Nucleation in undercooled melts of pure zirconium and zirconium based alloys [Elektronische Ressource] / von Stefan Klein

Klein Sébastien, Stefan

Sujets

• Physik

Informations

• Publié par: ruhr-universitat_bochum
• Publié le: 01 janvier 2010
• Nombre de lectures: 15
• Langue: English
• Poids de l'ouvrage: 12 Mo

Extrait

Nucleation in undercooledmelts
of pure zirconium and zirconium
based alloys
DISSERTATION
zur
Erlangungdes Grades
”Doktorsder Naturwissenschaften”
¨an der Fakultatfur¨ Physikund Astronomie
¨der Ruhr-UniversitatBochum
von
Stefan Klein
aus
¨Koln
Bochum20101. Gutachter: Prof. Dr. Dieter M. Herlach
2.: Prof. Dr. Ulrich Kohler¨
Tag der mundlichen¨ Prufung:¨ 19. November 2010Contents
1. Introduction 1
2. Undercooledliquids 5
2.1. Thermodynamic description . . . . . . . . . . . . . . . . . . . . . . 6
2.2. Thermodynamics of binary systems . . . . . . . . . . . . . . . . . 9
2.3. Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1. Homogeneous nucleation . . . . . . . . . . . . . . . . . . . 12
2.3.2. Nucleation rate . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3. Heterogeneous nucleation . . . . . . . . . . . . . . . . . . . 18
2.3.4. Nucleation of alloys . . . . . . . . . . . . . . . . . . . . . . 20
2.3.5. Limits of the classical nucleation theory . . . . . . . . . . . 23
2.4. Solid-liquid interfacial energy . . . . . . . . . . . . . . . . . . . . . 24
2.4.1. The negentropic model by Spaepen . . . . . . . . . . . . . 25
2.4.2. Modeling of the solid liquid interfacial energy . . . . . . . . 28
2.5. Structural ordering in undercooled liquids . . . . . . . . . . . . . . 31
2.5.1. Short-range order in undercooled liquids . . . . . . . . . . . 31
2.6. Skripov model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.7. Scattering theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.7.1. Structure factor . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.7.2. X-ray and neutron scattering . . . . . . . . . . . . . . . . . 41
2.7.3. Scattering investigations at liquids . . . . . . . . . . . . . . 42
3. Experimentalmethods 47
3.1. Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2. Electromagnetic levitation - EML . . . . . . . . . . . . . . . . . . . 48
3.3. Electrostatic levitation - ESL . . . . . . . . . . . . . . . . . . . . . . 52
3.4. EML versus ESL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
i3.5. Temperature measurements . . . . . . . . . . . . . . . . . . . . . . 58
3.6. Scanning electron microscope and energy-dispersive X-ray spec-
troscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.7. Scattering experiments . . . . . . . . . . . . . . . . . . . . . . . . 62
4. Investigated samples 67
4.1. Zirconium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2. Zr Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692
4.3. Zr Pd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712
5. Results 73
5.1. Undercooling experiments on zirconium . . . . . . . . . . . . . . . 73
5.2. Statisticalinvestigationsofthenucleationinundercooledzirconium
melts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3. Results for Zr Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822
5.4. for Zr Pd . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852
5.4.1. Short-range order of Zr Pd . . . . . . . . . . . . . . . . . . 892
5.4.2. Simulation of the structure factor . . . . . . . . . . . . . . . 90
6. Conclusion 95
Appendix 99
A. Pre-exponential factorK ....................... 99V
B. Vapor pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
C. Phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
D. Nucleation undercooling results . . . . . . . . . . . . . . . . . . . . 104
E. Evaluation of the X-ray diffraction measurements . . . . . . . . . . 106
Bibliography 113
Acknowledgments 125
CurriculumVitæ 127
iiCHAPTER1
Introduction
Nucleation initiates the formation of a new phase within the environment of the
parent phase. It is a phenomenon in nature and technology which is involved
in a large variety of phase transformations [1]. Typical examples of phases that
are formed by nucleation are bubbles that appear in a liquid that starts to boil,
droplets that are formed in a condensing vapor, and crystals that are formed by
solidification of a molten metal. At the beginning of the 18th century Fahrenheit
performed first experiments to investigate the undercoolability of pure water [2].
Approximately 200 year later the firstattempt for a phenomenological description
of nucleation was made by Volmer & Weber [3] in 1926. However, nucleation is a
physicalphenomenon studied forcenturies butdetails arestillpoorly understood.
Foraphasetransitionfromliquidtosolidasthecrystallizationofaliquidmetalthe
