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不同尺寸Cu64Zr36纳米液滴的快速凝固过程分子动力学模拟

韦国翠 田泽安

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不同尺寸Cu64Zr36纳米液滴的快速凝固过程分子动力学模拟

韦国翠, 田泽安

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

Wei Guo-Cui, Tian Ze-An
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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.
      通信作者: 田泽安, tianzean@hnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 51661005, U1612442)和贵州大学智能制造产教融合创新平台及研究生联合培养基地(批准号: 2020-520000-83-01-324061)资助的课题.
      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).
    [1]

    Duan S B, Wang R M 2013 Prog. Nat. Sci. 23 113Google Scholar

    [2]

    Taylor M G, Austin N, Gounaris C E, Mpourmpakis G 2015 ACS Catal. 5 6296Google Scholar

    [3]

    Yan Y, Warren S C, Fuller P, Grzybowski B A 2016 Nat. Nanotechnol. 11 603Google Scholar

    [4]

    Mpourmpakis G, Andriotis A N, Vlachos D G 2010 Nano Lett. 10 1041Google Scholar

    [5]

    Yan Y C, Du J S S, Gilroy K D, Yang D R, Xia Y N, Zhang H 2017 Adv. Mater. 29 1605997Google Scholar

    [6]

    Cuenya B R, Behafarid F 2015 Surf. Sci. Rep. 70 135Google 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 3349Google Scholar

    [8]

    Kelly K L, Coronado E, Zhao L L, Schatz G C 2003 J. Phys. Chem. B 107 668Google Scholar

    [9]

    De M, Ghosh P S, Rotello V M 2008 Adv. Mater. 20 4225Google Scholar

    [10]

    Kim M, Lee C, Ko S M, Nam J M 2019 J. Solid State Chem. 270 295Google Scholar

    [11]

    Ferrando R, Jellinek J, Johnston R L 2008 Chem. Rev. 108 845Google Scholar

    [12]

    Talapin D V, Lee J S, Kovalenko M V, Shevchenko E V 2010 Chem. Rev. 110 389Google Scholar

    [13]

    Bratlie K M, Lee H, Komvopoulos K, Yang P and Somorjai G A 2007 Nano Lett. 7 3097Google Scholar

    [14]

    Cuenya B R 2010 Thin Solid Films 518 3127Google Scholar

    [15]

    Johnston R L 1998 Philos. Trans. R. Soc. London, Ser. A 356 211Google Scholar

    [16]

    Adibi S, Branicio P S, Ballarini R 2016 RSC Adv. 6 13548Google Scholar

    [17]

    Yuan S Y, Branicio P S 2020 Int. J. Plast. 134 102845Google Scholar

    [18]

    Zheng K, Branicio P S 2020 Phys. Rev. Mater. 4 076001Google Scholar

    [19]

    Zhang M, Li Q M, Zhang J C, Zheng G P, Wang X Y 2019 J. Alloys Compd. 801 318Google 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 181Google Scholar

    [21]

    Mendelev M I, Kramer M J, Ott R T, Sordelet D J, Yagodin D, Popel P 2009 Philos. Mag. 89 967Google Scholar

    [22]

    Zhong L, Wang J W, Sheng H W, Zhang Z, Mao S X 2014 Nature 512 177Google Scholar

    [23]

    Nelli D, Ferrando R 2019 Nanoscale 11 13040Google 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 184109Google Scholar

    [25]

    Honeycutt J D, Andersen H C 1987 J. Phys. Chem. 91 4950Google Scholar

    [26]

    Liu R S, Li J Y, Dong K J, Zheng C X, Liu H R 2002 Mater. Sci. Eng. B 94 141Google Scholar

    [27]

    Tian Z A, Liu R S, Dong K J, Yu A B 2011 EPL 96 36001Google Scholar

    [28]

    Tian Z A, Dong K J, Yu A B 2015 Ann. Phys. 354 499Google Scholar

    [29]

    Tian Z A, Dong K J, Yu A B 2014 Phys. Rev. E 89 032202Google Scholar

    [30]

    Tian Z A, Dong K J, Yu A B 2013 AIP Conf. Proc. 1542 373Google 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 28088Google 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 111Google 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 1184Google Scholar

    [34]

    栗晶晶, 田泽安 2020 低温物理学报 42 81Google Scholar

    Li J J, Tian Z A 2020 Low. Temp. Phys. Lett. 42 81Google 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 4220Google Scholar

    [36]

    Sheng H W, Luo W K, Alamgir F M, Bai J M, Ma E 2006 Nature 439 419Google Scholar

    [37]

    Inoue A, Kimura H 2001 J. Light Metals 1 31Google 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 119531Google Scholar

    [39]

    Luo W K, Sheng H W, Alamgir F M, Bai J M, He J H, Ma E 2004 Phys. Rev. Lett. 92 145502Google Scholar

    [40]

    Lee M, Kim H K, Lee J C 2010 Met. Mater. Int. 16 877Google Scholar

  • 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 = 10000

    Fig. 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.

