Angela Barthes

Jean-Marc Lange

Researchers' positions and construction of curricula of education for sustainable development in France

Keywords: Education for sustainable development, curriculum, researchers 'positions, France

The article sets the international context for the development of a curriculum of education for sustainable development and shows the directions being taken in the Francophone community. Building on a significant number of studies carried out in France, we constitute a typology of the positions of French-speaking researchers involved in those studies and contributing to the establishment of the national curriculum. This typology is constructed using a methodology based on the frequency of lexical occurrences in a bibliographic database, combined with a methodology of research on the social representations of the researchers of this community. We first present a broad comparison with the Anglo-Saxon sphere, we postulate that these positions influence the curriculum construction and raise the issue of the social responsibility of education science researchers in the face of international political demands.

Introduction

In accordance with UN/UNESCO prescription, education for sustainable development (ESD) emerged in France, in the early 2000, in the wake of the international development of environmental education [START_REF] Jickling | Globalization and environmental education: Looking beyond sustainable development[END_REF][START_REF] Lucas | Environmental education[END_REF][START_REF] Reid | Major works in environmental education[END_REF][START_REF] Smyth | Environment and education: A view of a changing scene[END_REF]. The specificity of ESD, its explicitly political nature, institutional instability and position as an emerging curriculum, have brought to light issues that concern all curricula [START_REF] Fien | Ideology, political education and teacher education: Matching paradigms and models[END_REF][START_REF] Goodson | Subjects for study: Aspects of a social history of curriculum[END_REF][START_REF] Gough | From epistemology to ecopolitics: Renewing a paradigm for curriculum[END_REF][START_REF] Reid | Curriculum challenges for and from environmental education, introduction of the 8th World Environmental Education Congress[END_REF]. Research in both the Francophone and English-speaking worlds, approach the issue of the curriculum by stressing the necessary articulation between the political, strategic and programmatic perspectives. Thus, the formal curriculum appears as a political issue, which varies according, among other things, to the degree of centralization of education systems. That is why, in line with the research conducted by English speaking scholars [START_REF] Reid | Curriculum challenges for and from environmental education, introduction of the 8th World Environmental Education Congress[END_REF], we propose to examine the question of ESD in France and look at how it is addressed by French researchers. For this purpose, we identify various positions found in the French research community and discuss their national implications in terms of curriculum development.

Issues pertaining to the curriculum of ESD in France

Today, just as in the past, supra-national political bodies can influence the local or national curriculum. This is true, for example, in the case of the implementation of the Decade of ESD (2004ESD ( -2014) ) by UNESCO-as an executive agency of the UN. The implementation of this project has been accompanied by academic research undertakings. Among them, the research group 'Education for sustainable development-supports and barriers' (ED2AO), supported by the ANR1 and its international networks, have initiated pioneering studies on formal and informal curricula related to the emergence and generalization of ESD, and in various educational forms and context. Thus, sustainable development potentially falls within the scope of controversial socio-scientific issues, also called socially acute issues, which are considered an educational challenge for society [START_REF] Levinson | Towards a theoretical framework for teaching controversial socio-scientific issues[END_REF], as shown, for example, by the studies on the emblematic question of climate change [START_REF] Fahey | Curriculum change and climate change: Inside outside pressures in higher education[END_REF][START_REF] Levinson | A perspective on knowing about global warming and a critical comment about schools and curriculum in relation to socio-scientific issues[END_REF]. Sustainable development is, indeed, a political idea. It is therefore necessarily challenged [START_REF] Jacobs | Sustainable development as a contested concept, fairness and futury[END_REF][START_REF] Jickling | Globalization and environmental education: Looking beyond sustainable development[END_REF]. Envisaged initially as a means of embarking on a virtuous path in terms of environmental protection, sustainable development can, for some authors, be considered as a failure because of the inability to reconcile growth and reduce the environmental impact, especially on resources [START_REF] Foster | Sustainability and the learning virtues[END_REF][START_REF] Zaccai | [END_REF]. However, the value of this idea lies in its having firmly placed in international political agendas, the question of development sustainability and that of development itself, 2 as well as that of a necessary development of critical education [START_REF] Gough | Towards a socially critical environmental education: Water quality studies in a coastal school[END_REF][START_REF] Greenwood | A critical pedagogy of place: From gridlock to parallax[END_REF]. There remains, therefore, to develop a new grammar of this primarily political and galvanizing idea [START_REF] Theys | Le développement durable face à sa crise : un concept menacé, inexploité ou dépassé? Développement durable et territoires[END_REF]. While, education is considered to be the condition and the means of promoting sustainable development, it is subject to the ideological risk of being exploited to serve a economistic [START_REF] Sauvé | L'organisation et la structuration du secteur de l'éducation en réponse au programme onusien du développement durable. In "Former et éduquer pour changer nos modes de vie[END_REF] or even a techno-economistic world vision [START_REF] Morin | Enseigner à vivre, manifeste pour changer l'éducation[END_REF][START_REF] Theys | Le développement durable face à sa crise : un concept menacé, inexploité ou dépassé? Développement durable et territoires[END_REF], which would then constitute the hidden curriculum of this education (Barthes & Alpe, 2013;[START_REF] Gough | Greening the future for education: Changing curriculum content and school organization[END_REF]. The teaching of sustainable development is conditioned by specific epistemological and didactic positions [START_REF] Fien | Ideology, political education and teacher education: Matching paradigms and models[END_REF][START_REF] Goodson | Subjects for study: Aspects of a social history of curriculum[END_REF][START_REF] Gough | From epistemology to ecopolitics: Renewing a paradigm for curriculum[END_REF][START_REF] Simonneaux | Légitimité des savoirs et des expertises en vue d'une éducation post normale : l'exemple du développement durable[END_REF], whose legitimacy is also debated and even challenged. These positions have a great impact in terms of potential variability in curriculum elaborations and didactic transpositions, which are associated to sometimes divergent and conflictual societal priorities. Thus, [START_REF] Ross | Curriculum: Construction and Critique[END_REF] has characterized three ideal types of curriculum development models, and has emphasized that these possible strategic choices and orientations are ideologically marked. In this context, examining the different positions of researchers in response to the emergence of ESD seems essential, and provides a representative overview of the positions adopted by the 'noosphere'. We propose to do so in the French-speaking community. Given the complexity of the task and the intellectual and applicative implications of this exercise, this article provides a preliminary analysis of the positions to consider, not as a final research result, but as the basis for future collective research and for comparison with the positions of Anglo-Saxon scholars.

Corpus and methodology

To this end, we have set up a solid working methodology based on two corpuses, studied according to two different processes, providing us with key indicators. Corpus 38 Researchers in the field of ESD 98 Works published about ESD (2008ESD ( -2015) ) The first corpus of 38 researchers' positions was developed on the basis of a questionnaire completed by the researchers participating in the ED2AO programme (or from the Frenchspeaking part of the 'noosphere'), one year before the end of that project (2012). This research project can be considered central in the French context as it brought together many of the researchers interested in the topic of ESD, at a time corresponding to phases 2 and 3 of the process of expansion of this type of education in the French education system. The questionnaire aimed to reveal the researchers' social representations concerning sustainable development and ESD. Social representation is understood here as 'natural' knowledge, a form of knowledge that enables individuals to integrate a reality and adapt their behaviour according to their representation. [START_REF] Abric | Pratiques sociales et représentations [Practice and social représentations[END_REF] argues that it is an appropriation of the object through cognitive reconstruction, which is shaped by the social and ideological context. It was therefore considered that the study of social representations took on a particular dimension in the context of this socially acute question of sustainable development [START_REF] Legardez | L'utilisation de l'analyse des représentations sociales dans une perspectivedidactique : l'exemple des questions économiques[END_REF], insofar as it provides a framework for interpreting 'natural knowledge', known information, how it is structured, and the behaviour of individuals towards the represented objects. The representational contents in the noosphere were analysed via a 'spontaneous response' questionnaire: 'What words or phrases come to mind when you think of ESD?' Thirty-eight respondents then proposed a list of about 10 words, which is a total of 378 words quoted and available for study. These constitute the second corpus. The meaning of the used world has been completed, as usual in social representations, by interviews of explicitation [START_REF] Vermersch | L'entretien d'explicitation, Issy-les-Moulineaux[END_REF]. Thus, the second stage of our work involved understanding the structure of the responses. For this purpose, we constructed graphs of co-occurrences-that is to say, a calculation of the number of links between the words quoted. For example, if individual 'A' respond with the words 'x' and 'y', then there is a co-occurrence of 'x' and 'y'. The sum of all these co-occurrences is calculated for the 38 individuals. The number of co-occurrences is then represented in a graph. The higher this number, the thicker the lines connecting the words. During this process, the terms were clustered according to their co-occurrences; But, as a result, clusters of unconnected words (or only connected through the two common terms 'education' and 'sustainable development') emerge. This process enabled us to group the responses of the researchers into the same number of self-organized categories. This yielded six families of interconnected words corresponding to different positions. These six families constituted the corpus used for analysing the researchers' positions. Indeed, building on this basic data (the six families of words), we looked for the bibliographic corpus to which these six families of words were connected. Thus, the 154 words selected from the bibliographic inventory, were linked, and added, to the words included in those six families. And it is on the basis of these six families, each associated with words extracted from publications linked to it, that we were able to conduct a 'literary' analysis of the researchers' positions (therefore, divided into six categories), determining the meaning of the words used in the original texts then considered as a significant basis3 (For method details concerning social representations studies for sciences education, see [START_REF] Barthes | Utiliser les représentations sociales en éducation[END_REF]. The second corpus, strictly bibliographical, was constructed from the inventory of the works published during the ED2AO research project (2008)(2009)(2010)(2011)(2012) and its extensions (2013)(2014)(2015). The inventory lists the 98 works published by the members of ED2AO and its partners-inthe wide sense of the term-whether they are isolated researchers or international institutional partners, with whom many exchanges of views have taken place. Those publications collective works, such as : that on 'Le développement durable et autres questions d'actualités, les questions socialement vives dans l'enseignement et la formation' (Sustainable development and other current issues, socially acute questions in education and training) [START_REF] Legardez | Développement durable et autres questions d'actualité. Questions socialement vives dans l'enseignement et la formation[END_REF] or 'Éducation, environnement et développement durable : Vers une écocitoyenneté critique' (Education, environment and sustainable development : towards a Critical Eco-Citizenship) [START_REF] Bader | Éducation, environnement et développement durable-Vers une écocitoyenneté critique[END_REF]; journals' issues such as Spirale n°50 on 'educations for …' [START_REF] Pagoni | Les éducations à, quelles recherches, quels questionnements? Les "éducations à[END_REF], Education relative à l'environnement: Regards-Recherches-Réflexions, n° 10 (Environment-related education : viewsresearch-reflections) n° 10 (Bidou, 2012), n° 11 [START_REF] Bader | Rapport aux savoirs, éducation relative à l'environnement et au développement durable[END_REF] and n° 12 [START_REF] Sauvé | Identités et engagements: Enjeux pour l'éducation relative à l'environnement[END_REF], les Dossiers des sciences de l'éducation n° 29 (Dossiers on educational science n° 29) [START_REF] Simonneaux | Les sciences et les crises contemporaines[END_REF], the Journal of social science education n° 11 [START_REF] Simonneaux | The epistemological and didactical challenges involved in teaching socially acute questions[END_REF], Environmental education research n° 18 and 19 [START_REF] Reid | Normalising catastrophe in environmental discourse: On educational values, responses and critical imagination[END_REF][START_REF] Reid | Environmental education research: towards and beyond passionate, scholarly conversation[END_REF], la Revue francophone du développement durable n°1 (Francophone journal of sustainable development n° 1) [START_REF] Diemer | L'éducation au développement durable[END_REF], penser l'éducation hors-série 2013 [START_REF] Lange | Actes du colloque international "Education au développement durable: appuis et obstacles à sa généralisation hors et dans l'Ecole[END_REF] In addition, the corpus includes proceedings of seminars : 'Education au développement durable et à la biodiversité' (ESD and biodiversity), Digne les Bains, 20-22 October, 2010 [START_REF] Alpe | Actes du colloque international « Education au développement durable et à la biodiversité : concepts, questions vives, outils et pratiques[END_REF]; 'Rapport aux savoirs, éducation relative à l'environnement et au développement durable' (relations to knowledge, education relative to the environment and sustainable development), 80th ACFAS congress, 8-9 May, 2012 Montréal [START_REF] Bader | Rapport aux savoirs, éducation relative à l'environnement et au développement durable[END_REF]; 'Les représentations Nord-Sud du développement durable' (North/South representations of sustainable development), Clermont-Ferrant, 8-10 December, 2012 [START_REF] Diemer | Colloque international. Les représentations Nord-Sud du développement durable[END_REF]; 'L'éducation au développement durable : appuis et obstacles à sa généralisation hors et dans l'Ecole' (ESD: Supports and barriers to its expansion at and outside school), Rouen, 26-28 November, 2012; and all isolated publications by researchers between 2008 and 2014. The inventory then enabled us to conduct an analysis of the lexical occurrences in the corpus, using the Tropes software,4 and to record those occurrences in an Excel table.5 This yielded a list of 9551 different terms. The frequencies of occurrences were then discretized (aggregated into classes) using the amplitude method. [START_REF]m' is the upper boundary of the class number 'n/2'. Notes on contributors Angela Barthes, PhD, Full Prof in sciences education. Angela's research interest includes knowledge transmission and education in territorial development (including[END_REF] We only considered the first class, which was deemed significant based on this criterion-generally, the words quoted more than 50 times: Thus, 154 words were eventually used for the analysis. These words, which were extracted from publications, constitute the second indicator used for the study. These indicators are used to verify the connection between studies of the social representations and to specify their meaning.

