decided to assess only the most important ternary systems for practical applications. The list of the selected ternary and pseudo-ternary systems is presented in tables 7 and 8 respectively.

For each system, the order number, source and provisional quality criterion are given. This criterion takes into account both phase diagram and thermodynamic properties, and thus cannot be indicated only on a phase diagram. This point is fundamental for the modelling of multi-component systems.

Moreover, it must be kept in mind that the set of a quality criterion remains somewhere subjective, and the improvement of existing sub-systems with newly available experimental results is a continuous task, which is part of the database management and updating.

SELECTED TERNARY AND PSEUDO-TERNARY SYSTEMS.

Table 6 Ternary systems.

Table 7

Pseudo-ternary systems.

DOMAIN OF APPLICATION AND LIMITATIONS.

In this version of NUCLEA most of the binary and pseudo-binary systems have been analysed and critically assessed either by THERMODATA or AEA-T.

Only a limited number of binary systems (mainly based on the C-Cr-Fe-Ni quaternary system) were taken in open literature. However, some of them are still insufficiently known, and further experimental work is needed for the ones interesting the nuclear field.

In a very high-number component system such as the one covered by NUCLEA, the number of possible ternaries and pseudo-ternaries is equal to 1271, while the time cost to assess only one is about one-man year. Few experimental data are available in open literature for ternaries of high interest for nuclear safety. Consequently, the complete assessment of all ternaries is not achievable in a human delay and only some selected ternary systems of main importance for nuclear safety applications were assessed at this time.

Moreover, a simple overlook of the stars attributed to all sub-systems is not the best approach to estimate the global quality of the database. In fact, only some sub-systems are especially relevant in the nuclear domain. The quality of these specific sub-systems, designated by principal users, is much more important for NUCLEA dedicated to severe accident applications. Thus, further work will still have to be done for the selected sub-systems with less than three stars.

In any case, well-selected global experiments will always have to be done to validate definitively the thermodynamic approach on the final user point of view. Simultaneously, fulfilling and improving the sub-systems in the NUCLEA is a continuous task, the assessment work being based on the CALPHAD method, and ideally never completely realised.

In summary, the Nuclear Thermodynamic Database could be considered as well validated if sufficient predicting power was reached for practical applications, both in the In-and Ex-Vessel fields.

FUTURE.

In the future, specific actions will have to be foreseen to improve the state of validation of NUCLEA, both for In-and Ex-Vessel applications.

On the one hand, such a database must be continuously updated for all binary or pseudo-binary, and selected ternary sub-systems, by taking into account the newly available experimental results in the optimisation process based on the CALPHAD method.

On the other hand, the database must also be compared to available experimental results in higher-order systems, in order to validate the global thermodynamic approach or eventually to identify remaining uncertainties or insufficient knowledge.

This task involves two different aspects :

Obviously a very high quality scientific work for obtaining reliable thermodynamic data, by using adapted thermodynamic models and sophisticated optimisation codes.

But also a considerable technical work, which is the database management, in order to maintain an updated experimental database (phase diagram and thermodynamic properties), and to be able to re-assess binary or ternary subsystems if necessary, when new experiments becomes available.

ASSESSMENT of FE-O-U-ZR

An important experimental and modelisation work was done in the last 10 years by many people in the world to obtain now a rather good knowledge and representation of that main quaternary system.

In the present version of the database all the available information (equilibrium points of phase diagrams, activities measurements, vapour pressures etc…), up to the year 2004, was taken into account in the optimisation procedure.

To allow the user to have an idea of the validity of the obtained results the calculated phase diagrams are compared, in the following pages, with some experimental points. But if anybody is interested more in detail by the experiments or by critical assessment and optimisation work he has to look at the numerous scientific papers published in the recent years.

BINARY SYSTEMS.

Fe-O, Fe-U, Fe-Zr, O-U, O-Zr, U,Zr.

PSEUDO-BINARY SYSTEMS.

O 2 U-O 2 Zr.

IMPORTANT NOTE :

It must be underlined that pseudo-binary systems including iron oxides are not real quasibinary phase diagrams. These ones are only used for evaluation of the interaction parameters, but they have to be further controlled by calculating them as valid sections of the ternary systems Fe-O-U or Fe-O-Zr.

TERNARY SYSTEMS.

Fe-O-U, Fe-O-Zr, Fe-U-Zr, O-U-Zr.

FE-O

The phase diagram of the Fe-O binary system presents the following condensed solutions and substances, with the symbols used in this work or found in open literature :

• the liquid phase, L, which shows a miscibility gap between an Fe rich liquid (L 1 ) and an FeO/Fe 2 O 3 rich liquid (L 2 ) ; • the intermediate solid oxides, Fe 3 O 4 (S) or magnetite, Fe 2 O 3 (S) or hematite, corundum ;

• the oxide solid solution, FeO 1+x , or wustite, with the face-centred cubic structure, of NaCl type, noted fcc_B1 ; • pure solid iron, with a negligible solubility of oxygen, and different allotropic structures, cubic face centred (fcc_A1) and body cubic centred (bcc_A2) ; • the gas phase, which shows an extended solubility of iron in oxygen above 2800 K.

The fundamental thermodynamic properties (Cp, ∆H 298 , S 298 ) of the stoichiometric compounds Fe 0.947 O 1 (fcc_B1), Fe 3 O 4 (S), Fe 2 O 3 (S) have been assessed separately in consistency with the available experimental data. The liquid phase has been described by a non-ideal associate model, with the formula (Fe 1 , Fe 1 O 1 , Fe 1 O 1.5 ,O 1 )(L), and the solid solution FeO 1+x by a simple one lattice model, with the formula (Fe 1 O 1 , Fe 1 O 1.5 )(fcc_B1). The gas phase has been described by an ideal mixture of gaseous species, with the formula (Fe 1 , Fe

1 O 1 , Fe 1 O 1.5 , O 1 , O 2 , O 3 ) 1 (G).
The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• the activity of iron and oxygen are in satisfactory agreement with the experimental ones in the solid state and are strongly constrained by the assessed thermodynamic properties of stoichiometric compounds ; • the wustite phase limits are very well reproduced ;

• the liquidus in the iron rich region is in satisfactory agreement with the experimental one up to 2200 K, as well as the melting point of Fe 3 O 4 (S) and all the invariant reactions ;

• the miscibility gap in the liquid state was assumed to be closed around 3000 K, in agreement with only one series of experimental points, which should be validated again.

FE-U

The phase diagram of the Fe-U binary system presents the following condensed solutions and substances, with the symbols used in this work or found in open literature :

• the liquid phase, L, which shows a complete miscibility from iron to uranium ;

• the intermetallic compounds, Fe 2 U 1 (S) with the Laves structure, and Fe 1 U 6 (S) ;

• pure solid iron, with a negligible solubility of uranium, with two allotropic structures, Fe 1 (bcc_A2) and Fe 1 (fcc_A1) ; • the uranium rich terminal solid solutions, tetragonal (tet) and body cubic centred, bcc_A2, with a small solubility of iron. • pure orthorhombic uranium U 1 (ort_A20), with a negligible solubility of iron.

The heat capacity (Cp) of the stoichiometric compounds Fe 2 U 1 (S) and Fe 1 U 6 (S) have been assessed separately in consistency with the available experimental data. The fundamental properties at room temperatures (∆H 298 , S 298 ) have been assessed in consistency with all other data. The liquid, bcc_A2 and tet phases (φ) have been described by a simple substitutional model, with the formula (Fe 1 , U 1 )(φ). A realistic extrapolation of the excess Gibbs energy of the liquid phase at high temperature is proposed. The gas phase has been described by an ideal mixture of gaseous species, with the formula (Fe 1 , U 1 ) 1 (G).

The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• the activity of iron and uranium are in satisfactory agreement with the experimental ones in the liquid state ; • the calculated and experimental phase diagrams are in very satisfactory agreement.

FE-ZR

The phase diagram of the Fe-Zr binary system presents the following condensed solutions and substances, with the symbols used in this work or found in open literature :

• the liquid phase, L, which shows a complete miscibility from iron to zirconium ; • the intermetallic compounds, Fe 765 Zr 265 (S), Fe 1 Zr 2 (S), Fe 1 Zr 3 (S) ;

• the intermediate non-stoichiometric Laves phase, Fe 2 Zr 1 (Laves) ;

• the terminal iron-rich solid solutions, bcc_A2 and fcc_A1, with a small solubility of zirconium ; • the terminal zirconium rich solution, bcc_A2, with a limited solubility of iron ;

• the terminal zirconium rich solution, with the hexagonal closed packed structure, hcp_A3, and a very small solubility of iron.

The heat capacity (Cp) of the stoichiometric compounds Fe 2 Zr 1 (Laves), Fe 1 Zr 2 (S), Fe 1 Zr 3 (S) have been estimated from the Neuman-Kopp rule. The fundamental properties at room temperatures (∆H 298 , S 298 ) have been assessed in consistency with all other data. The liquid, bcc_A2 and fcc_A1 phases (φ) have been described by a simple substitutional model, with the formula (Fe 1 ,Zr 1 )(φ). The Laves phase has been described with a two sublattice model, with the formula (Fe 1 , Zr 1 ) 2 (Fe 1 , Zr 1 ) 1 . A realistic extrapolation of the excess Gibbs energy of the liquid phase at high temperature is proposed. The gas phase has been described by an ideal mixture of gaseous species, with the formula (Fe 1 , Zr 1, Zr 2 ) 1 (G).

