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Abnormal viscosity changes in high-temperature metallic melts

Shang Ji-Xiang Zhao Yun-Bo Hu Li-Na

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Abnormal viscosity changes in high-temperature metallic melts

Shang Ji-Xiang, Zhao Yun-Bo, Hu Li-Na
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  • The viscosity of high-temperature metallic melt, which is an important index for evaluating dynamics of liquid melt, is one of the basic physical properties. It not only influences the mold-filling capacity of melting metal in traditional casting techniques, but also exhibits more distinct influence on the fabrication of advanced material, such as metallic glass. According to the variation tendency of viscosity with temperature in alloy melt, the fragility of superheated melt could be obtained, which has proved to correlate with the ability of alloy to form glass. Besides, the viscosity of alloy well above the liquidus temperature also plays a key role in probing into the characteristic of liquid-liquid phase transition, the fragile-to-strong transition phenomenon, how the potential energy landscape evolves during cooling, etc. It has been generally accepted that the viscosity of metallic melt at high temperatures increases with temperature decreasing and could be fitted by an Arrhenius curve in the whole temperature range. However, recently more and more studies show that the viscosity of metallic melt cannot be fitted by only one Arrhenius curve. Instead, there exists at least one specific temperature below which the viscosity data begins to deviate from the Arrhenius curve at high temperature during cooling. These data could be described by another Arrhenius curve. In order to in depth understand this phenomenon, in this paper we summarize the viscosity data of different metallic melts in the literature. On the basis of introducing the method of detecting high-temperature melt viscosity, we discuss comprehensively the changing tendency of viscosity with temperature and the characteristics of abnormal viscosity changes in pure metal, binary and multivariate alloys well above the liquidus temperature. It is found that the abnormal viscosity changes generally occur in alloys that could form the types of intermetallic compounds. The abnormal viscosity change in metallic melt is accompanied with exothermic or endothermic effect, depending on alloy system, and reflects the existence of liquid-liquid transition well above the liquidus temperature. Besides, such an abnormal change of viscosity influences the ability to form metallic glass liquids. Although the abnormal dynamic change of metallic melt hints the existence of complexity of structural change in liquid during cooling, what is the key factor underlying this phenomenon remains a mystery. By combining the advanced experimental techniques such as high-energy X-ray diffraction and neutron scattering with the computer simulation method, this problem may be understood further. Besides, the relation between viscosity abnormity and the phase diagram is another problem that deserves to be noticed in the future.
      Corresponding author: Hu Li-Na, hulina0850@sina.com
    • Funds: Project supported by National Science and Technology Major Project, China (Grant No. 2016YFB0300500) and National Natural Science Foundation of China (Grant No. 51571131).
    [1]

    Han X F 2005 M. S. Dissertation (Jinan:Shandong University) (in Chinese)[韩秀峰 2005 硕士学位论文 (济南:山东大学)]

    [2]

    Angell C A 1985 J. Non-Cryst. Solids 73 1

    [3]

    Bian X F, Sun B A, Hu L N, Jia Y B 2005 Phys. Lett. A 335 61

    [4]

    Meng Q G, Zhou J K, Zheng H X, Li J G 2006 Scr. Mater. 54 777

    [5]

    Hu L N, Bian X F 2003 Chin. Sci. Bull. 48 2393 (in Chinese)[胡丽娜, 边秀房 2003 科学通报 48 2393]

    [6]

    Hu L N, Zhang C Z, Yue Y Z, Bian X F 2010 Chin. Sci. Bull. 55 115 (in Chinese)[胡丽娜, 张春芝, 岳远征, 边秀房 2010 科学通报 55 115]

    [7]

    Books R F, Dinsdale A T, Quested P N 2005 Meas. Sci. Technol. 16 354

    [8]

    Dinsdale A T, Quested P N 2004 J. Mater. Sci. 39 7221

    [9]

    Torklep K, Oye H A 1979 J. Phys. E 12 875

    [10]

