Contents of Today S.J.T.0. Phase Transformation and Applications Page 1/34 Review previous Immiscibility Spinodal Points Compounds etc. Conclusion Remarks Examples SJTU Thermodynamics of Materials Fall 2011 @X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 1/34 Contents of Today Review previous Immiscibility Spinodal Points Compounds etc. Conclusion Remarks Examples
Review of Last S.J.T.U. Phase Transformation and Applications Page2/34■ ·The lever rule Simple eutectic diagram ·Cooling curves SJTU Thermodynamics of Materials Fall 2011 @X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 2/34 Review of Last • The lever rule • Simple eutectic diagram • Cooling curves
Binary System S.J.T.0. Phase Transformation and Applications Page334■ Degrees of freedom available in the system(F): F=C-P+1 F=C-P+2 F:the number of system variables that we may freely vary,or arbitrarily fix C:components P:phase C=2 P=1,F=2 单相区 P=2,F=1 平衡线包围的两相区 P=3,F=0 三相平衡线 SJTU Thermodynamics of Materials Fall 2011 @X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 3/34 Binary System Degrees of freedom available in the system (F): F: the number of system variables that we may freely vary, or arbitrarily fix C: components P: phase F = C − P + 2 C = 2 3, 0 2, 1 1, 2 = = = = = = P F P F P F F = C − P +1 单相区 平衡线包围的两相区 三相平衡线
9.1 Freezing Point Depress4ion(4) S.J.T.0. Phase Transformation and Applications Page 4/34 稀溶液的依数性 Liquid Liquid T→x Tm (melting temperature) L+S T T Solid A XB.1 XB→ B XB L(T-T) RT △T=Tm-T ln(1-z)=-z small z SJTU Thermodynamics of Materials Fall 2011 X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 4/34 9.1 Freezing Point Depress4ion (4) 2 ( ) m m B RT L T T x − = z z small z T Tm T − = − Δ = − ln(1 ) 稀溶液的依数性 T ↔ x T Liquid Tm (melting temperature) Solid A B Tm T xB T1 Liquid xB,l L+S
9.2 The Lever Rule (1) S.J.T.0. Phase Transformation and Applications Page 5/34 In a two-phase region of a condensed system,if the overall composition is given,the quantities of the various phases can be calculated,beside to the the composition. Liquid F=fraction liquid Fs=fraction solid L+S F Fs=1,and a mass balance FXB-XBs F= XB-XB.s (XB-XB,s） FS XBI-XB XBI-XB.S A B XB.S XB XB.1 XB→ Fig.9.4 Illustration of the lever rule. SJTU Thermodynamics of Materials Fall 2011 X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 5/34 9.2 The Lever Rule (1) In a two-phase region of a condensed system, if the overall composition is given, the quantities of the various phases can be calculated, beside to the the composition. Fig. 9.4 Illustration of the lever rule. Fl=fraction liquid FS=fraction solid Fl+ FS=1, and a mass balance B l B B B s S x x x x F F − − = , 1 , B l B S B B s x x x x F , , , 1 − − = B xB A Tm T xB,S xB xB,l T1 Fig. 9.4 Illustration of the lever rule. B xB A Tm Liquid xB,l L+S xB,S xB ( ) B B,S x − x ( ) B,l B x − x Fig. 9.4 Illustration of the lever rule
9.3 Simple Eutectic Diagram S.J.T.0. Phase Transformation and Applications Page 6/34 A-B system,A and B are immiscible in the solid state,but completely miscible in the liquid state. When the melting point depression lines intersect,the material will solidify totally into T solid A and solid B,eutectic temperature. ,B The lowest temperature at which a liquid Liquid solution of A and B may exist at equilibrium L+Solid B with solid A and B.eutectic composition. L+Solid A At eutectic point:phase rule TEutectic Liquid solida solidB T Solid A:+Solid B F=C-P+1=2-3+1=0 XEutectic A B If all three phases are present,at equilibrium, XB the system must at the eutectic temperature and the liquid will have the eutectic composition. Fig.9.5 Simple eutectic phase diagram. SJTU Thermodynamics of Materials Fall 2011 X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 6/34 9.3 Simple Eutectic Diagram A-B system, A and B are immiscible in the solid state, but completely miscible in the liquid state. When the melting point depression lines intersect, the material will solidify totally into solid A and solid B, eutectic temperature. The lowest temperature at which a liquid solution of A and B may exist at equilibrium with solid A and B. eutectic composition. At eutectic point: / phase rule Liquid = solidA + solidB F = C − P +1 = 2 − 3+1 = 0 If all three phases are present, at equilibrium, the system must at the eutectic temperature and the liquid will have the eutectic composition. TEutectic A B T xB Tm,A Tm,B Liquid L+Solid A L+Solid B Solid A + Solid B xEutectic Fig. 9.5 Simple eutectic phase diagram
S.J.T.0. Phase Transformation and Applications Page 7/34 T G 公切线符合多相平衡 G*9 条件 C*9 G* 残= △，G 处于平衡条件两相的 =μ △-x 平衡组成 0 图6-8两相平衡时的成分-自由能曲线 SJTU Thermodynamics of Materials Fall 2011 @X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 7/34 公切线符合多相平衡 条件 处于平衡条件两相的 平衡组成
G S.J.T.0. Phase Transformation and Applications 34 固液完全互溶 的体系 T G G r (a) (b) SJTU Thermodynamics of Ma 图6-9两组元完全互溶的相图
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 8/34 固液完全互溶 的体系
Nomenclature S.J.T.0. Phase Transformation and Applications Page 9/34 Immiscibility:不溶性 Spinodal Points:Spinodal Simple Eutectic Diagram:简单共晶相图 Peritectic Phase Diagrams:包晶相图 Ternary Phases Reaction:三相反应 SJTU Thermodynamics of Materials Fall 2011 ©X.J.Jin Lecture 15 Phase Diagram ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 9/34 Nomenclature Immiscibility：不溶性 Spinodal Points：Spinodal点 Simple Eutectic Diagram：简单共晶相图 Peritectic Phase Diagrams：包晶相图 Ternary Phases Reaction：三相反应
Immiscibility S.J.T.0. Phase Transformation and Applications Page10/34■ Complete immscibility Complete miscibility in solid state Ideality of the mixture Partial miscibility Non-ideality of the mixture Temperature dependence A regular solid solution of two components GM RT(xa Inx+x8 InxB)+@xXB SJTU Thermodynamics of Materials Fall 2011 @X.J.Jin Lecture 15 Phase Diagram Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2011 © X. J. Jin Lecture 15 Phase Diagram II Page 10/34 Immiscibility Complete immscibility Complete miscibility in solid state Partial miscibility Temperature dependence A regular solid solution of two components ( ) M A A B B A B G = RT x ln x + x ln x +ωx x Non-ideality of the mixture Ideality of the mixture
