Magnesium Deoxidation Equilibrium of Molten Fe Cr Ni Alloy Expressed by Quadratic Formalism and Redlich-Kister Type Polynomial

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1 ISIJ International, Vol. 5, No. 6, pp Magnesium Deoxidation Equilibrium of Molten Fe Ni Alloy Expressed by Quadratic Formalism and Redlich-Kister Type Polynomial Ryo YAMAMT, Hiroshi FUKAYA, Naoya SATH, 3 Takahiro MIKI 4 and Mitsutaka HIN 5 Formerly Graduate Student, Tohoku University. Now at Nippon Steel and Sumikin Stainless Steel Corp., Japan. Graduate Student, Tohoku University, Japan. 3 Formerly Department of Metallurgy, Graduate School of Engineering, Tohoku University. Now at Yasuki Works, Hitachi Metal Corporation. 4 Department of Metallurgy, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-, Sendai, Japan. 5 Professor Emeritus, Tohoku University. Now at Hokkaido Polytechnic College, Japan. Received on February, ; accepted on March 7, Ni alloy was determined by a chemical equilibrium method at temperature of 873 to 973 K. Extreme care was taken of oxygen analysis of the samples. Numerical analysis on deoxidation of molten Fe Ni alloy has been carried out by utilizing the model based on Darken s quadratic formalism and Redlich-Kister type polynomial. Magnesium deoxidation equilibrium can be pressed in wide composition region of the Fe Ni alloy. KEY WRDS: quadratic formalism; thermodynamics; activity; cess free Gibbs energy; Redlich-Kister polynomial; magnesium deoxidation equilibrium; iron; chromium; nickel.. Introduction Magnesium has been used as a deoxidizer due to its strong affinity with oxygen. Reliable thermodynamic information of deoxidation equilibrium is important for inclusion control in clean steel and its alloy production. Many researchers have reported deoxidation equilibrium of molten iron. However, deoxidation equilibrium measurements on Ni and Fe Ni, Fe alloy are limited. Ishii et al. and Zhao et al. have reported deoxidation of Ni at temperature of K and K, respectively. hta and Suito 3 have measured deoxidation equilibrium of Fe to 6 mass%ni, Fe to 4 mass% and Fe 8mass% 8 mass%ni alloys at 873 K. Yonemoto et al. 4 have reported deoxidation equilibrium of whole Fe Ni alloy composition at temperature of K. However, deoxidation equilibrium of Fe Ni alloy has not been determined at various temperatures and in wide alloy composition range. Recently, some of the present authors have developed a thermodynamic treatment to press deoxidation equilibrium on not only pure metals and but also alloys. This model is based on Darken s quadratic formalism 5,6 and Redlich- Kister type polynomial, 7,8 and the details are plained in the previous papers. 9 3 mass% mass%ni, Fe 4mass% mass%ni and Fe mass% 4massNi% alloys was determined by a chemical equilibrium method at temperature of 873 to 973 K in the present. Also, numerical analysis on deoxidation of molten Fe Ni alloy has been carried out by application of the above-mentioned solution model.. Experimental Procedures Measurement was performed with an induction furnace of kva described elsewhere. 4,5 The apparatus consisted of a ing quartz tube, gas purification trains and gas flow meters. The melt temperature was measured with an optical pyrometer calibrated with the m.p. of iron and nickel. Electrolytic metals of nickel, chromium and iron were utilized in the periment. Iron purity 99.99%, chromium purity 99.99% and nickel purity 99.99% weighing approximately g were placed in a magnesia crucible, mm in ID and 9 mm in depth, which was put in an outer protective magnesia crucible, and the space between the two was filled with magnesia sand. After completion of the ing tube assembly, the metal was melted in a purified 67 vol%hydrogen-argon gas mixture atmosphere for 3 h in order to reduce the oxygen dissolved in the melt. The atmosphere was then changed to purified argon maintained at about ml/min. After the melt was kept at the desired perimental temperature, nickel-magnesium alloy was added from the top of the ing tube. Nickel-magnesium alloy was pre-produced by melting highly purified magnesium of mass% into molten nickel with an induction furnace. After the sample was held for required time, the furnace power was switched off and the sample was quenched by inpinsing He gas. It was found that magnesium content gradually decreases with holding 895 ISIJ

