| Citation: | Qiao J C, Zhang L T, Tong Y, Lyu G J, Hao Q, Tao K. Mechancial properties of amorphous alloys: In the framework of the microstructure heterogeneity. Advances in Mechanics, 2022, 52(1): 117-152 doi: 10.6052/1000-0992-21-038 | 
	                | [1] | 
					 陈迎红, 王云江, 乔吉超. 2020. La30Ce30Al15Co25 金属玻璃应力松弛行为. 力学学报, 52: 740-748 (Chen Y H, Wang Y J, Qiao J C. 2020. Stress relaxation of La30Ce30Al15Co25 metallic glass. Chinese Journal of Theoretical and Applied Mechanics, 52: 740-748 (in Chinese)). doi:  10.6052/0459-1879-20-013 
					
					 | 
			
| [2] | 
					 管鹏飞, 王兵, 吴义成, 张珊, 尚宝双, 胡远超, 苏锐, 刘琪. 2017. 不均匀性: 非晶合金的灵魂. 物理学报, 66: 176112 (Guan P F, Wang B, Wu Y C, Zhang S, Shang B S, Hu Y C, Su R, Liu Q. 2017. Heterogeneity: The soul of metallic glasses. Acta Physica Sinica, 66: 176112 (in Chinese)). doi:  10.7498/aps.66.176112 
					
					 | 
			
| [3] | 
					 蒋敏强, 高洋. 2021. 金属玻璃的结构年轻化及其对力学行为的影响. 金属学报, 57: 425-438 (Jiang M Q, Gao Y. 2021. Structural rejuvenation of metallic glasses and its effect on mechanical behaviors. Acta Metallurgica Sinica, 57: 425-438 (in Chinese)). doi:  10.11900/0412.1961.2020.00431 
					
					 | 
			
| [4] | 
					 蒋敏强, 戴兰宏. 2017. 非晶合金“拉伸转变区”模型. 科学通报, 21: 2346-2357 (Jiang M Q, Dai L H. 2017. The “tension transformation zone” model of amorphous alloys. Chin Sci Bull, 21: 2346-2357 (in Chinese)). 
					
					 | 
			
| [5] | 
					 卢博斯基.1989. 非晶态金属合金. 北京: 冶金工业出版社. 
					
					 | 
			
| [6] | 
					 汪卫华. 2013. 非晶态物质的本质和特性. 物理学进展, 33: 177-351 (Wang W H. 2013. The nature and properties of amorphous matter. Progress in Physics, 33: 177-351 (in Chinese)). 
					
					 | 
			
| [7] | 
					 王云江, 魏丹, 韩懂, 杨杰, 蒋敏强, 戴兰宏. 2020. 非晶态固体的结构可以决定性能吗? 力学学报, 52: 303-317 (Wang Y J, Wei D , Han D , Yang J , Jiang M Q, Dai L H. 2020. Does structure determine property in amorphous solids? Chinese Journal of Theoretical and Applied Mechanics, 52: 303-317 (in Chinese)). doi:  10.6052/0459-1879-19-368 
					
					 | 
			
| [8] | 
					 王峥, 2013. 金属玻璃中流动单元的探测和表征 [博士论文], 北京: 中国科学院物理研究所. 
					Wang Z, 2013. Verification  and characterization of flow units in metallic glasses [PhD Thesis ]. Beijing: Institute of Physics, Chinese Academy of Sciences (in Chinese). 
						
					 | 
			
| [9] | 
					 Afonin G V, Mitrofanov Y P, Kobelev N P, da Silva Pinto M W, Wilde G, Khonik V A. 2019. Relationship between the enthalpies of structural relaxation, crystallization and melting in metallic glass-forming systems. Scr. Mater, 166: 6-9. doi:  10.1016/j.scriptamat.2019.02.030 
						
					 | 
			
| [10] | 
					 Argon A. 1979. Plastic deformation in metallic glasses. Acta Metall., 27: 47-58. doi:  10.1016/0001-6160(79)90055-5 
						
					 | 
			
| [11] | 
					 Barkema G T, Mousseau N. 1996. Event-Based Relaxation of Continuous Disordered Systems. Phys. Rev. Lett., 77: 4358-4361. doi:  10.1103/PhysRevLett.77.4358 
						
					 | 
			
| [12] | 
					 Bei H B, Xie S J, George E P. 2006. Softening caused by profuse shear banding in a bulk metallic glass. Phys. Rev. Lett., 96: 105503. doi:  10.1103/PhysRevLett.96.105503 
						
					 | 
			
| [13] | 
					 Bergman R. 2000. General susceptibility functions for relaxations in disordered systems. J. Appl. Phys., 88: 1356-1365. doi:  10.1063/1.373824 
						
					 | 
			
| [14] | 
					 Bouchaud J P, Dupuis V, Hammann J, Vincent E. 2001. Separation of time and length scales in spin glasses: Temperature as a microscope. Phys. Rev. B., 65: 024439. doi:  10.1103/PhysRevB.65.024439 
						
					 | 
			
| [15] | 
					 Bünz J, Brink T, Tsuchiya K, Meng F, Wilde G, Albe K. 2014. Low temperature heat capacity of a severely deformed metallic glass. Phys. Rev. Lett., 112: 135501. doi:  10.1103/PhysRevLett.112.135501 
						
