Ti<sub>3</sub>Al合金凝固过程晶核形成及演变过程的模拟研究

李昌; 侯兆阳; 牛媛; 高全华; 王真; 王晋国; 邹鹏飞

doi:10.7498/aps.71.20211415

摘要

采用分子动力学方法对Ti₃Al合金的形核机理进行了模拟研究, 采用团簇类型指数法(CTIM), 对凝固过程不同尺度的原子团簇结构进行了识别和表征, 深入研究了临界晶核的形成和长大过程. 结果表明, 凝固过程体系包含了数万种不同类型的原子团簇结构, 但其中22种团簇结构类型对结晶形核过程起关键性作用. 在晶核的形成和长大过程, 类二十面体(ICO)原子团簇、类BCC原子团簇和缺陷FCC及缺陷HCP原子团簇在3个特征温度点T₁ (1110 K), T₂ (1085 K)和T₃ (1010 K)时达到数量上的饱和, 并根据数量和空间分布随温度的变化, 得到了它们在形核和长大过程相互竞争的关系. 跟踪平行孪生晶粒形成和长大的过程发现, 临界晶核是由FCC原子构成的单相结构, 并未观察到亚稳BCC相优先形核的过程; 平行孪生结构是由FCC单相晶核在沿密排面逐层生长过程中形成的. 结果还表明, CTIM相比于其他微观结构表示方法, 能更为准确地揭示凝固过程微观结构的转变特征.

关键词:

TiAl合金 /
形核机理 /
分子动力学模拟 /
原子团簇

Abstract

The nucleation mechanism of Ti₃Al alloy is simulated by the molecular dynamics method in this work. The atomic clusters on different spatial scales are identified in the solidification process by the cluster-type index method (CTIM), and the formation process and the growth process of critical nucleus are studied in depth. It is found that the solidification system contains ten thousands of different types of atomic cluster structures, but only 22 types play a key role in the nucleation process. In the nucleation and growth process of nuclei, the ICO-like cluster, the BCC-like cluster, and the defective FCC cluster and the defective HCP cluster respectively reach their saturation points at the characteristic temperature T₁ (1110 K), T₂ (1085 K) and T₃ (1010 K). And the competition processes of these clusters are revealed according to the changes of their number and spatial distribution with temperature. By tracing the nucleation and growth process of the grain with parallel twin, it is found that the critical crystal nucleus is composed of single-phase FCC structures, and the preferent nucleation of metastable bcc structure is not observed. The twinned structure is formed by the layer-by-layer growth along the close-packed plane. It is also found that the CTIM is more accurate than other methods in revealing the microstructural characteristics during the solidification.

Keywords:

TiAl alloy /
nucleation mechanism /
molecular dynamics simulation /
atomic cluster

作者及机构信息

李昌,
侯兆阳,
牛媛,
高全华,
王真,
王晋国,
邹鹏飞

长安大学理学院, 西安　710064

通信作者: 侯兆阳, zhaoyanghou@163.com

基金项目: 国家自然科学基金(批准号: 50831003)资助的课题.

Authors and contacts

Li Chang,
Hou Zhao-Yang,
Niu Yuan,
Gao Quan-Hua,
Wang Zhen,
Wang Jin-Guo,
Zou Peng-Fei

School of Science, Chang’an University, Xi’an 710064, China

Corresponding author: Hou Zhao-Yang, zhaoyanghou@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 50831003).