    Sato Y, Kameda Y, Nagasawa T, Sakamoto T, Moriguchi S, Yamamura T, Waseda Y 2003 J. Cryst. Growth 249 404

    [11]

    Kehr M, Hoyer W, Egry I 2007 Int. J. Thermophys. 28 1017

    [12]

    Nunes V M B, Santos F J V, de Castro C A N 1998 Int. J. Thermophys. 19 427

    [13]

    Schenck H, Frohberg M G, Hoffmann K 1963 Steel Res. Int. 34 93

    [14]

    Emadi D, Gruzleski J E, Toguri J M 1993 Metall. Trans. B 24 1055

    [15]

    Xu Y P, Zhao X L, Yan T L 2017 Chin. Phys. B 26 036601

    [16]

    Wu Y Q, Bian X F, Mao T, Li X L, Li T B, Wang C D 2006 Phys. Lett. A 361 265

    [17]

    Sun C, Geng H, Liu J, Gneg H, Yang Z 2004 Phys. Meas. 1 16

    [18]

    Wang C Z 2017 M. S. Dissertation (Jinan:Shandong University) (in Chinese)[王春震 2017 硕士学位论文 (济南:山东大学)]

    [19]

    Guo H D 2008 M. S. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[郭海东 2008 硕士学位论文(哈尔滨:哈尔滨工业大学)]

    [20]

    Sun C J, Geng H R, Zhang N, Teng X Y, Ji L L 2008 Mater. Lett. 62 73

    [21]

    Mao T, Bian X F, Morioka S, Wu Y Q, Li X L, L X Q 2007 Phys. Lett. 366 155

    [22]

    Sun M H, Geng H R, Bian X F, Liu Y 2000 Acta Metal. Sin. 36 1134 (in Chinese)[孙民华, 耿浩然, 边秀房, 刘燕 2000 金属学报 36 1134]

    [23]

    Wang L, Bian X F, Liu J T 2004 Phys. Lett. A 326 429

    [24]

    Ofte D, Wittenberg L J 1963 Trans. Metall. Soc. Aime. 227 706

    [25]

    Rothwell E 1961 J. Inst. Metals 90 389

    [26]

    Gebhardt E, Kostlin K 1957 Z. Metallkd. 48 636

    [27]

    Schenck H, Frohberg M G, Hoffmann K 1963 Arch. Eisenhuettenw. 34 93

    [28]

    Cavalier G 1963 Compt. Rend. 256 1308

    [29]

    Kaplun A B, Avaliani M 1977 High Temp. 15 259

    [30]

    Nikolaev B, Vollmann J 1996 J. Non-Cryst. Solids 208 145

    [31]

    Martin-Garin L, Martin-Garin R, Despre P 1978 J. Less Common. Met. 59 1

    [32]

    Zhao X, Wang C Z, Zheng H J, Tian Z A, Hu L N 2017 Phys. Chem. Chem. Phys. 19 15962

    [33]

    Zhao Y, Hou X X, Bian X F 2008 Mater. Lett. 62 3542

    [34]

    Zhou C, Hu L N, Sun Q J, Bian X F, Yue Y Z 2013 Appl. Phys. 103 171904

    [35]

    Ning S, Bian X F, Ren Z F 2010 Phys. B:Condens. Matter 405 3633

    [36]

    Mao T, Bian X F, Xue X Y, Zhang Y N, Guo J, Sun B A 2007 Phys. B:Phys. Condens. Matter 387 1

    [37]

    Konstantinova N Y, Popel' P S, Yagodin D A 2009 High Temp. 47 336

    [38]

    Inoue A, Takeuchi A 2010 Int. J. Appl. Glass Sci. 1 273

    [39]

    Wang L, Liu J T 2004 Phys. Lett. A 328 241

    [40]

    Zheng H J, Hu L N, Zhao X, Wang C Z, Sun Q J, Wang T, Hui X D, Yue Y Z, Bian X F 2017 J. Non-Cryst. Solids 471 120

    [41]

