Densities of Liquid Tm₂O₃, Yb₂O₃, and Lu₂O₃ Measured by an Electrostatic Levitation Furnace Onboard the International Space Station

Abstract

Liquid densities of three lanthanoid sesquioxides (Tm₂O₃, Yb₂O₃, and Lu₂O₃), whose melting temperatures are above 2400 °C, were measured using an electrostatic levitation furnace onboard the International Space Station (ISS). Each sample was positively charged, and its position was controlled by Coulomb forces between the sample and the surrounding electrodes. Following heating and melting of the sample by high-power lasers, its volume was calculated from its spherical shape in its liquidus phase. After weighing the mass of the sample returned to Earth, its density was determined. The densities (ρ) of Tm₂O₃, Yb₂O₃, and Lu₂O₃ can be expressed as ρ_Tm2O3 = 8304 − 0.18 × (T − T_m), ρ_Yb2O3 = 8425 − 0.55 × (T − T_m), and ρ_Lu2O3 = 8627 − 0.43 × (T − T_m), respectively, where T_m is their melting temperatures.

1. Introduction

As the additive manufacturing (3D printing) techniques progress with ceramics materials [1], demands for the measurement of the thermophysical properties of oxide melts are increasing [2]. However, due to their high melting temperatures and the risk of contamination from walls, thermophysical property measurements of molten oxides with conventional techniques such as crucibles are difficult. Among oxides, molten lanthanoid sesquioxides (Ln₂O₃, where Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) are very hard to investigate due to their extremely high melting temperatures (above 2400 °C).

Densities of Ln₂O₃ were measured by direct [2,3] and indirect methods [4]. As for the indirect methods, Courtial and Dingwell measured the density of Na-disilicates, which contained 0 to 6% of Ln₂O₃ and had melting temperatures below 1300 °C, using the double-bob Archimedean method. Then, they obtained a partial molar volume of Ln₂O₃ as a function of the concentration, and this was extrapolated to get the molar volume of 100% Ln₂O₃ [4].

The direct methods utilize containerless processing techniques. These methods circumvent the problems associated with the crucibles and enable the property measurements of high-temperature melts. One of the most common levitation methods for high-temperature material is electromagnetic levitation. It has been widely used for high-temperature melts of metals and alloys on the ground [5,6,7,8] as well as in space [9,10,11,12]. However, this method cannot handle oxide materials due to their low electric conductivities.

Another method utilizes gas flow to levitate samples. Aerodynamic levitation (ADL) uses a conical nozzle through which a gas flows and creates a stable point (pressure minimum) where a sample can be levitated. The levitated sample can be heated and melted using high-power lasers. Granier and Heurtault [3] used this method to measure the densities of several Ln₂O₃s.

The aero-acoustic levitator (AAL) levitates a sample with a gas jet and stabilizes it by acoustic forces using surrounding transducers. The sample position is monitored, and the acoustic pressures are adjusted using a feedback control algorithm. The densities of Ln₂O₃s obtained by this method are reported by Ushakov et al. [2].

The electrostatic levitation method (ESL) [13] utilizes Coulomb force between a charged sample and surrounding electrodes to levitate a sample against gravity. In principle, any sample can be handled as long as it has enough charges on its surface. High-temperature melts were successfully levitated electrostatically in the 1990s [14]. Since then, thermophysical properties (density [15], surface tension [16], viscosity [16], and heat capacity [17]) of molten refractory metals/alloys have been measured using this method on the ground [18]. However, levitation of oxide samples with this method on the ground is very challenging due to the following reasons. To levitate a sample (typically a size of 2 mm in diameter and mass of around 30 mg) against gravity, a certain amount of surface charge (around 10⁻¹⁰ C) and a huge electric field (10–20 kV/cm) are needed. These requirements can be easily satisfied for conductive samples such as metals/alloys under a high-vacuum environment. However, it is very difficult to accumulate enough electrical charges on the oxide samples. Moreover, the oxide samples need to be processed under a gaseous environment to prevent evaporation, where a huge electric field cannot be applied because electric discharges between electrodes occur easily.

In microgravity, a large electric field is not necessary, and restrictions are drastically relieved, allowing the handling of oxide samples with much fewer electrical charges. Moreover, levitation experiments can be conducted in a gaseous environment. Microgravity is, therefore, a suitable environment for thermophysical property measurements of high-temperature oxide melts with an electrostatic levitation method.

