Simultaneous Evaluation of Viscous and Crystallization Behaviors of Silicate Melts by Capacitance and Viscosity Measurements

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1 ISIJ International, Vol. 58 (2018), ISIJ International, No. 7 Vol. 58 (2018), No. 7, pp Simultaneous Evaluation of Viscous and Crystallization Behaviors of Silicate Melts by Capacitance and Viscosity Measurements Yusuke HARADA, 1) Hideaki YAMAMURA, 2) Yoshiyuki UESHIMA, 3) Toshiaki MIZOGUCHI, 3) Noritaka SAITO 1) * and Kunihiko NAKASHIMA 1) 1) Department of Materials Science and Engineering, Kyushu University, 744, Motooka, Nishi ku, Fukuoka, Japan. 2) Research and Development Laboratories, Nippon Steel & Sumitomo Metal Corporation. Now at The Japan Institute of Metals and Materials, , Ichibancho, Aoba-ku, Sendai, Japan. 3) Research and Development Laboratories, Nippon Steel & Sumitomo Metal Corporation, 20-1, Shintomi, Futtsu, Chiba, Japan. (Received on January 12, 2018; accepted on April 9, 2018) This study set out to develop a device capable of simultaneously measuring viscosity and capacitance. The viscosity measurements required prior calibration of the device. However, room-temperature calibration using silicone oil is affected by the immersion depth of the rod, rotational speed of the crucible, and diameter/length of the torsion wire. The calibration results revealed that the potential produced by the torque acting on the torsion wire, generated by the viscous resistance of the silicone oil, was stable when the rod was immersed to a depth of 10 mm. Upon varying the rotational speed of the crucible and viscosity of the silicone oil, the rotational speed of the crucible was found to be proportional to the potential. Furthermore, the measured potential was found to be proportional to the viscosity. Based on the roomtemperature calibration results, the immersion depth of the rod was set to 10 mm. By adjusting the diameter and length of the torsion wire, a wide range of viscosities could be measured. High-temperature calibration was performed using the SRM2 standard-viscosity material and involved comparing the measured viscosity with the recommended value for SRM2 or with the results of viscosity measurements obtained by other laboratories. The viscosity measurements obtained in the present study were in good agreement with both the recommended values and the results obtained by other laboratories. Therefore, the device designed in the present study was capable of precisely measuring the viscosity. Finally, the device could also simultaneously measure the viscosity and capacitance of the simple 50CaO-50SiO 2 (mol%) and complex 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 and 43.6CaO-36.4SiO 2-10CaF 2-10B 2 O 3 (mol%) melts. Furthermore, a drastic increase in the viscosity led to a drastic decrease in the capacitance, corresponding to the crystallization of the melt, which is assumed to affect the viscosity of the melt. KEY WORDS: viscosity; capacitance; simultaneous measurement; oxide melt. * Corresponding author: saito@zaiko.kyushu-u.ac.jp DOI: 1. Introduction Oxide melts that have a microscopic network structure are important materials in various fields and are employed for various purposes; for example, as a lubricant between the molten iron and the copper molds used in continuous casting. The performance of an oxide melt is determined by its physical properties, namely, viscosity, 1 4) surface tension, 5 7) density, 8 10) and thermal conductivity ) In particular, the viscosity of a material is greatly influenced by its chemical composition and crystallization. Thus, it is necessary to investigate the crystallization behavior of oxide melts to optimize their performance. In a continuous casting process, through oscillation of the mold, the mold flux provides a shear stress field to maintain lubrication between the copper mold and the molten iron and prevent burning out the surface of the steel. 14) Therefore, investigating the crystallization behavior under a shear stress field is needed to optimize the continuous casting process. The viscosity has been measured with crucible rotation, oscillating crucible, ball pull-up methods, etc. The crystallization behavior of quenched samples after heat treatment has been observed by scanning electron microscopy (SEM) and X-ray diffraction (XRD). Furthermore, differential thermal analysis (DTA) can be used to observe the crystallization behavior in a continuous cooling process. The above methods have been combined to investigate the relationship between viscosity and crystallization, both qualitatively and quantitatively. Although some authors have reported that crystallization could be detected by measuring the capacitance of the mold flux, these studies required separate examination of the viscosity and crystallization behavior. As such, these investigations were very time consuming. Furthermore, the crystallization of the mold flux leads to ISIJ

