Kinetic Study on Recovery of Antimony in Anode Slime from Used Lead Batteries Utilizing Volatile Oxide Formation

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1 Materials Transactions, Vol. 46, No. 3 (2005) pp. 658 to 664 #2005 The Japan Institute of Metals Kinetic Study on Recovery of Antimony in Anode Slime from Used Lead Batteries Utilizing Volatile Oxide Formation Satoshi Itoh 1, Junji Ono 2; *, Mitsutaka Hino 2 and Tetsuya Nagasaka 1 1 Department of Environmental Studies, Graduate School of Environmental Studies, Tohoku University, Sendai , Japan 2 Department of Metallurgy, Graduate School of Engineering, Tohoku University, Sendai , Japan From the viewpoint of recycling and recovery of metal values from used lead-batteries, especially from lead anode slime, recovery of antimony has been studied experimentally. First, oxidation kinetics has been investigated for pure liquid antimony in the temperature range between 973 and 1373 K to elucidate the reaction mechanism. Since lead anode slime generally consists of antimony, lead and bismuth, oxidation experiments have also been carried out using antimony-lead-bismuth alloy. It was found that gas phase mass transfer step mainly controls the overall oxidation rate. The overall rate was expressed as the sum of antimony oxide and metallic antimony evaporation rates. The oxide evaporation is dominant at lower temperature around 1073 K with higher oxygen partial pressure. In the experiment of the antimony-leadbismuth alloy simulated for anode slime, only the oxide Sb 4 O 6 evaporation was observed, indicating that antimony was preferentially oxidized followed by evaporation of antimony oxide. The oxidation rate of the alloy was substantially identical with that of pure antimony. This is the advantage of oxidation treatment for anode slime. (Received December 3, 2004; Accepted January 19, 2005) Keywords: antimony oxidation followed by evaporation as antimony oxide Sb 4 O 6, kinetics, lead-battery, recycling, reaction mechanism, ratedetermining step 1. Introduction Lead batteries are used worldwide for automobiles and emergency power sources and are accepted for storing of electric power. Lead-batteries generally consist of leadantimony alloy grid, lead sulfate, lead peroxide, lead paste, and dilute sulfuric acid for electrolytic solutions, glass wool and plastics for separators. Recently lead-calcium alloys have been applied to electrodes instead of lead-antimony alloys for a maintenance-free battery so as to inhibit both from selfdischarge of batteries and generation of hydrogen gas. This kind of electrode, however, runs down in a short time, since it has weakness in heat. A hybrid battery has been thus developed in which lead-antimony and lead-calcium alloys are used for positive and negative electrodes, respectively. 1 3) Used lead-batteries are crushed and fractionized to remove nonmetallic materials, and then melted in a lead blast furnace to produce a crude lead metal after control the antimony content. However, a pure lead is required to prepare a leadcalcium alloy electrode. The pure lead can be obtained by means of electrolytic and/or pyrometallurgical refining. In the lead electrorefining, antimony is concentrated in anode slime. Anode slime consists of mass% Pb, mass% Sb and mass% Bi. 4) Since antimony has a stronger affinity for oxygen than the other element such as lead and bismuth in the anode slime, an oxidation of anode slime leads to form antimony oxide and then the oxide will evaporate as Sb 4 O 6 vapor because of its high vapor pressure. As a result, lead and bismuth will be concentrated. With respect to the recycling and recovery of metal values from used lead-batteries, especially from anode slimes produced in the lead electrorefining, oxidation experiments were conducted with pure liquid antimony to elucidate the oxidation kinetics and mechanism. Oxidation experiments *Graduate Student, Tohoku University. Present address: NSK Ltd., Fujisawa, Japan were also carried out using antimony-lead-bismuth alloy simulated for anode slime, since lead anode slime generally consists of antimony, lead and bismuth as mentioned before. 2. Oxidation Reaction of Antimony The oxidation reaction of antimony with oxygen is given by eq. (1) due to the high vapor pressure of Sb 4 O 6. Sb(l) þ 3/4O 2 (g) ¼ 1/4Sb 4 O 6 (g) ð1þ The equilibrium constant of eq. (1), which is given by eq. (2), is 10 7 to in the temperature range between 973 and 1373 K according to Barin 5) and Itoh et al. 6) as shown in Table 1, indicating that the reaction proceeds thermodynamically in the right-hand-side direction. K ¼ ðp Sb 4 O 6 =P Þ 1=4 a Sb ðp O2 =P Þ 3=4 ð2þ where K, P i, P and a Sb are equilibrium constant of eq. (1), partial pressure of component i, standard pressure Pa (¼ 1 atm) and activity of antimony, respectively. The reaction sequence in the gas-liquid system consists of gas phase mass transfer step, chemical reaction step at liquidgas interface and liquid phase mass transfer step. In general, the gas phase mass transfer step is not so influenced by temperature, while it depends on gas flow rate, gas concentration (oxygen partial pressure) and reactor geometry such Table 1 Equilibrium constant of eq. (1). T/K K ( ) 973 4: : : : :