					 | 
			
| [16] | 
					 Cangialosi D, Boucher V. M, Alegría A, Colmenero. 2013. Direct evidence of two equilibration mechanisms in glassy polymers. Phys. Rev. Lett., 111: 095701. doi:  10.1103/PhysRevLett.111.095701 
						
					 | 
			
| [17] | 
					 Cao P, Short M P, Yip S. 2017. Understanding the mechanisms of amorphous creep through molecular simulation. Proc. Natl. Acad. Sci., 114: 13631-13636. doi:  10.1073/pnas.1708618114 
						
					 | 
			
| [18] | 
					 Carini G, Carin G, D’Angelo G, Tripodo G, Di Marco G, Vasi C, Gilioli E. 2013. Influence of Packing on Low Energy Vibrations of Densified Glasses. Phys. Rev. Lett., 111: 245502. doi:  10.1103/PhysRevLett.111.245502 
						
					 | 
			
| [19] | 
					 Casalini R, Roland C M. 2009. Aging of the Secondary Relaxation to Probe Structural Relaxation in the Glassy State. Phys. Rev. Lett., 102: 035701. doi:  10.1103/PhysRevLett.102.035701 
						
					 | 
			
| [20] | 
					 Castellero A, Moser B, Uhlenhaut D I, Torre F H. D, Löffler J F. 2008. Room-temperature creep and structural relaxation of Mg–Cu–Y metallic glasses. Acta Mater, 56: 3777-3785. doi:  10.1016/j.actamat.2008.04.021 
						
					 | 
			
| [21] | 
					 Cheng Y Q, Cao A J, Ma E. 2009. Correlation between the elastic modulus and the intrinsic plastic behavior of metallic glasses: The roles of atomic configuration and alloy composition. Acta Mater., 57: 3253-3267. doi:  10.1016/j.actamat.2009.03.027 
						
					 | 
			
| [22] | 
					 Cheng Y Q, Ma E. 2011. Atomic-level structure and structure-property relationship in metallic glasses. Prog. Mater. Sci., 56: 379-473. doi:  10.1016/j.pmatsci.2010.12.002 
						
					 | 
			
| [23] | 
					 Cheng Y T, Hao Q, Qiao J C, Crespo D, Pineda E, Pelletier J M. 2021. Effect of minor addition on dynamic mechanical relaxation in ZrCu-based metallic glasses. J. Non·Cryst. Solids, 553: 120496. doi:  10.1016/j.jnoncrysol.2020.120496 
						
					 | 
			
| [24] | 
					 Cohen M H, Turnbull D. 1959. Molecular transport in liquids and glasses. J. Chem. Phys., 31: 1164-1169. doi:  10.1063/1.1730566 
						
					 | 
			
| [25] | 
					 Cost J R. 1983. Nonlinear regression least-squares method for determining relaxation time spectra for processes with first-order kinetics. J. Appl. Phys., 54: 2137-2146. doi:  10.1063/1.332390 
						
					 | 
			
| [26] | 
					 Debenedetti P G, Stillinger F H. 2001. Supercooled liquids and the glass transition. Nature, 410: 259-267. doi:  10.1038/35065704 
						
					 | 
			
| [27] | 
					 Ding G, Li C, Zaccone A, Wang W, Lei H, Jiang F, Ling Z, Jiang M Q. 2019. Ultrafast extreme rejuvenation of metallic glasses by shock compression. Sci. Adv., 5: eaaw6249. doi:  10.1126/sciadv.aaw6249 
						
					 | 
			
| [28] | 
					 Ding J, Cheng Y Q, Ma E. 2014a. Full icosahedra dominate local order in Cu64Zr34 metallic glass and supercooled liquid. Acta Mater., 69: 343-354. doi:  10.1016/j.actamat.2014.02.005 
						
					 | 
			
| [29] | 
					 Ding J, Patinet S, Falk M L, Cheng Y, Ma E. 2014b. Soft spots and their structural signature in a metallic glass. Proc. Natl. Acad. Sci., 111: 14052-14056. doi:  10.1073/pnas.1412095111 
						
					 | 
			
| [30] | 
					 Dixon P K, Wu L, Nagel S R, Williams B D, Carini J P. 1990. Scaling in the relaxation of supercooled liquids. Phys. Rev. Lett., 65: 1108-1111. doi:  10.1103/PhysRevLett.65.1108 
						
					 | 
			
| [31] | 
					 Dmowski W, Yokoyama Y, Chuang A, Ren Y, Umemoto M, Tsuchiya K, Inoue A, Egami T. 2010. Structural rejuvenation in a bulk metallic glass induced by severe plastic deformation. Acta Mater., 58: 429-438. doi:  10.1016/j.actamat.2009.09.021 
						
					 | 
			
| [32] | 
					 Ebner C, Escher B, Gammer C, Eckert J, Pauly S, Rentenberger C. 2018. Structural and mechanical characterization of heterogeneities in a CuZr-based bulk metallic glass processed by high pressure torsion. Acta Mater., 160: 147-157. doi:  10.1016/j.actamat.2018.08.032 
						
