Structure and properties of levitated liquid metals

Journal of Non-Crystalline Solids 250±252 (1999) 63±69

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Structure and properties of levitated liquid metals I. Egry

*

Institut f ur Raumsimulation, Deutsches Zentrum f ur Luft- und Raumfahrt, D-51170 K oln, Germany

Abstract One major advantage of electromagnetic levitation used in our experiments, is its capability to access the metastable state of an undercooled liquid. This paper reports on measurements of surface tension, viscosity, electrical conductivity and density of undercooled liquid metallic liquids such as Au56 Cu44 , Pd76 Cu6 Si18 , Si, Co80 Pd20 as well as on Extended X-ray Absorption Fine Structure (EXAFS) investigations of Co80 Pd20 . The measurements of surface tension, viscosity and electrical conductivity were performed under microgravity conditions which reduce the strength of the required electromagnetic levitation ®elds by orders of magnitude and lead to a higher precision. Ó 1999 Elsevier Science B.V. All rights reserved.

1. Introduction In contrast to solids and gases, our understanding of the liquid phase is still unsatisfactory. Liquid metals are assumed to be simple liquids in theory, but in practice they are dicult to handle, due to the high temperatures involved. Undoubtedly, more experimental information on liquid metal properties and structure is needed. For metallic melts, electromagnetic levitation [1] is an elegant method which allows containerless melting and solidi®cation. It provides conditions of minimum contamination, and consequently, for maximum undercooling of the melt [2]. To investigate the structure and properties of undercooled melts, electromagnetic levitation must be complemented by non-contact diagnostic tools. We have developed and applied optical methods for the measurement of surface tension, viscosity, density and an inductive method for the mea-

* Tel.: +49 2203 601 2844; fax: +49 2203 61768; e-mail: [email protected]

surement of electrical conductivity. We have also performed extended X-ray absorption ®ne structure (EXAFS) studies on levitated undercooled samples which yield information about the short range order in the melt. The synopsis of the experimental results should give us insight into ordering e€ects and transport properties in liquid metals.

2. Experimental procedures 2.1. Electromagnetic levitation Levitation of electrically conducting samples can be achieved by applying a high frequency alternating inhomogeneous electromagnetic ®eld ~ B, produced by a levitation coil. The levitation coil is connected to a RF-generator, with a frequency of about 300 kHz and a power of 6±10 kW, to produce the levitation ®eld. The coil and the sample are housed in a vacuum chamber, made of stainless steel, which is equipped with di€erent windows to allow visual observation by a video camera,

0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 2 1 3 - 6

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I. Egry / Journal of Non-Crystalline Solids 250±252 (1999) 63±69

temperature measurement by a pyrometer and illumination by a synchrotron beam for the EXAFS measurements. To cool the sample, He±4%H2 gas mixture was used. The gas ¯ow was variable and controlled by the pyrometer. This control made it possible to maintain a constant temperature for several hours. For the microgravity experiments, we used the electromagnetic levitation facility Tiegelfreies Elektro-Magnetisches Prozessieren unter Schwerelosigkeit (TEMPUS) [3]. In microgravity, heating and positioning are decoupled, and gas cooling is not necessary. 2.2. Surface tension and viscosity Surface tension and viscosity of a liquid sample can be measured by the oscillating drop technique. This is a non-contact method which makes use of the fact that the radius, R, of a liquid drop undergoes damped oscillations of the form ÿ
…1† R…t† ˆ R0 1 ‡ e cos …xt† eÿCt ; where e is the amplitude of the oscillation, R0 the unperturbed radius and C is the damping constant. The frequency x of these oscillations is related to the surface tension c. For a drop of mass, M, free of external forces, it is given by Rayleigh's formula [4]: 32p c : …2† 3 M The frequencies can be obtained from high speed video recordings of the visible cross section of the oscillating drop, and subsequent digital image processing. In terrestrial levitation experiments, corrections to the simple formula, Eq. (2) have to be made to account for the Lorentz force and the gravitational force [5]. These forces result in a distortion of an otherwise spherical sample and lead to a splitting of the fundamental frequency into as many as ®ve frequencies (due to the broken symmetry), and to a shift of the frequencies (due to a magnetic pressure e€ect). Cummings and Blackburn [5] have derived an (approximate) correction formula which reads x2R ˆ

