Microstructure Evolution Diffusion ByeongJoo Lee POSTECH MSE calphadpostech
Microstructure Evolution Diffusion Byeong-Joo Lee POSTECH - MSE calphad@postech. ac. kr 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 Byeong-Joo Lee www. postech. ac. kr/~calphad
When metal A meets metal B Interstitial solid solution Substitutional solid solution precipitation Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusional Reactions – binary & multicomponent systems Byeong-Joo Lee www. postech. ac. kr/~calphad
Multicomponent Diffusion Darken’s uphill diffusion B. -J. Lee, J. Phase Equilibria 22, 241 (2001). Fe-3. 8 Si-C Diffusion between multiphase layers A. Engström, Scand. J. Metall. 24, 12 (1995). Fe-C 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 Byeong-Joo Lee www. postech. ac. kr/~calphad
Fick’s 1 st Law Consider net flux from plane 1 to plane 2 atoms m-2 s-1 m 2 s-1 Byeong-Joo Lee www. postech. ac. kr/~calphad
Fick’s 1 st Law Byeong-Joo Lee www. postech. ac. kr/~calphad
Fick’s 2 nd Law Consider the change of solute concentration between plane 1 and plane 2 during δt for a constant DB Byeong-Joo Lee www. postech. ac. kr/~calphad
Fick’s 2 nd Law Byeong-Joo Lee www. postech. ac. kr/~calphad
More about Diffusion Coefficient – Thermal Activation As a thermally activated process for interstitial diffusion How about for substitutional diffusion? Byeong-Joo Lee www. postech. ac. kr/~calphad
Steady State Solution of Diffusion Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion - Superposition Principle Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion - Superposition Principle Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution – Application of Superposition Principle Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution – Leak Test & Error Function Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Semi- Infinite Source Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Semi- Infinite Source Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Semi- Infinite Source Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Semi- Infinite Source Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Semi- Infinite Source Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Semi- Infinite Source Byeong-Joo Lee www. postech. ac. kr/~calphad
Determination of Diffusivity – Grube method Byeong-Joo Lee www. postech. ac. kr/~calphad
Determination of Diffusivity – Boltzmann-Matano Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Separation of Variable Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Separation of Variable Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Separation of Variable Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Separation of Variable Byeong-Joo Lee www. postech. ac. kr/~calphad
Non-Steady State Solution of Diffusion – Separation of Variable Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusion along High Diffusion Path – Grain Boundary Diffusion Model Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusion Coefficient – Inter Diffusion Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusion Coefficient – Inter Diffusion Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusion Coefficient – Self/Tracer Diffusion Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusion Coefficient – Intrinsic Diffusion Coefficient Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusion Coefficient – Inter Diffusion Coefficient Byeong-Joo Lee www. postech. ac. kr/~calphad
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 Byeong-Joo Lee www. postech. ac. kr/~calphad
Diffusion Coefficient – Modeling • Linear composition dependence of QB in a composition range N 1 ~ N 2 Ø assuming composition independent D o v Tracer diffusion Coefficient at an intermediate composition is a geometrical mean of those at both ends – from experiments Ø the same for the D v Both Q o o term & Q are modeled as a linear function of composition Byeong-Joo Lee www. postech. ac. kr/~calphad
Moving Boundary Problem – Basic Equation Byeong-Joo Lee www. postech. ac. kr/~calphad
Binary Diffusion Byeong-Joo Lee www. postech. ac. kr/~calphad
Application to Interfacial Reactions – Ti/Al 2 O 3 Reaction Byeong-Joo Lee www. postech. ac. kr/~calphad
Application to Interfacial Reactions – Ti/Al 2 O 3 Reaction Byeong-Joo Lee www. postech. ac. kr/~calphad
Multi-Component Diffusion Simulation – between Multi- A. Engström, Scand. J. Metall. 24, 12 (1995). Phase Layers B. -J. Lee, Scripta Mater. 40, 573 (1999) Byeong-Joo Lee www. postech. ac. kr/~calphad
Multi-Component Diffusion Simulation – between Multi- Phase Layers B. -J. Lee, Scripta Mater. 40, 573 (1999) Byeong-Joo Lee www. postech. ac. kr/~calphad
Multi-Component Diffusion Simulation – between Multi- Phase Layers B. -J. Lee, Scripta Mater. 40, 573 (1999) Byeong-Joo Lee www. postech. ac. kr/~calphad
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