					 | 
			
| [33] | 
					 Egami T, Iwashita T, Dmowski W. 2013. Mechanical properties of metallic glasses. Metals, 3: 77-113. doi:  10.3390/met3010077 
						
					 | 
			
| [34] | 
					 Elliott S R. 1991. Medium-range structural order in covalent amorphous solids. Nature, 354: 445-452. doi:  10.1038/354445a0 
						
					 | 
			
| [35] | 
					 Elliott S R. 1992. A Unified Model for the Low-Energy Vibrational Behaviour of Amorphous Solids. Europhysics Letters (EPL) 
						
					 | 
			
| [36] | 
					 Falk M L, Langer J S. 1998. Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E, 57: 7192-7205. doi:  10.1103/PhysRevE.57.7192 
						
					 | 
			
| [37] | 
					 Fan Y, Iwashita T, Egami T. 2014. How thermally activated deformation starts in metallic glass. Nat. Commun., 5: 5083. doi:  10.1038/ncomms6083 
						
					 | 
			
| [38] | 
					 Fan Y, Iwashita T, Egami T. 2017. Energy landscape-driven non-equilibrium evolution of inherent structure in disordered material. Nat. Commun., 8: 15417. doi:  10.1038/ncomms15417 
						
					 | 
			
| [39] | 
					 Feng S D, Qi L, Wang L M, Yu P F, Zhang S L, Ma M Z, Zhang X Y, Jing Q, Ngai K L, Greer A L, Li G, Liu R P. 2016. Structural feature of Cu64Zr36 metallic glass on nanoscale: Densely-packed clusters with loosely-packed surroundings. Scr. Mater., 115: 57-61. doi:  10.1016/j.scriptamat.2015.12.038 
						
					 | 
			
| [40] | 
					 Gauthier C, David L, Ladouce L, Quinson R, Perez J. 1997. Nonlinear mechanical response of amorphous polymers below and through glass transition temperature. J. Appl. Polym. Sci., 65: 2517-2528. doi:  10.1002/(SICI)1097-4628(19970919)65:12<2517::AID-APP22>3.0.CO;2-W 
						
					 | 
			
| [41] | 
					 Greer A, Sun Y. 2016. Stored energy in metallic glasses due to strains within the elastic limit. Philos. Mag., 96: 1643-1663. doi:  10.1080/14786435.2016.1177231 
						
					 | 
			
| [42] | 
					 Grigera T S, Martín-Mayor V, Parisi G, Verrocchio P. 2003. Phonon interpretation of the ‘boson peak’ in supercooled liquids. Nature, 422: 289-292. doi:  10.1038/nature01475 
						
					 | 
			
| [43] | 
					 Gurevich V, Parshin D, Pelous J, Schober H. 1993. Theory of low-energy Raman scattering in glasses. Phys. Rev. B, 48: 16318. doi:  10.1103/PhysRevB.48.16318 
						
					 | 
			
| [44] | 
					 Herrero-Gomez C, Samwer K. 2016. Stress and temperature dependence of the avalanche dynamics during creep deformation of metallic glasses. Sci. Rep., 6: 33503. doi:  10.1038/srep33503 
						
					 | 
			
| [45] | 
					 Huang B, Bai H Y, Wang W H. 2014. Relationship between boson heat capacity peaks and evolution of heterogeneous structure in metallic glasses. J. Appl. Phys., 115: 153505. doi:  10.1063/1.4871676 
						
					 | 
			
| [46] | 
					 Huang B, Zhu Z G, Ge T P, Bai H Y, Sun B A., Yang Y, Liu C T, Wang W H. 2016. Hand in hand evolution of boson heat capacity anomaly and slow β-relaxation in La-based metallic glasses. Acta Mater., 110: 73-83. doi:  10.1016/j.actamat.2016.03.016 
						
					 | 
			
| [47] | 
					 Hufnagel T C, Schuh C A, Falk M L. 2016. Deformation of metallic glasses: Recent developments in theory, simulations, and experiments. Acta Mater., 109: 375-393. doi:  10.1016/j.actamat.2016.01.049 
						
					 | 
			
| [48] | 
					 Hutnik M, Argon A S, Suter U W. 1993. Simulation of elastic and plastic response in the glassy polycarbonate of 4, 4'-isopropylidenediphenol. Macromolecules, 26: 1097-1108. doi:  10.1021/ma00057a034 
						
					 | 
			
| [49] | 
					 Ichitsubo T., Matsubara E, Yamamoto T, Chen H, Nishiyama N, Saida J, Anazawa K. 2005. Microstructure of fragile metallic glasses inferred from ultrasound-accelerated crystallization in Pd-based metallic glasses. Phys. Rev. Lett., 95: 245501. doi:  10.1103/PhysRevLett.95.245501 
						
					 | 
			
| [50] | 
					 Inoue A, Takeuchi A. 2011. Recent development and application products of bulk glassy alloys. Acta Materialia, 59: 2243-2267. doi:  10.1016/j.actamat.2010.11.027 
						
					 | 
			
| [51] | 
					 Jiang M Q, Ling Z, Meng J X, Dai L H. 2008. Energy dissipation in fracture of bulk metallic glasses via inherent competition between local softening and quasi-cleavage. Philos. Mag., 88: 407-426. doi:  10.1080/14786430701864753 
						
