Reliable data for high-temperature viscosity and surface tension: results from a European project

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1 High Temperatures ^ High Pressures, 2001, volume 33, pages 631 ^ ECTP Proceedings pages 1135 ^ 1141 DOI: /htwu323 Reliable data for high-temperature viscosity and surface tension: results from a European project Robert F Brooks National Physical Laboratory, Queens Road, Teddington, TW11 0LW, UK; fax: ; rob.brooks@npl.co.uk Ivan Egry German Aerospace Centre (DLR), Linder Hoehe, D-5000 Koeln-90, Germany Seshadri Seetharaman Division of Theoretical Metallurgy, Kungliga Tekniska Hogskolan, Stockholm, SE , Sweden David Grant Department of Materials Engineering, University of Nottingham, University Park, Nottingham, NG7 2RD, UK Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany, 5 ^ 9 September 1999 Abstract. Results are reported of work carried out for the European Commission under contract number MAT1 CT , between 1994 and The project provided recommended surface tension ^ temperature relationships for copper and nickel samples prepared by cold crucible melting to 3%, by the levitation and sessile drop methods, and values were also obtained for iron and gold in preliminary studies. For copper, g= Nm 1 ) ˆ 1:304 0: [(y 1083)=8C]; for nickel, g= Nm 1 ) ˆ 1:781 0: [(y 1455)=8C]. Comparison of terrestrial measurements with those made in microgravity have shown that the Cumming's equation is a reliable and satisfactory method of correcting the surface tensions derived with the levitated drop method for the effect of electromagnetic pressure. For measurements with an oscillating cylinder viscometer, recommended viscosity ^ temperature relationships are given for copper, nickel, and iron. For copper, log 10 (Z=mPa s ˆ 0:2791 [1245:5=(T=K)]; for nickel, log 10 (Z=mPa s ˆ 0:5038 [2029=(T=K)]; and for iron, log 10 (Z=mPa s ˆ 0:6494 [2568= T=K)]. 1 Introduction Metals manufacturing and fabrication industries are increasingly using computer-based mathematical models to obtain better understanding or control of their processes, or to predict defects in the final product. These models are highly developed in terms of the mathematical equations used, but they rely on the accuracy of the physical property data of the materials they are modelling to give a true prediction. In many cases these data are not available, and this is particularly true in the case of surface tension, g, and viscosity, Z, which are critical factors in the modelling of such processes as welding, spray forming, powder and metallic ribbon manufacture. Unfortunately, measurements of viscosity and surface tension are currently prone to large errors, and literature data for absolute values for even `pure' liquid metals can show scatter of the order of 100% and 20%, respectively. For many materials, data for the relationship of the property with temperature are even worse, and there is a paucity of any form of data for the alloys used in engineering today. One reason for this is the lack of a suitable reference material, or reference values, with which the measurement apparatus can be calibrated. This project, funded by the European Commission (contract number MAT1 CT ), aimed to improve the accuracy of the measurements by providing reliable, certified values for materials for the subsequent calibration of instruments. The project was divided into a preliminary test and development phase, and a final measurement phase of a reference material. The principal aims of the preliminary phase

2 632 R F Brooks, I Egry, S Seetharaman, D Grant 15 ECTP Proceedings page 1136 were to compare test methods for surface tension, to test the validity of the Cummings equation (Cummings and Blackburn 1991) used in levitation techniques, reinforced with microgravity measurements, to develop an oscillating cylinder viscometer, and to evaluate a microgravity viscosity measurement. Laboratories from the UK, Germany, and Sweden were principally involved. 2 Materials The tin (viscosity), gold (surface tension), copper, nickel, and iron materials used in phase one of the project were commercially available high-purity metals (typically % metallic purity), obtained from various sources, in different batches. For the final phase materials were prepared as 50 g buttons, from single batches of master metals. Any impurities in the samples were removed by levitation melting in a Crystallox cold crucible (Crystalox, Wantage OX12 9AJ, UK) under atmospheres of argon and hydrogen. Samples of high-purity low-oxygen copper and nickel were distributed, together with a sample of oxygen-saturated iron (450 ppm), prepared in the cold crucible under an argon atmosphere. As the surface tension of metals with low oxygen levels is very dependent upon the soluble oxygen content (O%), but becomes insensitive to oxygen content at higher oxygen contents, it was envisaged that this Fe ^ O material would give low values which would remain unaffected by minor contamination within an apparatus, while the low oxygen samples would provide high surface tension values to test the atmosphere control in any apparatus. These materials would also provide values and temperatures in ranges suitable for the measurement of surface tensions and viscosities of the majority of commercial alloys (aluminium being discounted because of processing difficulties in the laboratory scale). 3 Methods 3.1 Surface tension Preliminary data were obtained by the sessile drop (SD) technique, the levitated drop (LD) technique (3 laboratories), the maximum bubble pressure (MBP) method, and drop weight (DW) method, the principles of which are well known and are described elsewhere (Iida and Guthrie 1989). In addition, to evaluate the Cummings equation, measurements were made by a levitation method in microgravity (Egry 1998). For the final evaluation of the recommended data, results obtained by the DW and MBP methods were not used. 3.2 Viscosity An oscillating cylinder viscometer was developed, which is described elsewhere (Brooks et al 2001). Data were compared with a similar apparatus constructed in Japan. Attempts to develop a capillary viscometer with which to compare results were not successful. Microgravity experiments allowed for the study of a novel viscosity method from the decay of oscillations of a levitated drop. Although some limitations were found in respect of the reference materials, values were obtained for Pd 78 Cr 6 Si 16, and are reported elsewhere (Egry 1998). 4 Validation of the Cummings equation Surface tensions are usually determined for the LD method by the use of the Rayleigh relationship (Lord Rayleigh 1879) where o R is the frequency of oscillation and m is the mass of the levitated drop: g ˆ 3 p m 8 o2 R. However, in practice, a frequency spectrum is obtained which contains three or five peaks and not the single frequency predicted by Lord Rayleigh, because the

