Chapter 10 Experiments in reduced gravity

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Chapter 10

Experiments in Reduced Gravity 10.1. 10.2.

Containerless Processing In Reduced Gravity Experiments in Drop Tubes 10.2.1 Nucleation Studies on Glass-Forming Systems 10.2.2 Kinetics of Phase Selection 10.2.3 Microstructure Development 10.2.4 Liquid–Liquid Phase Separation 10.3. Electromagnetic Processing in Reduced Gravity 10.3.1 Thermophysical Properties 10.3.1.1 Thermal Expansion 10.3.1.2 Electrical Resistivity 10.3.1.3 Specific Heat and Thermal Conductivity 10.3.1.4 Surface Tension and Viscosity 10.3.2 Nucleation Investigations and Phase Selection 10.3.3 Measurements of Dendrite Growth Velocities References

377 379 379 380 382 386 389 389 389 390 392 394 397 401 403

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Chapter 10

Experiments in Reduced Gravity 10.1. CONTAINERLESS PROCESSING IN REDUCED GRAVITY

So far, containerless processing of undercooled melts in reduced gravity has been conducted either by processing small droplets during free fall in drop tubes on Earth or by the application of electromagnetic positioning and processing in Space (TEMPUS) during parabolic flight campaigns and NASA spacelab missions (IML2-1994, MSL1-1997). Drop tube experiments on Earth are easily performed and were first developed by David Turnbull [10.1]. Such drop tube experiments are devoted to studies of nucleation in glass-forming metallic alloys and, more recently, in the formation of metastable crystalline solids from the state of undercooled melts. They have also demonstrated their potential in investigating crystallization processes of various microstructure and phases as a function of cooling rate. But these experiments are related to the conditions of containerless processing and undercooling rather than those of reduced gravity. Real experiments of containerless processing under the conditions of reduced gravity in Space became accessible by the development of the TEMPUS facility for its use in the Spacelab during Shuttle missions of NASA. The application of electromagnetic levitation on Earth has serious drawbacks. It requires relatively high power absorption to levitate the sample, which is accompanied by an equivalent large heating effect. Under vacuum conditions heat transfer takes place by radiation only. This will limit the applicability of electromagnetic levitation technique under vacuum conditions to undercooling experiments on refractory metals and high melting alloys. Additional convective cooling of gas makes the technique suitable for undercooling of transition metals such as Fe or Ni. Even thoroughly cleaned cooling gases are dirty compared with ultra-high-vacuum conditions and have shown to induce heterogeneous nucleation by metal oxide formation on the surface of the samples [10.2]. Levitation forces on a molten material inevitably introduce dynamic motion in the liquid. Its influence on the solidification process is largely unknown to date. At the same time, levitating forces lead to a deformation of the liquid drop, so any measurements relying on a particular sample shape becomes difficult in a gravity field. These limitations of the electromagnetic levitation technique for undercooling experiments are circumvented by using the special environment in Space, where the positioning forces to compensate disturbing accelerations are about three orders of magnitude smaller than that under terrestrial conditions. TEMPUS 377

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provides means of containerless processing in Space [10.3]. TEMPUS and its technical specifications are described in Section 10.2. So far, TEMPUS was used to perform experiments during Spacelab missions of NASA and during parabolic flight campaigns of ESA and DLR. Different classes of experiments were conducted. TEMPUS is a powerful instrument to measure thermophysical properties of melts both in the stable regime above the melting temperature and in the metastable regime of the undercooled liquid below the melting temperature. Thermophysical parameters of high reliability are a necessary precondition for quantitative modelling of solidification and casting processes. The experimental determination of any transport properties is essentially influenced by gravity-driven heat and mass transport on Earth. Therefore, the reduced gravity environment offers unique opportunities for high accuracy measurements of thermophysical properties. A second class of experiments concerns investigations of solidification of undercooled melts. Experiments by undercooling and measuring multistep recalescence profiles provide information on primary crystallization of metastable crystallographic phases. Measurements of the growth velocity as a function of undercooling are interesting with respect to the formation criteria for non-equilibrium microstructures. They also give insight into growth phenomena, where influences of convection and fluid flow play a role in e.g. dendritic/eutectic growth and its influence on pattern formation in microstructure development. The TEMPUS facility had its maiden flight on board of NASA’s Spacelab mission International Microgravity Laboratory IML-2 in 1994. The technical operation of the device with all subsystems worked nominally during the entire mission of 14 days. Important scientific results have been obtained. The element Zr was melted and undercooled several times. Melting of Zr requires a temperature of more than 2125 K; this means it was the highest temperature ever achieved in the Spacelab [10.4]. TEMPUS was reflown on board of NASA’s Spacelab-mission Materials Science Laboratory MSL-1 in 1997. Altogether 17 different experiments of 10 research groups were performed. Experimental results of relevance to the present topic of metastable phases have been obtained. Studies of nucleation statistics in the microgravity environment were conducted on Zr and analysed using nucleation theory [10.5]. For the first time dendrite growth velocities on metallic systems have been measured in Space [10.6]. An advanced facility is under consideration to be accommodated on board of the International Space Station (ISS). An international community of scientists is presently preparing experiments to be performed onboard ISS using the multiuser facility materials science laboratory – electro-magnetic levitator (MSL-EML).

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10.2. EXPERIMENTS IN DROP TUBES

10.2.1 Nucleation studies on glass-forming systems Drop tubes are frequently used to study glass formation in metallic alloys and phase transformation during solidification of undercooled melts. Fully glass spheres, in diameter ranging up to 1.5 mm of Pd77.5Cu6Si16.5 alloys were produced during free fall of liquid droplets in the 105-m drop tube at NASA Marshall Space Flight Center [10.7]. Drehmann and Turnbull [10.1] studied nucleation phenomena by drop tube processing of the glass formers Pd82Si18 and Pd83Si17. They found that individual droplets were either fully amorphous or fully crystalline. As illustrated in Figure 10.1, the variation with diameter of the fraction of amorphous droplets indicated a crystal nucleation probability scaling with droplet surface area rather than with droplet volume. This finding suggests that surface heterogeneous nucleation is the dominant process in the early stage of crystallization of Pd᎐Si alloys as it is further supported by the observation that careful drying of the environmental He gas in the drop tube decreased the nucleation probability. Similar experiments were performed on metallic glass-forming alloys of Au55Pb22.5Sb22.5 [10.8], Pd40Ni40P20 [10.9], Pd77.5Cu6Si16.5 [10.10, 10.11], Ni58.5Nb41.5 [10.12], Cu62Zr38 and Cu56Zr44 [10.13] and Fe40Ni40P14B6 [10.14]. The type of curve shown in Figure 10.1 are useful in revealing influences on nucleation. As shown by such investigations, melt superheat prior to undercooling and solidification is an important variable. For Cu᎐Zr alloys it was found that the glass-forming ability in drop tube processing significantly increased with the 1.0 Glassy Fraction X

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X = exp [-(d/do)3] heterogeneous volume nucleation

0.8 Pd82Si18

0.6

X = exp [-(d/do)4.6] homogeneous nucleation

X = exp [-(d/do)2] heterogeneous surface nucleation

0.4

0.2 do = 190 µm 0.0

0

50

100

150

200

250

300

350

d [µm]

Figure 10.1. Glass fraction X of Pd82Si18 as function of droplet size d, for drop tube processing. The fitting to the experimental data (closed dots) implies heterogeneous surface nucleation [10.1].

