Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr

1. Microstructure Evolution • Diffusion Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr

2. Objectives 1. Introduction   ․ Definition   ․ Diffusion Mechanism: Vacancy Mechanism, Interstitial Mechanism 2. Diffusional Flux and Application of Fick's law   ․Fick's first law in two component system   ․Fick's second law      Application - Steady State Solution 3. Non-Steady State Diffusion   ․ Thin Film Source (Thin Layer)   ․ Semi-Infinite Source (Diffusion Couple)      ․ Laplace/Fourier Transformation      ․ Error function      ․ Homogenization/Solute penetration   ․ Trigonometric-Series Solutions   ․ Determination of diffusion coefficient (Grube, Boltzman-Matano method)   ․ Other Examples   ․ Diffusion along high diffusion paths 4. Diffusion Coefficients   ․ Reference Frame of Diffusion ⇒ Darken's Equation   ․ Intrinsic, Inter, Self, Trace, Impurity Trace Diffusion Coefficient   ․ Reference : Smithells Metals Reference Book, Chap. 13., Reed-Hil

3. When metal A meets metal B Interstitial solid solution Substitutional solid solution precipitation

4. Diffusional Reactions – binary & multicomponent systems

5. Multicomponent Diffusion Diffusion between multiphase layers Darken’s uphill diffusion A. Engström, Scand. J. Metall. 24, 12 (1995). B.-J. Lee, J. Phase Equilibria 22, 241 (2001). Fe-3.8Si-C Fe-C

6. Definition Homogenization phenomena by non-convective mass transport due to chemical potential or electrochemical potential difference in a multicomponent single phase

7. Fick’s 1st Law Consider net flux from plane 1 to plane 2 atoms m-2 s-1 m2 s-1

8. Fick’s 1st Law

9. Fick’s 2nd Law Consider the change of solute concentration between plane 1 and plane 2 during δt for a constant DB

10. Fick’s 2nd Law

11. More about Diffusion Coefficient – Thermal Activation As a thermally activated process How about for substitutional diffusion? for interstitial diffusion

12. Steady State Solution of Diffusion

13. Non-Steady State Solution of Diffusion

14. Non-Steady State Solution of Diffusion - Superposition Principle

15. Non-Steady State Solution of Diffusion - Superposition Principle

16. Non-Steady State Solution – Application of Superposition Principle

17. Non-Steady State Solution – Leak Test & Error Function

18. Non-Steady State Solution of Diffusion – Semi-Infinite Source

19. Non-Steady State Solution of Diffusion – Semi-Infinite Source

20. Non-Steady State Solution of Diffusion – Semi-Infinite Source

21. Non-Steady State Solution of Diffusion – Semi-Infinite Source

22. Non-Steady State Solution of Diffusion – Semi-Infinite Source

23. Non-Steady State Solution of Diffusion – Semi-Infinite Source

24. Determination of Diffusivity – Grube method

25. Determination of Diffusivity – Boltzmann-Matano

26. Non-Steady State Solution of Diffusion – Separation of Variable

27. Non-Steady State Solution of Diffusion – Separation of Variable

28. Non-Steady State Solution of Diffusion – Separation of Variable

29. Non-Steady State Solution of Diffusion – Separation of Variable

30. Non-Steady State Solution of Diffusion – Separation of Variable

31. Diffusion along High Diffusion Path – Grain Boundary Diffusion Model

32. Diffusion Coefficient – Inter Diffusion

33. Diffusion Coefficient – Inter Diffusion

34. Diffusion Coefficient – Self/Tracer Diffusion

35. Diffusion Coefficient – Intrinsic Diffusion Coefficient

36. Diffusion Coefficient – Inter Diffusion Coefficient

37. Diffusion Coefficient – Modeling • Inter-diffusion Coefficient in a binary alloy • – linked to intrinsic diffusion by the Darken’s relation • Intrinsic diffusion Coefficient • – composed of mobility term (Tracer Diffusion) and thermodynamic factor • Tracer diffusion Coefficient – as a function of composition & temp. : tracer impurity diffusion coefficient : self-diffusion of A in the given structure

38. Diffusion Coefficient – Modeling • Linear composition dependence of QB in a composition range N1 ~ N2 • assuming composition independent D o • Tracer diffusion Coefficient at an intermediate composition • is a geometrical mean of those at both ends – from experiments • the same for the D o term • Both Q o & Q are modeled as a linear function of composition

39. Moving Boundary Problem – Basic Equation

40. Binary Diffusion

41. Application to Interfacial Reactions – Ti/Al2O3 Reaction

42. Application to Interfacial Reactions – Ti/Al2O3 Reaction

43. Multi-Component Diffusion Simulation – between Multi-Phase Layers A. Engström, Scand. J. Metall. 24, 12 (1995). B.-J. Lee, Scripta Mater. 40, 573 (1999)

44. Multi-Component Diffusion Simulation – between Multi-Phase Layers B.-J. Lee, Scripta Mater. 40, 573 (1999)

45. Multi-Component Diffusion Simulation – between Multi-Phase Layers B.-J. Lee, Scripta Mater. 40, 573 (1999)