Determination of thermophysical properties of liquid metals at high temperatures by levitation methods

Materials Science and Engineering, A178 (1994) 83-88

83

Determination of thermophysical properties of liquid metals at high temperatures by levitation methods J o h n L. M a r g r a v e

Department of Chemistry, Rice University and Materials Science Research Center, HARC, Houston, TX 77251 (USA)

Abstract

Levitation techniques offer unique opportunities for the accurate determination of thermophysical properties of liquid metals and alloys at high temperatures. Supercooled liquid metals can be studied at temperatures 200-500 K below their freezingpoints.

1. Introduction

for more efficient heating to very high temperatures with concentrators are discussed by Xiao and Hauge

Some of the most elusive thermophysical properties are those of undercooled liquid metals at high temperatures, including enthalpy increments, heats of fusion, heat capacities, spectral emissivities and reflectivities, indices of refraction, dielectric constants, surface tensions, viscosities, thermal conductivities, thermal diffusivities, densities, thermal expansion coefficients and compressibilities [1]. In order to realize a wide range of temperature for the accurate establishment of these properties, one needs a rapid heating-cooling technique with minimum likelihood of contamination yet with maximum opportunity for visual, photographic or video observation and ease of mechanical manipulation. Also, one needs a high precision calorimeter for evaluating thermodynamic properties. An almost perfect answer to these requirements is the technique of electromagnetic levitation. Although early patents described usable levitation systems [2[, it was not until the 1950s when engineers and scientists at Westinghouse devised a practical system for levitation and heating of kilogram samples of titanium aimed at the production of ultrapure metal [3]. Interest in the applications of levitation was still minimal, however, when a review paper describing experimental designs of levitation coils and some quantitative studies of the F e - C - O system was presented in 1964 [4]. Some typical coil designs which have been used for levitation techniques are presented in Fig. 1. Improved designs

[5].

*Associate researchers: R. H. Hauge, Z. Xiao, D. W. Ball, T. Baykara, D. W. Bonnell, M. S. Chandrasekhararah, A. K. Chaudhurl, L. A. Ford, R. T. Brow, G. P. Hansen, S. Krlshnan, R. L. Montgomery, E C. Nordine, R. A. Schiffman, B. Stephenson, P. C. Sundareswaran, J. A. Treverton, A. J. Valerga, J. K. R. Weber and P. W. Wilson.

SSD10921-5093(93)04516-K

For the last 30 years there has been active research interest in levitation and simultaneous heating by use of induction heaters, commonly in the frequency range 300-5000 kHz. Most of the published studies have utilized commercially available oscillators operating in the 400-600 kHz range with power ratings in the 10-50 kW range. Small laboratory samples (0.5-10 g) do not require such massive power supplies but there is inefficient coupling (poor impendance matching) with conventional equipment. An illustration of the advantages of induction heating is given in Fig. 2 which follows temperature as a function of time for a small Mo sample [6]. After about 10 s, the Mo melts but continues to absorb energy until it reaches a steady state brightness temperature of approximately 2528 K in 60 s. Frost and associates at General Electric [7]

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J. L. Margrave /

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Thermophysical properties of liquid metals of Rh, Re, Ir and Os metals by levitation calorimetry [9]. Bautista and associates studied liquid rare earth elements [10]; Stephens studied liquid uranium [11]; Margrave and associates have studied Ti, V, Fe, Co, Ni, Zr, Nb, Mo, Pd, Pt, Cu, Ag, Au, Ta, W, Ga, A1, etc. [12]; Frohberg and associates have studied Ta and Ta alloys and W by use of quantitative levitation calorimetry [13]. Also there have been levitation studies of various alloys and superalloys [14].

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Fig. 3. Schematic diagram of the Rice University levitation calorimeter. studied levitation forces and efficiency of levitationheating for several different metals (A1, Fe, etc.) in different coil designs at different frequencies. Interestingly, a coil with a contour like the seams of a baseball has good levitation characteristics while allowing excellent optical viewing and physical access to heated samples. In 1968, Bonnell, Ford and Margrave built and operated the first levitation calorimeter and by 1970 had completed studies of Cu, Pt, Pd and Ni [8]; a schematic diagram of this levitation (drop) calorimeter is given in Fig. 3. At about the same time, Chekovskoi, Sheindlin, and associates in the USSR reported studies