					 | 
			
| [52] | 
					 Jiang M Q, Ling Z, Meng J X, Gao J B, Dai L H. 2010. Nanoscale periodic corrugation to dimple transition due to “beat” in a bulk metallic glass. Scr. Mater, 62: 572-575. doi:  10.1016/j.scriptamat.2009.12.046 
						
					 | 
			
| [53] | 
					 Johari G P, Goldstein M. 1970. Viscous liquids and the glass transition. II. Secondary relaxations in glasses of rigid molecules. J. Chem. Phys., 53: 2372-2388. doi:  10.1063/1.1674335 
						
					 | 
			
| [54] | 
					 Johnson W L. 1986. Thermodynamic and kinetic aspects of the crystal to glass transformation in metallic materials. Prog. Mater. Sci., 30: 81-134. doi:  10.1016/0079-6425(86)90005-8 
						
					 | 
			
| [55] | 
					 Johnson W L. 1999. Bulk Glass-Forming Metallic Alloys: Science and Technology. MRS Bulletin, 24: 42-56. doi:  10.1557/S0883769400069980 
						
					 | 
			
| [56] | 
					 Ju J D, Jang D, Nwankpa A, Atzmon M. 2011. An atomically quantized hierarchy of shear transformation zones in a metallic glass. J. Appl. Phys., 109: 053522. doi:  10.1063/1.3552300 
						
					 | 
			
| [57] | 
					 Kelton K F, Lee G W, Gangopadhyay A K, Hyers R W, Rathz T J, Rogers J R, Robinson M B, Robinson D S. 2003. First X-Ray Scattering Studies on Electrostatically Levitated Metallic Liquids: Demonstrated Influence of Local Icosahedral Order on the Nucleation Barrier. Phys. Rev. Lett., 90: 195504. doi:  10.1103/PhysRevLett.90.195504 
						
					 | 
			
| [58] | 
					 Krisponeit J O, Pitikaris S, Avila K E, Kuchemann S, Kruger A, Samwer K. 2014. Crossover from random three-dimensional avalanches to correlated nano shear bands in metallic glasses. Nat. Commun., 5: 3616. doi:  10.1038/ncomms4616 
						
					 | 
			
| [59] | 
					 Lei T J, DaCosta L R, Liu M, Shen J, Sun Y H, Wang W H, Atzmon M. 2020. Composition dependence of metallic glass plasticity and its prediction from anelastic relaxation – A shear transformation zone analysis. Acta Mater., 195: 81-86. doi:  10.1016/j.actamat.2020.04.053 
						
					 | 
			
| [60] | 
					 Lei T J, DaCosta L R, Liu M, Wang W H, Sun Y H, Greer A L, Atzmon M. 2019a. Microscopic characterization of structural relaxation and cryogenic rejuvenation in metallic glasses. Acta Mater, 164: 165-170. doi:  10.1016/j.actamat.2018.10.036 
						
					 | 
			
| [61] | 
					 Lei T J, Rangel DaCosta L, Liu M, Wang W H, Sun Y H, Greer A L, Atzmon M. 2019b. Shear transformation zone analysis of anelastic relaxation of a metallic glass reveals distinct properties of alpha and beta relaxations. Phys Rev E, 100: 033001. doi:  10.1103/PhysRevE.100.033001 
						
					 | 
			
| [62] | 
					 Lewandowski J J, Greer A L. 2006. Temperature rise at shear bands in metallic glasses. Nat. Mater., 5: 15-18. doi:  10.1038/nmat1536 
						
					 | 
			
| [63] | 
					 Li B S, Xie S H, Kruzic J J. 2019. Toughness enhancement and heterogeneous softening of a cryogenically cycled Zr–Cu–Ni–Al–Nb bulk metallic glass. Acta Mater., 176: 278-288. doi:  10.1016/j.actamat.2019.07.012 
						
					 | 
			
| [64] | 
					 Li Y, Yu P, Bai H Y. 2008. Study on the boson peak in bulk metallic glasses. J. Appl. Phys., 104: 013520. doi:  10.1063/1.2948926 
						
					 | 
			
| [65] | 
					 Liu Y H, Wang D, Nakajima K, Zhang W, Hirata A, Nishi T, Inoue A, Chen M W. 2011. Characterization of nanoscale mechanical heterogeneity in a metallic glass by dynamic force microscopy. Phys. Rev. Lett., 106: 125504. doi:  10.1103/PhysRevLett.106.125504 
						
					 | 
			
| [66] | 
					 Lunkenheimer P, Schneider U, Brand R, Loid A. 2000. Glassy dynamics. Contemp. Phys., 41: 15-36. doi:  10.1080/001075100181259 
						
					 | 
			
| [67] | 
					 Lunkenheimer P, Wehn R, Schneider U, Loidl A. 2005. Glassy Aging Dynamics. Phys. Rev. Lett., 95: 055702. doi:  10.1103/PhysRevLett.95.055702 
						
					 | 
			
| [68] | 
					 Luo P, Wen P, Bai H, Ruta B, Wang W H. 2017. Relaxation decoupling in metallic glasses at low temperatures. Phys. Rev. Lett., 118: 225901. doi:  10.1103/PhysRevLett.118.225901 
						