Results

The responses showed, first of all, that the researchers did not share the same social representation of ESD. Indeed, the members of a community are considered to share a social representation only if several words are used by at least 30% of the respondents, considering usual social representations epistemology and method [START_REF] Barthes | Utiliser les représentations sociales en éducation[END_REF]. In this case, the dispersion of the terms is such that we only found four shared words, which had little significance in this context: education, training, teacher and sustainable development. This is in no way surprising given the many discussions that punctuated all meetings held throughout the research programme in repeated attempts to reach a consensual definition of the object of study. Although it was studied in its curricular aspects and in many different contexts, particularly in terms of its implications, the object 'SD' remains a polysemous concept. The Anglo-American understanding of the term is controversial [START_REF] Jacobs | Sustainable development as a contested concept, fairness and futury[END_REF] for the French research community and the latter has therefore not reached a consensus on the topic. The results are presented in six graphs of co-occurrences: The analyses show that various positions exist among researchers and that they can be found in the six categories (Graphs 1-6). To characterize these positions, we then used the main components of the graphs of co-occurrences (the words and their main links) associated with the 154 terms extracted from the publications used as additional indicative guides, and examined the publications themselves when specifications were required. From that point onward, we produced a word of the different, self-organized, positions and named them, on the basis of the central terms in the cooccurrence graph that describes them. Once this stage was completed, we were able to define more the following six classes, helped by bibliographic indicators and interviews of explicitation. We name and present them below.

Characterization of researchers' positions concerning ESD

The first position, that of the 'accepting' consists in adopting, de facto, the concept of SD. The researchers in this class accept the concept of SD as a basis for their work. The studies they undertake are based on their almost 'natural' integration of the concept, without involving real critical distance, either in relation to this new ideology, or in relation to the new scientific practices that it implies. We observe a surreptitious introduction of the term 'sustainable' scientific language; a scientific language undergoing a lexical rather than semantic transformation-in line with political directives-into a kind of newspeak denounced by others [START_REF] Bonneuil | L'évènement anthropocène, la Terre, l'histoire et nous[END_REF]. This position concerns a large number of studies and is characterized by the researchers' acceptance of a change in vocabulary imposed by the political ideology, but without the latter generating any shift in the scientific approach, any particular reflection on the subject. This position is most often observed in isolatedcase studies or in research/actor interactions characterized by a lack of critical distance.

These researchers describe field experiences and seem to adopt their orientations, as though the sometimes militant positions of education practitioners were self-evident and needed to scientifically legitimated. Consequently, there seems, as yet, to be no research movement built around this position and characterized by any specific lexical field or method.

The second position, that of 'the individuals describing/prescribing new procedures' consists of using the concept of sustainable development as a basis to produce a new mode of knowledge creation. This involves reassessing the knowledge produced through research by taking into account issues related to sustainable development. The studies in this group do provide analyses of sustainability but fail to analyse the foundations on which sustainable development can be realized, and are based on an inference principle that can sometimes lead to a lack of robustness. This position is frequently adopted by researchers trying to analyse the introduction of new procedures, such as green chemistry [START_REF] Ducamp | La chimie verte, approche nouvelle et responsable de la chimie[END_REF], Agenda 21 [START_REF] Lebatteux | La représentation sociale du développement durable d'élèves de lycée professionnel en démarche d'Agenda 21, Appuis et obstacles[END_REF], or its application by teachers [START_REF] Sarda | Enseigner une question socialement vive, les intentions d'enseignants du ministère de l'agriculture[END_REF]. A thorough description of the new procedures is then developed and serves to model their implementation.

The third position, that of the 'systemic' consists in approaching ESD by taking into consideration the relevance of temporal and spatial categories, as well as its systemic aspects, in order to envisage the introduction of ESD in its complexity. The researchers who adopt this theoretical position recommend considering development as 'necessarily engaged in multiple interactions with other places, which must be intelligible from different spatial scales ranging from the local to the global, and which involve relations of domination and competition, implying conflicts, collective choices, trade-offs' (Mathieu, 2006, p. 58). This position draws attention to existing tensions and contradictions in the concept and to the urgent need to precisely define the scope of relevance of such a problem. This position is strongly represented among researchers interested in territory related issues [START_REF] Barthes | Éducation au développement durable et territoires ruraux, Problématique, projet de territoire et réduction fonctionnelle de l'enseignement[END_REF]-such as those among geographers and economists who study educational issues (Barthes et al. 2013;[START_REF] Diemer | Comment construire des savoirs transversaux face à l'excès d'économie[END_REF][START_REF] Tutiaux-Guillon | Le développement durable en France, suffit-il de prescrire une question vive pour qu'elle existe à l'Ecole[END_REF][START_REF] Vergnolle-Mainar | La géographie dans l'enseignement, une discipline en dialogue[END_REF]-and is supported by the Swiss research team (Audigier, 2011a).

The fourth position, that of the 'controversies' consists of stating, from the offset, the objective of building a common object of study, i.e. ESD, whose social dimensions (representations, practices, controversies, risks) cannot be dissociated. But for this hybrid object to meet the challenge of what appears to be a political utopia, it is necessary to approach it as such (as an acute question), to untangle the complex causal system and to identify and evaluate opportunities to shift towards solutions that reconcile often conflicting, and even incompatible objectives, and, finally, to detect actual or potential conflicts of interest. Ensuring and implementing ESD […] implies organizing the reflection on education around a specific issue, or a socially acute question, laden with controversy [START_REF] Urgelli | Complexité et médiatisation d'une question socialement vive, le cas du réchauffement climatique[END_REF] and risk, and conducive to educational innovation. This is evidenced by the introduction of simulation games [START_REF] Vidal | Jeux de rôle et simulation, sensibiliser les élèves à la gestion d'écosocio-systèmes conflictuels[END_REF], serious games [START_REF] Genevois | Les «serious games " : un outil d'éducation au développement durable?[END_REF], multi-agent systems, or by the limitations of education (Moreau, Brugiere, & Triquet , 2012). A school of thought representing this position is that of Aix and Toulouse [START_REF] Legardez | L'école à l'épreuve de l'actualité[END_REF], 2011;Simonneaux & Simonneaux, 2012). It is partly adopted by Quebec researchers and is sometimes combined with the critical position [START_REF] Groleau | Le rapport au savoir comme outil théorique pour explorer la façon dont de futures enseignantes du primaire envisagent la physique et son enseignement[END_REF][START_REF] Bader | Conception des sciences d'élèves de 4 ème secondaire engagés dans une démarche interdisciplinaire d'enseignement des sciences sur les changements climatiques[END_REF]. This position is also, in some cases, combined with philosophical considerations [START_REF] Martinez | Pour l'éducation à l'écocitoyenneté, à la responsabilité et à la confiance durable, observer la formation des identités singulières, sociales et professionnelles[END_REF].