2 a major change in viscosity. In the above method for estimating the viscosity and crystallization behavior, the flux of the sample used to measure the viscosity was subjected to a shear stress field caused by the rotation of the crucible under measurement, but the flux of the sample being used to observe the crystallization behavior was not subjected to the shear stress field. Thus, the viscosity and crystallization behavior must be investigated under the same conditions, e.g., shear stress field, cooling rate, and temperature. In the present study, a device capable of simultaneously measuring viscosity and capacitance was designed using a capacitance-measuring device previously fabricated by some authors. The device was calibrated and tested by measuring the room-temperature viscosity of normalized samples with a simple (50SiO 2-50CaO (mol%)) or complex (46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 and 43.6CaO-36.4SiO 2-10CaF 2-10B 2 O 3 (mol%)) chemical composition at high temperatures. 2. Experimental 2.1. Viscosity Measurement Calibration at Room Temperature The viscosity of the mold flux was measured using the crucible rotation method, which is a coaxial double-cylinder rotational viscosity measurement method generally capable of measuring a wide range of viscosities. Figure 1 is a schematic illustration of the device used to simultaneously measure the viscosity and capacitance. This device consists of a heating, rotating, and measuring system. The crucible and rod are made of a Pt 20 mass% Rh alloy and are utilized as the contact materials. Figure 1(a) shows the configuration of the crucible and rod. In a viscosity measurement, the viscous resistance of a melt generates a torque in the rod when the inner cylinder (rod) is placed in the outer cylinder (crucible) containing the sample and the crucible is rotated at a constant angular velocity. This generated torque is detected as a potential difference, which is then converted by a differential transformer as shown in Fig. 1(b). The crucible is rotated by a motor connected to the supporting base of the crucible. Furthermore, an oil damper installed below the differential transformer is utilized to keep the rod horizontal and quickly stabilize the displacement angle. The sample is heated and melted by six U-shaped MoSi 2 heating elements located around the crucible. A B-type thermocouple installed on the side of the crucible is used to measure the temperature. The device fabricated to simultaneously measure the viscosity and capacitance required the calibration of the cell constant for the precise measurement of the viscosity. Thus, the device was calibrated according to the following factors. Immersion depth of the rod Effect of the rotational speed of the crucible Effect of the dimensions of the torsion wire Measurement of SRM2: standard melt for high-temperature viscosity Eight types of silicone oils were utilized as standard materials to calibrate the device. The silicone oils (Shin-Etsu Chemical Co., Ltd., Tokyo, Japan) were calibrated with temperature measurements after potentiometry measurements High-Temperature Calibration of Viscosity Measurement The Pt 20 mass% Rh alloy crucible containing the sample was placed in the furnace, which was heated to the measuring temperature. To attain a uniform melt without any bubbles, the sample was held at the measuring temperature for 60 min. Then, the rod was immersed exactly 10 mm away from the point of contact with the surface of the melt. The Fig. 1. Schematic of the device designed for measuring the viscosity and capacitance: (a) crucible and rod, (b) differential transformer ISIJ 1286