2 Kinetic Study on Recovery of Antimony in Anode Slime from Used Lead Batteries Utilizing Volatile Oxide Formation 659 as shape and volume. The liquid phase mass transfer step is commonly affected by stirring condition of melt, however, it is unaffected by temperature. The chemical reaction rate is generally independent of gas flow rate, but it depends on temperature and oxygen partial pressure. From the above-mentioned viewpoint, oxidation kinetics of pure liquid antimony was investigated for the effects of gas flow rate, oxygen partial pressure and temperature. Experiments were also carried out using antimony-lead-bismuth alloy simulated for anode slime to clarify the oxidation kinetics and mechanism. 3. Experimental 3.1 Materials Pure antimony and antimony-lead-bismuth alloy were used for the oxidation experiments. The alloy was preliminarily prepared by melting antimony, lead and bismuth with mass ratio of 2:1:1 corresponding to the typical composition of anode slime. 4) The purity of each metal was mass%. 3.2 Experimental setup and procedure Figure 1 shows the schematic diagram of the experimental setup. The oxidation rate was measured by a gravimetric method with crucible-type reactor at constant temperature of 973, 1073, 1173, 1273 and 1373 K. The sample was put in an alumina crucible with internal diameter 18 mm. The crucible was suspended from an electronic balance into a quartz reaction tube with internal diameter 29 mm by a stainless steel wire to measure the sample mass change. While the sample was being heated to the experimental temperature, argon gas was passed into the reaction tube through a quartz nozzle with internal diameter 3.4 mm. The gas inlet nozzle was set mm above the liquid sample surface. When the temperature of the sample had reached the desired constant temperature, inert argon gas was switched to O 2 -Ar gas mixture, and then the measurement of the mass change was commenced. The oxygen partial pressure was adjusted by regulating the gas ratio of O 2 /Ar gas mixture and then set P O2 =P to be constant 0, 0.05, 0.10, 0.15 and The gas flow rate was set to be constant in the range of 4: m 3 (STP)s 1 to 16: m 3 (STP)s 1. The mass of pure antimony and alloy used for each experimental run were about 30 g and 39 g, respectively. All the experiments were carried out more than twice for each experimental condition in order to confirm the reproducibility of the experimental data. 4. Results and Discussions 4.1 Oxidation rates of pure antimony The linear relation was observed between the mass loss of pure antimony and time as shown in the last Fig. 9, indicating that the reaction steadily proceeds at constant rate. The phase in the evaporated reaction product that condensed at room temperature was identified to be antimony oxide Sb 2 O 3 by using X-ray diffraction technique. This indicates that the antimony oxide vapor Sb 4 O 6 produced was cooled to room temperature followed by condensation as Sb 2 O 3. Therefore, the mass loss was regarded due to the oxide evaporation as Sb 4 O 6. Thus the oxidation rate was calculated from the mass loss as mole of antimony per unit area and time, where the area of liquid antimony surface was estimated from the cross section of the alumina crucible by assuming that the liquidgas interface was flat plane. Figure 2 shows the effect of gas flow rate on the oxidation rates of pure antimony at 1073 K as an example, where solid lines correspond to the calculated overall oxidation rates mentioned later. The oxidation rates increase with increasing gas flow rate. However, in the case of oxygen partial pressure P O2 =P ¼ 0 shown by the broken line corresponding to the simple metal evaporation rate, the reaction rate was significantly small compared to the oxidation rates. The abovementioned observation was also found at the other temperatures. The effect of oxygen partial pressure on the oxidation rates of pure antimony at 1073 K is shown in Fig. 3 as an example, Fig. 1 Schematic diagram of experimental setup. Fig. 2 Effect of gas flow rate on the oxidation rates of pure antimony at 1073 K.