The electrostatic levitation furnace onboard the ISS (ISS-ELF) has been developed by the Japan Aerospace Exploration Agency (JAXA) and has been operational since 2016 [19]. To validate and demonstrate the capability of thermophysical property measurements of molten oxides at extremely high temperatures, Ln₂O₃s have been selected as the main target of the ISS-ELF project. Densities of Gd₂O₃, Tb₂O₃, Ho₂O₃, and Er₂O₃ were successfully measured from 2017 to 2019 and reported in earlier publications [20,21,22]. Subsequently, densities of Tm₂O₃, Yb₂O₃, and Lu₂O₃ were measured in 2021. This paper briefly describes the facility as well as the measurement method and reports the density data of these Ln₂O₃s.

2. Experimental Setup

2.1. Electrostatic Levitation Furnace

A detailed description of the facility is found in earlier publications [19,20], but a summary is given here for completeness.

A positively charged sample can be levitated among three pairs of electrodes orthogonally located against each other (Figure 1). To achieve this, a collimated laser beam (around 20 mm in diameter) from a diode laser emitting at a wavelength of 660 nm projects a shadow of the sample on a position sensor where vertical and horizontal sample positions are measured. Two sets of the projection lasers and position sensors are orthogonally placed to allow measuring the tridimensional sample position. The position signals are sent to a controller, where the position control voltages are calculated using a PD (proportional-differential) control algorithm.

The sample is heated by four semiconductor lasers (980 nm, 40 W power each) in which beams are focused to a 0.5 mm spot size at the sample position. To maintain good temperature homogeneity of the sample, these lasers are arranged in a tetrahedral heating geometry around the sample. Furthermore, the power of each laser can be controlled by commands from the ground.

The sample temperature is measured at a 100 Hz frequency over the 300 °C to 3000 °C range by a commercial pyrometer (IMPAC IGA140) through sapphire windows. The pyrometer measures the radiation intensity (1.45–1.8 μm in wavelength) from the sample. Because the emissivity setting on the pyrometer cannot be changed from the ground, it remains at 1.0. The actual sample temperature can be determined using the temperature plateau after recalescence and the known melting temperature of the material. The pyrometer contains a built-in video camera that helps ensure that the sample stays in the measuring spot of the pyrometer (Figure 2a).

The other camera (a black and white camera with a non-telecentric zoom lens) gives a magnified image of a UV backlit sample (Figure 2b). Using the video images (taken at a 60 Hz frequency interval) from this camera, the density of the sample can be calculated.

Other than the exchanges of sample holders by crew members, all operations of the ISS-ELF are remotely conducted from the ground. Experiments were carried out under a dry air pressurized atmosphere (2 × 10⁵ Pa).

2.2. Density Measurement

Spherical samples were prepared on the ground from compacted powder melted using an aerodynamic levitator in an ambient air atmosphere. Purities and manufacturers of the powders are listed in

Table 1. Source and mass fraction purity of samples used in this study.

Chemical Name	Source	Initial Mass Fraction Purity
Tm2O3	High Purity Chemical Lab.	0.999
Yb2O3	High Purity Chemical Lab.	0.9999
Lu2O3	High Purity Chemical Lab.	0.999

. Because these samples (Tm₂O₃, Yb₂O₃, and Lu₂O₃) do not absorb the radiation close to 980 nm, special surface treatments were needed. To achieve this, the spherical samples were aerodynamically levitated and melted in an argon gaseous environment for around 30–60 s so that their surfaces were chemically reduced and covered with a thin metallic layer (Figure 3a). Following this treatment, some of the samples were heated with a semiconductor laser in a dry air environment, and it was confirmed that the samples could absorb the laser radiation and that the samples temperatures could be raised. This also helped confirm that the samples’ surfaces were oxidized again at high temperatures.

Among 10 samples, 5 samples were selected for each specimen, weighed, inserted in a sample holder, and sent to the ISS.

In the ISS-ELF, a stainless-steel ball (2.0 mm in diameter) was levitated, and its images were taken for the camera calibration. Then, an oxide sample was levitated and heated by the semiconductor lasers. When the sample was successfully melted, the heating lasers were powered off. The sample cooled down, solidified, and then returned back to the sample holder. This process was repeated for all samples in the holder.