    Zhang F, Du Y, Liu S H, Jie W Q 2015 Comput. Coupling Phase Diagrams Thermochem. 49 79

    [42]

    Jia R, Bian X F, Lu X Q, Song K K, Li X L 2010 Phys. Mech. Astron. 53 390

    [43]

    Gancarz T, Gasior W 2016 Fluid Phase Equilib. 418 57

    [44]

    Liu Y H, Lu X W, Bai C G, Lai P S, Wang J S 2015 J. Ind. Eng. Chem. 30 106

    [45]

    Xiong L H, Lou H B, Wang X D, Debela T T, Cao Q P, Zhang D X, Wang S Y, Wang C Z, Jiang J Z 2014 Acta Mater. 68 1

    [46]

    Xiong L H, Chen K, Ke F S, Lou H B, Yue G Q, Shen B, Dong F, Wang S Y, Chen L Y, Wang C Z, Ho K M, Wang X D, Lai L H, Xiao T Q, Jiang J Z 2015 Acta Mater. 92 109

    [47]

    Xiong L H, Yoo H, Lou H B, Wang X D, Cao Q P, Zhang D X, Cao Q P, Zhang D X, Jian J Z, Xie H L, Xiao T Q, Jeon S, Lee G M 2015 J. Phys.:Condens. Matter 27 035102

    [48]

    Xiong L H, Guo F M, Wang X D, Cao Q P, Zhang D X, Ren Y, Jiang J Z 2017 J. Non-Cryst. Solids 459 160

    [49]

    Xiong L H, Wang X D, Cao Q P, Zhang D X, Xie H L, Xiao T Q, Jiang J Z 2017 J. Phys.:Condens. Matter 29 035101

    [50]

    Su Y, Wang X D, Yu Q, Cao Q P, Ruett U, Zhang D X, Jiang J Z 2018 J. Phys.:Condens. Matter 30 015402

    [51]

    Wang C W, Hu L N, Chen W, Tong X, Zhou C, Sun Q J, Hui X D, Yue Y Z 2014 J. Phys. Chem. 141 164507

    [52]

    Hu L N, Zhou C, Zhang C Z, Yue Y Z 2013 J. Phys. Chem. 138 174508

    [53]

    Sun Q J, Hu L N, Zhou C, Zheng H J, Yue Y Z 2015 J. Phys. Chem. Lett. 143 164504

    [54]

    Sun Q J, Zhou C, Yue Y Z, Hu L N 2014 J. Phys. Chem. Lett. 5 1170

    [55]

    Iida T, Roderick I L, 1993 The Properties of Liquid Metals (Oxford:University Press) pp147-199

    [56]

    Gui M C 1994 Ph. D. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[桂满昌 1994 博士学位论文 (哈尔滨:哈尔滨工业大学)]

    [57]

    Iidia T, Ueda M, Morita Z 1976 Tetsu to Hagane 62 1169

    [58]

    Morita Z, Iida T, Ueda M 1997 Inst. Phys. Conf. Ser. 30 600

    [59]

    Djemili B, Martin-Garin L, Hicter P 1980 J. Phys. Colloq. C8 41 363

    [60]

    Enskog D 1922 Arkiv. Mth. Astron. Fys. 16 16

    [61]

    Tham M K, Gubbins K E 1971 J. Chem. Phys. 55 268

  • [1]

    Han X F 2005 M. S. Dissertation (Jinan:Shandong University) (in Chinese)[韩秀峰 2005 硕士学位论文 (济南:山东大学)]

    [2]

    Angell C A 1985 J. Non-Cryst. Solids 73 1

    [3]

    Bian X F, Sun B A, Hu L N, Jia Y B 2005 Phys. Lett. A 335 61

    [4]

    Meng Q G, Zhou J K, Zheng H X, Li J G 2006 Scr. Mater. 54 777

    [5]

    Hu L N, Bian X F 2003 Chin. Sci. Bull. 48 2393 (in Chinese)[胡丽娜, 边秀房 2003 科学通报 48 2393]

    [6]

