Thermophysical Properties of the Liquid Ga–In–Sn Eutectic Alloy

Article pubs.acs.org/jced

Thermophysical Properties of the Liquid Ga−In−Sn Eutectic Alloy Yuriy Plevachuk,*,† Vasyl Sklyarchuk,† Sven Eckert,‡ Gunter Gerbeth,‡ and Rada Novakovic§ †

Department of Metal Physics, Ivan Franko National University, Lviv, 79005 Ukraine Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328 Dresden, Germany § National Research Council (IENI-CNR), Genoa, 16149 Italy ‡

ABSTRACT: Among different Ga-based alloys the properties of the Ga−In−Sn eutectic alloy make it particularly suitable for many applications, in particular as it is liquid at room temperature. However, the experimental data on its thermophysical properties are rather discrepant. In this work, the electrical and thermal conductivity, thermoelectric power, viscosity, surface tension and density of the Ga−In−Sn eutectic have been investigated in the temperature range between the melting temperature and 700 K. The experimental results obtained are compared with the data available in the literature.

measuring techniques for flow diagnostics. For example, GaInSn was used for flow modeling in crystal growth technologies,6 for modeling of the continuous casting of steel,7 for investigations of liquid metal two-phase flows,8 or for a laboratory experiment on the occurrence of the astrophysically relevant magneto-rotational instability.9 In view of the growing number of applications of GaInSn the detailed knowledge of respective material data becomes more and more important. Furthermore, corresponding numerical simulations require the availability of an extensive database of thermophysical properties as a function of temperature. Some measurements of the thermophysical properties are already known for GaInSn, however, discrepancies in the reported results, different eutectic compositions10 and the investigated temperature ranges as well as a very limited number of measured points require new precise measurements in order to obtain reliable data over a wide temperature range.5 The present paper presents measurements of electrical conductivity, thermoelectric power, viscosity, thermal conductivity, surface tension and density of the GaInSn eutectic alloy at the specific composition Ga77.2In14.4Sn8.4 at. %, which corresponds to the composition of Ga67In20.5Sn12.5 in wt %. The measurements were carried out for temperatures ranging from the melting point to 700 K. The new thermophysical properties data are compared with the corresponding data available in the literature. The new data obtained together with the parameters describing the temperature dependence of each property can be used for modeling, simulation, and optimization of processes involving liquid metals.

1. INTRODUCTION Liquid metals are applied in many technical fields such as heating and cooling systems, thermostats, switches, or measuring devices like thermometers and barometers. Gabased alloys exhibit low melting points, and hence, they appear to be very attractive for many applications.1 The ternary system GaInSn involves a eutectic composition which is liquid at room temperature. Owing to the low reactivity and toxicity of the components, GaInSn is often used or considered as a potential substitute for mercury such as, for example, in liquid metal thermometers.2 It is well-known that mercury is particularly toxic, mainly because it evaporates readily at room temperature. In contrast, the vapor pressure of GaInSn is extremely low at room temperature. Unlike many liquid metals, the eutectic alloy GaInSn is chemically compatible with a wide variety of metals (except aluminum and its alloys), plastics, rubbers, and glasses at low temperatures. GaInSn plays an important role as operating fluid in liquid metal experimental facilities, which are used for modeling of various liquid metal processes in the industrial fields of metallurgy, casting, crystal growth, energy process engineering, or magnetohydrodynamics. The use for this modeling purpose started mainly in the eighties,3 though first examples of using this room-temperature melt date back to the sixties.4 The usage in the research laboratory together with various handling and safety aspects was recently reviewed by Morley et al.5 Experimental studies on an industrial scale with hot metallic melts (T > 573 K) require formidable effort and expense. The low melting point of the GaInSn alloy enables the realization of cost-saving model experiments and permits detailed investigations of the flow structure and related problems with a high grade of flexibility. The manageable chemistry guarantees an efficient handling and an unproblematic use of various © 2014 American Chemical Society