3 660 S. Itoh, J. Ono, M. Hino and T. Nagasaka Fig. 3 Effect of oxygen partial pressure on the oxidation rates of pure antimony at 1073 K. Fig. 4 Effect of temperature on the oxidation rates of pure antimony under the condition of V G /m 3 (STP)s 1 = 16: where solid lines correspond to the calculated overall oxidation rates mentioned later. The oxidation rates increase in proportion to the oxygen partial pressure. This trend was also observed at the other temperatures. Consequently, it should be noted that the oxidation rates considerably depend on both the gas flow rate and the oxygen partial pressure. Figure 4 shows the effect of temperature on the oxidation rates of pure antimony under the condition of V G / m 3 (STP)s 1 = 16: as an example, where solid lines are the calculated overall oxidation rates mentioned later. The temperature dependence of the oxidation rates is relatively small, while that of the metal evaporation rate shown by the broken line is considerably large. At low temperature 973 K, the metal evaporation rate is almost two orders of magnitude smaller than the oxidation rates. This suggests that metal evaporation is negligible at lower temperatures. Such tendency was also found with the other gas flow rates. The oxidation rates were considerably affected by gas flow rate and the temperature dependence of the oxidation rates was relatively small as mentioned before. It can thus be Fig. 5 Pressure profile in the gas phase under the condition of P b O2 = P ¼ 0:20 at 1073 K. inferred that chemical reaction does not control the oxidation rate, but gas phase mass transfer mainly controls the oxidation rate. Then in the present work kinetic analysis was conducted by assuming gas phase mass transfer control. Figure 5 shows the partial pressure profile in the gas phase under the condition of P b O 2 =P ¼ 0:2 at 1073 K. Since the gas phase consists of O 2,Sb 4 O 6 and Ar, the Stefan-Maxwell equations shown by eq. (3) 7) were applied, where x i, C, D ij, N i are mole fraction of i in gas phase, gas concentration, diffusivity of the pair ij in a binary mixture and molar flux of i, respectively. rx i ¼ Xn 1 ðx i N j x j N i Þ ð3þ CD ij j¼1 D O2 -Ar can be estimated by using the Chapman-Enskog equation, 8) while both the binary diffusivities of D O2 -Sb 4 O 6 and D Ar-Sb4 O 6 can not be estimated, because the Lennard-Jones potential concerning antimony oxide is not known. Then the molar flux of antimony oxide was not taken into account, although it is one-third of that of oxygen. That is to say, gas phase is simplified and assumed to be oxygen-argon pseudo-binary system. Then eq. (3) becomes eq. (4). rx O2 ¼ 1 CD O2 -Ar ðx O2 N Ar x Ar N O2 Þ Since the molar flux of argon is zero and x Ar þ x O2 ¼ 1, eq. (4) gives eq. (5). rx O2 ¼ 1 CD O2 -Ar ðx O2 1ÞN O2 Consequently, eq. (6) is derived by integrating eq. (5). N O2 ¼ P RT k g ln P Pb O 2 P P e ð6þ O 2 where P, R, T, k g, P b O 2 and P e O 2 are total pressure, gas constant, temperature, mass transfer coefficient in gas phase, oxygen partial pressure in bulk of gas and oxygen partial pressure in equilibrium, respectively. Equation (7) is given stoichiometrically from eq. (1) that is the oxidation reaction of antimony with oxygen. r Sb ¼ 4=3N O2 ð7þ ð4þ ð5þ

4 Kinetic Study on Recovery of Antimony in Anode Slime from Used Lead Batteries Utilizing Volatile Oxide Formation 661 where r Sb and N O2 denote oxidation rate of antimony and molar flux of oxygen, respectively. On substituting eq. (6) for eq. (7), the following eq. (8) is derived. r Sb ¼ 4P 3RT k g ln P Pb O 2 P P e ð8þ O 2 The equilibrium partial pressure of oxygen P e O 2 =P is 7: to 3: in the temperature range of 973 to 1373 K. 5,6) Hence, the equilibrium partial pressure of oxygen is negligibly small compared to total pressure P=P ¼ 1, and then eq. (8) gives eq. (9). r Sb ¼ 4P! 3RT k g ln 1 Pb O 2 ð9þ P By substituting the measured oxidation rate r Sb and the oxygen partial pressure in bulk of gas P b O 2 in eq. (9), the gas phase mass transfer coefficient k g can be obtained. Then the Sherwood, Schmidt and Reynolds numbers defined by eqs. (10), (11) and (12) were calculated by