Molecular dynamics simulation of effect of cooling rate on the microstructures and deformation behaviors in metallic glasses

Zhou Bian; Yang Liang

doi:10.7498/aps.69.20191781

Abstract

Since the discovery of the first metallic glass (MG) in 1960, vast efforts have been devoted to the understanding of the structural mechanisms of unique properties, in particular, mechanical properties in MGs, which is helpful for the applications of such novel alloys. As is well known, the cooling rate during the quenching as well as the sample size, significantly affects the mechanical properties in MGs. In order to study the effect of cooling rate on microstructure and deformation behavior in MG by excluding the size effect, Zr₄₈Cu₄₅Al₇ ternary composition with good glass-forming ability is selected as a research prototype in this work. The classical molecular dynamics simulation is utilized to construct four structural MG models with the same size under different cooling rates, and the uniaxial compressive deformation for each model is also simulated. It is found that an MG model prepared at a lower cooling rate has a higher yield strength and is more likely to form shear bands that lead the strain to be localized, resulting in a lower plasticity. The Voronoi tessellation, together with atomic packing efficiency and free volume algorithms that have been designed by ourselves, is used to analyze the four as-constructed models and high-temperature liquid model. It is found that the as-constructed model, which is prepared by quenching metallic melt at a higher cooling rate, can preserve more structural characteristics of the high-temperature liquid. In other words, the higher cooling rate leads to more clusters with relatively low five-fold symmetry, loose atomic packing and large fraction of free volumes in MG. By calculating the distribution of the free volumes, a new computational approach to detecting liquid-like regions in MG models is adopted. It is found that there are more liquid-like regions in the as-constructed model which is prepared by quenching metallic melt at a relatively high cooling rate. This should be the structural origin of the effect of cooling rate on the deformation behavior, in particular, the yield strength and the plasticity. This work provides an understanding of how the cooling rate during quenching affects the microstructure and deformation behavior, and will shed light on the development of new MGs with relatively large plasticity.

Keywords:

amorphous alloy /
cooling rates /
microstructures and mechanical properties /
molecular dynamics simulation

Authors and contacts

College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Corresponding author: Yang Liang, yangliang@nuaa.edu.cn

FullText HTML

References

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Cited By

图 1 不同冷速制备态模型的(a)结构因子S(Q)和(b)对分布函数G(r)

Figure 1. Structural data of as-constructed models with different cooling rates, including: (a) The normalized structural factor S(Q); (b) the total pair distribution function, G(r).

DownLoad: Full-Size Img PowerPoint

图 2 应变速率为1 × 10⁸ /s时, 不同冷却速率Zr₄₈Cu₄₅Al₇非晶合金模型的压缩应力应变曲线

Figure 2. Compressive stress-strain curves of Zr₄₈Cu₄₅Al₇ amorphous alloy models prepared using different cooling rates at the strain rate of 1 × 10⁸ /s.

DownLoad: Full-Size Img PowerPoint

图 3 压缩变形过程中应变量为20%时, 不同冷却速率获得的Zr₄₈Cu₄₅Al₇非晶合金模型的原子剪切应变图　(a) 10¹⁰ K/s; (b) 10¹¹ K/s; (c) 10¹² K/s; (d) 10¹³ K/s

Figure 3. Distributions of atomic local shear strains of Zr₄₈Cu₄₅Al₇ amorphous alloy models at macrostrain of 20% during the compressive deformation, including those prepared with different cooling rates: (a) 10¹⁰ K/s; (b) 10¹¹ K/s; (c) 10¹² K/s; (d) 10¹³ K/s.

DownLoad: Full-Size Img PowerPoint

图 4 Voronoi团簇类型及含量分布　(a) 不同冷却速率的Zr₄₈Cu₄₅Al₇非晶合金制备态模型(列出了含量超过4%的Voronoi团簇); (b) 2000 K时Zr₄₈Cu₄₅Al₇液体结构模型(列出了含量较多与五次对称性较高的几种Voronoi团簇)

Figure 4. Distributions of major Voronoi clusters in (a) The as-constructed models of Zr₄₈Cu₄₅Al₇ amorphous alloy with different cooling rate (Note only Voronoi clusters possessing a weight larger than 4% are selected), and (b) a liquid model of Zr₄₈Cu₄₅Al₇ with a temperature of 2000 K (Note only Voronoi clusters with highest fractions and relatively higher five-fold symmetry are selected).