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effect saturating for superheats of ⬎200 K. The improvement of glass-forming ability by drop tube processing of Cu᎐Zr alloys was evidenced by a critical cooling rate to avoid crystallization, being about two orders of magnitude smaller compared with critical cooling rates for glass solidification estimated from splat cooling experiments [10.15]. It is not yet clear whether the observed improvement of glass forming ability can be exclusively attributed to reduction of heterogeneous nucleation by containerless processing or could originated partly by reduction of heat and mass transport because of the lack of convection. The latter effect would lead to a more sluggish crystallization kinetics, which in turn will favour the avoiding crystal nucleation and reduction of growth of the crystals. 10.2.2 Kinetics of phase selection Drop tube experiments are also useful in measuring the phase selection during solidification of undercooled droplets as a function of their size. Because the droplet size scales directly with the cooling rate with which the droplets are cooled during free fall in an environmental gas, the temperature–time–transformation (TTT) behaviour is studied by investigating the solidified structures of droplets of various size classes. As an example, Figure 10.2 shows the volume fractions of the various phases formed in drop-tube-processed Al88Mn12 alloy as a function of droplet diameter [10.16]. Quasicrystalline phases of fivefold symmetry were discovered as a new class of solid-state matter in between crystalline and amorphous solids in melt-spun ribbons of Al88Mn12 alloy [10.17]. Depending on the preparation conditions, an icosahedral

10 5

1

T (K/s) 10 3

10 4

Equilibrium

Al88Mn12

I-Phase Volume fraction

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T-Phase

Al6Mn Al6Mn Alss

4 at% Mn 0

101

102

2.5 at% Mn

Al

103 d (µm)

Figure 10.2. Phase mixture in droplets of Al88Mn12 alloy as a function of droplet diameter. The large droplets crystallize a mixture of equilibrium Al6Mn phase and supersaturated solid solution Alss, while with decreasing droplet size (increasing cooling rate) quasicrystalline T- and I-phase are formed progressively [10.16].

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I-phase with quasiperiodicity in three dimensions, a decagonal T-phase with quasiperiodicity in two dimensions and periodicity in the third dimension and different crystalline phases are solidified in this alloy. The drop tube experiments reveal that the I-phase is formed far from equilibrium in the smallest droplets and at highest cooling rate. At medium droplet size, T-phase and supersaturated Alss-phase is found. The mass fraction of Alss-phase increases with droplet size (decreasing cooling rate) at the expense of T-phase. At largest droplet size of drops, of the order of 1 mm in diameter, also the equilibrium intermetallic phase Al6Mn is crystallized. Nucleation–kinetics plots reproduce the experimentally observed phase selection behaviour of drop-tube-processed Al88Mn12 alloy [10.18]. Drop tube experiments are also used to determine the formation of different phases selected kinetically by the cooling rate. TTT curves are constructed such that they show the kinetics of phase formation of the various phases individually involved in solidification of undercooled melts in multicomponent multiphase alloys. To do so the well-known Avrami analysis [10.19] is utilized that describes the time t necessary to produce a mass fraction X =10⫺3, which is hardly detectable by experimental diagnostics (X-ray diffraction, optical and electronic microscopy) of the equivalent phases formed at a certain undercooling. It is given by X = I ss v 3t 4 ,

(10.1)

where Iss is the steady-state nucleation rate (cf. Chapter 5) and V the crystal growth rate. The crystal growth in quasicrystal-forming alloys is extremely sluggish because it requires short-range diffusion of the various atomic species to arrange them correctly at the solid–liquid interface to form the complex structure of quasicrystalline phases [10.20]; the advancement of the solidification front into the undercooled melt is essentially driven by a kinetic undercooling of the interface. Under such circumstances the speed of the solidification front is estimated by the rate theory (cf. Chapter 6) leading to V=


GLS   D 1 − exp  . ao   k BT  

(10.2)

The TTT curves suggest an undercooling range of 150–200 K in drop tube processing. They predict a sequence of phase formation with the cooling rate as experiment parameter. At small cooling rates Al6Mn intermetallic and crystalline Al preferably solidify. At cooling rates exceeding 1000 K/s, the intermetallic Al6Mn phase disappears, while the quasicrystalline T-phase progressively forms. Further increasing the cooling rate to 1⫻104 K/s leads to solidification of the

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Metastable Solids from Undercooled Melts AI88 Mn12 : 1200

T - T - T Diagram

(x = 10-3)

TL (AI6 Mn)

1150 TL (T-phase) TL (I-phase)

1100 1050 Temperature (K)

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1000

2x105 K/s

950 T (AI)

900

1 K /s

5x103 K/s

2x106 K/s

850

200K/s

800 750 AI I-phase

700 650 600

-6

10

-4

10

-2

10 10 Time (S)

0

T-phase AI6Mn

10

2

10

4

Figure 10.3. Temperature–time transformation diagrams of the various phases involved in the solidification of undercooled droplets of Al88Mn12 assuming a fixed volume fraction of X = 10⫺3 [10.16]. Critical cooling rates are also shown for the avoidance of crystallization of various phases. The solid triangle corresponds to the maximum undercoolability of the Al-phase in Al᎐Mn alloys as investigated by the droplet-dispersion technique [10.66].

quasicrystalline I-phase. To avoid the nucleation of quasicrystalline phases, and in particular the crystalline Al-phase, very large cooling rates greater than 106 K/s are needed. This is in accordance with the observation that quasicrystalline phases nucleate quite easily in undercooled melts (cf. Chapter 5) and the formation of amorphous phases in quasicrystal-forming alloys during rapid cooling of a liquid is very difficult. Figure 10.3 summarizes the TTT diagrams for the various phases formed from the undercooled melt of Al88Mn12 alloy taking into account the experimental results of the drop tube experiments [10.16]. 10.2.3 Microstructure development Another example to note the importance of drop tube experiments in phase selection of undercooled droplets can be seen in Nd᎐Fe᎐B alloys. The intermetallic compound Nd2Fe14B1 or -phase reveals extraordinary hard magnetic properties, which make Nd᎐Fe᎐B alloys suitable for materials as permanent magnets [10.21, 10.22]. Under equilibrium conditions -phase is formed via a

