Undercooling and solidification of tetragonal Ni_1tn2B under different convective flow conditions [Elektronische Ressource] / von Sven Binder

Binder, Sven

Sujets

• Physik

Informations

• Publié par: ruhr-universitat_bochum
• Publié le: 01 janvier 2010
• Nombre de lectures: 21
• Langue: English
• Poids de l'ouvrage: 23 Mo

Extrait

Undercooling and solidi cation
of tetragonal Ni B under2
di erent convective ow conditions
DISSERTATION
zur
Erlangung des Grades
Doktor der Naturwissenschaften\
"
an der Fakultat fur Physik und Astronomie
der Ruhr{Universitat Bochum
von
Sven Binder
aus
Koln
Bochum 20101. Gutachter: Prof. Dr. Dieter M. Herlach
2. Gutachter: Prof. Dr. Kurt Westerholt
Datum der Disputation: 10.12.2010To CoraiiContents
1 Introduction 1
2 Thermodynamics of undercooled liquids 5
2.1 The driving force for solidication . . . . . . . . . . . . . . . . . . 6
2.1.1 Binary alloys . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Homogeneous nucleation . . . . . . . . . . . . . . . . . . . 9
2.2.2 Heterogeneous nucleation . . . . . . . . . . . . . . . . . . . 14
2.2.3 Nucleation in alloys . . . . . . . . . . . . . . . . . . . . . . 16
2.3 The solid{liquid interfacial energy . . . . . . . . . . . . . . . . . . 16
3 Non{equilibrium solidi cation 21
3.1 Deviations from local equilibrium . . . . . . . . . . . . . . . . . . 21
3.1.1 The Gibbs{Thomson e ect . . . . . . . . . . . . . . . . . . 22
3.1.2 Attachment kinetics . . . . . . . . . . . . . . . . . . . . . 24
3.1.3 Solute trapping and disorder trapping . . . . . . . . . . . . 27
3.2 Morphology of the solid{liquid interface . . . . . . . . . . . . . . . 30
3.3 Dendrite growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 General considerations: the planar interface . . . . . . . . . . . . 32
3.4.1 Governing equations . . . . . . . . . . . . . . . . . . . . . 32
3.4.2 Stability of a planar solid{liquid interface . . . . . . . . . . 34
3.5 Solidication of a needle crystal . . . . . . . . . . . . . . . . . . . 37
3.6 Selection criteria for the dendrite tip radius . . . . . . . . . . . . 38
3.6.1 The marginal stability criterion . . . . . . . . . . . . . . . 38
3.6.2 Microscopic solvability theory . . . . . . . . . . . . . . . . 41
3.7 Mesoscopic modeling of dendrite growth . . . . . . . . . . . . . . 42
3.8 Inuence of convection on dendrite growth . . . . . . . . . . . . . 45
3.9 Fluid ow in external static magnetic elds . . . . . . . . . . . . . 50
iiiiv
4 Experimental methods 51
4.1 Electromagnetic levitation (1g EML) . . . . . . . . . . . . . . . . 51
4.2 EML in reduced gravity (g EML) . . . . . . . . . . . . . . . . . 57
4.3 Melt{ uxing experiments (MF) . . . . . . . . . . . . . . . . . . . 59
4.4 Melt{ uxing in a static magnetic eld . . . . . . . . . . . . . . . . 61
4.5 Electrostatic levitation (ESL) . . . . . . . . . . . . . . . . . . . . 62
4.6 Microstructure analysis . . . . . . . . . . . . . . . . . . . . . . . . 63
5 Sample system and sample preparation 65
5.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 A suitable sample system: Ni B . . . . . . . . . . . . . . . . . . . 672
5.3 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6 Experimental results and discussion 71
6.1 Morphology of the solidi