substituting the mass transfer coefficient obtained. Sh dk g =D G Sc =ðd G Þ Re du= ð10þ ð11þ ð12þ where d,,, D G and u are internal diameter of nozzle, viscosity of gas, density of gas, diffusivity of gas and characteristic velocity of gas, respectively. Table 2 shows the diffusivity of oxygen-argon binary mixture, viscosity and density of gas for each P b O 2 at various temperatures. Figure 6 shows the obtained correlation between Sh=Sc 0:5 and Re for pure antimony at 973 and 1073 K, together with that for water at 301 and 304 K. The evaporation experiments of water were conducted in argon gas stream at room Table 2 Diffusivity of oxygen-argon binary mixture, viscosity and density of gas for each P b at various temperatures. O2 T (K) D O2-Ar (m 2 s 1 ) P b =P O2 ( ) (kgm 1 s 1 ) (kgm 3 ) 973 1: : : : : : : : : : : : : : : : : : : : : : Fig. 6 Correlation between Sh=Sc 0:5 and Re for pure antimony at 973 and 1073 K, together with that for water at 301 and 304 K. temperature in order to determine the mass transfer characteristics in the gas phase. The evaporation rate of water is given by eq. (13). 9) r H2 O ¼ k g RT ðps H 2 O Pb H 2 O Þ ð13þ where r H2 O, P s H 2 O and Pb H 2 O are evaporation rate of water, partial pressure of water at surface and partial pressure of water in bulk of gas, respectively. The partial pressure of water in bulk of gas is negligibly small compared to that at surface, yielding the following eq. (14). r H2 O ¼ k g RT Ps H 2 O ð14þ Based on eq. (14), the gas phase mass transfer coefficient k g was obtained for water by substituting the evaporation rate of water measured and the partial pressure of water at surface. 10) Table 3 shows vapor pressure of water, diffusivity of water-argon binary mixture for water vapor diffusing through argon, viscosity and density of argon gas at room temperature. The Sherwood, Schmidt and Reynolds numbers were calculated from eqs. (10), (11) and (12), respectively. The equation relating to the mass transfer characteristics in the gas phase is expressed as eqs. (15) and (16) in the Reynolds number range of 36 to 485 and is shown in Fig. 6, together with the results of Taniguchi et al. 11) for oxidation of graphite at 1773 K and Brimacombe et al. 12) for oxidation of copper sulfide in the temperature range of 1473 to 1573 K. Sh ¼ 0:0239Re 0:86 Sc 0:5 ¼ 0:104ðr s =dþ 1:5 Re 0:86 Sc 0:5 ð15þ ð16þ Table 3 Vapor pressure of water, diffusivity of water-argon binary mixture, viscosity and density of argon gas at room temperature. T (K) P s H2O =P ( ) D H2O-Ar (m 2 s 1 ) (kgm 1 s 1 ) (kgm 3 ) 301 3: : : : : :

5 662 S. Itoh, J. Ono, M. Hino and T. Nagasaka Fig. 8 Fraction of oxide and metal evaporations as a function of oxygen partial pressure under the condition of V G /m 3 (STP)s 1 = 16: Fig. 7 Correlation between Sh=Sc 0:5 and Re at 1173, 1273 and 1373 K for pure antimony. where r s is radius of alumina crucible. The correlation for water agrees with that of Taniguchi et al. 11) The correlation for antimony is independent of both the oxygen partial pressure and the temperature, and exhibits good agreement with eq. (15). This indicates that gas phase mass transfer step mainly controls the overall reaction rate at lower temperatures of 973 and 1073 K in the oxidation reaction of pure antimony. Figure 7 shows the correlation at higher temperatures above 1173 K for the sake of comparison with that at lower temperatures. The deviations from eq. (15) are observed. At the higher temperatures metal evaporation may simultaneously proceed in addition to oxide evaporation. Since the deviation becomes large with decreasing oxygen partial pressure and with increasing temperature, the deviation is considered owing to metal evaporation. A kinetic model for antimony oxidation with oxygen is then proposed by assuming gas phase mass transfer control, where metal evaporation occurs in parallel with oxide evaporation. The following eq. (17) is given. n Sb ¼ n Sb, oxide þ n Sb, metal ð17þ where n Sb, n Sb, oxide and n Sb, metal denote the antimony mole loss of overall, oxide and metal evaporations, respectively. Thus the overall reaction rate is described by eq. (18) as