2.1 Electrostatic Levitator

Properties were measured using an improved electrostatic levitator (Figure 1) (2, 3) in a vacuum environment (~10^–5 Pa) originally based on a design by Rhim et al. (14). With this instrument, ca. 2 mm diameter samples charged by electronic emission were levitated one at a time between electrodes. A feedback loop between the applied electric fields and the position information obtained from the shadow of the sample illuminated with helium-neon lasers and detected by sensors ensured stable levitation. The sample was heated with up to four focused laser beams: three carbon dioxide laser beams (10.6 μm, total power 200 W) separated by 120º in a horizontal plane and one neodymium-doped yttrium aluminium garnet (Nd:YAG) laser beam (1.064 μm, 500 W) from the top. A complete description of the facility and the levitation initiation procedures can be found elsewhere (2, 3, 10, 12). This configuration provided temperature homogeneity and sample position stability and allowed control of sample rotation. The radiance temperature was measured with a single-colour pyrometer (0.90 μm, 120 Hz acquisition rate). The sample was observed by black and white high-resolution charged-coupled-device cameras. The cameras were located at right angles from each other and were equipped with telephoto lenses in conjunction with background illumination lamps. This provided magnified views of the sample and helped to monitor the sample position and to align the heating laser beams.

2.2 Property Measurements

This levitation furnace was particularly suitable to measure the density, surface tension and viscosity of pgms in their equilibrium and undercooled liquid phases. Since sample heating and levitation were independent, a precise laser heating control allowed undercooled melts to be maintained for time scales much longer than those required for the measurements.

2.2.1 Density

Density measurements were carried out using an imaging technique described elsewhere (3, 15). Once a levitated sample was melted, it took a spherical shape due to surface tension and the distribution of surface charge and images from a high-resolution camera (30 frames per second) and temperature data were simultaneously recorded with time (Figure 2). The laser beams were then blocked with mechanical shutters allowing the sample to cool radiatively. After the experiment, each image was matched with the thermal history of the sample (Figure 3), digitised and the sample radius was extracted by software. Since the sample was axi-symmetric and because its mass was known, the density was found as a function of temperature. Calibration was done by levitating a sphere with a precisely known radius under identical experimental conditions.

2.2.2 Surface Tension and Viscosity

The surface tension was determined by the oscillation drop technique, a method in which the frequency of the oscillation of a levitated molten sample about its equilibrium shape is measured (16). This technique was explained earlier (17) and is summarised below for completeness. In this method, a sample was first heated, melted and brought to a selected temperature, while ensuring excellent position stability, low sample rotation and sample sphericity. Then, a P₂ cos(θ)-mode drop oscillation was induced to the sample by superimposing a small sinusoidal electric field on the levitation field. Following the termination of the excitation field, the transient signal generated by the change in diameter of the oscillating drop was detected and analysed using a custom made program. This was done many times for a given temperature and repeated for numerous temperatures. Using the characteristic oscillation frequency ω_c of this signal, which was calculated by a fast Fourier transform and then corrected for nonuniform surface charge distribution (18), the surface tension σ could be found from Equation (i) (17, 19):

ω_c² = (8σ/r_o³ρ) [1 – (Q²/64π²r_o³σε_o)][1 – F(σ,q,e)] (i)

where

F(σ,q,e) = [243.31σ² – 63.14q²σ + 1.54q⁴]e² / [176σ³ – 120q²σ² + 27σq⁴ – 2q⁶] (ii)

and r_o is the radius of the sample when it assumed a spherical shape, ρ is the liquid density, Q is the drop charge, ε_o is the permittivity of vacuum and q and e are respectively defined by Equations (iii) and (iv):

q² = Q²/16 π²r_o³ε_o (iii)

and

e² = E²r_o ε_o (iv)

with E being the applied electric field (levitation and excitation). Similarly (17, 20), using the decay time τ given by the same signal, the viscosity η was found by Equation (v):

η = ρr_o²/(5τ) (v)

In Equations (i) and (v), the value of the density ρ at the corresponding temperature and the real-time value of the radius r_o, obtained by the imaging technique, were used so that sample evaporation does not distort the surface tension and the viscosity data.

3.1 Density

All pgm samples were successfully levitated, melted, undercooled and solidified with the electrostatic levitator (4–8, 10, 11) and the processing data specific for each metal are listed in Table I. During these experiments, the density of equilibrium and non-equilibrium liquid phases was measured over large temperature ranges that cover the superheated and undercooled regions. Figure 4 presents typical plots for all pgms. The data measured by electrostatic levitation (4–6, 8, 10, 11) together with the literature values (21–36) are summarised in Table II. To our knowledge, these levitation measurements are the only ones that explore the undercooled region to date. The density of the pgms, like that of other pure metals, exhibited a linear behaviour as a function of temperature. In the density measurements, the uncertainty was estimated to be less than 2% from the resolution of the video grabbing capability (640 × 480 pixels) and from the uncertainty in mass (±0.0001 g).