3 rod was gradually lowered, while the crucible was rotated at a constant speed until a large torque is detected when the rod reaches the surface of the melt. The generated twist in the torsion wire, caused by the viscous resistance of the melt, was balanced by the torque, and the potential produced by the twist of the torsion wire was measured. In the present study, the viscosity-measuring device was calibrated using standard materials at room temperature. The results of this calibration were corrected to account for the thermal expansion of the crucible and rod. Parameter η is the measured apparent viscosity without taking into account the thermal expansion of the crucible and rod and is expressed by Eq. (1). M 1 1 h... (1) 4 R1 2 R2 2 Here, M is the torque generated by the viscous resistance of the liquid, ω is the angular velocity, h is the immersion depth, and R 1 and R 2 are the radius of the rod and crucible, respectively. Taking the thermal expansion into account, the real viscosity η is expressed by Eq. (2): M 1 1 h R R 1 4 ( 1 T ) (2) where α and T are the liner thermal expansion coefficient of the crucible and rod and the absolute temperature, respectively. Thus, the relationship between the apparent and real viscosity is calculated using Eqs. (1) and (2). ( 1 T ) 3... (3) When α << 1, Eq. (3) can be rearranged to give Eq. (4).... (4) ( 1 3 T ) Thus, the measured potential was changed to the apparent viscosity η by a calibration line, and the real viscosity was then calculated using Eq. (4) Measurement of Capacitance The same types of crucible and rod as those used to measure the viscosity and Pt wires as the contact material were used to perform the capacitance measurements. The ends of the Pt wire were connected to an impedance analyzer (IM3570, HIOKI E.E. Corporation Nagano, Japan), and an AC circuit of cylindrical electrodes was formed between the crucible and rod. The principle for detecting crystallization by measuring the capacitance is given in the literature ) The measurement frequency and applied potential were 10 khz and 5.0 V, respectively. Furthermore, a slip ring installed below the support base of the crucible was utilized to detect the electric signal from the rotating crucible Sample Preparation and Simultaneous Measurement of Viscosity and Capacitance In the present study, 50CaO-50SiO 2, 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3, and 43.6CaO-36.4SiO 2-10CaF 2-10B 2 O 3 (mol%) melts were employed. Powder batches of CaCO 3 and SiO 2 (99.9%, Sigma-Aldrich Japan Inc., Tokyo, Japan) were thoroughly mixed to attain the required compositions. The sample batches were melted at C under air and were quenched on a copper plate. The viscosity and capacitance of the 50CaO-50SiO 2 melt were measured. The sample was placed in the crucible, and the temperature was increased to C. Then, to attain a uniform melt without any bubbles, the melt was maintained at this temperature for 30 min. The rod was immersed in the melt to a depth of 10 mm, and the viscosity and capacitance were measured while rotating the crucible at 45 and 90 rpm and cooling at a rate of 5 C/min. Mother batches consisting of binary systems of the desired compositions of CaO and SiO 2 were crushed and mixed into CaF 2 (99.9%, KANTO CHEMICAL Co., Inc., Tokyo, Japan) and B 2 O 3 (99.9%, Sigma-Aldrich Japan Inc., Tokyo, Japan) to prepare the 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 and 43.6CaO-36.4SiO 2-10CaF 2-10B 2 O 3 (mol%) melts. Oxide samples containing CaF 2 are known to lose fluorine as a result of the following reaction. CaF2 H2O CaO 2HF Therefore, to prevent any undesirable loss of fluorine, the powder reagents were dried in a furnace at a constant temperature of 105 C for 24 h. After maintaining the temperature at C for 30 min, the viscosity and capacitance of the 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 and 43.6CaO- 36.4SiO 2-10CaF 2-10B 2 O 3 (mol%) melts were measured under continuous cooling at a rate of 2.5 C/min while rotating the crucible at 45 rpm. The other measurement conditions were the same as those applied to the 50CaO- 50SiO 2 melt Estimating the Crystallinity of the Melts A novel technique for determining crystallinity that relies on the variation in the capacitance of silicate melts was recently introduced. 