Extended elastic model for flow of metallic glasses

Wang Jun-Qiang; Ouyang Su

doi:10.7498/aps.66.176102

Abstract

Glass-liquid transition phenomenon, usually known as glass transition, has been valuated as one of the most important challenges in condensed matter physics. As typical amorphous solid, metallic glass is composed of disordered-packing atoms, which is akin to a liquid. Thus, metallic glass is also known as frozen liquid. Metallic glass is an ideal model material for studying glass transition phenomenon. When heated up to glass transition temperature or stressed to yielding point, metallic glass flows. The flow behavior at elevated temperature or under stress plays an important role in the applications of metallic glass. In this paper, we briefly review the research developments and perspectives for the flow behavior and extended elastic model for flow of metallic glasses. In elastic models for flow, i.e., free volume model, cooperative shear transformation model, it is assumed that the activation energy for flow (E) is a combination of shear modulus (G) and a characteristic volume (Vc), E=GVc. Most recently, it has been widely recognized that in amorphous materials, e. g. metallic glass, shear flow is always accompanied by dilatation effect. This suggests that besides shear modulus, bulk modulus (K) should also be taken into account for energy barrier. However, what are the contributions of K is still unknown. On the other hand, the physical meaning of characteristic volume Vc and the determination of its value are also important for quantitatively describing the flow behavior of metallic glass. Based on the statistical analyses of a large number of experimental data, i. e., elastic modulus, glass transition temperature, density and molar volume for 46 kinds of metallic glasses, the linear relationship between RTg/G and Vm is observed. This suggests that the molar volume (Vm) is the characteristic volume involved in the flow activation energy. To determine the contribution of K as a result of shear-dilatation effect, flow activation energy density is defined as E =E/Vm. According to the harmonic analysis of the energy density landscape, we propose that both shear and bulk moduli be involved in flow activation energy density, as E = (1-)G+K, with 9%. This result is also verified by the relationship between elastic modulus and glass transition temperature: (0.91G+ 0.09K)Vm/RTg is a constant, that is, independent of property of metallic glass. This result is also consistent with the evolution of sound velocity with glass transition temperature. In the end of this review, we address some prospects about the applications of the extended elastic model and its significance in designing new metallic glasses with advanced properties. This extended elastic model is also fundamentally helpful for understanding the nature of glass transition and kinetic properties of shear band of metallic glasses.

Keywords:

Authors and contacts

1.
CAS Key Laboratory of Magnetic Materials and Devices, Key Laboratory of Magnetic Materials and Application Technology of Zhejiang Province, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China

Corresponding author: Wang Jun-Qiang, jqwang@nimte.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11504391) and the 100 Talents Project of Chinese Academy of Sciences.

References

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[51]	Jiang M Q, Jiang S Y, Dai L H 2009 Chin. Phys. Lett. 26 016103
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[53]	Jiang M Q, Wilde G, Dai LH 2015 Mech. Mater. 81 72
[54]	Jiang M Q, Wilde G, Chen J H, Qu C B, Fu S Y, Jiang F, Dai L H 2014 Acta Mater. 77 248
[55]	Schmidt V, Rosner H, Peterlechner M, Wilde G 2015 Phys. Rev. Lett. 115 035501
[56]	Wang J Q, Wang W H, Bai H Y 2011 J. Non-Cryst. Solids 357 223
[57]	Wang J Q, Wang W H, Liu Y H, Bai H Y 2011 Phys. Rev. B 83 012201
[58]	Wang W H 2006 J. Appl. Phys. 99 093506
[59]	Ke H B, Wen P, Zhao D Q, Wang W H 2010 Appl. Phys. Lett. 96 251902
[60]	Wang J Q, Wang W H, Yu H B, Bai H Y 2009 Appl. Phys. Lett. 94 121904
[61]	Wang J Q 2010 Ph. D. Dissertation (Beijing: Institute of Physics, CAS) (in Chinese) [王军强 2010 博士学位论文 (北京: 中国科学院物理研究所)]
[62]	Jiang M, Dai L 2007 Phys. Rev. B 76 054204
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[66]	Dyre J C 2006 Rev. Mod. Phys. 78 953
[67]	Zhang B, Bai H, Wang R, Wu Y, Wang W 2007 Phys. Rev. B 76 012201
[68]	Egami T, Poon S J, Zhang Z, Keppens V 2007 Phys. Rev. B 76 024203
[69]	Liu Z Q, Wang W H, Jiang M Q, Zhang Z F 2014 Phil. Mag. Lett. 94 658
[70]	Liu Z Q, Wang R F, Qu R T, Zhang Z F 2014 J. Appl. Phys. 115 203513
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Cited By