At the melting point, the values obtained by levitation agree generally very well with those measured by other techniques (for example, the drop weight technique, isobaric expansion, pendant drop and sessile drop) when respective experimental uncertainties are taken into account (Table II) (21–36). The discrepancies observed in the temperature coefficients could be attributed to the difference in processing techniques and the extent to which evaporation losses have been considered. The containerless approach presented in this report operates under high vacuum, isolating the reactive molten samples from container walls and gases and can process samples in such a short time (<3 s for Pt and Rh; <2 s for Pd, Ru and Ir, and <1 s for Os) that evaporation is not an issue. This is supported by measurements of the sample mass before and after the experiment that lead to values within the uncertainties of the balance (0.1 mg). Evaporation rates were not measured in these experiments but could be obtained by levitating a sample for a long time (for example, 15 minutes) as explained elsewhere (37). The conventional methods often imply chemical reactions between the melt and a crucible, a support or residual gases. This can alter the final density values.

Other possible sources of error could arise from the imaging technique (for example, optical focusing or image digitisation) and the measurements of sample mass. Material purity, oxygen solubility in the samples and gasification could also, to some extent, explain the discrepancies. Temperature measurements too are subject to errors and are complicated by the fact that emissivity data are scarce for metals above their melting temperature and, to our knowledge, have not been reported for undercooled materials (38). The interested reader can find a detailed analysis for each of the pgms elsewhere (4–6, 8, 10, 11) together with a complete comparison with the literature data, when available, obtained with conventional methods (21–36).

3.2 Surface Tension

The surface tension was measured over large temperature ranges, well above the melting temperature and down into the undercooled region as shown in Figure 5 for all pgms except Pd (4, 5, 8, 10, 11). Although the density as a function of temperature was known and the radius could be tracked in real time, severe evaporation for Pd samples hindered these measurements because of the time needed to perform the experiments (one hour) and because the window of the vacuum chamber as well as the electrodes of the levitator became coated which made the sample unstable.

The uncertainty of the measurements was estimated to be better than 5% from the response of the oscillation detector and from the uncertainty in density measurements. In all measurements, the surface tension exhibited a linear behaviour as a function of temperature. The data, including those reported in the literature, are listed in Table III. At the melting point, the values obtained by electrostatic levitation (4, 5, 8, 10–12) show very good agreement with most published values when the respective experimental uncertainties are considered (22, 28, 32, 34, 36, 39–41) and the temperature coefficients compare generally well with those calculated by Allen (23).

Here again, the discrepancy observed between the results (values at the melting temperature as well as temperature coefficients) obtained with electrostatic levitation and other methods could be understood due to the fact that the containerless approach in high vacuum isolated the samples from container walls and gases, whereas the other methods imply possible chemical reactions between the reactive melts and a crucible, a support or residual gases. Melt contamination is possible and can drastically impact the surface tension. Sources of discrepancy or contamination include material purity, oxygen solubility in the samples, gasification and surface oxidation or nitridation from residual gases. Temperature measurements can also affect the end results. A full comparison with the data reported in the literature, when available, as well as a complete analysis could be found in prior papers (4, 5, 8, 10–12).

3.3 Viscosity

The viscosity could also be measured over large temperature ranges, well above the melting temperature and down into the undercooled region as shown in Figure 6 for all pgms except Pd (4, 5, 8, 10–13). Although the density as a function of temperature was known and the radius could be tracked in real time, severe evaporation for Pd samples again hindered these measurements because of the time needed to perform the experiments (one hour) and because the window of the vacuum chamber as well as the electrodes of the levitator became coated and made the sample unstable. The data shown in Figure 6 were taken using a new procedure that consisted of measuring the viscosity on small samples and using a lower feedback control frequency to minimise the effect on the damping oscillation (20). Data from the literature (Zhuchenko et al. (42) and Demidovich et al. (43)) are also superimposed in Figure 6. The temperature dependence of the viscosity exhibited an Arrhenius behaviour for all measured metals. The uncertainty of the measurements was estimated to be better than 15% from the response of the oscillation detector. The values of the levitation measurements (4, 5, 8, 10–13) and the very scarce literature data (42, 43) are summarised in Table IV for completeness.

Acknowledgments

The authors would like to thank the Japan Society for the Promotion of Science for a Grant-in-Aid for Scientific Research (B). The authors are also grateful to Y. Watanabe and H. Tomioka (AES Co Ltd) for technical help in several experiments and post-levitation microstructure analysis.