DownLoad: Full-Size Img PowerPoint

图 5 LFV原子分布图　(a) 2000 K液体模型; (b) 10¹⁰ K/s制备态模型; (c) 10¹¹ K/s制备态模型; (d) 10¹² K/s制备态模型; (e) 10¹³ K/s制备态模型

Figure 5. 3 D distributions of LFV atoms in (a) a liquid model at 2000 K, and those as-constructed models prepared by using with cooling rates of (b) 10¹⁰ K/s, (c) 10¹¹ K/s, (d) 10¹² K/s, and (e) 10¹³ K/s.

DownLoad: Full-Size Img PowerPoint

表 1 不同冷速制备态模型与2000 K液体模型的原子堆积效率η

Table 1. The atomic packing efficiencies, η, in the as-constructed models prepared by using different cooling rates and a liquid model with a temperature of 2000 K.

10¹⁰ K/s 10¹¹ K/s 10¹² K/s 10¹³ K/s 2000 K

η/% 70.547 70.473 70.399 70.320 63.983

DownLoad: CSV

表 2 Zr₄₈Cu₄₅Al₇非晶合金不同冷却速制备态模型和液体模型的自由体积大小与自由体积占总体积的比值

Table 2. The total free volume and fraction of free volume in the as-constructed models prepared by using different cooling rates and a liquid model with a temperature of 2000 K.

10¹⁰ K/s 10¹¹ K/s 10¹² K/s 10¹³ K/s 2000 K

总自由体积/Å 11117.05 11430.34 11758.24 12052.57 42825.75
自由体积占比/% 3.440 3.532 3.628 3.715 12.059

DownLoad: CSV

表 3 不同冷速制备态模型的LFV原子数

Table 3. The number of LFV atoms in the as-constructed models prepared by using different cooling rates.

