Viscosity of molten Mo, Ta, Os, Re, and W measured by electrostatic levitation

J. Chem. Thermodynamics 65 (2013) 1–6

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Viscosity of molten Mo, Ta, Os, Re, and W measured by electrostatic levitation Takehiko Ishikawa a,⇑, Paul-François Paradis a, Junpei T. Okada a, Malahalli Vijaya Kumar a, Yuki Watanabe b a b

Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan Advanced Engineering Services Co. Ltd., 1-6-1 Takezono, Tsukuba, Ibaraki 305-0032, Japan

a r t i c l e

i n f o

Article history: Received 20 February 2013 Received in revised form 11 May 2013 Accepted 20 May 2013 Available online 28 May 2013

a b s t r a c t Viscosities of tungsten, rhenium, osmium, tantalum, and molybdenum have been measured by the oscillation drop method with an improved procedure. The measured data exhibit less-scatter than our previous measurements. Viscosity at the melting temperature of the investigated metals showed a good agreement with literature values and some predicted values. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Levitation Viscosity Refractory metals

1. Introduction To improve the accuracy of computer simulations in materials processing for casting and crystal growth, the knowledge of thermophysical properties of high temperature metals and alloys is of paramount importance. Noncontact techniques have been widely used for property determination of high temperature materials [1–5]. Among thermophysical properties, the viscosity is one of the most important since it corresponds to atomic mobility in the melt. Because of their high melting points and their reactivity at high temperatures, it is challenging to perform the viscosity measurements of refractory metals in their liquid state using conventional methods. Electrostatic levitators bypass the difficulties associated with high temperature processing and allow quick viscosity measurements of refractory metals [6–8]. Viscosities of refractory metals whose melting temperatures are above 2000 K have been measured using oscillating drop method in our laboratory [9–15]. This oscillating drop technique [16] assumes that the levitated droplet is free from any external forces. However, it is difficult to satisfy this condition on the ground, because a strong external force is necessary to levitate a sample against gravity. The effects of the external field on viscosity measurements were experimentally confirmed by changing the sample size and the parameters of sample position control [17]. Moreover, a numerical simulation

⇑ Corresponding author. Tel.: +81 5033626087; fax: +81 298683956. E-mail address: [email protected] (T. Ishikawa). 0021-9614/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2013.05.036

based on a simple mass-spring-damper system was conducted to reproduce the experimental observations. Based on the above results, it was found that our previous viscosity measurements were affected by the sample positioning force. It was also found that this effect could be minimized when the frequency range of the sample position control and the oscillation frequency of the levitated sample were separated. Viscosities of Ti, Ni, Zr, Nb, Ru, Rh, Hf, Ir, and Pt were measured again using the improved procedure and were reported in an earlier publication [18]. In this paper, the viscosities of the refractory metals whose melting temperature is above 2800 K are reported. This paper briefly describes the experimental setup, the improved procedure for the viscosity measurement, and presents the viscosity data for molten molybdenum, tantalum, osmium, rhenium, and tungsten.

2. Experiment setup 2.1. Electrostatic levitator The electrostatic levitation system used in our laboratory is similar to the one developed by Rhim et al. [19] but includes several modifications. A detailed description of the facility is given elsewhere [9]. Figure 1 depicts schematically the apparatus. It consisted of a stainless steel chamber that was evacuated to a pressure of around 105 Pa. The chamber housed a pair of parallel disk electrodes, typically 10 mm apart between which a positively charged sample was levitated. The top electrode was kept electrically

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T. Ishikawa et al. / J. Chem. Thermodynamics 65 (2013) 1–6

(9 ) (5 )

(a)

(9 )

(2 )

(8 )

(5 ) (7 )

(7 )

(b) Photo detector with slit

(1 )

Position control + oscillation signal

(10)

He-Ne laser beam

(4 )

Sample shadow

(7 )

(3 )

(11)

(6 ) (10)

(c)

FIGURE 1. Schematic view of the electrostatic levitation furnace and its diagnostic apparatus: (1) sample, (2) top electrode, (3) bottom electrode, (4) side electrodes, (5) He-Ne lasers, (6) position detectors, (7) CO2 laser beams, (8) Nd:YAG laser beam, (9) pyrometers, (10) CCD cameras with telephoto objective lens, (11) beam splitter, and (12) oscillation sensor.