2 ISIJ International, Vol. 5, No. 6 time. However, the product of magnesium and oxygen content didn t change after holding time of min in the preliminary periments. Hence, 3 min was chosen as perimental holding time. All quenched samples were cut, polished by SiC abrasive paper and then electrolytically-polished for 3 min. under the condition of 5V.5A. Mixed acid that contains 8 mass% acetic acid and mass% perchloric acid was used for electrolyte. The samples were ultrasonically cleaned in acetone and immediately submitted to oxygen analysis by inert gas fusion infrared absorptionmetry to avoid effect of oxygen Table. Experimental results on deoxidation equilibrium of molten Fe Ni alloy. T/K [mass%] [mass%ni] [mass ppm ] [mass ppm ] adsorped on sample surface. Iron, chromium, nickel and magnesium contents were analyzed by an induction coupled plasma emission spectrometry. 3. Results and Discussion Experimental results are shown in Table and plotted in Figs. to 3. The perimental results of hta and Suito 3 for Fe 8mass% 8mass%Ni alloy at 873 K were compared with the present results in Fig.. The magnesium content of the present result was lower than that reported value of hta and Suito. The magnesium deoxidation equilibrium determined in the present does not agree with their reported values. Lines in Figs. to 3 were obtained from the numerical analysis shown later. Quadratic formalism and Redlich- Kister type polynomial were used in the present numerical analysis and were plained in the previous papers. 9 3 Pure substance is chosen as a standard state Raoultian stan- Fig.. Fig.. Ni alloy at 873 K. Ni alloy at 93 K. ISIJ 896

3 ISIJ International, Vol. 5, No. 6 Fig. 3. Ni alloy at 973 K. dard state for condensed phases in the present. Hypothetical dissolved oxygen in the melt equilibrating with 35 Pa atm oxygen gas has been selected as a standard state for oxygen. The relation between the oxygen activity and oxygen partial pressure in this standard state can be pressed as following equation. a = P... Therefore, the oxygen activity is independent of the kind of metal solvent and can be pressed by the equilibrium oxygen partial pressure. Magnesium deoxidation reaction can be pressed by Eq.. + = s... Pure liquid is chosen as a standard state for. This equation can be separated into following equations. l + g = s... 3 = g... 4 The Gibbs free energy change of Eq. 4 is zero due to the relation of Eq.. Therefore, the Gibbs free energy change of Eq. is identical to the Gibbs free energy change of formation ΔG f, o. Equation and the Gibbs free energy change of formation can be utilized on deoxidation of any metals or alloys. The equilibrium constant of Eq., K, can be pressed as following equation. ΔG f, ln K = RT = ln a lnγ lnγ ln X ln X =lnγ lnγ ln X ln X a =... 5 Where, the activity of is taken as unity, since deoxidation product is pure. Here, a i, X i and γ i are the activity, mole fraction and the activity coefficient of component i, respectively. The cess Gibbs free energy change for Fe Ni system, ΔG, can be pressed as Eq. 6 using Redlich- Kister type polynomial. { } { X X } { } ΔG = X X + X X Fe Fe Fe Fe + X X + Fe Ni FeNi FeNi Fe Ni Fe Fe Fe Fe FeX { Fe + Fe XFe X } Ni Ni Ni Ni + X X + X X + X { } { + X X } { } { + } { } { } { efeni + X X + X X + X X + X X + X X + X X X X Ni Ni Ni Ni + X X + X X Ni Ni Ni Ni + X X + X X + X X X + X Fe Ni Fe Ni Fe F + X FeNi + XNi NiFeNi} + X ΔG fus,... 6 Here, and ΔG fus, are interaction parameters in Redlich- Kister type polynomial and the Gibbs free energy change of chromium fusion. The partial molar cess free energy changes of and can be derived as following equations. ΔG = RT lnγ ΔG = ΔG X XNi + X X XNi X =X X Fe Fe XFe X XFe X Fe XFeXNi FeNi XFeXNi XFe XNi FeNi X XNi Ni X XNi X XNi Ni XFe X Fe XFe X XFe X Fe X X X X X X X X X X X X X X Ni Ni Ni Ni Ni + + X + X X X X X + X X Ni + XNi XNi X XNiX + X + X X X X X + X FeNi + 3XFe FeFeNi + 3X FeNi + X X X X X X X X + X... 7 Fe Fe Fe Fe Fe Fe + X Ni + X X X X X Fe Ni + 3XNi NiFeNi Ni ΔG = RT lnγ = ΔG X XNi X X XNi X =X X X X X X XFe X X X X X X X X X X X Fe Fe Fe Fe Fe Ni Fe Ni Fe Ni Fe Ni Fe Ni Ni Ni Ni Ni Ni X X X X X X Fe Fe Fe Fe Fe + X ΔG X 897 ISIJ