After the experiment, still images of the molten samples were captured from the recorded video for image analysis to obtain the sample volume. The detailed method of image analysis is described in Ref. [15]. In short, 400 edge points were detected and converted to polar coordinates (R,θ). Then, these points were fit with the spherical harmonic functions through sixth order as:

$$R\left(\theta \right)={\displaystyle \sum _{n=0}^6{c}_n}{P}_n\left(\cos \theta \right)$$

(1)

where P_n(cosθ) are the n-th order Legendre polynomials, and c_n are the coefficients that were determined to minimize the following value:

$$F={{\displaystyle \sum _{j=1}^{400}\left\{R_j-R_j\left(\theta \right)\right\}}}^2$$

(2)

Then, the volume was calculated by the following equation with the assumption that the sample shape is axisymmetric:

$$V=\frac{2\pi }{3}{\displaystyle {\int }_0^{\pi }{R}^3\left(\theta \right)}\sin \theta d\theta$$

(3)

The mass (m) of the processed sample was weighed once it returned to the ground, allowing to obtain the density from:

$$\rho =\frac{m}{V}$$

(4)

The temperature data were corrected using the temperature plateau and the given melting temperatures of the materials with the assumption that the emissivity values of the molten samples remained constant over the temperature range. By synchronizing the time–temperature with time–density data, the density as a function of temperature could be obtained. This density measurement procedure with the ISS-ELF was validated with Al₂O₃ [19].

3. Results and Discussion

In some experiments, the sample position control became unstable during heating due to the sudden reduction of surface charges at high temperatures, which resulted in the loss of samples. Nonetheless, some samples could be successfully melted, and the density data could be obtained.

Figure 4 shows typical time–temperature profiles of the molten samples in their cooling phases. Temperature data were adjusted so that their temperature plateau matched the given melting temperatures [23,24]. Usually, levitated samples reach deeply undercooled temperatures, but these samples did not exhibit such deep undercoolings. Masuno et al. melted Lu₂O₃ samples with an ADL and observed an undercooling of 100 K as well as a double recalescence phenomenon [25]. Such temperature profiles were not obtained in our experiments. They measured the sample temperatures with a very fast pyrometer (with a 100 kHz sampling rate), and their samples were cooled at relatively higher cooling rates than the samples in our experiment (due to gas flow). These differences may be reflected in the difference on the temperature profiles.

All the samples were successfully recovered and returned to Earth. The samples were entirely white (Figure 3b), indicating that the reduced sample surfaces were oxidized and back to original Ln₂O₃ compositions at high temperatures. Typical sample masses before and after the flight experiments are listed in

Table 2. Typical sample mass before and after the flight experiments.

Chemical Name	Mass before Launch (mg)	Mass after Retrieval (mg)
Tm2O3	17.62	17.55
Yb2O3	26.96	26.80
Lu2O3	14.62	14.62

. Slight mass losses are identified due to evaporation during the experiment. The densities were determined using the final masses weighed on the ground. The results are shown in Figure 5 and summarized in

Table 3. Measured densities at the melting temperature (ρ_m), temperature coefficients (dρ/dT), and thermal expansion coefficients (β) of Tm₂O₃, Yb₂O₃, and Lu₂O₃. The literature values are also listed.

Samples	Tm (K)	rm (kg·m−3)	dr/dT (kg·m−3·K−1)	b (10−5K−1)	Remarks
Tm2O3	2698 [12]	8304 ± 148	−0.18 ± 0.05	2.2 ± 0.6	Present work
Yb2O3	2708 [12]	8425 ± 217	−0.55 ± 0.08	6.5 ± 0.9	Present work
	2708	7940	−0.74 ± 0.13		Granier et al. [3]
	2708	8400±200			Ushakov et al. [2]
Lu2O3	2763 [12,13]	8627 ± 240	−0.43 ± 0.08	5.0 ± 0.9	Present work

with the literature values. Moreover, detailed density values are provided as a Supplementary Material.

The measured densities exhibited linear behaviors as a function of temperature and could be fitted by the following equations with a confidence interval of 95%:

$${\rho }_{T{m}_2{O}_3}\left(T\right)=\left(8304\pm 148\right)-\left(0.18\pm 0.05\right)\times (T-T_m) (\mathrm{kg}·\mathrm{m}{-}^3)$$

(5)

$${\rho }_{Y{b}_2{O}_3}\left(T\right)=\left(8425\pm 217\right)-\left(0.55\pm 0.08\right)\times (T-T_m) (\mathrm{kg}·\mathrm{m}{-}^3)$$

(6)

$${\rho }_{L{u}_2{O}_3}\left(T\right)=\left(8627\pm 240\right)-\left(0.43\pm 0.08\right)\times (T-T_m) (\mathrm{kg}·\mathrm{m}{-}^3)$$

(7)

The uncertainty of density measurements is mainly derived from the volume calculation with the image analysis. The relative uncertainty of volume (ΔV/V) is [15]:

$$\frac{\Delta V}{V}=\frac{3\Delta R}{R}$$

(8)

A typical image of a molten Ln₂O₃ sample gives R = 120 pixels, and ΔR = 1 pixel. Therefore, the uncertainty of the density measurement is estimated to be 2.5%.