The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• the activity of iron and zirconium are in satisfactory agreement with the experimental ones in the liquid state ; • the selected enthalpy of mixing of the liquid phase is incompatible with the liquidus shape in the zirconium rich region ; • the calculated and experimental phase diagrams are in satisfactory agreement : the non-stoichiometry.. range of the Laves phase and the temperatures of the invariant reactions are perfectly reproduced ; the liquidus shape in the zirconium rich region should be improved.

O-U

The phase diagram of the O-U binary system presents the following condensed solutions and substances, with the symbols used in this work or found in open literature :

• the liquid phase, L, which shows a miscibility gap between an UO 2 rich liquid (L 1 ) and an uranium rich liquid (L 2 ) ; • the intermediate solid oxides, O 3 U 1 (S) or UO 3 , O 8 U 3 (S) or U 3 O 8-z , O 9 U 4 (S) or U 4 O 9-y ; the compounds U 5 O 13 +x , U 8 O 21 , UO 2.61 , have also been cited ; • the oxide solid solution, UO 2 +x , with the face-centred cubic structure, of CaF 2 (fluorite) type, Fm 3 m, cF 12 , noted fcc_C1 ; • pure solid uranium, with a negligible solubility of oxygen, and different allotropic structures, orthorhombic, U 1 (ort_A20), tetragonal, U 1 (tet), and body cubic centred, U 1 (bcc_A2) ; • the gas phase, which shows an extended solubility of uranium above 2000 K.

The fundamental thermodynamic properties (Cp, ∆H 298 , S 298 ) of the stoichiometric compounds O 3 U 1 (S), O 8 U 3 (S), O 9 U 4 (S) and O 2 U 1 (S) have been assessed separately in consistency with the available experimental data. The liquid phase has been described by a non-ideal associate model, with the formula (O 1 , O 2 U 1 , U 1 ) (L), and the solid solution UO 2 +x by a three sublattice model, with the formula (U 1 ) 1 (O 1 , □) 2 (O 1 , □) 1 (fcc_C1). In order to be compatible with the whole thermodynamic database and to allow the introduction of iron, the model has been simplified in a simple one lattice model, with the formula (O 1 , O 2 U 1 , U 1 ) 1 (fcc_C1). The gas phase has been described by an ideal mixture of gaseous species, with the formula

(O 1 , O 1 U 1 , O 2 U 1 , O 2 , O 3 , O 3 U 1 , U 1 ) 1 (G).
The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• the oxygen potential experimental database is perfectly reproduced in the UO 2+x region, while the calculated curvature is stronger than the experimental one in the UO 2-x region, especially with the simplified model. However, the values in the diphasic domains are in good agreement ; • the phase equilibria (solid UO 2 +x region, liquidus, miscibility gap tie line) are well represented, but the UO 2+x region at high temperature has to be experimentally validated. The non-stoichiometry range of U 3 O 8-z and U 4 O 9-y have not been taken into account. The hypothesis of a small solubility of oxygen in liquid uranium has been retained.

O-ZR

The phase diagram of the O-Zr binary system presents the following condensed solutions and substances, with the symbols used in this work or found in open literature :

• the liquid phase, L, which shows a complete miscibility from O 2 Zr 1 oxide to Zr metal ;

• the pure solid oxides, with the allotropic forms monoclinic O 2 Zr 1 (mon) and tetragonal O 2 Zr 1 (tet) ; • the oxide solid solution, ZrO 2-x , with the face-centred cubic structure, of CaF 2 (fluorite) type, Fm 3 m, cF 12 , noted fcc_C1 ; • the terminal zirconium rich solid solutions, body cubic centred (bcc_A2), and hexagonal closed packed (hcp_A3) pure solid uranium, with a solubility of oxygen limited to about 10 at% and 30 at% respectively ; • the gas phase, which shows an extended solubility of zirconium above 3000 K.

The fundamental thermodynamic properties (Cp, ∆H 298 , S 298 ) of the stoichiometric compound O 2 Zr 1 (mon, tet, fcc_C1) have been assessed separately in consistency with the available experimental data. The liquid phase has been described by a non ideal associate model, with the formula (O 1 , O 2 Zr 1 , Zr 1 ) 1 (L), and the solid solution ZrO 2-x, bcc_A2 and hcp_A3 by three and two sublattice models, with the respective formula (Zr 1 ) 1 (O 1 , □) 2 ((O 1 , □) 1 (fcc_C1), (Zr 1 ) 1 (O 1 , □) 3 (bcc_A2), and (Zr 1 ) 1 (O 1 , □) 0.5 (hcp_A3). In order to be compatible with the whole thermodynamic database and to allow the introduction of iron, the model of the fcc_C1 solid solution has been simplified in a simple one lattice model, with the formula (O 1 , O 2 Zr 1 , Zr 1 ) 1 (fcc_C1). The gas phase has been described by an ideal mixture of gaseous species, with the formula

(O 1 , O 1 Zr 1 , O 2 , O 2 Zr 1 , O 3 , Zr 1 , Zr 2 ) 1 (G).
The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• the oxygen potential experimental database is correctly reproduced in the monophasic regions ZrO 2-x , fcc_C1 and hcp_A3, while some disagreements have been observed in the diphasic region fcc_C1+hcp_A3 ; • the phase equilibria (solid ZrO 2-x region, diphasic regions O 2 Zr 1 (mon, tet) + hcp_A3, fcc_C1 + hcp_A3, hcp_A3 + bcc_A2) are well represented, but the liquidus L + ZrO 2-x should be validated ; • several stoichiometric oxides observed in the zirconium rich domain at low temperature (T < 750 K) could be included.

U-ZR

The phase diagram of the U-Zr binary system presents the following condensed solutions and substances, with the symbols used in this work or found in open literature :

• the liquid phase, L, which shows a complete miscibility from uranium to zirconium ;

• the body cubic centred solid solution, bcc_A2, with also a complete miscibility at high temperature and a small miscibility gap deported on the uranium side between 950 K and 1000 K ; • the terminal solid solutions, uranium rich orthorhombic and tetragonal, ort_A20 and tet, with a small solubility of zirconium, and zirconium rich hexagonal closed packed, hcp_A3, with a small solubility of uranium ; • the intermetallic solid solution, δ, which extents from 64 to 78 at% Zr.

The liquid, bcc_A2, ort_A20, tet and hcp_A3 phases (φ) have been described by a simple substitutional model, with the formula (U 1 , Zr 1 )(φ), and the δ intermetallic solid solution by a two sublattice model, with the formula (U 1 , Zr 1 ) 2 (Zr 1 )(δ). The gas phase has been described by an ideal mixture of gaseous species, with the formula (U 1 , Zr 1 ) 1 (G). The excess Gibbs energy of the liquid and bcc_A2 solid solution has been assessed more physically than in other assessments found in open literature.

The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• some experimental activities were found to be too negative and discarded for experimental reasons (interaction with crucible, impurities) ; • the calculated phase diagram is in satisfactory agreement with the experimental one ;

• thermodynamic properties in the liquid phase should be determined at high temperature.

FE-O-U

The phase diagram of the Fe-O-U ternary system presents the following solutions and substances, with the symbols used in this work :

• the liquid phase, L, which shows a miscibility gap between an Fe-U-O rich metal-oxygen liquid ( • pure solid iron, with a negligible solubility of oxygen and uranium, and two allotropic structures, body cubic centred, Fe 1 (bcc_A2), and cubic face centred, Fe 1 (fcc_A1) ; • pure orthorhombic uranium U 1 (ort_A20), with a negligible solubility of iron and oxygen ; • the gas phase (G), which shows an extended solubility in oxygen of iron above 2800 K and of uranium above 2000 K.

The fundamental thermodynamic properties (Cp, ∆H 298 , S 298 ) of the stoichiometric compounds Fe 0.947 O 1 (fcc_B1), Fe 3 O 4 (S), Fe 2 O 3 (S), O 3 U 1 (S), O 8 U 3 (S), O 9 U 4 (S), O 2 U 1 (fcc_C1) have been assessed in the individual sub-systems, as well as the thermodynamic modelling of all binary or pseudobinary phases. The ternary liquid phase has been described by a non-ideal associate model, with the formula (Fe 1 , Fe 1 O 1 , Fe 1 O 1.5 , O 1 , O 2 U 1 , U 1 ) 1 (L). The fcc_C1 and fcc_B1 solid solutions have been described will a one lattice model, with the formula (Fe 1 O 1 ,O 2 U 1 ) 1 (fcc_C1) and (Fe 1 O 1 , Fe 1 O 1.5 ) 1 (fcc_B1) respectively. The Gibbs energy of the ternary solid oxide Fe 1 O 4 U 1 (S) has been assessed from the experimental information (thermodynamics and phase diagram). The gas phase has been described by an ideal mixture of gaseous species, with the formula (Fe 1 , Fe

1 O 1 , Fe 1 O 1.5 , O 1 , O 1 U 1 , O 2 , O 2 U 1 , O 3, O 3 U 1 , U 1 ) 1 (G).
In the metal-oxygen field, the only used experimental information [1997Kle] on phase diagram is located on the line Fe-UO 2 and indicate a very low solubility of UO 2 in liquid iron at very high temperature (2873 K).