文章全文 : translate this paragraph

参考文献

[1]	Mayer S, Erdely P, Fischer F D, Holec D, Kastenhuber M, Klein T, Clemens H 2017 Adv. Eng. Mater. 19 1600735 Google Scholar
[2]	Chen G, Peng Y, Zheng G, Qi Z, Wand M, Yu H, Dong C, Liu C T 2016 Nat. Mater. 15 876 Google Scholar
[3]	杨锐 2015 金属学报 51 129 Google Scholar Yang R. 2015 Acta Metall. Sin. 51 129 Google Scholar
[4]	Hao Y, Liu J, Li J, Liu X, Feng X 2017 Mater. Sci. Eng., A 705 210 Google Scholar
[5]	Edwards J E T, Gioacchino F D, Clegg W J 2019 Int. J. Plast. 118 291 Google Scholar
[6]	Christoph K, Christian L 2015 J. Alloys. Compd. 637 242 Google Scholar
[7]	Ilyas M U, Kabir M R 2021 Intermetallics 132 107129 Google Scholar
[8]	Pei Q X, Lu C, Fu M W 2004 J. Phys. Condens. Matter 16 4203 Google Scholar
[9]	Xie Z C, Gao T H, Guo X T, Qin X M, Xie Q 2014 J. Non-Cryst. Solids 394–395 16
[10]	Xie Z C, Gao T H, Guo X T, Xie Q 2014 J. Non-Cryst. Solids 406 95 Google Scholar
[11]	Li P T, Yang Y Q, Zhang W, Luo X, Jin N, Liu G 2016 RSC Adv. 6 54763 Google Scholar
[12]	Li P T, Yang Y Q, Zhang W, Luo X, Jin N, Liu G 2017 RSC Adv. 7 48315 Google Scholar
[13]	刘永利, 赵星, 张宗宁, 张林, 王绍青, 叶恒强 2009 物理学报 58 246 Google Scholar Liu Y L, Zhao X, Zhang Z N, Zhang L, Wang S Q, Ye H Q 2009 Acta Phys. Sin. 58 246 Google Scholar
[14]	宋成粉, 樊沁娜, 李蔚, 刘永利, 张林 2011 物理学报 60 063104 Google Scholar Song C F, Fan Q N, Li W, Liu Y L, Zhang L 2011 Acta Phys. Sin. 60 063104 Google Scholar
[15]	Honeycutt J D, Andersen H C 1987 J. Phys. Chem. 91 4950 Google Scholar
[16]	Finney J L 1970 Proc. R. Soc. London, Ser. A 319 479 Google Scholar
[17]	Liu R S, Dong K J, Tian Z A, Liu H R, Peng P, Yu A B 2007 J. Phys. Condens. Matter 19 751 Google Scholar
[18]	Hou Z Y, Li C, Liu L X, Gao Q H, Dong K J 2021 Comput. Mater. Sci. 197 110639 Google Scholar
[19]	大东, 彭平, 蒋元祺, 田泽安, 刘让苏 2013 物理学报 62 196101 Google Scholar Da D, Peng P, Jiang Y Q, Tian Z A, Liu R S 2013 Acta Phys. Sin. 62 196101 Google Scholar
[20]	Plimpton S J 1995 J. Comput. Phys. 117 1 Google Scholar
[21]	Zope R R, Mishin Y 2003 Phys. Rev. B 68 366 Google Scholar
[22]	Fu R, Rui Z, Dong Y, Luo D, Yan C 2021 Comput. Mater. Sci. 194 110428 Google Scholar
[23]	Bizot Q, Politano O, Nepapushev A A, Vadchenko S G, Baras F 2020 J. Appl. Phys. 127 145304 Google Scholar
[24]	Wang J S, Horsfield A, Schwingenschlögl U, Lee P D 2010 Phys. Rev. B 82 184203 Google Scholar
[25]	Gasser U, Weeks ER, Schofield A, Pusey P N, Weitz D A 2001 Science 292 258 Google Scholar
[26]	Wang Z, Wang F, Peng Y, Zheng Z, Han Y 2012 Science 338 87 Google Scholar
[27]	E J C, Wang L, Cai Y, Wu H A, Luo S N 2015 J. Chem. Phys. 142 064704 Google Scholar

施引文献

图 1 公共近邻分析方法中不同H-A键对拓扑结构示意图. 根对原子和其公共近邻原子分别用红色和绿色表示

Fig. 1. Schematic diagram of topological structure of H-A bond types in common neighbour analysis. The root-pair atoms and their common neighbours are represented in red and green colours, respectively.

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图 2 CTIM表征基本原子团簇结构方法示意图 (a) FCC基本原子团簇(12, 12/1421); (b)缺陷FCC基本原子团簇(12, 2/1311 1/1411 9/1421)

Fig. 2. Schematic diagram of topological structure of basic atomic cluster characterized by CTIM: (a) FCC basic atomic cluster (12, 12/1421); (b) defective FCC basic atomic cluster (12, 2/1311, 1/1411, 9/1421).

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图 3 CTIM表征的较大尺寸原子团簇结构 (a)由1个HCP基本原子团簇(12, 6/1421 6/1422)和1个FCC基本原子团簇(12, 12/1421)构成的包含20个原子的团簇结构; (b)由6个FCC基本原子团簇(12, 12/1421)构成的包含38个原子的纳米级团簇结构. 灰色原子为团簇的中心原子

Fig. 3. Topological structure of larger atomic clusters characterized by CTIM: (a) Cluster with 220 atoms consisting of one HCP basic atomic cluster (12, 6/1421, 6/1422) and one FCC basic atomic cluster (12, 12/1421); (b) nano-cluster with 38 atoms consisting of six FCC basic atomic clusters (12, 12/1421). The gray atoms are central atoms of basic atomic clusters.