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peritectic reaction from pro-peritectic
-Fe. Incomplete peritectic transformation leads to a high amount of soft-magnetic -Fe that reduces the quality of the magnetic Nd᎐Fe᎐B material. Undercooling may open up the possibility of primary solidification of -phase at the expense of
-Fe. In fact, it is accomplished by melt spinning of thin ribbons [10.22] and inert gas atomization of very small droplets [10.23]. Undercooling of bulk melts of Nd᎐Fe᎐B alloys suffers from the extreme reactivity of Nd with oxygen forming very stable Nd2O3 oxides on the surface of the samples, which act as heterogeneous nucleation sites. Even in electromagnetic levitation experiments, which are conducted under a purified inert gas atmosphere, undercooling of Nd᎐Fe᎐B is very limited and solidification starts with the crystallization of the pro-peritectic
-phase [10.24]. More recently, a method has been developed to dissolve Nd oxides by evaporation during electromagnetic levitation of bulk melts [10.25]. Using this method undercoolings up to 150 K are reached in levitation experiments, sufficiently high to observe three different solidification pathways [10.26]. The three metastable solidification paths are schematically depicted in Figure 10.4. Each solidification mode produces a characteristic microstructure. At small undercooling of
T = 16 K (left), dendrites of
-Fe are primarily formed, followed by peritectic formation of metastable -phase Nd2Fe17Bx (x  1) and -phase Nd2Fe14B. Nd2Fe17Bx decomposes at small undercoolings into
-Fe and -phase owing to small cooling rates (100 K/s). At medium undercoolings of
T = 60 K (middle) the hard magnetic -phase primarily solidifies from the melt and is the only solidification mode. At large undercoolings of
T = 110 K (right), metastable -phase primarily solidifies and subsequently decomposes into
-Fe and -phase. Due to the fact that the undercooling level achieved by drop tube processing should correlate to the droplet size in a statistical manner (it increases with reducing the droplet size), one can attribute the observed microstructure to the droplet size and can construct the phase selection map of an alloy of specific composition. Figure 10.5 shows the volume fractions of the various phases formed as a function of droplet size of Nd13Fe80.5B6.5 alloy. At large droplet size always a phase mixture of
-Fe and metastable Nd2Fe17By is observed. With decreasing droplet size (i.e. increasing undercooling) the volume fraction of
-Fe decreases and diminishes while hard magnetic -phase is progressively formed primarily from the undercooled melt at the expense of Nd2Fe17Bx (-phase). The physical mechanism underlying this process is that primary iron formation is suppressed due to its higher nucleation barrier and its more sluggish growth kinetics than the primary growth of Nd2F14B hard magnetic phase. In this way the peritectic reaction is circumvented. However, new metastable phases as the -phase also crystallize directly from the undercooled melt.

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Liquid

-Fe

Nd2Fe17Bx

Nd2Fe14B

Figure 10.4. Schematic summary of three different solidification pathways of hyperperitectic Nd13Fe80.5B6.5 alloy observed at three different undercoolings. Small undercooling
T  16 K (left): primary -Fe formation, subsequent peritectic formation of Nd2Fe17Bx (-phase) and Nd2Fe14B (-phase); medium undercooling
T  60 K (middle): primary Nd2Fe14B formation; large undercooling
T = 110 K (right): primary Nd2Fe17Bx formation, decomposition of Nd2Fe17Bx into
-Fe and (-phase) [10.27].

As far as the three crystalline phases are concerned, their growth kinetics are quite different. The iron phase has a very limited solubility of either Nd or B, i.e. a very small equilibrium partition coefficient. Therefore, its growth at undercoolings less than the critical undercooling for partitionless solidification requires much solute rejection. This will restrict its growth velocity to very small values (cf. Chapter 6). In contrast, Nd2Fe14B growth needs less solute rejection and, hence, can achieve a higher velocity. According to the criterion for phase selection at high growth velocities [10.27], it will be kinetically favoured if the nucleation is abundant. However, chemical order as present in the superlattice structures of intermetallic phases is also able to influence growth kinetics. An ordered intermetallic compound experiences a lower growth velocity than a disordered solid

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100

Droplet Fraction (%)

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80 60 40 20 0 2.0

1.6 1.2 1.0 0.80 0.63 0.34 0.25 0.10 Droplet Size (mm)

Figure 10.5. Primary phase selection map of Nd13Fe80.5B6.5 alloy, processed in a drop tube, droplet fraction as a function of droplet size, shadowed column =
-Fe, gridded column = Nd2Fe17By, (-phase) and blank column = Nd2Fe14B (-phase) [10.28].

solution. Considering the chemically highly ordered structure of the Nd2Fe14B compound, its primary growth is also constrained at high undercoolings. As a result, the growth of the metastable Nd2Fe17Bx (x1) phase with its disordered structure will replace the growth of the ordered compound Nd2Fe14B at large undercoolings, i.e. at small droplet size. The growth conditions control the evolution of different microstructures and their volume fractions. As shown in Figure 10.5 the droplet size in drop tube experiments is an efficient experiment parameter for the production of droplet charges of varying volume fractions of the respective phases. For an alloy of stoichiometric composition of the hard magnetic phase Nd2Fe14B (Nd13Fe80.5B6.5), a mixture of
-Fe and -phase is observed at large droplet size, while at medium droplet size
-Fe completely disappeared with an essentially enhanced volume fraction of -phase and, finally, metastable -phase grows at the expense of -phase at the smallest droplet size. There is another characteristic feature in drop tube experiments concerning microstructure evolution. As discussed in Section 8.6, undercooling plays an essential role in the formation of microstructures of different morphology and grain size. In particular, the formation of grain-refined equiaxed microstructures from the undercooled melt was deduced to the fragmentation of dendrites, which grow during recalescence of a rapidly solidifying undercooled melt. The fragmentation process in turn needs solute diffusion in the interdendritic liquid region during the post-recalescence period
tpl of solidification. Whether grain refinement occurs or not depends on the time duration of the post-recalescence period
tpl. While the rapid increase in temperature during recalescence depends exclusively

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on the internal heat and mass transport of a solidifying droplet,
tpl depends on the heat transfer from the drop to the environment. This is completely different in drop tube experiments compared with levitation experiments. Owing to the rapid heat transfer in particular at small droplet size in drop tube experiments, it can happen that the post-recalescence solidification period vanishes. This means that the primarily formed dendrites will not find an opportunity to fragment to form equiaxed grain-refined microstructures. In fact, it was observed that in semiconducting Ge even single crystals can be formed in drop-tube-processed samples at droplet size smaller than 300 m, while in levitation experiments with much smaller heat transfer conditions, i.e. smaller cooling rates, equiaxed grain-refined microstructures were observed in Ge drops at the largest undercoolings [10.28]. 10.2.4 Liquid–liquid phase separation Monotectics showing a miscibility gap in the liquid state have been subject to microgravity experiments for a long time. They attracted attention as model systems to study nucleation, growth and coagulation of a liquid phase L1 within the environment of a liquid L2 as the parent phase. Moreover, monotectics offer fascinating opportunities to produce fine dispersed materials for various applications [10.29]. A stable monotectic melt leads to liquid–liquid phase separation under thermodynamic equilibrium conditions at temperatures above the liquidus temperature. However, there are also metallic alloy systems showing miscibility gap in the metastable region of the undercooled melts. Such alloys offer the advantage that the driving force for crystallization of an undercooled melt is used to rapidly freeze in the instantaneous state of demixing at preselected temperatures and defined exposure times. Our particular interest is Co᎐Cu. This alloy combines a good electrical conductor (copper) with a strong ferromagnet (cobalt) of high Curie temperature. Recently, the phase diagram was reinvestigated with particular emphasis on the position of the binodal [10.30], it is shown in Figure 10.6. If the single phase melt is cooled and undercooled into the metastable miscibility gap to a temperature below the binodal liquid–liquid phase separation sets in. During liquid-phase separation the following processes have to be considered: ●