negative. These electrodes were utilized to control the vertical position (z) of the specimen. The typical sample size was 2 mm in diameter. In addition, four spherical electrodes distributed around the bottom electrode were used for horizontal control (x and y). The lower electrode was surrounded by four coils that generated a rotating magnetic field which was used to control sample rotation [20]. Sample heating was achieved using two 100 W CO2 lasers and a 500 W YAG laser. One CO2 laser beam was sent directly to the sample whereas the other beam was divided into two portions such that three focused beams, separated by 120° in a horizontal plane, hit the sample. The YAG laser hit the sample from a through hole in the top electrode. This multiple beam configuration minimized the laser induced disturbances along the horizontal direction. The position stability was around 200 lm along the vertical axis and 100 lm along the horizontal axis [21]. The sample temperature data were obtained using single-color pyrometers. The sample was observed by three charge-coupled-device cameras. The first camera offered a view of both the electrode assembly and the sample. The second camera was a high-resolution black and white camera (60 Hz sampling rate) equipped with a telephoto objective in conjunction with a background lamp. This camera provided a magnified view of the sample to measure its radius. The third camera, located at right angle to the second camera, was also equipped with a telephoto objective to provide a magnified view of the sample to observe the condition of the surface. The active feedback sample position control system consisted of position sensing, proportional–integral–derivative (PID) algorithm implementation, and variation of the electric field. Position sensing was achieved with a set of orthogonally disposed He–Ne laser that projected a sample image on position sensors. One sensor detected the y–z position whereas another sensor was dedicated to the x position. These position data were fed to a computer where the PID calculations took place. The voltages of electrodes were changed based on the calculation. The sampling frequency for the vertical feedback control could be selected as 720 Hz or 240 Hz, while the control rate for the horizontal direction was fixed to 30 Hz. 2.2. Viscosity measurement system The viscosity was determined using the drop oscillation method by measuring the decay time of the surface oscillation of the levitated sample [16]. A sample was molten and brought to a selected temperature. During the sample heating, electric currents were applied to the four coils to rotate the sample along the vertical axis at

40 Amplitude (a. u.)

(12)

(6 )

Sample

0

-40 0

0.2

0.4 Time (s)

0.6

FIGURE 2. Sample oscillation detection for viscosity measurements: (a) mode-2 oscillation, (b) diameter sensing system, and (c) decay of the signal of the oscillation following electrical excitation for a molten sample measured by the sensing system.

a rate of around 5 Hz. This amount of sample rotation stabilized the rotation axis, improved the temperature homogeneity of the sample, and reduced the measurement error due to the random rotation of the sample. Based on the work by Lee et al., the decay time is affected by the sample rotation [22]. However, compared with the characteristic oscillation frequency of the levitated samples (usually over 150 Hz), our rotation rate (5 Hz) was small enough to neglect its effect on the decay time. The rotating magnetic field was removed before viscosity measurements were carried out. Then, a mode-2 drop oscillation, illustrated in figure 2(a), was induced to the sample by superimposing the oscillation signal on the position control signal along the z direction (figure 2(b)). The oscillation signal was a sinusoidal signal with small amplitude, whose frequency matched with the characteristic oscillation frequency of the sample xc determined by [16]

xc ¼ ð8c=qr30 Þ1=2 ;

ð1Þ

where r0 was the radius of the sample when a spherical shape was assumed, q was the density, and c was the surface tension of the sample. An oscillation detection system, illustrated in figure 2(b), measured the fluctuation of the vertical diameter of the molten sample with a 4096 Hz sampling frequency. The transient signal that followed the termination of the excitation field was shown in figure 2(c). This signal was analyzed using an in-house written LabVIEWTM program and the decay time s was obtained. This was done many times for a given temperature and repeated for several temperatures. Using the decay time s given by the signal, the viscosity g could be found by [23]:

g ¼ qr20 =5s:

ð2Þ

During the measurement, magnified images of the sample were taken so that r0 could be obtained thorough image analysis after the experiment.

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T. Ishikawa et al. / J. Chem. Thermodynamics 65 (2013) 1–6

The viscosity measurements with the oscillating drop technique assume that the levitated droplet is free from any external forces. However, in order to levitate a sample against gravity, a strong electric field is applied. Moreover, since a high speed feedback position control is applied, viscosity measurements with electrostatic levitators are conducted under strong electric fields with DC and AC components. The effect of this position control force on the viscosity measurements was studied and is summarized in figure 3 [17]. When the frequency range of the sample position control overlaps with the characteristic oscillation frequency of the molten sample, the sample positioning force interacts with the sample oscillation. Sometimes, it suppresses the sample oscillation whereas sometimes it promotes the oscillation. This introduces a large experimental uncertainty on the decay time, and the measured viscosity values contain large experimental errors. In order to minimize this effect, it is important to select the sample size and the position control parameters so that the control frequency will not overlap with the characteristic oscillation frequencies of the sample. In our previous measurements, the position control frequency range was from DC to 360 Hz (720 Hz sampling rate) which overlapped the sample oscillation frequency (150 to 300 Hz) and introduced large experimental uncertainties. In this experiment, the position control frequency range was reduced from DC to 120 Hz (240 Hz sampling rate).