Received: October 3, 2013 Accepted: February 11, 2014 Published: February 18, 2014 757

dx.doi.org/10.1021/je400882q | J. Chem. Eng. Data 2014, 59, 757−763

Journal of Chemical & Engineering Data

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temperature field over the height of the apparatus. Tungsten− rhenium WR5/20 thermocouples were used in the experiments. Two thermocouples placed in the body of the inner cylinder allow for an examination of the radial temperature distribution. The coefficient of the thermal conductivity can be calculated from the formula for the heat transfer in a cylindrical layer. The design of the apparatus assures a maximum reduction of convection and heat loss. The resultant error of the thermal conductivity measurements is about 7 %. 2.3. Viscosity. The measurements of the viscosity were carried out using a computer-controlled oscillating-cup viscosimeter.13 The dynamic viscosity has been calculated from the corresponding logarithmic decrement of damping and the period of oscillations by using the Roscoe equation. The experiments were performed in argon atmosphere under a negligible excess pressure of about (0.02 to 0.03) MPa. Each sample of about 30 g was accurately weighed and subsequently placed in a cylindrical graphite crucible with internal diameter of 14 mm. A homogeneous temperature field up to 0.3 K in the range of absolute values between the alloy melting temperature Tm and 800 K was created inside the furnace. The temperature was measured with a WRe-5/20 thermocouple arranged just below the crucible. This method of viscosity determination is accurate to within ± 3 %. 2.4. Surface Tension and Density. The surface tension and the density were measured using the large drop method, which is a modification of the sessile drop method.14 A detailed description of a typical setup was given by Lee et al.15 where the large drop method has been used to determine the surface tension of liquid metals. A circular crucible, which upper circumferential edge is chamfered to an acute angle, will be overfilled with the fluid to be measured. As a result, an axisymmetric meniscus is produced standing above the rim with a diameter exceeding the diameter of the crucible. A detailed analysis shows that this construction reduces the error of the drop volume determination, which accounts for the main error in density determination. The error resulting from mass determination is negligibly small. In order to avoid oxidation of the samples, the working volume of the chamber was evacuated to 10−6 Pa prior to the experiment, and backfilled with a reducing atmosphere of a mixture of Ar−10 % H2. The pressure inside the chamber slightly exceeded the ambient pressure at about 1.05·105 Pa. The surface tension of metallic melts is significantly affected even by a very low oxygen content in the surrounding atmosphere, as reported by Ozawa et al.16 Although a high purity H2-containing gas has been used for the measurements, some amount of oxygen and moisture are always included in the gas as impurities. Using an Ar−10 % H2 mixture, (moisture level 0.5 ppm; maximum impurity level 1.0 ppm), the oxygen partial pressure of the gas is thermodynamically deduced from the chemical reaction H2 + (1/2)O2 ↔ H2O. The equilibrium constant K of this reaction is very large and thus the concentrations of generated hydrogen and oxygen are very low even at relatively high temperatures. Indeed, the oxygen partial pressure of an Ar − 10 % H2 containing 0.5 ppm of moisture was calculated for different temperatures using the standard Gibbs free energy of formation of H2O,17 and for the initial and the final temperatures, the values of pO2 = 10−80 Pa (with K = 8.86·1084) and pO2 =10−26 Pa (with K = 1.13·1031), respectively, were obtained. Accordingly, the surface active elements within the ambient atmosphere had negligible effect on the surface tension measurements. The temperature was

The paper is organized as follows. At first, the main characteristics of the measurement methods and instruments used to measure the thermophysical properties are described in detail. Second, the results obtained for each property are presented and discussed in view of the corresponding data available in literature.

2. MATERIALS, MEASUREMENT METHODS, AND INSTRUMENTATION Almost spherical specimens of about (15 to 25) mm3 have been prepared from the pure components with a mass purity of 99.999 % (ChemPur: In, Sn rods, Ga granules; Table 1) by Table 1. Sample Information chemical name

