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Byeong-Joo Lee Byeong-Joo Lee POSTECH - MSE Diffusion.

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1 Byeong-Joo Lee www.postech.ac.kr/~calphad Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr Diffusion

2 Byeong-Joo Lee www.postech.ac.kr/~calphad 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 Byeong-Joo Lee www.postech.ac.kr/~calphad When metal A meets metal B Interstitial solid solution Substitutional solid solution precipitation Interstitial solid solution Substitutional solid solution precipitation

4 Byeong-Joo Lee www.postech.ac.kr/~calphad Diffusional Reactions – binary & multicomponent systems

5 Byeong-Joo Lee www.postech.ac.kr/~calphad Multicomponent Diffusion Fe-3.8Si-C Fe-C Darken’s uphill diffusion Diffusion between multiphase layers A. Engström, Scand. J. Metall. 24, 12 (1995). B.-J. Lee, J. Phase Equilibria 22, 241 (2001).

6 Byeong-Joo Lee www.postech.ac.kr/~calphad Definition Homogenization phenomena by non-convective mass transport due to chemical potential or electrochemical potential difference in a multicomponent single phase

7 Byeong-Joo Lee www.postech.ac.kr/~calphad Fick’s 1 st Law atoms m -2 s -1 Consider net flux from plane 1 to plane 2 m 2 s -1

8 Byeong-Joo Lee www.postech.ac.kr/~calphad Fick’s 1 st Law

9 Byeong-Joo Lee www.postech.ac.kr/~calphad Consider the change of solute concentration between plane 1 and plane 2 during δt for a constant D B Fick’s 2 nd Law

10 Byeong-Joo Lee www.postech.ac.kr/~calphad Fick’s 2 nd Law

11 Byeong-Joo Lee www.postech.ac.kr/~calphad As a thermally activated process for interstitial diffusion More about Diffusion Coefficient – Thermal Activation How about for substitutional diffusion?

12 Byeong-Joo Lee www.postech.ac.kr/~calphad Steady State Solution of Diffusion

13 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion

14 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion - Superposition Principle

15 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion - Superposition Principle

16 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution – Application of Superposition Principle

17 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution – Leak Test & Error Function

18 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Semi-Infinite Source

19 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Semi-Infinite Source

20 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Semi-Infinite Source

21 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Semi-Infinite Source

22 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Semi-Infinite Source

23 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Semi-Infinite Source

24 Byeong-Joo Lee www.postech.ac.kr/~calphad Determination of Diffusivity – Grube method

25 Byeong-Joo Lee www.postech.ac.kr/~calphad Determination of Diffusivity – Boltzmann-Matano

26 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Separation of Variable

27 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Separation of Variable

28 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Separation of Variable

29 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Separation of Variable

30 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Steady State Solution of Diffusion – Separation of Variable

31 Byeong-Joo Lee www.postech.ac.kr/~calphad Diffusion along High Diffusion Path – Grain Boundary Diffusion Model

32 Byeong-Joo Lee www.postech.ac.kr/~calphad Diffusion Coefficient – Inter Diffusion

33 Byeong-Joo Lee www.postech.ac.kr/~calphad Diffusion Coefficient – Inter Diffusion

34 Byeong-Joo Lee www.postech.ac.kr/~calphad Diffusion Coefficient – Self/Tracer Diffusion

35 Byeong-Joo Lee www.postech.ac.kr/~calphad Diffusion Coefficient – Intrinsic Diffusion Coefficient

36 Byeong-Joo Lee www.postech.ac.kr/~calphad Diffusion Coefficient – Inter Diffusion Coefficient

37 Byeong-Joo Lee www.postech.ac.kr/~calphad 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 Diffusion Coefficient – Modeling

38 Byeong-Joo Lee www.postech.ac.kr/~calphad  assuming composition independent D o Linear composition dependence of Q B in a composition range N 1 ~ N 2  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 Diffusion Coefficient – Modeling

39 Byeong-Joo Lee www.postech.ac.kr/~calphad Moving Boundary Problem – Basic Equation

40 Byeong-Joo Lee www.postech.ac.kr/~calphad Binary Diffusion

41 Byeong-Joo Lee www.postech.ac.kr/~calphad Application to Interfacial Reactions – Ti/Al 2 O 3 Reaction

42 Byeong-Joo Lee www.postech.ac.kr/~calphad Application to Interfacial Reactions – Ti/Al 2 O 3 Reaction

43 Byeong-Joo Lee www.postech.ac.kr/~calphad 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 Byeong-Joo Lee www.postech.ac.kr/~calphad B.-J. Lee, Scripta Mater. 40, 573 (1999) Multi-Component Diffusion Simulation – between Multi-Phase Layers

45 Byeong-Joo Lee www.postech.ac.kr/~calphad B.-J. Lee, Scripta Mater. 40, 573 (1999) Multi-Component Diffusion Simulation – between Multi-Phase Layers

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