In the ternary oxide field, the Fe 1 O 4 U 1 (S) was found to be decomposed at 1310 K.

Most of the more recent experimental informations are located in the pseudo-binary vertical sections, FeO-UO 2 ([1998Hel], [2003Pet], [2004Cor]) and Fe 2 O 3 /Fe 3 O 4 -UO 2 ([1969Ril], [2005Kis]), and come from the CORPHAD and SARNET international projects.

The main features of the FeO-UO 2 isopleth to section [2004Cor] are a complete solubility between FeO and UO 2 in the oxide liquid (L 2 ), and a non negligible solubility of iron oxide in the UO 2 rich fcc_C1 solid solution. The eutectic point was experimentally assessed as T = 1615 K (1342°C) and 4 mol% UO 2 (13.6 wt%). The solubility of iron oxide in fcc_C1 at the eutectic temperature was assessed as 17 mol% FeO (5 wt%).

The Fe 2 O 3 /Fe 3 O 4 -UO 2+x isopleth section has been experimentally studied in air [1969Ril], and its edges vary with composition from UO 2+x , U Kiselova and Petrov [2005Kis]. According to these authors, the eutectic L UO 2 + FeO 1.33 was located at 1621 K (1348 °C) and 68.5 wt% UO 2 , 31.5 wt% Fe 3 O 4 , and a miscibility gap was found between 1673 K (1400 °C) and 1973 K (1700 °C) on the iron oxide rich side.

In a first approximation, the excess interaction parameters between Fe 1 O 1 and O 2 U 1 on the one hand and Fe 1 O 1.5 and O 2 U 1 on the other hand have been estimated by assuming the pseudo-binary sections as quasi-binary ones.

The real isothermal or isopleth sections may be then calculated from the complete thermodynamic modelling. The main features of the FeO-UO 2 pseudo-binary system are qualitatively well reproduced, but the residual uncertainty on the Fe 2 O 3 /Fe 3 O 4 -UO 2 pseudo-binary system leads to quantitative differences between re-calculated liquidus and experimental one, due to the presence of Fe 1 O 1.5 species in the liquid phase.

The Fe 2 O 3 /Fe 3 O 4 -UO 2 pseudo-binary system has been considered without the new assumption of a liquid miscibility gap and the corrected eutectic temperature [2005Kis].

Finally, the refinement of the liquid interaction parameters between Fe 1 O 1 and O 2 U 1 and Fe 1 O 1 . 5 and O 2 U 1 will be mainly linked to the improvement of the description of the Fe 2 O 3 /Fe 3 O 4 -UO 2 pseudo-binary system.

At high temperatures (T > 2273 K), the ternary phase diagram is characterised by the following phase equilibria :

L 1 + fcc_C1, L 1 + L 2 + fcc_C1, L 2 + fcc_C1, L 2 + G, L 2 + G + fcc_C1, L 1 + L 2 .

FE-O-ZR

The phase diagram of the Fe-O-Zr ternary system presents the following solutions and substances, with the symbols used in this work :

• the liquid phase, L, which shows a miscibility gap between an Fe-Zr rich metallic liquid (L 1 ) and an FeO/Fe 2 O 3 -ZrO 2 rich oxide liquid (L 2 ) ; it extends from the Fe-O side and closes at zirconium rich content ; it may also exist a liquid miscibility gap in the oxide field, observed in the Fe 2 O 3 /Fe 3 O 4 -ZrO 2 system between 2100 K and 2600 K, while there is a complete liquid miscibility in the FeO-ZrO 2 system. • the ZrO 2 rich oxide solid solution, with the face-centred cubic structure, of CaF 2 (fluorite) type, Fm 3 m, cF 12 , noted fcc_C1, and which can dissolves until 18 mol% FeO in ZrO 2 ; • the ZrO 2 rich oxide solid solution, with the tetragonal structure, noted tet_oxide, and which can dissolve until 7 mol% Fe 1 O 1.5 in ZrO 2 ; • the oxide solid solution, FeO 1+x , or wustite, with the face-centred cubic structure, of NaCl type, noted fcc_B1 ; no solubility of zirconia in wustite is reported ; • the terminal zirconium rich solid solution, body cubic centred (bcc_A2), with a solubility of oxygen limited to about 10 at% and a solubility of iron limited to 5 at% ; • the terminal zirconium rich solid solution, hexagonal closed packed (hcp_A3) with a solubility of oxygen limited to about 30 at% and a very small solubility of iron ; • the terminal iron-rich solid solutions, bcc_A2 and fcc_A1, with a small solubility of zirconium and a negligible solubility of oxygen ; • the intermediate non-stoichiometric Laves phase, Fe 2 Zr 1 (Laves) ; • the pure solid oxides, Fe 3 O 4 (S) or magnetite, Fe 2 O 3 (S) or hematite, corundum, O 3 U 1 (S), O 8 U 3 (S), O 9 U 4 (S) ; • the intermetallic compounds, Fe 765 Zr 265 (S), Fe 1 Zr 2 (S), Fe 1 Zr 3 (S) ; • the pure solid zirconium oxide, with the allotropic form monoclinic O 2 Zr 1 (mon) ; • the gas phase (G), which shows an extended solubility in oxygen of iron above 2800 K and of zirconium above 3000 K.

The fundamental thermodynamic properties (Cp, ∆H 298 , S 298 ) of the stoichiometric compounds Fe 0.947 O 1 (fcc_B1), Fe 1 O 1.5 (S), Fe 3 O 4 (S), Fe 2 O 3 (S), O 2 Zr 1 (fcc_C1, tet, mon), Fe 2 Zr 1 (Laves), Fe 765 Zr 265 (S), Fe 1 Zr 2 (S), Fe 1 Zr 3 (S) have been assessed in the individual sub-systems, as well as the thermodynamic modelling of all binary or pseudo-binary phases. The ternary liquid phase has been described by a non ideal associate model, with the formula (Fe 1 ,Fe 1 O 1 ,Fe 1 O 1.5 ,O 1 ,O 2 Zr 1 ,Zr 1 ) 1 (L). The fcc_C1, tet_oxide and fcc_B1 solid solutions have been described with a one lattice model, whith the formula (Fe 1 O 1 ,O 2 Zr 1 ) 1 (fcc_C1), (Fe 1 O 1 ,Fe 1 O 1.5 ,O 2 Zr 1 ) 1 (tet_oxide) and (Fe 1 O 1 ,Fe 1 O 1.5 )(fcc_B1) respectively. The terminal iron-zirconium rich solid solutions, bcc_A2 and hcp_A3, have been described by a two-sublattice model, with the respective formula (Fe 1 ,Zr 1 ) 1 (O 1 ,□) 3 (bcc_A2), and (Fe 1 ,Zr 1 ) 1 (O 1 ,□) 0.5 (hcp_A3). The gas phase has been described by an ideal mixture of gaseous species, with the formula (Fe 1 , Fe 1 O 1 , Fe 1 O 1.5 , O 1 , O 1 Zr 1 , O 2 , O 2 Zr 1 , O 3, Zr 1, Zr 2 ) 1 (G).

In the metal-oxygen field, the only used experimental information on phase diagram is located on the line Fe-ZrO 2 and gives the solubility of oxygen in iron rich-zirconium liquid alloys. (1873 K -2073 K).

Most of the more recent experimental informations are located in the pseudo-binary vertical sections, FeO-ZrO 2 ([1997Fis], [1998Hel], [1999Bec], [2003Gus], [2004Cor]) coming from the CORPHAD international project, and Fe 2 O 3 /Fe 3 O 4 -ZrO 2 ([2003Pil], [2004Pet]) coming from the ECOSTAR international project.

The main features of the FeO-ZrO 2 isopleth section [2004Cor] are a complete solubility between FeO and ZrO 2 in the oxide liquid (L 2 ), and a non negligible solubility of iron oxide in the ZrO 2 rich fcc_C1 and tet_oxide solid solutions.