source

mass purity

Ga granules In rods Sn rods

ChemPur ChemPur ChemPur

99.999 % 99.999 % 99.999 %

mixing the pure metals and melting in evacuated ((10 to 15) Pa) and sealed quartz ampules. The risk of contamination by oxygen and silicon coming from the contact with the silica ampule was negligible. Prior to the measurement, each sample has been mechanically abraded by using a stainless steel cutter and carefully cleaned by chemical means in ultrasonic bath with propanol. The nominal alloy composition was confirmed by SEM-EDS analyses. The samples were weighed before and after the experiments and no loss of their initial mass was observed. 2.1. Electrical Conductivity and Thermoelectric Power. The electrical conductivity and the thermoelectric power were measured by a contact method in accordance with the 4-point scheme. The experiments were performed in an argon atmosphere. Graphite electrodes for current and potential measurements were placed in the wall of a cylindrical BN-ceramic measuring cell along its vertical axis. These potential electrodes were equipped with thermocouples for temperature measurements. Single thermoelectrodes of these thermocouples were used for electrical conductivity and thermoelectric power determination. The melting temperature was measured by WRe-5/20 thermocouples in close contact with the liquid. The cell construction permits to carry out the electrical conductivity and thermoelectric power measurements simultaneously in one run. More details on this method and its experimental realization can be found in Plevachuk and Sklyarchuk.11 In order to obtain reliable data the measurements were performed several times. The resultant errors of the electrical conductivity and thermoelectric power measurements are about 2 % and 5 %, respectively. 2.2. Thermal Conductivity. An experimental arrangement based on the steady-state concentric cylinder method was used for thermal conductivity measurements.12 The apparatus comprises two coaxial cylinders (stainless steel and boron nitride BN or graphite) separated by a gap, into which the melt is poured. A central hole is drilled in the inner cylinder for an internal heater made of a molybdenum wire, wound on an alumina form. The inner heater is used to produce the necessary temperature gradient in the investigated melt layer. The cell is closed by a BN cover, which is sealed with a special glue based on a finely dispersed BN powder. The outer threesection furnace is made of molybdenum wire wound on a BN form. The outer heater produces an overall temperature level, whereas its upper and lower sections permit a regulation of the 758



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measured by a WRe5/20 thermocouple placed near the specimen and was held constant within a tolerance of 1 K. A computer-controlled CCD camera was used for the determination of the drop parameters. An image of the drop profile is captured by the CCD camera and analyzed using an edge detection algorithm that locates the edge curve r(φ), where r and φ are the radius and the azimuthal angle with respect to the drop center at the rim level. The surface tension was calculated using the Kozakevitch method,18 which is based on the Laplace−Young equation. The surface tension data were obtained with an accuracy of about ± 3 %. Each sample was measured several times in order to get representative values for the density. The total uncertainty for the density measurements is estimated to be about 1.5 %.

Table 2. Temperature Dependence of Electrical Conductivity, Thermoelectric Power, and Thermal Conductivity for the Liquid GaInSn Eutectic Alloya K 291 293 296 300 303 304 306 310 312 314 316 321 333 352 373 393 414 433 454 473 494 513 533 553 573 593 613 631 653 673 693 723

3. RESULTS AND DISCUSSION 3.1. Electrical Conductivity and Thermoelectric Power. There is only a limited number of papers related to electrical conductivity studies of the GaInSn eutectic alloy. Our new electrical conductivity results are listed in Table 2 and shown in Figure 1 together with the literature data.1,19,20 For comparison, recent electrical conductivity data of pure Ga as well as of pure Sn are also shown here.21 The electrical conductivity σ(T) and the thermoelectric power S(T) of the sample were measured several times with a heating and cooling rate of 20 K·h−1 between the melting temperature Tm = 283.7 K and approximately 700 K. Some data scattering and discrepancies between heating and cooling curves were observed in the first experimental run, but the variance of the measured data became less pronounced during subsequent cycles indicating a better homogenization of the melt. Fitting the experimental data (Figure 1) with a parabolic function, the temperature dependence of the electrical conductivity obtained (in units of Ω−1·cm−1) in the investigated temperature range can be approximated by the following relationship: σ(T ) = σ0 − 49.8(T − Tm) + 0.0476(T − Tm)2 −1

(1)

dS (T − Tm) dT

−1

Ω

T

cm

−1

K

33 000 32 900 32 700 32 600 32 400 32 300 32 200 31 900 31 800 31 700 31 500 31 200 31 000 29 400 28 800 28 200 27 200 26 700 26 100 25 600 24 800 24 500 24 100 23 300 23 000 22 200 21 900 21 500 21 200 21 000 20 700 20 200