The fifth position, that of the 'critical', emerges in a context where ESD imposes itself as a frame of reference. The latter is the subject of national/international educational projects that offer an opportunity to reflect on the teaching contents of ESD and on their dominant and invasive nature (Jicking, 2008(Jicking, , 2009;;[START_REF] Robbotom | Research in environmental education[END_REF][START_REF] Sauvé | L'organisation et la structuration du secteur de l'éducation en réponse au programme onusien du développement durable. In "Former et éduquer pour changer nos modes de vie[END_REF][START_REF] Sterling | Higher education and ESD in England: A critical commentary on recent initiative[END_REF]. It also prompts reflection on 'the meaning of education, which is now put at the service of a development, intended to be sustainable' (Girault & Sauvé, 2008, p. 33). This position leads to a distancing from sustainable development and from ESD through the underlying of the practices resulting therefrom, and opens itself up to alternative positions. Fortin-Debart and Girault (2006, p. 41) state that 'This critical approach has little penetrated field of educational practices' and yet, open up possibilities of reflection and controversy in the construction of multi-paradigmatic knowledge. This position is very well represented in the Quebec school [START_REF] Sauvé | Environnement et développement: la culture de la filière ONU. Éducation relative à l'environnement-Regards[END_REF] and in the Anglo-Saxon community [START_REF] Jickling | Environmental education research: To what ends?[END_REF] and extends into France (Barthes & Alpe, 2012;[START_REF] Barthes | Questions and positions on education for sustainable development at university in France: Example of short professional cycles[END_REF][START_REF] Barthes | what kind of critical university education for sustainable development? A comparative study of European students and social representations[END_REF][START_REF] Barthes | Sous la bannière développement durable, quels rapports aux savoirs scientifiques? Rapport aux savoirs, éducation relative à l'environnement et au développement durable[END_REF][START_REF] Girault | Rapport aux savoirs induits dans la mise en place de différentes éducations au développement durable (EDD)[END_REF].

The sixth, highly 'didactic' position, consists of paying particular attention to curriculum construction, its difficulties and potentialities, by exploring the various possible approaches (Lange, 2012;[START_REF] Lange | Education au développement durable et éducation scientifique : Repères pour un curriculum[END_REF], 2011;[START_REF] Lebeaume | Effervescence contemporaine des propositions d'éducations à, Regards prospectifs pour le tournant curriculaire à venir[END_REF]. Attempts are also being made to integrate alternative teaching modalities, often with the idea of a different curriculum construction [START_REF] Bidou | Impliquer une population rurale dans la préservation de la biodiversité ? L'expérience du projet nichoirs dans la plaine en Poitou-Charentes[END_REF][START_REF] Chevallard | La pédagogie de l'enquête dans l'éducation au développement durable[END_REF][START_REF] Giral | Analyser les débats sur des questions vives environnementales, quelles conditions pour une co-construction des savoirs par l'action[END_REF]Lange, 2014b), which often counterbalances the questions in science didactics concerning disciplines or the legitimacy of the teachings. Questions regarding teacher training are also raised [START_REF] Lebeaume | Quelle(s) didactique(s) pour une formation des enseignants "aux éducations à " ? Convoquer la complémentarité et la spécificité des didactiques[END_REF] as well as issues concerning changes or difficulties in the various disciplines (Audigier, 2011a;[START_REF] Lange | La question de la production alimentaire et le défi de la durabilité dans les rescriptions de l'enseignement général : analyse curriculaire[END_REF][START_REF] Vergnolle-Mainar | La géographie dans l'enseignement, une discipline en dialogue[END_REF]. This didactic stance sometimes has its roots in the previously mentioned approaches such as, for example, the critical position [START_REF] Brière | Vivre ensemble sur Terre: un projet éducatif à dimension politique[END_REF] or that of controversies (Simonneaux & Simonneaux, 2012). It sometimes has an epistemological dimension, in which case it is inspired from the educations for' movement [START_REF] Albe | Des sciences à fortes vivacité sociale à l'école: entre disciplines et éducations in Pagoni et Tutiaux Guillon Les éducations à, quelles recherches[END_REF]Lange, 2014b).

Discussion

This essay on the positions of researchers in response to the emergence of ESD provides a snapshot of the community of the researchers involved in the Francophone research programs associated with the ESD decade network (2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014). This first overview shows at least the polysemic nature of ESD and of the different senses given to the term; it also reveals the emergence of various, more or less compatible positions. Thus, one of the authors of article recognizes itself more in the critical posture and the other in the didactic posture. This presentation of the different positions serves as a framework for interpreting what is undertaken, at a given time, by the French-speaking scientific community in command of curricular development, and the basic doctrinal choices, which may shape didactic work. A researcher is obviously characterized by more complexity: The position of an individual is not set in stone and one position may be combined with others. An individual evolves as time and debates go by and according to the general collective orientation. Thus, without losing sight of the complexity of individual thoughts and of the power relations at play in the debates held in the context of research programmes, this interpretive grid provides a basis for a detailed and evolving collective reflection and is not a fixed result of research. However, the heterogeneity of the positions, the lack of social, or in other words, of shared representations, highlighted in this study are probably an important factor in the orientation of the prescribed or produced curriculum, but they are without a doubt an important parameter in the direction of a possible curriculum for ESD. Furthermore, given the particular subject of this essay, ESD, it is also probably revealing of the other 'educations for'. The positions, as they are described above, also implicitly reveal that the three orientations proposed by [START_REF] Godard | Le développement durable et la recherche scientifique ou la difficile conciliation des logiques de l'action et de la connaissance[END_REF] are actually at work in the community of researchers in educational science, and involve three modalities of researchers' social responsibility. Some researchers only respond to the social demand as they would to any other demand (the 'Accepting'). Others are more in favour of reproblematizing the existing contents but without questioning the basis on which the recommendation is made ('descriptors/prescribers') and of envisaging research as a means of enriching institutional recommendations. Others tend to favour a critical deconstruction of the object ('critical positions'), using their conceptual elaborations and methodology as a basis for this endeavour, based on an examination of institutional recommendations. Finally, there are researchers who explicitly question their practices and call for the development of new research procedures (the 'systemic', the 'didactic'), taking 'seriously' the implications of alternative directives, and approaching the question from an external and/or internal viewpoint. The graph below summarizes these relationships:

These different positions, which correspond to the different ways in which researchers respond to their social responsibility (Graph 7), lead to negotiations, power relations or collaborations that result in curricular recommendations, which are then examined by State institutions. These positions structure the type of research that is conducted, and give rise to different curriculum possibilities [START_REF] Morris | Ecological consciousness and curriculum[END_REF]. They also add to the heterogeneity and fluctuations in institutional propositions (the prescribed), which generates confusion among practitioners and therefore makes implementations more difficult (self-prescribed). Faced with this unstable situation, most of them probably prefer to fall back on their customary practices. A study on the English-speaking community, based on a similar methodology, should obviously be undertaken to identify the similarities and differences between French and English speaking researchers, and their results in terms of national curricula. The positions of Francophone researchers probably have characteristics in common with those of English-speaking researchers, but a study of the Anglo-Saxon research community is necessary in order to truly identify the similarities and differences in the views and rationales that characterize each community. However, it appears, at least in light of the publications we examined, that the critical stance is quite common in the Anglo-Saxon community [START_REF] Gough | Towards a socially critical environmental education: Water quality studies in a coastal school[END_REF][START_REF] Jickling | Globalization and environmental education: Looking beyond sustainable development[END_REF]. Similarly, we find that the views of those describing/prescribing new procedures are also strongly represented among English speakers [START_REF] Gayford | Environmental education and the secondary school curriculum[END_REF][START_REF] Greenwood | A critical pedagogy of place: From gridlock to parallax[END_REF][START_REF] Lee | Teacher receptivity to curriculum change in the implementation stage: The case of environmental education in Hong Kong[END_REF][START_REF] Ross | Environment in the curriculum: Representation and development in the Scottish physical and social sciences[END_REF]. The 'controversy' approach also has followers [START_REF] Levinson | Towards a theoretical framework for teaching controversial socio-scientific issues[END_REF][START_REF] Levinson | A perspective on knowing about global warming and a critical comment about schools and curriculum in relation to socio-scientific issues[END_REF], and the epistemological questions seem to be raised more frontally in the Anglo-Saxon community [START_REF] Goodson | Subjects for study: Aspects of a social history of curriculum[END_REF][START_REF] Gough | From epistemology to ecopolitics: Renewing a paradigm for curriculum[END_REF][START_REF] Moroye | Complementary curriculum: The work of ecologically minded teachers[END_REF]. It appears furthermore that the view advocating citizen participation [START_REF] Dillon | Special section: Moving from citizen to civic science to address wicked conservation problems[END_REF] is much more common in the English-speaking than in the French-speaking community.

Conclusion

The curriculum question, as it is raised by researchers, synthesizes the tension between various objectives: objectives of knowledge creation, objectives in terms of comprehension and praxeological objectives. Thus, the existing research studies have not only influenced the orientations of the 'noosphere', but also probably the institutional curriculum propositions, and even the actual implementations by practitioners. Not only do they reflect those tensions, but the views they present are rooted in researchers' implicit or explicit conceptions of their social responsibility and in their relationship to the object of study, including in ideological terms. The study reported here, has identified six positions observed among French-speaking researchers; positions which structure the construction of curricula. This first overview contributes to revealing the tensions at work in the Francophone community. Those tensions probably have a crucial impact on the ways in which international recommendations (in the form of missions) are applied, in the long term, on the national education system and on the strategic orientations or actual educational practices. A similar study, using the same methodology, should be conducted on English-speaking researchers in order to identify the similarities and differences between both communities.


X Cao

G Debaecker

E Poirier

S Marya

J Cuddy

A Birur

P Wanjara

Tolerances of joint gaps in Nd:YAG laser welded Ti-6Al-4V alloy with the addition of filler wire

Keywords: laser welding, titanium alloy, joint gap, filler wire

The effect of joint gap on the butt joint quality of Ti-6Al-4V alloy welded using a4kWNd:yttrium aluminum garnet laser was evaluated in terms of the welding defects, microstructure, hardness, and tensile properties. The joint gap was proportionally filled using the filler wire with the compositions of the parent alloy. Fully penetrated welds without cracking were obtained up to a joint gap of 0.5 mm. The main defects observed in the welds were porosity and underfill. Specifically, the porosity area increased with increasing joint gap but remained less than 1% of the fusion zone area. Large underfill defects appeared in the weldments in the absence of a joint gap, but filler wire addition was observed to reduce this defect in the presence of a joint gap. The weld hardness decreased slightly with increasing joint gap, but the tensile properties were optimized at an intermediary gap size, probably due to the compromise between the low underfill ͑after the use of a filler wire͒ and a limited amount of porosity.