● ●

● ●

liquid–liquid decomposition L → L1 + L2 starting with nucleation of the minority phase in the environmental majority phase; growth of the nuclei either by diffusion or by convective diffusion; movement of the nucleated particles within the matrix liquid by Brownian, Stokes or Marangoni motion; particle motion due to fluid flow in the majority liquid; and rapid solidification of the undercooled melt.

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1800

L 1700

α - Co 1600 T [K]

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1500

L1 + L2 1400

TP

1300 0

20

40

60

80

100

at.% Cu

Figure 10.6. Phase diagram of Co᎐Cu with the metastable miscibility gap in the undercooled region: ♦, measured by DTA; ♦, concentration of the two separated phases from samples processed in an EML facility.

The individual contributions are of different importance for phase separation in containerlessly processed drops and droplets of Co᎐Cu alloy. In contrast to solidification of undercooled melts the nucleation of the minority liquid in the majority liquid is of homogeneous nature. Stokes sedimentation can be neglected for Co᎐Cu alloys since the mass density of both liquids L1(Co-rich) and L2 (Cu-rich) are comparable. Marangoni convection occurs if there are strong temperature gradients in the phase boundary. In small drops containerlessly processed the temperature gradients inside the drop are small. Consequently, Marangoni convection does not play a significant role. Therefore, only concurrent growth by collisions and diffusion has to be considered. For this situation, a simplified model has been developed [10.31]. As a result, the time dependence of the particle size is calculated as [10.32]  3 R(t ) =    4 

1/ 3

(2 DSsst)

1/ 2

2  exp  c n0 ( 2 DSss t )3 / 2 t 3 / 2 , 15 

(10.3)

where D is the diffusion coefficient, Sss the supersaturation, c a collision constant and n0 the initial number density of particles. Eq. 10.3 allows for the calculation of the particle size under isothermal conditions after a time t. This equation can be applied both to samples processed in a drop tube and in electromagnetic levitation. To apply Eq. (10.3) the collision constant and the processing time to solidification is estimated leading to the relation R ( d ) = ad exp(bd p +4 ),

(10.4)

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Figure 10.7. The average droplet radius of L2 drops of the minority phase in undercooled Co᎐Cu droplets as a function of diameter d of droplets processed containerlessly during free fall in a drop tube [10.35].

where d is the diameter of the sample and a and b are numerical constants. For drop-tube-processed samples the average diameter of particles of minority phase L2 is computed as a function of the droplet size, which determines the cooling conditions. The results are shown in Figure 10.7. In fact, size, morphology and particle distribution depend very much on the processing conditions. This is illustrated by the micrographs of Figure 10.8, which show microstructures of Co᎐Cu alloys of intermediate composition undercooled into the metastable immiscibility gap by different techniques and subsequently rapidly solidified from the state of a deeply undercooled melt. A bulk sample of Co–41 at.%Cu was undercooled by 261 K by applying the melt flux technique in a DSC apparatus [10.33]. According to Figure 10.8(left), a serious macrosegregation pattern is formed. The Co-rich phase (dark coloured) is completely coagulated into a large sphere, which occupies most of the volume of the sample. Except for one large and many small Cu-rich spherulites (light coloured) embedded in the Co-rich L1 phase, most of the Cu-rich L2 phase is distributed at the outer surface of the sample. The density of liquid Co is slightly higher than that of liquid Cu leading to the tendency that the Cu-rich liquid moves upwards driven by the buoyancy force. The surface tension of Cu is smaller than that of Co [10.34]. Therefore, Cu-rich liquid has the

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Figure 10.8. Microstructures of Co᎐Cu alloy of intermediate composition rapidly solidified upon undercooling into the metastable miscibility gap, applying melt fluxing technique in DSC experiments (left), electromagnetic levitation technique (middle) and drop tube technique (right).

tendency to encapsulate the Co-rich liquid. A sample of Co41.8Cu58.2 undercooled by 207 K prior to solidification using electromagnetic levitation leads to a completely different microstructure [10.35]. There is also macrosegregation but the Co-rich phase (dark coloured) is distorted due to the electromagnetic stirring of the melt inside the levitation coil. The coalescence of the separated phase is strongly developed with the reduction of the interface energy as its driving force. Some Co-rich spheres fuse together and lose their original shapes. Applying solidification under reduced gravity during the free fall of droplets inside a drop tube changes the morphology of the microstructure of Co41.8Cu58.2 drastically. As obvious from Figure 10.8(right) many small spheres of Co-rich phase are homogeneously distributed inside the volume of the droplet. In the middle of the droplet the diameter of the Co-rich spheres is approximately 1.5 m while it increases to 3 m when going to the outer regions of the droplet. Drop tube experiments offer the easiest way to solidification experiments under reduced gravity. They possess a large potential to perform investigations concerning in particular solidification statistics since a large number of droplets of different size groups are produced during each single shot of such an experiment. However, they suffer from the fact that solidification of individual droplets cannot be directly observed during the course of the experiment. This disadvantage will be overcome by making use of electromagnetic levitation in flight missions of reduced gravity. 10.3. ELECTROMAGNETIC PROCESSING IN REDUCED GRAVITY

10.3.1 Thermophysical properties 10.3.1.1 Thermal expansion. The electromagnetic levitation technique has been used on Earth to measure the mass density of liquid Ni [10.36] and liquid Cu [10.37]. The change in diameter of a levitated sphere as a function of temperature has been observed by an optical arrangement photographing the profile of the

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drop. This allowed the measurement of the mass density and the thermal expansion over an extended undercooling regime. An interesting result has been obtained by extrapolating the experimental data of the undercooled liquid to lower temperatures. This extrapolation suggests that at an undercooling of about 480 K the mass density of the undercooled melt reaches the mass density of the solid. Since metals mostly show a lower mass density in the liquid state, a constraint for maximum undercooling could exist at this undercooling. The accuracy of such measurements improves if the shape of the liquid drop approaches the ideal geometry of a sphere as it is favoured by the conditions of an almost force-free liquid under reduced gravity. In fact, measurements of the mass density and thermal expansion were performed on board of the Space shuttle during the NASA Spacelab mission MSL1 using the TEMPUS facility. The containerlessly processed sample was imaged by a high resolution CCD camera with on-board recording of the data. After the mission the on board recorded pictures were analysed with digital image processing giving the volume of the sample as a function of time and temperature [10.38]. Six glass-forming alloys were investigated [10.39]. From the measurements of the volume as a function of temperature the volumetric thermal expansion th =

