TY - JOUR
T1 - Noncontact modulated laser calorimetry of liquid silicon in a static magnetic field
AU - Kobatake, Hidekazu
AU - Fukuyama, Hiroyuki
AU - Minato, Izuru
AU - Tsukada, Takao
AU - Awaji, Satoshi
N1 - Funding Information:
The authors thank Professor T. Hibiya (Keio University), Professor M. Watanabe (Gakushuin University), Dr. R. K. Wunderlich (University of Ulm), Professor H. Fecht (University of Ulm), Professor I. Egry (DLR), and Dr. Ozawa (Tokyo Metropolitan University) for their helpful discussions and critical comments. The author (H.F.) appreciates financial support from the Japan Society for the Promotion of Science (Grants-in-Aid for Scientific Research), the JFE 21st Century Foundation, and the Iron and Steel Institute of Japan. This study was subsidized by the Japan Keirin Association through its Promotion funds from KEIRIN RACE and was supported by the Mechanical Social Systems Foundation and the Ministry of Economy, Trade, and Industry of Japan. This work was performed at the High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University. Table I. List of uncertainty factors of the isobaric molar heat capacity measurement. Experimental condition: T = 1827 K , R = 4.1 mm , ω = 0.63 rad s − 1 , and c p = 26.71 J mol − 1 K − 1 . Factor Standard uncertainty Sensitivity coefficient Contribution ε s 0.223 ± 0.001 ∂ c p ∂ ε s = 121.69 J mol − 1 K − 1 0.122 P 19.40 ± 0.46 W ∂ c p ∂ P = 1.31 s mol − 1 K − 1 0.61 ω 0.63 ± 1.5 × 10 − 5 rad s − 1 ∂ c p ∂ ω = − 40.56 J rad mol − 1 K − 1 s − 1 6.44 × 10 − 4 Δ T ac 10.14 ± 0.5 K ∂ c p ∂ Δ T ac = − 2.52 J mol − 1 K − 2 1.26 m 0.701 ± 0.01 g ∂ c p ∂ m = − 36.46 J g − 2 K − 2 0.36 Combined uncertainty ⋯ ⋯ 1.9 Table II. List of uncertainty factors for total hemispherical emissivity measurement Factor Standard uncertainty Sensitivity coefficient Contribution c p 29.8 ± 5.2 J mol − 1 K − 1 ∂ ε ∂ c p = 0.31 J − 1 mol K 0.063 τ r 12.1 ± 0.1 s ∂ ε ∂ τ r = − 0.02 s − 1 −0.002 T 0 1792 ± 18 K ∂ ε ∂ T o = − 4.88 × 10 − 4 K − 1 −0.009 m 0.701 ± 0.01 g ∂ ε ∂ m = − 0.44 g − 1 −0.004 r 4.03 ± 10 × 10 − 5 mm ∂ ε ∂ r = − 0.01 m − 1 − 1.00 × 10 − 7 Combined uncertainty ⋯ ⋯ 0.05 FIG. 1. (a) Schematic illustration of the electromagnetic levitation apparatus and (b) heat flow model for this noncontact modulated laser calorimetry. FIG. 2. Schematic diagram of modulated laser calorimetry in spherical coordinates. FIG. 3. ω Δ T amp and phase difference ϕ as a function of the modulation angular frequency. The solid line depicts the curve fit for determination of the hemispherical total emissivity and thermal conductivity. FIG. 4. An example of time dependence of the laser power and the temperature response of liquid silicon during modulated laser calorimetry. FIG. 5. Temperature response in an ac steady state. FIG. 6. The isobaric molar heat capacity measured in a static magnetic field at 0.5 T (diamond), 1.0 T (cross), 2.0 (square), 3.0 T (triangle), and 4.0 T (circle) with data from literature. The numbers denote reference numbers. The dotted line indicates the average of our experimental data. The solid line depicts the average of this study. FIG. 7. The hemispherical total emissivity of the liquid silicon obtained from the phase shift measured in a static magnetic field at 0.5 T (diamonds), 1.0 T (crosses), 2.0 (squares), 3.0 T (triangles), and 4.0 T (circles). The solid line depicts the average obtained in this study. FIG. 8. (a) Change in temperature of silicon droplet after turning off the laser power. (b) The hemispherical total emissivity determined from the radiative cooling curve measured in a static magnetic field at 0.5 T (diamond), 1.0 T (cross), 2.0 (square), 3.0 T (triangle), and 4.0 T (circle). The solid line in (b) depicts the average of this study. FIG. 9. (a) The thermal conductivity measured in a static magnetic field at 0.5 T (diamonds), 1.0 T (crosses), 2.0 (squares), 3.0 T (triangles), and 4.0 T (circles) together with data from literature. The numbers are reference numbers. The solid lines show the average of our experimental data obtained at respective strengths of the static magnetic field. (b) The apparent thermal conductivity measured at respective strengths of the static magnetic field. FIG. 10. AQ: PLEASE PROVIDE CAPTION FOR FIGURE 10, SINCE IT IS CITED IN TEXT.
PY - 2008
Y1 - 2008
N2 - Accurate thermal transport properties of high-temperature liquid silicon, such as those of heat capacity, emissivity, and thermal conductivity, are required for improving numerical modeling to produce high-quality silicon crystals using the Czochralski method. However, contamination from contact material and convection complicates measurements of these properties. The authors developed a noncontact modulated laser calorimetry using electromagnetic levitation in a static magnetic field. The isobaric molar heat capacity, thermal conductivity, and hemispherical total emissivity of liquid silicon were measured simultaneously at temperatures of 1750-2050 K. Convection in the levitated liquid silicon was suppressed above a static magnetic field of 2 T.
AB - Accurate thermal transport properties of high-temperature liquid silicon, such as those of heat capacity, emissivity, and thermal conductivity, are required for improving numerical modeling to produce high-quality silicon crystals using the Czochralski method. However, contamination from contact material and convection complicates measurements of these properties. The authors developed a noncontact modulated laser calorimetry using electromagnetic levitation in a static magnetic field. The isobaric molar heat capacity, thermal conductivity, and hemispherical total emissivity of liquid silicon were measured simultaneously at temperatures of 1750-2050 K. Convection in the levitated liquid silicon was suppressed above a static magnetic field of 2 T.
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U2 - 10.1063/1.2966455
DO - 10.1063/1.2966455
M3 - Article
AN - SCOPUS:51849134492
SN - 0021-8979
VL - 104
JO - Journal of Applied Physics
JF - Journal of Applied Physics
IS - 5
M1 - 054901
ER -