3 High-temperature viscosity and surface tension ECTP Proceedings page 1137 electromagnetic pressure exerted on the surface by the electromagnetic forces results in an asymmetric droplet and frequency splitting. Cummings and Blackburn (1991) showed that the magnetic pressure could be correlated with the translational frequency (o tr ) and that an equation could be used to calculate the Rayleigh frequency (o R ),wherea is the radius of the drop, g the gravitational constant, and the subscripts 1 to 5 denote the various peaks: o 2 R ˆ 1 5 o2 1 o 2 2 o 2 3 o 2 4 o 2 5 o 2 tr 1:9 1:2 g 2a 2p o tr 2 2. The translational frequency will be dependent upon both the mass of the droplet and the specific levitation facility. The validity of the Cummings relationship was tested by measuring the apparent surface tension of several pure metals (iron, nickel, gold, and copper) for a range of sample masses in two different levitation apparatus, with different coil geometries. The results obtained for iron are given in figure 1. Surface tension=n m m ˆ 0:5 g m ˆ 0:8 g T liq m ˆ 1:0 g 1.7 uncorrected corrected Temperature=8C Figure 1. Surface tension of iron as a function of temperature: open and closed symbols refer to values obtained from the Rayleigh equation and Cummings and Rayleigh equations, respectively. It can be seen that the surface tensions calculated from the mean frequency and Rayleigh equation (i) increase with increasing mass, and (ii) are higher than those calculated from the Cummings and Rayleigh equations, which, in turn, were found to be only slightly higher than those obtained by conventional methods as given in the review by Keene (1993). Thus it was concluded that the surface tension values for all four metals derived from the Cummings and Rayleigh equations were independent of mass and in agreement with recommended values, thus proving the validity of Cummings' work. Further confirmation of its validity comes from the experiments carried out in microgravity, where, because of the low magnetic pressures required to maintain the levitated drop, a single Rayleigh oscillation frequency was obtained, which yielded a surface tension value for gold in excellent agreement with that obtained terrestrially. 5 Results 5.1 Surface tension Results are given in table 1 in the form g ˆ a b 10 3 (T T liquidus ). Measurements from phase 2 were made on identical materials and were used to provide recommended data. These data include values measured on both superheated and undercooled samples (from levitation experiments) and are shown in figures 2 and 3 for copper and nickel, respectively.

4 634 R F Brooks, I Egry, S Seetharaman, D Grant 15 ECTP Proceedings page 1138 Table 1. Surface tension results. dg. Material Method Lab Phase g=n m 1 at T liquidus 10 3 Nm 1 8C 1 dt Gold LD 1, Copper LD 1, Copper DW Copper MBP Copper LD Copper LD Copper LD Copper SD Nickel LD 1, Nickel MBP Nickel LD Nickel LD Nickel LD Iron LD 1, Fe ± O MBP Surface tension=n m Temperature=8C Figure 2. Measurements of surface tension of the phase 2 copper sample, with (öö) recommended values, and () statistical limits. Surface tension=n m Temperature=8C Figure 3. Measurements of surface tension of the phase 2 nickel sample, with (öö) recommended values, and () statistical limits.

