Nucleation in undercooled melts of pure zirconium and zirconium based alloys

131 Pages·2010·12.84 MB·English

by  Klein, Stefan

Nucleation in undercooled melts
of pure zirconium and zirconium
based alloys
DISSERTATION
zur
Erlangung des Grades
”Doktors der Naturwissenschaften”
an der Fakulta¨t fu¨r Physik und Astronomie
der Ruhr-Universita¨t Bochum
von
Stefan Klein
aus
Ko¨ln
Bochum 2010
1. Gutachter: Prof. Dr. Dieter M. Herlach
2. Gutachter: Prof. Dr. Ulrich Ko¨hler
Tag der mu¨ndlichen Pru¨fung: 19. November 2010
Contents
1. Introduction 1
2. Undercooled liquids 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. Experimental methods 47
3.1. Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2. Electromagnetic levitation - EML . . . . . . . . . . . . . . . . . . . 48
3.3. Electrostatic levitation - ESL . . . . . . . . . . . . . . . . . . . . . . 52
3.4. EML versus ESL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
i
3.5. 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2
4.3. Zr Pd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2
5. Results 73
5.1. Undercooling experiments on zirconium . . . . . . . . . . . . . . . 73
5.2. Statisticalinvestigationsofthenucleationinundercooled zirconium
melts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3. Results for Zr Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2
5.4. Results for Zr Pd . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2
5.4.1. Short-range order of Zr Pd . . . . . . . . . . . . . . . . . . 89
2
5.4.2. Simulation of the structure factor . . . . . . . . . . . . . . . 90
6. Conclusion 95
Appendix 99
A. Pre-exponential factor K . . . . . . . . . . . . . . . . . . . . . . . 99
V
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
Curriculum Vitæ 127
ii
1
CHAPTER
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 first attempt for a phenomenological description
of nucleation was made by Volmer & Weber [3] in 1926. However, nucleation is a
physical phenomenon studied for centuries butdetails are stillpoorly understood.
Foraphasetransitionfromliquidtosolidasthecrystallizationofaliquidmetalthe
formation of the new solid phase is initiated by thermally activated nucleation 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, nucleation is involved in many modern
production routinese.g. castingprocessesoftraditional andnewmaterialsforthe
1
Chapter 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
without a catalyzing foreign phase. Since metals that are subject of this studyare
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 heterogeneous
nucleation 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 and is used for the analysis of the nucleation of
deeply undercooled liquids in the present work. The model isbased of theframe-
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
metastable regime ofthe undercooled 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
2
1. 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 melts with compact local order and
isotropic bonding Frank hypothesized an polytetrahedral short-range order in the
liquid phase independent of the structure of the corresponding solid phase [7].
Frank’s hypothesis was later experimentally confirmed for several metallic melts
[8, 9, 10, 11]. As a result the solid-liquid interfacial energy should increase due
to the fivefold symmetry of polythetrahedral short-range order which needs to be
broken before a crystal with its translational symmetry can be formed and growth
further into the melt.
As shown by Holland-Moritz and co-workers zirconium shows a polytetrahedral
short-range order in the liquid state [8, 10]. This results in a higher activation
energy for the formation of a nucleus of a crystalline phase with its translational
symmetry and consequently large undercoolings should be achievable. The in-
vestigation of the nucleation undercooling of pure Zr was performed to obtain
information about the nucleation mechanism, the undercoolability and the solid-
liquid interfacial energy of the undercooled melt. The interaction of short-range
order of the liquid phase and the solid-liquid interfacial energy governed the nu-
cleation and is subject of recent experimental and theoretical works. Therefore,
as a second systema sample without polytetrahedral short-range order was cho-
sen. The zirconium based intermetallic Zr Ni alloy complies with that and meets
2
the conditions of the experimental methods. Again the results obtained by both
levitation techniques are compared. For a second zirconium based alloy, Zr Pd,
2
indications exist that polytetrahedral short-range order dominates the liquid state.
Duetomissinginformationoftheshort-rangeorderandtheirinfluencesonthenu-
cleation both the nucleation undercooling and the short-range order were inves-
tigated. To determine the short-range order in liquid Zr Pd a recently developed
2
electrostatic levitation device of the Washington University in St. Louis in com-