1 ∂v v(T = 273 K) ∂T

(10.5)

was determined. Collects the results of the measurements of the volumetric thermal expansion of glass-forming metallic alloys performed during MSL1 Spacelab mission are shown in Table 10.1. 10.3.1.2 Electrical resistivity. Consider a sample of spherical shape placed within a rf levitation coil, which is integrated into a free oscillating circuit. The frequency of Table 10.1. Thermal expansion of liquid alloys of glass-forming metals. Alloy Zr57Cu15.4Ni12.6Nb5Al10 Zr65Cu17.5Al7.5Ni10 Zr11Cu47Ti34Ni8 Zr60Cu18Al10Ni9Co3 Pd78Cu6Si16 Pd82Si18

 th [10⫺5 K⫺1]

T range [K]

TL [K]

5.9⫾1.8 6.8⫾1.3 7.7⫾0.5 5.5⫾0.7 7.9⫾0.3 7.7⫾0.1

1073 1473 1003 1253 1108 1398 1108 1473 1193 1473 1253 1623

1092 1110 1115 1133 1033 1094

Note: The volume jump during solidification was measured to be less than 2%. The values measured under reduced gravity complement previous measurements on the same alloys at lower temperatures on Earth.

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the coil current will depend on the inductivity of the system consisting of coil and sample. The inductivity and, consequently, the frequency will change if the electrical resistivity of the sample increases with temperature. A method has been developed to use the alternating electromagnetic field of the heating coil of TEMPUS to measure the temperature change of the electrical resistivity el. The sample positioned inside the heating coil represents an additional, inductively coupled electric circuit (transformer) of resistance Rel. It increases the resistance Rec of the empty coil. At high angular frequencies , the ratio between radius r of the spherical sample inside a levitation coil and the skin depth sd(el,) is high, the electrical resistance Rel is given by [10.40]   1 1 Rel (el , ) = const × r 3  − 2 ,  q(el , ) q (el , ) 

(10.6)

where const is a constant, and describes the geometry of the coil and q = r/ sd(el,). Making use of the free oscillating heating circuit of TEMPUS and assuming in good approximation that all ohmic resistances are small compared to the inductive resistance, I C Rec + R el (el , ) ) = o cos( ) ( L Uo

(10.7)

holds. The current and voltage amplitude Io and Uo as well as the phase difference  between Uo and Io are measured during the experiment [10.41]. Hence, by measuring of Uo, Io,  and the frequency  and by knowing of the electric circuit constants C, L and Rec as well as the coupling constant and the sample radius r, it is possible to determine the sample resistivity Rel. As a particularly interesting example, Figure 10.9 shows the specific electrical resistivity of solid and liquid Co80Pd20 alloy. At temperatures T ⬎ 1350 K for the solid sample and T ⬎ 1370 K for the liquid sample, the resistivity data of the alloy follow a linear temperature dependence as is well known for metals at high temperatures. However, if the temperature falls below 1350 K the resistivity of liquid and solid samples increase with decreasing temperature. This behaviour reflects the onset of long-range magnetic ordering when the temperature approaches the ferromagnetic Curie temperature of solid Co80Pd20. In this temperature range, the data points should no longer be interpreted as resistivities, because the applied inductive measurement technique reacts also very sensitively on the magnetic state of the sample as represented by the magnetic permeability, which changes drastically when the magnetically disordered

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Figure 10.9. Electrical resistivity el of Co80Pd20 in the solid and liquid state, together with corresponding mean values and linear fits (solid lines) as a function of temperature T [10.44].

paramagnetic state changes to a long-range magnetically ordered state on approaching the Curie temperature. 10.3.1.3 Specific heat and thermal conductivity. Modulation calorimetry as non-contact ac-calorimetry for measurements of highly reactive or metastable metallic liquids was proposed [10.42] and developed as an experimental tool for the TEMPUS facility [10.43]. The heater power is sinusoidally modulated. The specific heat is obtained from the measurement of the temperature response of the sample. Variation of the modulation frequency, mf, and analysis of the transient response following a step function change in the heater power allows the evaluation of thermal transport inside the sample, such as an effective thermal conductivity and the total hemispherical emissivity [10.44]. The heating coil works under steady-state conditions, i.e. there is a constant power input P0. Steady state conditions with respect to the temperature of the sample are reached at a temperature T0, where the absorbed power is equal to the heat transferred to the environment, i.e. P0 = Q. Under UHV conditions, Q = A SBT0 (A is the surface area of the sample, the emissivity, SB Stefan–Boltzmann constant, and T0 the ambient temperature). Consider now a modulation of the power input by adding a time-varying power modulation to the drop inside the heating

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coil of the form P(t) = Pocos2(t/2). This will give rise to temperature oscillations of the sample of the form

(
T ) =

P 0 1 1 + 2 2 +  2 22 , 2 C P  1

(10.8)

where 1 2 are the external and the internal relaxation times, respectively. Under the condition  1 ⬎ 1 ⬎ 10 2 the relaxation times are given as

1 =

CP 4 A te  SBT03

(10.9)

and


2 =

CP  with k + kc

4 k =  tc  3 gR, 3

(10.10)

where CP is the heat capacity, k and kc are the conductive and convective heat transfer coefficients, respecitvelyy, g1 the geometrical factor,  the conductively heated volume fraction, R the radius and tc the thermal conductivity of the sample. 1 is determined experimentally from the temperature response to a step function change in heating power input and 2 is inferred from the measurement of the phase shift  by a variation of the modulation frequency, mf, according to −1

2   1   
( mf , 1 , 2 ) = 1 +  −  mf 2  .    mf 1    

(10.11)

A representative temperature–time profile of an ac-calorimetry experiment using the TEMPUS facility is illustrated in Figure 10.10a. On melting ac-calorimetry is applied both in the stable and in the metastable undercooled melt. The sample is cooled stepwise to temperature plateaus during which the power of the heating coil is modulated leading to the oscillating ripple on the plateaus. The amplitude of the temperature oscillations is evaluated by averaging over all modulation cycles and a Fourier transform of the modulated signal. The external relaxation time 1 is inferred from the transient temperature signal following a change in heating power input. As indicated in Figure 10.10b, the ac-calorimetry leads to high-quality measurements of the specific heat (triangles), and the external relaxation time (triangles) both above and below the liquidus temperature of the glass-forming alloy Zr60Al10Cu18Ni9Co3. The error is less than 4%. The temperature dependence of CP is described by a linear increase in the specific heat with increasing undercooling

