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 − − =