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图 4 Ti₃Al合金不同冷速凝固过程平均原子能量随温度的变化曲线

Fig. 4. Changes of average energy per atom with temperature during the solidification of Ti₃Al alloy under different cooling rates.

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图 5 不同冷却速率下Ti₃Al合金的凝固结构(273 K) (a) 2 K/ps; (b) 1 K/ps; (c) 0.5 K/ps; (d) 0.01 K/ps. 其中绿色、红色和蓝色小球分别代表FCC, HCP和BCC晶态结构原子; 其他类型结构原子用灰色小球表示

Fig. 5. Microstructures of solidification solids (273 K) under different cooling rates: (a) 2 K/ps; (b) 1 K/ps; (c) 0.5 K/ps; (d) 0.01 K/ps. The crystal atoms with FCC, HCP and BCC structures are shown in green, red and blue, other atoms are shown in gray.

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图 6 Ti₃Al合金凝固过程双体分布函数随温度的演变过程

Fig. 6. Evolution of pair distribution function with temperature during the solidification process of Ti₃Al alloy.

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图 7 Ti₃Al合金结晶形核过程体系中基本原子团簇类型的总数量和其中22种主要基本原子团簇所涉及原子数目的比率随温度的变化

Fig. 7. Changes of the total number of basic atomic clusters and the ratio of involved atoms in the 22 major basic atomic clusters during the nucleation process of Ti₃Al alloy.

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图 8 Ti₃Al合金凝固过程体系内22种主要基本原子团簇的数目随温度的变化　(a1)类FCC基本原子团簇; (a2)类HCP基本原子团簇; (a3)类BCC基本原子团簇; (a4)类ICO基本原子团簇. 为了清晰起见, (b1)−(b4)分别给出了图(a1)−(a4)在(1110−814 K)温度区间的局部图. 类ICO、类BCC和缺陷FCC、缺陷HCP基本原子团簇分别在温度T₁= 1110 K, T₂= 1085 K和T₃= 1010 K达到饱和

Fig. 8. Relationship of the number of 22 major basic atomic clusters with temperature during the solidification process of Ti₃Al alloy: (a1) FCC-like basic atomic cluster; (a2) HCP-like basic atomic cluster; (a3) BCC-like basic atomic cluster; (a4) ICO-like basic atomic cluster. For clarity, (b1)−(b4) show the enlarged views of (a1)−(a4) in the temperature range (1110−814 K), respectively. The numbers of ICO-like, BCC-like and defective FCC, defective HCP basic atomic clusters reach saturation point at T₁= 1110 K, T₂= 1085 K and T₃= 1010 K.

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图 9 Ti₃Al合金凝固过程中类FCC、类HCP、类BCC和类ICO原子结构空间分布的演化过程　(a) 2073 K; (b) 1110 K; (c) 1085 K; (d) 1010 K; (e) 273 K. 其中, 绿色、红色、蓝色和黄色小球分别代表类FCC、类HCP、类BCC和类ICO原子. 其中G1和G2分别为选定的两个平行孪生晶粒和五重孪生晶粒.

Fig. 9. Evolution of spatial distribution of FCC-like, HCP-like, BCC-like and ICO-like atoms during the solidification process of Ti₃Al alloy: (a) 2073 K; (b) 1110 K; (c) 1085 K; (d) 1010 K; (e) 273 K. The FCC-like, HCP-like, BCC-like and ICO-like atoms are shown in green, red, blue and yellow color, respectively. The parallel and fivefold twin grains are labelled in G1 and G2, respectively.

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图 10 图9(e)中标记为G1的平行孪生晶粒的形成过程　(a) 团簇遗传率和尺寸(包含的中心原子数)与温度的变化关系; (b) 原子团簇结构演变过程. 其中绿色和红色小球分表代表类FCC和类HCP原子

Fig. 10. Formation process of parallel twin grains labeled G1 in Fig. 9(e): (a) Relationship of heritability and size (number of central atoms) of tracing clusters with temperature; (b) evolution process of the structure of atomic clusters. The FCC-like and HCP-like atoms are shown in green and red color, respectively.

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图 11 图10(b)中临界晶核形成过程不同局域结构的竞争过程　(a)不同结构类型原子数目占比的变化; (b)不同结构原子的空间分布. 类FCC、类HCP、类BCC、类ICO和无序结构(其他)原子分别用绿色、红色、橘黄色和白色表示

Fig. 11. Competition process of different local structures in the formation process critical nucleus shown in Fig. 10(b): (a) Change of the proportion of the atoms with different local structures; (b) spatial distribution of the atoms with different local structures. The FCC-like, HCP-like, BCC-like and ICO-like atoms are shown in green, red, blue and yellow color, respectively. Others with disordered structure are shown in white color.