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(a)

(b)

Figure 10.10. (a): Experimental temperature–time profile measured during ac-calorimetry on a liquid levitated Zr᎐Ni sample, power modulation and temperature response [10.46]; (b): Specific heat (circles) and external relaxation time (triangles) as determined by ac-calorimetry on Zr60Al10Cu18Ni9Co3 alloy [10.47].

with a lower T⫺1 component. The external relaxation time 1 scales with temperature according to 1 ⬀ T⫺1/2T⫺3, where T1/2 dependence was taken from the te ⬀ (elT)1/2 dependence of the total hemispherical emissivity in the free electron model [10.45]. 10.3.1.4 Surface tension and viscosity. In the previous section temperature oscillations of a levitated drop have been discussed. Consider now surface oscillations of a freely suspended liquid drop excited by a modulation of the positioning field. The frequency of the surface oscillations of a liquid drop is related to the surface tension by Rayleigh’s formula [10.46]. If the radius R of a spherical droplet undergoes oscillations of the form R = R0 (1 + A0 cos(t ) exp( −t ) ) ,

(10.12)

where A0 is the amplitude of the oscillation,  the angular frequency, and  the damping factor. The angular frequency l of mode l is correlated with the surface tension
via [10.47] l =

l (l − 1)(l − 2)
, 3 m

(10.13)

where m is the mass of the sample. Measuring the frequency of the surface oscillation modes allows the determination of the surface tension [10.48]. Fourier analysis of the frequency spectrum delivers the oscillation frequencies of mode l. The electromagnetic and gravitational fields lead to a splitting of the single peak into five peaks according to five oscillation modes represented by the “quantum

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number” l. Although an approximate correction has been worked out to take into account the external fields acting on the liquid sample [10.49], it is advantageous to perform such experiments under the condition of reduced gravity, where both fields are negligible. Usually, if deviations from the ideal spherical shape are present, the fundamental l = 2 mode is split into three sidebands. On the other hand, if the shape of the sample corresponds to an ideal sphere, the l modes are degenerated so that all five peaks of the spectrum coincide. This allows the determination of
from the frequency of the surface oscillation . In addition, the damping behaviour of the surface oscillations allows to determining the viscosity of the droplet according to an idea originally developed by Lord Kelvin [10.50]. He derived an expression for the damping factor : =

20 R0 , 3 m

(10.14)

where is the viscosity. This equation is only correct for spherical drops in the absence of external fields. Experiments under reduced gravity guarantee an almost force free liquid drop with a shape approaching that of an ideal sphere. They may be the only possibility to measure the viscosity by the oscillating drop technique. The oscillating drop technique was used in TEMPUS experiments during the NASA Spacelab missions IML2 (1994) and MSL1 (1997) to measure the surface tension and the viscosity for various pure metals and alloys [10.49, 10.51–10.53]. The raw data deliver a spectrum comprising surface and translational oscillations. A carefully designed filter to the Fourier spectra was designed to obtain a corrected time signal by removing the unwanted translational oscillations. An example of such a spectrum measured on pure liquid gold is shown in Figure 10.11. By fitting an exponential law to the envelope of the oscillations, a damping factor  = 0.74 s⫺1 is determined. Inserting this value into Eq. (10.14) and taking the numerical data of R0 = 4 mm and m = 5 g, the viscosity of pure gold at temperature 1133 K was calculated as = 46 mPa s. Results of measurements of the surface tension and the viscosity of Co80Pd20 alloy are depicted in Figure 10.12. This alloy has a liquidus temperature of TL = 1610 K and a solidus temperature TS = 1565 K, and therefore only a small temperature interval of 45 K in which liquid and solid phases coexist. Hence this alloy is easy to handle in electromagnetic levitation. During MSL1 mission, the sample could be undercooled by ⬎340 K. At such a large undercooling the hypercooling of the alloy was exceeded and the Curie temperature Tc = 1257 K of the liquid alloy was approached [10.55]. Figure 10.12 shows the surface tension (left) and the viscosity (right) as a function of temperature both above and below the liquidus temperatures, TL, of Co80Pd20 alloy.

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Figure 10.11. Damping of surface oscillations for molten gold at 1133 K [10.49].

Figure 10.12. Surface tension (left) and viscosity (right) as a function of temperature for a Co80Pd20 alloy measured by the oscillating drop technique during MSL1 Spacelab mission [10.55]. Measurements of a liquid sample were possible to large undercooling values of 340 K. Such undercoolings exceed the hypercooling limit and the temperature of the undercooled melt approaches the Curie temperature of the liquid alloy.

Using Eqs. (10.13) and (10.14) to convert frequencies and damping factors into surface tension and viscosity, the temperature dependence of both quantities are expressed as
Co᎐Pd = 1675–0.17 (T⫺16⫻10) (mN/m) Co᎐Pd = 0.15 exp (9.37⫻10⫺20/kBT) (mPa s)

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The Boltzmann constant kB is expressed in terms of J/K and temperature T in K. The viscosities measured range from 5 to 30 mPa s, covering nearly one order of magnitude. 10.3.2 Nucleation investigations and phase selection Nucleation is a stochastic process. Investigations of nucleation statistics open up the possibility to gain insight into the physical nature of nucleation. For each heterogeneous or homogeneous nucleation site there is a range of undercoolings associated with the operative nucleation mechanism. If a single mechanism is responsible for nucleation under a given set of experiments the distribution of undercoolings measured for many discrete events of nucleation should obey a Poisson statistics. Studies of nucleation statistics can be realized either by measuring the undercooling of an ensemble of small droplets as e.g. in experiments on droplet dispersions or by a sequence of undercooling experiments on a single sample (cf. Chapter 4). The advantage of the latter method is that the undercooling of the sample is directly measured after each undercooling cycle. Terrestrial experiments on zirconium as a function of initial sample purity have been conducted using an electrostatic levitator (ESL) [10.54]. Both electrostatic levitation and electromagnetic positioning under reduced gravity allow for containerless undercoolings experiments under the condition of ultra-high-vacuum environment. Studies of nucleation statistics on pure Zr were performed using the TEMPUS facility during MSL1 Spacelab mission [10.55]. Liquid zirconium is a metal with very high melting temperature (2128 K) and is suitable for such investigations because it is a good solvent and shows a high solubility for contaminations. Oxides, nitrides and carbides which can act as heterogeneous nucleation sites do not exist in the melt and do not form on the surface of molten zirconium. Figure 10.13 shows results of undercooling experiments under different conditions of electromagnetic processing in TEMPUS. During cooling the heater power is set to the lowest value, and the primary power input to the sample comes from the positioning field. One sample was repeatedly melted and cooled to solidification, keeping all experimental variables constant except for the positioner power settings on cooling. Different positioner power supply settings were used. At the low positioner power (31 V) the cooling rate was 50 K/s and at the high positioner power (71 V) it was 48 K/s. Fluid flow velocities were calculated for these different experiment conditions as 5 and 27 cm/s [10.56]. These experiments of undercooling statistics with about 50 cooling cycles each reveal that there is no significant change in the nucleation behaviour in the range of flow conditions. The results obtained from the Space experiments can be directly compared with those of the terrestrial investigations in the ESL, if the different values of the volume and the cooling rates of the samples are taken into consideration. The