18) The crystallinity of a melt can be estimated from the capacitance of the uniform melt and crystalline phase. The value of the capacitance depends on the crystallinity. When the size and shape of the electrode are the same, the value of the capacitance is primarily a function of the relative permittivity. Thus, the crystallinity can be estimated as follows: 18) n V1 1 n ( 1 V1) 2 n... (5) Here, ε, ε 1, and ε 2 are the relative permittivity values of the dual-phase mixture, the first phase, and the second phase, respectively, and V 1 is the volume fraction of the first phase. In the present study, the first phase is the uniform melt and the second phase is the crystallized phase. n is a dimensionless number that varies with the mechanism of current propagation through the sample melt. In the present study, a value of 1/3, typically used for crystallized phases randomly distributed against the current propagation direction, was employed. 19) When the capacitance of uniform or crystallized melts is measured, the relative permittivity can be calculated by taking into account the shape and dimension of the crucible and rod used as electrodes. 18) The crystallinity and the volume fraction of the second phase can be estimated with Eq. (6), which is derived from Eq. (5) when the relative permittivity of the crystalline phase is known ISIJ

4 n V ( 1 V1 ) n 1 1 n 2... (6) 3. Results and Discussion 3.1. Immersion Depth of the Rod To measure the viscosity, the rod must be immersed into the sample. Thus, preliminary investigations are needed to determine the appropriate immersion depth of the rod. Figure 2 shows the potential generated by the viscous resistance as a function of the immersion depth of the rod with torsion wires of different diameters in silicone oils of different viscosities. In Fig. 2, the horizontal and vertical axes represent the immersion depth of the rod and the measured potential, respectively. Each point in Fig. 2 corresponds to the average of 10 measurements under the same conditions. Furthermore, Fig. 3 shows the standard deviation of the 10 data points used in Fig. 2. As shown in Fig. 2, the potential initially increases with the immersion depth of the rod and is then stabilized at an immersion depth of about 10 mm. From Fig. 3, it is evident that the standard deviation is smallest when the rod is immersed to a depth of about 10 mm. It is thought that the`increase in the standard deviation with the immersion depth was caused by the shear stress on the bottom of the rod as it approaches the crucible. However, even when the rod was immersed to a relatively shallow depth, the standard deviation also tended to increase. This was thought to be caused by the small torque applied to the rod, which is not capable of stabilizing the twist in the torsion wire. Therefore, the influence of the shear stress caused by fluid flow at the bottom of the rod could be ignored, and the viscosity of the oxide melts could be precisely measured by using an immersion depth of 10 mm in the experiments Effect of the Rotational Speed of the Crucible In the present study, the crucible rotation method was employed to measure the viscosity. This method can geometrically estimate the viscosity, as follows: M 1 1 h R R 1 4 ( 1 T ) (2) where η is the viscosity, M is the torque generated by the viscous resistance of the liquid, ω is the angular velocity, h is the immersion depth, α is the liner thermal expansion coefficient of the crucible and rod, T is the absolute temperature, and R 1 and R 2 are the radius of the rod and crucible, respectively. As given by Eq. (2), the rotational speed of the crucible (angular velocity of crucible) is proportional to the torque acting on the rod. In the present study, the twist angle of the torsion wire is proportional to this torque and is converted to a potential by a differential transformer capable of detecting the displacement angle. However, it is not known whether the potential itself is proportional to the torque. Thus, the effect of the rotational speed of the crucible on the potential generated by the differential transformer was investigated. Figure 4 shows the relationship between the rotational speed of the crucible and the generated potential in different silicone oils. The horizontal and vertical axes represent the rotational speed of the crucible and the measured potential, respectively. As shown in Fig. 4, when silicone oils of different viscosities are employed, the potential is proportional to the rotational speed of the crucible. Therefore, this device can measure viscosity while the crucible is rotating between 40 and 90 rpm. Fig. 2. Relationship between the generated potential and the immersion depth of the rod in silicone oils of various viscosities. Fig. 3. Relationship between the standard deviation of the measured potential and the immersion depth of the rod with torsion wires of different diameters in silicone oils of different viscosities ISIJ 1288

