Molecular dynamics simulation of rapid solidification of Cu<sub>64</sub>Zr<sub>36</sub> nanodrops of different sizes

Wei Guo-Cui; Tian Ze-An

doi:10.7498/aps.70.20211235

Abstract

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.

Keywords:

Authors and contacts

Wei Guo-Cui¹,
Tian Ze-An^2,1

1.
Institute of Advanced Optoelectronic Materials and Technology, School of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China
2.
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China

Corresponding author: Tian Ze-An, tianzean@hnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51661005, U1612442) and the Industry Education Integration Innovation Platform and Postgraduate Joint Training Base of Intelligent Manufacturing of Guizhou University, China (Grant No. 2020-520000-83-01-324061).

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References

[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
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Cited By

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

Figure 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.

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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

Figure 2. Evolution of average atomic potential energy of per atom with temperature during rapid solidification of Cu₆₄Zr₃₆ nanodroplets of different sizes.

DownLoad: Full-Size Img PowerPoint

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

Figure 3. (a) Pair distribution functions g(r) curves and (b) three-dimensional visualization of atomic arrangement of Cu₆₄Zr₃₆ nanoparticles at 300 K.

DownLoad: Full-Size Img PowerPoint

图 4 E-T曲线的(a)斜率和(b)二阶导数的变化

Figure 4. (a) Slope and (b) the second derivative of the E-T curves.

DownLoad: Full-Size Img PowerPoint

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 = 10000

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 7 纳米液滴凝固过程中TCP团簇的数量N_C随温度的变化　(a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000

Figure 7. Evolution of the number of TCP clusters N_C 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.

DownLoad: Full-Size Img PowerPoint

图 8 纳米液滴在凝固过程中最大TCP团簇的尺寸S_max随温度的变化　(a) N = 1000; (b) N = 2000; (c) N = 4000; (d) N = 5000; (e) N = 7500; (f) N = 10000

Figure 8. Evolution of the size of the maximum TCP cluster (S_max) 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.

DownLoad: Full-Size Img PowerPoint

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T_s; (b)液-固相变的起始温度T_ls; (c)玻璃转变温度T_g; (d) 300 K时纳米颗粒内TCP原子的百分含量

Figure 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 (T_s); (b) initial temperature of the liquid-solid transformation (T_ls); (c) glass transition temperature (T_g); (d) percentage of TCP atoms in nanoparticles at 300 K.

DownLoad: Full-Size Img PowerPoint

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(N_C); (c) 最大Z12团簇的尺寸S_max; (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

Figure 10. Evolution of Z12-based structure parameters with temperature during solidification of nano-droplets: (a) Number of Z12 atoms; (b) number of Z12 clusters (N_C); (c) size of the largest Z12 cluster (S_max); (d) evolution of the percentage of Z12 atoms with the size of nanoparticles at 300 K.

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map

[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
[29]	Tian Z A, Dong K J, Yu A B 2014 Phys. Rev. E 89 032202 Google Scholar
[30]	Tian Z A, Dong K J, Yu A B 2013 AIP Conf. Proc. 1542 373 Google Scholar
[31]	Wu Z Z, Mo Y F, Lang L, Yu A B, Xie Q, Liu R S, Tian Z A 2018 Phys. Chem. Chem. Phys. 20 28088 Google Scholar
[32]	Mo Y F, Tian Z A, Lin L, Riu R S, Zhou L L, Hou Z Y, Peng P, Zhang T Y 2019 J. Non-Cryst. Solids 513 111 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
[34]	栗晶晶, 田泽安 2020 低温 42 81 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
[38]	Jiang H, Wei X, Lu W, Liang D D, Wen Z, Wang Z, Xiang H, Shen J 2019 J. Non-Cryst. Solids 521 119531 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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Molecular dynamics simulation of rapid solidification of Cu₆₄Zr₃₆ nanodrops of different sizes

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Corresponding author: Tian Ze-An, tianzean@hnu.edu.cn

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Molecular dynamics simulation of rapid solidification of Cu64Zr36 nanodrops of different sizes

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Corresponding author: Tian Ze-An, tianzean@hnu.edu.cn

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Molecular dynamics simulation of rapid solidification of Cu₆₄Zr₃₆ nanodrops of different sizes