Contents of Today S.J.T.U. Phase Transformation and Applications Page 1/42 Review previous Surface energy surface tension Effect of surface curvature Vapor pressure Solubility of small particles Wetting of surfaces Gibbs Adsorption Isotherm SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 1/42 Contents of Today Review previous Surface energy / surface tension Effect of surface curvature Vapor pressure Solubility of small particles Wetting of surfaces Gibbs Adsorption Isotherm
Isolated System and Boltzmann Hypothesis S.J.T.U. Phase Transformation and Applications Page 2/42 Microcanonical ensemble An isolated system with N particals in a volume,V,with a fixed energy,E Premise:all microstates are equally probable Boltzmann hypothesis The entropy of a system is linearly related to the logarithm of S=kIn thermodynamic probability the number of different ways that macro-configuration can be achieved. N! Q= Entropy of mixing of two components N!Nu! Distribution of balls SJTU Thermodynamics of Materials Spring2008©X.J.Jimn Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 2/42 Isolated System and Boltzmann Hypothesis Microcanonical ensemble An isolated system with N particals in a volume, V, with a fixed energy, E Premise: all microstates are equally probable Boltzmann hypothesis The entropy of a system is linearly related to the logarithm of Ω Ω：thermodynamic probability the number of different ways that macro-configuration can be achieved. !! ! ΠΙ =Ω NN N Entropy of mixing of two components = kS lnΩ Distribution of balls
ldeal Gas S.J.T.U. Phase Transformation and Applications Page 3/42 22--2 m小 In- =Nka) N kT RT P V V SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 3/42 Ideal Gas V h mkT L h mkT ZZZZ zyxxyz 2/3 2 3 2/3 2 2 2 ⎟⎠⎞ ⎜⎝⎛ ⎟ = ⎠⎞ ⎜⎝⎛ == π π T V F P ⎟⎠⎞ ⎜⎝⎛ ∂∂ −= ⎟⎟⎠⎞ ⎜⎜⎝⎛ −= +1ln A A NZ kTNF T A T A A V Z kTN V N Z kTN P ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎟⎟⎟⎠⎞ ⎜⎜⎜⎜⎜⎝⎛ ∂ ⎥⎦⎤ ⎢⎣⎡ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂ + = ln 1ln V RT V kTN P A ==
Today S.J.T.U. Phase Transformation and Applications Page 4/42 Surface energy surface tension Effect of surface curvature ·Vapor pressure Solubility of small particles ·Vetting of surfaces Gibbs absorption isotherm SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 4/42 Today • Surface energy / surface tension • Effect of surface curvature • Vapor pressure • Solubility of small particles • Wetting of surfaces • Gibbs absorption isotherm
Introduction (1) S.J.T.U. Phase Transformation and Applications Page 5/42 Surfaces and Interfaces Everything is made of something and has to end somewhere. An atom at a free surface of a solid has greater energy than an atom in the interior of a crystal because it is less tightly bound. Surface energy The sum of all the excess energies of the surface atoms Can be defined in terms of energy,enthalpy, Helmholtz free energy,or Gibbs free energy, depending on the physical constraints placed on (a)由劈开晶体形成的自由键 the definition 本来应该担任配角”的界面比本当是主角”的构成相扮演更 重要的演出角色”！ SJTU Thermodynamics of Materials Spring 2008 X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 5/42 Introduction (1) Surfaces and Interfaces Everything is made of something and has to end somewhere. An atom at a free surface of a solid has greater energy than an atom in the interior of a crystal because it is less tightly bound. Surface energy The sum of all the excess energies of the surface atoms Can be defined in terms of energy, enthalpy, Helmholtz free energy, or Gibbs free energy, depending on the physical constraints placed on the definition 本来应该担任“配角”的界面比本当是“主角”的构成相扮演更 重要的“演出角色”！