2

2

x2R ˆ X2 ÿ 1:9x2tr ÿ 0:3xÿ2 tr …g=R0 † :

…3†

2

In this formula, X2 is the mean of the split frequencies due to surface oscillations, x2tr the mean of the frequencies of the translational oscillations, g the gravitational acceleration and R0 is the radius of the sample. To measure the viscosity, g, the damping, C, of the oscillations must be analysed. The damping of surface oscillations of spherical viscous drops has been calculated by Kelvin [6] and is given by 20p gR0 : …4† 3 M Again, this formula is not applicable to groundbased experiments, due to the presence of strong electromagnetic ®elds [7]. It should, however, work for microgravity experiments.

Cˆ

2.3. Density We use a videographic method in combination with electromagnetic levitation to measure the density of undercooled melts. The mass, M, of the sample is determined before and after levitation to account for evaporation losses. The volume is determined from a ®t to the visible lateral cross section of the sample, assuming rotational symmetry of the equilibrium shape. The ®t is performed using a series expansion in Legendre polynomials, Pn , yielding the radius, R, as a function of angle, h: X R…u† ˆ an Pn …u†; u ˆ cos …h†: …5† n

The volume is then given as 2p V ˆ 3

Z1

R3 …u† du

…6†

ÿ1

and, ®nally, the density is obtained from q ˆ M=V :

…7†

The major experimental diculties lie in the spatial resolution required to resolve volume changes in the order of DV =V  10ÿ4 . 2.4. Electrical conductivity The non-contact measurement of the electrical conductivity r of a material, liquid or solid, can be

I. Egry / Journal of Non-Crystalline Solids 250±252 (1999) 63±69

based on electromagnetic induction. The sample is placed inside a coil carrying a RF-current. By the presence of the sample, the complex impedance, Z…r†, of the coil changes. The impedance can be determined by measuring the current and voltage through the coil simultaneously: Z…r† ˆ U =I. Therefore, since the impedance depends on the conductivity of the sample, this method can be used to measure electrical conductivities in a noncontact manner. The relation between impedance and conductivity for a spherical sample of radius, R0 , is given in Ref. [8]. The coil is part of an oscillatory circuit with resistance R, inductance L and capacitance C. If the frequency is high, i.e. of the order pof  300 kHz, and the damping is low, i.e. R C=L < 0:1, the sample conductivity can be derived from the following approximate formula:  q R0 1 ÿ 1 ÿ A…I0 =U0 cos/ ÿ B†=R30 ; d…r† ˆ 2 …8† where d…r†, the skin depth, de®ned as s 2 d…r† ˆ xrl0

…9†

has to be small, i.e. d < R0 =3. Here, x is the frequency of the oscillatory circuit and l0 is the magnetic permeability. The ratio I0 =U0 of the amplitudes of the ac coil current and voltage as well as their phase di€erence / can be measured directly. The constants A and B are parameters of the coil and the oscillatory circuit and have to be determined beforehand via calibration experiments. The principle of this measurement can be combined with electromagnetic levitation, where the levitation coil can be simultaneously used as probing coil. If the experiment is performed under microgravity conditions, the liquid sample remains spherical and the formula outlined above is applicable.

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between the actual absorption, a…k†, and the absorption of an isolated atom, a0 …k†, normalized to a0 …k†. The function, v…k†, displays oscillations at energies greater than the absorbtion edge. It contains information about the short range order in the vicinity of the absorbing atom, namely the distances and numbers of the nearest neighbours. In fact, v…k† is related to the pair correlation function, g…r†, through a (weighted) Fourier transformation [9]: 3j f …p; k†j 2k Z1 g…r† ÿ2r=k…k† e sin …2kr ‡ /…k†† dr;  r2

v…k† ˆ ÿ

0

…10† where f …p; k† is the backscattering amplitude, /…k† the phase shift and k…k† is the mean free path of the photoelectron. By using monochromatic synchrotron radiation we scan through the energy region near and above an absorption edge and measure the actual absorbtion to obtain v…k†. For levitated samples, a few mm diameter, the absorbtion is too strong to allow for such a straightforward approach. Fortunately, the secondary ¯uorescence emitted following the primary absorbtion contains the same information and can be detected by photodiodes. The information about short range order is contained in g…r†. To extract this information, the integral in Eq. (10) must be deconvoluted. Due to the limited k-range available experimentally, the best method is to use a model function gmodel …r† and to calculate a model vmodel …k†, which is then ®tted to the experimental data. We have employed the GNXAS-algorithm of Filipponi [10] and have allowed for asymmetric model partial pair correlation functions. 3. Results

