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Entropy and glass formation

Li Rui-Xuan Zhang Yong

Entropy and glass formation

Li Rui-Xuan, Zhang Yong
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  • Entropy is a state function of the real physical system, which relates to the chaos of a system. During the long-term exploring glass-forming systems, many empirical rules are put forward, including “confusion principle” and three empirical rules.Over a long period of exploring, many glass-forming alloys are developed based on those principles, while some questions have been raised in recent years based on the experimental results, because some other uncertain factors also have influence on the glass-forming ability (GFA) except a number of constituents, e.g., entropy. Greer claimed that in the “confusion principle” the higher the entropy value, the better the glass-formation ability will be, which does not accord with the recent experimental results.The effects of entropy on the glass-formation ability are summarized from the viewpoints of thermodynamics, kinetics, and complexity of atomic structures. In the aspects of thermodynamics and structure, the increase of entropy has a positive effect on glass formation, while in kinetics, the influence is negative. From the viewpoint of thermodynamics, the increase of entropy leads to the decrease of the entropy difference between solid phase and liquid phase, and therefore, the difference in Gibbs free energy between these two phases decreases. At a certain time during solidification, compared with the low-entropy alloy, the high-entropy alloy in the solid phase has an atomic arrangement close to that in the liquid, and it is more likely to form the amorphous phase.In the aspect of kinetics, the increase of entropy results in the decrease of the viscosity of the system according to the Adam-Gibbs equation. As a result, atoms diffuse easily in the system and the ordered-phase is more likely to form, which means that the glass-formation ability decreases with the increase of entropy. Furthermore, in the aspect of atomic structure, the increase of mismatch entropy relates to the big misfit degree between atoms, i. e., the large atomic size difference. Atoms in the high-entropy alloy tend to distribute disorderly in the system, and therefore the stress between atoms increases. As a result, with the increase of the entropy, the ordered-phase becomes unstable and the GFA will be enhanced.Furthermore, the high-entropy-glass is briefly reviewed and analyzed, which is a new system between high-entropy alloy and amorphous alloy. There have been many high-performance high-entropy-glass systems reported up to now. Researches about this unique system will contribute to developing some new amorphous alloys with excellent performances, and more importantly, to exploring the complex relationship between GFA and multicomponent alloys.
      Corresponding author: Zhang Yong, drzhangy@ustb.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51471025, 51671020).
    [1]

    Kramer J 1934 Annln. Phys. 19 37

    [2]

    Johnson W L 1986 Prog. Mater. Sci. 30 81

    [3]

    Klement W, Willens R, Duwez P 1960 Nature 187 869

    [4]

    Chen H S 1974 Acta Metall. 22 1505

    [5]

    Inoue A, Kato A, Zhang T, Kim S G, Masumoto T 1991 Mater. Trans. JIM 32 609

    [6]

    Inoue A, Kita K, Zhang T, Masumoto T 1989 Mater. Trans. JIM 30 722

    [7]

    Inoue A, Zhang T, Masumoto T 1990 Mater. Trans. JIM 31 177

    [8]

    Jiao W, Zhao K, Xi X K, Zhao D Q, Pan M X, Wang W H 2010 J. Non-Cryst. Solids 356 1867

    [9]

    Li H F, Zhao K, Wang Y B, Zheng Y F, Wang W H 2012 J. Biomed. Mater. Res. B: Appl. Biomater. 100 368

    [10]

    Wang W H, Dong C, Shek C H 2004 Mater. Sci. Eng. R 44 45

    [11]

    Peker A, Johnson W L 1993 Appl. Phys. Lett. 63 2342

    [12]

    Inoue A, Nakamura T, Nishiyama N, Masumoto T 1992 Mater. Trans. JIM 33 937

    [13]

    Inoue A, Zhang T, Masumoto T 1989 Mater. Trans. JIM 30 965

    [14]

    Inoue A, Zhang T, Nishiyama N, Ohba K, Masumoto T 1993 Mater. Trans. JIM 34 1234

    [15]

    Cantor B, Chang I T H, Knight P, Vincent A J B 2004 Mater. Sci. Eng. A 375-377 213

    [16]

    Takeuchi A, Inoue A 2000 Mater. Trans. JIM 41 1372

    [17]

    Takeuchi A, Amiya K, Wada T, Yubuta K, Zhang W, Makino A 2013 Entropy 15 3810

    [18]

    Samaei A T, Mohammadi E 2015 Mater. Res. Express 2 096501

    [19]

