P10
電磁浮遊法による酸化物融体の放射率測定
Measurement of the normal spectral emissivity of molten
oxide by electromagnetic levitation method佐藤諒平 1, 高橋圭太 1, 渡邉匡人 1,Ryohei SATO1,Keita TAKAHASHI1, Masahito WATANABE1
1

学習院大学，Gakushuin University,

1. Introduction
In thermophysical property measurement using a containerless levitation method is using non-contact measurement of its
temperature by a pyrometer. Temperature measurement by a pyrometer needs the normal spectral emissivity of sample
materials. However, there are few reports of the normal spectral emissivity of molten oxide and the investigation of theemissivity is also important for thermophysical property measurement.
Therefore, we propose to measure the normal spectral emissivity of molten oxides by utilizing the radiance difference
between liquid metals and molten oxides that form immiscible compound droplets by electromagnetic levitation (EML).
The normal spectral emissivity, which is defined ratio of the radiance of the sample materials 𝑅s and the blackbody
radiance 𝑅b is expressed as:
𝜀=𝑅s𝑅b(1)where R is defined by Planck's law as a function of temperature 𝑇 and wavelength of radiation λ and is given by
𝐶11)𝑅b (λ, 𝑇) = ( 5 ) (λexp(𝐶2 /λ𝑇) − 1(2)where 𝑐 is the speed of light, ℎ is Planck's constant, and 𝑘B is Boltzmann's constant, and 𝐶1 and 𝐶2 are the first and second
radiation constants denoted by 𝐶1 = 2ℎ𝑐 2 and 𝐶2 = ℎ𝑐/𝑘B . Typically, such emissivity measurements are performed
using a cavity at a known temperature instead of a blackbody1,2). Paradis et al. successfully determined the normal spectral
emissivity of molten alumina using an electrostatic levitation (ESL) method3). Sample materials that can be used in theESL method must have low evaporation rates under high vacuum conditions, so many molten oxides are not suitable forthis method.
Therefore, we proposed to measurement method of the normal spectral emissivity at wavelength λ by a pyrometer4). In
this experiment, we chose Fe as a reference material because many reports on normal spectral emissivity, and this melt
temperature can use proofreading. Assume that the emissivity εr of the reference material is not a function of temperature,and let 𝑅r and 𝑅s be the radiance of the reference and sample materials. The normal spectral emissivity at the detection
wavelength of pyrometer of molten oxides is expressed as:𝜀 = 𝜀r𝑅s (𝑇)𝑅r (𝑇)(3)

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Thus, ε is determined by measuring 𝑅s and 𝑅r at the same temperature. In this report, we describe the process ofdetermining the normal spectral radiance of molten oxide using pyrometer and discuss the experimental characterizationof the emissivity of molten oxides from the SiO2 -CaO-FeO system.
2. Experiment
Since the EML method uses electromagnetic force, it is a method that can be applied to substances with highconductivity, but it is difficult to apply to substances with low conductivity such as oxide samples. Therefore,
since the oxide sample alone cannot be electromagnetically levitated, it can be levitated by combining it withFe.
Since the molten oxide and liquid Fe that we deal with are immiscible, the molten oxide and molten Fe float
while being separated during electromagnetic levitation. At this time, since the oxide melt and liquid Fe havedifferent radiances, the state of separation can be confirmed. This is because the emissivity of molten oxide
and liquid Fe are different.
The oxide sample sintered to form this composite droplet was sealed in a Fe cylindrical container with apurity of 99.9%. As an assumption for this experiment, it is important that the temperature of the molten oxide
and liquid Fe be the same. If the film thickness, which is estimated from the typical thermal conductivity ofthe oxide melt (1.0Wm-1 K-1)5), is greater than 5μm, the difference in surface temperature between the molten
oxide and the liquid Fe occurs. Make adjustments for optimal levitation.
3. Result and discussion

Figure 1. Photograph of complex droplet made from liquid Fe and molten SiO2:CaO:FeO=20:20:40mass%(SCF) levitated by EML from side view.

Figure 1 is a high-speed camera image of an electromagnetically suspended molten SCF and liquid Fe. From
here, the molten SCF and liquid Fe regions can be distinguished from each other. SCF is used forthermophysical property measurements using the Electrostatic Levitation Furnace (ELF) installed on theInternational Space Station. In ELF, sample temperature is measured with an emissivity of 1, and temperaturecorrection using the normal spectral emissivity is necessary.
Due to the presence of FeO, the interfacial tension between the SCF and the liquid Fe is reduced, and themolten SCF spreads on the surface of the liquid Fe as shown in Fig. 1, and the shape changes randomly withtime and stabilizes into a band state. The pyrometer (FTXX-ANE, JAPANENSOR Corp.) used had a spot
diameter of 0.9 mm and a bandpass interference filter (900±10 nm), and the normal spectral radiance at 900
nm was incidentally obtained. The data to be acquired is measured with an emissivity of 1.
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Molten SCF radiance

Melting temperature of Fe

Liquid Fe radiance

Figure 2. Normal spectral radiance of liquid Fe and molten SCF using the pyrometer set at emissivity of
1. Large fluctuation of Molten SCF radiance is caused by the half drop shape of molten SCF. Pyrometer
detected the radiation from molten SCF and liquid Fe in periodically by the rotating complex droplet.