					 | 
			
| [69] | 
					 Ma E. 2015. Tuning order in disorder. Nat. Mater., 14: 547-552. doi:  10.1038/nmat4300 
						
					 | 
			
| [70] | 
					 Mitrofanov Y P, Peterlechner M, Divinski S V, Wilde G. 2014. Impact of Plastic Deformation and Shear Band Formation on the Boson Heat Capacity Peak of a Bulk Metallic Glass. Phys. Rev. Lett., 112: 135901. doi:  10.1103/PhysRevLett.112.135901 
						
					 | 
			
| [71] | 
					 Monnier X, Cangialosi D, Ruta B, Busch R, Gallino I. 2020. Vitrification decoupling from α-relaxation in a metallic glass. Sci. Adv., 6: eaay1454. doi:  10.1126/sciadv.aay1454 
						
					 | 
			
| [72] | 
					 Ngai K L, Wang Z, Gao X Q, Yu H B, Wang W H. 2013. A connection between the structural α-relaxation and the β-relaxation found in bulk metallic glass-formers. J. Chem. Phys., 139: 014502. doi:  10.1063/1.4812281 
						
					 | 
			
| [73] | 
					 Nomoto K, Ceguerra A V, Gammer C, Li B, Bilal H, Hohenwarter A, Gludovatz B, Eckert J, Ringer S P, Kruzic J J. 2021. Medium-range order dictates local hardness in bulk metallic glasses. Mater. Today, 44: 48-57. doi:  10.1016/j.mattod.2020.10.032 
						
					 | 
			
| [74] | 
					 Pan J, Wang Y X, Guo Q, Zhang D, Greer A L, Li Y. 2018. Extreme rejuvenation and softening in a bulk metallic glass. Nat. Commun., 9: 560. doi:  10.1038/s41467-018-02943-4 
						
					 | 
			
| [75] | 
					 Pelletier J M , Louzguine-Luzgin D V , Li S , Inoue A. 2011. Elastic and viscoelastic properties of glassy, quasicrystalline and crystalline phases in Zr65Cu5Ni10Al7.5Pd12.5 alloys. Acta Mater, 59: 2797-2806. doi:  10.1016/j.actamat.2011.01.018 
						
					 | 
			
| [76] | 
					 Peng H L, Li M Z, Wang W H. 2011. Structural Signature of Plastic Deformation in Metallic Glasses. Phys. Rev. Lett., 106: 135503. doi:  10.1103/PhysRevLett.106.135503 
						
					 | 
			
| [77] | 
					 Perez J. 1990. Quasi-punctual defects in vitreous solids and liquid-glass transition. Solid State Ionics, 39: 69-79. doi:  10.1016/0167-2738(90)90028-P 
						
					 | 
			
| [78] | 
					 Peter G W. 2009. Spatiotemporal structures in aging and rejuvenating glasses. Proc. Natl. Acad. Sci., 106: 1353-1358. doi:  10.1073/pnas.0812418106 
						
					 | 
			
| [79] | 
					 Priezjev N V. 2019. Aging and rejuvenation during elastostatic loading of amorphous alloys: A molecular dynamics simulation study. Comput. Mater. Sci., 168: 125-130. doi:  10.1016/j.commatsci.2019.05.054 
						
					 | 
			
| [80] | 
					 Qiao J C, Liu X D, Wang Q, Liu C T, Lu J, Yang Y. 2018. Fast secondary relaxation and plasticity initiation in metallic glasses. Natl. Sci. Rev., 5: 616-618. doi:  10.1093/nsr/nwx113 
						
					 | 
			
| [81] | 
					 Qiao J C, Pelletier J M. 2012. Mechanical relaxation in a Zr-based bulk metallic glass: Analysis based on physical models. J. Appl. Phys., 112: 033518. doi:  10.1063/1.4745019 
						
					 | 
			
| [82] | 
					 Qiao J C, Pelletier J M, Yao Y. 2019a. Creep in bulk metallic glasses. Transition from linear to non linear regime. Mater. Sci. Eng. A, 743: 185-189. doi:  10.1016/j.msea.2018.11.066 
						
					 | 
			
| [83] | 
					 Qiao J C, Wang Q, Pelletier J M, Kato H, Casalini R, Crespo D, Pineda E, Yao Y, Yang Y. 2019b. Structural heterogeneities and mechanical behavior of amorphous alloys. Prog. Mater. Sci., 104: 250-329. doi:  10.1016/j.pmatsci.2019.04.005 
						
					 | 
			
| [84] | 
					 Qiao J C, Wang Y J, Zhao L Z, Dai L H, Crespo D, Pelletier J M, Keer L M, Yao Y. 2016a. Transition from stress-driven to thermally activated stress relaxation in metallic glasses. Phys. Rev. B, 94: 104203. doi:  10.1103/PhysRevB.94.104203 
						
					 | 
			
| [85] | 
					 Qiao J C, Yao Y, Pelletier J M, Keer L M. 2016b. Understanding of micro-alloying on plasticity in Cu46Zr47− xAl7Dy x (0≤ x ≤ 8) bulk metallic glasses under compression: Based on mechanical relaxations and theoretical analysis. Int. J. Plast., 82: 62-75. doi:  10.1016/j.ijplas.2016.02.002 
						
