上海交通大学：《材料热力学》教学资源_2010课件 lecture 17 phase diagram 4

Contents of Today S.J.T.U. Phase Transformation and Applications Page 1/34 Review previous Examples Ternary system Review of phase diagrams etc. SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 1/34 Contents of Today Review previous Examples Ternary system Review of phase diagrams etc

Summary of Binary Phase Diagrams S.J.T.U. Phase Transformation and Applications Page 2/34 ① ② ③ 4 ⑤ ⑥ ① 图6-25 二元相图的7种基本类型 SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 2/34 Summary of Binary Phase Diagrams

Ternary Phases Reaction in Binary Systems S.J.T.U. Phase Transformation and Applications Page 3/34 表6-1二元系的各种三相平衡反应 转变类型 反应式 图型特征 B 共晶转变 l-a+B 共析转变 Y-a+B 共晶型 偏晶转变 h=h+a 熔晶转变 8=l+y 3 包晶转变 I+Ba 包晶型 包析转变 Y+B=a 3 a 合晶转变 h+h=a SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 3/34 Ternary Phases Reaction in Binary Systems

相图的用处 S.J.T.U. Phase Transformation and Applications Page 4/34 处理系统是多种物质的复杂系统 -相律 一相图 说明系统在不同条件下以哪几相共存；当温 度、压力、组成改变时会出现什么相变化 各相存在的范围，相变发生的条件等 探索新材料 分析合金组织、化学成分、制定生产和热处理工艺的重 要依据！ SJTU Thermodynamics of Materials Spring2o08©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 4/34 相图的用处 • 处理系统是多种物质的复杂系统 – 相律 – 相图 说明系统在不同条件下以哪几相共存；当温 度、压力、组成改变时会出现什么相变化 各相存在的范围，相变发生的条件等 探索新材料 分析合金组织、化学成分、制定生产和热处理工艺的重 要依据！

相图的用处2 S.J.T.U. Phase Transformation and Applications Page 5/34 M 液相 区域熔炼提纯 析出固溶体杂质的含 固溶体 量比平衡液相的少 WB 熔 熔 图5-15区域熔炼示意图 SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 5/34 相图的用处 2 区域熔炼提纯 析出固溶体杂质的含 量比平衡液相的少

相图的用处3 S.J.T.U. Phase Transformation and Applications Page 6/34 估算热力学数据，如 熔化热 从相图上查出一定成 分的合金系统中，作 LT-T) 为溶剂的金属熔点降 XB 低了多少度，然后用 RTa 稀溶液凝固点下降的 依数性公式，即可估 算溶剂金属的摩尔熔 化焓 SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 6/34 相图的用处 3 • 估算热力学数据，如 熔化热 – 从相图上查出一定成 分的合金系统中，作 为溶剂的金属熔点降 低了多少度，然后用 稀溶液凝固点下降的 依数性公式，即可估 算溶剂金属的摩尔熔 化焓 2 )( m m B RT TTL x − =

相图的用处4 S.J.T.U. Phase Transformation and Applications Page 7/34 Weight Percent Cadmium 0 300 ·求出活度数据 300 442℃ 20 一在两相共存区，某组 分在这两个共存相中 1480 的化学势应相等 (cd)- 36 40 60 0070 (sIn)= Alomie Percent Cadmium Lg (sIn)=uo +RT InaB LB)+RT In am AG=4W-4asT→Tm T △G=△Hm-T△Sm=△Hm(1- Solid->liquid T SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 7/34 相图的用处 4 • 求出活度数据 – 在两相共存区，某组 分在这两个共存相中 的化学势应相等 D * )( ln)( Bi sBi s = μμ Bi Bi Bi lBi Bi sln)( ln aRT ln aRT * )( 0 μμ += μ += G lBi −=Δ sBi →TT m * )( * )( μμ )1( m m m m T T HSTHG −Δ=Δ−Δ=Δ Solid -> liquid

Liquid Liquid S.J.T.U. Phase Transformation and Al L+a L+B e8/34 L+a L+B ainjejadwaL C B B a+B a+B 1 A B A & Mole fraction of B,xB-> Mole fraction of B,xB-> (a) (b) Liquid Liquid L+B L+a L+Y a+L Y B B+Y a+B a a+B B B A B Mole fraction of B,xB-> Mole fraction of B,xB-> SJTU (c) (d)

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 8/34

二元例题2b S.J.T.U. Phase Transformation and Applications Page 9/34 Molar Gibbs free energy of What is the most stable state solution,drawn at T and P of the system at an average constant for an a phase and composition of X,？ B phase. Suppose the a-phase was somehow prevented from forming (i.e., consider the B-phase equilibrium under the a-phase constraint that the a-phase is absent).In this case,what would be the equilibrium state of the system with average composition X,？ XB SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 9/34 二元例题 2b • What is the most stable state of the system at an average composition of X0? • Suppose the α-phase was somehow prevented from forming (i.e., consider the equilibrium under the constraint that the α-phase is absent). In this case, what would be the equilibrium state of the system with average composition X0? Molar Gibbs free energy of solution, drawn at T and P constant for an α phase and β phase

Ternary Diagrams S.J.T.U. Phase Transformation and Applications Page 10/34 Degrees of freedom available in the system(F): F=C-P+1 F:the number of system variables that we may freely vary,or arbitrarily fix C:components P:phase C=3 P=1,F=3 Binary 2D P=2,F=2 D P=3,F=1 Ternary 3D P=4,F=0 Quaternary SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 18 Phase Diagram IV

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 18 Phase Diagram IV Page 10/34 Ternary Diagrams 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 +1 C = 3 0,4 1,3 2,2 3,1 == == == = = FP FP FP FP Binary Ternary 2D 3D Quaternary