291 299 305 316 322 334 345 350 362 379 391 407 430 442 452 477 483 495 500 516 528 539 551 563 574 595 608 621 632 656 668 687

S μV·K

λ

T −1

−0.52 −0.59 −0.60 −0.65 −0.68 −0.73 −0.78 −0.81 −0.86 −0.95 −1.10 −1.16 −1.20 −1.27 −1.37 −1.40 −1.43 −1.46 −1.52 −1.60 −1.66 −1.74 −1.77 −1.85 −1.87 −1.96 −2.00 −2.05 −2.13 −2.23 −2.29 −2.36

K

−1

W·m ·K−1

292 299 305 312 319 325 335 350 363 370 384 401 416 424 431 439 450 460 468 479 488 499 508 517 527 537 549 558 568 577 588 598

23.9 24.4 24.7 25.1 25.5 25.9 26.4 27.3 27.9 28.2 29.4 29.8 30.7 31.1 31.4 32.0 32.2 32.4 33.5 33.6 34.1 34.4 34.9 35.2 35.5 35.9 36.2 36.5 36.8 37.2 37.5 38.0

Standard uncertainty u is u(T) = ± 1 K, and the combined expanded uncertainties Uc are Uc (σ) = ± 300 Ω−1·cm−1, Uc (S) = ± 0.04 μV· K−1, Uc (λ) = ± 2.3 W·m−1·K−1 (level of confidence = 0.95). a

−1

where σ0 = 33170 Ω ·cm is the electrical conductivity at the melting temperature. The electrical conductivity data obtained in the present study are lower than those reported previously.1,19 At the same time, our data are higher than the curve suggested in the book of Müller and Bühler.20 The latter correlation exhibits a drastic difference in slope that was not confirmed by any other measurements. Unfortunately, we do not know the source of the data reported by Müller and Bühler20 as well as by which method they were obtained. A negative temperature coefficient of the electrical conductivity was reported by all authors; however, Figure 1 reveals a disagreement between different sources of electrical conductivity data. Even the two data sets obtained by the same authors1,19 show significant deviations. The discrepancy between the experimental data might be attributed to possible contaminations of the alloy. In particular, a modification of the sample composition due to oxidation may have had an influence in the previous measurements. The thermoelectric power of the GaInSn eutectic alloy slightly decreases from its melting temperature to 700 K and our measured data obey a linear law as S(T ) = S0 +

σ

T

where S0 = −0.5 μV·K−1 is the thermoelectric power at the melting temperature and dS/dT = −4.679·10−3 μV·K−2 is the temperature coefficient of thermoelectric power. The values of the thermoelectric power remain negative in the liquid and the data obtained in this study are in good agreement with the data reported by Prokhorenko et al.1 3.2. Thermal Conductivity. The experimental determination of thermal conductivity λ(T) of the GaInSn eutectic alloy has been carried out in the temperature range from its melting point up to 600 K. The temperature dependence of λ(T) can be described by an empirical second-order polynomial λ(T) = λ 0 + 0.0614(T − Tm) + 4.9·10−5(T − Tm)2 −1

(3)

−1

where λ0 = 23.4 W·m ·K is the thermal conductivity at the melting temperature. The new experimental data together with the corresponding literature data are shown in Figure 2 and listed in Table 2. The data derived from the electrical conductivity data by the Wiedemann−Franz-Lorenz law22 are also presented here for comparison. The thermal conductivity increases linearly with temperature from its melting temperature up to approximately 390 K, while the data obtained at

(2) 759



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results and to check the previous runs. Our analysis revealed that the main source of discrepancies was associated with the temperature measurements by the thermocouples. From several experimental runs and corresponding analysis we found that the chemical reaction between gallium and at least one of the imperfectly insulated thermocouples may cause an error in temperature determination, which in turn affects the thermal conductivity values. In the measurements presented here the thermocouples were inserted in an alundum tube placed in slots in the inner cylinder of the device. Therefore, all thermocouples were not in direct contact with the sample and protected against the gallium. This effect may explain why the data obtained here differ from the respective measurements published so far.1,19 3.3. Viscosity. The dynamic viscosity η(T) of the GaInSn eutectic alloy has been measured during heating and cooling over a wide temperature range between the melting temperature and 700 K with steps ranging from (5 to 10) K. All samples were subjected to at least two heating−cooling cycles. Several experiments with different samples of the same composition revealed a good reproducibility of the results. The GaInSn melt is a Newtonian liquid and the temperature dependence of its viscosity can be described by an Arrheniustype empirical equation

