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Guillaume Deffrennes
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Guillaume Deffrennes. Étude expérimentale et évaluation thermodynamique du système Al-C-Mg.
Matériaux. Université de Lyon, 2018. Français. �NNT : 2018LYSE1301�. �tel-02269304�
THESE de DOCTORAT DE L’UNIVERSITE DE LYON
opérée au sein de
l’Université Claude Bernard Lyon 1 au
Laboratoire des Multimatériaux et Interfaces
Ecole DoctoraleN°34 Matériaux
Spécialité de doctorat : Matériaux
Soutenue publiquement le 20/12/2018 par :
Guillaume Deffrennes
Étude expérimentale et
évaluation thermodynamique du système Al-C-Mg
Devant le jury composé de :
Annie Antoni-Zdziobek Maître de Conférences (SIMaP) Rapporteure Jean-Marc Joubert Directeur de recherche CNRS (ICMPE) Rapporteur
Caroline Antion Maître de Conférences (SYMME) Examinatrice Gabriel Ferro Directeur de recherche CNRS (LMI) Examinateur Michel Perez Professeur (MATEIS) Examinateur Olivier Dezellus Maître de Conférences (LMI) Directeur de thèse
Jérôme Andrieux Maître de Conférences (LMI) Co-directeur de thèse, invité Alexander Pisch Chargé de recherche CNRS (SIMaP) Invité
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Résumé ________________________________________________________________________________ i Remerciements ____________________________________________________________________ iii Table des matières ________________________________________________________________vii Liste des tables ____________________________________________________________________ xiii Liste des figures __________________________________________________________________ xvii Liste des sigles et des abréviations ___________________________________________ xxv
Chapitre I Contexte industriel et scientifique de l'étude _____________________ 1
I.1 Vers une démocratisation du magnésium et ses alliages? _______________________________ 1 ǤͳǤͳ±±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ ǤͳǤʹ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷ ǤͳǤʹǤͳ±°±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷ ǤͳǤʹǤʹ ±±̵±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴
ǤͳǤʹǤ͵± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻ ǤͳǤ͵̵±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳ ǤͳǤͶ±̵ ±̵ ̴̴̴̴̴̴̴ͳͶ
I.2 L'affinement des grains des alliages Mg-Al par inoculation de carbone ______________ 18 ǤʹǤͳ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͺ ǤʹǤʹ±± ± ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹʹ I.3 Les limites des bases de données thermodynamiques du système Al-C-Mg __________ 25
I.4 Les approches CALPHAD et ICME ____________________________________________________________ 28 ǤͶǤͳ±±̵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹͺ ǤͶǤʹ± à̵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴͵Ͳ ǤͶǤ͵ ̵ ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴͵ʹ I.5 Démarche de l'étude __________________________________________________________________________ 34
II.1 Les systèmes unaires ________________________________________________________________________ 35
II.2 Le binaire Al-Mg ______________________________________________________________________________ 37 ǤʹǤͳ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͵
ǤʹǤʹ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ Ͷͳ
II.3 Le binaire C-Mg _______________________________________________________________________________ 42 Ǥ͵Ǥͳ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ Ͷʹ Ǥ͵Ǥʹ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͶͶ
II.4 Le binaire Al-C ________________________________________________________________________________ 45 ǤͶǤͳ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ Ͷͷ ǤͶǤʹ±Ͷ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ Ͷ
ǤͶǤʹǤͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ Ͷ
ǤͶǤʹǤͳǤͳ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ Ͷ
ǤͶǤʹǤͳǤʹ ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷͲ ǤͶǤʹǤʹ ±ǡ ±
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷͶ ǤͶǤʹǤʹǤͳ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷͶ ǤͶǤʹǤʹǤʹ ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷ
ǤͶǤ͵±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷ
ǤͶǤ͵Ǥͳ± ǯ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷ
ǤͶǤ͵ǤͳǤͳ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷ
ǤͶǤ͵ǤͳǤʹ ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͷͻ ǤͶǤ͵Ǥʹ±± Ͷ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴
ǤͶǤ͵ǤʹǤͳ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴
ǤͶǤ͵ǤʹǤʹ ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͺ ǤͶǤͶ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳ
II.5 Le ternaire Al-C-Mg __________________________________________________________________________ 72 ǤͷǤͳ± ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹ ǤͷǤʹ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ Ͷ II.6 Notes de synthèse ____________________________________________________________________________ 75
III.1 Avant-propos _________________________________________________________________________________ 79
III.2 Considérations préliminaires ______________________________________________________________ 82 ǤʹǤͳ ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺʹ ǤʹǤʹ ± ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺͷ ǤʹǤʹǤͳ±̵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺͷ ǤʹǤʹǤʹ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺ
ǤʹǤ͵ °ǦǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻͷ III.3 Tentatives de synthèses en creuset graphite et tube en fer ___________________________ 96
III.4 Développement d'un montage en creusets scellés en Ta et W ________________________ 99 ǤͶǤͳ ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻͻ ǤͶǤʹ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͲͳ ǤͶǤ͵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͲ
ǤͶǤ͵Ǥͳ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͲ
ǤͶǤ͵Ǥʹ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͲͻ ǤͶǤͶ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͳͳ ǤͶǤͷ±± ±± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͳ͵
ǤͶǤ ǯ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͳ
III.5 Extraction de Al2MgC2 par évaporation de la matrice ________________________________ 118 ǤͷǤͳ ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͳͺ ǤͷǤʹ± ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹͲ
III.6 Détails expérimentaux ____________________________________________________________________ 123 ǤǤͳ°°̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹ͵
ǤǤͳǤͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹ͵
ǤǤͳǤʹ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹͷ ǤǤʹ±± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹ
ǤǤ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹ
ǤǤ͵Ǥͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹ
ǤǤ͵Ǥʹ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳʹͻ
ǤǤʹ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵͵
ǤǤ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵Ͷ ǤǤͶ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵ͷ ǤǤͷ ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵
Chapitre IV Méthodologie computationnelle _______________________________ 139
IV.1 Modélisation thermodynamique _________________________________________________________ 139 ǤͳǤͳ±̵±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵ͻ ǤͳǤͳǤͳ±±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵ͻ ǤͳǤͳǤʹ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͶͳ ǤͳǤͳǤ͵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͶͶ ǤͳǤͳǤ͵Ǥͳ ̶ ̶̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͶͶ ǤͳǤͳǤ͵Ǥʹ ̵±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͶ
ǤͳǤͳǤ͵Ǥ͵ ̵ ±ȋǡȌȋǡȌ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷʹ ǤͳǤʹ± ±±°ǡ
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷͶ
IV.2 Calculs DFT __________________________________________________________________________________ 157 ǤʹǤͳ±² ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷ
ǤʹǤʹ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷͻ ǤʹǤ͵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͶ ǤʹǤͶ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͺ
Chapitre V Résultats et discussion ____________________________________________ 171
V.1 Le système binaire Al-C _____________________________________________________________________ 171 ǤͳǤͳ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳ ǤͳǤͳǤͳ±Ͷ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳ ǤͳǤͳǤͳǤͳ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳ ǤͳǤͳǤͳǤʹ±̵±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹ ǤͳǤͳǤͳǤ͵ ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵
ǤͳǤͳǤͳǤͶ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷ ǤͳǤͳǤʹ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ
ǤͳǤͳǤʹǤͳ±± Ͷ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ
ǤͳǤʹǤʹ± ±±°ǡ
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͺʹ ǤͳǤʹǤ͵±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͺͺ
ǤͳǤʹǤ͵Ǥͳ ± ±Ͷ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͺͺ ǤͳǤʹǤ͵ǤʹͶ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͻͲ ǤͳǤʹǤ͵Ǥ͵Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͻʹ ǤͳǤʹǤ͵ǤͶ°̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͻͷ
V.2 Le système ternaire Al-C-Mg ______________________________________________________________ 198 ǤʹǤͳ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͻͺ ǤʹǤͳǤͳ±ʹǦʹʹ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͻͺ ǤʹǤͳǤͳǤͳ°̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ͳͻͺ ǤʹǤͳǤͳǤʹ ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹͲͳ ǤʹǤͳǤͳǤ͵ ± ̴̴̴̴̴ ʹͲ͵
ǤʹǤͳǤͳǤͶ±̵±̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹͲͺ ǤʹǤͳǤͳǤͷ ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹͲͻ ǤʹǤͳǤͳǤ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹͳͳ ǤʹǤͳǤʹ±ͳǦʹʹ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹͳʹ ǤʹǤͳǤ͵±ǦͶ͵̴̴̴̴̴̴̴̴̴ ʹͳ͵
ǤʹǤͳǤ͵ǤͳǦ̴̴̴̴̴̴̴̴̴̴̴̴ ʹͳ͵
ǤʹǤͳǤͶ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹͳͶ ǤʹǤͳǤͶǤͳ±± ʹʹ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹͳͶ ǤʹǤͳǤͶǤʹ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹʹͲ ǤʹǤʹ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹʹʹ ǤʹǤʹǤͳ°Ǧ°̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹʹʹ ǤʹǤʹǤʹ2°± ±ǡ
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹʹͶ ǤʹǤʹǤ͵±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹʹͺ ǤʹǤʹǤ͵Ǥͳ ±ʹʹ̴̴̴̴̴̴̴ ʹʹͺ ǤʹǤʹǤ͵ǤʹʹʹǦʹʹ͵ʹʹͻ ǤʹǤʹǤ͵Ǥ͵±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹ͵Ͳ ǤʹǤʹǤ͵ǤͶ°̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ ʹ͵ͷ