    Yeh J W, Chen S K, Lin S J, Gan J Y, Chin T S, Shun T T, Tsau C H, Chang S Y 2004 Adv. Eng. Mater. 6 299

    [20]

    Zhao K, Xia X X, Bai H Y, Zhao D Q, Wang W H 2011 Appl. Phys. Lett. 98 141913

    [21]

    Takeuchi A, Chen N, Wada T, Yokoyama Y, Kato H, Inoue A, Yeh J W 2011 Intermetallics 19 1546

    [22]

    Li H F, Xie X H, Zhao K, Wang Y B, Zheng Y F, Wang W H, Qin L 2013 Acta Biomater. 9 8561

    [23]

    Li Y, Zhang W, Qi T 2017 J. Alloy. Compd. 693 25

    [24]

    Cheng C Y, Yeh J W 2016 Mater. Lett. 181 223

    [25]

    Ding H Y, Yao K F 2013 J. Non-Cryst Solids 364 9

    [26]

    Ding H Y, Shao Y, Gong P, Li J F, Yao K F 2014 Mater. Lett. 125 151

    [27]

    Gao X Q, Zhao K, Ke H B, Ding D W, Wang W H, Bai H Y 2011 J. Non-Cryst. Solids 357 3557

    [28]

    Huo J, Huo L, Men H, Wang X, Inoue A, Wang J, Chang C, Li R W 2015 Intermetallics 58 31

    [29]

    Zhao S F, Yang G N, Ding H Y, Yao K F 2015 Intermetallics 61 47

    [30]

    Qi T, Li Y, Takeuchi A, Xie G, Miao H, Zhang W 2015 Intermetallics 66 8

    [31]

    Zhao S F, Shao Y, Liu X, Chen N, Ding H Y, Yao K F 2015 Mater. Design 87 625

    [32]

    Cheng C Y, Yeh J W 2016 Mater. Lett. 185 456

    [33]

    Zhang Y, Zhou Y J, Lin J P, Chen G L, Liaw P K 2008 Adv. Eng. Mater. 10 534

    [34]

    Guo S, Hu Q, Ng C, Liu C T 2013 Intermetallics 41 96

  • [1]

    Kramer J 1934 Annln. Phys. 19 37

    [2]

    Johnson W L 1986 Prog. Mater. Sci. 30 81

    [3]

    Klement W, Willens R, Duwez P 1960 Nature 187 869

    [4]

    Chen H S 1974 Acta Metall. 22 1505

    [5]

    Inoue A, Kato A, Zhang T, Kim S G, Masumoto T 1991 Mater. Trans. JIM 32 609

    [6]

    Inoue A, Kita K, Zhang T, Masumoto T 1989 Mater. Trans. JIM 30 722

    [7]

    Inoue A, Zhang T, Masumoto T 1990 Mater. Trans. JIM 31 177

    [8]

    Jiao W, Zhao K, Xi X K, Zhao D Q, Pan M X, Wang W H 2010 J. Non-Cryst. Solids 356 1867

    [9]

    Li H F, Zhao K, Wang Y B, Zheng Y F, Wang W H 2012 J. Biomed. Mater. Res. B: Appl. Biomater. 100 368

    [10]

    Wang W H, Dong C, Shek C H 2004 Mater. Sci. Eng. R 44 45

    [11]

    Peker A, Johnson W L 1993 Appl. Phys. Lett. 63 2342

    [12]

    Inoue A, Nakamura T, Nishiyama N, Masumoto T 1992 Mater. Trans. JIM 33 937

    [13]

    Inoue A, Zhang T, Masumoto T 1989 Mater. Trans. JIM 30 965

    [14]

    Inoue A, Zhang T, Nishiyama N, Ohba K, Masumoto T 1993 Mater. Trans. JIM 34 1234

    [15]

    Cantor B, Chang I T H, Knight P, Vincent A J B 2004 Mater. Sci. Eng. A 375-377 213

    [16]

    Takeuchi A, Inoue A 2000 Mater. Trans. JIM 41 1372

    [17]

    Takeuchi A, Amiya K, Wada T, Yubuta K, Zhang W, Makino A 2013 Entropy 15 3810

    [18]

    Samaei A T, Mohammadi E 2015 Mater. Res. Express 2 096501

    [19]

    Yeh J W, Chen S K, Lin S J, Gan J Y, Chin T S, Shun T T, Tsau C H, Chang S Y 2004 Adv. Eng. Mater. 6 299