2.5. EXAFS

3.1. Surface tension

The EXAFS signal, v…k†, due to an atom embedded in condensed matter and excited by synchrotron radiation, is de®ned as the di€erence

During the Spacelab missions IML-2 and MSL1, we performed surface tension measurements in microgravity on a number of pure metals and

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alloys using the electromagnetic levitation facility TEMPUS. The oscillation spectra obtained in microgravity show one single peak only, as predicted by Rayleigh's theory, and in contrast to terrestrial spectra. Fig. 1 shows oscillation spectra of Au56 Cu44 recorded in microgravity and on ground for comparison. The results for the surface tension were compared with our ground based data. The two data sets agree only, if the terrestrial data are corrected according to the Cummings± Blackburn formula [11] and yield cAuCu …T † ˆ 1:21 ÿ 0:15  10ÿ3 …T ÿ 1183† …N=m†; …11†

Fig. 2. Viscosity of Pd76 Cu6 Si18 measured by the oscillating drop technique in microgravity during missions STS-83 (full squares) and STS-94 (open diamonds). Arrhenius ®t to STS-83 data is also shown (full line).

Viscosity measurements using the oscillating drop technique have not been attempted so far in terrestrial experiments, due to experimental diculties and the lack of an appropriate correction formula. Recently, we have carried out such experiments during the MSL-1 Spacelab mission on Co80 Pd20 and the eutectic alloy Pd76 Cu6 Si18 [12]. It was possible to measure the viscosity of this alloy in the temperature range from 1000 to 1300 K. The result is shown in Fig. 2. The ®gure shows the data points collected with the TEMPUS facility. In spite of the extended temperature range, they can be ®tted equally well with an Arrhenius-type ex-

pression, a Vogel±Fulcher-type expression, or even with a power-law function. Our data con®rm those of Lee et al. [13]. Using the Arrhenius Ansatz, we obtain

where temperature T is given in K. 3.2. Viscosity

gPdCuSi …T † ˆ 0:1338 exp…6021=T † …mPa s†:

…12†

3.3. Density We have measured the density, q, of metallic melts such as Cu, Ni, Cu±Ni, Co±Pd [14] as well as the density of liquid Si [15] with the method described in Section 2.3. For the measurement of Si, indirect heating was necessary, because the electrical conductivity of solid Si is not large enough to be inductively heated. In contrast to other ®ndings [16], our data do not show an anomaly of the density of Si near the melting point. This can be seen from Fig. 3. This ®gure also shows that our data span a wide temperature range, from 1400 to 2000 K, including an undercooling of about 300 K. A ®t of a linear function to the data gives qSi …T † ˆ 2:52 ÿ 3:53  10ÿ4 …T ÿ 1683† …g=cm3 †: …13† 3.4. Electrical conductivity

Fig. 1. Oscillation spectrum of a levitated drop under terrestrial conditions and in microgravity. Frequency is normalized to Rayleigh frequency xR .

During the recent MSL-1 Spacelab mission, we have measured the electrical conductivity of

I. Egry / Journal of Non-Crystalline Solids 250±252 (1999) 63±69

Fig. 3. Density of liquid silicon as function of temperature. No singularity is observed at the melting point Tm , and the data can be ®tted by a linear relation (full line).

Co80 Pd20 in a wide temperature range. In this microgravity experiment, we have used the TEMPUS facility to levitate, melt and undercool the sample. Current and voltage through the TEMPUS heating coil were recorded during several melt cycles as well as afterwards, when the sample was retracted. This procedure provided the necessary in situ calibration. When converting the measured resistance of the sample into speci®c conductivity, a spherical shape of the sample was assumed with a value of the radius determined at room temperature; in other words, the data are not corrected for thermal expansion. The result is shown in Fig. 4. The conductivities of this alloy are given by rCoPd;liq ˆ …163:8 ‡ 0:0584…T ÿ 1610† …lX cm††ÿ1 ; ÿ1

rCoPd;sol ˆ …121:2 ‡ 0:0443…T ÿ 1565 …lX cm†† : …14† 3.5. EXAFS For the EXAFS experiments, we have chosen again Co80 Pd20 due to its interesting magnetic properties and its range of undercooling. The synchrotron beam entered the levitation chamber through a Beryllium window and was focused or collimated onto a small spot on the levitated sample. Four detectors were placed concentrically every 90 around the incident beam, to measure the ¯uorescence radiation in the backward direc-