The eutectic temperature was located in the temperature range 1588 -1603 K (1315 -1330 °C) and the corresponding composition 10.26 mol% ZrO 2 (16.4 wt%). The solubility of iron oxide in

  is a thermodynamic database for in and ex-vessel applications containing 18 + 2 elements : O-U-Zr-Ag-In-B-C-Fe-Cr-Ni-Ba-La-Sr-Ru-Al-Ca-Mg-Si + Ar-H and including the 15 oxide system : UO 2 -ZrO 2 -In 2 O 3 -B 2 O 3 -FeO-Fe 2 O 3 -Cr 2 O 3 -NiO-BaO-La 2 O 3 -OSr-Al 2 O 3 -CaO-MgO-SiO 2

Figure 1

 1 Figure 1 Calculated Fe-O phase diagram with special points and invariant reactions.

Figure 2

 2 Figure 2 Calculated Fe-O phase diagram compared with selected experimental data.

Figure 3

 3 Figure 3 Calculated Fe-O phase diagram compared with selected experimental data.

Figure 1

 1 Figure 1Calculated Fe-U phase diagram with special points and invariant reactions.

Figure 2

 2 Figure 2Calculated Fe-U phase diagram compared with selected experimental data.

Figure 1

 1 Figure 1Calculated Fe-Zr phase diagram with special points and invariant reactions.

Figure 1

 1 Figure 1Calculated O-U phase diagram with special points and invariant reactions.

Figure 2

 2 Figure 2Calculated O-U phase diagram compared with selected experimental data.

Figure 3 Calculated

 3 Figure 3Calculated UO 2+x solid region compared with selected experimental data.

Figure 4 Calculated

 4 Figure 4Calculated UO 2+x region compared with selected experimental data.

Figure 1

 1 Figure 1Calculated O-Zr phase diagram with special points and invariant reactions.

Figure 1

 1 Figure 1Calculated U-Zr phase diagram with special points and invariant reactions.

  Figure 1 Calculated O 2 U 1 -O 2 Zr 1 pseudo-binary phase diagram with special points and invariant reactions.

  Figure 2 Calculated O 2 U 1 -O 2 Zr 1 pseudo-binary phase diagram compared with selected experimental data.

Figure 1

 1 Figure 1Calculated Fe-O-U isothermal section at 1273 K.

Figure 2

 2 Figure 2Calculated Fe-O-U isothermal section at 1773.15 K.

Figure 3

 3 Figure 3 Calculated Fe-O-U isothermal section at 2273.15 K.

Figure 4

 4 Figure 4Calculated Fe-O-U isothermal section at 2273.15 K.

Figure 2

 2 Figure 2 Calculated Fe-O-Zr isothermal section at 2473.15 K.

Figure 3

 3 Figure 3Calculated Fe-O-Zr isothermal section at 2773.15 K.

Figure 4

 4 Figure 4Calculated Fe-O-Zr isothermal section at 3073.15 K.

Figure 1

 1 Figure 1Calculated Fe-U-Zr isothermal section at 1073.15 K.

Figure 2

 2 Figure 2Calculated Fe-U-Zr isothermal section at 1273.15 K.

Figure 3

 3 Figure 3Calculated Fe-U-Zr isothermal section at 1473.15 K.

Figure 4

 4 Figure 4Calculated Fe-U-Zr isothermal section at 1673.15 K.

  Figure 1Calculated O-U-Zr isothermal section at 1773.15 K.

