20071050 오승재. Contents 1. 지정 주제 -Computer Simulation of Darken’s Uphill Diffusion 2. 자유 주제 -Diffusion couple -(Sudoku)

Presentation on theme: "20071050 오승재. Contents 1. 지정 주제 -Computer Simulation of Darken’s Uphill Diffusion 2. 자유 주제 -Diffusion couple -(Sudoku)"— Presentation transcript:

1 20071050 오승재

2 Contents 1. 지정 주제 -Computer Simulation of Darken’s Uphill Diffusion 2. 자유 주제 -Diffusion couple -(Sudoku)

3 Problem Si : 3.8wt% C : 0.478wt% Si : 3.8wt% C : 0.478wt% Si : 0.005wt% C : 0.441wt% Si : 0.005wt% C : 0.441wt% 50mm 열처리 온도 : 1323K 열처리 시간 : 13days

4 Thermodynamics 다원 합금계에서 Diffusion Coefficient 는 (n-1) 차원의 행렬 형태가 되며, Fe-M-C 3 원 계에서 용질 C 와 M 의 확산 유속은 다음과 같이 표현된다. Fcc Fe-M-C 침입형 고용상은 (Fe,M) 1 (Va,C) 1 의 formula unit 을 이용하여 1 mol of formula unit 당 Gibbs free energy 를 다음과 같이 표현한다.

5 Thermodynamics Gibbs Energy 식으로부터 각 원소의 Chemical Potential 을 얻는 공식은 다음과 같다. For substitutional M, For interstitial C,

6 Finite Differential Method Diffusion equation

7 Result

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10 Free Topic Diffusion couple Calculate concentration profile by solving 2 nd differential equation – (ref. Young-won Chang, phase transformations in metals and alloys 강의 자료, chap 2.)

11 (1) Steady state solution (2) Non-steady state solution c(x)=A 1 x+A 2 D: const ex) H 2 gas tank 0 x c  coco  Solutions of diffusion equation - bounded solution in an infinite medium: with the initial condition; c(x,0) = g(x) - Use the Fourier transformation method - Fourier transformation of Fick’s 2 nd law AMSE 312 Diffusion & Phase transitions

12 - Partial integration of the right hand side term twice yields transformed diffusion eq. c(x’,0) - Inverse transformation I (x’)   2 /Dt 0 1.0 Gaussian error fcn - bounded solution in an infinite medium AMSE 312 Diffusion & Phase transitions

13 Diffusion couple c x o cscs coco t=0 t=t 1 erf(0)=0, erf(0.5)=0.5, erf( )=1.0, erf(-z)= - erf(z) z erf(z) +1 0.5 - 0.5 AMSE 312 Diffusion & Phase transitions cscs coco

14 Diffusion couple Error function Integrated by RK4 method

15 Diffusion couple Initial condition – Left side : 0.6wt% C – Right side : 0.1wt% C – D = 4x10 -8 m 2 /s – (Random value)

16 번외 - Sudoku

17 Code to find solution…. But…. Failed