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Figure 10.13. Two distributions from experiments on zirconium using TEMPUS on MSL1 Spacelab mission. To change electromagnetic stirring inside the molten Zr, the power of the positioning field is altered. The low positioner distribution is in the laminar flow regime with maximum flows of 5 cm/s, while the high positioner cause maximum flow rates of 27 cm/s [10.59].

nucleation rate Iss of the samples can be scaled denoting v1 and v2 and T
1 and T
2 as the volumes and cooling rates of the sample processed in TEMPUS and in ESL, respectively. It then holds that I ss v1 I ss v2 = . T
1 T
2

(10.15)

The cooling rate in the ESL experiments is 240 K/s compared to 48 K/s in the MSL1 experiments. The mass of the sample processed in the TEMPUS facility was 1.18 g, while that of the sample processed in ESL was 0.14 g. For equal Iss values and a known undercooling in the ESL case where the undercooling is measured as
T = 348 K, one can calculate the undercooling obtained by an identical mechanism for the larger sample at the smaller cooling rate by solving I ss (
T = 348) =

v2 v1

T
1 I ss (
T2 ) = 414 I ss (
T2 ). T
2

(10.16)

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Assuming the Turnbull nucleation rate (see Chapter 4), the pre-exponential terms are equal and insensitive to temperature so that the Eq. (10.16) can be reduced to
G1*
G2* = + ln( 414), k BT1 k BT2

(10.17)

where
G* is the activation energy to form clusters of critical size. If the solid–liquid interfacial energy is assumed to be constant over the temperature range, and the change in volume free energy is proportional to
T2, then the computation yields
T2 = 336 K. This value agrees within an uncertainty of a few Kelvins with the results of the measurements during the MSL1 mission. These experiments show that fluid flow with maximum velocities of 43 cm/s has apparently no effects on crystal nucleation in deeply undercooled melts of pure Zr. Nucleation is the first step of crystallization of an undercooled melt preselecting the crystallographic phase as stable or metastable. If a metastable phase is primarily nucleated solidification takes place in a two-step process. After the primary nucleation of the metastable phase this phase subsequently grows into the undercooled melt by a dendrite growth mode. After a delay time secondary nucleation of the stable can occur within the interdendritic liquid, which can lead either to a two phase mixture of solid and liquid or after remelting of the metastable phase to a solid consisting exclusively of the stable phase. The latter transformation is usually a slow process and can be at least partly avoided by rapid quenching the sample after the first recalescence event [10.56]. The mechanism for nucleation of the second phase and the delay time observed in this transformation appear to be dependent on solid movement and coalescence within the solid–liquid phase mixture probably the result of convective flow [10.57]. Phase selection in undercooled melts of Fe᎐Ni᎐Cr austenite steel alloys was investigated with a reduction of melt convection under reduced gravity making use of TEMPUS facility during MSL1 Spacelab mission [10.58]. Similar to the terrestrial experiments, double-recalescence events are observed in the temperature–time profiles during solidification of Fe᎐Nr᎐Cr austenite steels in the Space experiments. Examples are shown for two alloys Fe᎐12% Cr᎐16% Ni and Fe᎐16% Cr᎐12%Ni in Figure 10.14. In both cases a double recalescence is observed, indicating the primary crystallization of a metastable bcc phase (ferrit) of the austenite alloys before the stable fcc (austenite) phase is formed. Qualitatively, such a behaviour is similar throughout as in terrestrial experiments [10.61, 10.62]. However, both the critical undercoolings for the observation of doublerecalescence events and the delay time of nucleation of the second stable fcc

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Figure 10.14. Temperature–time profiles of recalescence measured on Fe᎐Ni᎐Cr alloys undercooled containerlessly in TEMPUS during MSL1 Spacelab mission: left: Fe᎐12% Cr᎐16%Ni, right: Fe᎐16% Cr᎐12%Ni [10.62].

Figure 10.15. Delay time measured during rapid solidification of Fe᎐Cr᎐Ni steel alloy under reduced gravity in Space (closed circles) and under terrestrial conditions (open boxes) with the T0bcc temperature of bcc phase [10.62].

phase after primarily formed metastable bcc phase depend apparently on the experiment conditions as shown in Figure 10.15. Significant deviations become obvious when the delay time of this transformation measured on ground is compared with that of the experimental results obtained by equivalent experiments performed during MSL1 mission in the TEMPUS facility. The delay time is enhanced if the gravitational driven mass and heat transport are essentially reduced in Space. This observation may support the

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hypothesis that convection could influence the formation of secondary nucleation sites of stable fcc phase in the interdendritic region of metastable bcc phase. But a detailed understanding of this mechanism is still lacking. Efforts to describe this phenomenon are in progress [10.59]. 10.3.3 Measurements of dendrite growth velocities The TEMPUS facility was also used to measure the dendrite growth velocity as a function of undercooling on pure nickel and dilute Ni᎐0.6 at.%C alloys during MSL1 Spacelab mission [10.60]. A metallic W-Re trigger needle coated at the Tipp with ZrO2 (to decrease the sticking tendency while touching the melt) was used for external stimulation of nucleation at selected undercoolings. The growth velocity was measured from recording the temperature–time profiles during recalescence in quite analogy to the measurements described in Chapter 2 for electromagnetic levitation on Earth. The results of investigations on pure Ni and dilute Ni99.4C0.6 are shown in Figure 10.16. For the dilute Ni᎐C alloy, g data on an extended undercooling range up to
T = 305 K have been obtained, whereas the g-data points on Ni are restricted to

Figure 10.16. Dendrite growth velocity V versus undercooling
T data on pure Ni (open symbols) and a dilute Ni᎐0.6 at.%C alloy (black symbols), obtained during the MSL1 Spacelab mission. Squares refer to triggered nucleation events with high accuracy of measurements, circles/dots to spontaneous nucleation events with reduced accuracy. An arrow marks the resolution limit of measurements of the pyrometer operating at a frequency of 100 Hz. Calculated curves according to the predictions of sharp interface model are plotted for Ni (dashed line) as well as for Ni᎐C (full line).