					 | 
			
| [86] | 
					 Rinaldi R, Gaertner R, Chazeau L, Gauthier C. 2011. Modelling of the mechanical behaviour of amorphous glassy polymer based on the Quasi Point Defect theory—Part I: Uniaxial validation on polycarbonate. International Journal of Non-Linear Mechanics, 46: 496-506. doi:  10.1016/j.ijnonlinmec.2010.11.004 
						
					 | 
			
| [87] | 
					 Ross P, Küchemann S, Derlet P M, Yu H, Arnold W, Liaw P, Samwer K, Maaß R. 2017. Linking macroscopic rejuvenation to nano-elastic fluctuations in a metallic glass. Acta Mater., 138: 111-118. doi:  10.1016/j.actamat.2017.07.043 
						
					 | 
			
| [88] | 
					 Ruta B, Chushkin Y, Monaco G, Cipelletti L, Pineda E, Bruna P, Giordano V, Gonzalez-Silveira M. 2012. Atomic-scale relaxation dynamics and aging in a metallic glass probed by x-ray photon correlation spectroscopy. Phys. Rev. Lett., 109: 165701. doi:  10.1103/PhysRevLett.109.165701 
						
					 | 
			
| [89] | 
					 Schall P, Weitz D A, Spaepen F. 2007. Structural rearrangements that govern flow in colloidal glasses. Science, 318: 1895-1899. doi:  10.1126/science.1149308 
						
					 | 
			
| [90] | 
					 Schirmacher W, Diezemann G, Ganter C. 1998. Harmonic vibrational excitations in disordered solids and the “boson peak”. Phys. Rev. Lett., 81: 136. doi:  10.1103/PhysRevLett.81.136 
						
					 | 
			
| [91] | 
					 Sokolov A P, Kisliuk A, Soltwisch M, Quitmann D. 1992. Medium-range order in glasses: Comparison of Raman and diffraction measurements. Phys. Rev. Lett., 69: 1540-1543. doi:  10.1103/PhysRevLett.69.1540 
						
					 | 
			
| [92] | 
					 Song K K , Pauly S, Zhang Y, Scudino S, Gargarella P, Surreddi K B, Kühn U, Eckert J. 2011. Significant tensile ductility induced by cold rolling in Cu47.5Zr47.5Al5 bulk metallic glass. Intermetallics, 19: 1394-1398. doi:  10.1016/j.intermet.2011.05.001 
						
					 | 
			
| [93] | 
					 Spaepen F. 1977. A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall., 25: 407-415. doi:  10.1016/0001-6160(77)90232-2 
						
					 | 
			
| [94] | 
					 Spaepen F, Turnbull D. 1974. A mechanism for the flow and fracture of metallic glasses. Scripta Metallurgica, 8: 563-568. doi:  10.1016/0036-9748(74)90070-2 
						
					 | 
			
| [95] | 
					 Sun Y, Concustell A, Greer A L. 2016. Thermomechanical processing of metallic glasses: extending the range of the glassy state. Nat. Rev. Mater., 1: 16036. 
						
					 | 
			
| [96] | 
					 Tan P, Xu N, Schofield A B, Xu L. 2012. Understanding the Low-Frequency Quasilocalized Modes in Disordered Colloidal Systems. Phys. Rev. Lett., 108: 095501. doi:  10.1103/PhysRevLett.108.095501 
						
					 | 
			
| [97] | 
					 Tang C, Harrowell P. 2013. Anomalously slow crystal growth of the glass-forming alloy CuZr. Nat. Mater, 12: 507-511. doi:  10.1038/nmat3631 
						
					 | 
			
| [98] | 
					 Tang M B, Bai H Y, Pan M X, Zhao D Q, Wang W H. 2005. Einstein oscillator in highly-random-packed bulk metallic glass. Appl. Phys. Lett., 86: 021910. doi:  10.1063/1.1849420 
						
					 | 
			
| [99] | 
					 Tao K, Qiao J C, He Q F, Song K K, Yang Y. 2021. Revealing the structural heterogeneity of metallic glass: Mechanical spectroscopy and nanoindentation experiments. Int. J. Mech. Sci. ,, 201: 106469. doi:  10.1016/j.ijmecsci.2021.106469 
						
					 | 
			
| [100] | 
					 Taraskin S, Loh Y, Natarajan G, Elliott S. 2001. Origin of the boson peak in systems with lattice disorder. Phys. Rev. Lett., 86: 1255. doi:  10.1103/PhysRevLett.86.1255 
						
					 | 
			
| [101] | 
					 Tong Y, Iwashita T, Dmowski W, Bei H, Yokoyama Y, Egami T. 2015. Structural rejuvenation in bulk metallic glasses. Acta Mater., 86: 240-246. doi:  10.1016/j.actamat.2014.12.020 
						
					 | 
			
| [102] | 
					 Tsai P, Kranjc K, Flores K M. 2017. Hierarchical heterogeneity and an elastic microstructure observed in a metallic glass alloy. Acta Mater., 139: 11-20. doi:  10.1016/j.actamat.2017.07.061 
						