Figure 4

 4 Figure 2Calculated O-U-Zr isothermal section at 2773.15 K.

Table Gaseous species stored in NUCLEA. Gibbs energy at T = 298.15 K

 Gaseous

	506 98	B2FE3O6(S) SI4ZR5(S) B2O2(G) C2SI2(G) H1MG1(G) SR2(G)	-2160504.75 -740504.31 -528356.26 565930.03 111463.34 228192.96	-196409.52 -82278.26 -132089.07 141482.51 55731.67 114096.48
	507 99	B2FE3U1(S) SI511U489(S) B2O3(G) C2SI3(G) H1MG1O1(G) U1(G)	-234009.51 -51020979.51 -920534.72 472155.08 -239351.24 476549.41	-39001.59 -51020.98 -184106.94 94431.02 -79783.75 476549.41
	508	B2H4O4(S) SI5U3(S) B3H3O3(G) C3(G) H1NI1(G) ZR1(G)	-1447850.19 -419390.36 -1304546.82 749329.1 330523.83 535132.84	-144785.02 -52423.8 -144949.65 249776.37 165261.92 535132.84
	509 510 511 N° 1 2 3 4 5 6 7 8 9	B2IN2O6(S) B2LA2O6(S) B2LA6O12(S) B2MG1(S) B2MG2O5(S) B2MG3O6(S) B2NI2O5(S) B2NI3O6(S) B2O4SR1(S) B2O5SR2(S) B2O6SR3(S) B2RU1(S) B2U1(S) B2ZR1(S) B3CR5(S) B3H3O3(S) B3NI4(S) B3RU2(S) B3RU7(S) B3SI1(S) B4BA1O7(S) B4CA1O7(S) B4CR1(S) B4CR3(S) B4FE1U1(S) B4LA1(S) B4MG1(S) B4MG1O7(S) B4O7SR1(S) B4U1(S) B4ZR3(S) B5H9(L) B6BA1(S) B6CA1(S) B6LA1(S) B6LA2O12(S) B6O10SR1(S) B6SI1(S) B6SR1(S) B7MG1(S) B8BA1O13(S) B9LA1(S) BA1(SER) BA13IN1(S) BA1C1O3(C) BA1C2(S) BA1CR1O4(S) BA1CR2O4(S) SR1(SER) U1(SER) ZR1(SER) SUBSTANCES AG1(G) AG1O1(G) AG2(G) AL1(G) AL1B1O2(G) AL1C1(G) AL1C2(G) AL1H1(G) AL1H1O1(G)1 AL1H1O1(G)2 AL1H1O2(G) AL1H2(G) AL1H2O2(G) AL1H3(G) AL1O1(G) AL1O2(G) AL2(G) AL2C2(G) AL2O1(G) AL2O2(G) AL2O3(G) AR1(G) B1(G) B10H14(G) B1BA1O2(G) B1C1(G) B1C2(G) B1H1(G) B1H1O1(G)1 B1H1O1(G)2 B1H1O2(G) B1H2(G) B1H2O1(G) B1H2O2(G) B1H3(G) B1H3O1(G) B1H3O2(G) B1H3O3(G) B1O1(G) B1O2(G) B1O2SR1(G) B2(G) B2C1(G) B2H4O4(G) B2H6(G) B2O1(G) C2SI1(G) H1IN1O1(G) SR1(G) C2O1(G) H1IN1(G) SI3(G) C2H8SI1(G) H1(G) SI2(G) C2H6O2(G) FE2(G) SI1(G) C2H6O1SI1(G) FE1O1(G) RU1(G) C2H6O1(G)2 FE1H2O2(G) O4RU1(G) C2H6O1(G)1 FE1(G) O3U1(G) C2H6(G) CR2(G) O3RU1(G) C2H5(G) CR1O3(G) O3(G) C2H4O4(G) CR1O2(G) O2ZR1(G) C2H4O2(G)2 CR1O1(G) O2U1(G) C2H4O2(G)1 CR1(G) O2SI2(G) C2H4O1(G)2 CA2(G) O2SI1(G) C2H4O1(G)1 CA1O1(G) O2(G) C2H4(G) CA1H2O2(G) O1ZR1(G) C2H3(G) CA1H1O1(G) O1U1(G) C2H2O2(G) CA1H1(G) O1SR1(G) C2H2O1(G) CA1(G) O1SI1(G) C2H2(G) C6CR1O6(G) O1(G) C2H1(G) C5FE1O5(G) NI1O1(G) C2(G) C5(G) NI1(G) C1SI4(G) C4NI1O4(G) MG2(G) C1SI3(G) C4(G) MG1O1(G) C1SI2(G) C3O2(G) MG1(G) C1SI1(G) C3H8O1(G)3 LA2O2(G) C1O2(G) C3H8O1(G)2 LA2O1(G) C1O1(G) C3H8O1(G)1 LA1O1(G) C1H4O1(G) C3H8(G) LA1(G) C1H4(G) C3H7(G)2 IN2O1(G) C1H3O1(G)2 C3H7(G)1 IN2(G) C1H3O1(G)1 C3H6O3(G) IN1O1(G) C1H3(G) C3H6O2(G) IN1(G) C1H2O2(G)T C3H6O1(G)5 H6SI2(G) C1H2O2(G)C C3H6O1(G)4 H4SI1(G) C1H2O1(G) C3H6O1(G)3 H3SI1(G) C1H2(G) C3H6O1(G)2 H2SI1(G) C1H1O2(G) C3H6O1(G)1 H2O2SR1(G) C1H1O1(G) C3H6(G)2 H2O2(G) C1H1(G) C3H6(G)1 H2O1(G) C1(G) C3H4O3(G) H2NI1O2(G) BA2O1(G) C3H4O2(G)2 H2MG1O2(G) BA1O1(G) C3H4O2(G)1 H2(G) BA1H2O2(G) C3H4O1(G)3 H1ZR1(G) BA1H1O1(G) C3H4O1(G)2 H1SR1(G) BA1H1(G) C3H4O1(G)1 H1SI1(G) BA1(G) C3H4(G)3 H1O2(G) B5H9(G) C3H4(G)2 H1O1SR1(G) B3H3O6(G) C3H4(G)1 H1O1(G) ZR2(G)	-2274346.65 -3200888.71 -6875312.02 -85027.23 -2586983.82 -3210718.06 -1786882.29 -2684614.08 -2039632.42 -2693841.04 -3345079.69 -64529.78 -180686.63 -332977.04 -305745.69 -1312211.18 -180515.06 -117375.7 -248863.36 -40318.35 -3353866.05 -3401581.06 -143702.66 -300194.72 -323844.87 -336133.98 -109898.64 -3281304.33 -3383923.05 -262832.38 -687794.06 -12113.99 -139573.03 -130370.27 -495419.13 -5805804.43 -4715632.16 -68841.13 -146468.5 -144815.93 -6022469.4 -513384.79 0 -337548.7 -1244422.84 -109126.62 -1493281.05 -1799480.43 0 0 0 J / mole 233486.92 236080.35 330017.71 264978.9 -621770.95 622924.02 610248.15 203428.25 -30727.26 -244386.47 -536048.12 183524.24 -727416.65 146618.21 12542.85 -161240.88 417169.13 480147.51 -261749.3 -561018.6 -643858.28 -46156.01 538182.95 -57690.78 -721293.83 766281.07 720235.12 391462.73 -258732.23 -84666.02 -632101.75 147135.1 -138946.62 -549473.36 50706.01 -358422.2 -720786.35 -1072202.07 -60631.53 -352997.53 -716271.78 792162.75 712324.94 -1388487.46 -28491.53 28362.76 562356.42 -177715.11 111785.53 217149.19 152854.46 542661.22 -161407.65 183796.42 511590.2 -485787.25 469463.25 400042.8 -274911.06 178944.32 600987.7 -263775.05 -414938.69 -269585.7 -318640.72 357670.39 -897302.47 -153107.32 558217.14 -160573.12 34994.68 -372207.2 70540.6 -920085.32 -155552.34 -477564.43 -439518.14 116976.46 -553546.13 -516784.01 364370.65 -490058.61 -244864.61 260561.61 -373666.79 -125057.23 -21543.41 -61164.58 -12894.53 -695884.08 14500.96 190611.68 -264083.57 -45138.27 -293215.66 168749.71 -70257.88 -119784.26 131470.25 -159349.18 166847.91 -1151001.24 201160.56 415160.63 -858789.13 237687.74 778291.25 906912.04 367484.91 551702.33 -722670.52 203668.81 529657.73 902613.79 -5395.48 484042.19 -175919.11 99565.8 667555.34 -364855.88 -715506.87 -457219.64 -351344.01 -141915.24 -169430.03 -308670.85 -192451.31 -272387.97 -184320.5 361792.21 -130372.16 1058.53 -132009.52 -93236.36 -9699.87 317670.57 -56395.19 -551960.79 99366.94 87828.46 -508581.67 188905.56 -436592.2 -221370.51 -960.95 -452963.2 -276757.48 -26675.76 -181090.29 -305159.22 139897.6 328605.08 -177491.66 211505.15 -288020.34 -223601.81 -673915.64 -23431.32 -59792.92 -205539.12 539587.82 -17441.99 -298082.19 669532.48 -593676.05 -342047.19 -327217.82 -382412.32 -651873.04 -197909.36 -415216.78 -38929.31 -719984.02 -167782.93 451889.28 -342305.72 -168823.64 155860.43 138270.27 -84410.12 317547.68 147398.23 110450.99 -65748.6 -8866.58 118253.14 -264116.81 -2375509.78 204503.03 -15399.56 851510.77	-227434.66 -320088.87 -343765.6 -28342.41 -287442.65 -291883.46 -198542.48 -244055.83 -291376.06 -299315.67 -304098.15 -21509.93 -60228.88 -110992.35 -38218.21 -145801.24 -25787.87 -23475.14 -24886.34 -10079.59 -279488.84 -283465.09 -28740.53 -42884.96 -53974.15 -67226.8 -21979.73 -273442.03 -281993.59 -52566.48 -98256.29 -865.28 -19939 -18624.32 -70774.16 -290290.22 -277390.13 -9834.45 -20924.07 -18101.99 -273748.61 -51338.48 0 -24110.62 -248884.57 -36375.54 -248880.18 -257068.63 0 0 0 187452.14 -59238.37 111785.53 9454.25 72383.06 76427.23 180887.07 -3561.44 -14673.42 183796.42 255795.1 -138848.75 -48578.73 234731.63 400042.8 237441.65 -27491.11 89472.16 600987.7 396081.38 -29308.34 -82987.74 -53917.14 -179067.94 -35404.52 357670.39 -224325.62 -117665.84 -19138.41 279108.57 -40143.28 -30315.76 4999.24 -93051.8 23513.53 -153171.72 -92008.53 -51850.78 -159188.14 -120131.06 -54939.77 58488.23 -184515.38 -71684.44 -64598 364370.65 -122514.65 12676.5 -34980.66 130280.81 -124555.6 -109894.67 -17865.32 -10771.71 -30582.29 -34736.66 -2149.09 -139176.82 7250.48 49045.03 38122.34 -88027.86 -22569.14 -158025.44 -48869.28 84374.85 -35128.94 -28222.01 -23956.85 131470.25 -79674.59 -86244.08 41711.98 -88538.56 201160.56 195731.36 138386.88 -78071.74 118843.87 240078.37 389145.63 181382.41 367484.91 383140.53 110340.47 -80296.72 101834.4 -180323.46 132414.43 225653.45 -2697.74 -2403.78 161347.4 -35183.82 99565.8 538182.95 333777.67 -30404.66 -178876.72 -46156.01 -152406.55 -29278.67 -47305.08 -128771.66 -84715.01 -25722.57 -96225.65 -140254.65 -45397.99 -16756.41 361792.21 -87249.77 -26074.43 105.85 -44003.17 120036.88 -18647.27 -969.99 158835.28 208584.57 -11279.04 -45996.73 49683.47 -53746.96 21957.11 -46234.7 188905.56 6271.42 -87318.44 -22137.05 -120.12 36654.55 -90592.64 -27675.75 -5335.15 -145483.33 -45272.57 -30515.92 34974.4 61174.75 109535.03 -17749.17 70501.72 -134012.03 -72005.08 -22360.18 -134783.13 -81462.16 -7810.44 -6643.66 -51384.78 -10242.42 269793.91 -1938 -99360.73 101714.13 669532.48 -59367.61 -68409.44 203416.05 -109072.61 -42490.26 -130374.61 311462.01 -98954.68 -46135.2 -19464.66 -155442.74 -143996.8 -20972.87 225944.64 264978.9 -114101.91 -21102.95 77930.22 165008.86 69135.14 -10551.27 158773.84 118040.18 147398.23 15778.71 -21916.2 233486.92 -633.33 16893.31 -88038.94 J / g-atom -197959.15 29214.72 -7699.78 425755.38	.

Table 5 Pseudo-binary systems.

 5

	System	Quality	Date of issue	System	Quality	Date of issue	System	Quality	Date of issue
	Al2O3-B2O3		03/2003	BaO-O2U		03/2003	Fe2O3-O2Si		03/2003
	Al2O3-BaO		03/2003	BaO-O2Zr		03/2003	Fe2O3-O2U		03/2003
	Al2O3-CaO		01/2006	CaO-Cr2O3		03/2003	Fe2O3-O2Zr		03/2003
	Al2O3-Cr2O3		03/2003	CaO-FeO		03/2003	In2O3-La2O3		03/2003
	Al2O3-FeO		03/2003	CaO-Fe2O3		03/2003	In2O3-MgO		03/2003
	Al2O3-Fe2O3		03/2003	CaO-In2O3		03/2003	In2O3-NiO		03/2003
	Al2O3-In2O3		03/2003	CaO-La2O3		03/2003	In2O3-OSr		03/2003
	Al2O3-La2O3		03/2003	CaO-MgO		03/2003	In2O3-O2Si		03/2003
	Al2O3-MgO		03/2003	CaO-NiO		03/2003	In2O3-O2U		03/2003
	Al2O3-NiO		03/2003	CaO-OSr		03/2003	In2O3-O2Zr		03/2003
	Al2O3-OSr		03/2003	CaO-O2Si		03/2003	La2O3-MgO		03/2003
	Al2O3-O2Si		03/2003	CaO-O2U		03/2003	La2O3-NiO		03/2003
	Al2O3-O2U		03/2003	CaO-O2Zr		03/2003	La2O3-OSr		03/2003
	Al2O3-O2Zr		03/2003	Cr2O3-FeO		03/2003	La2O3-O2Si		03/2003
	B2O3-BaO		03/2003	Cr2O3-Fe2O3		12/2004	La2O3-O2U		03/2003
	B2O3-CaO		03/2003	Cr2O3-In2O3		03/2003	La2O3-O2Zr		03/2003
	B2O3-Cr2O3		03/2003	Cr2O3-La2O3		03/2003	MgO-NiO		03/2003
	B2O3-FeO		03/2003	Cr2O3-MgO		03/2003	MgO-OSr		03/2003
	B2O3-Fe2O3		03/2003	Cr2O3-NiO		12/2004	MgO-O2Si		03/2003
	B2O3-In2O3		03/2003	Cr2O3-OSr		03/2003	MgO-O2U		03/2003
	B2O3-La2O3		03/2003	Cr2O3-O2Si		03/2003	MgO-O2Zr		03/2003
	B2O3-MgO		03/2003	Cr2O3-O2U		03/2003	NiO-OSr		03/2003
	B2O3-NiO		03/2003	Cr2O3-O2Zr		03/2003	NiO-O2Si		03/2003
	B2O3-OSr		03/2003	FeO-Fe2O3		03/2003	NiO-O2U		03/2003
	B2O3-O2Si		03/2003	FeO-In2O3		03/2003	NiO-O2Zr		03/2003
	B2O3-O2U		03/2003	FeO-La2O3		03/2003	OSr-O2Si		03/2003
	B2O3-O2Zr		03/2003	FeO-MgO		03/2003	OSr-O2U		03/2003
	BaO-CaO		03/2003	FeO-NiO		03/2003	OSr-O2Zr		03/2003
	BaO-Cr2O3		03/2003	FeO-OSr		03/2003	O2Si-O2U		03/2003
	BaO-FeO		03/2003	FeO-O2Si		03/2003	O2Si-O2Zr		03/2003
	BaO-Fe2O3		03/2003	FeO-O2U		03/2003	O2U-O2Zr		01/2005
	BaO-In2O3		03/2003	FeO-O2Zr		03/2003
	BaO-La2O3		03/2003	Fe2O3-In2O3		03/2003
	BaO-MgO		03/2003	Fe2O3-La2O3		03/2003
	BaO-NiO		03/2003	Fe2O3-MgO		03/2003
	BaO-OSr		03/2003	Fe2O3-NiO		03/2003
	BaO-O2Si		03/2003	Fe2O3-OSr		03/2003

