上海交通大学：《材料热力学》教学资源_2010课件 lecture 15 phase diagram 2

Contents of Today S.J.T.U. Phase Transformation and Applications Page 1/30 Review previous Immiscibility Spinodal Points Compounds etc. Conclusion Remarks Examples SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 1/30 Contents of Today Review previous Immiscibility Spinodal Points Compounds etc. Conclusion Remarks Examples

Review of Last S.J.T.U. Phase Transformation and Applications Page 2/30 Freezing Point Depression ·The lever rule Simple eutectic diagram ·Cooling curves SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 16 Phase Diagram Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 2/30 Review of Last • Freezing Point Depression • The lever rule • Simple eutectic diagram • Cooling curves

Binary System S.J.T.U. Phase Transformation and Applications Page 3/30 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 Spring2o07©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 3/30 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 = − PCF + 2 C = 2 0,3 1,2 2,1 == == = = FP FP FP −= PCF +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.U. Phase Transformation and Applications Page 4/30 The liquid solution is in equilibrium with 稀溶液的依数性 the pure solid, aA.L.pure =1 △G= L(T-T) T分X RTIn a1solution 主0 1.pure asolid=1 L(Tm-T)=-RTInXAJ.solmon ideal solution If T is close to the Tm In xA1.solution L(T-T) RT A XB→ B Melting point depression Fig.9.2 Plot of the activity of Aliqui L(T -T) △T=Tm-T at T<Tm.A versus composition. XB 二 ln(1-z）=-z small z SJTU Thermodynamics of Materials Spring 2007 ©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 4/30 9.1 Freezing Point Depress4ion (4) Fig. 9.2 Plot of the activity of Aliquid at T < Tm,A versus composition. A B 1.0 a A (liquid) xB asolid=1 aA,l,pure=1 The liquid solution is in equilibrium with the pure solid, ln 0 )( , , + = − =Δ purel solutionl m m a a RT T TTL G If T is close to the Tm xRT ideal solution T TTL solutionlA m m ,, ln )( −= − ,, 2 )( ln m m solutionlA RT TTL x − −= 2 )( m m B RT TTL x − = zsmallzz m TTT −=− Δ = − )1ln( Melting point depression 稀溶液的依数性 ↔ xT

9.2 The Lever Rule (1) S.J.T.U. Phase Transformation and Applications Page 5/30 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. The relative quantities or fractions of liquid and solid using a mass balance. 人 Liquid xg=FXBI+FsxB.s F(xBI-xB)=Fs(xB-XB.s) L+S F=fraction liquid Fs=fraction solid (XB-XB.S) F+Fs=1,and a mass balance A B FXB-XB.s XB-XB.s XB.S XB XB.I F XB→ Fs XBI-XB XBI-XB.S Fig.9.4 Illustration of the lever rule. SJTU Thermodynamics of Materials Spring 2007 ©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 5/30 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. B xB A Tm T Liquid xB,l L+S xB,S xB T1 )( ,SBB − xx )( , BlB − xx Fig. 9.4 Illustration of the lever rule. The relative quantities or fractions of liquid and solid using a mass balance. Fl=fraction liquid FS=fraction solid Fl+ FS=1, and a mass balance )()( ,1 , ,1 , sBBSBlB B sBSlB xxFxxF xFxFx −=− = + BlB sBB S xx xx F F − − = , 1 , SBlB sBB xx xx F ,, , 1 − − =

9.3 Simple Eutectic Diagram S.J.T.U. Phase Transformation and Applications Page 6/30 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 m.B solid A and solid B,eutectic temperature. Liquid The lowest temperature at which a 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 XB B If all three phases are present,at equilibrium, 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 Spring2007©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 6/30 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 = − PCF =+ − + = 01321 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.U. Phase Transformation and Applications Page 7/30 T G 公切线符合多相平衡 G*9 条件 p Gjp G G =唱 △，G 处于平衡条件两相的 = △x 平衡组成 个一个 图6-8两相平衡时的成分-自由能曲线 SJTU Thermodynamics of Materials Spring 2007 ©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 7/30 公切线符合多相平衡 条件 处于平衡条件两相的 平衡组成

S.J.T.U. 下 a Phase Transformation and Applications 30 固液完全互溶 的体系 d T 5 G (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 Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 8/30 固液完全互溶 的体系

吉布斯相律 S.J.T.U. Phase Transformation and Applications Page 9/30 吉布斯相律是处于热力学平衡状态的系统中自 由度与组元和相数之间关系的规律 基本概念包括相、组元和自由度等。 相为系统中性质与成分均匀的一部分；相平衡指的 是在多相体系中所有相的强度性质均相等，体系的 性质不会自发地随时间变化的状态即相平衡状态； 组元为决定各平衡相的成分，而且是可以独立变化 的组分（元素或化合物）； 自由度是可以在一定范围内任意改变而不引起任何 相的产生与消失的最大变量数。 F=C-P+2 SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 9/30 吉布斯相律 • 吉布斯相律是处于热力学平衡状态的系统中自 由度与组元和相数之间关系的规律。 • 基本概念包括相、组元和自由度等。 – 相为系统中性质与成分均匀的一部分；相平衡指的 是在多相体系中所有相的强度性质均相等，体系的 性质不会自发地随时间变化的状态即相平衡状态； – 组元为决定各平衡相的成分，而且是可以独立变化 的组分（元素或化合物）； – 自由度是可以在一定范围内任意改变而不引起任何 相的产生与消失的最大变量数。 = − PCF + 2

Nomenclature S.J.T.U. Phase Transformation and Applications Page 10/30 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 Spring2o07©X.J.Jin Lecture 16 Phase Diagram ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 16 Phase Diagram II Page 10/30 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