Approximate Calculation of Solid Surface S.J.T.U. Energy Phase Transformation and Applications Page 11/42 The binding energy of an atom to a solid is the result of discrete bonds to its nearest neighbors,then the energy of one bond,8,can be written as follows: △Hs 8= 0.5ZNA AHs The molar enthalpy of sublimation(breaking all the bonds) Z The coordination number N Avogadro's number There are 0.5ZNA bonds per mole 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 11/42 Approximate Calculation of Solid Surface Energy The binding energy of an atom to a solid is the result of discrete bonds to its nearest neighbors, then the energy of one bond, ε, can be written as follows: A S ZN H 5.0 Δ ε = ΔH S The molar enthalpy of sublimation (breaking all the bonds) Z The coordination number NA Avogadro’s number There are 0.5ZNA bonds per mole
Approximate Calculation of Solid Surface S.J.T.U. Energy (2) Phase Transformation and Applications Page 12/42 If we cleave a face-centered cubic crystal along a(111)plane,three bonds per atom will be broken.Two surfaces formed,the work required to form the surfaces will be 38/2 per surface atom. 3 △Hs W= (for Z=12) 2 ANA △H 4N4 A aov2 N/A is the number of atoms per unit (Face diagonal) area.For fcc structure: Figure 4.2 Atomic packing on the (111)face of a face-centered N 4 cubic crystal. A √3a 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 12/42 Approximate Calculation of Solid Surface Energy (2) If we cleave a face-centered cubic crystal along a (111) plane, three bonds per atom will be broken. Two surfaces formed, the work required to form the surfaces will be 3ε/2 per surface atom. )12( 423 = Δ == Zfor NH w AS ε N/A is the number of atoms per unit area. For fcc structure: ⎟⎠⎞ ⎜⎝ Δ ⎛ = AN NHAS 4 γ 2 3 0 4 A a N =
Approximate Calculation of Solid Surface S.J.T.U. Energy (3) Phase Transformation and Applications Page 13/42 For copper,the enthalpy of sublimation:170000 J/(g.mol) Lattice spacing,3.615 A Calculated.1400 erg/cm2 Measured,1600 erg/cm2 The surface energy of a solid depends on the crystallographic plane. The work required to create the surface y aov2 depends on the number of bonds broken per (Face diagonal) atom when the surface is created,and the Figure 4.2 Atomic packing on number of atoms per area of surface.(N/A) the (111)face of a face-centered cubic crystal. 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 13/42 Approximate Calculation of Solid Surface Energy (3) For copper, the enthalpy of sublimation: 170000 J/(g.mol) Lattice spacing, 3.615 A The surface energy of a solid depends on the crystallographic plane. The work required to create the surface γ depends on the number of bonds broken per atom when the surface is created, and the number of atoms per area of surface. (N/A) Calculated. 1400 erg/cm2 Measured, 1600 erg/cm2
Approximate Calculation of Solid Surface S.J.T.U. Energy (4) Phase Transformation and Applications Page 14/42 For a(100)plane there are four broken bonds per atom,and the number of atoms per unit area: 2 /(100) a The ratio of the two surface energies: 2 Yam= =1.15 ao Ya00) 3 Figure 4.3 Atomic packing on the (100)face of a face-centered cubic crystal. 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 14/42 Approximate Calculation of Solid Surface Energy (4) For a (100) plane there are four broken bonds per atom, and the number of atoms per unit area: 2 )100( 0 2 aA N ⎟ = ⎠⎞ ⎜⎝⎛ 15.1 3 2 )100( )111( == γ γ The ratio of the two surface energies:
表面能和晶界能的近似计算 S.J.T.U. Phase Transformation and Applications Page 15/42 三原子间距 B 非晶态 (a)由劈开晶体形成的自由键 b)随机晶界的三原子层模型 图5.2表面能和晶界能的近似计算 (作为“面”来考察时，是计算穿过该面的原子对的能量； From T.Nishizawa 作为“薄膜”来考察时，是计算膜状“相”的能量) 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 15/42 表面能和晶界能的近似计算 From T. Nishizawa