  L 1 ) and a FeO-Fe 2 O 3 -UO 2 rich oxide liquid(L 2 ) ; it extends from the Fe-O side to the O-U side it could present a miscibility gap between a Fe 2 O 3 /Fe 3 O 4 rich phase(L 2 ) and a UO 2 rich liquid (L 3 ) ; • the oxide solid solution, (U,Fe)O 2 +x , with the face-centred cubic structure, of CaF 2 (fluorite) type, Fm 3 m, cF 12 , noted fcc_C1, and which can dissolves until 15 mol% FeO in UO 2 ; • the oxide solid solution, FeO 1+x , or wustite, with the face-centred cubic structure, of NaCl type, noted fcc_B1 ; no solubility of urania in wustite is reported ; • the uranium rich terminal solid solutions, tetragonal, tet_metal, and body cubic centred, bcc_A2, with a small solubility of iron. • the pure solid oxides, Fe 3 O 4 (S) or magnetite, Fe 2 O 3 (S) or hematite, corundum, O 3 U 1 (S), O 8 U 3 (S), O 9 U 4 (S) ; • the inter-metallic compounds, Fe 2 U 1 (S) with the Laves structure, and Fe 1 U 6 (S) ;• the ternary solid oxide, Fe 1 O 4 U 1 (S) ;

  3 O 8 or U 4 O 8 below 2126 K and 1394 K, and from Fe 2 O 3 to Fe 3 O 4 (melting point, 1869 K) above 1730 K ; according to Riley [1969Ril], the eutectic reaction L U 3 O 8 + Fe 2 O 3 is located at 1513 K (1240 °C) and 30 wt% Fe 2 O 3 , 70 wt% UO 2 , corresponding to 59.2 mol% Fe 1 O 1.5 , 40.8 mol% UO 2 . Whatever, this diagram is still imprecise and presumption of a liquid miscibility gas was recently put in evidence by

FE-U-ZR

The phase diagram of the Fe-U-Zr ternary system presents the following condensed solutions and substances, with the symbols used in this work or found in open literature :

• the liquid phase, L, which shows a complete miscibility between all elements ;

• the intermetallic Laves phase, Fe 2 (U, Zr)(Laves), which shows a miscibility gap at low temperature between a Fe 2 U 1 rich Laves phase and a Fe 2 Zr 1 rich Laves phase ; • the terminal iron rich solid solutions, body cubic centred, bcc_A2, and face cubic centred, fcc_A1, with a negligible solubility of uranium and a small solubility of zirconium ; • the terminal uranium-zirconium solid solution, body cubic centred, bcc_A2, with a limited solubility of iron ; • the terminal uranium rich solid solution, tetragonal (tet_metal), with a very small solubility of iron and zirconium ; • the terminal uranium rich orthorhombic solid solution, ort_A20, with a negligible solubility of iron and a very small solubility of zirconium ; • the terminal zirconium rich solution, with the hexagonal closed packed structure, hcp_A3, and a very small solubility of iron and uranium ; • the intermetallic solid solution, δ, which extents from 64 to 78 at % Zr ;

• the binary intermetallic compounds, Fe 1 U 6 (S), Fe 765 Zr 265 (S), Fe 1 Zr 2 (S) and Fe 1 Zr 3 (S) ;

• the ternary intermetallic compounds, Fe 0.333 U 0.25 Zr 0.417 (ε), Fe 0.06 U 0.71 Zr 0.23 (λ), Fe 0.50 U 0.18 Zr 0.32 (χ).

The fundamental thermodynamic properties (Cp, ∆H 298 , S 298 ) of substances, Fe 2 U 1 (Laves), Fe 1 U 6 (S), Fe 2 Zr 1 (Laves), Fe 765 Zr 265 (S), Fe 1 Zr 2 (S) and Fe 1 Zr 3 (S) have been assessed in the individual sub-systems, as well as the thermodynamic modelling of all binary phases. The liquid, bcc_A2, fcc_A1, hcp_A3 phases (φ) have been described by a non ideal substitutional model, with the formula (Fe 1 ,U 1 ,Zr 1 )(φ). The intermetallic Laves phase, Fe 2 (U,Zr)(Laves), has been described by a two-sublattice model, with the formula (Fe 1 , U 1 , Zr 1 ) 2 (Fe 1 , U 1 , Zr 1 ) 1 . In order to reproduce the non-stoichiometric field in the Fe-Zr binary system. The thermodynamic properties of the three ternary intermetallic compounds, Fe 0.333 U 0.25 Zr 0.417 (ε), Fe 0.06 U 0.71 Zr 0.23 (λ), Fe 0.50 U 0.18 Zr 0.32 (χ) have been estimated from the phase diagram information. The gas phase has been described by an ideal mixture of gaseous species, with the formula (Fe 1 , U 1 , Zr 1 , Zr 2 ) 1 (G).

The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• the ternary intermetallic compounds are reproduced in accordance with experimental phase diagram at temperatures below 1000 K ; • the miscibility gap in the ternary Laves phase is present up to 1373 K ; • above 1573 K, the only solid phases are the Fe 2 Zr 1 rich Laves phase, the iron rich (fcc_A1, bcc_A2) and uranium-zirconium rich (bcc_A2) solution phases. Then, the liquid domain is more and more extended, pure iron melts at 1811 K, pure Fe 2 Zr 1 at 1950 K, and pure zirconium at 2128 K. There is no available experimental information at high temperature (T > 1500 K).

O-U-ZR

The phase diagram of the O-U-Zr ternary system presents the following solutions and substances, with the symbols used in this work :

• the liquid phase, L, which shows a miscibility gap between an uranium-zirconium rich metallic liquid (L 1 ) and a UO 2 -ZrO 2 rich oxide liquid (L 2 ) ; the miscibility gap is closed at high zirconium content ; • the oxide solid solution, (U,Zr)O 2 +x , with the face-centred cubic structure, of CaF 2 (fluorite) type, Fm 3 m, cF 12 , noted fcc_C1 ; • the terminal zirconia rich solid solution, (U,Zr)O 2 , tetragonal, tet_oxide, with a solubility of O 2 U 1 limited to about 23 mol% ; • the terminal uranium-zirconium rich solid solution, body cubic centred, bcc_A2, with a limited solubility of oxygen on the O-Zr side, showing a complete miscibility at high temperature and a small miscibility gap deported on the uranium side between 950 K and 1000 K in the U-Zr system ; • the terminal zirconium rich hexagonal closed packed solid solution, hcp_A3, with a solubility of oxygen limited to about 10 at% and 30 at% respectively, and a small solubility of uranium (< 3 at%) ; • the intermediate solid oxides, O 3 U 1 (S), O 8 U 3 (S), O 9 U 4 (S) ;

• the pure solid oxide, with the allotropic form monoclinic, O 2 Zr 1 (mon) ; • pure solid uranium, with a negligible solubility of oxygen, and different allotropic structures, orthorhombic, U 1 (ort_A20), tetragonal, U 1 (tet) ; • the terminal uranium rich solid solutions, orthorhombic, ort_A20, and tetragonal, tet_metal, with a small solubility of zirconium ; • the intermetallic solid solution, δ, which extents from 64 to 78 at% Zr ; • the gas phase, which shows an extended solubility of uranium above 2000 K and zirconium above 3000 K.