I. INTRODUCTION

The high temperature performance, low density, biocompatibility, and excellent corrosion-resistance of titanium and its alloys have led to a wide range of applications in demanding service conditions for the aerospace, automotive, medical, power generation, oil and gas extraction, chemical plant, and sporting industries. Ti-6Al-4V, a workhorse grade that accounts for more than half of all the titanium tonnage in the world, 1 is a two-phase ␣ + ␤ titanium alloy which contains aluminum as the alpha stabilizer and vanadium as the beta stabilizer. Due to its high strength-to-weight ratio, along with good tensile and creep properties up to a service temperature of 300 °C, Ti-6Al-4V has been successfully used for diverse applications including ͑1͒ medical, dental, and surgical devices; ͑2͒ turbine disks, compressor blades, and rings for jet engines; ͑3͒ airframe and space capsule components; ͑4͒ pressure vessels; ͑5͒ rocket engine casings; ͑6͒ helicopter rotor hubs; and ͑7͒ critical structural forgings. [START_REF]Technical data sheet: Allvac titanium 6Al-4V alloy[END_REF] Conventionally, gas tungsten-arc, gas metal-arc, plasma arc welding, and electron beam welding have been used to weld titanium alloys. [START_REF] Baeslack | Advances in titanium alloy welding metallurgy[END_REF][START_REF] Tsay | The effect of microstructures on the fatigue crack growth in Ti-6Al-4V laser welds[END_REF][START_REF] Sun | Proceedings of the 6th International Conference: Trends in Welding Research[END_REF] To date, the laser welding of Ti-6Al-4V has mainly concentrated on using CO 2 lasers. [START_REF] Casalino | Investigation on Ti-6Al-4V laser welding using statistical and Taguchi approaches[END_REF][START_REF] Sun | Proceedings of the 6th International Conference: Trends in Welding Research[END_REF][START_REF] Caiazzo | Ti-6Al-4V sheets lap and butt joints carried out by CO 2 laser: Mechanical and morphological characterization[END_REF][START_REF] Memola | Proceed-ings of XV International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers[END_REF] Limited work has been reported about the weldability of Ti-6Al-4V using high power continuous wave ͑CW͒ solid-state Nd:yttrium aluminum garnet ͑YAG͒ and fiber lasers. [START_REF] Cao | Effect of welding speed on butt joint quality of Ti-6Al-4V alloy welded using a high power Nd:YAG laser[END_REF][START_REF] Cao | Effect of post-weld heat treatment on Nd:YAG laser welded Ti-6Al-4V alloy quality[END_REF] Laser welding has many advantages including low and precise heat input, deep and narrow fusion zone ͑FZ͒, small heat-affected zone ͑HAZ͒, low thermal distortion, high productivity, and good process flexibility and reliability. However, since the spot size of the laser beam and the associated molten pool are relatively small, laser welding processes in general have a low tolerance for seam gaps. [START_REF] Aalderink | Seam gap bridging of laser based processes for the welding of aluminum sheets for industrial applications[END_REF] Therefore, there is an exigent challenge for workshop practice to achieve precise joint preparation, workpiece clamping, and manipulator accuracy, which can reduce the cost-effectiveness of manufacturing. a͒ Electronic mail: xinjin.cao@cnrc-nrc gc.ca 1

Clearly, an increased gap tolerance can potentially increase productivity and improve the process stability and joint quality in an industrial environment.

Recently, Aalderink et al. [START_REF] Aalderink | Seam gap bridging of laser based processes for the welding of aluminum sheets for industrial applications[END_REF] compared some laser-based welding techniques for their gap bridging capabilities for 1-2-mm-thick AA5182 aluminum alloy sheets. It was found that the use of the filler wire is indispensable to increase the gap tolerance. For the single spot laser welding with the use of the cold filler wire, a gap up to 0.6 mm can be bridged as opposed to a maximum allowable gap of 0.2 mm without the use of the filler wire. However, Sun and Kuo 11 investigated bridging ability of CO 2 laser welding for carbon and stainless steels. It was found that a large gap of up to 1.0 mm for 2.0-mm-thick butt joint was successfully welded with the use of a filler wire. The maximum joint gap accommodated is almost equal to the diameter of the filler wire. In spite of the inconsistency in the reported gap tolerances, as a rule of thumb, the allowable joint gap is around 10% of the workpiece thickness. [START_REF] Sun | Bridging the joint gap with wire feed laser welding[END_REF] For example, a joint gap of 0.3 mm is the maximum allowable gap to produce a satisfactory joint for 3-mm-thick sheets.

To further improve the bridging capacities, laser-arc hybrid welding process has been widely investigated. It was reported that the laser-arc hybrid welding process can bridge a gap up to 1.0 mm. [START_REF] Aalderink | Seam gap bridging of laser based processes for the welding of aluminum sheets for industrial applications[END_REF] Yao et al. [START_REF] Yao | Influence of joint geometry and fit-up gaps on hybrid laser-metal active gas ͑MAG͒ welding[END_REF] even reported that laser-arc hybrid welding process is rather insensitive to a joint gap below 3 mm as long as the arc parameters are set high enough to bridge these gaps. In laser-arc hybrid welding, the filler wire is required to ignite/maintain arc and compensate for the lack of metal in a relatively large joint gap. The filler wire can be melted by partial consumption of the laser energy or auxiliary electric arc, or by both. [START_REF] Kristensen | Proceedings of the 63rd Annual Assembly & International Conference of International Institute of Welding[END_REF] In the hybrid process, laser generates a deeper melt, while the arc supplies the molten filler metal to the weld pool. Although laser-arc hybrid process has been successfully implemented in ship building, transport, and construction industry, 14 its application requires more elaborate tuning of multiple process parameters related to arc as well as to laser. [START_REF] Katayama | Hybrid-Laser Arc Welding[END_REF] In addition, the laser-arc interactions can also help to stabilize the arc, particularly at high welding speeds. [START_REF] Denney | Proceedings of the 15th International Offshore and Polar Engineering Conference[END_REF] Compared with the laser alone welding process, laser-arc hybrid technique demonstrated significant advantages for its gap bridging capacities. However, laser alone process is relatively simple and hence is still preferred for aerospace applications. To date, limited work has been carried out for aerospace titanium alloys using a high power laser. In addition, a systematic investigation on the effect of the joint gap on the quality of aerospace titanium welds is still lacking. This is essential to provide practical technical guidelines for aerospace industry. To this end, the tolerance of the joint gap for 3-mm-thick Ti-6Al-4V alloy was systematically studied using a 4 kW CW Nd:YAG laser with a beam size of approximately 0.45 mm. The joint quality is characterized in terms of dimensions, porosity, underfill, microstructure, hardness, and tensile properties.

II. EXPERIMENTAL PROCEDURES

As-received mill-annealed grade 5 Ti-6Al-4V sheets ͑AMS 4911͒ were sectioned into coupons with dimensions of the roughly 102 mm in lengthϫ 63 mm in width ϫ 3.05 mm in thickness. Laser welding was performed along the specimen length, which was perpendicular to the rolling direction of the sheet material. The faying and adjacent surfaces of each specimen were brushed and then cleaned with ethanol to remove any contaminants prior to fixturing. The welding equipment consisted of a 4 kW CW solid-state Nd:YAG laser system equipped with an ABB robot and a magnetic holding fixture. A collimation lens of 200 mm, a focal lens of 150 mm, and a fiber diameter of 0.6 mm were employed to produce a laser beam with a focusing spot diameter of approximately 0.45 mm and a Rayleigh length of 2.34 mm. Since titanium is highly reactive with atmospheric elements, especially in the liquid state and at high temperatures, adequate measures were taken to shield the fusion zone and the heated surfaces until these regions were cooled below 100 °C. In this work, high purity argon at a flow rate of 23.6 l/min ͑50 cfh͒ was used to shield the top surface of the workpieces. The shielding of the root and the trailing gas shield on the top surface were performed using helium at a total flow rate of 66.1 l/min ͑140 cfh͒. All experiments were carried out at a laser power of 4.0 kW, a defocusing distance of Ϫ1 mm ͑i.e., 1 mm below the sheet top surface͒ and a welding speed of 3.0 m/min. The joint gap used was varied from 0 ͑no gap͒ to 0.6 mm ͑Table I͒. A Ti-6Al-4V filler wire ͑AMS 4956A ELI͒ with a nominal diameter of 1.14 mm was fed at a fixed angle of 30°toward the top surface of the workpiece. It is noteworthy that the filler wire was usually impinged by the laser beam on the top surface of the workpiece. The feed rate of the filler wire was calculated by using the volume flow rate constancy equation Wire feed rate = Welding speed ϫ Gap area Filler wire area .

Selected joints were then examined for defects using x-rays. The surface quality of the laser welds was visually evaluated in the as-welded condition. Three transverse sections were cut from each weld to examine the weld integrity and microstructure using optical microscopy. After sectioning, the specimens were mounted using cold-setting resin, ground and polished using automated techniques to produce a mirrorlike finish. Etching of specimens was performed by immersion in Kroll's reagent ͑1-3 ml HF+2-6 ml HNO 3 + 100 ml H 2 O͒ for 10-25 s. Microstructural examination was carried out using an inverted optical microscope ͑Olym- pus GX710͒, equipped with a digital camera and ANALYSIS FIVE image analysis software for measurement of the joint geometry. The microstructure was also observed for selected specimens using a Hitachi S-3600N scanning electron microscope ͑SEM͒ with an EDAX Genesis energy dispersive x-ray spectroscopy ͑EDS͒ system. The Vickers microindentation hardness was performed using a Struers Duramin A-300 hardness tester at a load of 500 g, a dwell period of 15 s, and an interval of 0.2 mm. Also for each joint, four subsize tensile specimens were machined according to ASTM E8M-01 to give gauge dimensions of 6.0 mm in width, 32 mm in parallel length, and 125 mm in overall length. The specimens were tested at room temperature using a 50 kN Instron machine, a 2620-604 Instron extensometer ͑gauge length of 25 mm used͒, and a crosshead speed of 2 mm/min.

III. RESULTS AND DISCUSSION

A. Joint geometry

Visual inspection of the welds revealed a silver metallic surface indicating that good shielding during welding was achieved. Figure 1 shows the overview of the transverse sections obtained at various joint gaps. It can be seen that the welds are fully penetrated for joint gap values up to 0.5 mm, i.e., the maximum gap tolerance was determined to be 0.5 mm, roughly equivalent to the beam size used. At 0.6 mm, a lack-of-penetration defect appears. The different areas, i.e., FZ, HAZ, and base metal ͑BM͒, can be clearly distinguished due to the microstructural differences across the welds.

As shown in Fig. 2, the area and width of the FZ ͑top, middle, and bottom͒ decrease with increasing joint gap. This decrease is more prominent at a small joint gap and then becomes relatively smooth above a gap size of 0.2 mm. It is noteworthy that in Fig. 2 the values at a joint gap of 0.6 mm are not taken into account due to the lack-of-penetration defect for this condition. In this latter case, a zero root width is assumed. Similarly, the HAZ area and width also decrease with increasing joint gap. For the middle HAZ width, there is an erratic value at a gap of 0.6 mm. This is due to the formation of the lack-of-penetration defect. In this case, the entire molten metal is located on the upper part of the weld, and the width is therefore increased ͓Figs. 1͑g͒ and 1͑h͔͒.