67

Fig. 4. Electrical resistivity of solid and liquid Co80 Pd20 , as measured in microgravity. Open circles indicate data in the liquid state, open diamonds in the solid state. The results of least-square ®ts to linear functions are shown as full lines. Solidus (Ts ) and liquidus (T1 ) temperatures are indicated by vertical bars. Below 1360 K, the impedance changes due to magnetic ordering e€ects, and the data cannot be used for the determination of the electrical resistivity.

tion. Their signals were added. The energy of the incident beam was scanned through the EXAFS region ranging from 7.6 to 8.3 keV for cobalt as the absorbing species (EK (Co) ˆ 7.7 keV). It was necessary to maintain the sample liquid at a constant temperature (to within 10 K) throughout the scan, which takes about 30 min. Applying the GNXAS ®tting procedure and allowing for asymmetric partial pair distribution functions, the nearest neighbour distances and their standard deviations (Debye±Waller factors) could be determined as functions of temperature. These are compared to the corresponding values of solid (polycrystalline) Co80 Pd20 in Figs. 5 and 6. Due to the possibility of performing measurements in the undercooled regime, there is a ®nite temperature range where data of the solid and the liquid phase can be compared. 4. Discussion Electromagnetic levitation in combination with non-contact diagnostics can provide data on thermophysical properties and structure of metallic melts. If the experiments can be carried out in

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I. Egry / Journal of Non-Crystalline Solids 250±252 (1999) 63±69

Fig. 5. Nearest neighbour Co±Pd and Co±Co distances in solid and liquid Co80 Pd20 as determined through EXAFS analysis. Linear functions are ®tted to the data.

Fig. 6. Debye±Waller factors of Co±Pd and Co±Co distances in solid and liquid Co80 Pd20 as determined through EXAFS analysis. Linear functions are ®tted to the data.

microgravity, the value of the method is further enhanced. In the case of surface tension, microgravity experiments validated terrestrial data and the correctness of the Cummings correction. Further microgravity experiments are therefore only necessary for materials which cannot be levitated on Earth. The situation is di€erent for viscosity measurements: these experiments are a€ected by electromagnetically induced (turbulent) ¯ows; at present, no terrestrial experiments exist, and it is not known if they are possible at all. Although the viscosity data cover a temperature range of about 400 K, it is not possible to discriminate between the di€erent models for the temperature dependence of the viscosity. While the

Arrhenius ansatz represents an analytical function, both the Vogel±Fulcher model, and the power-law function predict a singularity near the glass transition. Di€erences in the models will therefore become evident in this region, where the viscosity is large, of the order of 1013 Pa. Unfortunately, the oscillating drop method may no longer work for viscosities larger than 1 Pa. Nevertheless, viscosity measurements with the oscillating drop technique in microgravity are a useful complementary tool supplementing conventional techniques. Some of these su€er from the formation of crystallites close to the freezing point, which lead to an apparent increase in the viscosity [17]. As a containerless technique, the oscillating drop method allows undercooling a melt and suppresses nucleation and formation of crystallites near the melting point. As we have shown, density measurements on levitated drops are possible on earth. One major diculty and source of error is the complicated shape of drops levitated against 1 g. Therefore, microgravity experiments on the density and thermal expansion should increase the accuracy of the results. First experiments have been carried out by Samwer et al. [18]. The same is true for electrical conductivity measurements. Apart from their intrinsic interest, these data can also be used to estimate the thermal conductivity through the Wiedemann±Franz relation, which is applicable to metallic melts [19]. In addition, the electrical conductivity is, like the viscosity, a€ected by clustering and ordering e€ects in the melt, and should therefore provide, albeit indirect, information about structural e€ects. The most direct tool, and the latest development, for obtaining insight into the short range order of undercooled metallic melts is the combination of a levitation technique with a synchrotron source. While we have combined electromagnetic levitation with EXAFS, other groups have used aerodynamic levitation in combination with either EXAFS [20] or X-ray di€raction [21]. Our data on solid and liquid Co±Pd show that the Co±Co and Co±Pd distances are essentially temperature independent. They are determined by the lattice constant in the crystalline state, and by the ionic radii of the constituent atoms in the liquid state. This similarity means that the

