Demonstration of the effect of stirring on nucleation from experiments on the International Space Station using the ISS-EML facility

The effect of fluid flow on crystal nucleation in supercooled liquids is not well understood. The variable density and temperature gradients in the liquid make it difficult to study this under terrestrial gravity conditions. Nucleation experiments were therefore made in a microgravity environment using the Electromagnetic Levitation Facility on the International Space Station on a bulk glass-forming Zr57Cu15.4Ni12.6Al10Nb5 (Vit106), as well as Cu50Zr50 and the quasicrystal-forming Ti39.5Zr39.5Ni21 liquids. The maximum supercooling temperatures for each alloy were measured as a function of controlled stirring by applying various combinations of radio-frequency positioner and heater voltages to the water-cooled copper coils. The flow patterns were simulated from the known parameters for the coil and the levitated samples. The maximum nucleation temperatures increased systematically with increased fluid flow in the liquids for Vit106, but stayed nearly unchanged for the other two. These results are consistent with the predictions from the Coupled-Flux model for nucleation.


INTRODUCTION
Crystal nucleation 1 and subsequent growth 2 in supercooled liquids (i.e. liquids at a temperature below the equilibrium melting temperature, ) are the two fundamental processes that determine the solidification microstructure. 3 Studies of these processes, then, occupy a central role in condensed matter physics, materials science, and biology. Both thermodynamic and kinetic factors influence nucleation and growth. In nucleation, spontaneous random processes in the liquid lead to the formation of dense, ordered, regions that are characteristic of the nucleating crystal. The growth of these ordered regions is stochastic, which may grow and shrink. Above a critical size it becomes thermodynamically favored for these aggregates to increase in size, eventually leading to their growth into crystalline solids. Homogeneous nucleation is controlled solely by the intrinsic properties of the liquid and nucleating phases and the amount of supercooling. In contrast, heterogeneous nucleation is catalyzed by foreign objects such as undissolved impurities or the container walls. The minimization of these catalytic sites is then crucial for the studies of homogeneous nucleation; containerless processing, using electrostatic (ESL), 4 electromagnetic (EML), 5 aerodynamic 6 and acoustic 7 levitation, allows such studies. While useful for oxide materials, aerodynamic and acoustic levitations are not recommended for metallic liquids since even the highest purity inert gases often contain impurities that catalyze nucleation.
Nucleation is known to be influenced by pressure, 8 electric 9,10 and magnetic fields, 11 and it has been shown to couple with other phase transitions, such as magnetic transition in a liquid. 12,13 The effect of forced convection on crystal growth has also been studied in a number of recent publications. 14,15 However, the effect of stirring (fluid flow) on nucleation in a liquid is not well established. A model was developed for cases where the nucleating phase has a different chemical composition than the initial phase (the coupled-flux model 16 ). In this case, the growth of the nuclei leads to a change in chemical composition near the cluster. This interacts with the long-range diffusion field, leading to a coupling of the stochastic processes of interfacial kinetics and diffusion. If the interfacial attachment/detachment rates are faster than the diffusion rate, the kinetics of nucleation can be significantly decreased. The coupled flux model has been explored numerically 17 and has been applied successfully for the precipitation of oxygen in single crystal silicon. 18 For crystal nucleation from a quiescent liquid of a different chemical composition, the coupled fluxes should decrease the nucleation rate. If the liquid is stirred, however, the fluid flow should enhance solute transport and the nucleation rate should increase towards the expected steady-state nucleation rate. To our knowledge a systematic study of the effect of stirring on nucleation of solids from supercooled liquids does not exist.
Here, we report the results of studies of the effect of stirring on nucleation in electromagnetically levitated metallic liquid drops under the microgravity environment of the International Space Station (ISS). Such controlled stirring experiments are not possible under terrestrial conditions because of the natural density and surface tension (Marangoni) 19 driven convection. Microgravity eliminates the first because of the absence of gravity-induced flows.
Nearly uniform heating of the sample with a radio-frequency (rf) electromagnetic field in the EML minimizes the second. The EML facility on the ISS, ISS-EML, 20 is capable of controlling the fluid flow by electromagnetic stirring. A brief description of the facility can be found in the Methods section. Three different alloys were chosen to investigate the effect of stirring on nucleation rates in supercooled liquids for different solidification motifs (polymorphic and multi-phase). A Ti39.5Zr39.5Ni21 alloy in which primary nucleation is to a quasicrystal of the same composition 21,22 was one choice. It was observed that, although metastable, the quasicrystal phase nucleates first from the supercooled liquid, followed by its decomposition into the stable Laves and solid-solution phases at higher temperatures as the liquid temperature increased due to the release of the heat of fusion. The other two were the bulk metallic glass forming Cu50Zr50 and Zr57Cu15.4Ni12.6Al10Nb5 (Vit106) alloys. The primary crystallizing phase from the Cu50Zr50 liquid is a cubic B2-phase of CuZr, 23 which is consistent with the phase diagram. 24 In contrast, crystalline phases of Zr2Ni, Zr2Cu, ZrCu, Zr3Al2, Zr4Al3, which also contain various amounts of other elements, crystallize from the glass of Vit106. 25 The results obtained clearly demonstrate that increased stirring increases the nucleation rate for the Vit106, which shifts the crystallization to higher temperatures; little or no effect of stirring was observed for the other two. The results are consistent with the expectations from the coupled-flux model. This is a new observation which is of considerable interest for a fundamental understanding of the nucleation mechanism in partitioning systems.
These results could be also vitally important for the future processing of materials in space, which will be necessary for long-term space explorations, and ultimately for manufacturing under extraterrestrial conditions on Mars and the Moon.

