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이 병 주 포항공과대학교 신소재공학과 calphad@postech.ac.kr

이 병 주 포항공과대학교 신소재공학과 calphad@postech.ac.kr. Grain Growth. Monte Carlo Simulation. Micro Monte Carlo Simulation - Literature (from N.M. Hwang). 1. “ Texture Evolution by Grain Growth in the System of Anisotropic Grain Boundary Energy ”

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이 병 주 포항공과대학교 신소재공학과 calphad@postech.ac.kr

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  1. 이 병 주 포항공과대학교 신소재공학과 calphad@postech.ac.kr Grain Growth Monte Carlo Simulation

  2. 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. Normal Grain Growth – The Mechanism

  4. Interface-Reaction Controlled Growth - Grain growth in polycrystalline solids ▷ Capillary Effect     Consider arbitrarily curved surface element · system condition : Vα=Vβ= V = const.      T = const. · dF   = -S dT - P dV + γdA          = - Pβ dVβ - Pα dVα + γdA          = - (Pβ - Pα) dVβ + γdA @ equilibrium      - (Pβ - Pα) dVβ + γdA = 0 ∴          dA  = (r1 + δr) θ1․(r2 + δr) θ2 - r1 θ1․r2 θ2        = (r1 + r2) δr θ1θ2 + (δr)2θ1 θ2 ≈ (r1 + r2) δr θ1θ2 dVβ 〓 r1r2θ1θ2 δr

  5. 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. Abnormal Grain Growth – The Mechanism?

  7. Grain Growth as a Parallel Process - Grain growth in polycrystalline solids A phase Field Simulation, H.K. Kim & B.-J. Lee (2012)

  8. Monte Carlo – Monte Carlo Integration y 1 x

  9. Monte Carlo Simulation - General Scheme (Potts Model: Srolovitz)

  10. [110]/[100] Tilt Grain Boundary Energy of Aluminum

  11. [100] Twist Grain Boundary Energy of Copper

  12. 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 (0~900o) J increases with increasing misorientation up to 15o and fluctuates within 20% above 15o Black lines mean high angle GB while white mean low angle (< 15o) grain boundary

  13. Check of Lattice Pinning and Choice of Initial Structure Initial structure of 65,679 grains

  14. Abnormal Grain Growth– Computer Simulation

  15. Effect of Anisotropy of Grain Boundary Mobility on Abnormal GG

  16. Effect of Anisotropy of Grain Boundary Energy on Abnormal GG

  17. Effect of Anisotropic GBE and precipitates on Abnormal GG C.-S. Park et al., Scripta Mater. (2012)

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