The overall decrease in the dimensions of the FZ and HAZ at higher joint gap values is directly linked to the increase in the gap size. The laser beam was set to be aligned with the joint in between the two workpieces to be butt welded. Hence, in the presence of a gap ͑between 0.1 and 0.6 mm in this work͒, part of the laser beam can be directly lost through the gap. In addition, laser energy may be lost due to the reflection caused by the filler wire surface. These losses of the laser energy increase obviously with increasing joint spacing and wire feed rate. Less effective energy available for welding leads to smaller FZ and HAZ. In addition, significant variations in the penetration depth are observed at a joint gap of 0.6 mm indicating the instability of laser energy absorption at a large joint gap ͓Figs. 1͑g͒ and 1͑h͔͒.

As shown in Figs. 3͑a͒ and3͑c͒, the joint gap has no clear influence on the weld reinforcement area and height. Generally speaking, the reinforcement height remains relatively low, 0.2-0.25 mm ͑less than 10% of the sheet thickness͒, for most of the fully penetrated joints and meets the acceptance criteria stipulated in AWSD17.

B. Welding defects

As shown in Fig. 1, no cracks are observed in the weldment, but porosity frequently appeared in the FZ. This was further confirmed by X-ray examination and analysis as indicated in Table I. In this study, the minimum dimensions that can be detected by X-ray were approximately 0.025 mm for the porosity and 0.025ϫ 0.127 mm 2 for linear indications ͑cracks, lack of fusion, etc.͒. In addition, underfill defects are visible on both the crown and root sides of the welds, as shown in Fig. 1. However as indicated in Fig. 3͑b͒, the overall underfill depth for gap sizes from 0.1 to 0.5 mm is less than 0.12 for the fully penetrated joints and meets the acceptance criteria stipulated in AWSD17.

C. Underfill defects

Large underfill defects are observed on both the crown and root sides of the welds in the absence of a joint gap. As is well known, underfill defects can weaken welds. For example, underfilling can reduce the sheet thickness and create stress concentration that will significantly reduce the tensile and fatigue strengths of the joints. Underfill defects, therefore, must be minimized. Specifically, the area and depth of the underfill defect on both the crown and root sides of the welds were measured as given in Fig. 3. It can be noticed that the average or maximum underfill depth appears at zero joint gap, namely, without the use of a filler wire. Compared with the zero joint gap, the average or maximum underfill depth is approximately halved at gap values from 0.1 to 0.5 mm. This trend is further intensified for the underfill area. The total underfill area including that on both the top and bottom sides obtained with zero gap was approximately five times greater than that at gap sizes from 0.1 to 0.5 mm. Therefore, the application of filler wire can increase the gap tolerance, reduce the underfill defects, and improve the process stability while saving both preparation time and costs for welding.

At zero joint gap, the overall underfill area is almost five times the reinforcement area indicating a significant loss of the molten metal, probably due to a combination of molten metal spattering and evaporation. When a filler metal was used, the loss of molten metal was significantly decreased. The measurement of the alloy chemistry using EDS with a SEM indicated a composition of 6.4 wt % Al and 3.0 wt % V for the base metal and 6.5 wt % Al and 2.6 wt % V for the FZ, which suggests that the evaporative losses from the molten weld pool are minor during laser welding. However, the reinforcement area was greater than the underfill area, at joint gaps from 0.1 to 0.5 mm ͓Fig. 3͑a͔͒, which may be related to combined effects of thermal expansion and phase transformation.

D. Porosity defects

In addition to the underfill defects discussed above, porosity is another main defect that was frequently observed, as shown in Fig. 1. Most of the porosity is nearly spherical in shapes but some are elongated. The pores can appear at various locations, depending on their origin. They are 5͒ and randomly distributed in the FZ ͑Fig. 6͒. It is well known that in laser welds the porosity can be formed due to the evolution of dissolved gas, collapse of unstable keyhole, entrapment of gases by surface turbulence, metal evaporation, and solidification shrinkage. [START_REF] Cao | A review of laser welding techniques for magnesium alloys[END_REF] In titanium welds shielded by inert gas, hydrogen is the main source for gas porosity. [START_REF] Petrov | The role of chemical reactions in the formation of pores in the welding of titanium alloys[END_REF] Figure 7 shows the solubility curve for hydrogen in titanium as a function of temperature at 1 atm external pressure. [START_REF] Mohandas | Fusion zone microstructure and porosity in electron beam welds of an ␣ + ␤ titanium alloy[END_REF] The solubility of hydrogen in both solid and liquid titanium decreases with increasing temperature. The effect of temperature and pressure on solubility of hydrogen in liquid titanium can be represented by the following equation: [START_REF] Mohandas | Fusion zone microstructure and porosity in electron beam welds of an ␣ + ␤ titanium alloy[END_REF] log S = 2370/T + 0.626 + 0.5 log PH 2 , where S is the solubility of hydrogen in liquid titanium ͑ml/100 g͒, T is the liquid temperature ͑Kelvin͒, and PH 2 is the equilibrium pressure of hydrogen above the surface of liquid titanium ͑mm Hg͒. It is clear that with an increase in the temperature of the weld pool and a decrease in the partial pressure, the solubility of hydrogen in liquid titanium decreases. At the melting point, however, liquid titanium has a higher solubility for hydrogen than solid titanium. [START_REF] Mohandas | Fusion zone microstructure and porosity in electron beam welds of an ␣ + ␤ titanium alloy[END_REF][START_REF] Mitchell | Porosity in titanium welds[END_REF] Therefore, hydrogen will precipitate at the liquid/solid interface during solidification. The decrease in solubility of hydrogen at the freezing point indicates that the gas porosity can be formed under certain conditions. As is well known, the occurrence of gas porosity comprises three stages, namely, nucleation, growth, and escape.

The nucleation of bubbles requires creation of a gasliquid interface, causing an increase in the free energy of the system. There are two mechanisms for nucleation, i.e., homogeneous and heterogeneous. In homogeneous nucleation, the pores form without the help of the discontinuous substrates. A pressure, as high as 50 000 atm, is required to fracture the liquid titanium, [START_REF] Karimzadeh | Effect of microplasma arc welding process parameters on grain growth and porosity distribution of thin sheet Ti6Al4V alloy weldment[END_REF] and hence homogeneous nucleation is unlikely a feasible mechanism for hydrogen pore formation in titanium and its alloys. In contrast, heterogeneous nucleation is much more favored. In the presence of discontinuities such as nonwetted solid inclusions, hydrogen can directly diffuse from hydrogensupersaturated regions into the discontinuous sites. In this case, bubbles can directly grow with no nucleation.

In titanium welds shielded by inert gas, hydrogen is the main source for gas porosity. [START_REF] Petrov | The role of chemical reactions in the formation of pores in the welding of titanium alloys[END_REF] Heating during welding gives a decrease in the solubility of hydrogen in liquid titanium with increasing temperature. The evolved hydrogen can form porosity by nucleation or direct diffusion into discontinuities or existing pores. Also, the pores can expand if they are heated to higher temperatures. In laser welding, the molten pool exists for only a short time due to the high welding speed and rapid cooling rate. Therefore, the gas porosity does not grow greatly in volume. Due to the low density, the bubbles formed in the liquid metal can float up. The driving force for the escape of bubbles is the reduction in interfacial energy and free energy of the system. Low viscosity, high fluidity, and low hydrostatic pressure of the liquid head will favor the flotation of the bubbles. During the rise, some small pores may meet and coalesce to form a large pore, causing a net increase in total pore volume due to both coalescence and reduction of surface tension pressure. [START_REF] Karimzadeh | Effect of microplasma arc welding process parameters on grain growth and porosity distribution of thin sheet Ti6Al4V alloy weldment[END_REF] Figure 8 shows some floating bubbles which are at the critical condition to coalesce during their rise.

Bubble rising and degassing may take place throughout the entire period of molten pool existence. The escape to the atmosphere is limited by the vapor pressure and diffusion rate, so that the metal may be "supersaturated" with hydrogen. If the bubbles cannot escape out of the surface of the weld pool, gas pores will form. Therefore, gas bubbles in titanium welds can form during the heating and melting stages of the metal ͑not only in the solidification stage͒.

At high heat inputs, both the temperature and the time at this temperature increase. The temperatures of the molten metal will be higher, and hence the lifetime of liquid pool would be longer. The solubility of hydrogen in titanium will thus be lower at higher temperatures ͑Fig. 7͒. In addition, the liquid has a lower viscosity and a higher fluidity at higher temperatures. At high heat input, therefore, the weld pool is relatively supersaturated with hydrogen and is favorable for the nucleation, growth, and escape of the bubbles. In a typical molten pool, the temperatures are highest in the keyhole and usually decrease from the evaporation temperatures at the keyhole to the melting point toward the fusion boundary. [START_REF] Mohandas | Fusion zone microstructure and porosity in electron beam welds of an ␣ + ␤ titanium alloy[END_REF] Therefore, the solubility of hydrogen is more supersaturated at the weld center than the fusion boundary. The weld center also remains at a temperature above the solidus for a longer period of time than the fusion periphery. The lower viscosity and higher fluidity in the weld center will favor the diffusion of hydrogen from the hot center to the cold fusion boundary. Therefore, bubbles tend to migrate from the weld center to the fusion boundary, explaining the presence of porosity near the fusion boundary as shown in Fig. 4. In this case, less porosity should appear at the weld center. In this work, however, porosity is still observed in the weld center as shown in Fig. 5. During solidification, the dissolved hydrogen is rejected from the liquid and appears at the solid/liquid interface. With the growth of columnar grains from the partially melted zone, the impurities and hydrogen will be richer in the remaining liquid. The center zone will be the last region of the weld to solidify and thus is usually enriched with hydrogen. In addition, the hydrogen-rich liquid in the center region has a low temperature at the late stage of solidification, and hence the gas cannot effectively escape, explaining the porosity in centerline grain boundaries. Therefore, the appearance of the centerline porosity indicates that the welds are heavily contaminated by hydrogen, which may come from the original titanium alloys, or pick up during welding. During the rapid cooling of the laser welds, some gas porosity may distribute randomly in the FZ, probably due to the energetic convective movement.

