Densities of liquid lanthanoid sesquioxides measured with the electrostatic levitation furnace in the ISS

The densities of several liquid lanthanoid sesquioxides (Ln 2 O 3 , Ln = Er, Ho, Tb, Gd) were measured over the temperature range from 2700 K (the approximate melting point of these materials) to 3200 K. These measurements were performed using the Electrostatic Levitation Furnace onboard the International Space Station (ISS-ELF). Based on the Coulomb force between the charged samples and surrounding electrodes and employing a rapid feedback control process, specimens were stably levitated and subsequently melted by high power lasers. The molten oxides exhibited spherical morphologies and their volumes were readily calculated from magnified images. Subsequent weighing of the samples on Earth allowed the densities of the oxides to be determined. The densities of Er 2 O 3 , Ho 2 O 3 , Tb 2 O 3 , and Gd 2 O 3 at their melting temperatures ( T m ) were found to be 8170, 8035, 7451, and 7268 kg/m 3 , respectively, and these density values were shown to exhibit a linear correlation with temperature. The molar volumes of these oxides at their T m values were calculated and compared with those of other sesquioxides (Al 2 O 3 , Ga 2 O 3 , and B 2 O 3 ). The molar volumes of the nonglass-forming sesquioxides (Er 2 O 3 , Ho 2 O 3 , Tb 2 O 3 , Gd 2 O 3 , Al 2 O 3 , and Ga 2 O 3 ) showed linear correlations with the cubes of their cation radii, whereas those of the glass-forming oxide (B 2 O 3 , As 2 O 3 , and Sb 2 O 3 ) showed different correlations.


Abstract
The densities of several liquid lanthanoid sesquioxides (Ln 2 O 3 , Ln = Er, Ho, Tb, Gd) were measured over the temperature range from 2700 K (the approximate melting point of these materials) to 3200 K. These measurements were performed using the Electrostatic Levitation Furnace onboard the International Space Station (ISS-ELF).
Based on the Coulomb force between the charged samples and surrounding electrodes and employing a rapid feedback control process, specimens were stably levitated and subsequently melted by high power lasers. The molten oxides exhibited spherical morphologies and their volumes were readily calculated from magnified images. showed linear correlations with the cubes of their cation radii, whereas those of the glass-forming oxide (B 2 O 3 , As 2 O 3 , and Sb 2 O 3 ) showed different correlations. density, surface tension, and viscosity of molten oxides at high temperatures.
Among the various oxides, lanthanoid sesquioxides (Ln 2 O 3 ) have extremely high melting temperatures on the order of 2700 K. Ln 2 O 3 compounds are representative of nonglass-forming oxides, and thus are commonly used as refractory materials and dopants for luminescent materials. Due to their high melting temperatures, the thermophysical properties of these compounds have rarely been assessed, 11 and so these oxides were considered suitably challenging materials to demonstrate the capability of the ISS-ELF to permit the high-temperature analysis of various substances.
Density is one of the most fundamental properties of a material and is used in the calculation of other thermophysical characteristics, such as surface tension and viscosity, and is also an important aspect of structural analysis. Specifically, density data are necessary to calculate the total pair-distribution function, G(r), from the total structure factor, S(Q), determined experimentally by X-ray or neutron scattering techniques. In our previous work, 12 the structure of liquid Er 2 O 3 was investigated by analyzing synchrotron X-ray diffraction data together with a density value obtained using the ISS-ELF. The goal of the present work was to obtain the densities of other Ln 2 O 3 oxides so as to assess the structures of these compounds. This report presents the results of density measurements of molten Ln 2 O 3 oxides (Ln = Er, Ho, Tb, Gd) using the ISS-ELF, as well as a comparison of the molar volumes of these materials with those of other liquid sesquioxides and dioxides.

| Sample preparation
Ln 2 O 3 powders (Ln = Er, Ho, Tb, Gd) with a purity of 99.99% (Koujundo Chemical Laboratory Co., Ltd.) were employed in this work. Prior to the ISS trials, each powder was sintered, melted, and solidified in ambient air, using an aerodynamic levitator in conjunction with a 100 W CO 2 laser. The resulting polycrystalline samples, typically 2 mm in diameter, were subsequently weighed, transferred into special sample holders and launched to the ISS. Figure 1 shows a photographic image of a levitated sample in the ISS-ELF. Each specimen had an accumulated positive charge in the range of 10 −11 -10 −12 C 10 and was levitated using six electrodes in dry air under a pressure of 2 atm. The specimen remained stable while levitated and its position was determined using a high-speed feedback control process. Each sample was heated to its melting point using four 980 nm diode lasers (each with a power of 40 W) arranged in a tetrahedral formation so as to heat the sample evenly. 13 The oxide temperature was determined by measuring the intensity of the radiation emitted using a pyrometer over the wavelength range of 1.45-1.8 μm. The actual sample temperature was determined by adjusting the emissivity value so that the temperature plateau matched with its the melting temperature. After each oxide transitioned to a molten state, it adopted a perfectly spherical shape as a result of the surface tension of the compound and the microgravity environment. The specimen was subsequently cooled by shutting off the heating lasers. During cooling, magnified sample images were acquired with ultraviolet back lighting ( Figure 2). Following these trials, the processed samples were returned to the sample holder and brought back to Earth.

