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由于冷却技术和合金非晶形成能力的限制, 实验室难以得到大块非晶, 而纳米液滴的快速冷却要相对容易, 因此纳米液滴的模拟研究更容易得到实验的验证. 本文运用分子动力学方法, 模拟不同尺寸的Cu64Zr36纳米液滴在1.0 × 1012 K/s冷却速率下的凝固过程, 并采用平均原子能量、双体分布函数、三维可视化和最大标准团簇分析等方法分析其微观结构的演化. 对能量曲线和微观结构短程序特征长度的统计分析表明, 所有纳米液滴的凝固过程都经历了液-液相变和液-固相变, 最后形成了非晶态纳米颗粒. 拓扑密堆(topologically close-packed, TCP)结构的演化过程能充分体现纳米液滴两次相变的基本特征, 但二十面体不能. 从TCP团簇的角度, 纳米液滴的整个凝固过程可以分为坯胎、聚集、长大和粗化4个阶段. TCP结构能体现出非晶纳米液滴和颗粒的基本结构特征, 对于完善凝固理论具有重要意义.It is difficult to obtain bulk amorphous alloys experimentally due to the limitation of cooling technology and the ability to form amorphous alloy. However, the rapid cooling of nano-droplets is relatively easy, so the simulation research of nano-droplets is easier to verify experimentally. In this work, the molecular dynamics simulation for the rapid cooling of Cu64Zr36 nano-droplets of different sizes is conducted at a cooling rate of 1.0 × 1012 K/s, and the evolution of microstructure is analyzed in terms of the average potential energy, the pair distribution function, the three-dimensional visualization, and the largest standard cluster analysis. The analysis of the energy curves and the characteristic length for short-range-ordered microstructure show that the solidification process for all nano-droplets undergoes liquid-liquid transition and liquid-solid transition, and finally forms amorphous nanoparticles. Comparing with the icosahedron, the evolution of the topologically close-packed (TCP) structures can reflect the basic characteristics of phase transitions effectively. Based on the evolution of TCP clusters, the entire solidification process of nano-droplets can be divided into four stages: embryo, aggregation, growth and coarsening. The TCP structure embodies the basic structural characteristics of amorphous nano-droplets and particles, which is of great significance in perfecting the solidification theory.
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Keywords:
- CuZr alloy /
- topologically close-packed structure /
- LaSC /
- molecular dynamics simulation /
- solidification process
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图 1 LaSC的基本概念及典型结构图示 (a)二十面体及其(b)构成单元 S555; (c) S555的共有近邻之间的连接关系; (d) BCC、(e) FCC和(f) HCP晶体的基本结构单元
Fig. 1. Basic concept and typical structure of LaSC: (a) Icosahedron and (b) a constituent unit S555; (c) onnection between CNNs of S555; basic structural units of three typical crystals of (d) BCC, (e) FCC, and (f) HCP.
图 2 不同尺寸的Cu64Zr36纳米液滴快速凝固过程中平均原子能量随温度的变化
Fig. 2. Evolution of average atomic potential energy of per atom with temperature during rapid solidification of Cu64Zr36 nanodroplets of different sizes.
图 3 300 K时Cu64Zr36纳米颗粒的(a) PDF曲线和(b)原子排列的三维可视化图
Fig. 3. (a) Pair distribution functions g(r) curves and (b) three-dimensional visualization of atomic arrangement of Cu64Zr36 nanoparticles at 300 K.
图 4 E-T曲线的(a)斜率和(b)二阶导数的变化
Fig. 4. (a) Slope and (b) the second derivative of the E-T curves.
图 5 纳米液滴凝固过程的局域结构平均截断半径
$ \bar R_{\rm c} $ 随温度的变化 (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000Fig. 5. Evolution of the
$ \bar R_{\rm c} $ with temperature during the solidification of nanodroplets: (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000.
图 6 纳米液滴凝固过程中TCP原子的百分含量随温度的变化 (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000
Fig. 6. Evolution of the percentage of TCP atoms with temperature during the solidification of nano-droplets: (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000.
图 7 纳米液滴凝固过程中TCP团簇的数量NC随温度的变化 (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000
Fig. 7. Evolution of the number of TCP clusters NC with temperature during the solidification of nano-droplets: (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000.
图 8 纳米液滴在凝固过程中最大TCP团簇的尺寸Smax随温度的变化 (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000
Fig. 8. Evolution of the size of the maximum TCP cluster (Smax) with temperature during the solidification of nano-droplets: (a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000.
图 9 临界温度和TCP原子数目与尺寸的相关性 (a)液-液相变的起始温度Ts; (b)液-固相变的起始温度Tls; (c)玻璃转变温度Tg; (d) 300 K时纳米颗粒内TCP原子的百分含量
Fig. 9. Correlation of critical temperature and the percentage of TCP atoms with the size of nano-droplets: (a) Initial temperature of the liquid-liquid transformation (Ts); (b) initial temperature of the liquid-solid transformation (Tls); (c) glass transition temperature (Tg); (d) percentage of TCP atoms in nanoparticles at 300 K.
图 10 纳米液滴在凝固过程中基于Z12的结构参数随温度的演化 (a) Z12原子数量; (b) Z12团簇数量(NC); (c) 最大Z12团簇的尺寸Smax; (d) 300 K时纳米颗粒内Z12 原子的百分含量随颗粒尺寸的变化
Fig. 10. Evolution of Z12-based structure parameters with temperature during solidification of nano-droplets: (a) Number of Z12 atoms; (b) number of Z12 clusters (NC); (c) size of the largest Z12 cluster (Smax); (d) evolution of the percentage of Z12 atoms with the size of nanoparticles at 300 K.
