OR3-9
密閉型ガスジェット浮遊装置による Hypercooling limitを利用した金属の融解熱測定
Measurement of the Heat of Fusion for Pure Metals
using Hypercooling Limit with a Closed Type
Aerodynamic Levitator
河本幹太 1, 小畠秀和 1, 後藤琢也 1,Kanta KAWAMOTO1, Hidekazu KOBATAKE1, Takuya GOTO1
1

同志社大学，Doshisha University#1,

1. Introduction
The heat of fusion of metals is a critical thermophysical property that governs the mass transfer phenomenon
at the solid-liquid interface. Therefore, obtaining reliable data of heat of fusion is crucial for the numericalsimulations of high temperature material processing via liquid phase such as the crystal growth or casting1).
Conventionally, the heat of fusion is measured using thermal analysis such as differential scanning calorimetry
with containers. However, the reactivity of metals with the container material can lead to sample
contamination and increased uncertainty in the heat of fusion measurement. To address this challenge, theelectrostatic levitation method has been employed for heat of fusion measurements by analyzing thetemperature profile during recalescence2). However, on the ground condition, electrostatic levitation has adifficulty in the controlling the atmosphere because measurement is needed to be conducted under vacuum.
In this study, we conducted the heat of fusion measurement for Fe, Ni, and Co using a closed type aerodynamic
levitator with controlling the oxygen partial pressure.
2. Principle of measurement
When recalescence was occurred at the temperature of the hypercooling limit, the heat of fusion ΔHf, can be
expressed with the following equation,∆𝐻f = 𝐶p ∆𝑇hyp ,(1)where, 𝐶p denotes the heat capacity at constant pressure, ∆𝑇hyp is hypercooling limit.
On the other hand, when the solidification processed with no undercooling, the heat of fusion is expressedwith the following equation, with considering both radiative heat loss and forced convection heat transfer,𝜎B 𝐴𝜀T 4(𝑇 − 𝑇r4 ) + ℎg (𝑇 − 𝑇r )} 𝑑𝑡.
∆𝐻f = ∫ − {𝑚(2)Here, 𝑚 is the mass of sample, 𝜎B is Stefan-Boltzmann constant, 𝐴 is surface area of the sample, 𝜀T is total
hemispherical emissivity, 𝑇 is temperature of the sample, 𝑇r is the surrounding temperature, ℎg is heattransfer rate.
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Alternatively, when the solidification processed with undercooling, the heat of fusion is expressed with thefollowing equation,
𝜎B 𝐴𝜀T 4(𝑇 − 𝑇r4 ) + ℎg (𝑇 − 𝑇r )} 𝑑𝑡.
∆𝐻f = 𝐶p ∆𝑇 + ∫ − {𝑚(3)3. Experiment
Fe, Ni, and Co samples with the 2.0 mm diameter were levitated within Ar-H2 gas flow using a closed typeaerodynamic levitator. The samples were subjected to heating by

CO2laser irradiation. Once the samples

were completely molten, the laser was turned off and samples were cooled, and then solidified. Temperatureof the samples was measured by two-color pyrometer that was calibrated using the Wien’s law at therespective melting point.
4. Results and discussion
An example of the temperature profile of Fe during solidification is shown in Figure. 1. From thetemperature profile, the undercooling, ∆𝑇, and the thermal plateau time, ∆𝑡, can be obtained. The correlation
between ∆𝑇 and ∆𝑡 of Fe sample is shown in Figure. 2. Since the term of𝜎B 𝐴𝜀T𝑚(𝑇 4 − 𝑇r4 ) + ℎg (𝑇 − 𝑇r ) in Eq(2) or Eq (3) cab be considered as constant when the temperature was kept the melting point, the correlation
between ∆𝑇 and ∆𝑡 has a linear function as shown in Figure. 2. By the extrapolating the linear relation of∆𝑇 vs. ∆𝑡 liner function to ∆𝑡 = 0 ∆𝑇hyp can be determined. From Figure. 2, the ∆𝑇hyp of Fe was determinedas 280 ± 16 K. When the 𝐶p of 45.4 J K-1 mol-1 in the literature value3) and the determined ∆𝑇hyp of 280 K were
substitute in Eq (1), ∆𝐻f of Fe was determined to be 12.7 ± 0.7 k J mol-1. By conducting similar measurement∆𝑇hyp of Ni and Co were determined to be 414 ± 46 K and 360 ± 30 K, respectively. These ∆𝑇hyp values
coupling with the literature 𝐶p values4) gave ∆𝐻f of Ni and Co as 16.1 ± 1.8 k J mol-1, and 14.6 ± 1.2 k J mol-1,respectively. These ∆𝐻f values of Fe, Ni and Co measured using closed type aerodynamic levitator showed agood consistence with the literature values4) within the uncertainty.

Figure 1. An example of temperature profile during solidification.

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Figure 2. Correlation between undercooling and thermal plateau time of Fe.

References
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4)

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S. Jeona, M.P. Sansoucieb and D.M. Matsona: Hypercooling limit, heat of fusion, and temperature-dependent specificheat of Fe-Cr-Ni melts. The Journal of chemical thermodynamics, 138 (2019) 51,
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