[1]	Weintraub H, Ashburner M, Goodfellow P N, Lodish H F, Arntzen C J, Anderson P W, Rice T M, Geballe T H, Means A R, Ranney H M, Cech T R, Colwell R R, Bourne H R, Richter B, Singer I M, Marrack P, Fearon D T, Penzias A, Bard A J, Brinkman W F, Marks P A, Vogelstein B, Kinzler K W, Bishop J M, Zare R N, Schatz G, Benkovic S J, Gray H B, Valentine J S, Crutzen P J, Choi D W, Nakanishi S, Kosslyn S M, Brauman J I, Rees D C, Brill W J, Schell J, Luhrmann R, Will C L, Wulf W, Vermeij G J, Arrow K J, Smelser N J, Anderson D L, Abelson P H 1995 Science 267 1609
[2]	Debenedetti P G, Stillinger F H 2001 Nature 410 259
[3]	Angell C A, Poole P H, Shao J 1994 Nuovo. Cimento. D 16 993
[4]	Mauro J C, Yue Y, Ellison A J, Gupta P K, Allan D C 2009 Proc. Natl. Acad. Sci. 106 19780
[5]	Wang W H, Dong C, Shek C H 2004 Mater. Sci. Eng. R 44 45
[6]	Chen M W 2008 Annu. Rev. Mater. Res. 38 445
[7]	Liu Y H, Wang G, Wang R J, Zhao D Q, Pan M X, Wang W H 2007 Science 315 1385
[8]	Das J, Tang M B, Kim K B, Theissmann R, Baier F, Wang W H, Eckert J 2005 Phys. Rev. Lett. 94 205501
[9]	Schroers J, Johnson W L 2004 Phys. Rev. Lett. 93 255506
[10]	Yao K F, Ruan F, Yang Y Q, Chen N 2006 Appl. Phys. Lett. 88 122106
[11]	Chen M W, Inoue A, Zhang W, Sakurai T 2006 Phys. Rev. Lett. 96 245502
[12]	Spaepen F 2006 Nature Mater. 5 7
[13]	Song S X, Nieh T G 2011 Intermetallics 19 1968
[14]	Stolpe M, Kruzic J J, Busch R 2014 Acta Mater. 64 231
[15]	Xia X X, Wang W H, Greer A L 2009 J. Mater. Res. 24 2986
[16]	Xia X X, Wang W H 2012 Small 8 1197
[17]	Liu Y H, Liu C T, Wang W H, Inoue A, Sakurai T, Chen M W 2009 Phys. Rev. Lett. 103 065504
[18]	Yang B, Liu C T, Nieh T G 2006 Appl. Phys. Lett. 88 221911
[19]	Guan P F, Chen M W, Egami T 2010 Phys. Rev. Lett. 104 205701
[20]	Wang W H, Yang Y, Nieh T G, Liu C T 2015 Intermetallics 67 81
[21]	Ye J C, Lu J, Liu C T, Wang Q, Yang Y 2010 Nature Mater. 9 619
[22]	Falk M L, Langer J S 1998 Phys. Rev. E 57 7192
[23]	Argon A S 1979 Acta Metall. 27 47
[24]	Langer J S 2006 Scr. Mater. 54 375
[25]	Johnson W L, Samwer K 2005 Phys. Rev. Lett. 95 195501
[26]	Falk M L, Langer J S, Pechenik L 2004 Phys. Rev. E 70 011507
[27]	Zhu Z G, Wen P, Wang D P, Xue R J, Zhao D Q, Wang W H 2013 J. Appl. Phys. 114 083512
[28]	Xue R J, Wang D P, Zhu Z G, Ding D W, Zhang B, Wang W H 2013 J. Appl. Phys. 114 123514
[29]	Liu S T, Wang Z, Peng H L, Yu H B, Wang W H 2012 Scr. Mater. 67 9
[30]	Ke H B, Zeng J F, Liu C T, Yang Y 2014 J. Mater. Sci. Tech. 30 560
[31]	Huo L S, Zeng J F, Wang W H, Liu C T, Yang Y 2013 Acta Mater. 61 4329
[32]	Wang J G, Zhao D Q, Pan M X, Wang W H, Song S X, Nieh T G 2010 Scr. Mater. 62 477
[33]	Liu A J, Nagel S R 1998 Nature 396 21
[34]	Mayr S G 2006 Phys. Rev. Lett. 97 195501