Drop calorimetric studies of metals and alloys over wide ranges of temperature, both below and above the melting points, have yielded (Hr-/-/298) for solids and liquids. From the discontinuity at the melting point, solid--, liquid, one can deduce the heat of fusion and from the slopes of the enthalpy increment plots, one obtains Cp (s or 1). Many of the transition metals supercool easily as they float in the levitation coils so that (HT-H298) for supercooled liquids can be measured. There is no discontinuity in (HT-H298) as one passes through the melting (freezing) temperature, i.e. Cp 1 does not change. Pyrometric observation of supercooled liquids shows that when nucleation and crystallization occur, a sudden flash of light is produced and the melt temperature rises rapidly to the melting point. A precision of + 0.5% and accuracy of + 1.0% are achieved in these measurements, with a major source of error being the temperature measurements. There is still a need for reliable temperature standards, especially for T> 2000 K, and a need for monochromatic spectral emissivities for liquid metals over a range of temperature so that one can convert brightness temperatures to true temperatures. Recently, emissivities cA.7- have been measured with a polarized laser ellipsometer device which allows evaluation of indices of refraction, dielectric constants and reflectivities as well as the spectral emissivities at various wavelengths and temperatures. The temperature dependences of the emissivities at 488, 514, 633 and 1064 nm for liquid Cu and Pt are illustrated in Fig. 4 [15]. Other liquid metals studied include AI, Si, Ti, Nb and Zr [16]. Levitation studies of transition metals have produced some unpredicted results for enthalpy increments and heat capacities for liquid metals. Consider a hypothetical Cp vs. T curve for a metal with no low temperature polymorphs and traditional DebyeEinstein behavior. In addition to the 3R (6 cal mol-1 K l) value for CpI expected for a monatonic, threedimensional liquid, there is an electronic contribution to Cp given by 6T where typical 6 values are 10-3-10 -4 cal mol -~ K -~. The 6 T contributions at 1000-3000 K could be 1-3 cal mol -~ K -~. Anhar-

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Thermophysical properties of liquid metals

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Fig. 4. (a) Normal incidence spectral emissivity of liquid copper as a function of temperature at 1064 ( A ), 632.8 (•), 514.5 ( x ), and 488 nm (o). The solid line represents the least-squares fit to the data. The melting point is indicated by the arrow. (b) Normal incidence spectral emissivity of liquid platinum as a function of temperature at 1064 ( l> ), 632.8 (Ez),514.5 ( x ), and 488 nm (o). The solid line represents the least-squares fit to the data, The melting point is indicated by the arrow.

monicity factors could contribute another 1-3 cal tool-1 K-1 to Cp1. What should one expect for Cp of the liquid? Figure 5 shows the possibilities. For a liquid metal, does Cp 1 increase, remain constant or decrease with increasing temperature? Experimental results indicate that Cp~ at the melting point is fairly constant over a temperature range of several hundred degrees. From exploding wire data, one expects Cpt to show a T 2 to T 3 d e p e n d e n c e at temperature in the 5000 K range [17]. Obviously, vaporization will be a limiting factor to being able to maintain a liquid phase at ambient pressure at very high temperatures. Table 1 lists measured and estimated heat capacities for many liquid metals.

Levitation techniques have several primary adfantages over traditional calorimetric methods for studying liquid metals: (1) The possibility of contamination from a container is eliminated. (2) Rapid heating to a desired temperature is possible. (3) Real-time emissivity measurements for a levitated sample guarantee accurate true temperatures from real-time brightness temperatures. (4) Supercooled liquids can be prepared and their properties measured. A major disadvantage is that non-conductors cannot be levitated by electromagnetic coils. Acoustic levitation at the nodes of standing sound waves can be used for studies up to about 1 0 0 0 K [18] and gas jet (Bernoulli) levitation of heated solids can be used up to about 2500 K or until the sample melts [19]. Continu-

J. L. Margrave

86

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Thermophysical properties of liquid metals TABLE 1. A comparison of liquid metal heat capacities (J molK- t ) at high temperatures

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ous wave or pulsed laser heating can be used. A n o t h e r alternative to provide levitation is the microgravity environment of space, with heating provided by solarpowered oscillators, resistors or lasers [20].

3. Densities of liquid metals Classical liquid density measurements (pycnometry or use of floats) are not feasible at 1 5 0 0 - 2 0 0 0 K or higher because chemical reactions with containers and floats are unavoidable. E v e n the most stable oxides yield suboxides in the presence of pure metal reducing agents; liquid metals are almost universal solvents to form alloys. Thus, there are essentially no reliable densities of liquids for T > 2000 K and only a few values for liquids in the range 1 5 0 0 - 2 0 0 0 K [1, 21]. Levitation offers a unique approach for determination of liquid metal densities since one can photograph a levitated droplet of known mass from several angles and at several temperatures. Since the levitation coils have cylindrical symmetry, the liquid droplets also tend to have cylindrical symmetry and, thus, their volumes and densities are easily determined. From the liquid densities just above the melting points one can derive A Vfusion , and from p ( T ) the isotropic thermal expansion coefficient. Further, one would like to know liquid metal compressibilities since these would allow one to predict Cpl(T) from the relation

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MP melting point; L levitation measurements, E exploding wire measurements, D drop calorimetry measurements; values in parentheses are estimated.

where a = ( 1 / v ) ( 6 v / 6 T ) p , t5 = - ( l / v ) ( d v / 6 p ) r , Ce, is the electronic contribution and Cv = 3R. These parameters would explain the relatively flat CpI (T) behavior for at least a few hundred degrees above the melting point but are consistent with an eventual T 2 or even T 3 trend at temperatures in the 3 0 0 0 - 5 0 0 0 K range.