					 | 
			
| [103] | 
					 Turnbull D, Cohen M H. 1970. On the free‐volume model of the iquid‐glass transition. J. Chem. Phys., 52: 3038-3041. doi:  10.1063/1.1673434 
						
					 | 
			
| [104] | 
					 Wagner H, Bedorf D, Küchemann S, Schwabe M, Zhang B, Arnold W, Samwer K. 2011. Local elastic properties of a metallic glass. Nat. Mater., 10: 439-442. doi:  10.1038/nmat3024 
						
					 | 
			
| [105] | 
					 Wang D P, Qiao J C, Liu C T. 2019. Relating structural heterogeneity to β relaxation processes in metallic glasses. Mater. Res. Lett., 7: 305-311. doi:  10.1080/21663831.2019.1604441 
						
					 | 
			
| [106] | 
					 Wang L M, Liu R, Wang W H. 2008. Relaxation time dispersions in glass forming metallic liquids and glasses. J. Chem. Phys., 128: 164503. doi:  10.1063/1.2904559 
						
					 | 
			
| [107] | 
					 Wang Q, Liu J, Ye Y, Liu T, Wang S., Liu C, Lu J, Yang Y. 2017. Universal secondary relaxation and unusual brittle-to-ductile transition in metallic glasses. Mater. Today, 20: 293-300. doi:  10.1016/j.mattod.2017.05.007 
						
					 | 
			
| [108] | 
					 Wang Q, Zhang S T, Yang Y, Dong Y D, Liu C T, Lu J. 2015a. Unusual fast secondary relaxation in metallic glass. Nat. Commun., 6: 7876. doi:  10.1038/ncomms8876 
						
					 | 
			
| [109] | 
					 Wang W H. 2012. The elastic properties, elastic models and elastic perspectives of metallic glasses. Prog. Mater. Sci., 57: 487-656. doi:  10.1016/j.pmatsci.2011.07.001 
						
					 | 
			
| [110] | 
					 Wang W H. 2019. Dynamic relaxations and relaxation-property relationships in metallic glasses. Prog. Mater. Sci., 106: 100561. doi:  10.1016/j.pmatsci.2019.03.006 
						
					 | 
			
| [111] | 
					 Wang Y J, Ishii A, Ogata S. 2013. Entropic effect on creep in nanocrystalline metals. Acta Mater., 61: 3866-3871. doi:  10.1016/j.actamat.2013.03.026 
						
					 | 
			
| [112] | 
					 Wang Y J, Zhang M, Liu L, Ogata S, Dai L H. 2015b. Universal enthalpy-entropy compensation rule for the deformation of metallic glasses. Phys. Rev. B, 92: 174118. doi:  10.1103/PhysRevB.92.174118 
						
					 | 
			
| [113] | 
					 Wang Y M, Zhang M, Liu L. 2015c. Mechanical annealing in the homogeneous deformation of bulk metallic glass under elastostatic compression. Scr. Mater., 102: 67-70. doi:  10.1016/j.scriptamat.2015.02.015 
						
					 | 
			
| [114] | 
					 Wang Y W, Li M, Xu J W. 2016. Toughen and harden metallic glass through designing statistical heterogeneity. Scr. Mater., 113: 10-13. doi:  10.1016/j.scriptamat.2015.09.038 
						
					 | 
			
| [115] | 
					 Wang Z, Sun B A, Bai H Y, Wang W H. 2014. Evolution of hidden localized flow during glass-to-liquid transition in metallic glass. Nat. Commun., 5: 5823. doi:  10.1038/ncomms6823 
						
					 | 
			
| [116] | 
					 Wang Z, Wang W H. 2019. Flow units as dynamic defects in metallic glassy materials. Natl. Sci. Rev., 6: 304-323. doi:  10.1093/nsr/nwy084 
						
					 | 
			
| [117] | 
					 Wei D, Yang J, Jiang M Q, Wei B C, Wang Y J, Dai L H. 2019. Revisiting the structure-property relationship of metallic glasses: Common spatial correlation revealed as a hidden rule. Phys. Rev. B, 99: 014115. doi:  10.1103/PhysRevB.99.014115 
						
					 | 
			
| [118] | 
					 Xu Z R, Yang D S, Qiao J C, Pelletier J M, Crespo D, Pineda E, Wang Y J. 2020. Unified perspective on structural heterogeneity of a LaCe-based metallic glass from versatile dynamic stimuli. Intermetallics, 125: 106922. doi:  10.1016/j.intermet.2020.106922 
						
					 | 
			
| [119] | 
					 Yang J, Wang Y J, Ma E, Zaccone A, Dai L H, Jiang M Q. 2019. Structural Parameter of Orientational Order to Predict the Boson Vibrational Anomaly in Glasses. Phys. Rev. Lett., 122: 015501. doi:  10.1103/PhysRevLett.122.015501 
						
					 | 
			
| [120] | 
					 Yang Q, Peng S X, Wang Z, Yu H B. 2020. Shadow glass transition as a thermodynamic signature of β relaxation in hyper-quenched metallic glasses. Natl. Sci. Rev., 7: 1896-1905. doi:  10.1093/nsr/nwaa100 
						