The fundamental thermodynamic properties (Cp, ∆H 298 , S 298 ) of substances, O 3 U 1 (S), O 8 U 3 (S), O 9 U 4 (S), O 2 U 1 (fcc_C1), O 2 Zr 1 (fcc_C1, tet, mon), have been assessed in the individual subsystems, as well as the thermodynamic modelling of all binary or pseudo-binary phases. The liquid phase has been described by a non ideal associate model, with the formula (O 1 , O 2 U 1 , O 2 Zr 1 , U 1 ,Zr 1 ) (L). The solid solution (U,Zr)O 2 +x has been described by a three sublattice model, with the formula (U 1 , Zr 1 ) 1 (O 1 , □) 2 (O 1 , □) 1 (fcc_C1), and simplified in a simple one lattice model, with the formula (O 1 , O 2 U 1 , O 2 Zr 1 , U 1 , Zr 1 ) 1 (fcc_C1), in order to be compatible with the whole thermodynamic database and to allow the introduction of iron and selected fission products, Ba, La and Sr. The terminal uraniumzirconium rich solid solutions, bcc_A2 and hcp_A3, have been described by a two sublattice model, with the respective formula (U 1 , Zr 1 ) 1 (O 1 , □) 3 (bcc_A2), and (U 1 , Zr 1 ) 1 (O 1 , □) 0.5 (hcp_A3). The gas phase has been described by an ideal mixture of gaseous species, with the formula

The comparison of the calculated thermodynamic properties and phase diagram with the experimental information leads to the following conclusions :

• on a qualitative point of view, the overall topology of the O-U-Zr ternary phase diagram is in agreement with the experimental data between 1273 K and 3173 K ; • on a quantitative point of view, the solubility of oxygen in uranium-zirconium liquid alloys, the liquid miscibility gap and the liquidus temperatures are in agreement with the selected experimental data ; • the remaining uncertainties are the accurate shape of the diphasic domain L 1 + fcc_C1 between 2000 K and 2500 K, the liquidus temperatures in the zirconium rich domain, the solidus temperatures, and the presence of an hyper-stoichiometric liquid at low temperatures, resulting from necessary improvement of the hyper-stoichiometric O-U region.


A Ben Hamida

A Benoit

P Lambert

L Klein

C Ben Amar

N Audebert
email: nicolas.audebert@irisa.fr

S Lefèvre

DEEP LEARNING FOR SEMANTIC SEGMENTATION OF REMOTE SENSING IMAGES WITH RICH SPECTRAL CONTENT

Keywords: Remote Sensing, Multispectral, Deep Learning, Semantic Segmentation, Noisy Training

With the rapid development of Remote Sensing acquisition techniques, there is a need to scale and improve processing tools to cope with the observed increase of both data volume and richness. Among popular techniques in remote sensing, Deep Learning gains increasing interest but depends on the quality of the training data. Therefore, this paper presents recent Deep Learning approaches for fine or coarse land cover semantic segmentation estimation. Various 2D architectures are tested and a new 3D model is introduced in order to jointly process the spatial and spectral dimensions of the data. Such a set of networks enables the comparison of the different spectral fusion schemes. Besides, we also assess the use of a "noisy ground truth" (i.e. outdated and low spatial resolution labels) for training and testing the networks.

INTRODUCTION

Automated land cover mapping based on satellite image analysis and classification is a well-known challenge which is of a great interest for many fields, such as agriculture [START_REF] Bokusheva | Satellite-based vegetation health indices as a criteria for insuring against drought-related yield losses[END_REF] and risk monitoring [START_REF] Esa | Satellite Earth Observations in Support of Disaster Risk Reduction, Special 2015 Edition for the World Conference on Disaster Risk Reduction[END_REF]. The recently launched Sentinel-2 satellite constellation provides a richer content in spatial, spectral and temporal domains, and produces a huge amount of images to process daily. In this context, Deep Learning (DL) appears as an appealing alternative to traditional shallow classification approaches to deal with such a massive amount of data. A DL architecture is a deep artificial neural network composed of a hierarchical succession of neuron layers performing linear and non-linear processing. Mimicking the human brain behavior, the network tuning (typically millions of parameters) is automatically performed thanks to a supervised training process on large datasets that are generally associated to some "ground truth" knowledge. However, the ground truth quality is essential to reach satisfying performances. Some recent works already use deep neural nets to process remotely sensed images. In [START_REF] Papadomanolaki | Benchmarking deep learning frameworks for the classification of very high resolution satellite multispectral data[END_REF], the authors compared different well-established deep architectures (AlexNet, AlexNetsmall, VGG) for the classification of SAT-4/SAT-6 dataset (from US National Agriculture Imagery Program, NAIP) using Convolutional Neural Networks (CNN). Pirotti et al. [START_REF] Pirotti | Benchmark of Machine Learning Methods for Classification of a SENTINEL-2 Image[END_REF] benchmarked different machine learning methods (including multilayered perceptron) for classification of Sentinel-2 images. In [START_REF] Ben Hamida | Deep learning approach for remote sensing image analysis[END_REF], we proposed a new 3D CNN architecture for hyperspectral data pixelwise classification (semantic segmentation). In [START_REF] Audebert | Semantic segmentation of earth observation data using multimodal and multi-scale deep networks[END_REF][START_REF] Audebert | Fusion of heterogeneous data in convolutional networks for urban semantic labeling[END_REF], we adapted the SegNet architecture to achieve semantic segmentation of multimodal airborne imagery.

In this paper, we rely on the recent DenseNet [START_REF] Volpi | Dense semantic labeling of subdecimeter resolution images with convolutional neural networks[END_REF] and Seg-Net [START_REF] Badrinarayanan | Seg-Net: A Deep Convolutional Encoder-Decoder Architecture for Scene Segmentation[END_REF] architectures to perform land cover semantic segmentation of large multispectral Sentinel-2 images. These architectures are experimentally assessed through two different use cases, namely fine and coarse resolution estimation. We also introduce a new 3D DenseNet network in order to jointly process both spatial and spectral dimensions. In addition, we suggest the use of a "noisy ground truth" (i.e. outdated and low spatial resolution labels) for both training and testing. The idea is to explore the feasibility of outdated low quality knowledge integration for modern image sensors and analysis methods. Experiments are conducted in a wide region between France, Switzerland and Italy relying on the reference areas of GlobCover (ESA 2009 Global Land Cover Map) annotation and 2016 ESA Sentinel-2 images.

SPECTRAL CHANNEL FUSION AND DEEP NEURAL NETWORKS

When dealing with multispectral images, strategies for processing and fusing spectral channels are numerous. Deep neural networks enable a large variety of choices from the component operator to architectural levels. At the low component level, the classical approach is to use 2D convolution layers from the first stages of the network. In such a configuration, each neuron applies a specific filter to each channel and then fuses (sums) the resulting maps. Such an approach enables the early combination of each channel of multispectral image sensors whatever their wavelength. One can also rely on 3D convolution neurons that consider input images as 3D volumes. These volumes are then filtered by 3D filters that locally combine the spatial and spectral information. With such a strategy, cascading 3D filters enables all the available wavelength bands to be combined in a growing bandwidth manner. From a coarse network architecture point of view, the advances in neural network modeling led to an increase in architecture depth and a variety of neural layers combination enabling data representation levels to be also fused together.

In classical approaches such as AlexNet [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF], a neuron layer is only fed by the previous layer output such that lowlevel representations are not directly included at the decision level that occurs in the last layer. However, recent ideas enable a given neuron layer to fuse the information coming from many more previous neural layers. The Residual Network (ResNet) components [START_REF] He | Deep residual learning for image recognition[END_REF] consist in the fusion (pixelwise sum) between the resulting representation of a block of 2D convolution filters and its input. This enables to mix input data with a new slightly increased representation level.

One step further, the SegNet architecture [START_REF] Badrinarayanan | Seg-Net: A Deep Convolutional Encoder-Decoder Architecture for Scene Segmentation[END_REF] for semantic segmentation adopts an auto-encoder structure, with an encoder that models the data at multiple scales and a decoder that up-samples the internal representation and projects it into the mapping space. To do so, the location of the locally maximal activation from the lower layers are fed forward directly to their up-sampling counterpart in the last layers, which allows the decoder to relocate abstract features into the most salient points originally detected. This information is actually crucial for accurate semantic map boundary reconstruction.

Even further, the recent DenseNet architecture [START_REF] Volpi | Dense semantic labeling of subdecimeter resolution images with convolutional neural networks[END_REF] proposes intensive layer fusion. Given a DenseBlock that consists in a set of convolution layers working at the same scale, each neural layer processes the concatenation of all its previous layers thus enabling the fusion of very numerous representation levels. Similarly to SegNet, its semantic segmentation extension [START_REF] Jégou | The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation[END_REF] adds a decoding path to generate the semantic map. However, on the decoding branch, the fusion not only consists in intra dense block layers fusion but it also relies, at the input of each decoding block, on the concatenation of the preceding high level feature maps and the ones coming from the encoding block at the same scale. The strength of such an approach is the intensive feature map reuse all along the network thus enabling the number of parameters to be significantly reduced while increasing performance.