I. Egry / Journal of Non-Crystalline Solids 250±252 (1999) 63±69

macroscopic temperature dependence of the density is not due to an increase in interatomic distance, but rather to a decrease in the number of neighbours, i.e. an increase of vacancies with increasing temperature. This interpretation is in agreement with conjectures of other groups, i.e. Takeuchi [22]. The temperature dependence of the Debye± Waller factors can be explained by a temperature dependent phononic contribution and an essentially temperature independent statistical disorder. While the vibrational part is similar in both, the solid and the liquid phase, the contribution due to disorder is dramatically larger in the liquid state. 5. Conclusions Electromagnetic levitation is a useful method for the study of metallic melts. As we have shown, it can be combined with a number of non-contact diagnostic tools to measure such quantities as surface tension, viscosity, density and electrical conductivity. Electromagnetic levitation is also compatible with synchrotron radiation sources, and EXAFS spectra can be obtained. References [1] D.M. Herlach, R. Cochrane, I. Egry, H. Fecht, L. Greer, Int. Mat. Rev. 38 (1993) 273. [2] D.M. Herlach, I. Egry, P. Baeri, F. Spaepen (Eds.), Undercooled Metallic Melts: Properties, Solidi®cation and Metastable Phases, Math. Sci. Eng., vol. A178, 1994.

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[3] Team TEMPUS, in: L. Ratke, H. Walter, B. Feuerbacher (Eds.), Materials and Fluids under Low Gravity, Springer, Berlin, 1996, p. 233. [4] Lord Rayleigh, Proc. Roy. Soc. 29 (1879) 71. [5] D.L. Cummings, D.A. Blackburn, J. Fluid Mech. 224 (1991) 395. [6] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, New York, 1961. [7] A. Bratz, I. Egry, J. Fluid. Mech. 298 (1995) 341. [8] G. Loh ofer, Int. J. Eng. Sci. 32 (1994) 107. [9] B.K. Teo, in: B.K. Teo, D.C. Joy (Eds.), EXAFS Spectroscopy, Plenum Press, New York, 1981. [10] A. Filipponi, J. Phys: Condens. Matter 6 (1994) 8415. [11] I. Egry, G. Loh ofer, G. Jacobs, Phys. Rev. Lett. 75 (1995) 4043. [12] I. Egry, G. Loh ofer, I. Seyhan, S. Schneider, B. Feuerbacher, Appl. Phys. Lett. 73 (1998) 462. [13] S.K. Lee, K.H. Tsang, H.W. Kui, J. Appl. Phys. 70 (1991) 4842. [14] E. Gorges, L.M. Racz, A. Schillings, I. Egry, Int. J. Thermophysics 17 (1996) 1163. [15] M. Langen, T. Hibiya, M. Eguchi, I. Egry, J. Cryst. Growth 186 (1998) 550. [16] S. Kimura, K. Terashima, J. Cryst. Growth 180 (1997) 323. [17] J. Steinberg, S. Tyagi, A.E. Lord Jr., Appl. Phys. Lett. 38 (1981) 879. [18] B. Damaschke, K. Samver, I. Egry, in: W. Hofmeister, J. Rogers, N. Singh, S. Marsh, P. Vorhees (Eds.), Solidi®cation 1999, TMS, Warrendale, PA, 1999. [19] K.C. Mills, B.J. Monaghan, B.J. Keene, Int. Matter Rev. 41 (1996) 209. [20] C. Landron, X. Launay, J.C. Ri‚et, P. Echegut, Y. Auger, D. Ruer, J.P. Coutures, M. Lemonier, M. Gailhanou, M. Bessiere, D. Bazin, H. Dexpert, Nucl. Instrum and Meth. B 124 (1997) 627. [21] S.A. Ansell, S. Krishnan, J.K.R. Weber, J.J. Felten, P.C. Nordine, M.A. Beno, D.L. Price, M.-L. Saboungi, Phys. Rev. Lett. 78 (1997) 464. [22] S. Takeuchi, Matter Trans. JIM 30 (1989) 647.