the sum of oxide and metal evaporation rates. ð r Sb Þ¼ð r Sb, oxide Þþð r Sb, metal Þ ð18þ where r Sb, r Sb, oxide and r Sb, metal are overall, oxide evaporation and metal evaporation rates, respectively. The oxide evaporation rate was estimated from eq. (15), since eq. (15) reproduces the correlation for antimony oxide evaporation as shown in Fig. 6. The metal evaporation rate is given by the measured data of P O2 =P ¼ 0. The calculated overall rates reproduce the measured data very well as above shown in Figs. 2, 3 and 4. Incidentally, solid lines in Fig. 4 are the calculated overall reaction rates, and the dash-dot and broken lines correspond to the oxide and metal evaporations, respectively. It can thus be inferred that the metal evaporation occurs in parallel with the oxide evaporation in the antimony oxidation reaction. The fraction of the oxide and metal evaporations was then calculated, where the fraction of the oxide and metal evaporations was defined as eqs. (19) and (20), respectively. f Sb, oxide ¼ð r Sb, oxide Þ=ð r Sb Þ ð19þ f Sb, metal ¼ð r Sb, metal Þ=ð r Sb Þ ð20þ The obtained fraction of the oxide and metal evaporations is shown in Fig. 8 as a function of oxygen partial pressure. It is found that the oxide evaporation is dominant at lower temperature around 1073 K with higher oxygen partial pressure. Currently antimony oxide is of great demand for flameproof agents, cosmetic and pigment. Therefore, from the view point of saving energy and recovery of antimony, as not metal but oxide, an oxidation of antimony concentrated in anode slime should be operated with higher oxygen partial pressure at lower temperature around 1073 K. 4.2 Oxidation rates of simulated anode slime The oxidation experiment was conducted using antimonylead-bismuth alloy with mass ratio of Sb:Pb:Bi = 2:1:1 simulated for anode slime 4) so as to recover antimony as oxide under the condition at lower temperature with higher oxygen partial pressure. Figure 9 shows the variation of the Fig. 9 Relation between the mass loss of the alloy simulated for anode slime and time, together with that of pure antimony.

6 Kinetic Study on Recovery of Antimony in Anode Slime from Used Lead Batteries Utilizing Volatile Oxide Formation 663 Table 4 Calculated equilibrium partial pressures of oxygen and antimony oxide Sb 4 O 6 at 1073 K for P b =P ¼ 0:20. O2 a Sb P e =P O2 P e =P Sb4O : : : : : : : : mass loss of the alloy simulated for anode slime with time. The dash-dot line corresponds to the alloy. Since the mass loss measured is the total mass loss of volatile components in the alloy, chemical analysis for the alloy and X-ray diffraction for the reaction product were conducted. It was found that only the antimony oxide evaporated. Therefore, antimony was preferentially oxidized and evaporated as antimony oxide Sb 4 O 6. The thick solid line shows the result of pure antimony. The oxidation rate of the alloy is almost equal to that of pure antimony. This indicates that the alloy oxidation proceeds with the same mechanism as pure antimony and liquid phase mass transfer step does not influence the overall reaction rate. This is the advantage of oxidation treatment for anode slime. Table 4 shows the calculated equilibrium partial pressures of oxygen and antimony oxide Sb 4 O 6 at 1073 K for P b O 2 =P ¼ 0:20. The activity of antimony in the starting alloy with mass ratio of Sb:Pb:Bi = 2:1:1 simulated for the anode slime is about 0.6 at 1073 K 13) in the antimony-leadbismuth alloy. The activity of antimony decreases as the oxidation reaction proceeds. Since the equilibrium partial pressure of oxygen is negligibly small compared to the total pressure, exactly the same equation as that of pure antimony is given, which is previously shown as eq. (9). Thus an oxidation reaction of anode slime proceeds with the same rate as that of pure antimony even with the activity of antimony 0.01, which corresponds to the concentration of 0.6 mass% Sb in the antimony-lead-bismuth alloy, as far as gas phase mass transfer is predominant. Consequently, from the view point of saving energy and recovery of antimony, as not metal but oxide Sb 2 O 3,an oxidation of antimony concentrated in anode slime followed by evaporation as antimony oxide Sb 4 O 6 should be operated with higher oxygen partial pressure and sufficient amount of gas flow rate at lower temperature around 1073 K. The antimony oxide vapor is cooled and recovered as Sb 2 O 3.Asa result, lead and bismuth are concentrated in the anode slime and finally in lead and bismuth litharge slags at the end of the oxidation. 