    Hu L N, Zhang C Z, Yue Y Z, Bian X F 2010 Chin. Sci. Bull. 55 115 (in Chinese)[胡丽娜, 张春芝, 岳远征, 边秀房 2010 科学通报 55 115]

    [7]

    Books R F, Dinsdale A T, Quested P N 2005 Meas. Sci. Technol. 16 354

    [8]

    Dinsdale A T, Quested P N 2004 J. Mater. Sci. 39 7221

    [9]

    Torklep K, Oye H A 1979 J. Phys. E 12 875

    [10]

    Sato Y, Kameda Y, Nagasawa T, Sakamoto T, Moriguchi S, Yamamura T, Waseda Y 2003 J. Cryst. Growth 249 404

    [11]

    Kehr M, Hoyer W, Egry I 2007 Int. J. Thermophys. 28 1017

    [12]

    Nunes V M B, Santos F J V, de Castro C A N 1998 Int. J. Thermophys. 19 427

    [13]

    Schenck H, Frohberg M G, Hoffmann K 1963 Steel Res. Int. 34 93

    [14]

    Emadi D, Gruzleski J E, Toguri J M 1993 Metall. Trans. B 24 1055

    [15]

    Xu Y P, Zhao X L, Yan T L 2017 Chin. Phys. B 26 036601

    [16]

    Wu Y Q, Bian X F, Mao T, Li X L, Li T B, Wang C D 2006 Phys. Lett. A 361 265

    [17]

    Sun C, Geng H, Liu J, Gneg H, Yang Z 2004 Phys. Meas. 1 16

    [18]

    Wang C Z 2017 M. S. Dissertation (Jinan:Shandong University) (in Chinese)[王春震 2017 硕士学位论文 (济南:山东大学)]

    [19]

    Guo H D 2008 M. S. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[郭海东 2008 硕士学位论文(哈尔滨:哈尔滨工业大学)]

    [20]

    Sun C J, Geng H R, Zhang N, Teng X Y, Ji L L 2008 Mater. Lett. 62 73

    [21]

    Mao T, Bian X F, Morioka S, Wu Y Q, Li X L, L X Q 2007 Phys. Lett. 366 155

    [22]

    Sun M H, Geng H R, Bian X F, Liu Y 2000 Acta Metal. Sin. 36 1134 (in Chinese)[孙民华, 耿浩然, 边秀房, 刘燕 2000 金属学报 36 1134]

    [23]

    Wang L, Bian X F, Liu J T 2004 Phys. Lett. A 326 429

    [24]

    Ofte D, Wittenberg L J 1963 Trans. Metall. Soc. Aime. 227 706

    [25]

    Rothwell E 1961 J. Inst. Metals 90 389

    [26]

    Gebhardt E, Kostlin K 1957 Z. Metallkd. 48 636

    [27]

    Schenck H, Frohberg M G, Hoffmann K 1963 Arch. Eisenhuettenw. 34 93

    [28]

    Cavalier G 1963 Compt. Rend. 256 1308

    [29]

    Kaplun A B, Avaliani M 1977 High Temp. 15 259

    [30]

    Nikolaev B, Vollmann J 1996 J. Non-Cryst. Solids 208 145

    [31]

    Martin-Garin L, Martin-Garin R, Despre P 1978 J. Less Common. Met. 59 1

    [32]

    Zhao X, Wang C Z, Zheng H J, Tian Z A, Hu L N 2017 Phys. Chem. Chem. Phys. 19 15962

    [33]

    Zhao Y, Hou X X, Bian X F 2008 Mater. Lett. 62 3542

    [34]

    Zhou C, Hu L N, Sun Q J, Bian X F, Yue Y Z 2013 Appl. Phys. 103 171904

    [35]

    Ning S, Bian X F, Ren Z F 2010 Phys. B:Condens. Matter 405 3633

    [36]

    Mao T, Bian X F, Xue X Y, Zhang Y N, Guo J, Sun B A 2007 Phys. B:Phys. Condens. Matter 387 1