4. Surface tensions and viscosities Levitated liquid metal droplets appear to be spherical to the naked eye but there is evidence of internal

J. L. Margrave /

Thermophysical properties of liquid metals

mixing and stirring caused by the skin-effect coupling between the r.f. induction coils and the sample producing eddy currents in the skin, which can cause density and temperature gradients. Slow movements of impurity islands on the surface are sometimes observed but these tend to be stirred into the melt a n d / o r to disappear via high temperature evolution of gases, CO, N2, MOx, etc., as clean metal surfaces are formed. Fast photography (1/1000 second stills, 1 0 0 0 10 000 frames per second strip camera shots or fast video cameras) reveal that levitated liquid drops are vibrating and rotating in complex, coupled modes as predicted by the mathematical analyses, of L a m b [22] and Chandrasekhar [23]. T h e s e workers derived equations which relate shape, mass, surface tension and viscosity to the characteristic vibration-rotational freqencies. T h e motions can be simplified by eliminating rotation either using oriented acoustic generators or by a slow flow of H e from a nozzle at an appropriate location. Damping of induced vibrations from acoustic sources or pulsed gas jets provides information about viscosities. Ultimately, one needs d ( T ) and r / ( T ) i n order to model liquid metals and undersand fully the interatomic potentials that characterize liquid metals. Although levitation-derived 6 ( T ) and t/(T) are available for only a few liquid metals, there are literature values derived from other types of measurements. Levitation measurements will make values derived from other types of measurements. Levitation measurements will make it possible to eliminate contamination from containers and to achieve isothermal conditions. New results for various liquid metals and alloys are becoming available.

5. Levitation of alloys and compounds Since binary, ternary and more complex alloys are still metallic conductors, it is convenient to levitate brasses, stainless steels, turbine blade alloys and many others. Actually one can levitate one metal, melt it and then add small amounts of another metal to produce an alloy. Since liquid metals are often totally miscible, one has the option of preparing arbitrary stoichiometries and, by splat cooling or other quenching techniques, to produce amorphous or glassy metallic alloys. Also, conducting compounds such as TiC, ZrC, TaC, TiB2,ZrB 2, etc. can be levitated. Thus, Cpl(T), AHfusion, % r, 6 ( T ) and t/(T) for alloy systems can be measured. T h e s e are important thermophysical properties which are critical in casting, molding and crystal operations as, for example, in preparing turbine blades for jet engines.

87

Acknowledgments Levitation studies at Rice University and at the Houston Advanced Research Center have been supported by the US Department of Energy, the National Aeronautics and Space Administration, the National Science foundation, and the Robert A. Welch Foundation.

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Thermophysical properties of liquid metals

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18 E.H. Trinh, Rev. Sci. Instrum., 56 ( 11 ) (1985) 2059. E. H. Trinh, J. Robey, A. Arie and M. Gaspar, Mater. Res. Soc. Symp. Proc., 87(1987) 57. R. E. Apfel, J. Acoust. Soc. Am., 59(2)(1976) 339. C. A. Rey, R. W. Whymark, T. J. Denley and D. R. Merkley, in G. E. Rindohe (ed.), Mater. Res. Soc. Symp. Proc., Reduced Gravity Environment of Space, Vol. 9, Materials Research Society, Pittsburgh, PA, 1981, p. 137. R. R. Whymark, C. A. Rey, J. Yeearud and R. Broz, 17th Aerospace Sci. Meet., 1979. C. S. Ray and D. Day, Mater. Res. Soc. Symp. Proc., 87 (1987)239. 19 S. Krishnan, P. C. Nordine, J. K. R. Weber and R. A. Schiffman, High Temp. Sci., 30(1990) 163. J. P. Coutures, J. C. Rilley and D. Billard, 6th European Symp. on Materials Science under Microgravity Conditions, 2-60, December, 1986. 20 R.E. Halpern, Prog. Astronaut. Aeronaut., 108(1986) 1. G. Rindone (ed.), Materials processing in the Reduced Gravity Environment of Space, North-Holland, Amsterdam, 1982. 21 T. Saito, Y. Shiraishi and Sakuma Y., Trans. AIME, 227 (1963) 1226. A. E. E1-Mehairy and R. G. Ward, Trans. AIME, 227(1963) 1226. S. Y. Shiraishi and R. G. Ward, Can. Met. Q., 3 (1) (1964) 117. 22 H. Lamb, Hydrodynamics, Cambridge University Press, Cambridge, 1932; Dover, New York, 1945, p. 473, 6th edn. 23 S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, 1961.