RESULTS
The experimental details are described in the Methods section of this paper and in refs. [20,26].
Independent control of the heating and positioning of a sample in the ISS-EML is one of the advantages compared to the ground-based EML facilities. Two different electronic circuits feed currents into a pair of identical Cu-coils for sample positioning and heating. The radio frequency (rf)-electromagnetic fields generated by these currents interact with the electrons in the solid/liquid generating eddy currents, which affect fluid flow. 26 Since these rf-fields can be controlled by  this particular thermal cycle. The cooling rate near the onset temperature for recalescence was 1.3 K/s, which was not sufficient to prevent crystallization. However, the higher cooling rate of 2.2 K/s in the Ar-atmosphere almost suppressed crystallization; only two small kinks near 926 K and 786 K were observed. When processed in He-atmosphere, a much faster cooling rate of 15 K/s was achieved around 850 K, which completely suppressed crystallization, as shown in Fig. 1. This thermal cycle was used for specific heat measurements by modulating the temperature at various hold temperatures. After the last modulation at 1050 K, the heater was turned off for rapid cooling.
No crystallization event was observed. That this sample transformed into a glass was evident when it was heated in the next thermal cycle. A sudden rise in temperature due to a glass-crystal transformation was observed between 834 and 922 K, as shown in the inset of Fig. 1. This thermal event is similar to observations made in ground-based ESL studies when a glass was heated rapidly. 27 Unfortunately, subsequent processing of the sample in the He-atmosphere caused contamination, possibly from trace amounts of oxygen in the gas, which prevented glass formation.
Our ground-based studies 27 indicated that 500-600 ppm oxygen is enough to prevent bulk glass formation in this alloy. A similar observation of glass formation in a Vit105 (Zr52.5Cu17.9Ni14.6Al10Ti5) alloy under microgravity was reported earlier; 28 this is then the second demonstration that a bulk metallic glass (6.0 mm diameter) can be manufactured in space.
Although not unexpected, this result may be of importance for future space-based manufacturing of intricate machine parts using bulk metallic glasses. phase under similar conditions because the structure of the icosahedral phase is similar to that of the liquid. 21,30 Note that if the transformation of the icosahedral phase into a mixture of stable Ti-Zr solid solution and Laves phase can be suppressed, it melts at 1063 K, compared to 1093 K for the phase mixture of the same composition. 31 A slightly higher undercooling of 110 K was possible in the ground-based ESL studies of this liquid. 32 These differences in undercoolability may be due to many factors, such as slower cooling rates (about 3 K/s near compared to about 12 K/s in the ESL) for the larger samples used in space, larger sample volume, larger stirring due to eddy currents induced in the liquid by the EML, and/or small differences in sample purities.
Also, heterogeneous nucleation due to small amounts of impurities cannot be completely ruled out.
Since nucleation is a stochastic process, a distribution of nucleation temperatures for a large number of heating and cooling cycles is usually observed. 33 Typically, many hundreds of cycles are required to obtain statistically significant data for this distribution. 29,32,34,35 To obtain a statistically significant result for the effect of stirring, then, many thermal cycles for the same heater and positioner voltages must be performed. However, processing in the ISS-EML is restricted by several considerations. To enhance the life of the facility, each sample is allotted a certain amount of mass loss due to evaporation, part of which deposits on the Cu-coils. In addition to nucleation studies, thermophysical properties (viscosity, surface tension, and specific heat) and electrical properties of the liquids were also measured. This restricted the number of melting cycles from three to five for a particular setting of the heater and positioner voltages. Lower vapor depositions on the Cu-coils in the He-gas atmosphere allowed more thermal cycles (ten to twenty) to be performed. However, once the samples were melted in gas atmospheres, the nucleation temperature started rising and reached a saturation level after a few cycles. Some surface features were also observed in the video images during the cooling of the liquid drops, indicating oxide precipitation. Therefore, the data collected in vacuum are considered to be more representative of homogeneous nucleation than those in the gas atmospheres. For that reason, the data presented here are from vacuum processing only. The experiments were conducted over several nights on the ISS due to restrictions on the allotted times on a given day.
According to the classical nucleation theory, 1 the homogeneous nucleation rate, ( ) at a temperature, , is given by, where, * = 16 3 3∆ 2 ⁄ , The prefactor, * primarily contains kinetic parameters, such as the diffusion coefficient, the atomic jump distance, and the number of possible sites for nucleation; * contains the interfacial free energy, σ, and the driving free energy, Δ . If the nucleation temperature, , is determined from several cycles for a sample of volume , cooled at a rate of , it follows a Poisson's distribution given by, 33 By fitting the experimentally measured distribution to eqn.