In addition to the hydrogen porosity, the collapse of unstable keyholes is usually considered to be another main mechanism for the formation of porosity in laser welds. [START_REF] Cao | A review of laser welding techniques for magnesium alloys[END_REF] Keyhole stability during laser welding depends on a high degree on the balance of forces active inside the keyhole. Upon the establishment of the vapor cavity, the fluid forces of the molten pool are balanced by the vaporization pressure within the cavity. The inherent instability of keyholes may lead to periodic collapse of the liquid metal surrounding the vapor cavity causing the formation of periodic voids. Pastor et al. [START_REF] Pastor | Pore formation during continuous wave Nd:YAG laser welding of aluminum for automotive applications[END_REF] schematically explained the mechanism for the formation of the porosity caused by the collapse of unstable keyholes. The pores caused by unstable keyholes are usually located at the lower half of the welds or at the weld root along the keyhole path. The essential point in reducing this porosity is to keep the keyhole stable, but it is only achievable in high speed welding. In this work, a welding speed of 3 m/min was used, and the collapse of unstable keyhole does not seem to be the main mechanism for the formation of porosity. In addition, interdendritic shrinkage porosity can form as shown in Fig. 9. Other possible mechanisms for porosity formation include entrapment of gases by surface turbulence, and metal evaporation. [START_REF] Cao | A review of laser welding techniques for magnesium alloys[END_REF] However, these are not main mechanisms as demonstrated in this work. The porosity in laser welded titanium joints is mainly due to hydrogen.

During solidification, the pore will shrink with the reduction in the temperature of the liquid metal. The shrinking continues until the solidus temperature is reached. Any further decrease in temperature can only slightly reduce the pore sizes in the solid state.

For each sample, the size and area of the porosity were measured in order to check their evolution with joint gap. As shown in Fig. 10, the porosity area increases with increasing joint gap for the fully penetrated welds. The percentage ratio of the porosity area to the FZ area also increases with increasing joint gap. It is noted that there is only a slight increase in the porosity area at small gaps but a large increase at large gaps. The increase in porosity comes particularly from the fact that more filler wires were used at higher joint gaps. The filler wire surface can absorb some moisture and is hard to clean, thereby producing more porosity. The presence of the joint gap itself is a source of defect generation. It should be noted that the porosity percentage to the FZ area remains well below 1%, which is low even at the maximum joint gap used in this work. In spite of the low porosity level, the presence of porosity can weaken the welds, particularly when several gas bubbles are merged together to form larger pores. This may happen more often in the centerline grain boundary ͑Fig. 5͒. In some extreme cases, the pores can be agglomerated and create a long porosity in the center of the welds.

E. Microstructure

The different regions of the weld macrostructure can be correlated with the maximum temperature reached in the material. [START_REF] Short | Gas tungsten arc welding of ␣ + ␤ titanium alloys: A review[END_REF] Figure 11 displays typical microstructures of the base metal and FZ in a weld. As indicated in Fig. 11͑a͒, the base metal is composed of dark ␤ phase regions in the dominating bright ␣ matrix, a typical annealed structure for the ␣ -␤ titanium alloy. In the SEM image ͓Fig. 11͑b͔͒, the ␤ phase appears to be bright ͑due to V͒ and is distributed at the boundaries of the elongated ␣ grains ͑dark due to Al͒.

The FZ is defined as the region where the temperature exceeds the alloy's effective liquidus temperature. As shown in Figs. 11͑c͒ and11͑d͒, the FZ consists mainly of acicular martensite ͑␣Ј͒. It was reported that cooling rates higher than 410 °C / s are usually required for Ti-6Al-4V alloy to attain a completely martensitic microstructure. [START_REF] Ahmed | Phase transformation during cooling in ␣ + ␤ titanium alloys[END_REF] The high self-quench rate associated with the laser beam welding process certainly promotes the diffusionless transformation of the ␤ phase into a martensitic structure. The boundaries of the prior ␤ grains were clearly revealed in the FZ ͑Figs. 5 and 6͒. As shown in Fig. 11͑c͒, the ␣ phase forms at ␤ grain boundaries indicating that the cooling rate is close to the lower limit of the ␣Ј transformation window. The small FZ exhibits coarse columnar ␤ grains which grow opposite to the heat flow direction. These coarse grains have epitaxially grown on the semimelted ␤ grains in the partially melted zone, i.e., atoms are just added to the substrate and neither activation energy nor undercooling is required. Then these prior ␤ grains undergo martensitic transformation upon cooling.

Within the HAZ, Ti-6Al-4V displays two regions, distinguished by the ␤-transus temperature T ␤ ͑ϳ985 °C͒. [START_REF] Short | Gas tungsten arc welding of ␣ + ␤ titanium alloys: A review[END_REF] The HAZ close to the FZ ͑near HAZ͒ is approximately the region where the maximum temperature is greater than T ␤ and less than liquidus, while the HAZ adjacent to the base metal ͑far HAZ͒ is at a temperature lower than T ␤ and greater than a minimum temperature required for microstructural change. This minimum temperature is difficult to define, as it depends on transformation kinetics. [START_REF] Short | Gas tungsten arc welding of ␣ + ␤ titanium alloys: A review[END_REF] Therefore, the near HAZ has a quenched structure. The far HAZ is a mixture of primary ␣ and ␤ phases with ␣Ј, which correspond to a structure quenched below the ␤-transus. Although the HAZ is very narrow, a significant variation in the microstructure is apparent.

In this study, the filler wire used has the same chemistry as the base metal. Therefore, the essential nature of the microstructures in different weld zones does not seem to be affected by the gap size. In fact, the phases formed depend essentially on the cooling rates experienced, and for the acceptable gaps that were well filled, little differences in microscopic structures were observed over the joint gaps from 0 to 0.5 mm in this work.

F. Hardness

Figures 12 and13 show the distribution of Vickers hardness. For all joint gaps from 0 to 0.6 mm, the hardness profiles are similar. The lowest hardness is obtained in the base metal, and then it increases from the HAZ to the FZ. The maximum value was obtained in the FZ due to the formation of much harder ␣Ј. As shown in Fig. 13, there is a valley of hardness in the center of the FZ which is probably due to the lower cooling rate in this region. Compared to the profile across the middle of the weld, the hardness values near the top and bottom surfaces are more uniformly distributed. In the near HAZ, the quenched structure produced a similar hardness to that in the FZ. In the far HAZ, there is a mixture of ␣Ј and primary ␣ and ␤ phases. Near the FZ side, the proportion of ␣Ј is close to 100% with very little ␣ + ␤. On contrary, near the border between the far HAZ and the base metal, the majority of the microstructure consists of ␣ + ␤ with a very small amount of ␣Ј. Between these two borders, the proportions vary depending on the distance to each zone. Therefore, the narrow HAZ has significant heterogeneity in both microstructure and mechanical properties. Figure 14 shows the variations in the average hardness in the FZ with increasing joint gap. It can be noticed that there is a slight decrease in hardness with increasing joint gap, probably due to small prior ␤ grain sizes. The average hardness is approximately 342 HV for base metal and 387 HV for the FZ.

G. Tensile properties

Figure 15 shows the variation in the tensile properties with increasing joint gap. The base metal has a tensile strength of 1062 MPa, a yield strength of 996 MPa, and an elongation at break of 14% ͑obtained over a gauge length of 50 mm͒. In this work, subsize specimens were used, and thus only the joint strength can be compared with that of the base metal. The tensile strength is similar to the base metal with joint efficiencies ranging from 86% to 101%.

It was reported that a low ductility in weld FZ and near HAZ significantly limits the use of welded titanium structures. [START_REF] Baeslack | Advances in titanium alloy welding metallurgy[END_REF] The poor ductility results in part from the coarse prior-␤ grain size and the preferential crack propagation along the prior-␤ grain boundaries. In laser welds, relatively small prior-␤ grain sizes can be obtained due to the rapid cooling rate. The poor elongation obtained at zero joint gap is probably due to the underfill defects that create a stress concentration ͑significant reduction in the joint transverse section͒. The use of a filler wire can decrease the underfill defect, and thus relatively high ductility can be obtained.

Table II shows the failure location of the tensile samples at various joint gaps. This information added to the previous measurements indicates the evolution of the tensile behavior. Logically, tensile characteristics ͑especially elongation͒ are higher when the break occurs in the base metal ͑at gaps of 0.2-0.3 mm͒ and lower when the break happens in the FZ. The tensile failure happens in the most fragile location. If the weld is weaker than the base metal, it is in the FZ where the rupture occurs. If the weld is stronger than the base metal, the latter will fail first.

The best results are for joint gap values of 0.2 and 0.3 mm, beyond which the results deteriorate again. On this basis it can be said that the increase of porosity in the FZ weakens the joint. For joint gaps of 0.2 and 0.3 mm, the porosity is low and the reduction of the underfill through the addition of filler wire optimizes the process. For a joint gap greater than 0.3 mm, the number of pores increases rapidly and the tensile properties are reduced. The values obtained at joint gaps of 0.4 and 0.5 mm are to be taken with caution because the results may also be influenced by other factors such as contamination of oxygen, which was not taken into account in this study. Therefore, the best joint gap for laser welding of Ti-6Al-4V is approximately 10% of the material thickness, but the maximum gap tolerance was determined to be 0.5 mm, roughly equivalent to the spot size used.

IV. CONCLUSIONS

͑1͒ When the filler wire with the compositions of the parent alloy is used, the butt joints can be welded with a full penetration up to a joint gap of 0.5 mm, roughly equivalent to the spot size used. ͑2͒ The dimensions of the fusion and heat-affected zones are reduced with increasing joint gap. ͑3͒ No cracks were detected in the laser welds. The main defects observed are underfill and gas porosity. The pore area increases with increasing joint gap but remains less than 1% of the FZ area. The underfill defect is more prominent in the absence of a joint gap, and the use of a filler wire can significantly reduce this defect. ͑4͒ The hardness of the welds is slightly decreased with increasing joint gap. The welds have good resistance for all gap sizes with a joint efficiency ranging from 86% to 101%. But the optimal tensile properties are obtained at an intermediary joint gap ͑0.2-0.3 mm͒, approximately 10% of the material thickness, which provides a balance between the low underfill, due to the use of a filler wire, and a limited amount of porosity.

FIG. 1 .

 1 FIG. 1. Overview of weld cross sections at various gaps.

FIG. 2 .

 2 FIG. 2. Effect of gap on FZ and HAZ area and width.

FIG. 3 .

 3 FIG.3. Effect of joint gap on underfill and reinforcement area and size.

FIG. 4 .

 4 FIG. 4. Porosity near HAZ/FZ interfaces.

FIG. 6 .