PROPOSED APPROACHES

In this paper we propose to explore the capabilities of some recent neural networks discussed in Sec. 2 for land cover mapping. Conversely to public datasets provided with recent contests such as the semantic labeling benchmark over IS-PRS Vaihingen and Potsdam cities that relies on high-quality ground truth, we propose to train deep networks on a wide area, relying on coarse and noisy reference data. This realistic scenario allows to exploit previous knowledge such as outdated and coarse resolution land cover maps. These maps bring both confident annotations on qualitative and temporally stable regions, while presenting erroneous values on area boundaries but also on areas where changes occurred before image acquisition. In this context, training neural networks in a supervised way is a delicate step and we propose two different use cases considering the following architectures, whose results are reported in Tab.1.

First, we consider fine-grained pixel-level land cover estimation using very light architectures with few parameters using DenseNet [START_REF] Volpi | Dense semantic labeling of subdecimeter resolution images with convolutional neural networks[END_REF]. 3 basic configurations are proposed, with either 2 or 3 dense blocks at the encoder and decoder levels, different number of layers per block and either 12 or 16 neurons per layer. As shown in Fig. 1, an extension of this architecture is proposed by introducing 3D convolution neurons in the first dense block. As already proposed in [START_REF] Ben Hamida | Deep learning approach for remote sensing image analysis[END_REF], we aim to early combine spectral channels but only for adjacent bands. To do so, the 48×2D convolution neurons input layer of the reference model is removed thus enabling all the input spectral bands to feed a new first dense block exclusively composed of 3D convolutions with kernel size 3×3×3 using 4 layers of 16 neurons each. Then, if 9 spectral bands regularly sampled along the wavelength dimension are chosen, the neurons of the 4th layer of the 3D dense block have processed data that depend on the full spectral bandwidth. An intermediate 3D convolution is then added next to ensure the 3D to 2D data transition by squeezing the spectral dimension. Com-pared to 2D convolution based models, the overall number of parameters decreases by at least 10%.

Second, we consider land cover estimation at the coarse ground truth scale using a very large architecture derived from SegNet [START_REF] Badrinarayanan | Seg-Net: A Deep Convolutional Encoder-Decoder Architecture for Scene Segmentation[END_REF]. We modify the original SegNet by allowing the input to have more than 3 bands by enlarging the first convolution layer. The encoder is based on VGG-16 [START_REF] Chatfield | Return of the devil in the details: Delving deep into convolutional networks[END_REF], which alternates blocks of 2 or 3 convolutions with 3 × 3 kernels with max-pooling layer that downsamples the data by a factor of two. The decoder is symmetric to the encoder, with sparse 2× up-sampling instead of pooling and convolutions to densify the activations. The up-sampling is performed using the locations of the maxima found during pooling in the encoder, that are skipped through the network. After each block in the decoder, a 1 × 1 convolution layer projects the feature maps into the label space. We add decoding blocks until the estimation has a higher resolution than the ground truth. The multiscale estimations are then interpolated at full scale and averaged for loss computation. The gradient is then back-propagated in a deeply supervised fashion, to enforce a better multiscale spatial regularity. The full architecture has more than 27M parameters and is the largest model presented in this work.

EXPERIMENTS

Our experiments have been made possible thanks to the MUST computing center of the University of Savoie Mont Blanc. The proposed neural networks are trained and evaluated on a dataset extracted from a region between France, Switzerland and Italy as shown in Fig. 2. Images have been acquired by the Sentinel-2 sensor within the May-October 2016 period, while land cover ground truth is the 2009 Glob-Cover map ESA/GLOBCOV ER L4 200901 200912 V 2 3. The Google Earth Engine [START_REF]Google earth engine: A planetary-scale geo-spatial analysis platform[END_REF] was used to extract Sentinel Images but only on the reference areas of GlobCover. Some subregions of this dataset have been put apart to serve as the test dataset. Two datasets are proposed and detailed in Tab.2: the first one covers all the May-October period and does not include areas with clouds (opaque and cirrus). The second one only covers the summer period but includes clouds so that they can be considered as an additional class to detect. Both datasets are then multitemporal with frequent observations of the same areas at different timestamps.

The Sentinel-2 data is interpolated to 20m/px resolution, while the GlobCover ground truth is at 300m/px resolution. The proposed networks are trained considering two strategies: the light ones are optimized at the image resolution level whatever the ground truth resolution is (i.e. the models are trained against an interpolated ground truth), thus trying to estimate at the scale of the input even if the reference is too coarse. The largest network (SegNet) however estimates multiple maps at several scales that are averaged and interpolated to the ground truth resolution. Training at a lower resolution As shown on Tab. 1, estimation at a higher resolution than the reference provides an overall accuracy ranging between 25.1% and 30.0% on dataset D1 and 39.5% and 57.9% on D2. However, the overall accuracy metric introduces a discrepancy that penalizes the reported values. The metric is actually confident on stable and large areas but is less confident on heterogeneous areas. In such a noisy training context, resembling classes such as "Rainfed croplands" and "Mosaic Cropland/Vegetation" are often confused. However, these network are expressive enough to well detect classes such as "Artificial surfaces", "Bare areas", "Water bodies" and the added class "Clouds". When working with only the regularly sampled spectral bands (9 bands tests), 3D DenseNets can be applied. 3D approaches are performing worse but performance increases with model depth. Nevertheless, many more training images are required to train for the fine-grained approach. However, coarse land cover estimation provides good results on both datasets. The large number of parameters of SegNet and the multiscale approach provides at least 66.9% accuracy on the long period dataset that shows strong aspect changes of the same areas (D1) and 83.9% on the more stable one (D2).

CONCLUSION

This paper reviews a variety of strategies provided by Deep Learning approaches to fuse the channels of multispectral sensors with the aim of land cover mapping. Optimizing such neural networks from a noisy land cover reference is challenging when dealing with reduced size datasets. Estimating at coarse image scale up to the one of the reference remains the most appropriate solution. Estimating at a higher resolution is difficult for the training step but also at the validation step to enable confident comparison. A first step forward would consist in enhancing the proposed models by enabling multiscale estimation for each of them. Going further, estimating at a finer resolution is challenging but required for land cover monitoring, and refined approaches should be investigated by taking advantage of the recently available mass of training data.

Fig. 1 :

 1 Fig. 1: Top: reference DenseNet architectures. Bottom: our proposed 3D DenseNet

Fig. 2 :

 2 Fig. 2: Experimental datasets, training images were extracted from the overall pink region while test regions are the small orange ones. Each image covers GlobCover reference areas. alleviate errors along class borders in the GlobCover data.As shown on Tab. 1, estimation at a higher resolution than the reference provides an overall accuracy ranging between 25.1% and 30.0% on dataset D1 and 39.5% and 57.9% on D2. However, the overall accuracy metric introduces a discrepancy that penalizes the reported values. The metric is actually confident on stable and large areas but is less confident on heterogeneous areas. In such a noisy training context, resembling classes such as "Rainfed croplands" and "Mosaic Cropland/Vegetation" are often confused. However, these network are expressive enough to well detect classes such as "Artificial surfaces", "Bare areas", "Water bodies" and the added class "Clouds". When working with only the regularly sampled spectral bands (9 bands tests), 3D DenseNets can be applied. 3D approaches are performing worse but performance increases with model depth. Nevertheless, many more training images are required to train for the fine-grained approach. However, coarse land cover estimation provides good results on both datasets. The large number of parameters of SegNet and the multiscale approach provides at least 66.9% accuracy on the long period dataset that shows strong aspect changes of the same areas (D1) and 83.9% on the more stable one (D2).

Table 1 :

 1 Description of the considered architectures and Overall Accuracy (OA) after reference class boundary erosion of 200m. For DenseNet, e[x,y], d[y,x] and b[z] list the number of blocks and their respective number of layers for respectively the encoding and symmetric decoding branches and the bottleneck block. The number of neurons per layer is parametrized by g.

	Use Case	Models	#params #scales OA/9 bands [B1-B8a]	OA/13 bands
				D1	D2	D1	D2
	Fine-grained estimation DenseNet
		e[2,3],b[4],d[3,2] g12	0.23M 3	30.1% 57.9%	35.9% 51.8%
		e[4,5],b[7],d[5,4] g16	1.00M 3	29.5% 55.3%	27.2% 55.4%
		e[4,4,4],b[4],d[4,4,4] g16	1.08M 4	25.7% 52.3%	28.5% 51.4%
	Fine-grained estimation 3D DenseNet
		e[4, 5] 3D ,b[7],d[5,4] g16	0.88M 3	25.1% 39.5%	-	-
		e[4, 4, 4] 3D ,b[4],d[4,4,4] g16	0.92M 4	26.5% 41.2%	-	-
	Coarse estimation	SegNet	27.00M 5	-	-	66.9% 83.9%

Table 2 :

 2 Considered datasets: images including clouds detected by the Sentinel-2 A60 additional band are excluded from the long period dataset (D1). The short period dataset (D2) includes clouds and enables training their detection. Both datasets collect more than 150M pixels each.

	Dataset		#images
	(period)	train test #class
	D1, Long period no clouds
	(May-Oct. 2016)	140	54	23
	D2, Short period with clouds
	(June-August 2016)	158	39	24