Figure 1. Temperature dependence of (a) electrical conductivity and (b) thermoelectric power for the liquid GaInSn eutectic alloy: ○, GaInSn; ●, Ga; this work. The literature data (a): Δ, ref 1; ▼, ref 19; −, ref 20; □, ref 21 (Sn) and (b) ○, GaInSn; ▲, ref 1, are taken for comparison.

⎛ E ⎞ ⎟ η(T ) = η0 exp⎜ ⎝ RT ⎠

(4)

where R = 8.3144 J·mol−1·K−1 is the gas constant, T is the absolute temperature (K), and η0 = 0.4352 mPa·s, and E = 3904 J·mol−1 are the fit parameters. The dynamic viscosity of the GaInSn decreases for increasing temperature. The experimental data are listed in Table 3, and the viscosity fit curve (eq 4) together with the available literature data20,23 are shown in Figure 3. Table 3. Temperature Dependence of Viscosity, Surface Tension, and Density for the Liquid GaInSn Eutectic Alloya η

T K

Figure 2. Temperature dependence of thermal conductivity for the liquid GaInSn eutectic alloy, ○, GaInSn, this work. The literature data: ∇, ref 1; ▲, ref 19; and , the values calculated from electrical conductivity σ(T) by the Wiedemann−Franz−Lorenz law are included for comparison.

mPa·s 299 307 313 324 339 354 369 386 404 424 443 464 487 509 533 555 577 598

higher temperatures deviate slightly from linearity, as shown in Figure 2. The corresponding values calculated from the electrical conductivity (dashed line) are consistent with our experimental findings within experimental error only in the low-temperature range up to about 390 K. Large discrepancies can be observed between the present experimental results and the experimental data reported by Prokhorenko.1,19 Experimental difficulties related to convection, uncertain wetting conditions, an insufficient level of purity, or oxidation effects can significantly reduce the accuracy of thermal conductivity measurements. Indeed, the aforementioned problems could be responsible for such a large variance between different data sets. The total error for thermal conductivity measurements in our facility is about 7 %. The experiments were repeated under different conditions in order to get more precise and accurate

γ

T 2.09 2.03 1.98 1.85 1.76 1.63 1.55 1.44 1.36 1.30 1.24 1.17 1.15 1.10 1.07 1.04 1.00 0.95

K

mN·m 306 346 361 385 415 452 485 520 552 573

−1

585 588 579 590 583 591 592 588 577 581

T

ρ

K

g·cm−3 293 299 313 324 333 344 363 373 383 393 414 424 433 444 454 473 484 493

6.36 6.33 6.31 6.34 6.31 6.34 6.30 6.32 6.29 6.23 6.29 6.25 6.22 6.24 6.25 6.20 6.18 6.20

Standard uncertainty u is u(T) = ± 1 K, and the combined expanded uncertainties Uc are Uc (η) = ± 0.05 mPa·s, Uc (γ) = ± 17 mN·m−1, and Uc (ρ) = ± 0.09 g·cm−3 (level of confidence = 0.95). a

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Figure 3. Temperature dependence of the viscosity for the liquid GaInSn eutectic alloy, ○, GaInSn, this work. The literature data: −, ref 20; ●, ref 23, are included for comparison.

Figure 4. Temperature dependence of the surface tension for the liquid GaInSn eutectic alloy, ○, this work. The surface tension of pure Ga, ; In, ·−· and literature data ▲, ref 1; ●, ref 5; −, ref 28, are given for comparison.