14) The lead litharge slag is then returned to a lead blast furnace. The bismuth litharge slag can be reduced to bismuth metal anode, which is refined by the conventional electrolysis, producing pure bismuth. 5. Conclusions (1) Gas phase mass transfer step mainly controls the overall oxidation rate for pure antimony in the present experimental range. Overall rate was expressed as the sum of oxide and metal evaporation rates. Oxide evaporation is dominant at lower temperature around 1073 K with higher oxygen partial pressure. (2) In the experiment of antimony-lead-bismuth alloy, only the antimony oxide Sb 4 O 6 evaporation was observed, that is, antimony was preferentially oxidized and the oxide evaporated. (3) Oxidation rate of the alloy was substantially identical with that of pure antimony. This is the advantage of oxidation treatment for anode slime. Gas phase mass transfer step is the rate-determining step in the alloy oxidation reaction. (4) From the view point of saving energy and recovery of antimony, as not metal but oxide, an oxidation of antimony concentrated in anode slime should be operated with higher oxygen partial pressure and sufficient amount of gas flow rate at lower temperature around 1073 K. Acknowledgments The authors would like to express appreciation to Mr. Saiboku Yamada (formerly Tohoku University) for assistance in part of the experiments. Nomenclature C: gas concentration (molm 3 ) D G : diffusivity of gas (m 2 s 1 ) K: equilibrium constant of reaction, Sb(l)+3/4O 2 (g) = 1/4Sb 4 O 6 (g) ( ) N O2 : molar flux of oxygen (molm 2 s 1 ) P: total pressure (Pa) P i : partial pressure of component i (Pa) P : standard pressure Pa (¼ 1 atm) (Pa) R: gas constant (Jmol 1 K 1 ) Re: Reynolds number ( du=) ( ) Sc: Schmidt number ( =ðd G Þ ( ) Sh: Sherwood number ( dk g =D G )( ) T: temperature (K) V G : gas flow rate (m 3 (STP)s 1 ) a Sb : activity of antimony ( ) d: internal diameter of nozzle (m) f Sb, metal : fraction of metal evaporation ( ) f Sb, oxide : fraction of oxide evaporation ( ) k g : mass transfer coefficient in gas phase (ms 1 ) n: mole of antimony (mol) m: mass loss (g) r s : radius of alumina crucible (m) r H2 O: evaporation rate of water (molm 2 s 1 ) r Sb : oxidation rate of antimony (molm 2 s 1 ) t: time (s) u: characteristic velocity (ms 1 ) x i : mole fraction of i in gas phase ( ) : density of gas (kgm 1 s 1 ) : viscosity of gas (kgm 3 ) Superscript b: bulk e: equilibrium s: surface

7 664 S. Itoh, J. Ono, M. Hino and T. Nagasaka REFERENCES 1) M. Hirano and F. Sakurai: J. Min. Mater. Proc. Inst. Japan 113 (1997) ) M. Shima, S. Kawakita and S. Mori: J. Min. Mater. Proc. Inst. Japan 107 (1991) ) T. Oishi: Materia Japan 35 (1996) ) A. Amano: Private Communication, Hosokura Smelting & Refining Co., Ltd., 17th, Nov ) I. Barin, ed.: Thermochemical Data of Pure Substances, 2nd ed., (Federal Republic of Germany, 1993) pp ) S. Itoh and T. Azakami: J. Japan Inst. Metals 48 (1984) ) R. B. Bird, W. E. Stewart and E. N. Lightfoot: Transport Phenomena, (John Wiley & Sons, Inc., Addison-Wesley, 1960) p ) R. B. Bird, W. E. Stewart and E. N. Lightfoot: Transport Phenomena, (John Wiley & Sons, Inc., Addison-Wesley, 1960) p ) S. Taniguchi, A. Kikuchi and S. Maeda: J. Iron Steel Inst. 62 (1976) ) National Astronomical Observatory ed.: Chronological Scientific Tables, (Maruzen Co., Ltd., 1991) p ) S. Taniguchi, A. Kikuchi and S. Maeda: J. Iron Steel Inst. 63 (1977) ) A. H. Alyaser and J. K. Brimacombe: Metall. Mater. Trans. B 26B (1995) ) J. Takahashi: Thermodynamic Study of Liquid Lead Ternary Alloys by Atomic Absorption Method, (Master Thesis of Tohoku University, 1985). 14) S. Itoh and A. Kikuchi: High Temperature Materials and Processes 23 (2004)