4 ISIJ International, Vol. 5, No. 6 X X X X X X X X X X X X Ni Ni Ni Ni Ni X + X X X X X X X X Fe Fe Fe Fe Fe + X X X X X X X X + Fe X Ni X Ni X Ni X Ni X X Ni X X Ni + X + X X X XX + X XFe X XNi FeNi + 3XFe FeFe Ni + 3X + 3XNi NiFeNi FeNi... 8 The following relation can be obtained by substituting Eqs. 7 and 8 into Eq. 5. XFe X Fe 4XFe X XFe X Fe XFe XNi FeNi 4XFeXNi XFe XNi FeNi X XNi Ni 4X XNi X XNi Ni + X X + X X X 4X X + 4X + X X + X X X 4X X + 4X Fe Fe Fe Fe Fe Fe + X X + XNi XNi X 4XNiX + 4X Ni Ni + X + X X X + X XFeX XN i FeNi + 3XFe FeFeNi + 3X FeNi + 3XNi NiFeNi + RT ln X + RT ln X ΔGf, =... 9 Equation 9 is the fundamental equation for numerical analysis on deoxidation of molten Fe Ni alloy. The parameters,6 3 utilized for numerical analysis in the present are shown in Table. The unknown parameters in Eq. 9,,, Ni and Ni were obtained by multiple regression from the present perimental results, parameters shown in Table and Eqs. 4. Values in parenthesis are the estimated errors. Magnesium deoxidation equilibria of molten Fe Ni Ni + X 4XX + X X + X X X X Fe Fe Fe Fe 4 FeX + 4X Fe + X X + X X X X X 4 + 4X + X X + X X X 4X X + 4X Ni Ni Ni Ni Ni < < Ni - / J = T ± 3 X., 873K 973K... < < - / J = 3 + 7T ± 3 X., 873K 973K... < < Ni- / J = 366 5T ± 3 X., 873K 973K... 3 < < Ni- / J = 3T ± 3 X., 873K 973K... 4 Table. Parameters utilized and determined in the present study. Temperature Function J/mol Region of Validity Ref. Fe T Fe 33 Fe Ni T Fe Ni T Fe T Fe T Fe T Fe T Ni T Ni T T T Ni T Ni T T Fe Ni 9 5T Fe Fe Ni Fe Ni 3 Ni Fe Ni T 3 +7T Ni 366 5T Ni 3T < X Fe < 83 < = T < = 973 K < X Fe < 83 < = T < = 973 K < X Fe < 83 < = T < = 973 K < X Fe < 83 < = T < = 973 K < X <. 83 < = T < = 973 K < X <. 83 < = T < = 973 K X < =.4 83 < = T < = 973 K X < =.4 83 < = T < = 973 K < X Fe < 83 < = T < = 973 K < X Fe < 83 < = T < = 973 K X < =.3 83 < = T < = 973 K X < =.3 83 < = T < = 973 K X < =. 83 < = T < = 973 K X < =. 873 < = T < = 973 K X < =. 873 < = T < = 973 K X < =. 873 < = T < = 973 K <X Fe<, < X Ni< 873 < = T < = 973 K <X Fe<, < X Ni< 873 < = T < = 973 K <X Fe<, < X Ni< 873 < = T < = 973 K <X Fe<, <X Ni< 873 < = T < = 973 K < X <. 873 < = T < = 973 K < X <. 873 < = T < = 973 K < X <. 873 < = T < = 973 K < X <. 873 < = T < = 973 K alloy at 873, 93 and 973 K obtained from the numerical analysis are shown in Figs. to 3 with the perimental results. The perimental results agree well with the numerical analysis and it was confirmed that the deoxidation equilibrium of molten Fe Ni alloys could be quantitatively pressed. The parameters obtained by multiple regressions were carefully checked to clarify the sensitivity of errors on deoxidation equilibrium. The values of each ΔG f, T 873 < = T < = 3 K 3 ISIJ 898

5 ISIJ International, Vol. 5, No. 6 Fig. 4. mass% mass%ni alloy considering the estimated errors of the parameters determined in the present. Fig. 7. Equilibrium oxygen content equilibrated with under the condition of ppm in Fe Ni alloy and 873 K. parameter were gradually varied and the possible error range was estimated by trial and error. As a result, errors of parameter obtained in Eqs. 4 were estimated to be 3 J. Estimated error range for deoxidation equilibrium are shown in Figs. 4 6 for Fe mass% mass%ni, Fe 4mass% mass%ni and Fe mass% 4mass%Ni, respectively. Areas between dashed lines are the possible deoxidation equilibrium using the estimated error of 3 J. Width of the estimated error increases with increase of and Ni content of alloy. It was found that most of the perimental results fall inside the estimated error. Therefore, estimated error in the present is considered to be reasonable. The equilibrium oxygen content equilibrated with under the condition of ppm in Fe Ni alloy and 873 K is shown in Fig. 7. It was found that the oxygen content increases with chromium or nickel content. Quadratic formalism and Redlich-Kister type polynomial could be utilized to press deoxidation equilibrium in the wide composition region of the Fe Ni alloy. Fig. 5. 4mass% mass%ni alloy considering the estimated errors of the parameters determined in the present. 4. Conclusion Ni alloy was determined by a chemical equilibrium method at temperature of 873 to 973 K by taking treme care of oxygen analysis. Magesium deoxidation equilibrium was quantitatively pressed by binary interaction parameters determined on basis of the quadratic formalism and Redlich- Kister type polynomial. Interaction parameters in Redlich- Kister type polynomial were determined as follows. - / J = T ± 3 X., 873K 973K < < - / J = 3 + 7T ± 3 X., 873K 973K < < Fig. 6. mass% 4mass%Ni alloy considering the estimated errors of the parameters determined in the present. < < Ni- / J = 366 5T ± 3 X., 873K 973K < < Ni- / J = 3T ± 3 X., 873K 973K Magnesium deoxidation can be pressed with high accuracy in wide composition and temperature for molten Fe Ni alloy. 899 ISIJ

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