Introduction(2) S.J.T.U. Phase Transformation and Applications Page 6/42 Surface energy based on Gibbs free energy dG =-SaT +VdP ydA aG OH OF aA T.P A )sy S.P A Commonly observed manifestations A liquid droplet tries to minimize its free energy,it assumes a spherical shape Small droplets tend to agglomerate into larger droplets,minimizing their combined surface-to-volume ratios Small particles of metals or ceramics,when pressed into a shape and heated at high temperatures,will"sinter"into a solid mass. SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 6/42 Introduction (2) Surface energy based on Gibbs free energy = − + + γdAVdPSdTdG A PT G , ⎟⎠⎞ ⎜⎝⎛ ∂∂ γ = Commonly observed manifestations A liquid droplet tries to minimize its free energy, it assumes a spherical shape Small droplets tend to agglomerate into larger droplets, minimizing their combined surface-to-volume ratios Small particles of metals or ceramics, when pressed into a shape and heated at high temperatures, will “sinter” into a solid mass. PT VS PS A VT F A H A U A G , , , , ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ γ =
Surface Energy Surface Tension S.J.T.U. Phase Transformation and Applications Page 7/42 Image a film of liquid stretched on a frame -dx- 21ydx =Fdx Film Y=F/21 Y Surface energy with units of Y←一≥f dynes per centimeter,or newtons per meter in the SI Soap film system. Y←—>f Detail of wire Figure 4.1 Stretching a film-increasing area. SJTU Thermodynamics of Materials Spring2o08©X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 7/42 Surface Energy / Surface Tension Image a film of liquid stretched on a frame 2 γ = Fdxdxl γ = 2/ lF γ Surface energy with units of dynes per centimeter, or newtons per meter in the SI system. dx
Surface Energy Surface Tension S.J.T.U. Phase Transformation and Applications Page 8/42 Surface energy with units of dynes per centimeter,or newtons per meter in the SI system. [界面张力] [界面能] SI单位制 N(牛顿)·m-1=J(焦耳)m-2 cgs单位制 dyn(达因)，cm-1=erg(尔格)·cm-2 SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 8/42 Surface Energy / Surface Tension γ Surface energy with units of dynes per centimeter, or newtons per meter in the SI system
Surface Energy Surface Tension(1) S.J.T.U. Phase Transformation and Applications Page 9/42 Surface tension or surface energy Liquid Isotropic Surface energy does not change as the surface is stretched Solids Function of the crystallographic plane that is expected The nature of a solid surface changes as the material is deformed. SJTU Thermodynamics of Materials Spring 2008 X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 9/42 Surface Energy / Surface Tension (1) Surface tension or surface energy Liquid Isotropic Surface energy does not change as the surface is stretched Solids Function of the crystallographic plane that is expected The nature of a solid surface changes as the material is deformed
纯物质的表面能和各种界面能 S.J.T.U. Phase Transformation and Applications Page 10/42 口△◇0固体 W e▣液/液 3 ■▲◆●液体 3 ⊙固/液 Al2O3/LFe Fe ⊙ Cu 晶界 日 Mgo SiO,/LFe 金属 Al A203 纯金属的 Fe Hg Ge Si 随机晶界 Cu 0.3 Sb 0.3 Al 类金属 SiOz Fe 无机化合物 NaCl 纯金属的 Cu 0.1 0.1 --- 固/液界面 回 AH2O Al 甘油 尼龙 e LCu/LPb 0.03甲醇 0.03 有机化合物 石蜡 Hg 石蜡/H20 特弗伦 0.0 0.01 100 300 1000 3000 100 300 1000 3000 熔点，Tm/K 熔点，Tm/K (a)纯物质的表面能 (b)各种界面能 图5.1 (a)固体或液体的表面能（金属最大，塑料最小）；(b)固/液或 液/液界面能和随机晶界能（因物质组合的不同而变得多种多样） From T.Nishizawa SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 20 surface
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 20 surface Page 10/42 纯物质的表面能和各种界面能 From T. Nishizawa