Our density value for Yb₂O₃ at its melting temperature showed a good agreement with the value reported by Ushakov et al. using an AAL [2]. The density data obtained by Granier and Heurtault with an ADL [3] were about 6% lower than our results.

These discrepancies are derived from the volume calculation from the sample image. In these three methods (AAL, ADL, and ESL), the sample volume is calculated with the assumption that the sample shape is axisymmetric. Even though it is not always true for the AAL (the sample is slightly asymmetric and experiences a slight precession [2]), good Yb₂O₃ sample images have been obtained. As for the data by Granier and Heurtault, they took the sample images from the top, from which axisymmetric sample image cannot be obtained. Therefore, the sample volumes are overestimated due to sagging. Moreover, the volumes of the sample at high temperatures would be overestimated due to their high luminosity. In our experiment, ultraviolet backlighting was employed to avoid the blurring effect of the intense infrared radiation [26]. Recently, improved ADLs with shallow nozzles have been developed so that the axisymmetrical sample image can be obtained from a horizontal view [27]. Density data measured by these improved ADLs are desired.

No reference values could be found for the densities of Tm₂O₃ and Lu₂O₃.

The thermal expansion coefficient β could be calculated by the following equation:

$$\beta =-\frac{1}{\rho \left(T_m\right)}\left(\frac{d\rho }{dT}\right)$$

(9)

and was listed in Table 3.

Finally, the molar volumes at the melting temperature (V_m) were calculated and compared with the values reported by Courtial and Dingwell [4] with the indirect method. The results are presented in

Table 4. Calculated molar volumes of Tm₂O₃, Yb₂O₃, and Lu₂O₃ at the melting temperature.

Samples	Ionic Radius r (10−11 m)	Molar Weight m (g/mol)	Molar Volume Vm (cm3/mol)	Remarks
Tm2O3	8.8	385.8	46.5	Present work
			31.2	Courtial [4]
Yb2O3	8.68	394	46.8	Present work
			38.77	Courtial [4]
Lu2O3	8.61	398	46.1	Present work

.

Our previous work has reported that molar volumes of Ln₂O₃s (Ln = Gd, Er, Ho, and Tb) as well as those of some non-glass forming A₂O₃s (A = Al, Ga) show strong linear relations with the cube of the ionic radius (r³) [22]. The molar volumes obtained in the present work also agree well with the relation, as shown in Figure 6.

The value for molar volume at the melting temperature of Ga₂O₃ was reported by Dingwell et al. using the double-bob method [28], whereas that of Al₂O₃ was measured by the ISS-ELF [20]. This linear relation could not be found with the scattered data (plotted in Figure 6) by the indirect method [4].

This relation suggests that their liquid atomic structures have similarities among them. The atomic structure of the Er₂O₃ melt has been measured by X-ray and neutron diffraction experiments [21]. Structural data of other Ln₂O₃ melts are currently being measured, and the similarity in their atomic structures will be evaluated.

The ISS-ELF has the capability to measure surface tension and viscosity of molten materials by the drop oscillation method [29]. Measurements of these properties on molten Ln₂O₃ are currently being conducted and will be reported later. Recently, many groups have been pursuing research with ADLs to improve density, surface tension, and viscosity measurements of high-temperature oxide melts on the ground [27,30,31,32,33,34]. Our results will represent good benchmark data, helpful for furthering the development of ADLs.

4. Conclusions

The densities of three molten lanthanoid sesquioxides (Tm₂O₃, Yb₂O₃, and Lu₂O₃) have been successfully measured using the ISS-ELF and exhibit a good agreement with literature values. Furthermore, their molar volumes at their melting temperatures show a clear correlation with their ionic radii, which is consistent with our previous results with Gd₂O₃, Er₂O₃, Ho₂O₃, and Tb₂O₃. Currently, JAXA’s development work on the ISS-ELF focuses on the improvement in the sample position stability at elevated temperatures. This will enable the measurement of the density of ZrO₂ and HfO₂, which have melting temperatures that are higher than those of lanthanoid sesquioxides, as well as the measurement of surface tension and viscosity. These results will be reported in future publications.