5 Fig. 4. Relationship between the measured potential and the rotational speed of the crucible for torsion wires of different diameters Effect of the Dimensions of the Torsion Wire The relationship between the viscosity of the silicone oils and the generated potential was investigated for torsion wires of different diameters and/or lengths. The results are shown in Fig. 5, in which the horizontal and vertical axes represent the measured potential and viscosity, respectively. As shown in Fig. 5, the generated potential is proportional to the viscosity of the silicone oil regardless of the diameter or length of the torsion wire. Therefore, a wide range of viscosities can be measured by varying the diameter or length of the torsion wire Calibration using SRM2 SRM2 20) is a standard material used to measure viscosity at high temperatures. Table 1 lists the published chemical composition of SRM2. For the calibration, a SRM2 sample was placed in a crucible, and the temperature was increased to C. The sample was held at that temperature for 30 min. Then, the viscosity was measured as the temperature was reduced from C to C by 50 C increments over 30 min. Figure 6 compares the measured viscosities of SRM2 (solid circles) to the values recommended by Iida et al. (solid line), which exhibit an error of ±10% (dotted line). The horizontal and vertical axes of Fig. 6 indicate the reciprocal of the temperature and the logarithm of the viscosity, respectively. As shown in Fig. 6, the measured viscosity is in good agreement with the recommended value, and the newly developed device is therefore capable of measuring the viscosity precisely Simultaneous Measurement of the Viscosity and Capacitance of CaO SiO 2 Melts The viscosity and capacitance of 50CaO-50SiO 2 (mol%) were simultaneously measured using the device designed in the present study. The conditions described in section 2.3 were used to measure the capacitance. Figure 7 shows the viscosity and capacitance measured as a function of the liquidus temperature obtained with the hot-thermocouple method. 21) The horizontal axis represents the temperature, the right vertical axis represents the viscosity, and the left vertical axis represents the capacitance. As seen in Fig. 7, at 45 rpm, the measured capacitance gradually decreased with the temperature, and drastically decreased at C. This sudden decrease corresponds to the crystallization of the melt. Furthermore, the measured viscosity gradually increased as the temperature decreased, then increased considerably at C. These results point to the viscosity of the melt drastically increasing as the crystallization progressed. On the other hand, for the result obtained at 90 rpm, the measured capacitance gradually decreased with the temperature, dropping drastically at C. Figure 7 thus shows that, as the rotational speed of the crucible increases, the temperature at which the major decrease in capacitance/ increase in viscosity occurs also increases. It was assumed that the effect of the agitation at 90 rpm would be larger than that at 45 rpm. As such, it was also assumed that the agitation accelerated the crystallization. In addition, it was assumed that the decrease in the capacitance was caused only by the crystallization of the melt. Therefore, the crystallinity in the temperature range shown in Fig. 7 can be quantified by the relative permittivity of a uniform melt at C and upon crystallization. As mentioned in section 2.5, at 90 rpm, the relative permittivity can be calculated from the capacitance at C. Assuming that the crystal formed is CaO SiO 2, whose relative permittivity of is 8.6, 22) the crystallinity at each temperature can be estimated, and the results are shown in Fig. 8. The crystallinity gradually increases as the capacitance decreases below the liquidus ISIJ

6 Fig. 5. Relationship between the viscosity of the silicone oil and the measured potential for torsion wires of different diameters and/or lengths. Table 1. Chemical composition of SRM2 (mass%). SiO 2 Al 2O 3 Li 2O K 2O Na 2O MgO CaO TiO 2 P 2O 5 SRM < <0.10 <0.01 Fig. 7. Simultaneous measurement of the temperature dependence of the viscosity and capacitance of the 50CaO- 50SiO 2 (mol%) melt. Fig. 6. Temperature dependence of the viscosity of the SRM2 melt. temperature. At C, where the drastic decrease in capacitance/increase in viscosity occurs, the crystallinity is about 51%. At 45 rpm, the crystallinity at C is esti ISIJ 1290