bination with synchrotron radiation of the Advanced Photon Source in Chicago
was used to perform X-ray scattering experiments on liquid Zr Pd. Additionally,
2
the short-range order was independently determined by scattering experiments
using an mobile electromagnetic levitation device from the German Aerospace
Center at the neutron source of the Institut Laue Langevin in Grenoble.
The results of the investigations of the maximum undercoolings off all three sys-
tem are compared in order to obtain information about the influence of the envi-
ronmental condition of the levitation devices on the nucleation. This information
3
Chapter 1. Introduction
may contribute to our understanding of the phase transition from liquid to solid.
4
2
CHAPTER
Undercooled liquids
Foralongtimeitiswell-knownthatliquidscanbecooleddownbelowtheirequilib-
rium melting temperature (a supercooled or undercooled liquid). In 1724 Fahren-
heit first recognized that liquid water can be maintained below its melting tem-
perature T = 273.16 K (32 F in units of Fahrenheit’s new temperature scale) for
L ◦
long periods without crystallizing into ice [2]. Fahrenheit was able to cool water
down to 264 K without solidification. The temperature difference ∆T = T −T be-
L
tween the liquids temperature T and the temperature of the undercooled liquid T
L
iscalledundercooling. Fahrenheitestablished thatadding icecrystalsorvibrating
the container, however, initializes the solidification of the undercooled water. This
was an early observation of a phenomenon called heterogeneous nucleation (cf.
subsection 2.3.3). Later on many experiments on the undercoolability of liquids
were performed.
At the beginning of the 20th century many publications reported the undercoola-
bility of metallic melts [12, 13, 14]. Based on the work of Volmer & Weber [3]
and Becker & Do¨ring [15], Turnbull & Fischer [16] developed a phenomenological
model of crystal nucleation in metallic melts. Turnbull applied the volume disper-
sion technique to investigate heterogeneous versus homogeneous (cf. subsec-
tion 2.3.1) nucleation. By subdividing a macroscopic melt into a large number
of small nano-sized droplets it was assumed that heterogeneous nucleation sites
which are distributed homogeneously over the entire volume are isolated in a
minority of the droplets while the majority of droplets should be free of heteroge-
neous nucleation sites. In fact, Turnbull found by experiments on a great variety
of metallic elements maximum undercoolings being in the order of 20% of the
liquidus temperature of the respective elements [17]. For a long time the limit of
5
Chapter 2. Undercooled liquids
the undercoolability was thought to be ∆T 0.2 T . The apparent universality
L
≈ ·
of these investigations led to the assumption that the physical limit of undercool-
ing as given by the onset of homogeneous nucleation is reached by the droplet
dispersion experiments. Moreover, Turnbull showed for mercury that nucleation
undercooling scales with the volume of the droplets and not with their surface
area supporting the assumption of homogeneous nucleation as a process occur-
ring stochastically inside the volume of the melt [18].
Turnbull and later Perepezko [19] used the volume dispersion technique to ex-
tend the relative undercoolings, ∆T = ∆T/T 0.2, up to one third of the melting
r L
≈
temperature in liquid mercury for example [18]. These findings were supported
byexperimentsperformed withcontainerless processingtechniquesdevelopedin
the middle of the 20th century [20]. These techniques allow a sample processing
without any influence of crucible walls on which heterogeneous nucleation typi-
cally sets in. With such techniques macroscopic melts were undercooled below
0.2 T [21]. The undercooled state is a non-equilibrium state of a system which,
L
·
within the statistical interpretation, can be considered as an ergodic system [22]
and therefore it can be described within the basic concepts of thermodynamics.
2.1. Thermodynamic description
The description of the equilibrium state of a system is based on macroscopic
thermodynamic variables. For a liquid-solid phase transition the pressure p, the
temperature T, and the particle number N are selected as thermodynamic vari-
ables. The corresponding thermodynamic potential to these variables is the free
enthalpy G(p,T,N) or Gibbs free energy and is given by the following equation:
G(p,T,N) = U−TS+pV. (2.1)
U denotes the internal energy and S the entropy of the system. With the enthalpy
H given by
H(S,N,p)= U+pV (2.2)
equation (2.1) can be rewritten in the following way
G(p,T,N) = H−TS. (2.3)
Changes in the state of the system can be described by this thermodynamic
potential.
In figure 2.1 the Gibbs free energies of a liquid and a solid phase are plotted
for constant pressure and constant particle number under the assumption that
both states may exist at all temperatures. The larger negative slope of G(T),
6