The discrepancy between the viscosity data obtained in this study and those reported by Galchak23 reaches values up to 7 %. Large differences are found between the two data sets especially at temperatures lower than 340 K. A good agreement exists in this temperature range between the present data and the values reported by Müller and Bühler20 up to temperatures of about 340 K. However, a distinct deviation becomes apparent for higher temperatures. It should be noted that the viscosity as a structurally sensitive property does not reveal any peculiarity and exhibits a smooth exponential variation in the entire temperature range. As mentioned in section 2.3, the uncertainty of the viscosity measurement in our experiment is about 3 %. An additional uncertainty of up to 2.7 % originates from the curve fitting according to eq 4. Thus, for the fit curve (4) a total uncertainty of about 4 % can be estimated as the square root of the sum of the squares of the separate uncertainties. 3.4. Surface Tension and Density. The surface tension of metallic melts γ(T) is strongly affected by certain surface-active elements (mainly oxygen and sulfur) that, even if occurring in traces, can drastically reduce the surface tension of metallic melts and affects the reliability of the experimental data.24 For these reasons, special care has to be taken for measurements of the surface tension for avoiding even the smallest surface-active quantities of surfactants or impurities. It has been established that the surface tension data obtained under the abovementioned clean conditions decrease with temperature linearly and obey the Eötvös law.25 The available surface tension data of liquid Ga−In−Sn alloys comprising our results and literature data1,5,26−32 including a review by Keene dedicated to Sn-based solders29 exhibit a significant scatter. Specific measurements concerning the surface tension of the GaInSn eutectic alloy were only reported in refs 1, 5, and 28. The temperature dependence of the surface tension of the GaInSn eutectic alloy, pure Ga and In, obtained in the present work and corresponding literature data1,28 are shown in Figure 4. The here measured values are listed in Table 3. The surface tension decreases only slightly with increasing temperature, following a linear relationship. γ(T ) = γ0 + dγ /dT (T − Tm)

value showed a deviation of about ± 5 mN·m−1around the mean value. In addition, the surface tension of pure metals Ga and In was also measured and, in both cases, the corresponding data obey a linear law, described by eqs 6 and 7, respectively. γGa = 712 − 0.072(T − 303)[mN· m−1] −1

γIn = 559 − 0.115(T − 430)[mN·m ]

(6) (7)

The surface tension γ0 of eutectic GaInSn determined at its melting point differs between (533 and 534) mN·m−1 in literature5,28 and the here measured value of 587 mN·m−1. The temperature coefficient dγ/dT was given as −0.127 mN·m−1· K−1 by Migai et al.,28 whereas the here obtained value is −0.0109 mN·m−1·K−1 (eq 5). Ga−In−Sn melts are prone to oxidation and behave similarly with respect to liquid Ga−Sn and Ga−In alloys. Several authors reported a nonlinear behavior of the surface tension polytherms.29 Dadashev et al.31 suggested a temperature dependence of the surface tension of In−Ga, Ga−Sn, and Ga−In−Sn melts being far from a linear relation. These authors investigated the aforementioned systems over a wide temperature range by using the maximum bubble pressure method and considered ternary alloys with a Ga-content higher than 25 at. %. The observed peculiarities in the surface tension polytherms are mainly caused by the presence of oxygen in the melts.24 Our new results do not confirm a nonlinear behavior, at least for the eutectic composition, as shown in Figure 4. Kononenko and Sukhman26 and Ibragimov et al.27 reported the iso-surface tension lines for the Sn−Ga−In system, calculated for (523 and 773) K. For near eutectic alloy compositions the surface tension values vary between (575 and 590) mN·m−1. These literature data26,27 agree well with our measurements (see Figure 4). The surface tension data obtained in our study have also been analyzed in view of theoretical models. Mathematical formalisms of different models and their application to calculate the surface tension of liquid Pb−Bi−Sn alloys were described in detail in a previous paper.33 In the present work we discuss only the comparison between the results obtained from the modeling and the new experimental data presented here. The surface tension of liquid Ga−In−Sn ternary alloys is predicted using the Butler model.33 The excess Gibbs energy terms of the liquid Ga−Sn, Ga−In, and In−Sn binary phases were taken from literature,34−36 respectively. The surface tension of liquid

(5)

−1

where γ0 = 587 mN·m is the surface tension at the melting temperature and dγ/dT = −0.0109 mN·m−1·K−1 is the temperature coefficient of the surface tension. Each measured 761