(a)

Sample oscillation freq. (150-300)

Samples of molybdenum, tantalum, osmium, rhenium, and tungsten were weighed and melted into spheroid using an arc melting furnace. The samples were weighed again and samples of proper size were selected so that the characteristic oscillation frequencies were above 160 Hz. The purities of the samples, their mass, and the frequency ranges of their characteristic oscillations are shown in Table 1. 3. Results The measured viscosity data of each element as a function of temperature are shown in figures 4–8, together with our previous measurement data. Other than our previous measurements, no reference data can be found in the literature. Viscosity values at the melting temperature gm, and coefficients g0 and E obtained from the data fitting to the following Arrhenius function

g ¼ g0 exp



 E ; RT

ð3Þ

10 8 -3 η/(10 Pa. s)

2.3. Improvement of viscosity measurement procedure

6 4

Tm

2 0

360

720 Sampling freq.

Position control frequency range

2700

2900

3100

3300

T/K

(b)

0

0 2500

Sample oscillation freq. (150-300)

120

FIGURE 4. Viscosity of molten molybdenum as a function of temperature. Open circles are our previous measurements while solid circles are our most recent results. Solid lines correspond to an Arrhenius function fitting.

240 Sampling freq.

20

FIGURE 3. Conceptual drawing showing how to avoid the effect of sample positioning force in the viscosity measurement using the oscillating drop method: (a) relationship between sample position control frequency and sample oscillation frequency when the feedback control frequency is up to 720 Hz and (b) relationship between sample position control frequency and sample oscillation frequency when the feedback control frequency is reduced to 240 Hz.

TABLE 1 Purity, mass, and typical characteristic oscillation frequencies of samples.

Mo Ta Os Re W

Purity/ mass%

Shape

Sample mass/ mg

Characteristic oscillation freq./Hz

99.95 99.95 99.9 99.97 99.95

Wire Wire Powder Wire Wire

33 69 50 47 40

235–240 160 190 220 230

-3 η/(10 Pa . s)

Position control frequency range

15

10

5

Tm 0 2800

3000

3200

3400

3600

T/K FIGURE 5. Viscosity of molten tantalum as a function of temperature. Open circles are our previous measurements while solid circles are our most recent results. Solid lines correspond to an Arrhenius function fitting.

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T. Ishikawa et al. / J. Chem. Thermodynamics 65 (2013) 1–6

10

-3 η/(10 Pa . s)

8 6 4 2

Tm

0 3200

3300

3400

3500

3600

3700

T/K FIGURE 6. Viscosity of molten osmium as a function of temperature. Open circles are our previous measurements while solid circles are our most recent results. Solid lines correspond to an Arrhenius function fitting.

25

15

η/(10

-3

Pa . s)

20

10 5 0 2800

Tm 3000

3200

3400

gm ¼ 1:7  107 3600

3800

T/K

-3

η/(10 Pa . s)

20

15

10

5

Tm 3300

3500



gm ¼ 0:454

FIGURE 7. Viscosity of molten rhenium as a function of temperature. Open circles are our previous measurements while solid circles are our most recent results. Solid lines correspond to an Arrhenius function fitting.