5 High-temperature viscosity and surface tension ECTP Proceedings page 1139 The values obtained were found to be slightly lower than those recommended in the review by Keene (1993), who suggested a relationship for copper of g=n m 1 ˆ 1:33 0: [(y 1085)=8C ], and of g=n m 1 ˆ 1:796 0: [(y 1455)=8C] for nickel. It should, however, be noted that Keene included LD data which had not been corrected for magnetic pressure, and were therefore higher than those obtained in this study. Unfortunately the results for the Fe ^ O material from each laboratory showed a large degree of scatter. Both time and mass dependence could be identified, indicating inhomogeneity of the sample, and it is possible that a coherent oxide skin could form on levitated drops, damping the oscillations. Reference values could not therefore be reported. 5.2 Statistical evaluation of results The statistical evaluation was made to test the consistency of the linear regression fits of the individual laboratories, and the 95% confidence limits of the total data for both the intercept and the slope. Calculations were based on the equations set out by Sachs (1982), testing the equality of more than two regression lines. This evaluation shows that the overall copper data are consistent with an uncertainty of 2:4% about the mean for the individual points, and that the regression data for nickel are consistent and that the bounds of the data are 3:0% about the mean. These are acceptable limits of the measurement. 5.3 Viscosity measurements Viscosity measurements were made with the oscillating cylinder viscometer on mercury and tin in the preliminary phase, and compared with the values recommended by Kawai and Shiraishi (1989), as shown in table 2. Averaged data for the viscosity of copper, nickel, and iron, together with standard deviations, are given in table 3, and shown in figure 4. It can be seen that nickel readily undercools. Table 2. Viscosity measurements compared to recommended values. Material y=8c Z=mPa s Difference=% this study Kawai and Shiraishi (1989) Mercury Tin Tin Tin Tin Table 3. Mean viscosity results for copper, nickel, and iron (* indicates samples readily undercooled; SD is the standard deviation). Copper Nickel Iron y=8c Z=mPa s SD=mPa s y=8c Z=mPa s SD=mPa s y=8c Z=mPa s SD=mPa s *

6 636 R F Brooks, I Egry, S Seetharaman, D Grant 15 ECTP Proceedings page 1140 Viscosity=mPa s Cu Ni Fe Temperature=8C Figure 4. Measurements of the viscosity of copper, nickel, and iron with the oscillating viscometer. 6 Conclusions The surface tension results obtained in the project show: (i) good agreement between the results reported by different laboratories; (ii) good agreement between the results obtained from the LD technique and conventional methods; (iii) good agreement of the results of the levitated (or oscillating) drop method in microgravity (where only small magnetic forces are needed) with those obtained terrestrially; (iv) that the Cummings relationship provides a valid method for correcting for the effect of magnetic pressure exerted by the electromagnetic coil; (v) that the Fe ^ O (candidate reference material) has proved unsatisfactory as a calibrant material. 6.1 Recommended values The recommended values from this study are as follows. For copper: g=n m 1 ˆ 1:304 0: y 1083 =8CŠ. For nickel: g=n m 1 ˆ 1:781 0: y 1455 =8CŠ. Recommended values for the surface tension of these materials are given in tables 4 and 5. Table 4. Recommended values for the surface tension of copper. y=8c Copper: (g 0:028 =N m 1 y 0 y 10 y 20 y 30 y

7 High-temperature viscosity and surface tension ECTP Proceedings page 1141 Table 5. Recommended values for the surface tension of nickel. y=8c Nickel: (g 0:054 =N m 1 y 0 y 10 y 20 y 30 y The recommended viscosity ^ temperature equations for the reference materials copper and nickel and that of pure iron, in the form of an Arrhenius relationship, are as follows. For copper: log 10 Z=mPa s ˆ 0: :5 T=K. For nickel: log 10 Z=mPa s ˆ 0: T=K. For iron: log 10 Z=mPa s ˆ 0: T=K. Experiments carried out in microgravity indicate that the oscillating drop method is promising for obtaining results for materials with viscosities greater than 20 mpa s. References Brooks R F, Day A P, Andon R J L, Chapman L A, Mills K C, Quested P Q, 2001 High Temp. ^ High Press ^ 82 Cummings D, Blackburn D, 1991 J. Fluid Mech ^ 416 Egry I, 1998 J. Jpn. Soc. Microgravity Appl ^ 224 Iida T, Guthrie R L, 1989 The Physical Properties of Liquid Metals (Oxford: Clarendon Press) Kawai Y, Shiraishi Y, 1989 Handbook of Physico-Chemical Properties at High Temperatures (Tokyo: JISI) special issue number 41 Keene B J, 1993 Int. Mater. Rev ^ 192 Lord Rayleigh, 1879 Proc. R. Soc. London, Ser. A ^ 97 Sachs L, 1982 Applied Statistics (Berlin: Springer-Verlag)

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