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Ga and In obtained in the present study are described by eqs 6 and 7. It is important to mention that the experimental values of surface tension of gallium and indium (eq 6 and eq 7) and GaInSn were obtained under the same environmental conditions. In order to reduce the overall error in the calculated surface tension values, the new surface tension data of liquid Ga and In (eqs 6 and 7) were taken together with that of Sn described by γSn = 556 − 0.064(T − 505)[mN·m−1]

(8)

and obtained by the same experimental method, i.e., the large drop method.37 The reference data for the pure components, such as the melting temperatures, densities and molar volumes were taken from Iida and Guthrie. 25 Combining the corresponding descriptions of the three binary subsystems, the surface tensions of liquid Ga−In−Sn alloys have been calculated by Butler’s model in the regular solution approximation for T = 480 K. The results of calculations are shown in Figure 5.

Figure 6. Temperature dependence of the density for the liquid GaInSn eutectic alloy, ○ and Ga, ●, this work. The literature data on liquid GaInSn: Δ, ref 19; ▼, ref 20 and pure Ga: −, ref 25; , ref 39, are taken for comparison.

The density of pure Ga has been measured several times. Published data show a significant scattering,25,39 which motivated us to measure the density of liquid Ga, too. We suggest that gallium, which is the major component of the GaInSn eutectic alloy and exhibits a strong oxidation liability, is responsible for the observed scattering.

4. CONCLUSIONS Several thermophysical structure-sensitive properties of the liquid GaInSn eutectic alloy have been measured in the temperature range from the melting temperature up to 700 K. The obtained temperature dependent experimental data on the electrical conductivity, thermoelectric power, thermal conductivity, dynamic viscosity, surface tension, and density have been analyzed and compared with the available literature data. For each property studied, a fitted relation is derived. For some properties, the obtained data differ from the literature data quite substantially. Our results demonstrate that measurements of the thermophysical properties of the eutectic GaInSn alloy depend significantly on experimental conditions such as the purity level of the alloy, the oxidation rate, the wetting behavior, etc.

Figure 5. Iso-surface tension line for liquid Ga−In−Sn alloys calculated by using the Butler model for T = 480 K. The square symbol (■) represents the GaInSn eutectic alloy.

■

The experimental value of the surface tension of the GaInSn eutectic alloy, obtained at T = 480.5 K was 593 mN·m−1 (Figure 4), while the corresponding calculated value amounts to 614 mN·m−1 as shown in Figure 5. The results demonstrate that our experimental data are in good agreement with the value calculated by the Butler model (Figure 5) as well as with the values for liquid Ga−In−Sn alloys predicted by different models at higher temperatures.38 The temperature dependence of density for liquid metals and alloys is linear.25 The same trend follow our data shown in Figure 6 and listed in Table 3 that can be described by ρ = ρ0 + dρ /dT (T − Tm)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The authors acknowledge Deutsche Forschungsgemeinschaft in frame of the Collaborative Research Centre SFB 609 and the Helmholtz Association in frame of the Helmholtz Alliance LIMTECH for the financial support of this work. Notes

The authors declare no competing financial interest.

■

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REFERENCES

(1) Prokhorenko, V. Y.; Roshchupkin, V. V.; Pokrasin, M. A.; Prokhorenko, S. V.; Kotov, V. V. Liquid Gallium: Potential Uses as a Heat-Transfer Agent. High Temp. 2000, 38, 954−968. (2) Geraberger Thermometerwerk Ltd., German patent DE 4227434C2, August 1994, U.S. patent 6019509, February 2000. (3) Bojarevics, A.; Gorbunov, L. Effect of magnetic fields of different orientation on thermogravitational convection in an electrically

where ρ0 = 6.58 g·cm−3 is the density at the melting temperature and dρ/dT = −7.76·10−4 g·cm−3·K−1 is the temperature coefficient of the density. The new data are in good agreement with results obtained by the method of hydrostatic weighing28 and are slightly lower than the data of Prokhorenko et al.,32 obtained by the “thermometer” method. 762



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Thermophysical Properties of the Liquid Ga–In–Sn Eutectic Alloy

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