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[1]	Mayer S, Erdely P, Fischer F D, Holec D, Kastenhuber M, Klein T, Clemens H 2017 Adv. Eng. Mater. 19 1600735 Google Scholar
[2]	Chen G, Peng Y, Zheng G, Qi Z, Wand M, Yu H, Dong C, Liu C T 2016 Nat. Mater. 15 876 Google Scholar
[3]	杨锐 2015 金属学报 51 129 Google Scholar Yang R. 2015 Acta Metall. Sin. 51 129 Google Scholar
[4]	Hao Y, Liu J, Li J, Liu X, Feng X 2017 Mater. Sci. Eng., A 705 210 Google Scholar
[5]	Edwards J E T, Gioacchino F D, Clegg W J 2019 Int. J. Plast. 118 291 Google Scholar
[6]	Christoph K, Christian L 2015 J. Alloys. Compd. 637 242 Google Scholar
[7]	Ilyas M U, Kabir M R 2021 Intermetallics 132 107129 Google Scholar
[8]	Pei Q X, Lu C, Fu M W 2004 J. Phys. Condens. Matter 16 4203 Google Scholar
[9]	Xie Z C, Gao T H, Guo X T, Qin X M, Xie Q 2014 J. Non-Cryst. Solids 394–395 16
[10]	Xie Z C, Gao T H, Guo X T, Xie Q 2014 J. Non-Cryst. Solids 406 95 Google Scholar
[11]	Li P T, Yang Y Q, Zhang W, Luo X, Jin N, Liu G 2016 RSC Adv. 6 54763 Google Scholar
[12]	Li P T, Yang Y Q, Zhang W, Luo X, Jin N, Liu G 2017 RSC Adv. 7 48315 Google Scholar
[13]	刘永利, 赵星, 张宗宁, 张林, 王绍青, 叶恒强 2009 物理学报 58 246 Google Scholar Liu Y L, Zhao X, Zhang Z N, Zhang L, Wang S Q, Ye H Q 2009 Acta Phys. Sin. 58 246 Google Scholar
[14]	宋成粉, 樊沁娜, 李蔚, 刘永利, 张林 2011 物理学报 60 063104 Google Scholar Song C F, Fan Q N, Li W, Liu Y L, Zhang L 2011 Acta Phys. Sin. 60 063104 Google Scholar
[15]	Honeycutt J D, Andersen H C 1987 J. Phys. Chem. 91 4950 Google Scholar
[16]	Finney J L 1970 Proc. R. Soc. London, Ser. A 319 479 Google Scholar
[17]	Liu R S, Dong K J, Tian Z A, Liu H R, Peng P, Yu A B 2007 J. Phys. Condens. Matter 19 751 Google Scholar
[18]	Hou Z Y, Li C, Liu L X, Gao Q H, Dong K J 2021 Comput. Mater. Sci. 197 110639 Google Scholar
[19]	大东, 彭平, 蒋元祺, 田泽安, 刘让苏 2013 物理学报 62 196101 Google Scholar Da D, Peng P, Jiang Y Q, Tian Z A, Liu R S 2013 Acta Phys. Sin. 62 196101 Google Scholar
[20]	Plimpton S J 1995 J. Comput. Phys. 117 1 Google Scholar
[21]	Zope R R, Mishin Y 2003 Phys. Rev. B 68 366 Google Scholar
[22]	Fu R, Rui Z, Dong Y, Luo D, Yan C 2021 Comput. Mater. Sci. 194 110428 Google Scholar
[23]	Bizot Q, Politano O, Nepapushev A A, Vadchenko S G, Baras F 2020 J. Appl. Phys. 127 145304 Google Scholar
[24]	Wang J S, Horsfield A, Schwingenschlögl U, Lee P D 2010 Phys. Rev. B 82 184203 Google Scholar
[25]	Gasser U, Weeks ER, Schofield A, Pusey P N, Weitz D A 2001 Science 292 258 Google Scholar
[26]	Wang Z, Wang F, Peng Y, Zheng Z, Han Y 2012 Science 338 87 Google Scholar
[27]	E J C, Wang L, Cai Y, Wu H A, Luo S N 2015 J. Chem. Phys. 142 064704 Google Scholar

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Ti₃Al合金凝固过程晶核形成及演变过程的模拟研究