Thermodynamic Calculation of Interfacial Tension between Liquid Iron Alloys and Molten Slag. Toshihiro Tanaka Osaka University, Japan.

Transcription

1 Thermodynamic Calculation of Interfacial Tension between Liquid Iron Alloys and Molten Slag Toshihiro Tanaka Osaka University, Japan. Thermodynamic Databases Surface Properties of of Alloys, Salts Salts etc. etc. Calculation of of Phase Diagrams 1) 1) Surface Tension of of Liq. Liq. Alloys & Molten Ionic Mixtures 2) 2) Interfacial Tension of of Liquid Fe Fe and and Molten Slag Slag 3) 3) Phase Diagram of of Nano-Particle

2 3 Surface Tension of A-B Binary Alloy σ : Butler's Equation RT (1-N BS ) 1 1 σ= σ A + ln + G E,S A (T,N BS ) - G E,B A (T,N BB ) A A (1-N BB ) A A RT N S B 1 1 = σ B + ln + G E,S B (T,N BS ) - G E,B B (T,N BB ) A N B B B σ X : Surface Tension of Pure Liq. X A X = LN 1/3 0 V 2/3 X Molar Volume Excess Gibbs Energy in in Surface A B G X E,S (T,N BS ) = β*g X E,B (T,N BS ) 1 A B 2 A A Superscripts: S : Surface =>(Outermost monolayer ) B : Bulk Thermodynamic Databases Speiser et al. (1989) Z S 9 β = = = 0.75? Z B 12 Liquid? Ionic Liq.? β =(Z S )'/Z B Apparent Ratio of Coordination Number in Surface / Bulk

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4 (Z S ) G Ex,Surface β = = (Z B ) G Ex,Bulk Coordination Number H Eva,X σ ={ ={ 1 - (Z S ) Ξ - } Ξ } = {{ 1 -- β }} (Z B ) A X H Eva,X A X

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6 Molten Salt Mixtures If If G Ex,Surface Ex,Surface = β G Ex,Bulk Ex,Bulk (Z S ) β = = Z B? (Z S ) β Additional Factor Factor? Z B for for Molten Molten Salt Salt Mixtures

7 In Bulk Lumsden (1961) In Surface Electric Charge Neutrality? Change in Ionic Distance at Surface? Surface Relaxation Struc. Sawada et al. (1979)

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9 Molten Molten CaO-SiO 2 2 Surface Tension of Molten Slag Molten Molten Fe Fe X O-CaO-SiO X 2 2

10 Evaluation of of Interfacial Tension between Liquid Fe Fe alloy alloy and and Molten Slag Slag in in Iron Iron & Steelmaking Processes Molten Slag Liq. Fe Alloy Calc. Calc. of of Compositions in in Liq. Liq. Fe Fe Alloy Alloy and and Molten Molten Slag Slag by by Thermodynamic Databases Calc. of Surface Tension of Liquid Fe Alloy Calc. of Surface Tension of Molten Slag Calc. of Interfacial Tension between Liquid Fe alloy and Molten Slag by Girifalco-Good Equation

11 Interfacial Tension between Liquid Fe Alloy and Molten Slag In Steelmaking Processes Gilifalco -- Good Equation (1957) σ Fe-Slag = Fe-Slag σ Fe + Fe σ Slag - Slag - 2 Φ(σ Fe Fe σ Slag ) Slag ) 1/2 1/2 σ Fe-Slag : Interfacial Tension between Liq. Fe & Molten Slag σ Fe &σ Slag : Surface Tension of Liq. Fe & Molten Slag Φ = N FeO : Cramb & Jimbo (1989)

12 Interfacial Tension between Liquid Liquid Fe Fe Alloy Alloy and and Molten Molten Slag Slag 1853K CaO-35 SiO SiO Al Al 2 O 2 3 +(5-30) 3 +(5-30) FeO FeO

13 Thermodynamic Databases Phase Diagram Bulk Size Smaller Surface Tension Effect of Surface on Phase Equilibria? Smaller Smaller Phase Diagram of Nano-Particle?

