Course Level Author Mentor

Transcription

1 Interfacial energy Course: Phase transformations Level: UG Author: Satish S Kamath, Department of Chemical Engineering, NITK-Surathkal Mentor: M P Gururajan

2 Interfacial energy In materials, the formation of interfaces cost the system energy. In this animation, we explore the atomistic origins of the interfacial energy and a simple model that incorporates the relevant thermodynamics and geometric factors for studying the interfaces in a crystalline solid

3 Learning objectives Understand interfacial energy as the excess free energy associated with the interfaces Understand the interfacial energy in crystalline solids in terms of a simple model that incorporates the relevant thermodynamics and geometry Appreciate that interfacial energy is inherently anisotropic in crystalline solids

4 Master layout Show the soap film stretching define interfacial energy Identify the interfacial energy in crystalline solids as excess free energy associated with the interface Build a simple bond-breaking model for interfacial energy Show the anisotropy in interfacial energy for a solid-vapour interface

5 Definitions/Key words Gibbs free energy: G = U + PV T S Internal energy, U Pressure, P Volume, V Temperature, T Entropy, S Enthalpy: H = U + PV Interfacial energy: excess Gibbs free energy

6 Definitions/Key words Anisotropy: the directional dependence of a property Surface tension: interfacial free energy in cases where the surface energy is independent of area

7 Stepwise description Soap film Area, A F Wire frame Show a soap film of area A in a wire frame pulled by a force F

8 Stepwise description Soap film Area, A F Wire frame Increase in area, da The area of the film increases by da

9 Work done = Raise in free energy Free energy of a system with interfacial area A is G = G 0 + A, where is the interfacial energy per unit area. dg = da + A d F da If interfacial energy did not change with area, F = that is, surface tension is the excess free energy. However, in solids, because shear stresses can be supported, interfacial energy can change with area. So, in general, surface tension is not the same as interfacial energy.

10 Stepwise description Why does the free energy increase at the surfaces?

11 Broken bond model Atom in the bulk: All bonds are satisfied Atoms at the surface: dangling/broken bonds

12 Broken bond model Atom in the bulk: All bonds are satisfied Atoms at the surface: dangling/broken bonds Broken bonds lead to increase in enthalpy

13 Broken bond model Atom in the bulk: All bonds are satisfied Atoms at the surface: dangling/broken bonds Broken bonds can also lead to increase in vibrational entropy

14 Broken bond model Atom in the bulk: All bonds are satisfied Broken bonds Atoms at the surface: dangling/broken bonds Increase in free energy

15 Stepwise description Let the latent heat of sublimation for a material be L; let the number of nearest neighbours be z. If an Avogadro number of atoms (N) evaporate, then, a total number of zn/2 bonds are borken. Let be the bond energy. Then, L = zn/2; this implies, =2L/zN Thus, if a be the number of broken bonds per unit area of a surface, then the enthalpy increase is 2aL/zN.

16 Interfacial energy anisotropy In a crystal, the number of broken bonds per unit area for different planes are different. Thus, the interfacial free energy for different planes is different; that is, the interfacial energy is anisotropic. With higher temperatures, the contribution from the interfacial (vibrational) entropy becomes important; this entropy can overcome the enthalpy and make the interfacial energy isotropic.

17 Summary Interfacial energy is the excess free energy associated with interfaces Interfacial energy can be understood in terms of a bond breaking model Bond breaking model, for a crystalline interface (with a vapour, for example) indicates that the interfacial energies are anisotropic

18 References/further reading Phase transformations in metals and alloys, Porter, Easterling, and Sherif, Third edition, CRC Press Materials science and engineering: a first course, V Raghavan, Fifth edition, Prentice-Hall of India Pvt Ltd.

19 Questions Calculate the number of atoms per unit area in (111), (110) and (100) planes of copper (FCC) with a lattice parameter of 3.61 Angstrom. Answer: 1.77x10 19, 1.08x10 19, 1.53x10 19 The surface energy of a (111) surface of copper is 2.49 J/m 2 ; what is the surface enthalpy of a (100) surface? Answer: 2.15 J/m 2

20 Questions At low temperatures, the interfacial energy of a material is anisotropic. As temperature increases, the anisotropy (a) increases (b) decreases (c) reamins the same Answer: (b)

21 Questions An atom is on the {100} surface of a bcc crystal. How many of its bonds are broken? Answer: 4

22 Questions Consider a cubic lattice of lattice parameter 'a'. Consider a plane in the lattice described by the angle that it makes with the x-axis as shown. Considering the unit length of the interface, show that the number of broken bonds per unit area is given by (cosθ + sin θ )/ a 2 a

23 Answer The answer follows from the figure below and considering a unit length in the perpendicular direction (to the page)