Figure 2 shows the normal spectral radiance obtained. Numerical simulations have shown that there is atemperature distribution in the entire mixed droplet of molten SCF and liquid Fe 6) [7]. However, since the spotof the pyrometer is operated near the interface between the molten SCF and the liquid Fe, it is assumed thatthe temperature is uniform as assumed in the experiment. The normal spectral radiance of the liquid Fe wasalmost constant, indicating that the temperature of the liquid Fe was kept almost constant during themeasurement. On the other hand, the normal spectral radiance of the molten SCF 𝑅s fluctuates much morethan that of liquid Fe. This is because liquid Fe alternately enters the spot of the pyrometer aligned with themolten SCF due to the flow of droplets. Therefore, it is difficult to determine the normal spectral radiance ofthe molten SCF. Based on this data, we evaluated 𝑅s of the molten SCF by constructing the envelope andhistogram of the normal spectral radiance data.

Liquid Fe radiance

Molten SCF radiance

Figure 3. Histogram of the normal spectral radiance from liquid Fe and molten SCF.

Figure 3 shows the histogram of normal spectral radiance data. Liquid Fe is concentrated in the region of6.2 × 108 Wsr-1 m-2 m-1, and the maximum normal spectral radiance of the molten SCF is 1.65 × 108 Wsr-1 m-2 m-1.
The value of liquid Fe is almost constant and can be easily determined. Considering the detection error of thepyrometer, we assumed the normal spectral radiance of the molten SCF is 1.6 × 108 ±5%Wsr-1 m-2 m-1 . The
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normal spectral emissivity of liquid Fe has been widely reported, such as 0.40 to 0.36 at a wavelength of 780 to920 nm7) [8] and 0.30 at a wavelength of 800 nm8) [9]. These discrepancies are believed to be caused by thepurity of the samples and the effects of surface oxidation. Based on the results of Kobatake et al. 7)[8] andWatanabe et al.8)[9], we extrapolated the normal spectral emissivity of liquid Fe at 900 nm to 𝜀Fe = 0.32. Using
this value, the normal spectral emissivity of the molten SCF was determined as 𝜀OX = 0.78 ± 0.01.
ε𝑂𝑋 and εFe obtained in the above procedure can be used to calibrate the sample temperature from Planck'slaw. However, it should be fixed using 𝐶s = 𝜀Fe (𝑅Fe /𝑅b ). The melting temperature of Fe (𝑇m = 1536℃8)[9]) is
used for correction, and the normal spectral emissivity 𝜀Fe = 0.32 is used for the normal spectral radiance 𝑅Fe .
The sample temperature corrected by 𝐶s is obtained by the expression:
𝑇i =𝐶2𝜆 ln (11+ 1)(𝐶1/𝜆5)(𝜀i /𝐶s 𝑅i )(4)

Figure 4 shows the calibrated sample temperature, and it can be confirmed that they match at about 1650℃.
Obtained from molten
SCF radiance using ε𝑂𝑋Obtained from liquid Fe
radiance using εFe

Obtained from liquid Feand molten SCF radianceusing ε = 1

Figure 4. Temperature obtained from the normal spectral radiance from liquid Fe part and molten SCF
part using the normal spectral emissivity of 0.32 for liquid Fe and 0.78 for molten SCF respectively.

Figure 5. Normal spectral emissivity of molten SCF in the temperature range 1550℃-1725℃ at thewavelength of 900nm.

Figure 5 shows the temperature dependence of the normal spectral emissivity of the SCF melt obtained by
4 of 6the above procedure. ε𝑂𝑋 = 0.78 was almost constant in the temperature range from 1550℃ to 1725℃.
The temperatures near the interface between molten Al2 O3 and liquid Fe were measured, and the normal
spectral emissivity of molten Al2 O3 turned out to be 0.80 ± 0.03%9) [10]. Several reports reported it, and Paradis
et al.3) determined a value of 0.8 based on the change in heat capacity. Petrov et al. 11) [6] demonstrated a rangeof 0.87 to 0.91 using a spectrometer and pyrometer at wavelengths of 520 nm and 720 nm. These results showthat the value of ε is smaller than that of εAL 12,13) [11-12]and the conduction electron density of molten SCF12,13)
is larger than that of molten Al2 O3 14,15). This is considered to be caused by the difference in the conduction
electron density of the samples.
To confirm this hypothesis, we investigated the normal spectral emissivity of the molten FeO. Since theelectrical conductivity of the molten FeO11,12) is lower than that of the A binary system, the normal spectralemissivity of the molten FeO is smaller than that of the molten SCF. Figure 6 shows the temperaturedependence of the normal spectral emissivity of molten FeO, which is almost constant at εOX = 0.68. This value
is smaller than the normal spectral emissivity of the molten SCF, and it can be seen that the normal spectral
radiance of the molten oxide is affected by the electrical conductivity. If the emissivity model of molten oxides
can be created in the future, it may be possible to predict the wavelength dependence of the emissivity ofmolten oxides.

Figure 6. Normal spectral emissivity of molten FeO in the temperature range 1550℃-1565℃at thewavelength of 900nm.

4. Conclusion
Using liquid Fe as a reference material and mixed droplets of molten oxide, the procedures for obtaining thenormal spectral emissivity of the molten oxide by the electromagnetic levitation method and pyrometer areshown. Our approach is based on the fact that the molten oxide and liquid Fe are immiscible and at the sametemperature. The normal spectral emissivity of the molten SCF was 0.78±0.01 for the ELF sample, and that of
the molten FeO was 0.68±0.03. This result indicates that the normal spectral emissivity of the molten oxide isaffected by the conduction electron density. In the future, the correlation between the emissivity andconductivity of molten oxides may be investigated, and an emissivity model for molten oxides may bedeveloped.
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