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the most interesting regime of small undercooling up to
T = 85 K. The growth velocity as a function of undercooling was calculated within sharp interface model of dendrite growth (cf. Chapter 4) for pure Ni (see dashed line in Figure 10.16) and for the dilute Ni᎐C alloy (see solid line in Figure 10.16). Whereas at medium and large undercoolings the data are well described by dendrite growth theory, the experimental data measured at small undercoolings are located above the theoretical curves. Thus, either the reduction of fluid flow motion in liquid samples processed in TEMPUS during MSL-1R mission was not sufficient to eliminate the enhancement of growth velocity due to the change in heat and mass transport by forced convection induced externally by the alternating electromagnetic field of the TEMPUS coil system or the samples were contaminated by very small amounts of impurities, which can also lead to a slight increase of the growth velocity. Future experiments on board of the ISS are in preparation to determine quantitatively in separate way the change of growth dynamics by small amounts of solute and increase of mass and heat transport by forced convection. Since the MSL1 Spacelab mission of NASA in 1997 no opportunity was given to refly TEMPUS in Space up to now. An advanced Facility of an ElectroMagnetic Levitator (EML) is considered by the European Space Agency and the German Aerospace Center to be accommodated on board of the ISS in 2009. However, during the recent years it was successfully demonstrated that containerless undercooling and solidification experiments on drops of metals and alloys can even be performed during the short duration of about 20 s time of reduced gravity in parabolic flights. By using 40 subsequently flown parabolas during one-day flight it is possible to perform in direct sequence measurements of the growth dynamics as a function of undercooling. Such experiments were performed on Fe60Co40 alloy, in which the dendrite growth velocity was measured as a function of undercooling [10.61]. The results of the measurements in reduced gravity (open symbols) are compared with analogous measurements on Earth (closed symbols) as exhibited in Figure 10.17. The circles represent the growth velocity of primarily formed fcc phase, while the triangles give the corresponding data of growth velocity of primarily formed metastable bcc phase. The growth velocity of the primarily solidified fcc phase increases with increasing undercooling up to a critical value of undercooling at which the growth velocity abruptly drops to a lower value. Such a sudden drop of the growth velocity in Fe-based alloys can be associated with a change of primary crystallization of stable fcc to metastable bcc phase [10.62]. The results of the measurements of growth velocity as a function of undercooling in reduced gravity on the same alloy show the same order of growth velocities for both phases in the undercooling range from 30 to 240 K. But a comparison of both data sets yield the important result that the critical undercooling
Tcrit for the onset of primarily

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Figure 10.17. Growth velocity as a function of undercooling measured on Fe60Co40 alloy on Earth (full symbols) and in reduced gravity (open symbols).

formed metastable bcc phase is decreased from about 90 K on Earth to 53 K in reduced gravity. Similar to the results of investigations on stainless-steel alloys during MSL1 Spacelab mission [10.62] it is concluded that the reduced critical undercooling for the primary crystallization of metastable bcc phase could be attributed to an increased lifetime of the metastable bcc phase and a retarded nucleation of the stable fcc phase in the mushy zone. A detailed understanding and theoretical modelling by taking into account convection in phase selection processes are, however, still lacking. REFERENCES

[10.1] Drehman, A.J., and Turnbull, D. (1981) Scripta Metallurgica 15, 543. [10.2] Notthoff, C., Feuerbacher, B., Frans, H., Herlach, D.M., and HollandMoritz, D. (2001) Physical Review Letters 86, 1038. [10.3] Piller, J., Knauf, R., Preu, P., Lohöfer, G., and Herlach, D.M. (1986) Proceedings of the 6th European Symposium on Materials Sciences under Microgravity, Vol. ESA SP-256 (Bordeaux), p. 437. [10.4] Team TEMPUS (1996) in: Materials and Fluids under Low Gravity, eds. Ratke, L., Walter, H., and Feuerbacher B. (Springer, Berlin), p. 233.

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[10.5] Hofmeister, W., Morton, C.M., Robinson, M.B., and Bayuzick, R.J. (1999) in: Solidification 1999, eds. Hofmeister, W.H., Rogers, J.R., Singh, N.B., Marsh, S.P., and Vorhees, P. (TMS, Warrendale, PA), p. 83. [10.6] Barth, M., Holland-Moritz, D., Herlach, D.M., Matson D.M., and Flemings, M.C. (1999) in: Solidification 1999, eds. Hofmeister, W.H., Rogers, J.R., Singh, N.B., Marsh, S.P., and Vorhees, P. (TMS, Warrendale, PA), p. 83. [10.7] Steinberg, J., Lord, A.E., Lacy, L.L., and Johnson, J. (1981) Applied Physics Letters 38, 135. [10.8] Lee, M.C., Kendall, J.M., and Johnson, W.L. (1982) Applied Physics Letters 40, 382. [10.9] Drehman, A.J., and Greer, A.L. (1984) Acta Metallurgica et Materialia 32, 323. [10.10] Kiminami, C.S., and Sahm, P.R. (1986) Acta Metallurgica et Materialia 34, 2129. [10.11] Gillessen, F., Herlach, D.M., and Feuerbacher, B. (1988) Journal of LessCommon Materials 145, 145. [10.12] Shong, D.S., Graves, J.A., Ujiie, Y., and Perepezko, J.H. (1987) Materials Research Society Symposium Proceedings 87, 17. [10.13] Gillessen, F., and Herlach, D.M. (1988) Materials Science & Engineering A 97, 147. [10.14] Dunst, A., Herlach, D.M., and Gillessen, F. (1991) Materials Science & Engineering A 133, 785. [10.15] Gillessen, F. (1989) Ph.D. Thesis, Ruhr-University Bochum, Germany. [10.16] Herlach, D.M., Gillessen, F., Volkmann, T., Wollgarten, M., and Urban, K. (1992) Physical Review B 46, 5203. [10.17] Shechtman, D., Blech, I., Gratias, D., and Cahn, J.W. (1984) Physical Review Letters 54, 1951. [10.18] Gillessen, F., and Herlach, D.M. (1991) Materials Science & Engineering A 134, 1220. [10.19] Mueller, B.A., Schaefer, R.J., and Perepezko, J.H. (1987) Journal of Materials Research 2, 809. [10.20] Avrami, M. (1939) Journal of Chemical Physics 7, 1103. [10.21] Schroers, J., Holland-Moritz, D., Herlach, D.M., and Urban, K. (2000) Physical Review B 61, 14500. [10.22] Croat, J.J., Herbst, J.F., Lee, R.W., and Pinkerton, F.E. (1984) Journal of Applied Physics 55, 2078. [10.23] Sagawa, M., Fujimura, S., Togawa, N., Yamamoto, H., and Matsuura, Y. (1984) Journal of Applied Physics 55, 2083. [10.24] Sellers, C.H., Hyde, T.A., Branagan, D.J., Lewis, L.H., and Panchanathan, V. (1997) Journal of Applied Physics 81, 1351. [10.25] Hermann, R., and Löser, W. (1988) Journal of Applied Physics 83, 6399. [10.26] Herlach, D.M., Volkmann, T., and Gao, J. (2003) German Patent No. 10106217.6. [10.27] Gao, J., Volkmann, T., and Herlach, D.M. (2002) Acta Materialia 50, 3003.

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