  • [1]

    Duan S B, Wang R M 2013 Prog. Nat. Sci. 23 113Google Scholar

    [2]

    Taylor M G, Austin N, Gounaris C E, Mpourmpakis G 2015 ACS Catal. 5 6296Google Scholar

    [3]

    Yan Y, Warren S C, Fuller P, Grzybowski B A 2016 Nat. Nanotechnol. 11 603Google Scholar

    [4]

    Mpourmpakis G, Andriotis A N, Vlachos D G 2010 Nano Lett. 10 1041Google Scholar

    [5]

    Yan Y C, Du J S S, Gilroy K D, Yang D R, Xia Y N, Zhang H 2017 Adv. Mater. 29 1605997Google Scholar

    [6]

    Cuenya B R, Behafarid F 2015 Surf. Sci. Rep. 70 135Google 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 3349Google Scholar

    [8]

    Kelly K L, Coronado E, Zhao L L, Schatz G C 2003 J. Phys. Chem. B 107 668Google Scholar

    [9]

    De M, Ghosh P S, Rotello V M 2008 Adv. Mater. 20 4225Google Scholar

    [10]

    Kim M, Lee C, Ko S M, Nam J M 2019 J. Solid State Chem. 270 295Google Scholar

    [11]

    Ferrando R, Jellinek J, Johnston R L 2008 Chem. Rev. 108 845Google Scholar

    [12]

    Talapin D V, Lee J S, Kovalenko M V, Shevchenko E V 2010 Chem. Rev. 110 389Google Scholar

    [13]

    Bratlie K M, Lee H, Komvopoulos K, Yang P and Somorjai G A 2007 Nano Lett. 7 3097Google Scholar

    [14]

    Cuenya B R 2010 Thin Solid Films 518 3127Google Scholar

    [15]

    Johnston R L 1998 Philos. Trans. R. Soc. London, Ser. A 356 211Google Scholar

    [16]

    Adibi S, Branicio P S, Ballarini R 2016 RSC Adv. 6 13548Google Scholar

    [17]

    Yuan S Y, Branicio P S 2020 Int. J. Plast. 134 102845Google Scholar

    [18]

    Zheng K, Branicio P S 2020 Phys. Rev. Mater. 4 076001Google Scholar

    [19]

    Zhang M, Li Q M, Zhang J C, Zheng G P, Wang X Y 2019 J. Alloys Compd. 801 318Google 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 181Google Scholar

    [21]

    Mendelev M I, Kramer M J, Ott R T, Sordelet D J, Yagodin D, Popel P 2009 Philos. Mag. 89 967Google Scholar

    [22]

    Zhong L, Wang J W, Sheng H W, Zhang Z, Mao S X 2014 Nature 512 177Google Scholar

    [23]

    Nelli D, Ferrando R 2019 Nanoscale 11 13040Google 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 184109Google Scholar

    [25]

    Honeycutt J D, Andersen H C 1987 J. Phys. Chem. 91 4950Google Scholar

    [26]

    Liu R S, Li J Y, Dong K J, Zheng C X, Liu H R 2002 Mater. Sci. Eng. B 94 141Google Scholar

    [27]

    Tian Z A, Liu R S, Dong K J, Yu A B 2011 EPL 96 36001Google Scholar

    [28]

    Tian Z A, Dong K J, Yu A B 2015 Ann. Phys. 354 499Google Scholar

    [29]

    Tian Z A, Dong K J, Yu A B 2014 Phys. Rev. E 89 032202Google Scholar

    [30]

    Tian Z A, Dong K J, Yu A B 2013 AIP Conf. Proc. 1542 373Google 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 28088Google 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 111Google 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 1184Google Scholar

    [34]

    栗晶晶, 田泽安 2020 低温物理学报 42 81Google Scholar

    Li J J, Tian Z A 2020 Low. Temp. Phys. Lett. 42 81Google 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 4220Google Scholar

    [36]

    Sheng H W, Luo W K, Alamgir F M, Bai J M, Ma E 2006 Nature 439 419Google Scholar

    [37]

    Inoue A, Kimura H 2001 J. Light Metals 1 31Google 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 119531Google Scholar

    [39]

    Luo W K, Sheng H W, Alamgir F M, Bai J M, He J H, Ma E 2004 Phys. Rev. Lett. 92 145502Google Scholar

    [40]

    Lee M, Kim H K, Lee J C 2010 Met. Mater. Int. 16 877Google Scholar

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出版历程
  • 收稿日期:  2021-07-01
  • 修回日期:  2021-08-18
  • 上网日期:  2021-08-30
  • 刊出日期:  2021-12-20

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