					 | 
			
| [121] | 
					 Yang Y, Zeng J F, Volland A, Blandin J J, Gravier S, Liu C T. 2012. Fractal growth of the dense-packing phase in annealed metallic glass imaged by high-resolution atomic force microscopy. Acta Mater., 60: 5260-5272. doi:  10.1016/j.actamat.2012.06.025 
						
					 | 
			
| [122] | 
					 Yang Y, Zhou J, Zhu F, Yuan Y, Chang D J, Kim D S, Pham M, Rana A, Tian X, Yao Y, Osher S J, Schmid A K, Hu L, Ercius P, Miao J. 2021. Determining the three-dimensional atomic structure of an amorphous solid. Nature, 592: 60-64. doi:  10.1038/s41586-021-03354-0 
						
					 | 
			
| [123] | 
					 Ye J C, Lu J, Liu C T, Wang Q, Yang Y. 2010. Atomistic free-volume zones and inelastic deformation of metallic glasses. Nat. Mater., 9: 619-623. doi:  10.1038/nmat2802 
						
					 | 
			
| [124] | 
					 Yu H B, Wang W H, Samwer K. 2013. The β relaxation in metallic glasses: an overview. Materials Today, 16: 183-191. doi:  10.1016/j.mattod.2013.05.002 
						
					 | 
			
| [125] | 
					 Yu H, Wang W, Bai H, Wu Y, Chen M. 2010. Relating activation of shear transformation zones to β relaxations in metallic glasses. Phys. Rev. B, 81: 220201. doi:  10.1103/PhysRevB.81.220201 
						
					 | 
			
| [126] | 
					 Yu H B, Richert R, Samwer K. 2017. Structural rearrangements governing Johari-Goldstein relaxations in metallic glasses. Sci. Adv., 3: e1701577. doi:  10.1126/sciadv.1701577 
						
					 | 
			
| [127] | 
					 Yu H B, Samwer K, Wu Y, Wang W H. 2012. Correlation between beta relaxation and self-diffusion of the smallest constituting atoms in metallic glasses. Phys. Rev. Lett., 109: 095508. doi:  10.1103/PhysRevLett.109.095508 
						
					 | 
			
| [128] | 
					 Zhang L T, Duan Y J, Crespo D, Pineda E, Wang Y, Pelletier J M, Qiao J C. 2021a. Dynamic mechanical relaxation and thermal creep of high-entropy La30Ce30Ni10Al20Co10 bulk metallic glass. Sci. China:Phys. , Mech. Astron., 64: 296111. doi:  10.1007/s11433-021-1722-y 
						
					 | 
			
| [129] | 
					 Zhang L T, Pelletier J M, Qiao J C. 2021b. Dynamic mechanical behavior of (La0.7Ce0.3)65Al10Co25 bulk metallic glass: Influence of the physical aging and heat treatment. J. Alloys Compd, 869: 159271. doi:  10.1016/j.jallcom.2021.159271 
						
					 | 
			
| [130] | 
					 Zhang M, Chen Y, Li W. 2019. On the origin of softening in the plastic deformation of metallic glasses. Int. J. Plast., 116: 24-38. doi:  10.1016/j.ijplas.2018.12.004 
						
					 | 
			
| [131] | 
					 Zhang P, Maldonis J J, Liu Z, Schroers J, Voyles P M. 2018. Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy. Nat. Commun., 9: 1129. doi:  10.1038/s41467-018-03604-2 
						
					 | 
			
| [132] | 
					 Zhao L Z, Wang W H, Bai H Y. 2014. Modulation of β-relaxation by modifying structural configurations in metallic glasses. J. Non·Cryst. Solids, 405: 207-210. doi:  10.1016/j.jnoncrysol.2014.08.034 
						
					 | 
			
| [133] | 
					 Zhao L Z, Xue R J, Zhu Z G, Ngai K L, Wang W H, Bai H Y. 2016. A fast dynamic mode in rare earth based glasses. J. Chem. Phys., 144: 204507. doi:  10.1063/1.4952421 
						
					 | 
			
| [134] | 
					 Zhong L, Wang J, Sheng H, Zhang Z, Mao S X. 2014. Formation of monatomic metallic glasses through ultrafast liquid quenching. Nature, 512: 177-180. doi:  10.1038/nature13617 
						
					 | 
			
| [135] | 
					 Zhou H, Hilke S, Pineda E, Peterlechner M, Chushkin Y, Shanmugam S, Wilde G. 2020. X-ray photon correlation spectroscopy revealing the change of relaxation dynamics of a severely deformed Pd-based bulk metallic glass. Acta Mater., 195: 446-453. doi:  10.1016/j.actamat.2020.05.064 
						
					 | 
			
| [136] | 
					 Zhu F, Song S X, Reddy K M, Hirata A, Chen M W. 2018. Spatial heterogeneity as the structure feature for structure–property relationship of metallic glasses. Nat. Commun., 9: 3965. doi:  10.1038/s41467-018-06476-8 
						
					 | 
			
| [137] | 
					 Zhu W Q, Liu J J, Mao S, Wei X D. 2021. A new continuum model for viscoplasticity in metallic glasses based on thermodynamics and its application to creep tests. J. Mech. Phys. Solids, 146: 104216. doi:  10.1016/j.jmps.2020.104216 
						
					 |