7 Fig. 8. Estimated crystallinity of the 50CaO-50SiO 2 (mol%) melt. Fig. 9. Temperature dependence of the viscosity and crystallinity of the 50CaO-50SiO 2 (mol%) melt. mated to be 49%. Based on these values, it is thought that the drastic increase in viscosity corresponds to a crystallinity of about 50%. Given the above results, the capacitance and viscosity can be measured simultaneously, and the crystallinity of the melts could be estimated from the measured capacitance. Figure 9 shows the relationship between the logarithm of the viscosity, the crystallinity of the CaO SiO 2 melt, and the reciprocal of the absolute temperature at a rotating speed of 90 rpm, which forms an Arrhenius plot. The solid line represents a linear relationship between the viscosity and the reciprocal of the temperature from C to C (liquidus temperature of 50CaO-50SiO 2 (mol%)). Generally, the viscosity of the melts increases with decreasing temperature, and the viscosity of a uniform melt in such a narrow temperature range reproduces an Arrhenius plot. As shown in Fig. 9, the measured viscosity is higher than the approximate straight line at approximately 7% of crystallinity. This suggests that the apparent viscosity of the melt increased not only because of the decrease in temperature but also owing to the coexistence of a solid-liquid state from the crystallization Simultaneous Measurement of the Viscosity and Capacitance of the CaO SiO 2 CaF 2 B 2 O 3 Melts Figure 10 shows the results of the simultaneous capacitance and viscosity measurements of 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 and 43.6CaO-36.4SiO 2-10CaF 2-10B 2 O 3 (mol%), with the liquidus temperature obtained by the Hot-thermocouple method. In Fig. 10, the horizontal axis represents the temperature, the right vertical axis represents the viscosity, and the left vertical axis represents the capacitance. As shown Fig. 10, for each additional amount of B 2 O 3, the viscosity significantly increased while the capacitance drastically decreased. With the addition of about 5 mol% of B 2 O 3, the capacitance exhibits a twostage variation below liquidus temperature of C. The capacitance first began to decrease at C, and then again at C. These decreases correspond to the detection of crystallization, with the first stage of crystallization causing a drastic increase in the viscosity. On the other hand, with the addition of 10 mol% B 2 O 3, the capacitance gradually decreased with the temperature. Subsequently, a greater decrease which deviated from the trend of decreasing in the capacitance with temperature was observed at 1291 Fig. 10. Simultaneous measurement of the temperature dependence of the viscosity and capacitance of the CaO SiO 2 CaF 2 B 2O 3 melt. temperature of about C. Conversely, the viscosity increased with this greater decrease in the capacitance. The super-cooling degree is the difference between the temperature of first decrease in capacitance, the crystallization temperature, and the liquidus temperature. As shown Fig. 10, the super-cooling degree of the slag containing 10 mol% B 2 O 3 (270 C) was larger than that of 5 mol% B 2 O 3 (50 C). Generally, B 2 O 3 is known to be an acidic oxide that forms a network structure in the melts and, we can state that B 2 O 3 is a network former. Therefore, compared to the addition of 5 mol% of B 2 O 3, the addition of 10 mol% of B 2 O 3 caused a decrease in the temperature at which the significant decrease in the capacitance began, as a result of suppressing the crystallization by hindering the transfer of the materials needed for crystallization. Figure 11 shows that the progress of the crystallization with the 5-mol% B 2 O 3 addition was faster than that with the 10-mol% B 2 O 3 addition. Furthermore, with the 5-mol% B 2 O 3 addition, the crystallinity at C, at which the drastic increase in viscosity occurred, could be estimated to be about 13%. This value is smaller than the result given in section 3.5 and is caused by the difference in the morphologies of the crystallized solids. At room temperature, the shape of the dispersed solids in a suspension has been observed to significantly affect the viscosity. 23) 2018 ISIJ

