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The in-situ reaction is an important method of preparing metal matrix composites: it can produce more uniform distribution of the reinforcement particles and more excellent structure of the phase boundary between the particles and the matrix. Therefore, the kinetics of in-situ reaction process deserves to be further studied. However, as the in-situ reaction is a rapid random process under high-temperature condition, it is difficult to observe the reaction process of metal-matrix composite materials experimentally. In this work, we propose a new phase-field model to describe the in-situ reaction process, and investigate the nucleation kinetic processes of in-situ reaction under different physical conditions. We find that the nucleation rate increases with the augment of curvature radius and noise intensity, and the size distribution of the particles is more uniform under the conditions of a small curvature radius and strong noise. With the increase of the undercooling, the nucleation rate first increases and then decreases, which is consistent with the classical nucleation theory.
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Keywords:
- phase-field model /
- in-situ reaction /
- nucleation /
- phase transformation
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Guo M X, Wang M P, Shen K, Zhang Z, Li S M 2007 Nonferrous Met. Soc. China 09 1440
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Yang B, Wang Y Q, Zhou B L 1998 Acta. Metall. Sin. 01 100
[3] 张来启, 孙祖庆, 张跃, 杨王玥 1998 金属学报 11 1206
Zhang L Q, Sun Z Q, Zhang Y, Yang W Y 1998 Acta. Metall. Sin. 11 1206
[4] 孙靖 2015 硕士学位论文 (上海: 上海交通大学)
Sun J 2015 M. S. Thesis (Shanghai: Shanghai Jiao Tong University) (in Chinese)
[5] Qu L, Zhao N, Zhao H J, Huang M L, Ma H T 2014 Scr. Mater. 72 43
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[9] Kavousi S, Novak B R, Hoyt J, Moldovan D 2020 Comput. Mater. Sci. 184 854
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Google Scholar
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Google Scholar
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图 1 (a)—(c)原位反应形核过程, 红色区域为c = 1的液相, 蓝色区域为c = 0的液相, 黄色区域为c = 0.5的固相; (d) 沿图(a)中黑直线上的成分场随时间的演化曲线
Figure 1. (a)–(c) Snapshots of the in-situ reactive process, the blue and red regions represent melt phases with c = 0 and c = 1, respectively. The yellow region is the new solid phase. (d) Temporal evolution of the concentration filed across the solid black line in panel (a).
图 2 不同曲率半径下的原位反应形核过程(左侧为bnds场(
${\text{bnds}} = c + \displaystyle\sum\nolimits_i {{\eta _i}}$ ), 右侧为成分场) (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80Figure 2. Snapshots of the in-situ reaction processes with different radius of curvatures: (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80. In each row, the left three figures show the temporal evolution of the bnds field, the right three figures show the temporal evolution of the concentration field.
图 3 不同曲率半径下的晶核数目随时间演化图 (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80
Figure 3. Temporal evolution of the particle numbers with different initial radius of curvatures: (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80
图 4 形核率随曲率半径的变化关系
Figure 4. Nucleation rate versus initial radius of curvatures.
图 5 不同界面曲率下的颗粒粒径分布 (a) ρ = 30; (b) ρ = 60; (c) ρ = 80; (d)平直界面
Figure 5. Particle size distributions with different curvatures: (a) ρ = 30; (b) ρ = 60; (c) ρ = 80; (d) ρ = ∞.
图 6 不同噪声强度下的原位反应形核过程 (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07
Figure 6. Snapshots of the in-situ reaction processes with different noise intensities: (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07.
图 7 形核率随噪声强度的变化关系
Figure 7. Nucleation rate versus initial noise intensity.
图 8 不同噪声下的颗粒粒径分布 (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07
Figure 8. Particle size distributions with different noise intensities: (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07.
图 9 不同过冷度参数下的原位反应形核过程 (a) A = 0.5; (b) A = 0.55; (c) A = 0.65
Figure 9. Snapshots of the in-situ reaction processes with different undercoolings: (a) A = 0.5; (b) A = 0.55; (c) A = 0.65.
图 10 形核率随过冷度参数的变化关系
Figure 10. Nucleation rate versus undercoolings.
图 11 不同过冷度参数下的颗粒粒径分布 (a) A = 0.5; (b) A = 0.55; (c) A = 0.65
Figure 11. Particle size distributions with different undercoolings: (a) A = 0.5; (b) A = 0.55; (c) A = 0.65.