0 3100

(where R is the gas constant and equals to 8.31 J  mol1  K1, and T is the temperature) with a confidence interval of 95% are summarized in Table 2. As for molybdenum and tantalum, viscosities of our present measurement are identical to our previous measurements [13,15]. Viscosity data of osmium, rhenium, and tungsten in our present measurement are respectively 67%, 25%, and 25% larger than those of our previous measurements [11,12,14]. This difference may be explained by the difference of density among these metals. The surface tensions of these metals are comparable to that of molybdenum, while the densities of osmium, rhenium and tungsten are more than 1.8 times higher than that of molybdenum. Since the shapes of the levitated droplets on the ground are determined by their surface tension and mass of the sample, the droplets of these higher density metals become prolate due to gravity. In the previous experimental conditions, those prolate sample shapes and sample positioning force tended to introduce self drop oscillations. Therefore, the measured viscosity data became smaller. In the present experiments, no self oscillations were introduced, which resulted in higher viscosity values because the positioning forces did not contain any components around characteristic oscillation frequency. In all the elements, it can be mentioned that the data in our present measurements are less scattered than those in our previous measurements, which indicates that experimental uncertainties induced by the sample position control are drastically minimized. In this situation, the main uncertainty is induced by the measurement of the decay time s. Judging by the obtained signal shown in figure 3(b), the uncertainty of s can be estimated as large as 0.02 s. Since the average decay time is around 0.2 s, uncertainty can be estimated to be 10%. Combining other uncertainties introduced by q (2%) and r0 (1%) with equation (3), the total uncertainty becomes 10.3%. The measured viscosities of refractory metals at their melting temperatures are compared with a few empirical equations.

3700

T/K FIGURE 8. Viscosity of molten tungsten as a function of temperature. Open circles are our previous measurements while solid circles are our most recent results. Solid lines correspond to an Arrhenius function fitting.

M Tm

ðMT m Þ1=2 2=3 Vm

1=2

gm ¼ 2:81  104

ð4Þ

;

cm ;

ðM cm Þ1=2 1=3 Vm

ð5Þ

;

ð6Þ

where M, V, and c are the atomic mass, molar volume, and surface tension respectively, and the subscript m denotes the melting temperature. Equation (4) is called Andrade’s equation, while equations (5) and (6) are based on the Fowler-Born-Green relation between viscosity and surface tension [24,25]. Figure 9 shows the comparison between equation (4) and our results for the refractory metals [18]. The literature data of other metal elements [26] are also plotted. Our viscosity data taken by the improved procedure shows generally a good agreement with Andrade’s equation except for osmium and iridium. The quantitative comparison between our measurements and calculations from equations (4)–(6) are summarized in Table 3. Our measurement data of density and surface tension [27] are used to for the calculations. It is hard to conclude which empirical equation is superior at this moment, but agreement between these equations and our measured data improved compared with our previous data. At last, the measured coefficients E in equation (3) are compared with the predicted values, and the results are shown in Table 4. According to Iida et al. [24], E can be expressed as

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T. Ishikawa et al. / J. Chem. Thermodynamics 65 (2013) 1–6 TABLE 2 Measured viscosities of Mo, Ta, Os, Re, and W. Metal

g(Tm)/103 Pa  s

Tm/K

g(T) = g0exp(E/RT) 3

g0/10 Mo

2896

Ta

3293

Os

3306

Re

3459

W

3695

5.0 ± 0.5 5.5 8.8 ± 0.9 8.5 7.0 ± 0.7 4.2 9.9 ± 1.0 7.9 8.5 ± 0.9 6.8

3

Pa  s

E/10 J  mol

0.48 0.27 0.50 0.0035 0.098 0.00167 0.54 0.08 0.16 0.108

Temperature range T/K

Reference

2573–3213 2650–3000 2880–3514 3000–3400 3265–3542 3230–3605 3034–3675 2800–3600 3155–3634 3350–3700

Present work Previous work Present work Previous work Present work Previous work Present work Previous work Present work Previous work

1

56.5 ± 11.1 73 78.7 ± 10.5 213.3 117.5 ± 25.7 220 83.7 ± 8.2 133 122 ± 24.1 128

[15] [13] [14] [12] [11]

Standard uncertainty u is u(T) = 20 K.

12

TABLE 4 Comparison of E between measured and calculated values. Re

10 Ta

-3 η/(10 Pa . s)

Hf

6

Zr

4

Zn Pb

2 K

Hg

Ga In Ca

Cs

V Ni Zr

Tl

Ru Rh Nb

66.0 77.7 78.1 82.7 90.0

our current system cannot measure the amount of oxygen or nitrogen in the liquid sample. Further work is needed to investigate the effect of possible contamination and the temperature dependence of viscosity. The second concern is the effect of flow in the levitated sample due to thermo capillary (Marangoni) effect [28] which should be evaluated. The effect of photon pressure due to the heating laser beams should also be assessed in the future. The last concern is still the effect of positioning force to the viscosity measurement. Even though the improved procedure minimizes the effect, the levitated sample cannot be free from the external forces. Microgravity is a suitable condition to alleviate this difficulty because no force will be needed to maintain the sample position. Currently, an electromagnetic levitator [29] and an electrostatic levitator [30] are planned to be onboard the International Space Station, and the thermophysical property measurements in microgravity will be conducted. These facilities are expected to offer viscosity data with higher accuracy.