8 Fig. 11. Estimated crystallinity of the CaO SiO 2 CaF 2 B 2O 3 melt. 4. Conclusion A device capable of simultaneously measuring viscosity and capacitance was designed and calibrated. The viscosity and capacitance of the simple 50CaO-50SiO 2 (mol%) and complex 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 and 43.6CaO- 36.4SiO 2-10CaF 2-10B 2 O 3 (mol%) melts were simultaneously measured using the device. The major findings were as follows. The optimum immersion depth of the rod for the viscosity measurement was investigated as part of the calibration of the device. It was found that the error in the torque generated by the viscous resistance of the silicone oil was minimal when the rod was immersed to a depth of 10 mm. To measure a wide range of viscosities, torsion wires of different diameters must be used. The viscosity of an SRM2 melt was measured at a high temperature, with the measured value being in good agreement with the recommended value and those obtained in other studies. Therefore, the device designed in the present study is capable of precise viscosity measurements. The device can simultaneously measure viscosity and capacitance and detect crystallization, which affects the viscosity of the melts. The new device can thus determine viscosity and crystallization more rapidly than has been possible in the past. It was observed that the viscosity of the melt drastically increases as the crystallization progresses. REFERENCES Fig. 12. Temperature dependence of the viscosity and crystallinity of the CaO SiO 2 CaF 2 B 2O 3 melt. Therefore, in the CaO SiO 2 - and CaO SiO 2 CaF 2 B 2 O 3 - based melts, the morphologies of the crystalline phases were assumed to be different. The change in the crystallinity led to the increase in the viscosity. Figure 12 shows the relationship between the logarithm of the viscosity, the crystallinity of the 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 (mol%) melt, and the reciprocal of the absolute temperature, which forms an Arrhenius plot. The solid line in Fig. 12 represents a linear relationship between the viscosity and the reciprocal of the temperature from C to C (the liquidus temperature of 46.4CaO-38.6SiO 2-10CaF 2-5B 2 O 3 (mol%)). As shown in Fig. 12, the measured viscosity is higher than the straight line at approximately 4% of crystallinity, which is lower than that of the CaO SiO 2 melt. This difference is considered to be caused by the difference in morphology of the crystalline phases. The simultaneous evaluation of the viscous and crystallization behavior, such as the one carried in this study, could be advantageous for the estimation of the viscosities of solid-liquid melts. 1) D. Elwell, P. Capper and C. M. Lawrence: J. Cryst. Growth, (1974), ) H. Y. Chang, T. F. Lee and T. Ejima: Trans. Iron Steel Inst. Jpn., 27 (1987), ) K. C. Mills: ISIJ Int., 33 (1993), ) N. Saito, S. Yoshimura, S. Haruki, Y. Yamaoka, S. Sukenaga and K. Nakashima: Tetsu-to-Hagané, 95 (2009), ) M. Askari and A. M. Cameron: Can. Metall. Q., 30 (1991), ) P. Vadasz, M. Havlik and V. Danek: Can. Metall. Q., 39 (2000), ) E. J. Jung and D. J. Min: Steel Res. Int., 83 (2012), ) L. W. Coughanour, L. Shartsis and H. F. Shermer: J. Am. Ceram. Soc., 41 (1958), ) S. Hara and K. Ogino: Can. Metall. Q., 20 (1981), ) H. Kania, K. Nowacki and T. Lis: Metalurgija, 52 (2013), ) A. Nagashima: Int. J. Thermophys., 11 (1990), ) M. Hayashi, H. Ishii, M. Susa, H. Fukuyama and K. Nagata: Phys. Chem. Glasses, 42 (2001), 6. 13) Y. Kang, J. Lee and K. Morita: Metall. Mater. Trans. B, 44 (2013), ) M. Suzuki, H. Mizukami, T. Kitagawa, K. Kawakami, S. Uchida and Y. Komatsu: ISIJ Int., 31 (1991), ) Y. Ohta, M. Kitayama, K. Kaneko, S. Toh, F. Shimizu and K. Morinaga: J. Am. Ceram. Soc., 88 (2005), ) N. Saito, K. Kusada, S. Sukenaga, Y. Ohta and K. Nakashima: ISIJ Int., 52 (2012), ) Y. Harada, K. Kusada, S. Sukenaga, H. Yamamura, Y. Ueshima, T. Mizoguchi, N. Saito and K. Nakashima: ISIJ Int., 54 (2014), ) Y. Harada, N. Saito and K. Nakashima: ISIJ Int., 57 (2017), ) H. Looyenga: Physica, 31 (1965), ) T. Iida and Y. Kita: Boundary, 10 (1996), ) Y. Ohta, K. Morinaga and T. Yanagase: J. Jpn. Inst. Light Met., 34 (1984), ) K. Hayashi, M. Fukui and I. Uei: J. Ceram. Assoc. Jpn., 89 (1981), ) S. Sukenaga, S. Haruki, Y. Yamaoka, N. Saito and K. Nakashima: Tetsu-to-Hagané, 95 (2009), ISIJ 1292