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[1] 郭明星, 汪明朴, 申坤, 张真, 李树梅 2007 中国有色金属学报 09 1440
Google Scholar
Guo M X, Wang M P, Shen K, Zhang Z, Li S M 2007 Nonferrous Met. Soc. China 09 1440
Google Scholar
[2] 杨滨, 王玉庆, 周本濂 1998 金属学报 01 100
Yang B, Wang Y Q, Zhou B L 1998 Acta. Metall. Sin. 01 100
[3] 张来启, 孙祖庆, 张跃, 杨王玥 1998 金属学报 11 1206
Zhang L Q, Sun Z Q, Zhang Y, Yang W Y 1998 Acta. Metall. Sin. 11 1206
[4] 孙靖 2015 硕士学位论文 (上海: 上海交通大学)
Sun J 2015 M. S. Thesis (Shanghai: Shanghai Jiao Tong University) (in Chinese)
[5] Qu L, Zhao N, Zhao H J, Huang M L, Ma H T 2014 Scr. Mater. 72 43
[6] Li H, Jiao L, Huang X P, Li F, Lu S B, Li Y L, Qiao Y P 2021 J. Mater. Eng. Perform. 30 7295
Google Scholar
[7] Jiang Y H, Li D, Liang S H, Zou J T, Liu F 2017 J. Mater. Sci. 52 2957
Google Scholar
[8] Lan T, Jiang Y H, Zhang X J, Cao F, Liang S H 2021 Int. J. Miner., Metall. Mater. 28 1090
Google Scholar
[9] Kavousi S, Novak B R, Hoyt J, Moldovan D 2020 Comput. Mater. Sci. 184 854
[10] 方辉, 薛桦, 汤倩玉, 张庆宇, 潘诗琰, 朱鸣芳 2019 物理学报 68 048102
Google Scholar
Fang H, Xue H, Tang Q Y, Zhang Q Y, Pan S Y, Zhu M F 2019 Acta Phys. Sin. 68 048102
Google Scholar
[11] 郭春文, 李俊杰, 马渊, 王锦程 2015 金属学报 54 657
Google Scholar
Guo C W, Li J J, Ma Y, Wang J C 2015 Acta Phys. Sin. 54 657
Google Scholar
[12] Zhang Z D, Cao Y T, Sun D K, Xing H, Wang J C, Ni Z H 2020 Chin. Phys. B 29 028103
Google Scholar
[13] 魏雷, 林鑫, 王猛, 黄卫东 2015 物理学报 64 018013
Google Scholar
Wei L, Lin X, Wang M, Huang W D 2015 Acta Phys. Sin. 64 018013
Google Scholar
[14] Rolchigo M R, LeSar R 2019 Comput. Mater. Sci. 163 148
Google Scholar
[15] Chen L Q 2002 Annu. Rev. Mater. Res. 32 113
Google Scholar
[16] Guo C, Wang J C, Li J J, Wang Z J, Huang Y H, Gu J W, Lin X 2018 Acta Mater. 145 175
Google Scholar
[17] Deng Y Y, Guo C, Wang J C, Liu Q, Zhao Y P, Yang Q 2021 Chin. Phys. B 30 611
Google Scholar
[18] 王锦程, 郭春文, 李俊杰, 王志军 2018 物理学报 54 657
Google Scholar
Wang J C, Guo C W, Li J J, Wang Z J 2018 Acta Phys. Sin. 54 657
Google Scholar
[19] 郭灿, 王锦程, 王志军, 李俊杰, 郭耀麟, 唐赛 2015 物理学报 64 028102
Google Scholar
Guo C, Wang J C, Wang Z J, Li J J, Guo Y L, Tang S 2015 Acta Phys. Sin. 64 028102
Google Scholar
[20] Guo M X, Shen K, Wang M P 2009 Acta Mater. 57 4568
Google Scholar
[21] Pan S Y, Zhu M F, Rettenmayr M 2017 Acta Mater. 132 565
Google Scholar
[22] 柯常波, 周敏波, 张新平 2014 金属学报 50 294
Google Scholar
Ke C B, Zhou M B, Zhang X P 2014 Metall. Sin. 50 294
Google Scholar
[23] Shi R P, Shen C, Dregia S A, Wang Y Z 2018 Scr. Mater. 146 276
Google Scholar
[24] Guo M X, Shen K, Wang M P 2012 Mater. Chem. Phys. 131 589
Google Scholar
[25] Guo C, Wang J C, Wang Z J, Li J J, Guo Y L, Huang Y H 2016 Soft Matter 12 4666
Google Scholar
[26] 王巍, 付立铭 2008 金属学报 06 723
Google Scholar
Wang W, Fu L M 2008 Metall. sin. 06 723
Google Scholar
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