VI.1 Conclusions __________________________________________________________________________________ 237 VI.2 Perspectives _________________________________________________________________________________ 242
Bibliographie _____________________________________________________________________ 247 Annexe A – Plan du dispositif de scellement des creusets ________________ 281 Annexe B – Plans du dispositif de scellement d'ampoules ________________ 283
ǤͳȂ±± ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ
ǤʹȂ±±±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹ
Ǥ͵Ȃ±±± ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴͵
ǤͶȂð± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷ
Ǥͷ Ȃ ± ±
ǯ± °̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹ
Ǥ Ȃ ± ± ±
̵Ǧ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͻ
ǤȂ ±̴̴̴̴̴ʹʹ
ǤͺȂ2 ±±
°ǦǦ ±±̴̴̴̴̴̴̴̴̴̴̴̴̴ʹ͵
ǤͳȂ± ±±
°Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴͵ͻ
Ǥʹ Ȃ Ͷ͵ ±
±±± ±±°Ǧ̴̴̴̴̴̴̴̴̴̴̴̴Ͷͻ
Ǥ͵ Ȃ ±ǡ ǡ ° ± ±
± ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͳ
ǤͶȂ±±±ǡ±
±± ± ±
± ̵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͳ
Ǥͷ Ȃ 2 ̵ ±ǡ
±ǡ ± ± ±
± ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ
ǤȂ±± Ͷ͵± ±
±±± °Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴
ǤͳȂ ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹ͵
ǤʹȂ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹͷ
Ǥ͵Ȃ ±± Ǥ
̵±± ±±Ǥ̴̴̴̴̴ͳ͵ͳ
ǤͳȂ°̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷ
ǤʹȂ± ̴̴̴ͳ
ǤͳȂ°Ͷ͵ȋ̵ Ǧ͵Ȍ
±°± ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳ
Ǥʹ Ȃ Ͷ͵ ȋ ̵ Ǧ͵Ȍ
±°± ±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳ
Ǥ͵Ȃ2̵± ±Ͷ͵
ǡ ± ± ±
Ͷ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷ
ǤͶȂ ±̵Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͺͷ
Ǥͷ Ȃ î ± ͳ ±± ± ±
̵Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͺ
ǤȂͶ͵ ±
±°Ǧ ±±±ǡ
± ±± ±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͻͲ
ǤȂ°°Ǧ±Ϊ ΪȋȌΪʹΪǦͳΪ ͵ǤǦͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͻͷ
Ǥͺ Ȃ ± ±
± Ͳ Ȃ ͳͻ Ȃ ͳͳ Ψ ͳʹ͵
ȋͳͲͲͲιȌʹͶͲǤǡ ±±
±Ǥ ʹǦʹʹ ±± ±±
ǤͻȂ± ʹǦʹʹ
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹͲ͵
ǤͳͲ Ȃ ʹǦʹʹ
̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹͲͶ
ǤͳͳȂ %ι ʹǦʹʹ̴̴̴̴̴̴̴̴ʹͲͶ
ǤͳʹȂ ʹǦʹʹ±±
Ǧ ± ±
̵ ±̴̴̴̴̴̴̴ʹͲ
Ǥͳ͵Ȃ2̵± ±ʹǦʹʹ
ǡ ± ± ±
ʹʹ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹͳͳ
ǤͳͶ Ȃ 2 ̵±
ǦͶ͵ ±
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹͳ͵
Ǥͳͷ Ȃ ± ± ̵
ʹͶͲͳʹ͵ȋͳͲͲͲιȌ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹʹͳ
ǤͳȂ ± ±̵
ǦǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹʹ
ǤͳȂ°°Ǧ±
ΪΪȋȌΪʹΪǦͳΪ ͵ǤǦͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹ͵ͷ
ǤͳȂ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͷ Ǥʹ Ȃ ̵ ±° ± ±± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͲ Ǥ͵ Ȃ ̵± ± ²
ͳͲͲ͵ȋ͵ͲιȌȋȌ±±±
ͷͲρȋȌǦͲǤͷΨǤ±
ͷͲρ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷ ǤͶȂ ±ǦͻʹͲͻ͵ͲȋͶ
ȂͷιȌ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ
ǤͷȂ ̵Ǧ͵ΨȋȌȋȌ°
ͲǤʹΨ ͳͲ͵͵ȋͲιȌͳͲ̴̴̴̴̴̴̴̴̴̴̴̴ͳ
ǤȂǦǦ±±±
ͳͲͲͲ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹ
ǤȂǦǦ ±ͳͲͲͲ̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹ
ǤͳȂǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴͵
ǤʹȂǦ ±ͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷ͵
Ǥ͵ȂǦ ±ͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷ͵
ǤͶȂǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷ
ǤͷȂ±̵± ̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷ
Ǥ Ȃ Ͷ͵ ±
±±± ±±°Ǧ̴̴̴̴̴̴̴̴̴̴̴̴Ͷͺ ǤȂ± ̵±Ͷ͵αͶȋȌΪ͵
± ±±± ±±°Ǧ