    [37]

    Konstantinova N Y, Popel' P S, Yagodin D A 2009 High Temp. 47 336

    [38]

    Inoue A, Takeuchi A 2010 Int. J. Appl. Glass Sci. 1 273

    [39]

    Wang L, Liu J T 2004 Phys. Lett. A 328 241

    [40]

    Zheng H J, Hu L N, Zhao X, Wang C Z, Sun Q J, Wang T, Hui X D, Yue Y Z, Bian X F 2017 J. Non-Cryst. Solids 471 120

    [41]

    Zhang F, Du Y, Liu S H, Jie W Q 2015 Comput. Coupling Phase Diagrams Thermochem. 49 79

    [42]

    Jia R, Bian X F, Lu X Q, Song K K, Li X L 2010 Phys. Mech. Astron. 53 390

    [43]

    Gancarz T, Gasior W 2016 Fluid Phase Equilib. 418 57

    [44]

    Liu Y H, Lu X W, Bai C G, Lai P S, Wang J S 2015 J. Ind. Eng. Chem. 30 106

    [45]

    Xiong L H, Lou H B, Wang X D, Debela T T, Cao Q P, Zhang D X, Wang S Y, Wang C Z, Jiang J Z 2014 Acta Mater. 68 1

    [46]

    Xiong L H, Chen K, Ke F S, Lou H B, Yue G Q, Shen B, Dong F, Wang S Y, Chen L Y, Wang C Z, Ho K M, Wang X D, Lai L H, Xiao T Q, Jiang J Z 2015 Acta Mater. 92 109

    [47]

    Xiong L H, Yoo H, Lou H B, Wang X D, Cao Q P, Zhang D X, Cao Q P, Zhang D X, Jian J Z, Xie H L, Xiao T Q, Jeon S, Lee G M 2015 J. Phys.:Condens. Matter 27 035102

    [48]

    Xiong L H, Guo F M, Wang X D, Cao Q P, Zhang D X, Ren Y, Jiang J Z 2017 J. Non-Cryst. Solids 459 160

    [49]

    Xiong L H, Wang X D, Cao Q P, Zhang D X, Xie H L, Xiao T Q, Jiang J Z 2017 J. Phys.:Condens. Matter 29 035101

    [50]

    Su Y, Wang X D, Yu Q, Cao Q P, Ruett U, Zhang D X, Jiang J Z 2018 J. Phys.:Condens. Matter 30 015402

    [51]

    Wang C W, Hu L N, Chen W, Tong X, Zhou C, Sun Q J, Hui X D, Yue Y Z 2014 J. Phys. Chem. 141 164507

    [52]

    Hu L N, Zhou C, Zhang C Z, Yue Y Z 2013 J. Phys. Chem. 138 174508

    [53]

    Sun Q J, Hu L N, Zhou C, Zheng H J, Yue Y Z 2015 J. Phys. Chem. Lett. 143 164504

    [54]

    Sun Q J, Zhou C, Yue Y Z, Hu L N 2014 J. Phys. Chem. Lett. 5 1170

    [55]

    Iida T, Roderick I L, 1993 The Properties of Liquid Metals (Oxford:University Press) pp147-199

    [56]

    Gui M C 1994 Ph. D. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[桂满昌 1994 博士学位论文 (哈尔滨:哈尔滨工业大学)]

    [57]

    Iidia T, Ueda M, Morita Z 1976 Tetsu to Hagane 62 1169

    [58]

    Morita Z, Iida T, Ueda M 1997 Inst. Phys. Conf. Ser. 30 600

    [59]

    Djemili B, Martin-Garin L, Hicter P 1980 J. Phys. Colloq. C8 41 363

    [60]

    Enskog D 1922 Arkiv. Mth. Astron. Fys. 16 16

    [61]

    Tham M K, Gubbins K E 1971 J. Chem. Phys. 55 268

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Publishing process
  • Received Date:  22 December 2017
  • Accepted Date:  23 March 2018
  • Published Online:  20 May 2019

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