14 G G Total Total = G G Bulk Bulk + G + G Surface Surface (1) Liquid-Solid Equilibrium of Alloy in Small Particle with Radius r 2σ L V L 2(N G G Surface A σ AS V S A + N B σ BS V BS ) Surface = -- (2) r r Reference State : Pure Solid r σ L & V L σ S X & V X S : Radius of a Particle : Surface Tension & Molar Volume of Liquid Alloy : Surface Tension & Molar Volume of Pure Solid X σ X Solid σ Xmp L 1.25σ Xmp L Liquid σ X L σ S X S = X σ L Xmp L + Xmp (T-T (T-T X,mp ) X,mp ) (3) (3) T Liquid m.p. Temp.

15 For For Pure Pure Metals Metals Phase Equilibria Melting Point G G Total Total = G = G Bulk Bulk + G G Surface Surface 2σ = G G X LS X LS + XL V L X 2σ - XS V S X - = 0 r r Expe. : Sambles(1971) Expe.:Coombes(1972)

16 (a) Bulk (b) 20 nm (c) 10 nm (d) 5 nm

17 Relationship between Activity & Surface tension

18 Cu-Pb alloy alloy Cu-Bi alloy alloy Au-Si alloy alloy Composition dependence of nano-particle phase diagrams depends on that of surface tension.

19 Interfacial Tension between Liq. Fe Alloy and Molten Slag Surface Tension of Liq. Alloys & Molten Ionic Mixtures Thermodynamic Databases Phase Diagrams of Nano-Particles Multi-functional Thermodynamic Databases

20 References (1) T. Tanaka and T. Iida, "Application of a Thermodynamic Database to Calculation of Surface Tension for Iron Base Liquid Alloys", Steel Research, 65 (1994), pp (2) T. Tanaka, K. Hack, T. Iida and S. Hara, "Application of Thermodynamic Databases to the Evaluation of Surface Tensions of Molten Alloys, Salt Mixtures and Oxide Mixtures", Z. Metallkde., 87 (1996), pp (3) T. Tanaka, S. Hara, M. Ogawa and T. Ueda, "Thermodynamic Evaluation of the Surface Tension of Molten Salt Mixtures in Common Ion Alkali-Halide Systems", Z. Metallkde., 89 (1998), pp (4) T. Tanaka, S. Hara, M. Ogawa and T. Ueda, "Evaluation of Surface Tension of Molten Salt Mixtures", Molten Salt Forum, 5-6 (1998), pp (5) T. Tanaka, K. Hack and S. Hara, "Use of Thermodynamic Data to Determine Surface Tension and Viscosity of Metallic Alloys", MRS Bulletin, 24 (1999), pp (6) T. Tanaka and S. Hara, "Thermodynamics of Surface Tension of Molten Salt Mixtures", Electrochemistry, 67, No.6, (1999), pp (7) T. Ueda, T. Tanaka and S. Hara, "Thermodynamic Evaluation of Surface Tension of Molten Salt Mixtures in Alkali-Halides, Nitrate, Carbonates and Sulfate Systems", Z. Metallkde., 90 (1999), pp (8) T. Tanaka and S. Hara, "Application of Thermodynamic Databases to Evaluation of Interfacial Tension between Liquid Steels and Molten Slag", Z. Metallkde., 90 (1999), pp (9) T. Tanaka, K. Hack and S. Hara, "Calculation of Surface Tension of Liquid Bi-Sn Alloy using Thermochemical Application Library ChemApp", CALPHAD, 24 (2001), pp (10) T. Tanaka and S. Hara, "Thermodynamic Evaluation of Binary Phase Diagrams in Small Particle Systems", Z. Metallkde., 92 (2001), pp (11) T. Tanaka and S. Hara, "Thermodynamic Evaluation of Surface Tension of Liquid Metal-Oxygen Systems", Steel Research, 72 (2001), pp (12) T. Tanaka and S. Hara, "Thermodynamic Evaluation of Nano-Particle Binary Alloy Phase Diagrams", Z. Metallkunde, 92 (2001), pp