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[1] Duan S B, Wang R M 2013 Prog. Nat. Sci. 23 113
Google Scholar
[2] Taylor M G, Austin N, Gounaris C E, Mpourmpakis G 2015 ACS Catal. 5 6296
Google Scholar
[3] Yan Y, Warren S C, Fuller P, Grzybowski B A 2016 Nat. Nanotechnol. 11 603
Google Scholar
[4] Mpourmpakis G, Andriotis A N, Vlachos D G 2010 Nano Lett. 10 1041
Google Scholar
[5] Yan Y C, Du J S S, Gilroy K D, Yang D R, Xia Y N, Zhang H 2017 Adv. Mater. 29 1605997
Google Scholar
[6] Cuenya B R, Behafarid F 2015 Surf. Sci. Rep. 70 135
Google Scholar
[7] Wessels J M, Nothofer H G, Ford W E, Wrochem F V, Scholz F, Vossmeyer T, Schroedter A, Weller H, Yasuda A 2004 J. Am. Chem. Soc. 126 3349
Google Scholar
[8] Kelly K L, Coronado E, Zhao L L, Schatz G C 2003 J. Phys. Chem. B 107 668
Google Scholar
[9] De M, Ghosh P S, Rotello V M 2008 Adv. Mater. 20 4225
Google Scholar
[10] Kim M, Lee C, Ko S M, Nam J M 2019 J. Solid State Chem. 270 295
Google Scholar
[11] Ferrando R, Jellinek J, Johnston R L 2008 Chem. Rev. 108 845
Google Scholar
[12] Talapin D V, Lee J S, Kovalenko M V, Shevchenko E V 2010 Chem. Rev. 110 389
Google Scholar
[13] Bratlie K M, Lee H, Komvopoulos K, Yang P and Somorjai G A 2007 Nano Lett. 7 3097
Google Scholar
[14] Cuenya B R 2010 Thin Solid Films 518 3127
Google Scholar
[15] Johnston R L 1998 Philos. Trans. R. Soc. London, Ser. A 356 211
Google Scholar
[16] Adibi S, Branicio P S, Ballarini R 2016 RSC Adv. 6 13548
Google Scholar
[17] Yuan S Y, Branicio P S 2020 Int. J. Plast. 134 102845
Google Scholar
[18] Zheng K, Branicio P S 2020 Phys. Rev. Mater. 4 076001
Google Scholar
[19] Zhang M, Li Q M, Zhang J C, Zheng G P, Wang X Y 2019 J. Alloys Compd. 801 318
Google Scholar
[20] Nandam S H, Ivanisenko Y, Schwaiger R, Śniadecki Z, Mu X, Wang D, Chellali R, Boll T, Kilmametov A, Bergfeldt T, Gleiter H, Hahn H 2017 Acta Mater. 136 181
Google Scholar
[21] Mendelev M I, Kramer M J, Ott R T, Sordelet D J, Yagodin D, Popel P 2009 Philos. Mag. 89 967
Google Scholar
[22] Zhong L, Wang J W, Sheng H W, Zhang Z, Mao S X 2014 Nature 512 177
Google Scholar
[23] Nelli D, Ferrando R 2019 Nanoscale 11 13040
Google Scholar
[24] Mauro N A, Wessels V, Bendert J C, Klein S, Gangopadhyay A K, Kramer M J, Hao S G, Rustan G E, Kreyssig A, Goldman A I, Kelton K F 2011 Phys. Rev. B 83 184109
Google Scholar
[25] Honeycutt J D, Andersen H C 1987 J. Phys. Chem. 91 4950
Google Scholar
[26] Liu R S, Li J Y, Dong K J, Zheng C X, Liu H R 2002 Mater. Sci. Eng. B 94 141
Google Scholar
[27] Tian Z A, Liu R S, Dong K J, Yu A B 2011 EPL 96 36001
Google Scholar
[28] Tian Z A, Dong K J, Yu A B 2015 Ann. Phys. 354 499
Google Scholar
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Google Scholar
[30] Tian Z A, Dong K J, Yu A B 2013 AIP Conf. Proc. 1542 373
Google Scholar
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Google Scholar
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Google Scholar
[33] Lin L, Deng H Q, Tian Z A, Gao F, Hu W Y, Wen D D, Mo Y F 2019 J. Alloys Compd. 775 1184
Google Scholar
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Google Scholar
Li J J, Tian Z A 2020 Low. Temp. Phys. Lett. 42 81
Google Scholar
[35] Zhou L L, Mo Y F, Tian Z A, Li F Z, Xie X L, Liu R S 2021 J. Mater. Sci. 56 4220
Google Scholar
[36] Sheng H W, Luo W K, Alamgir F M, Bai J M, Ma E 2006 Nature 439 419
Google Scholar
[37] Inoue A, Kimura H 2001 J. Light Metals 1 31
Google Scholar
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Google Scholar
[39] Luo W K, Sheng H W, Alamgir F M, Bai J M, He J H, Ma E 2004 Phys. Rev. Lett. 92 145502
Google Scholar
[40] Lee M, Kim H K, Lee J C 2010 Met. Mater. Int. 16 877
Google Scholar
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