 6 FIG. 6. Porosity randomly distributed in the fusion zone.

FIG. 8 .

 8 FIG. 8. Coalescence of porosity obtained at joint gaps of ͑a͒,͑b͒ 0.1 and ͑c͒ 0.2 mm.

FIG. 9 .FIG. 10 .

 910 FIG. 9. Gas and shrinkage porosity.

FIG. 12 .FIG. 13 .

 1213 FIG. 12. Vickers hardness in the weld with zero gap.

FIG. 14 .

 14 FIG.14. Effect of joint gap on fusion zone hardness.

TABLE I .

 I Welding processing parameters used. a

		Joint gap	Wire feed rate
	Trial No.	͑mm͒	͑m/min͒	X-ray examination
	1	0	0	Not examined
	2	0.1	0.9	Three voids
	3	0.2	1.8	One void
	4	0.3	2.7	Four voids
	5	0.4	3.6	Five voids
	6	0.5	4.5	Two voids
	7	0.6	5.4	Not examined
	a Note: Pore size ranges from 0.25 to 0.5 mm.

TABLE II .

 II Failure locations after tensile testing.

						Joint gap
						͑mm͒	Failure location
						0	4 F Z
						0.2	4 BM
						0.3	4 BM
						0.4	1 BM+3 FZ
						0.5	2 BM+3 FZ
						0.6
		1200			20
	Strength (MPa)	400 800	YS UTS		15 10 5	(%) Elongation
			El
		0			0
		0.0	0.2	0.4	0.6
			Joint gap (mm)

FIG.

15

. Effect of joint gap on tensile properties.

ACKNOWLEDGMENTS

Thanks are due to B. Marius for the technical support provided during tensile property testing.


Amelia Carolina Sparavigna

The Shwedagon Pagoda and the Zenith Passage of the Sun

Here we discuss the orientation of the Shwedagon Pagoda, the gilded stupa situated on Singuttara Hill in Yangon, Myanmar, and a possible link with the sunrise on the days of the zenith passage of the sun. These days are also linked to the Festival of the Full Moon of the month of Kason, the second month of the traditional Burmese calendar. In Myanmar, this is the festival of the Vesak Day of Buddha.

The Shwedagon Pagoda, also known as the Great Dagon Pagoda or the Golden Pagoda, is a gilded stupa situated on Singuttara Hill, in Yangon, Myanmar. This Pagoda is the most sacred Buddhist temple in Myanmar. Wikipedia tells that historians and archaeologists consider the pagoda built by the Mon people between the 6th and 10th centuries AD [START_REF] Maung | The Shwe Dagon Pagoda[END_REF]. However, a tradition exists which is telling that the Shwedagon Pagoda was constructed more than 2,600 years ago. In this manner, the Golden Pagoda would be the oldest Buddhist stupa in the world [START_REF] Mahayazawindawgyi | The Great Glass Palace Chronicle[END_REF]. This tradition is described in detail at the web site [3].

As explained in [3], the pagoda's beauty derives from the geometry of its shape and of the surrounding structures and by its golden glow (see Figures 1 and2). The pagoda rises 99 m on the Singuttara Hill (51 m), above the city. The stupa is plated with solid gold bars. Its tip is set with diamonds, rubies, sapphires, and other gems and golden bells. At the very top, there is a single 76carat diamond. For what concerns the architecture of this temple, Ref.3 is telling that, from an aerial view of it (Figure 3), we can see that the Stupa has four small pagodas "at the 4 cardinal point" [3], 64 pagodas encircling the base, a plinth, terraces and an octagonal base. Actually, as we can see from the figure, the complex is not cardinally oriented. It is customary to circumnavigate Buddhist stupas in a clockwise direction. "In accordance with this principle, one may begin at the eastern directional shrine, which houses a statue of Kakusandha, the first Buddha of the present kalpa (Sanskrit word meaning an aeon). Next, at the southern directional shrine, is a statue of the second Buddha, Konagamana. Next, at the western directional shrine, is that of the third Buddha, Kassapa. Finally, at the northern directional shrine, is that of the fourth Buddha, Gautama" [4]. In [START_REF] Billinge | Shwedagon Paya. The Temple Trail[END_REF], we can find more details on the temple and the statues and shrines we can find there.

In [3], we read that the many religious festivals linked to the Myanmar lunar calendar are drawing people to pagodas. Among the most important festivals mentioned in [3] we find the Festival on the Full Moon Day of the Myanmar month Tabaung (February-March), and the Myanmar New Year Festival in April. We find also the Buddha Day Festival, known as Kason Festival, in the month of Kason (April-May). The Festival of the Kason Full Moon day is the Vesak Day in Myanmar. During this festival, people "carry earthen pots filled with water and flowers to offer to banyan trees, in memory of the Buddha. Legend goes that the holiday falls on the hottest day of the year. Buddhists in Burma use water to cool off and protect the holy tree, under which the Buddha achieved enlightenment" [6]. Let us note that Kason is popularly called the water-pouring month.The Kason Festival marks the birth, enlightenment and death of Gautama Buddha (Vesak) [7]. This day is more universally known as Vesak, and is celebrated in countries where Buddhism is widely practised, such as India, Sri Lanka, Thailand, Cambodia and Laos.

It is remarkable that, in Myanmar, the Vesak holiday is considered "the hottest day of the year".

However, what is, symbolically, the hottest day of the year? For the tropical zone, we can imagine it as a day of zenith passage of the sun. In some previous papers [START_REF] Sparavigna | The Solar Orientation of the Lion Rock Complex in Sri Lanka[END_REF][START_REF] Sparavigna | On the alignment of Sanchi monuments[END_REF][START_REF] Sparavigna | Solar Alignments of the Planning of Angkor Wat Temple Complex[END_REF][START_REF] Sparavigna | The Sewu Temple and the zenithal passage of the sun[END_REF][START_REF] Sparavigna | A short note about the zenithal sun and the Sewu, Prambanan and Borobudur temples in Java[END_REF][START_REF] Sparavigna | The Zenith Passage of the Sun and the Architectures of the Tropical Zone[END_REF][START_REF] Sparavigna | The Zenith Passage of the Sun at the Mesoamerican Sites of Tula and Chichen Itza[END_REF][START_REF] Sparavigna | The Zenith Passage of the Sun at Candi Borobudur[END_REF][START_REF] Sparavigna | The Ruins of the Buddhist Temples in the Progo Valley, Borobudur, Mendut and Pawon, Described by Isaac Groneman in his Book of 1912[END_REF], we have discussed that the layout of the architectures of tropics can show some links or even alignments along the directions of sunrise/sunset on the days of the zenith passage of the sun. Therefore, let us consider again the image in the Figure 3, and try to investigate if we can find in this layout of the Shwedagon complex a link to the zenithal sun and, consequently, a link to the "hottest day of the year", that popularly, in Myanmar is the day of the Kason Festival.

As we have already told, the Shwedagon complex has not the main axes aligned along the northsouth and east-west directions. These axes have an angle of about 16 degrees from the cardinal axes. So AB axis in the Figure 3 is not aligned along the direction of sunrise/sunset on equinoxes. It corresponds to a sunrise azimuth of 74 degrees. In Yangon, this is the azimuth of the sunrise on the days from the First of May to May 3 (according to software sollumis.com). From May 3 to May 12, the noon altitude of the sun is greater than 89 degrees.

Using another software, the SunCalc.org software that, like sollumis.com, is an online application which can be used to ascertain the sun movement with an interactive map, we can see that we have the zenith passage of the sun on May 7 (the other day of zenith passage is August 5). So we can tell that AB axis of the Shwedagon temple is aligned along the sunrise of the first day of a period during which the sun has an altitude equal or greater than 89 degrees. That is, symbolically, it could be the first of the hottest days of the year. Now, let us consider the Full Moon Day of Kason.

In 2018, it will be on 29 April [17]. Using SunCalc.org, for April 29, we obtain the Figure 4. We see that axis AB in Figure 3 is practically coincident with the direction of the sunrise on the Kason Day 2018 (sunrise azimuth 75 degrees).

In 2017, the Kason Day was on May 10 [18], and in 2016 it was on May 20. Since the Festival is determined by the full moon, its date changes year after year. Of course, the directions of the sunrise on these days are rather different, and therefore, we cannot have a specific alignment according to the Festival. But, since the lore goes that the Full Moon of Kason is linked to "the hottest day of the year", we can conclude telling that the temple complex of the Shwedagon Pagoda was probably planned with an alignment along the direction of the sunrise on the day which represent the beginning of the period of the hottest days of the year, that is, the period during which we have the zenith passage of the sun.

Figure 1 :

 1 Figure 1: The south-eastern side of Shwedagon Pagoda. Image Courtesy: Bjørn Christian Tørrissen.

Figure 2 :

 2 Figure 2: A monk is walking on the facade. Image Courtesy: Bjørn Christian Tørrissen.

Figure 3 :

 3 Figure 3: Shwedagon Pagoda in Google Earth.

Figure 4 :

 4 Figure 4: Sunrise direction on the day of the Kason Festival, 29 April 2018 (Courtesy SunCalc.org).

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Published on Monday 29th January, 2018 at 22:39:09.

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Amelia Carolina Sparavigna

On the orientation of the Avenue of Sphinxes in Luxor

The Avenue of Sphinxes is a 2.8 kilometres long Avenue linking Luxor and Karnak temples. This avenue was the processional road of the Opet Festival from the Karnak temple to the Luxor temple and the Nile. For this Avenue, some astronomical orientations had been proposed. After the examination of them, we consider also an orientation according to a geometrical planning of the site, where the Avenue is the diagonal of a square, a sort of best-fit straight line in a landscape constrained by the presence of temples, precincts and other processional avenues. The direction of the rising of Vega was probably used as reference direction for the surveying.

The Avenue of Sphinxes is a 2.8 kilometres long Avenue linking Luxor and Karnak temples. This avenue was a processional road built by King Amenhotep III (Amenhotep the Magnificent, the ninth pharaoh of the Eighteenth Dynasty, who ruled Egypt from about 1390 to 1350 BC) and took its final form under Nectanebo I in 400 BCE (en.wikipedia.org/wiki/Luxor). Also the Queen Hatshepsut was involved in the evolution of this architectural complex. As recorded on her red chapel in Karnak temple, she built six chapels dedicated to the god Amun-Re on the route of this Avenue during her reign [START_REF] Wuyts | Excavation and restoration on the Avenue of Sphinxes. Independent[END_REF]. In the past, a large part of the Avenue was covered by silt and buildings. Restoration started around 2004 (en.wikipedia.org/wiki/Luxor) [START_REF] Boraik | The Sphinxes Avenue Excavations to the East Bank of Luxor[END_REF]. We can see the evolution of this restoration by means of the time series of satellite images in Google Earth (Figure 1).