| Calculation of density and thermal expansion
The density values (ρ) of the molten samples were calculated from the volumes obtained based on analysis of the images together with the sample masses. The details of the image analysis technique are described in Ref. [14]. Briefly, 400 edge points were detected and converted to polar coordinates (R, θ) that were fit with spherical harmonic functions up to sixth order, as where P n (cosθ) are n-th order Legendre polynomials and c n are coefficients that minimize the value calculated as The volume was subsequently calculated using the equation Pixels in the images were converted to actual sample sizes (in units of mm) based on images acquired of a 2.0 mm diameter stainless steel ball levitated in the ISS-ELF.
The mass, m, of each specimen was determined by weighing after the samples were returned to Earth, and densities were obtained from the formula  with literature data from Granier and Heurtault, who determined the densities of these oxides via aerodynamic levitation. 16 Other than their work, no other literature data were found. The T m values for these oxides as indicated in the plots were obtained from a publication by Sarou-Kanian et al. 17 The uncertainty in these measurements was estimated to be 2% based on the respective uncertainties in the mass and volume of each specimen. 14 Specifically, each sample mass (m) of approximately 20 mg had an associated uncertainty (Δm) of 0.05 mg, such that the relative uncertainty (Δm/m) was estimated to be 0.3%. The uncertainty in the volume (ΔV/V) was 3Δr/r, where Δr is the uncertainty in the radius of the sample and r is the radius. As Δr and r in these experiments were approximately 1 and 160 pixels, respectively, ΔV/V was estimated to be 1.9%. Thus, the overall uncertainty in the density values (Δρ/ρ) was 2.0%. The variation between datasets 1 and 2 is within this uncertainty. The density data exhibited linear correlations with temperature and, using a least square regression with a confidence interval of 95%, could be fitted to the equation where ρ m is the liquid density at T m and α is the thermal expansion coefficient, which is assumed to be constant over the liquidus temperature range. Because the correlation coefficients for dataset 1 were larger than those for dataset 2, the fitting results for the former are included in Table 1 as the recommended values. It should be noted that the densities reported in Ref. [16] are lower than the present values, and this discrepancy is primarily attributed to the difference in the backlighting illumination used to acquire the sample images. In the experiments reported herein, ultraviolet backlighting was employed to remove the effect of the intense infrared radiation emitted by the high-temperature samples. 7 On the other hand, no backlighting was used and images of the bright samples were analyzed in Ref. [16]. According to our earlier work, 7 these types of measurements can potentially lead to overestimation of the sample volume such that the density is underestimated.

| RESULTS AND DISCUSSION
Courtial and Dingwell calculated molar volume of Ln 2 O 3 (Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb) with indirect method. 18 They measured the density of Nadisilicates which contained 0 to 6 mol % of lanthanide sesquioxide using the double bob Archimedean method. The partial molar volumes of Ln 2 O 3 were determined using these density data. The measured partial molar volumes were linearly fitted as a function of the concentration of lanthanide sesquioxide, and this relation was extrapolated to 100% to get the molar volume of lanthanide sesquioxide.
Molar volumes calculated from our density measurements were compared with the ones by Courtial and Dingwell. As shown in Table 2, the volumes except Ho 2 O 3 are significantly different with each other. The deviations are larger than the uncertainties in both works. They are assumed to be originated from the extrapolations form 0-6 mol% partial molar volume to 100%, as indicated in Ref. [18]. This result indicates that the excess volumes in the mixing of the silicate and Ln 2 O 3 derived from the interaction between these two components should be taken into account for more accurate extrapolation.
As shown in Table 2   GeO 2 , 27 and TeO 2 28 ) exhibited that two different correlations, respectively, as depicted in Figure 4. Therefore, V m (r) might be a good indicator of the ability of a single component oxide to form a glass. However, because most of the single-component oxides have very high melting temperatures, the reported liquid density data for these compounds are very limited. Thus, to pursue this hypothesis, further density measurements of a wide range of sesquioxides are needed. Currently, density measurements of high-temperature oxides such as Y 2 O 3 , Yb 2 O 3 , Tm 2 O 3 , and Lu 2 O 3 using the ISS-ELF are planned and the results will be reported in a future publication by our group.

| CONCLUSION
The densities of a number of different liquid Ln 2 O 3 compounds were ascertained with the ISS-ELF. This process prevented contamination of the samples such that precise density values could be obtained over a wide temperature range. The molar volumes at T m exhibited a linear relationship with the cubes of the Ln 3+ radii in these oxides, as was also the case for other nonglass-forming sesquioxides such as Al 2 O 3 and Ga 2 O 3 . In contrast, the data for B 2 O 3 , a glass-forming oxide, as well as As 2 O 3 and Sb 2 O 3 glasses showed different correlations with the cubes. The molar volumes of nonglass-forming dioxide and glass-forming dioxides also exhibited that two different linear correlations, respectively.