[35]	Zink M, Samwer K, Johnson W L, Mayr S G 2006 Phys. Rev. B 73 172203
[36]	Dyre J C, Wang W H 2012 J. Chem. Phys. 136 224108
[37]	Hecksher T, Dyre J C 2015 J. Non-Cryst. Solids 407 14
[38]	Spaepen F 1977 Acta Metall. 25 407
[39]	Wang W H 2012 Prog. Mater. Sci. 57 487
[40]	Wang W H 2012 Nature Mater. 11 275
[41]	Ma D, Stoica A D, Wang X L, Lu Z P, Clausen B, Brown D W 2012 Phys. Rev. Lett. 108 085501
[42]	Wang W H 2005 J. Non-Cryst. Solids 351 1481
[43]	Li J F, Wang J Q, Liu X F, Zhao K, Zhang B, Bai H Y, Pan M X, Wang W H 2010 Sci. China: Phys. Mech. 53 409
[44]	Wang J Q, Wang W H, Bai H Y 2009 Appl. Phys. Lett. 94 041910
[45]	Zhang B, Zhao D Q, Pan M X, Wang W H, Greer AL 2005 Phys. Rev. Lett. 94 205502
[46]	Wang Z, Yu H B, Wen P, Bai H Y, Wang W H 2011 J. Phys. Cond. Matter 23 142202
[47]	Torre D F H, Dubach A, Loffler J F 2010 J. Alloy. Compd. 495 341
[48]	Jiang W H, Atzmon M 2011 J. Alloy. Compd. 509 7395
[49]	Liu Z Q, Li R, Wang G, Wu S J, Lu X Y, Zhang T 2011 Acta Mater. 59 7416
[50]	Yi J, Wang W H, Lewandowski J J 2015 Acta Mater. 87 1
[51]	Jiang M Q, Jiang S Y, Dai L H 2009 Chin. Phys. Lett. 26 016103
[52]	Chen Y, Jiang M Q, Dai L H 2011 Sci. China: Phys. Mech. 54 1488
[53]	Jiang M Q, Wilde G, Dai LH 2015 Mech. Mater. 81 72
[54]	Jiang M Q, Wilde G, Chen J H, Qu C B, Fu S Y, Jiang F, Dai L H 2014 Acta Mater. 77 248
[55]	Schmidt V, Rosner H, Peterlechner M, Wilde G 2015 Phys. Rev. Lett. 115 035501
[56]	Wang J Q, Wang W H, Bai H Y 2011 J. Non-Cryst. Solids 357 223
[57]	Wang J Q, Wang W H, Liu Y H, Bai H Y 2011 Phys. Rev. B 83 012201
[58]	Wang W H 2006 J. Appl. Phys. 99 093506
[59]	Ke H B, Wen P, Zhao D Q, Wang W H 2010 Appl. Phys. Lett. 96 251902
[60]	Wang J Q, Wang W H, Yu H B, Bai H Y 2009 Appl. Phys. Lett. 94 121904
[61]	Wang J Q 2010 Ph. D. Dissertation (Beijing: Institute of Physics, CAS) (in Chinese) [王军强 2010 博士学位论文 (北京: 中国科学院物理研究所)]
[62]	Jiang M, Dai L 2007 Phys. Rev. B 76 054204
[63]	Zhang Z F, He G, Eckert J, Schultz L 2003 Phys. Rev. Lett. 91 045505
[64]	Dyre J C, Olsen N B 2004 Phys. Rev. E 69 042501
[65]	Wang Z C 2003 Thermodynamics and Statistics (Beijing: Higher Education Press) pp261-268 (in Chinese) [汪志诚 2003 热力学·统计物理 (北京: 高等教育出版社)第261-268页]
[66]	Dyre J C 2006 Rev. Mod. Phys. 78 953
[67]	Zhang B, Bai H, Wang R, Wu Y, Wang W 2007 Phys. Rev. B 76 012201
[68]	Egami T, Poon S J, Zhang Z, Keppens V 2007 Phys. Rev. B 76 024203
[69]	Liu Z Q, Wang W H, Jiang M Q, Zhang Z F 2014 Phil. Mag. Lett. 94 658
[70]	Liu Z Q, Wang R F, Qu R T, Zhang Z F 2014 J. Appl. Phys. 115 203513
[71]	Liu Z Q, Zhang Z F 2013 J. Appl. Phys. 114 243519
[72]	Lewandowski J J, Wang W H, Greer A L 2005 Phil. Mag. Lett. 85 77
[73]	Gu X J, Poon S J, Shiflet G J 2011 J. Mater. Res. 22 344

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