Along the Avenue, it moved the procession of the Opet Festival. The statues of the deities of the Theban Triad, that is Amun, Mut and their child Khonsu, hidden from sight in a sacred barque, were escorted from the temple of Amun in Karnak, to the temple complex of Luxor. This complex is composed by the temples of Amenhotep III and Ramses II. The Amenhotep III Temple was the cult temple of the goddess Mut [START_REF] Furlong | Egyptian Temple Orientation, Astronomical Alignment in the Temples of Egypt, Part 4B[END_REF]. As explained in [START_REF] Furlong | Egyptian Temple Orientation, Astronomical Alignment in the Temples of Egypt, Part 4B[END_REF], originally a Middle kingdom temple existed on this site but it was substantially rebuilt by Amenhotep.

The Amenhotep temple was extensively surveyed by Schwaller de Lubicz in 1937, "who suggested many subtle aspects woven into its design". Ramses II "added an extension to the temple on a slightly different azimuth, … The Ramses additions are aligned with an avenue of sphinxes which runs directly through to the Karnak temple, … Effectively this extension skews the axis of the temple" [START_REF] Furlong | Egyptian Temple Orientation, Astronomical Alignment in the Temples of Egypt, Part 4B[END_REF]. The azimuths of these temple -Furlong notes -could only be aligned to the stars. At the latitude of Luxor, alignments along sunrise/sunset or moonrise/moonset are not possible.

Furlong continues telling that, in the case of Amenhotep's temple, there are no 1st magnitude stars or constellations that fit construction dates, "whether looking towards the north or south". In his work, De Lubicz suggested the rising of Vega, but for this alignment, the temple construction has to be dated back to around 3600 BC, "a very improbable date". The best-fit offered by an astronomical orientation is that according to the setting of the Southern-Cross. It "broadly fits the southern azimuth but this would have been too high in the sky to produce an exact alignment" [START_REF] Furlong | Egyptian Temple Orientation, Astronomical Alignment in the Temples of Egypt, Part 4B[END_REF]. As concluded by Furlong, it seems that it was the Nile that forced the orientation, which is close and runs parallel to the axis of the temple. As we can see from the Figure 2, the Ramses II temple is strongly linked with the Sphinx Avenue.

And the Avenue does align with the rising of star Vega [START_REF] Furlong | Egyptian Temple Orientation, Astronomical Alignment in the Temples of Egypt, Part 4B[END_REF]. "However it is also aligned to the sanctuary of Amun in the Karnak temple. Without clear textual evidence it is impossible to say what the intentions of the original architect might have been in this alignment" [START_REF] Furlong | Egyptian Temple Orientation, Astronomical Alignment in the Temples of Egypt, Part 4B[END_REF] (Furlong gives an azimuth of 44°36' for the rising of Vega around 1290 BC, the assumed construction date of the temple). The avenue runs in a straight line from the Ramses II temple to the south-west corner of the boundary wall of the Karnak temple. Then, the avenue joins a secondary avenue of sphinxes from the Mut temple. "At first glance the sighting to Vega suggests this had to be a primary element in the alignment of the avenue. However, by hypothetically projecting the avenue a little further, one finds that it is exactly aligned to the main sanctuary of Amun-Ra at the heart of the Karnak complex". Furlong describes this alignment in the following manner: a "bow shot from the sanctuary roof in Karnak, would exactly follow the avenue of sphinxes, through the entrance gateway of Ramses temple to the middle of the its far end". For what concerns the Karnak temple, its alignment along the sunrise on winter solstice is well-known (see [START_REF] Sparavigna | The Stellarium Planetarium for the Simulation of the Astronomical Landscapes of Ancient Stargazers[END_REF] and references therein).

We see that both Schwaller de Lubicz and David Furlong have mentioned the alignment along the direction of the rising Vega. Let us use Stellarium, an open source free software planetarium, that we considered for simulating the astronomical landscapes of the ancient stargazers and also for more recent astronomical events [START_REF] Sparavigna | The Karnak Temple and the Motion of the Earth's Axis[END_REF][START_REF] Sparavigna | Maria Reiche's line to Archaeoastronomy and Ancient Technologies[END_REF][START_REF] Sparavigna | The Nazca Frigatebird and Fomalhaut[END_REF][START_REF] Sparavigna | A Possible Role of Alpha Crucis in the Astronomical Landscape of Silbury Hill[END_REF][START_REF] Sparavigna | Stellarium software and the occultation of Aldebaran observed by Copernicus[END_REF]. We can simulate for 1290 BC at Luxor. In the Figure 3 Let us turn the view towards the southern temple. We can see that in the range from 40 to 50 degrees (from West), we had the setting of the Crux, the Southern-Cross (Figure 5). Also in [START_REF] Magli | Architecture, Astronomy, and Sacred Space: The Case of the Avenue of the Sphinxes[END_REF], we find the astronomical orientation of the Avenue considered. Magli tells that in 2014 he proposed the Avenue as having an inter-cardinal azimuth, that is, of 45 degrees (Magli's data) [START_REF] Magli | Architecture, Astronomy, and Sacred Space: The Case of the Avenue of the Sphinxes[END_REF][START_REF] Magli | A Cognitive approach to the Luxor-Karnak relationship[END_REF]. In [START_REF] Magli | Architecture, Astronomy, and Sacred Space: The Case of the Avenue of the Sphinxes[END_REF], it is told that the choice of an inter-cardinal orientation is "hardly random, and its most likely explanation is astronomical"; moreover, it is present in Egypt since the Early Dynastic times [START_REF] Belmonte | On the orientation of ancient Egyptian temples: (1) Upper Egypt and Lower Nubia[END_REF][START_REF] Lehner | A contextual approach to the Giza pyramids[END_REF]. Then Magli continues giving references to the stars. "From the astronomical point of view," the inter-cardinal orientation corresponded to the Milky Way," in a band 12 degrees wide, "from approximatively 3200-1100 BC. Close to 45 degrees at rising, we can see "the "northern branch" of the Milky Way with Cygnus, (but also Arcturus and Vega)" [START_REF] Magli | Architecture, Astronomy, and Sacred Space: The Case of the Avenue of the Sphinxes[END_REF]. To the other end, we had the Southern Cross-Centaurus group. Considering the Milky Way, Magli argues that the "orientation of the avenue was therefore deliberate and highly symbolic".

Let us conclude our discussion, considering again Ref.3. Furlong notes that, for the Avenue of Sphinxes and in other cases, we have to face the following problem in assessing star alignments: "What takes precedence? Was the alignment to Vega a fortuitous co-incidence or was it deliberate?

These are insuperable questions and may never be satisfactorily answered, even if it is possible to establish the precise date when the avenue … was first laid down". The same is true for an intercardinal orientation. Is it linked to the stars of the Milky Way? Or was dictated by a geometrical approach, to have the Avenue as the diagonal of a square?

For the Avenue of Sphinxes, let us imagine the Furlong's bow shot from Karnak to Luxor. Let us consider a planning as in the Figure 6. We have two points: A is the end of the Avenue at Ramses II court and B is the point where the Avenue meets another processional avenue. Drawing two perpendicular lines we have point C. If we use the satellite image, the angle of the Avenue is of 45,5 degrees (the complementary angle is the azimuth of the rising of Vega, around 1300 BC), AC is 280 pixels long and BC is 285 pixels long. AC is 400 pixels long. Actually, AC is the diagonal of a square. The persons that planned the Avenue were well aware of the involved geometric figure, and it is possible that decided it after a surveying of the local environment and related constraints. They were probably the architects of Amenhotep the Magnificent.

The court of Amenhotep "was luxurious beyond imagination, with the wealth of the Mediterranean world flowing into Egypt's coffers" [START_REF] Hawass | Bibliotheca Alexandria[END_REF]. The architects who worked for him had the possibility to live in a privileged environment where, besides the luxury and exotic goods, also knowledge and science were flowing, from the Mediterranean and Eastern countries into the cultural elite of Egypt.

We know one of these architects. He was Kha, a high-ranking official, whose tomb was found by the Italian Egyptologist Ernesto Schiaparelli in February 1906 [START_REF] Moiso | Ernesto Schiaparelli e la Tomba di Kha[END_REF] in Deir el Medina. This was a village located on the west bank of the Nile, across the river from Luxor, that was inhabited by people working for the two great royal necropolises of the Valleys of the Queens and of the Kings. Kha, his wife Merit and all the objects found in the tomb are today in the Egyptian Museum of Torino. Among the remarkable objects that we have in Torino [START_REF] Sparavigna | The Architect Kha's Protractor[END_REF][START_REF] Sparavigna | A Possible Use of the Kha's Protractor[END_REF], one is showing that the use of compass and straightedge was common in the Egypt of the time [START_REF] Sparavigna | Overlapping Circles Grid Drawn with Compass and Straightedge on an Egyptian Artifact of 14th Century BC[END_REF]. Therefore, it is possible that the architect who planned the Avenue used, after a proper land surveying, a layout based on a geometric compass and straightedge construction, to have a line, the diagonal of the square, as a sort of bestfit of the data concerning the layout of the Avenue. These data consisted in the presence of other temples, precincts and other avenues, which were constraining the line. In this framework, the direction of the rising of Vega was the proper reference for the surveying.

Figure 1 :

 1 Figure 1: The Avenue of the Sphinxes in a satellite image of Google Earth.

Figure 2 :

 2 Figure 2: The Ramses II Temple in Google Earth.

  , we see Vega, the direction of the rising of the star is that of the Avenue; therefore, we can imagine in the Figure the Karnak temple below the star. Using Stellarium, we can see that also Arcturus and the Cassiopeia constellation (Figure 4) are rising in the range from 40° to 50° degrees.

Figure 3 :

 3 Figure 3: Rising of Vega, simulated 1290 BC, Luxor. If we simulate for a year during the reign of Amenhotep the Magnificent, we cannot see any appreciable difference. The blue line represents the astronomical horizon.

Figure 4 :

 4 Figure 4: Rising of the Cassiopeia constellation, 1290 BC, Luxor.

Figure 5 :

 5 Figure 5: Setting of the Crux, 1290 BC, Luxor.

Figure 6 :

 6 Figure 6: The geometry of the square.

Information about this Article

Published on Sunday 4th February, 2018 at 17:10:13.

The full citation for this Article is:

Sparavigna, A. C. (2018). On the orientation of the Avenue of Sphinxes in Luxor. PHILICA Article number 1236.