V

Bi Al

1

56.5 ± 11.1 78.7 ± 10.5 117.5 ± 25.7 83.7 ± 8.2 122 ± 24.1

Ir

Na Rb Li

0

Calculated E/103 J  mol1

Mo

La Sn

Os

Pt

Au

Fe

Cu Ag Ce

Ti

0

Mo Ta Os Re W

W

8

Measured E/103 J  mol1

2

3

1/2

1/2

5

4

M T m V m /10 -2/3

6

4

FIGURE 9. Andrade relationship for the melting-point viscosities of metallic liquids. Open circles are the literature data of metal elements. Solid circles are viscosity data of refractory metals measured by ESL. X marks indicate our previous measurements.

1:27 E ¼ 2:65T m :

ð7Þ

The values of molybdenum, tantalum, and rhenium show good agreements with the calculated ones. However, discrepancies between the measured value and the predicted ones are large in the case of osmium and tungsten. As far as the temperature dependence of viscosity is concerned, more efforts are needed on both experimental and theoretical sides. There are a few technical concerns on the viscosity measurements with our electrostatic levitation system. The first one is the solubility of residual gases (oxygen or nitrogen). The authors are aware that the presence of residual oxygen and nitrogen is virtually unavoidable in the chamber and that the high solubility tendency of some refractory metals could alter the data. However,

4. Conclusions The viscosity of several refractory metals has been measured by the oscillation drop method with an improved procedure. The measured data exhibited less-scatter when compared with our previous measurements, and showed better agreement with Andrade’s prediction.

TABLE 3 Comparison of viscosities at melting temperatures between measured and predicted values.

gm/103Pa  s Mo Ta Os Re W

Properties used for calculations

This work

Equation (3)

Equation (4)

Equation (5)

M/kg  mol1

Vm/106m3  mol1

cm/N  m1

5.0 ± 0.5 8.8 ± 0.9 7.0 ± 0.7 9.9 ± 1.0 8.5 ± 0.9

5.9 7.8 9.2 9.4 9.0

6.0 7.2 8.5 9.0 7.9

6.0 7.6 9.0 9.3 8.6

95.94 180.9 190.2 186.2 183.8

10.5 12.3 9.96 9.9 10.9

2.29 2.15 2.48 2.71 2.48

The relative standard uncertainties are ur(Vm) = 0.02 and ur(cm) = 0.03.

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Acknowledgment This work was partially supported by a Grant-in-Aid for Science Research (B) from the Japan Society for the Promotion of Science. References [1] J. Brillo, I. Egry, Int. J. Thermophys. 28 (2007) 1004. [2] G. Lohöfer, Meas. Sci. Technol. 16 (2005) 417. [3] H. Kobatake, H. Fukuyama, T. Tsukada, S. Awaji, Meas. Sci. Technol. 21 (2010) 025901. [4] H.P. Wang, J. Chang, B. Wei, J. Appl. Phys. 106 (2009) 033506. [5] S. Ozawa, K. Morohoshi, T. Hibiya, H. Fukuyama, J. Appl. Phys. 107 (2010) 014910. [6] G.J. Fan, M. Freels, H. Choo, P.K. Liaw, J.J.Z. Li, W.-K. Rhim, W.L. Johnson, P. Yu, W.H. Wang, Appl. Phys. Lett. 89 (2006) 241917. [7] R.W. Hyers, R.C. Bradshaw, J.R. Rogers, T.J. Rathz, G.W. Lee, A.K. Gangopadhyay, K.F. Kelton, Int. J. Thermophys. 25 (2004) 1155. [8] P.-F. Paradis, W.-K. Rhim, J. Mater. Res. 14 (1999) 3713. [9] T. Ishikawa, P.-F. Paradis, T. Itami, S. Yoda, Meas. Sci. Technol. 16 (2005) 443. [10] T. Ishikawa, P.-F. Paradis, J. Electron. Mater. 34 (2005) 1526. [11] P.-F. Paradis, T. Ishikawa, S. Yoda, J. Appl. Phys. 97 (2005) 106101. [12] T. Ishikawa, P.-F. Paradis, S. Yoda, Appl. Phys. Lett. 85 (2004) 5866. [13] P.-F. Paradis, T. Ishikawa, S. Yoda, J. Appl. Phys. 97 (2005) 053506. [14] P.-F. Paradis, T. Ishikawa, N. Koike, J. Appl. Phys. 100 (2006) 103523.

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JCT 13-114