formation ofthenewsolid phase isinitiated bythermally activatednucleation and
completed by subsequent crystal growth. This transition shows a discontinuous
change in density, which is the first derivative of the free energy with respect to
chemical potential and can be classified as a phase transition of first order.
The properties of the as solidified material depend on the condition of solidifica-
tion. The resulting microstructure determines e.g mechanical, thermal and elec-
trical properties of the material. Therefore, it is essential to have a profound
understanding of the physical processes involved in solidification as nucleation
and crystal growth. Within this work the nucleation in undercooled metallic melts
is investigated. In the field of applications, n is involved in many modern
productionroutinese.g. castingprocessesoftraditionalandnewmaterialsforthe
1Chapter 1. Introduction
needs of various technologies, which is why nucleation theory, experiments and
practice is an interdisciplinary topic.
The thermodynamics can describe the driving forces for nucleation and crys-
tallization, respectively. However the phenomenon of an undercooled melt can
not be explained without taking the nucleation process into account. Generally
two different nucleation mechanisms are distinguished; heterogeneous nucle-
ation and homogeneous nucleation. The first type is initiated by foreign sources,
for example at the interface between the melt and the crucible or by an oxide
layer on the surface of the liquid. If these nucleation sites are eliminated, it is
possible to deeply undercool the melt even at low cooling rates. In this case ho-
mogeneous nucleation might occur. The characteristic feature of homogeneous
nucleation is that the nucleation starts randomly and spontaneously in the liquid
withoutacatalyzing foreign phase. Since metalsthatare subjectofthisstudyare
non-transparent systems, nucleation can not be investigated directly. Neverthe-
less, a distinction between heterogeneous and homogeneous nucleation can be
realizedbyathoroughstatisticalanalysisofmultiplesolidificationeventsofdeeply
undercooled liquids. In order to achieve deep undercoolings the heterogeneous
nucleation sites need to be fairly reduced. In this work dominant
n sites due to crucible walls are circumvented. This is realized by using
containerless processing techniques like electromagnetic and electrostatic levi-
tation. These methods allow to deeply undercool the liquids under well defined
processing conditions under high purity environmental conditions. This ensures
a good repeatability of the performed nucleation experiments.
Nucleationisastochasticprocess. TheSkripovmodel[4]describesthestatistical
nature ofnucleation undercooling andisusedfortheanalysisofthenucleation of
deeply undercooled liquids inthepresentwork. The modelisbased oftheframe-
work of the classical nucleation theory which is a phenomenological theory reg-
ularly used to explain a broad range of nucleation processes [1]. One important
parameter in the classical nucleation theory is the solid-liquid interfacial energy.
It determines the activation barrier of nucleation and thereby the undercoolability
of a melt. Direct measurements of the interfacial energy are not possible in the
metastableregime oftheundercooled melt. Toevaluate thesolid-liquid interfacial
energy atomistic theories as e.g. molecular dynamic simulations are frequently
used [5]. The only method to experimentally determine the solid-liquid interfacial
energy is given by measurements of the maximum undercooling under the as-
sumption of the presence of homogeneous nucleation. This enables to compare
the results of theoretical models with the experimentally obtained results based
on the assumption of the validity of the classical nucleation theory.
As nucleation is sensitive to foreign phases the nucleation mechanism of un-
dercooled samples processed with the electromagnetic levitation under inert gas
atmosphere is compared to samples investigated with the electrostatic levitation
21. Introduction
under ultra high vacuum conditions. For simplicity a pure metal was chosen first.
The highly reactive transition metal zirconium meets the requirement of electro-
magnetic and electrostatic levitation and allows for a comparison of the two ex-
perimental techniques utilized in the present work.
The interfacial energy between liquid and solid acts as nucleation barrier and
shall depend on the similarity of short-range order in liquid and solid state. As
emphasized by the negentropic model by Spaepen [6] the interfacial energy is
mainly of entropic origin. For pure metallic m