Phase Transformations Grain Growth Monte Carlo Simulation ByeongJoo

Phase Transformations Grain Growth - Monte Carlo Simulation Byeong-Joo Lee POSTECH - MSE calphad@postech. ac. kr Byeong-Joo Lee cmse. postech. ac. kr

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 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). Byeong-Joo Lee cmse. postech. ac. kr

Normal Grain Growth – The Mechanism Byeong-Joo Lee cmse. postech. ac. kr

Interface-Reaction Controlled Growth - Grain growth in polycrystalline solids ▷ Capillary Effect Consider arbitrarily curved surface element · system condition : Vα = Vβ = V = const. T = const. · d. F = -S d. T - P d. V + γd. A = - Pβ d. Vβ - Pα d. Vα + γd. A = - (Pβ - Pα) d. Vβ + γd. A @ equilibrium - (Pβ - Pα) d. Vβ + γd. A = 0 ∴ d. A = (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 d. Vβ 〓 r 1 r 2 θ 1 θ 2 δr Byeong-Joo Lee cmse. postech. ac. kr

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). Byeong-Joo Lee cmse. postech. ac. kr

Abnormal Grain Growth – The Mechanism? Byeong-Joo Lee cmse. postech. ac. kr

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

Monte Carlo – Monte Carlo Integration y 1 x Byeong-Joo Lee cmse. postech. ac. kr

Monte Carlo Simulation - General Scheme (Potts Model: Srolovitz) Byeong-Joo Lee cmse. postech. ac. kr

[110]/[100] Tilt Grain Boundary Energy of Aluminum Byeong-Joo Lee cmse. postech. ac. kr

[100] Twist Grain Boundary Energy of Copper Byeong-Joo Lee cmse. postech. ac. kr

Procedure – Initial Grain Structure and GB Energy anisotropy 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 Byeong-Joo Lee cmse. postech. ac. kr

Check of Lattice Pinning and Choice of Initial Structure Initial structure of 65, 679 grains Byeong-Joo Lee cmse. postech. ac. kr

Abnormal Grain Growth – Computer Simulation Byeong-Joo Lee cmse. postech. ac. kr

Effect of Anisotropy of Grain Boundary Mobility on Abnormal GG Byeong-Joo Lee cmse. postech. ac. kr

Effect of Anisotropy of Grain Boundary Energy on Abnormal GG Byeong-Joo Lee cmse. postech. ac. kr

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

Grain Boundary Energy in bcc Fe Symmetric Twist GBs Symmetrical Tilt GBs Byeong-Joo Lee cmse. postech. ac. kr