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Byeong-Joo Lee www.postech.ac.kr/~calphad. Byeong-Joo Lee www.postech.ac.kr/~calphad Micro Monte Carlo Simulation - Literature (from N.M. Hwang) 1. “Texture.

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Presentation on theme: "Byeong-Joo Lee www.postech.ac.kr/~calphad. Byeong-Joo Lee www.postech.ac.kr/~calphad Micro Monte Carlo Simulation - Literature (from N.M. Hwang) 1. “Texture."— Presentation transcript:

1 Byeong-Joo Lee www.postech.ac.kr/~calphad

2 Byeong-Joo Lee www.postech.ac.kr/~calphad Micro Monte Carlo Simulation - Literature (from N.M. Hwang) 1. “Texture Evolution by Grain Growth in the System of Anisotropic Grain Boundary Energy” N.M. Hwang, B.-J. Lee and C.H. Han, Scripta Materialia 37, 1761-1767 (1997). 2. “Grain Growth Behavior in the System of Anisotropic Grain Boundary Mobility” Nong Moon Hwang, Scripta Materialia 37, 1637-1642 (1997). 3. “Formation of Island and Peninsular Grains during Secondary Recrystallization of Fe-3%Si Alloy” S.B. Lee, N.M. Hwang C.H. Hahn, D.Y. Yoon, Scripta Mater. 39, 825-829 (1998). 4. “Simulation of Effect of Anisotropic Grain Boundary Mobility and Energy on Abnormal Grain Growth”, N.M. Hwang, J. Mater. Sci. vol. 33, 5625-5629 (1998). 5. “Abnormal Grain Growth by Solid-State Wetting along Grain Boundary or Triple Junction” N.M. Hwang, S.B. Lee and D.Y. Kim, Scripta Mater. 44, 1153-1160 (2001). 6. “Comparison of the advantages conferred by mobility and energy of the grain boundary in inducing abnormal grain growth using Monte Carlo simulations” Dong-Kwon Lee, Byeong-Joo Lee, Kyung-Jun Ko and Nong-Moon Hwang, Mater. Trans. 50, 2521-2525 (2009). 7. “Three-dimensional Monte Carlo simulation for the effect of precipitates and sub-boundaries on abnormal grain growth” Chang-Soo Park, Tae-Wook Na, Hyung-Ki Park, Byeong-Joo Lee, Chan-Hee Han and Nong-Moon Hwang, Scripta Mater. 66, 398-401 (2012).

3 Byeong-Joo Lee www.postech.ac.kr/~calphad Normal Grain Growth – The Mechanism

4 Byeong-Joo Lee www.postech.ac.kr/~calphad Interface-Reaction Controlled Growth - Grain growth in polycrystalline solids ▷ Capillary Effect Consider arbitrarily curved surface element · system condition : V α = V β = V = const. T = const. · dF = -S dT - P dV + γdA = - P β dV β - P α dV α + γdA = - (P β - P α ) dV β + γdA @ equilibrium - (P β - P α ) dV β + γdA = 0 ∴ dA = (r 1 + δr) θ 1 ․ (r 2 + δr) θ 2 - r 1 θ 1 ․ r 2 θ 2 = (r 1 + r 2 ) δr θ 1 θ 2 + (δr) 2 θ 1 θ 2 ≈ (r 1 + r 2 ) δr θ 1 θ 2 dV β 〓 r 1 r 2 θ 1 θ 2 δr

5 Byeong-Joo Lee www.postech.ac.kr/~calphad Interface-Reaction Controlled Growth - Grain growth in polycrystalline solids ▶ Grain Growth - no composition change & no phase (crystal structure) change - capillary pressure is the only source of driving force · α and β is the same phase · ∴ : normal growth equation ※ Role of Mobility / Role of Anisotropy in Grain boundary Energy 1. "Grain Growth Behavior in the System of Anisotropic Grain Boundary Mobility," Nong Moon Hwang, Scripta Materialia 37, 1637-1642 (1997). 2. "Texture Evolution by Grain Growth in the System of Anisotropic Grain Boundary Energy," Nong Moon Hwang, B.-J. Lee and C.H. Han, Scripta Materialia 37, 1761-1767 (1997).

6 Byeong-Joo Lee www.postech.ac.kr/~calphad Abnormal Grain Growth – The Mechanism?

7 Byeong-Joo Lee www.postech.ac.kr/~calphad A phase Field Simulation, H.K. Kim & B.-J. Lee (2012) Grain Growth as a Parallel Process - Grain growth in polycrystalline solids

8 Byeong-Joo Lee www.postech.ac.kr/~calphad Monte Carlo – Monte Carlo Integration x y 1

9 Byeong-Joo Lee www.postech.ac.kr/~calphad Monte Carlo Simulation - General Scheme (Potts Model: Srolovitz)

10 Byeong-Joo Lee www.postech.ac.kr/~calphad [110]/[100] Tilt Grain Boundary Energy of Aluminum

11 Byeong-Joo Lee www.postech.ac.kr/~calphad [100] Twist Grain Boundary Energy of Copper

12 Byeong-Joo Lee www.postech.ac.kr/~calphad Procedure – Initial Grain Structure and GB Energy anisotropy 80×80×80 3-dim grain structure, with 4×4×4 pixel points in each grain Each Grain has its own orientation (0~900 o ) J increases with increasing misorientation up to 15 o and fluctuates within 20% above 15 o Black lines mean high angle GB while white mean low angle (< 15 o ) grain boundary

13 Byeong-Joo Lee www.postech.ac.kr/~calphad Check of Lattice Pinning and Choice of Initial Structure Initial structure of 65,679 grains

14 Byeong-Joo Lee www.postech.ac.kr/~calphad Abnormal Grain Growth – Computer Simulation

15 Byeong-Joo Lee www.postech.ac.kr/~calphad Effect of Anisotropy of Grain Boundary Mobility on Abnormal GG

16 Byeong-Joo Lee www.postech.ac.kr/~calphad Effect of Anisotropy of Grain Boundary Energy on Abnormal GG

17 Byeong-Joo Lee www.postech.ac.kr/~calphad Effect of Anisotropic GBE and precipitates on Abnormal GG C.-S. Park et al., Scripta Mater. (2012)

18 Byeong-Joo Lee www.postech.ac.kr/~calphad Symmetric Twist GBsSymmetrical Tilt GBs Grain Boundary Energy in bcc Fe

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