10¹⁰ K/s 10¹¹ K/s 10¹² K/s 10¹³ K/s

LFV原子数/个 317 404 437 485

DownLoad: CSV

[1]	Jung H Y, Choi S J, Prashanth K G, Stoica M, Scudino S, Yi S, Kühn U, Kim D H, Kim K B, Eckert J 2015 Mater. Des. 86 703 Google Scholar
[2]	Reichel L, Schultz L, Pohl D, Oswald S, Fahler S, Werwinski M, Edstrom A, Delczeg-Czirjak E K, Rusz J 2015 J. Phys-Condens Mat. 27 476002 Google Scholar
[3]	Zhang C, Guo R Q, Yang Y, Wu Y, Liu L 2011 Electrochim. Acta 56 6380 Google Scholar
[4]	Schuh C, Hufnagel T, Ramamurty U 2007 Acta Mater. 55 4067 Google Scholar
[5]	Wang W H, Dong C, Shek C H 2004 Mater. Sci. Eng., R 44 45 Google Scholar
[6]	Yang L, Guo G Q, Chen L Y, LaQua B, Jiang J Z 2014 Intermetallics 44 94 Google Scholar
[7]	Liu Y, Bei H, Liu C T, George E P 2007 Appl. Phys. Lett. 90 071909 Google Scholar
[8]	Liu Z Y, Yang Y, Guo S, Liu X J, Lu J, Liu Y H, Liu C T 2011 J. Alloys Compd. 509 3269 Google Scholar
[9]	Hu Y, Yan H H, Yan Z J, Wang X G 2018 Aip. Adv. 8 105002 Google Scholar
[10]	Li C, Kou S, Zhao Y, Liu G, Ding Y 2012 Prog. Nat. Sci. 22 21 Google Scholar
[11]	Yokoyama Y, Yamano K, Fukaura K, Sunada H, Inoue A 2001 Scr. Mater. 44 1529 Google Scholar
[12]	Conner R D, Johnson W L, Paton N E, Nix W D 2003 J. Appl. Phys. 94 904 Google Scholar
[13]	Lin X H, Johnson W L 1995 J. Appl. Phys. 78 6514 Google Scholar
[14]	Liao W, Zhao Y, He J, Zhang Y 2013 J. Alloys Compd. 555 357 Google Scholar
[15]	Jiang W H, Liu F X, Wang Y D, Zhang H F, Choo H, Liaw P K 2006 Mat. Sci. Eng., A 430 350 Google Scholar
[16]	Huang Y J, Shen J, Sun J F 2007 Appl. Phys. Lett. 90 081919 Google Scholar
[17]	Yang L, Guo G Q, Chen L Y, Wei S H, Jiang J Z, Wang X D 2010 Scr. Mater. 63 879 Google Scholar
[18]	郭古青, 杨亮, 张国庆 2011 物理学报 60 016103 Google Scholar Guo G Q, Yang L, Zhang G Q 2011 Acta Phys. Sin. 60 016103 Google Scholar
[19]	Cheng Y Q, Ma E, Sheng H W 2009 Phys. Rev. Lett. 102 245501 Google Scholar
[20]	Zeng Q, Sheng H, Ding Y, Wang L, Yang W, Jiang J Z, Mao W L, Mao H K 2011 Science 332 1404 Google Scholar
[21]	Cheng Y Q, Cao A J, Sheng H W, Ma E 2008 Acta Mater. 56 5263 Google Scholar
[22]	Park K W, Fleury E, Seok H K, Kim Y C 2011 Intermetallics 19 1168 Google Scholar
[23]	Ghidelli M, Idrissi H, Gravier S, Blandin J J, Raskin J P, Schryvers D, Pardoen T 2017 Acta Mater. 131 246 Google Scholar
[24]	Lewandowski J J, Greer A L 2006 Nat. Mater. 5 15 Google Scholar
[25]	Feng S D, Chan K C, Zhao L, Pan S P, Qi L, Wang L M, Liu R P 2018 Mater. Des. 158 248 Google Scholar
[26]	汪卫华 2014 中国科学: 物理学力学天文学 44 396 Google Scholar Wang W H 2014 Sci. China: Phys. Mech. Astron. 44 396 Google Scholar
[27]	管鹏飞, 王兵, 吴义成, 张珊, 尚宝双, 胡远超, 苏锐, 刘琪 2017 物理学报 66 176112 Google Scholar Guan P F, Wang B, Wu Y C, Zhang S, Shang B S, Hu Y C, Su R, Liu Q 2017 Acta Phys. Sin. 66 176112 Google Scholar
[28]	Wang W H 2012 J. Appl. Phys. 111 123519 Google Scholar
[29]	Miracle D B 2004 Nat. Mater. 3 697 Google Scholar
[30]	Cheng Y Q, Ma E 2011 Prog. Mater Sci. 56 379 Google Scholar
[31]	Peng H L, Li M Z, Wang W H 2011 Phys. Rev. Lett. 106 135503 Google Scholar
[32]	郭古青, 吴诗阳, 蔡光博, 杨亮 2016 物理学报 65 096402 Google Scholar Guo G Q, Wu S Y, Cai G B, Yang L 2016 Acta Phys. Sin. 65 096402 Google Scholar
[33]	李茂枝 2017 物理学报 66 176107 Google Scholar Li M Z 2017 Acta Phys. Sin. 66 176107 Google Scholar
[34]	Yang L, Guo G Q, Chen L Y, Huang C L, Ge T, Chen D, Liaw P K, Saksl K, Ren Y, Zeng Q S, LaQua B, Chen F G, Jiang J Z 2012 Phys. Rev. Lett. 109 105502 Google Scholar
[35]	Cohen M H, Turnbull D 1959 J. Chem. Phys. 31 1164 Google Scholar
[36]	Turnbull D, Cohen M H 1961 J. Chem. Phys. 34 120 Google Scholar
[37]	Turnbull D, Cohen M H 1970 J. Chem. Phys. 52 3038 Google Scholar
[38]	Sietsma J, Thijsse B J 1995 Phys. Rev. B 52 3248 Google Scholar
[39]	Zhang Y, Hahn H 2011 J. Non-Cryst. Solids 357 1420 Google Scholar
[40]	Li F, Liu X J, Hou H Y, Chen G, Chen G L, Li M 2009 Intermetallics 17 98 Google Scholar
[41]	Liao B, Wu S Y, Yang L 2017 Aip Adv 7 105101 Google Scholar
[42]	Qi L, Zhang H F, Hu Z Q 2004 Intermetallics 12 1191 Google Scholar
[43]	Wakeda M, Shibutani Y, Ogata S, Park J 2007 Intermetallics 15 139 Google Scholar
[44]	Da W, Wang P W, Wang Y F, Li M F, Yang L 2018 Materials 12 98 Google Scholar

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