上海交通大学：《材料热力学》教学资源_2014课件_lecture 13 Phase rule and One-component phase diagram

Contents of Today S.J.T.0. Phase Transformation and Applications Page 1/45 Review previous Phase rule etc. SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 1/45 Contents of Today Review previous Phase rule etc

Review of Previous S.J.T.U. Phase Transformation and Applications Page 2/45 Non-ideal Solution:非理想溶液 Activity coefficient:活度系数 Gibbs-Duhem Relation:Gibbs-Duhem关系式 Dilute Solution:稀溶液 Colligative Properties:依数性 Osmotic Pressure:渗透压 Regular Solution:规则溶液 SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 2/45 Review of Previous Non-ideal Solution: 非理想溶液 Activity coefficient: 活度系数 Gibbs-Duhem Relation：Gibbs-Duhem关系式 Dilute Solution：稀溶液 Colligative Properties：依数性 Osmotic Pressure：渗透压 Regular Solution：规则溶液

稀溶液及其依数性 S.J.T.U. Phase Transformation and Applications Page 3/45 o Dilute solution/.稀溶液 溶剂符合Raoult?定量，即理想溶液 溶质符合Henry定量，非理想，活度系数为常数 SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 3/45 稀溶液及其依数性 • Dilute solution/稀溶液 溶剂符合Raoult定量，即理想溶液 溶质符合Henry定量，非理想，活度系数为常数

Raoult's law and Henry's law S.J.T.0. Phase Transformation and Applications Page 4/45 Raoult's law 1887年， 经验定律，PA=Px4→a4=xA “溶液中溶剂的蒸气压P等于同一温度下纯溶剂的蒸气压 P*与溶液中溶剂的摩尔分数x的乘积” Henry's law 1803年，经验定律 XB =ks.BPB P8=kx.8XB YB =1 Kx.8?P8 “在一定温度下微溶气体在溶液中的平衡组成与该气体的 平衡气相分压成正比” SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 4/45 Raoult’s law and Henry’s law Raoult’s law 1887年，经验定律， A A A A A P = P x ⇒ a = x * Henry’s law 1803年，经验定律 , B 1 , xB = kx,B PB ⇒ PB = kx B xB → γ = * , ? x B PB k “溶液中溶剂的蒸气压PA等于同一温度下纯溶剂的蒸气压 P*A与溶液中溶剂的摩尔分数xA的乘积” “在一定温度下微溶气体在溶液中的平衡组成与该气体的 平衡气相分压成正比

Dilute Solution and Colligative Properties(2) S.J.T.0. Phase Transformation and Applications Page 5/45 The vapor pressure of the solvent is reduced. Colligative properties The boiling point of the solvent is elevated. 依数性：？ The freezing point of the solvent is lowered. The solvent will display an osmotic pressure. SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 5/45 Dilute Solution and Colligative Properties (2) The vapor pressure of the solvent is reduced. The boiling point of the solvent is elevated. The freezing point of the solvent is lowered. The solvent will display an osmotic pressure. Colligative properties 依数性：？

Dilute Solution and Colligative Properties(3) S.J.T.0. Phase Transformation and Applications Page 6/45 p 溶剂 溶液 固体溶剂 △T T T ti 温度 图5-6稀溶液中溶液的沸点升高 图5-7稀溶液的凝固点下降 SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 6/45 Dilute Solution and Colligative Properties (3)

Osmotic Pressure(1) S.J.T.0. Phase Transformation and Applications Page 7/45 a-u=RT'Inx4 Raoult's law 半透膜！ HA-H=RTIn(1-xB)=-RTXB -Etan Aqueous solution (impure water) Flexible wall Π=RT Semipermeable Pure water membrane Figure 7.14 Osmotic pressure. SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 7/45 Osmotic Pressure (1) A A A − = RT ln x o μ μ ( ) A A B RTxB − = RT ln 1− x = − o μ μ ∫ +Π − = = − Π PP A A V AdP V A o μ μ A B V x Π = RT Raoult’s law 半透膜！

规则溶液 S.J.T.0. Phase Transformation and Applications Page 8/45 ·非理想溶液 Iny= 0 S*M =0 GM=H”=0xAxB SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 8/45 规则溶液 • 非理想溶液 ( ) 2 2 ln 1 A B A x RT x RT = = − ω ω γ A B xs M xs M G = H = ωx x M = 0 xs S

Regular Solution Atomistic Interpretation(3) S.J.T.0. Phase Transformation and Applications Page 9/45 For the regular solution:S=0 GM=H应=rAXB i8=H数+xB aH” H8=@XXB+xx0(XA-XB) HB=ox XS ↑ 破 Justify the algebraic form c RT in a regular solution. XA XB→ Figure 7.13 Plot of excess enthalpy of mixing versus com- position for a nonideal solution. SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 9/45 Regular Solution Atomistic Interpretation (3) For the regular solution: = 0 M S A B xsM xsM G = H = ωx x T B xs M A xs M xs B x H H H x ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = + ( ) B T A B A B A xsB xx x H x x x ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂ ∂ = + ω ω ( ) A B A A B xs H B = ωx x + x ω x − x 2 A xs H B = ωx B xs GB = RT lnγ 2 ln B A x RTω γ = Justify the algebraic form of the activity coefficient in a regular solution

Regular Solution:Atomistic Interpretation(1) S.J.T.0. Phase Transformation and Applications Page 10/45 A,B二元完全无序分布 Random distribution 只考虑最近邻原子间的相互作用 Z:coordination number NA个A原子与N个B原子混合形成规则溶液 EAA:bonding energy Table 7.1 Bond Energies After Mixing Atoms A and B in a Solid Solution Number of Bonds Energy per Bond Energy NAB EAB NAN N Z EAB NA NL EA ZEA N NAB Nr ge SJTU Thermodynamics of Materials Fall 2010 X.J.Jin Lecture 13 Phase Rule

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2010 © X. J. Jin Lecture 13 Phase Rule Page 10/45 Regular Solution: Atomistic Interpretation (1) A,B二元完全无序分布 只考虑最近邻原子间的相互作用 NA个A原子与NB个B原子混合形成规则溶液 Random distribution Z: coordination number EAA: bonding energy Z Z