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴Ͷͺ ǤͺȂ ±Ͷ͵± ±±
± ±±°Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͷͷ
ǤͳͲȂͳͲͲǦ͵ͲͲͲ± ±
±±± °Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͷͺ ǤͳͳȂͳʹͲͲǦͳ͵ͲͲ± ±
±±± °Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͷͺ ǤͳʹȂǦǦ±±±
ͳͲͲͲȋʹιȌ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ʹ Ǥͳ Ȃ Ͳ Ȃ ͳͻ Ȃ ͳͳ Ψ ±±
±±ͳͲͲͲȋʹιȌǤ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺͲ ǤʹȂ̵ ͲȂͳͻȂͳͳΨ
± ±±± ͳǤͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺʹ Ǥ͵Ȃ±̵ ͺ͵
ǤͶ Ȃ ± ±
ǤǦ͵ ͲȂͳͻȂͳͳΨ ± ±
±± ͳǤͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺͶ ǤͷȂ± ±±̵± ±
̵ ͳǤͷ̵±°ͳͷ
ͳͲͲͲ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺͷ ǤȂ ±̵± ±
Ǧ±ͷͲ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺ
ǤȂ Ǧ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺͻ ǤͺȂǦ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͺͻ ǤͻȂǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻͳ ǤͳͲȂǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻͳ ǤͳͳȂǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻʹ ǤͳʹȂǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻ͵
ǤͳͶȂǦ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻͶ ǤͳͷȂ±±Ǥ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻ
Ǥͳ Ȃ ̵ ̵ ͳ °
ʹͳͲͲͲ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻͺ ǤͳȂ±±̵± ͲȂͳͻ
Ȃͳͳ ± ͲǤʹʹ ͵ ±
±±± ͳǤͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͻͻ ǤͳͺȂ ±ͲǤͲͷ̵
± ͲȂͳͻȂͳͳǤ̵± ±
±±± ͳǤͳ Ǥ
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͲʹ ǤͳͻȂ ±
± °±̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͲͶ ǤʹͲ Ȃ ± ±± Ǥ ȋȌ
± ǡ ȋȌ ͲǤʹͷ ̵±
± ǦǦ ±±ͺͳͷͻ͵ȋͳ͵ʹͲιȌǡ ȋ Ȍ ͲǤͷ̵± ± ǦǦ ±±
ͳͶͳͷʹȋͳͶͻιȌȋȌ ͳ̵±
± Ǧ ±±ͶͳʹͲͻͶȋͳͺʹͳιȌ̴̴̴̴̴̴ͳͲͷ ǤʹͳȂ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͲ
ǤʹʹȂ̵ ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͲ
Ǥʹ͵ Ȃ ± ±± ̵ ± Ͳ Ȃ ͳͻȂͳͳ ± ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳʹ ǤʹͶȂ̵ ± ͲȂͳͻȂͳͳΨ
°͵Ͳͳ͵ͷ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳͶ ǤʹͷȂ ̵± Ͳ ȂͳͻȂͳͳΨ°
͵Ͳͳ͵ͷ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳͶ
ǤʹȂ± ̵̴̴̴̴̴̴ͳͳ
ǤʹͺȂ ±±̵± Ǧͳͳͺ Ǥʹͻ Ȃ ± ̵± Ǧ
̵ ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͳͺ Ǥ͵Ͳ Ȃ ± ± ± ±
± ± ° ±
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹʹ Ǥ͵ͳȂ ±Ͷ͵ ±
±± ͲͲǦͲ͵ͷǦͲͻͻ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹͶ Ǥ͵ʹ Ȃ ̵ ± ± ° ͳʹ͵
ȋͳͲͲͲιȌ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹ
Ǥ͵͵Ȃ ʹͶͲ
ͳʹ͵ ±̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹ
Ǥ͵ͶȂ±
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ͵Ͳ ǤͳȂ± ̵±̵ɅȋǡȌͳͳǤ
±ʹͻͺ±±± ±Ǥ ±ǡ̵±
ǦͳͳǦʹǤǦͳ ǦͳͳǦͳͲǤǦ
ͳǤ°̵ ±ͲǡǣǦͳͲǤǦͳ±
±± ±Ǥ̴̴̴ͳͶͶ Ǥʹ Ȃ ± °
̵ ± ȋǡ Ȍ
ǡαͳͲǤǦͳ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͶͺ Ǥ͵Ȃ±±±±±
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷͲ
ǤȋȌ
²Ǥȋ Ȍ²
Ǥ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͷͷ ǤͷȂ Ͷ͵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͶ ǤȂ ʹǦʹʹȋ Ǥ ǤʹǤͳǤͳǤ͵Ȍ̴̴̴̴̴̴̴̴̴̴̴̴ͳͶ ǤͳȂ±̵± ±±±Ͷ͵
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳʹ ǤʹȂ ±Ͷ͵±±±
± ±±±̴̴̴̴̴̴̴̴̴ͳ͵
Ǥ͵ Ȃ Ͷ͵ ±
±±±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳ
ǤͶȂ±̵± ͳǤͻ͵Ͷ͵ͳ
ǤͷȂ ̵± Ͷ͵±±
±±̵̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͻ ǤȂ ̵± Ͷ͵±±
±± ° ̵ Ǥ ±
±ͳͲ͵ͲιʹɅ± ̵
±̵± ̵Ǥ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͻ ǤȂ ±Ͷ͵ ±±
° Ǧ ± ± ± ± ±
±ÚǤ̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͺͺ ǤͺȂ ±Ͷ͵ ±±
°Ǧ ±±±± ±±
̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͺͻ Ǥͻ Ȃ ̵± Ǧ Ͷ͵ ±
±°Ǧ ±±±± ±
±̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴̴ͳͻͳ