Stirring effect on nucleation during processing in vacuum
Extensive studies of homogeneous nucleation using the ground-based ESL to measure many hundreds of solidification cycles for Cu50Zr50 29 and Ti39.5Zr39.5Ni21 32 liquids were reported earlier.
Similar studies could not be made for the Vit106 alloy since the smaller (~2.5 mm diameter) samples required for the ESL studies formed glasses upon cooling, bypassing crystal nucleation.
Unfortunately, as mentioned earlier, such a large number of cycles to obtain statistically significant  Table 2. The values of * and σ from the ESL studies for Ti39.5Zr39.5Ni21 32 were 2.7 10 25 −3 −1 and 0.057 J −2 , respectively, which are again slightly different from those obtained from the nucleation studies on the ISS under vacuum (Table 3). Such differences may be due to different purities of the samples in the ISS than those used in the ground-based ESL studies. However, since the same starting material and same preparation conditions were used for all alloys prepared    To demonstrate that the changes in the nucleation parameters are due to stirring, Fig. 2 shows the logarithm of the prefactor, * as a function of shear rates for processing in vacuum for the Vit106 liquid. Clearly, * increases with the maximum shear rate at the nucleation temperature in the liquid due to electromagnetic stirring. Although * correlates well with both the maximum fluid flow velocity and the maximum shear rate at (see Tables 1-3), only the correlation with the shear rate is shown in fig. 2 for clarity. The Cu50Zr50 liquid showed a small increase in * when the maximum fluid velocity increased from 2.5 10 −4 to 3.5 10 −4 −1 ( Table 2). This small increase may not be statistically significant. Therefore, the results are consistent with expectations from the coupled-flux model, since the compositions of the liquid and the primary crystallizing phase are the same. However, more data are needed to make this conclusion statistically significant. Similar consideration applies to the changes in * with fluid flows for the Ti39.5Zr39.5Ni21 liquid ( Table 3). Note that the changes in * for the nearly similar values of for this liquid are due to the slower cooling rates for the higher positioner voltages and heater on conditions.
. pressures so that nucleation data from a large number of thermal cycles can be obtained; the higher liquidus temperatures for these liquids will also facilitate higher levels of stirring.

Sample preparation and nucleation measurements
Nearly spherical samples of Ti39.5Zr39.5Ni21 (6.0 mm diameter), Zr57Cu15.4Ni12.6Al10Nb5 (Vit106, The experiments on each sample were conducted over several nights. The samples were stored in Helium gas during the intervening periods. In some cases, the nucleation temperatures increased during the initial thermal cycles compared to the previous night's operations. After a few melting cycles it reverted back to the previous values. Therefore, those initial cycles were excluded from the analysis. It was also observed that if the liquid was disturbed during cooling by pulsing for the viscosity measurements, or the positioner/heater voltages were changed during cooling, the nucleation temperature changed. For those reasons, the nucleation data from those cycles were also excluded. The reason for such changes is not clear at the moment. Maximum undercooling for the Ti39.5Zr39.5Ni21 liquid was achieved after many melting cycles under vacuum over several nights. Possibly, the liquid purified during such repeated melting. The data presented here are from these later melting cycles when consistent maximum undercoolings could be achieved.

Model calculations for fluid flow
Fluid flow velocities and shear rates are the two parameters that give a direct measure of the stirring. Since they cannot be measured directly in the present experimental arrangement, model calculations were necessary. The voltages and currents applied to the positioner and heater coils, their frequencies, the position and diameter of the sample with respect to the coils, sample electrical resistivity and coupling coefficient to the rf fields, the liquid viscosity and density as a function of temperature are the input parameters in this model. 37,38 The particular details of the coil geometry and the rf fields can be found elesewhere. 39 The temperature dependent viscosities of the liquids were measured by a ground-based electrostatic levitation facility 40

DATA AVAILABILITY
The experimental data are available from the corresponding author on reasonable request.