    [20]

    Zhao K, Xia X X, Bai H Y, Zhao D Q, Wang W H 2011 Appl. Phys. Lett. 98 141913

    [21]

    Takeuchi A, Chen N, Wada T, Yokoyama Y, Kato H, Inoue A, Yeh J W 2011 Intermetallics 19 1546

    [22]

    Li H F, Xie X H, Zhao K, Wang Y B, Zheng Y F, Wang W H, Qin L 2013 Acta Biomater. 9 8561

    [23]

    Li Y, Zhang W, Qi T 2017 J. Alloy. Compd. 693 25

    [24]

    Cheng C Y, Yeh J W 2016 Mater. Lett. 181 223

    [25]

    Ding H Y, Yao K F 2013 J. Non-Cryst Solids 364 9

    [26]

    Ding H Y, Shao Y, Gong P, Li J F, Yao K F 2014 Mater. Lett. 125 151

    [27]

    Gao X Q, Zhao K, Ke H B, Ding D W, Wang W H, Bai H Y 2011 J. Non-Cryst. Solids 357 3557

    [28]

    Huo J, Huo L, Men H, Wang X, Inoue A, Wang J, Chang C, Li R W 2015 Intermetallics 58 31

    [29]

    Zhao S F, Yang G N, Ding H Y, Yao K F 2015 Intermetallics 61 47

    [30]

    Qi T, Li Y, Takeuchi A, Xie G, Miao H, Zhang W 2015 Intermetallics 66 8

    [31]

    Zhao S F, Shao Y, Liu X, Chen N, Ding H Y, Yao K F 2015 Mater. Design 87 625

    [32]

    Cheng C Y, Yeh J W 2016 Mater. Lett. 185 456

    [33]

    Zhang Y, Zhou Y J, Lin J P, Chen G L, Liaw P K 2008 Adv. Eng. Mater. 10 534

    [34]

    Guo S, Hu Q, Ng C, Liu C T 2013 Intermetallics 41 96

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  • Received Date:  01 June 2017
  • Accepted Date:  21 June 2017
  • Published Online:  05 September 2017

Entropy and glass formation

    Corresponding author: Zhang Yong, drzhangy@ustb.edu.cn
  • 1. State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 51471025, 51671020).

Abstract: Entropy is a state function of the real physical system, which relates to the chaos of a system. During the long-term exploring glass-forming systems, many empirical rules are put forward, including “confusion principle” and three empirical rules.Over a long period of exploring, many glass-forming alloys are developed based on those principles, while some questions have been raised in recent years based on the experimental results, because some other uncertain factors also have influence on the glass-forming ability (GFA) except a number of constituents, e.g., entropy. Greer claimed that in the “confusion principle” the higher the entropy value, the better the glass-formation ability will be, which does not accord with the recent experimental results.The effects of entropy on the glass-formation ability are summarized from the viewpoints of thermodynamics, kinetics, and complexity of atomic structures. In the aspects of thermodynamics and structure, the increase of entropy has a positive effect on glass formation, while in kinetics, the influence is negative. From the viewpoint of thermodynamics, the increase of entropy leads to the decrease of the entropy difference between solid phase and liquid phase, and therefore, the difference in Gibbs free energy between these two phases decreases. At a certain time during solidification, compared with the low-entropy alloy, the high-entropy alloy in the solid phase has an atomic arrangement close to that in the liquid, and it is more likely to form the amorphous phase.In the aspect of kinetics, the increase of entropy results in the decrease of the viscosity of the system according to the Adam-Gibbs equation. As a result, atoms diffuse easily in the system and the ordered-phase is more likely to form, which means that the glass-formation ability decreases with the increase of entropy. Furthermore, in the aspect of atomic structure, the increase of mismatch entropy relates to the big misfit degree between atoms, i. e., the large atomic size difference. Atoms in the high-entropy alloy tend to distribute disorderly in the system, and therefore the stress between atoms increases. As a result, with the increase of the entropy, the ordered-phase becomes unstable and the GFA will be enhanced.Furthermore, the high-entropy-glass is briefly reviewed and analyzed, which is a new system between high-entropy alloy and amorphous alloy. There have been many high-performance high-entropy-glass systems reported up to now. Researches about this unique system will contribute to developing some new amorphous alloys with excellent performances, and more importantly, to exploring the complex relationship between GFA and multicomponent alloys.

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